Properties

Label 3840.2.d
Level $3840$
Weight $2$
Character orbit 3840.d
Rep. character $\chi_{3840}(2689,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $38$
Sturm bound $1536$
Trace bound $35$

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Defining parameters

Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3840.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(1536\)
Trace bound: \(35\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(31\), \(37\), \(43\)

Dimensions

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

Total New Old
Modular forms 816 96 720
Cusp forms 720 96 624
Eisenstein series 96 0 96

Trace form

\( 96q + 96q^{9} + O(q^{10}) \) \( 96q + 96q^{9} - 96q^{49} + 32q^{65} + 96q^{81} + 64q^{89} + O(q^{100}) \)

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.d.a \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) \(q-q^{3}+(-2+i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.b \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) \(q-q^{3}+(-2-i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.c \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(0\) \(q-q^{3}+(-2+i)q^{5}+q^{9}-2iq^{11}+\cdots\)
3840.2.d.d \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-q^{3}+(-1+i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.e \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-q^{3}+(-1+i)q^{5}+iq^{7}+q^{9}-3iq^{11}+\cdots\)
3840.2.d.f \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-q^{3}+(-1+i)q^{5}+q^{9}+2iq^{11}+\cdots\)
3840.2.d.g \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-q^{3}+(-1-i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.h \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-q^{3}+(-1+i)q^{5}+2iq^{7}+q^{9}+\cdots\)
3840.2.d.i \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+(1+i)q^{5}+2iq^{7}+q^{9}-6q^{13}+\cdots\)
3840.2.d.j \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+(1-i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.k \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+(1+i)q^{5}+iq^{7}+q^{9}+3iq^{11}+\cdots\)
3840.2.d.l \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+(1-i)q^{5}+q^{9}+2iq^{11}+2q^{13}+\cdots\)
3840.2.d.m \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+(1+i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.n \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) \(q-q^{3}+(2+i)q^{5}+q^{9}+2iq^{11}-2q^{13}+\cdots\)
3840.2.d.o \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) \(q-q^{3}+(2-i)q^{5}+4iq^{7}+q^{9}+4iq^{11}+\cdots\)
3840.2.d.p \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(0\) \(q-q^{3}+(2+i)q^{5}+4iq^{7}+q^{9}+4q^{13}+\cdots\)
3840.2.d.q \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) \(q+q^{3}+(-2-i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.r \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) \(q+q^{3}+(-2+i)q^{5}+4iq^{7}+q^{9}+\cdots\)
3840.2.d.s \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(0\) \(q+q^{3}+(-2+i)q^{5}+q^{9}+2iq^{11}+\cdots\)
3840.2.d.t \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+q^{3}+(-1+i)q^{5}+q^{9}-2iq^{11}+\cdots\)
3840.2.d.u \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+q^{3}+(-1-i)q^{5}+iq^{7}+q^{9}-3iq^{11}+\cdots\)
3840.2.d.v \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+q^{3}+(-1-i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.w \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+q^{3}+(-1-i)q^{5}+2iq^{7}+q^{9}+\cdots\)
3840.2.d.x \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+q^{3}+(-1+i)q^{5}+iq^{7}+q^{9}+iq^{11}+\cdots\)
3840.2.d.y \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) \(q+q^{3}+(1+i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.z \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) \(q+q^{3}+(1-i)q^{5}+2iq^{7}+q^{9}-6q^{13}+\cdots\)
3840.2.d.ba \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) \(q+q^{3}+(1-i)q^{5}+iq^{7}+q^{9}-iq^{11}+\cdots\)
3840.2.d.bb \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) \(q+q^{3}+(1-i)q^{5}+q^{9}-2iq^{11}+2q^{13}+\cdots\)
3840.2.d.bc \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(2\) \(0\) \(q+q^{3}+(1-i)q^{5}+iq^{7}+q^{9}+3iq^{11}+\cdots\)
3840.2.d.bd \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) \(q+q^{3}+(2-i)q^{5}+q^{9}+2iq^{11}-2q^{13}+\cdots\)
3840.2.d.be \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) \(q+q^{3}+(2+i)q^{5}+4iq^{7}+q^{9}+4iq^{11}+\cdots\)
3840.2.d.bf \(2\) \(30.663\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(0\) \(q+q^{3}+(2-i)q^{5}+4iq^{7}+q^{9}+4q^{13}+\cdots\)
3840.2.d.bg \(4\) \(30.663\) \(\Q(i, \sqrt{5})\) None \(0\) \(-4\) \(0\) \(0\) \(q-q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
3840.2.d.bh \(4\) \(30.663\) \(\Q(i, \sqrt{5})\) None \(0\) \(4\) \(0\) \(0\) \(q+q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
3840.2.d.bi \(6\) \(30.663\) 6.0.350464.1 None \(0\) \(-6\) \(0\) \(0\) \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
3840.2.d.bj \(6\) \(30.663\) 6.0.350464.1 None \(0\) \(-6\) \(0\) \(0\) \(q-q^{3}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
3840.2.d.bk \(6\) \(30.663\) 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) \(q+q^{3}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
3840.2.d.bl \(6\) \(30.663\) 6.0.350464.1 None \(0\) \(6\) \(0\) \(0\) \(q+q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( 1 - T^{2} + 16 T^{3} - 5 T^{4} + 125 T^{6} \))(\( 1 - T^{2} - 16 T^{3} - 5 T^{4} + 125 T^{6} \))(\( 1 - T^{2} + 16 T^{3} - 5 T^{4} + 125 T^{6} \))(\( 1 - T^{2} - 16 T^{3} - 5 T^{4} + 125 T^{6} \))
$7$ (\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( ( 1 - 10 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 49 T^{4} )^{2} \))(\( 1 - 10 T^{2} + 31 T^{4} + 116 T^{6} + 1519 T^{8} - 24010 T^{10} + 117649 T^{12} \))(\( 1 - 10 T^{2} + 31 T^{4} + 116 T^{6} + 1519 T^{8} - 24010 T^{10} + 117649 T^{12} \))(\( 1 - 10 T^{2} + 31 T^{4} + 116 T^{6} + 1519 T^{8} - 24010 T^{10} + 117649 T^{12} \))(\( 1 - 10 T^{2} + 31 T^{4} + 116 T^{6} + 1519 T^{8} - 24010 T^{10} + 117649 T^{12} \))
$11$ (\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 2 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 121 T^{4} )^{2} \))(\( 1 - 22 T^{2} + 375 T^{4} - 3988 T^{6} + 45375 T^{8} - 322102 T^{10} + 1771561 T^{12} \))(\( 1 - 22 T^{2} + 375 T^{4} - 3988 T^{6} + 45375 T^{8} - 322102 T^{10} + 1771561 T^{12} \))(\( 1 - 22 T^{2} + 375 T^{4} - 3988 T^{6} + 45375 T^{8} - 322102 T^{10} + 1771561 T^{12} \))(\( 1 - 22 T^{2} + 375 T^{4} - 3988 T^{6} + 45375 T^{8} - 322102 T^{10} + 1771561 T^{12} \))
$13$ (\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 6 T + 35 T^{2} + 148 T^{3} + 455 T^{4} + 1014 T^{5} + 2197 T^{6} )^{2} \))(\( ( 1 - 6 T + 35 T^{2} - 148 T^{3} + 455 T^{4} - 1014 T^{5} + 2197 T^{6} )^{2} \))(\( ( 1 + 6 T + 35 T^{2} + 148 T^{3} + 455 T^{4} + 1014 T^{5} + 2197 T^{6} )^{2} \))(\( ( 1 - 6 T + 35 T^{2} - 148 T^{3} + 455 T^{4} - 1014 T^{5} + 2197 T^{6} )^{2} \))
$17$ (\( ( 1 - 17 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 14 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 289 T^{4} )^{2} \))(\( 1 + 6 T^{2} + 431 T^{4} + 5908 T^{6} + 124559 T^{8} + 501126 T^{10} + 24137569 T^{12} \))(\( 1 + 6 T^{2} + 431 T^{4} + 5908 T^{6} + 124559 T^{8} + 501126 T^{10} + 24137569 T^{12} \))(\( 1 + 6 T^{2} + 431 T^{4} + 5908 T^{6} + 124559 T^{8} + 501126 T^{10} + 24137569 T^{12} \))(\( 1 + 6 T^{2} + 431 T^{4} + 5908 T^{6} + 124559 T^{8} + 501126 T^{10} + 24137569 T^{12} \))
$19$ (\( 1 + 26 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 22 T^{2} + 361 T^{4} )^{3} \))(\( ( 1 - 22 T^{2} + 361 T^{4} )^{3} \))(\( ( 1 - 22 T^{2} + 361 T^{4} )^{3} \))(\( ( 1 - 22 T^{2} + 361 T^{4} )^{3} \))
$23$ (\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 10 T^{2} + 255 T^{4} - 9100 T^{6} + 134895 T^{8} - 2798410 T^{10} + 148035889 T^{12} \))(\( 1 - 10 T^{2} + 255 T^{4} - 9100 T^{6} + 134895 T^{8} - 2798410 T^{10} + 148035889 T^{12} \))(\( 1 - 10 T^{2} + 255 T^{4} - 9100 T^{6} + 134895 T^{8} - 2798410 T^{10} + 148035889 T^{12} \))(\( 1 - 10 T^{2} + 255 T^{4} - 9100 T^{6} + 134895 T^{8} - 2798410 T^{10} + 148035889 T^{12} \))
$29$ (\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 10 T + 29 T^{2} )^{2}( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )^{2}( 1 + 10 T + 29 T^{2} )^{2} \))(\( 1 - 50 T^{2} + 2631 T^{4} - 77276 T^{6} + 2212671 T^{8} - 35364050 T^{10} + 594823321 T^{12} \))(\( 1 - 50 T^{2} + 2631 T^{4} - 77276 T^{6} + 2212671 T^{8} - 35364050 T^{10} + 594823321 T^{12} \))(\( 1 - 50 T^{2} + 2631 T^{4} - 77276 T^{6} + 2212671 T^{8} - 35364050 T^{10} + 594823321 T^{12} \))(\( 1 - 50 T^{2} + 2631 T^{4} - 77276 T^{6} + 2212671 T^{8} - 35364050 T^{10} + 594823321 T^{12} \))
$31$ (\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 18 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{6} \))(\( ( 1 - 2 T + 31 T^{2} )^{6} \))(\( ( 1 - 2 T + 31 T^{2} )^{6} \))(\( ( 1 + 2 T + 31 T^{2} )^{6} \))
$37$ (\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 8 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 8 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 54 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 54 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 6 T + 107 T^{2} + 404 T^{3} + 3959 T^{4} + 8214 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 6 T + 107 T^{2} - 404 T^{3} + 3959 T^{4} - 8214 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 6 T + 107 T^{2} + 404 T^{3} + 3959 T^{4} + 8214 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 6 T + 107 T^{2} - 404 T^{3} + 3959 T^{4} - 8214 T^{5} + 50653 T^{6} )^{2} \))
$41$ (\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{4} \))(\( ( 1 + 10 T + 41 T^{2} )^{4} \))(\( ( 1 + 10 T + 103 T^{2} + 684 T^{3} + 4223 T^{4} + 16810 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 10 T + 103 T^{2} + 684 T^{3} + 4223 T^{4} + 16810 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 10 T + 103 T^{2} + 684 T^{3} + 4223 T^{4} + 16810 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 10 T + 103 T^{2} + 684 T^{3} + 4223 T^{4} + 16810 T^{5} + 68921 T^{6} )^{2} \))
$43$ (\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{4} \))(\( ( 1 + 65 T^{2} - 128 T^{3} + 2795 T^{4} + 79507 T^{6} )^{2} \))(\( ( 1 + 65 T^{2} - 128 T^{3} + 2795 T^{4} + 79507 T^{6} )^{2} \))(\( ( 1 + 65 T^{2} + 128 T^{3} + 2795 T^{4} + 79507 T^{6} )^{2} \))(\( ( 1 + 65 T^{2} + 128 T^{3} + 2795 T^{4} + 79507 T^{6} )^{2} \))
$47$ (\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( ( 1 - 30 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 30 T^{2} + 2209 T^{4} )^{2} \))(\( 1 - 170 T^{2} + 14895 T^{4} - 852620 T^{6} + 32903055 T^{8} - 829545770 T^{10} + 10779215329 T^{12} \))(\( 1 - 170 T^{2} + 14895 T^{4} - 852620 T^{6} + 32903055 T^{8} - 829545770 T^{10} + 10779215329 T^{12} \))(\( 1 - 170 T^{2} + 14895 T^{4} - 852620 T^{6} + 32903055 T^{8} - 829545770 T^{10} + 10779215329 T^{12} \))(\( 1 - 170 T^{2} + 14895 T^{4} - 852620 T^{6} + 32903055 T^{8} - 829545770 T^{10} + 10779215329 T^{12} \))
$53$ (\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 8 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( ( 1 - 8 T + 53 T^{2} )^{2} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 8 T + 53 T^{2} )^{2} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 8 T + 53 T^{2} )^{2} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 86 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 86 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 12 T + 191 T^{2} - 1288 T^{3} + 10123 T^{4} - 33708 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 12 T + 191 T^{2} + 1288 T^{3} + 10123 T^{4} + 33708 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 - 12 T + 191 T^{2} - 1288 T^{3} + 10123 T^{4} - 33708 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 12 T + 191 T^{2} + 1288 T^{3} + 10123 T^{4} + 33708 T^{5} + 148877 T^{6} )^{2} \))
$59$ (\( ( 1 - 59 T^{2} )^{2} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( ( 1 + 62 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 62 T^{2} + 3481 T^{4} )^{2} \))(\( 1 - 214 T^{2} + 19415 T^{4} - 1211796 T^{6} + 67583615 T^{8} - 2593115254 T^{10} + 42180533641 T^{12} \))(\( 1 - 214 T^{2} + 19415 T^{4} - 1211796 T^{6} + 67583615 T^{8} - 2593115254 T^{10} + 42180533641 T^{12} \))(\( 1 - 214 T^{2} + 19415 T^{4} - 1211796 T^{6} + 67583615 T^{8} - 2593115254 T^{10} + 42180533641 T^{12} \))(\( 1 - 214 T^{2} + 19415 T^{4} - 1211796 T^{6} + 67583615 T^{8} - 2593115254 T^{10} + 42180533641 T^{12} \))
$61$ (\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )^{2}( 1 + 12 T + 61 T^{2} )^{2} \))(\( ( 1 - 12 T + 61 T^{2} )^{2}( 1 + 12 T + 61 T^{2} )^{2} \))(\( ( 1 - 86 T^{2} + 3721 T^{4} )^{3} \))(\( ( 1 - 86 T^{2} + 3721 T^{4} )^{3} \))(\( ( 1 - 86 T^{2} + 3721 T^{4} )^{3} \))(\( ( 1 - 86 T^{2} + 3721 T^{4} )^{3} \))
$67$ (\( ( 1 - 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{4} \))(\( ( 1 - 8 T + 67 T^{2} )^{4} \))(\( ( 1 + 8 T + 137 T^{2} + 816 T^{3} + 9179 T^{4} + 35912 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 + 8 T + 137 T^{2} + 816 T^{3} + 9179 T^{4} + 35912 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 - 8 T + 137 T^{2} - 816 T^{3} + 9179 T^{4} - 35912 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 - 8 T + 137 T^{2} - 816 T^{3} + 9179 T^{4} - 35912 T^{5} + 300763 T^{6} )^{2} \))
$71$ (\( ( 1 - 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 62 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 62 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 16 T + 85 T^{2} + 96 T^{3} + 6035 T^{4} + 80656 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 16 T + 85 T^{2} - 96 T^{3} + 6035 T^{4} - 80656 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 16 T + 85 T^{2} - 96 T^{3} + 6035 T^{4} - 80656 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 16 T + 85 T^{2} + 96 T^{3} + 6035 T^{4} + 80656 T^{5} + 357911 T^{6} )^{2} \))
$73$ (\( ( 1 - 73 T^{2} )^{2} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 2 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 2 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 2 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 2 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( ( 1 - 66 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 66 T^{2} + 5329 T^{4} )^{2} \))(\( 1 - 134 T^{2} + 18559 T^{4} - 1367252 T^{6} + 98900911 T^{8} - 3805364294 T^{10} + 151334226289 T^{12} \))(\( 1 - 134 T^{2} + 18559 T^{4} - 1367252 T^{6} + 98900911 T^{8} - 3805364294 T^{10} + 151334226289 T^{12} \))(\( 1 - 134 T^{2} + 18559 T^{4} - 1367252 T^{6} + 98900911 T^{8} - 3805364294 T^{10} + 151334226289 T^{12} \))(\( 1 - 134 T^{2} + 18559 T^{4} - 1367252 T^{6} + 98900911 T^{8} - 3805364294 T^{10} + 151334226289 T^{12} \))
$79$ (\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 78 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 78 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 2 T + 25 T^{2} + 212 T^{3} + 1975 T^{4} + 12482 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 2 T + 25 T^{2} - 212 T^{3} + 1975 T^{4} - 12482 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 2 T + 25 T^{2} - 212 T^{3} + 1975 T^{4} - 12482 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 + 2 T + 25 T^{2} + 212 T^{3} + 1975 T^{4} + 12482 T^{5} + 493039 T^{6} )^{2} \))
$83$ (\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 16 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 8 T + 83 T^{2} )^{2} \))(\( ( 1 + 8 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 16 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 16 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 8 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 8 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 16 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{4} \))(\( ( 1 + 4 T + 83 T^{2} )^{4} \))(\( ( 1 + 12 T + 233 T^{2} + 1928 T^{3} + 19339 T^{4} + 82668 T^{5} + 571787 T^{6} )^{2} \))(\( ( 1 + 12 T + 233 T^{2} + 1928 T^{3} + 19339 T^{4} + 82668 T^{5} + 571787 T^{6} )^{2} \))(\( ( 1 - 12 T + 233 T^{2} - 1928 T^{3} + 19339 T^{4} - 82668 T^{5} + 571787 T^{6} )^{2} \))(\( ( 1 - 12 T + 233 T^{2} - 1928 T^{3} + 19339 T^{4} - 82668 T^{5} + 571787 T^{6} )^{2} \))
$89$ (\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{4} \))(\( ( 1 - 6 T + 89 T^{2} )^{4} \))(\( ( 1 - 6 T + 89 T^{2} )^{6} \))(\( ( 1 - 6 T + 89 T^{2} )^{6} \))(\( ( 1 - 6 T + 89 T^{2} )^{6} \))(\( ( 1 - 6 T + 89 T^{2} )^{6} \))
$97$ (\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( 1 + 62 T^{2} + 9409 T^{4} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 97 T^{2} )^{2} \))(\( ( 1 - 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( 1 + 62 T^{2} + 9409 T^{4} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( 1 + 62 T^{2} + 9409 T^{4} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( 1 + 62 T^{2} + 9409 T^{4} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( ( 1 + 126 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 + 126 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 97 T^{2} )^{6} \))(\( ( 1 - 97 T^{2} )^{6} \))(\( ( 1 - 97 T^{2} )^{6} \))(\( ( 1 - 97 T^{2} )^{6} \))
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