Properties

Label 2450.2.c
Level 2450
Weight 2
Character orbit c
Rep. character \(\chi_{2450}(99,\cdot)\)
Character field \(\Q\)
Dimension 62
Newform subspaces 24
Sturm bound 840
Trace bound 31

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Defining parameters

Level: \( N \) = \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2450.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(840\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

Total New Old
Modular forms 468 62 406
Cusp forms 372 62 310
Eisenstein series 96 0 96

Trace form

\( 62q - 62q^{4} + 2q^{6} - 80q^{9} + O(q^{10}) \) \( 62q - 62q^{4} + 2q^{6} - 80q^{9} + 10q^{11} + 62q^{16} - 6q^{19} - 2q^{24} + 4q^{26} - 24q^{29} + 4q^{31} + 2q^{34} + 80q^{36} + 40q^{39} - 14q^{41} - 10q^{44} + 4q^{46} + 34q^{51} - 26q^{54} + 4q^{59} + 32q^{61} - 62q^{64} - 42q^{66} + 12q^{69} + 16q^{71} - 44q^{74} + 6q^{76} - 20q^{79} + 78q^{81} + 8q^{86} - 14q^{89} + 8q^{94} + 2q^{96} - 92q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2450.2.c.a \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{8}+\cdots\)
2450.2.c.b \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.c \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.d \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.e \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.f \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.g \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
2450.2.c.h \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
2450.2.c.i \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+3q^{9}-2q^{11}+\cdots\)
2450.2.c.j \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2q^{11}+\cdots\)
2450.2.c.k \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}+4q^{11}+\cdots\)
2450.2.c.l \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots\)
2450.2.c.m \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots\)
2450.2.c.n \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.o \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.p \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.q \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.r \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots\)
2450.2.c.s \(2\) \(19.563\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots\)
2450.2.c.t \(4\) \(19.563\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
2450.2.c.u \(4\) \(19.563\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{1}q^{8}+\cdots\)
2450.2.c.v \(4\) \(19.563\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
2450.2.c.w \(4\) \(19.563\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(2+\cdots)q^{6}+\cdots\)
2450.2.c.x \(8\) \(19.563\) 8.0.959512576.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{3}-\beta _{7})q^{3}-q^{4}+\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))
$3$ (\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( ( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} )( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} ) \))(\( ( 1 + T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} )( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} ) \))(\( ( 1 + 7 T^{4} + 81 T^{8} )^{2} \))
$5$ 1
$7$ 1
$11$ (\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 + 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 5 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 5 T + 11 T^{2} )^{4} \))(\( ( 1 + 2 T + 11 T^{2} )^{4} \))(\( ( 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 15 T^{2} - 44 T^{3} + 121 T^{4} )^{4} \))
$13$ (\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( 1 - T^{2} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - T^{2} + 169 T^{4} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 28 T^{2} + 406 T^{4} - 4732 T^{6} + 28561 T^{8} \))(\( ( 1 + 2 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( 1 - 28 T^{2} + 406 T^{4} - 4732 T^{6} + 28561 T^{8} \))(\( ( 1 - 4 T^{2} + 166 T^{4} - 676 T^{6} + 28561 T^{8} )^{2} \))
$17$ (\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( 1 + 15 T^{2} + 289 T^{4} \))(\( 1 + 15 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 - 33 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 32 T^{2} + 706 T^{4} - 9248 T^{6} + 83521 T^{8} \))(\( ( 1 - 27 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 32 T^{2} + 289 T^{4} )^{2} \))(\( 1 - 32 T^{2} + 706 T^{4} - 9248 T^{6} + 83521 T^{8} \))(\( ( 1 - 8 T^{2} + 55 T^{4} - 2312 T^{6} + 83521 T^{8} )^{2} \))
$19$ (\( ( 1 + 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 6 T + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 - 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( ( 1 - T + 19 T^{2} )^{2} \))(\( ( 1 + 3 T + 19 T^{2} )^{2} \))(\( ( 1 - 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 40 T^{2} + 76 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 25 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 12 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 64 T^{2} + 1735 T^{4} + 23104 T^{6} + 130321 T^{8} )^{2} \))
$23$ (\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 30 T^{2} + 529 T^{4} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 + 35 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 37 T^{2} + 529 T^{4} \))(\( 1 - 44 T^{2} + 1030 T^{4} - 23276 T^{6} + 279841 T^{8} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 1030 T^{4} - 23276 T^{6} + 279841 T^{8} \))(\( ( 1 + 4 T^{2} + 358 T^{4} + 2116 T^{6} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{4} \))(\( ( 1 + 2 T + 29 T^{2} )^{4} \))(\( ( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 8 T + 30 T^{2} + 232 T^{3} + 841 T^{4} )^{4} \))
$31$ (\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 5 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 7 T + 31 T^{2} )^{2} \))(\( ( 1 - 7 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 5 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 8 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 54 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 54 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 30 T^{2} + 961 T^{4} )^{4} \))
$37$ (\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 76 T^{2} + 3670 T^{4} - 104044 T^{6} + 1874161 T^{8} \))(\( ( 1 - 58 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 1369 T^{4} )^{2} \))(\( 1 - 76 T^{2} + 3670 T^{4} - 104044 T^{6} + 1874161 T^{8} \))(\( ( 1 - 52 T^{2} + 2710 T^{4} - 71188 T^{6} + 1874161 T^{8} )^{2} \))
$41$ (\( ( 1 - 7 T + 41 T^{2} )^{2} \))(\( ( 1 + 4 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 + 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 9 T + 41 T^{2} )^{2} \))(\( ( 1 - 9 T + 41 T^{2} )^{2} \))(\( ( 1 + 7 T + 41 T^{2} )^{2} \))(\( ( 1 - 7 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 9 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 4 T + 41 T^{2} )^{2} \))(\( ( 1 + 3 T + 41 T^{2} )^{2} \))(\( ( 1 + 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 + 11 T + 41 T^{2} )^{2} \))(\( ( 1 + 7 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 48 T^{2} - 328 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 75 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 16 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 8 T + 48 T^{2} + 328 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 104 T^{2} + 5527 T^{4} + 174824 T^{6} + 2825761 T^{8} )^{2} \))
$43$ (\( 1 - 61 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 37 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 37 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 22 T^{2} + 1849 T^{4} \))(\( 1 - 61 T^{2} + 1849 T^{4} \))(\( 1 - 84 T^{2} + 4310 T^{4} - 155316 T^{6} + 3418801 T^{8} \))(\( ( 1 - 22 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 84 T^{2} + 4310 T^{4} - 155316 T^{6} + 3418801 T^{8} \))(\( ( 1 - 42 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 13 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 13 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \))(\( ( 1 - 66 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \))(\( ( 1 - 140 T^{2} + 9142 T^{4} - 309260 T^{6} + 4879681 T^{8} )^{2} \))
$53$ (\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 25 T^{2} + 2809 T^{4} \))(\( 1 - 97 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 + 38 T^{2} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 97 T^{2} + 2809 T^{4} \))(\( 1 - 25 T^{2} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 60 T^{2} + 5366 T^{4} - 168540 T^{6} + 7890481 T^{8} \))(\( ( 1 - 14 T + 53 T^{2} )^{2}( 1 + 14 T + 53 T^{2} )^{2} \))(\( ( 1 - 102 T^{2} + 2809 T^{4} )^{2} \))(\( 1 - 60 T^{2} + 5366 T^{4} - 168540 T^{6} + 7890481 T^{8} \))(\( ( 1 - 42 T^{2} + 2809 T^{4} )^{4} \))
$59$ (\( ( 1 - 10 T + 59 T^{2} )^{2} \))(\( ( 1 + 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 10 T + 59 T^{2} )^{2} \))(\( ( 1 + 20 T + 216 T^{2} + 1180 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 90 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 116 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 20 T + 216 T^{2} - 1180 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 176 T^{2} + 14002 T^{4} + 612656 T^{6} + 12117361 T^{8} )^{2} \))
$61$ (\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 - 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 - 5 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 14 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2} \))(\( ( 1 + 5 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 - 4 T + 61 T^{2} )^{2} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T - 2 T^{2} + 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 94 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 + 114 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 4 T - 2 T^{2} - 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 196 T^{2} + 16870 T^{4} + 729316 T^{6} + 13845841 T^{8} )^{2} \))
$67$ (\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 109 T^{2} + 4489 T^{4} \))(\( 1 - 85 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 + 10 T^{2} + 4489 T^{4} \))(\( 1 - 109 T^{2} + 4489 T^{4} \))(\( 1 + 35 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 - 53 T^{2} + 4489 T^{4} \))(\( 1 - 172 T^{2} + 14326 T^{4} - 772108 T^{6} + 20151121 T^{8} \))(\( ( 1 - 109 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 10 T^{2} + 4489 T^{4} )^{2} \))(\( 1 - 172 T^{2} + 14326 T^{4} - 772108 T^{6} + 20151121 T^{8} \))(\( ( 1 - 130 T^{2} + 8803 T^{4} - 583570 T^{6} + 20151121 T^{8} )^{2} \))
$71$ (\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + T + 71 T^{2} )^{2} \))(\( ( 1 + T + 71 T^{2} )^{2} \))(\( ( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{4} \))(\( ( 1 + 12 T + 71 T^{2} )^{4} \))(\( ( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 2 T + 71 T^{2} )^{8} \))
$73$ (\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( ( 1 - 6 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( 1 - 121 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 + 50 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( ( 1 - 6 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( 1 - 25 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 46 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 97 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 160 T^{2} + 16546 T^{4} - 852640 T^{6} + 28398241 T^{8} \))(\( ( 1 - 139 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 144 T^{2} + 5329 T^{4} )^{2} \))(\( 1 - 160 T^{2} + 16546 T^{4} - 852640 T^{6} + 28398241 T^{8} \))(\( ( 1 - 232 T^{2} + 23575 T^{4} - 1236328 T^{6} + 28398241 T^{8} )^{2} \))
$79$ (\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 5 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 2 T + 79 T^{2} )^{2} \))(\( ( 1 + 14 T + 79 T^{2} )^{2} \))(\( ( 1 - 11 T + 79 T^{2} )^{2} \))(\( ( 1 - 11 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 2 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 5 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 2 T + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 166 T^{2} - 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{4} \))(\( ( 1 - 4 T + 79 T^{2} )^{4} \))(\( ( 1 - 8 T + 166 T^{2} - 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 16 T + 178 T^{2} + 1264 T^{3} + 6241 T^{4} )^{4} \))
$83$ (\( 1 - 117 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( 1 - 157 T^{2} + 6889 T^{4} \))(\( 1 - 85 T^{2} + 6889 T^{4} \))(\( 1 + 30 T^{2} + 6889 T^{4} \))(\( 1 + 30 T^{2} + 6889 T^{4} \))(\( 1 - 102 T^{2} + 6889 T^{4} \))(\( 1 - 157 T^{2} + 6889 T^{4} \))(\( 1 - 85 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 45 T^{2} + 6889 T^{4} \))(\( 1 - 117 T^{2} + 6889 T^{4} \))(\( 1 - 288 T^{2} + 34226 T^{4} - 1984032 T^{6} + 47458321 T^{8} \))(\( ( 1 - 159 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 68 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 288 T^{2} + 34226 T^{4} - 1984032 T^{6} + 47458321 T^{8} \))(\( ( 1 - 96 T^{2} + 13607 T^{4} - 661344 T^{6} + 47458321 T^{8} )^{2} \))
$89$ (\( ( 1 - T + 89 T^{2} )^{2} \))(\( ( 1 - 8 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 3 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 7 T + 89 T^{2} )^{2} \))(\( ( 1 - 7 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 15 T + 89 T^{2} )^{2} \))(\( ( 1 - 15 T + 89 T^{2} )^{2} \))(\( ( 1 + 8 T + 89 T^{2} )^{2} \))(\( ( 1 + 3 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 11 T + 89 T^{2} )^{2} \))(\( ( 1 + T + 89 T^{2} )^{2} \))(\( ( 1 + 16 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 3 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 128 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 16 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 248 T^{2} + 30327 T^{4} + 1964408 T^{6} + 62742241 T^{8} )^{2} \))
$97$ (\( 1 + 2 T^{2} + 9409 T^{4} \))(\( ( 1 - 97 T^{2} )^{2} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 145 T^{2} + 9409 T^{4} \))(\( 1 - 145 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( ( 1 - 97 T^{2} )^{2} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 64 T^{2} + 9474 T^{4} - 602176 T^{6} + 88529281 T^{8} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 96 T^{2} + 9409 T^{4} )^{2} \))(\( 1 - 64 T^{2} + 9474 T^{4} - 602176 T^{6} + 88529281 T^{8} \))(\( ( 1 - 176 T^{2} + 9409 T^{4} )^{4} \))
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