Properties

Label 7200.2.f
Level 7200
Weight 2
Character orbit f
Rep. character \(\chi_{7200}(6049,\cdot)\)
Character field \(\Q\)
Dimension 90
Newform subspaces 37
Sturm bound 2880
Trace bound 49

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Defining parameters

Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(2880\)
Trace bound: \(49\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7200, [\chi])\).

Total New Old
Modular forms 1536 90 1446
Cusp forms 1344 90 1254
Eisenstein series 192 0 192

Trace form

\( 90q + O(q^{10}) \) \( 90q + 20q^{29} + 28q^{41} - 122q^{49} - 4q^{61} - 76q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7200, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7200.2.f.a \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-5q^{11}+5iq^{17}-5q^{19}+\cdots\)
7200.2.f.b \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4q^{11}+iq^{13}-iq^{17}-8q^{19}+\cdots\)
7200.2.f.c \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-4q^{11}+3iq^{13}+iq^{17}+\cdots\)
7200.2.f.d \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-4q^{11}-3iq^{13}-4iq^{17}+\cdots\)
7200.2.f.e \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}-4q^{11}-7iq^{13}+4iq^{17}+\cdots\)
7200.2.f.f \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-4q^{11}-iq^{13}-3iq^{17}+\cdots\)
7200.2.f.g \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-4q^{11}+3iq^{13}-iq^{17}+\cdots\)
7200.2.f.h \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-2q^{11}+iq^{17}-4q^{19}+2q^{29}+\cdots\)
7200.2.f.i \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-2q^{11}+iq^{17}+4q^{19}-2q^{29}+\cdots\)
7200.2.f.j \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}-5iq^{13}-5q^{19}-4iq^{23}+\cdots\)
7200.2.f.k \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{13}-3iq^{17}-4q^{19}-4iq^{23}+\cdots\)
7200.2.f.l \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-iq^{13}-3q^{19}+4iq^{23}+\cdots\)
7200.2.f.m \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3iq^{13}+iq^{17}-10q^{29}+iq^{37}+\cdots\)
7200.2.f.n \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-3iq^{13}+4iq^{17}-4q^{29}+iq^{37}+\cdots\)
7200.2.f.o \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}-iq^{13}-3iq^{17}+2iq^{23}+\cdots\)
7200.2.f.p \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+iq^{13}+3iq^{17}+2iq^{23}+\cdots\)
7200.2.f.q \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-3iq^{13}-4iq^{17}+4q^{29}+iq^{37}+\cdots\)
7200.2.f.r \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+iq^{13}+3q^{19}+4iq^{23}+\cdots\)
7200.2.f.s \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{13}+3iq^{17}+4q^{19}-4iq^{23}+\cdots\)
7200.2.f.t \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+5iq^{13}+5q^{19}-4iq^{23}+\cdots\)
7200.2.f.u \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+2q^{11}-iq^{17}-4q^{19}-2q^{29}+\cdots\)
7200.2.f.v \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+2q^{11}-iq^{17}+4q^{19}+2q^{29}+\cdots\)
7200.2.f.w \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+4q^{11}-3iq^{13}+iq^{17}+\cdots\)
7200.2.f.x \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+4q^{11}+iq^{13}+3iq^{17}+\cdots\)
7200.2.f.y \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{7}+4q^{11}+7iq^{13}-4iq^{17}+\cdots\)
7200.2.f.z \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+4q^{11}+3iq^{13}+4iq^{17}+\cdots\)
7200.2.f.ba \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+4q^{11}-3iq^{13}-iq^{17}+\cdots\)
7200.2.f.bb \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4q^{11}+iq^{13}-iq^{17}+8q^{19}+\cdots\)
7200.2.f.bc \(2\) \(57.492\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+5q^{11}-5iq^{17}+5q^{19}+\cdots\)
7200.2.f.bd \(4\) \(57.492\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{7}-2q^{11}-3\beta _{1}q^{13}-2\beta _{2}q^{17}+\cdots\)
7200.2.f.be \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}-\beta _{3}q^{11}-2\beta _{1}q^{13}-\beta _{1}q^{17}+\cdots\)
7200.2.f.bf \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}-2\beta _{3}q^{11}-\beta _{1}q^{13}+2\beta _{1}q^{17}+\cdots\)
7200.2.f.bg \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{7}+\beta _{3}q^{11}+4\beta _{1}q^{13}-7\beta _{1}q^{17}+\cdots\)
7200.2.f.bh \(4\) \(57.492\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}-\zeta_{8}q^{13}+\zeta_{8}q^{17}+\cdots\)
7200.2.f.bi \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+2\beta _{3}q^{11}-\beta _{1}q^{13}-2\beta _{1}q^{17}+\cdots\)
7200.2.f.bj \(4\) \(57.492\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+\beta _{3}q^{11}-2\beta _{1}q^{13}+\beta _{1}q^{17}+\cdots\)
7200.2.f.bk \(4\) \(57.492\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{7}+2q^{11}-3\beta _{1}q^{13}+2\beta _{2}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(7200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3600, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ 1
$7$ (\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 - 5 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 5 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 5 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 5 T^{2} + 49 T^{4} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 9 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 9 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - T^{2} + 49 T^{4} )^{2} \))
$11$ (\( ( 1 + 5 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 5 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{4} \))(\( ( 1 + 2 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 17 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 2 T + 11 T^{2} )^{4} \))
$13$ (\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 17 T^{2} + 169 T^{4} \))(\( 1 + 23 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 + 23 T^{2} + 169 T^{4} \))(\( 1 - 17 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 25 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 22 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 25 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( 1 - 9 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 9 T^{2} + 289 T^{4} \))(\( ( 1 - 4 T + 17 T^{2} )^{2}( 1 + 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 + 15 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 + 8 T + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 17 T^{2} )^{2}( 1 + 4 T + 17 T^{2} )^{2} \))
$19$ (\( ( 1 + 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 3 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 3 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 25 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 - 7 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 7 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 - 7 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 + 25 T^{2} + 361 T^{4} )^{2} \))
$23$ (\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( ( 1 - 10 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 34 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 34 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 529 T^{4} )^{2} \))
$29$ (\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{4} \))(\( ( 1 + 6 T + 29 T^{2} )^{4} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 - 6 T + 29 T^{2} )^{4} \))(\( ( 1 - 6 T + 29 T^{2} )^{4} \))(\( ( 1 - 6 T + 29 T^{2} )^{4} \))(\( ( 1 + 6 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 - 10 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + T + 31 T^{2} )^{2} \))(\( ( 1 + 3 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 5 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 7 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 - 7 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 5 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 3 T + 31 T^{2} )^{2} \))(\( ( 1 - T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 10 T + 31 T^{2} )^{2} \))(\( ( 1 + 49 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 57 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 42 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 57 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 49 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( ( 1 + 26 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))
$41$ (\( ( 1 + 5 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 5 T + 41 T^{2} )^{2} \))(\( ( 1 + 30 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{4} \))(\( ( 1 - 2 T + 41 T^{2} )^{4} \))(\( ( 1 + 5 T + 41 T^{2} )^{4} \))(\( ( 1 + 2 T + 41 T^{2} )^{4} \))(\( ( 1 + 2 T + 41 T^{2} )^{4} \))(\( ( 1 - 8 T + 41 T^{2} )^{4} \))(\( ( 1 + 30 T^{2} + 1681 T^{4} )^{2} \))
$43$ (\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 35 T^{2} + 1849 T^{4} \))(\( 1 + 35 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 85 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 5 T^{2} + 1849 T^{4} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( 1 - 5 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 85 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 35 T^{2} + 1849 T^{4} \))(\( 1 + 35 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( ( 1 - 73 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 41 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 10 T + 43 T^{2} )^{2}( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 - 41 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 73 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( ( 1 - 78 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 78 T^{2} + 2209 T^{4} )^{2} \))
$53$ (\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( ( 1 - 54 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 54 T^{2} + 2809 T^{4} )^{2} \))
$59$ (\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 10 T + 59 T^{2} )^{2} \))(\( ( 1 + 8 T + 59 T^{2} )^{2} \))(\( ( 1 - 10 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 10 T + 59 T^{2} )^{2} \))(\( ( 1 - 8 T + 59 T^{2} )^{2} \))(\( ( 1 - 10 T + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{4} \))(\( ( 1 + 98 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 38 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 38 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 38 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 98 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{4} \))
$61$ (\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 11 T + 61 T^{2} )^{2} \))(\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 6 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 5 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 5 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 6 T + 61 T^{2} )^{2} \))(\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 11 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + T + 61 T^{2} )^{4} \))(\( ( 1 - 10 T + 61 T^{2} )^{4} \))(\( ( 1 + 5 T + 61 T^{2} )^{4} \))(\( ( 1 - 10 T + 61 T^{2} )^{4} \))(\( ( 1 + 2 T + 61 T^{2} )^{4} \))(\( ( 1 + 5 T + 61 T^{2} )^{4} \))(\( ( 1 - 10 T + 61 T^{2} )^{4} \))(\( ( 1 + T + 61 T^{2} )^{4} \))
$67$ (\( 1 - 125 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 + 91 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 98 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 125 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 125 T^{2} + 4489 T^{4} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( 1 - 125 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 125 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 98 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 + 91 T^{2} + 4489 T^{4} \))(\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 125 T^{2} + 4489 T^{4} \))(\( ( 1 - 17 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 54 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 129 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 129 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 126 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 129 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 54 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 17 T^{2} + 4489 T^{4} )^{2} \))
$71$ (\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 14 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 14 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{4} \))(\( ( 1 + 62 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 122 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 62 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 110 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 122 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 62 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{4} \))
$73$ (\( 1 - 121 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 121 T^{2} + 5329 T^{4} \))(\( ( 1 - 46 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 16 T + 73 T^{2} )^{2}( 1 + 16 T + 73 T^{2} )^{2} \))(\( ( 1 - 16 T + 73 T^{2} )^{2}( 1 + 16 T + 73 T^{2} )^{2} \))(\( ( 1 - 65 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 16 T + 73 T^{2} )^{2}( 1 + 16 T + 73 T^{2} )^{2} \))(\( ( 1 - 16 T + 73 T^{2} )^{2}( 1 + 16 T + 73 T^{2} )^{2} \))(\( ( 1 - 16 T + 73 T^{2} )^{2}( 1 + 16 T + 73 T^{2} )^{2} \))(\( ( 1 - 46 T^{2} + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 50 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 78 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 78 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 138 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 30 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 78 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 78 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 6241 T^{4} )^{2} \))
$83$ (\( 1 - 165 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 66 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 + 30 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 + 158 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 + 158 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 + 30 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 66 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 165 T^{2} + 6889 T^{4} \))(\( ( 1 - 150 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 41 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2} \))(\( ( 1 - 86 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 150 T^{2} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 + 9 T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 16 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 12 T + 89 T^{2} )^{2} \))(\( ( 1 - 12 T + 89 T^{2} )^{2} \))(\( ( 1 - 16 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 16 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 16 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 16 T + 89 T^{2} )^{2} \))(\( ( 1 - 12 T + 89 T^{2} )^{2} \))(\( ( 1 + 12 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 16 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 + 9 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{4} \))(\( ( 1 - 4 T + 89 T^{2} )^{4} \))(\( ( 1 + 16 T + 89 T^{2} )^{4} \))(\( ( 1 + 5 T + 89 T^{2} )^{4} \))(\( ( 1 - 10 T + 89 T^{2} )^{4} \))(\( ( 1 - 16 T + 89 T^{2} )^{4} \))(\( ( 1 + 4 T + 89 T^{2} )^{4} \))(\( ( 1 + 89 T^{2} )^{4} \))
$97$ (\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 73 T^{2} + 9409 T^{4} \))(\( 1 - 25 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 185 T^{2} + 9409 T^{4} \))(\( ( 1 - 8 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} ) \))(\( ( 1 - 8 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} ) \))(\( ( 1 - 8 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} ) \))(\( ( 1 - 8 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} ) \))(\( ( 1 - 8 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} ) \))(\( 1 - 185 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 25 T^{2} + 9409 T^{4} \))(\( 1 - 73 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( ( 1 - 193 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 190 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 145 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 190 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 190 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 145 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 190 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 193 T^{2} + 9409 T^{4} )^{2} \))
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