Properties

Label 5376.2.c
Level 5376
Weight 2
Character orbit c
Rep. character \(\chi_{5376}(2689,\cdot)\)
Character field \(\Q\)
Dimension 96
Newform subspaces 40
Sturm bound 2048
Trace bound 17

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Defining parameters

Level: \( N \) \(=\) \( 5376 = 2^{8} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5376.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 40 \)
Sturm bound: \(2048\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(23\), \(31\), \(47\), \(71\), \(79\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5376, [\chi])\).

Total New Old
Modular forms 1072 96 976
Cusp forms 976 96 880
Eisenstein series 96 0 96

Trace form

\( 96q - 96q^{9} + O(q^{10}) \) \( 96q - 96q^{9} - 96q^{25} + 96q^{49} + 64q^{65} - 64q^{73} + 96q^{81} - 64q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5376, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5376.2.c.a \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+4iq^{5}-q^{7}-q^{9}-6iq^{11}+\cdots\)
5376.2.c.b \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+4iq^{5}-q^{7}-q^{9}+2iq^{11}+\cdots\)
5376.2.c.c \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.d \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-6iq^{13}+\cdots\)
5376.2.c.e \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.f \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}+2iq^{13}+\cdots\)
5376.2.c.g \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}-q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots\)
5376.2.c.h \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}-q^{7}-q^{9}-2iq^{11}+4iq^{13}+\cdots\)
5376.2.c.i \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-q^{9}+6iq^{11}+2iq^{13}+\cdots\)
5376.2.c.j \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
5376.2.c.k \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-q^{9}+6iq^{11}-4iq^{13}+\cdots\)
5376.2.c.l \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.m \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.n \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}+2q^{15}+\cdots\)
5376.2.c.o \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{13}+\cdots\)
5376.2.c.p \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}+4iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
5376.2.c.q \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+4iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
5376.2.c.r \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.s \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.t \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2q^{15}+\cdots\)
5376.2.c.u \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2iq^{13}+\cdots\)
5376.2.c.v \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots\)
5376.2.c.w \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+q^{7}-q^{9}-2iq^{11}-4iq^{13}+\cdots\)
5376.2.c.x \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+q^{7}-q^{9}+6iq^{11}-2iq^{13}+\cdots\)
5376.2.c.y \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
5376.2.c.z \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+q^{7}-q^{9}-6iq^{11}-4iq^{13}+\cdots\)
5376.2.c.ba \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots\)
5376.2.c.bb \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}-6iq^{13}+\cdots\)
5376.2.c.bc \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots\)
5376.2.c.bd \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{13}+\cdots\)
5376.2.c.be \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+4iq^{5}+q^{7}-q^{9}+6iq^{11}+\cdots\)
5376.2.c.bf \(2\) \(42.928\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+4iq^{5}+q^{7}-q^{9}-2iq^{11}+\cdots\)
5376.2.c.bg \(4\) \(42.928\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-q^{7}-q^{9}+(2\zeta_{8}+\cdots)q^{11}+\cdots\)
5376.2.c.bh \(4\) \(42.928\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)
5376.2.c.bi \(4\) \(42.928\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots\)
5376.2.c.bj \(4\) \(42.928\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots\)
5376.2.c.bk \(4\) \(42.928\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots\)
5376.2.c.bl \(4\) \(42.928\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots\)
5376.2.c.bm \(4\) \(42.928\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{8}+\cdots)q^{11}+\cdots\)
5376.2.c.bn \(4\) \(42.928\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5376, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5376, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2688, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$5$ (\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 - 2 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 25 T^{4} )^{2} \))(\( 1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8} \))(\( 1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8} \))(\( 1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8} \))(\( 1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8} \))(\( ( 1 - 2 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 25 T^{4} )^{2} \))
$7$ (\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))
$11$ (\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( 1 - 12 T^{2} + 86 T^{4} - 1452 T^{6} + 14641 T^{8} \))(\( 1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8} \))(\( 1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8} \))(\( 1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8} \))(\( 1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8} \))(\( 1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( 1 - 12 T^{2} + 86 T^{4} - 1452 T^{6} + 14641 T^{8} \))
$13$ (\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( ( 1 - 22 T^{2} + 169 T^{4} )^{2} \))(\( 1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8} \))(\( 1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8} \))(\( 1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8} \))(\( 1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( ( 1 - 22 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 30 T^{2} - 68 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 8 T + 38 T^{2} - 136 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 + 2 T + 30 T^{2} + 34 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 + 2 T + 30 T^{2} + 34 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 4 T + 30 T^{2} - 68 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 8 T + 38 T^{2} - 136 T^{3} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 + 10 T^{2} + 361 T^{4} )^{2} \))(\( 1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8} \))(\( 1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8} \))(\( 1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8} \))(\( 1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 + 10 T^{2} + 361 T^{4} )^{2} \))
$23$ (\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( ( 1 - 2 T + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 - 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 - 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( ( 1 + 38 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 4 T + 38 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 2 T + 42 T^{2} + 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T + 42 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 38 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 4 T + 38 T^{2} + 92 T^{3} + 529 T^{4} )^{2} \))
$29$ (\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( 1 - 54 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( ( 1 - 54 T^{2} + 841 T^{4} )^{2} \))(\( 1 - 12 T^{2} + 950 T^{4} - 10092 T^{6} + 707281 T^{8} \))(\( 1 - 44 T^{2} + 886 T^{4} - 37004 T^{6} + 707281 T^{8} \))(\( ( 1 - 38 T^{2} + 841 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 886 T^{4} - 37004 T^{6} + 707281 T^{8} \))(\( ( 1 - 38 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 54 T^{2} + 841 T^{4} )^{2} \))(\( 1 - 12 T^{2} + 950 T^{4} - 10092 T^{6} + 707281 T^{8} \))
$31$ (\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 8 T + 30 T^{2} - 248 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{4} \))(\( ( 1 + 4 T + 31 T^{2} )^{4} \))(\( ( 1 + 4 T + 31 T^{2} )^{4} \))(\( ( 1 - 4 T + 31 T^{2} )^{4} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 8 T + 30 T^{2} + 248 T^{3} + 961 T^{4} )^{2} \))
$37$ (\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 12 T^{2} - 1834 T^{4} - 16428 T^{6} + 1874161 T^{8} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( 1 + 20 T^{2} + 1558 T^{4} + 27380 T^{6} + 1874161 T^{8} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( 1 + 20 T^{2} + 1558 T^{4} + 27380 T^{6} + 1874161 T^{8} \))(\( 1 - 12 T^{2} - 1834 T^{4} - 16428 T^{6} + 1874161 T^{8} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))
$41$ (\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 + 4 T + 14 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 10 T + 102 T^{2} + 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 2 T + 78 T^{2} + 82 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 10 T + 102 T^{2} + 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 2 T + 78 T^{2} + 82 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 4 T + 14 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 36 T^{2} - 586 T^{4} - 66564 T^{6} + 3418801 T^{8} \))(\( ( 1 - 22 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 100 T^{2} + 4918 T^{4} - 184900 T^{6} + 3418801 T^{8} \))(\( ( 1 - 66 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 100 T^{2} + 4918 T^{4} - 184900 T^{6} + 3418801 T^{8} \))(\( ( 1 - 66 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 36 T^{2} - 586 T^{4} - 66564 T^{6} + 3418801 T^{8} \))(\( ( 1 - 22 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 4 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 4 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 + 4 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 4 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{4} \))(\( ( 1 + 8 T + 62 T^{2} + 376 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{4} \))(\( ( 1 + 8 T + 30 T^{2} + 376 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{4} \))(\( ( 1 - 8 T + 30 T^{2} - 376 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 47 T^{2} )^{4} \))(\( ( 1 - 8 T + 62 T^{2} - 376 T^{3} + 2209 T^{4} )^{2} \))
$53$ (\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 + 52 T^{2} + 4246 T^{4} + 146068 T^{6} + 7890481 T^{8} \))(\( ( 1 - 102 T^{2} + 2809 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 982 T^{4} - 123596 T^{6} + 7890481 T^{8} \))(\( ( 1 - 86 T^{2} + 2809 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 982 T^{4} - 123596 T^{6} + 7890481 T^{8} \))(\( ( 1 - 86 T^{2} + 2809 T^{4} )^{2} \))(\( 1 + 52 T^{2} + 4246 T^{4} + 146068 T^{6} + 7890481 T^{8} \))(\( ( 1 - 102 T^{2} + 2809 T^{4} )^{2} \))
$59$ (\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( ( 1 - 59 T^{2} )^{2} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 - 102 T^{2} + 3481 T^{4} \))(\( 1 + 26 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( ( 1 - 102 T^{2} + 3481 T^{4} )^{2} \))(\( 1 - 12 T^{2} - 5290 T^{4} - 41772 T^{6} + 12117361 T^{8} \))(\( ( 1 - 38 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 102 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 102 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 102 T^{2} + 3481 T^{4} )^{2} \))(\( 1 - 12 T^{2} - 5290 T^{4} - 41772 T^{6} + 12117361 T^{8} \))
$61$ (\( ( 1 - 61 T^{2} )^{2} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 106 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 106 T^{2} + 3721 T^{4} \))(\( ( 1 - 61 T^{2} )^{2} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 58 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 58 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 58 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 106 T^{2} + 3721 T^{4} \))(\( ( 1 - 61 T^{2} )^{2} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 + 74 T^{2} + 3721 T^{4} \))(\( 1 - 58 T^{2} + 3721 T^{4} \))(\( 1 - 106 T^{2} + 3721 T^{4} \))(\( 1 - 118 T^{2} + 3721 T^{4} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( ( 1 - 61 T^{2} )^{2} \))(\( 1 - 86 T^{2} + 3721 T^{4} \))(\( 1 - 148 T^{2} + 10870 T^{4} - 550708 T^{6} + 13845841 T^{8} \))(\( 1 - 140 T^{2} + 11574 T^{4} - 520940 T^{6} + 13845841 T^{8} \))(\( 1 - 52 T^{2} + 2998 T^{4} - 193492 T^{6} + 13845841 T^{8} \))(\( ( 1 - 106 T^{2} + 3721 T^{4} )^{2} \))(\( 1 - 52 T^{2} + 2998 T^{4} - 193492 T^{6} + 13845841 T^{8} \))(\( ( 1 - 106 T^{2} + 3721 T^{4} )^{2} \))(\( 1 - 148 T^{2} + 10870 T^{4} - 550708 T^{6} + 13845841 T^{8} \))(\( 1 - 140 T^{2} + 11574 T^{4} - 520940 T^{6} + 13845841 T^{8} \))
$67$ (\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 34 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 + 62 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 62 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 34 T^{2} + 4489 T^{4} \))(\( 1 + 122 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 34 T^{2} + 4489 T^{4} \))(\( 1 + 122 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 + 62 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 62 T^{2} + 4489 T^{4} \))(\( 1 - 34 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 4 T^{2} + 6934 T^{4} - 17956 T^{6} + 20151121 T^{8} \))(\( 1 - 140 T^{2} + 10806 T^{4} - 628460 T^{6} + 20151121 T^{8} \))(\( ( 1 - 98 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 98 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 98 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 98 T^{2} + 4489 T^{4} )^{2} \))(\( 1 - 4 T^{2} + 6934 T^{4} - 17956 T^{6} + 20151121 T^{8} \))(\( 1 - 140 T^{2} + 10806 T^{4} - 628460 T^{6} + 20151121 T^{8} \))
$71$ (\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 14 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 14 T + 71 T^{2} )^{2} \))(\( ( 1 + 14 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 14 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 12 T + 166 T^{2} - 852 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 10 T + 122 T^{2} - 710 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 6 T + 146 T^{2} + 426 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 10 T + 122 T^{2} + 710 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 6 T + 146 T^{2} - 426 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 12 T + 166 T^{2} + 852 T^{3} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 14 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 73 T^{2} )^{2} \))(\( ( 1 - 14 T + 73 T^{2} )^{2} \))(\( ( 1 + 10 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 118 T^{2} + 292 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 16 T + 190 T^{2} + 1168 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 126 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 16 T + 190 T^{2} + 1168 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 126 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 4 T + 118 T^{2} + 292 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 142 T^{2} + 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 8 T + 126 T^{2} - 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 12 T + 174 T^{2} - 948 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 20 T + 238 T^{2} + 1580 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 12 T + 174 T^{2} + 948 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 20 T + 238 T^{2} - 1580 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 8 T + 142 T^{2} - 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 8 T + 126 T^{2} + 632 T^{3} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 102 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 102 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 140 T^{2} + 10486 T^{4} - 964460 T^{6} + 47458321 T^{8} \))(\( ( 1 - 150 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 92 T^{2} + 7894 T^{4} - 633788 T^{6} + 47458321 T^{8} \))(\( 1 + 36 T^{2} + 11222 T^{4} + 248004 T^{6} + 47458321 T^{8} \))(\( 1 - 92 T^{2} + 7894 T^{4} - 633788 T^{6} + 47458321 T^{8} \))(\( 1 + 36 T^{2} + 11222 T^{4} + 248004 T^{6} + 47458321 T^{8} \))(\( 1 - 140 T^{2} + 10486 T^{4} - 964460 T^{6} + 47458321 T^{8} \))(\( ( 1 - 150 T^{2} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 18 T + 89 T^{2} )^{2} \))(\( ( 1 + 4 T + 89 T^{2} )^{2} \))(\( ( 1 + 16 T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 12 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 12 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 16 T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 18 T + 89 T^{2} )^{2} \))(\( ( 1 + 4 T + 89 T^{2} )^{2} \))(\( ( 1 + 28 T + 366 T^{2} + 2492 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 166 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 10 T + 78 T^{2} + 890 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 2 T + 134 T^{2} + 178 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 10 T + 78 T^{2} + 890 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 2 T + 134 T^{2} + 178 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 28 T + 366 T^{2} + 2492 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 166 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 18 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 + 18 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 166 T^{2} + 388 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 4 T + 150 T^{2} + 388 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 16 T + 238 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 14 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 16 T + 238 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 14 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 + 4 T + 166 T^{2} + 388 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 4 T + 150 T^{2} + 388 T^{3} + 9409 T^{4} )^{2} \))
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