Properties

Label 2352.2.q
Level 2352
Weight 2
Character orbit q
Rep. character \(\chi_{2352}(961,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 80
Newform subspaces 33
Sturm bound 896
Trace bound 13

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 33 \)
Sturm bound: \(896\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 992 80 912
Cusp forms 800 80 720
Eisenstein series 192 0 192

Trace form

\( 80q + 2q^{3} - 40q^{9} + O(q^{10}) \) \( 80q + 2q^{3} - 40q^{9} - 8q^{11} + 10q^{19} - 20q^{23} - 36q^{25} - 4q^{27} - 32q^{29} - 14q^{31} + 4q^{33} + 16q^{37} - 2q^{39} - 16q^{41} + 20q^{43} + 12q^{47} + 24q^{53} + 56q^{55} + 8q^{57} + 16q^{59} + 8q^{61} + 8q^{65} + 2q^{67} - 16q^{71} - 12q^{73} + 14q^{75} - 22q^{79} - 40q^{81} + 24q^{83} + 32q^{85} - 12q^{87} - 16q^{89} - 16q^{93} + 60q^{95} - 8q^{97} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2352.2.q.a \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(0\) \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.b \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(0\) \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.c \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.d \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.e \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.f \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
2352.2.q.g \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.h \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4+\cdots)q^{17}+\cdots\)
2352.2.q.i \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.j \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.k \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.l \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.m \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.n \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.o \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}-2q^{13}+\cdots\)
2352.2.q.p \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.q \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.r \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.s \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.t \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
2352.2.q.u \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(5-5\zeta_{6})q^{11}+\cdots\)
2352.2.q.v \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
2352.2.q.w \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}-6q^{13}+\cdots\)
2352.2.q.x \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.y \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.z \(2\) \(18.781\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.ba \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bb \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bc \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bd \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.be \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bf \(4\) \(18.781\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(2\) \(-1\) \(0\) \(q-\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{9}+\cdots\)
2352.2.q.bg \(4\) \(18.781\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(4\) \(0\) \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$5$ (\( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} \))(\( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 + 4 T + 4 T^{2} + 8 T^{3} + 39 T^{4} + 40 T^{5} + 100 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 - 4 T + 4 T^{2} - 8 T^{3} + 39 T^{4} - 40 T^{5} + 100 T^{6} - 500 T^{7} + 625 T^{8} \))(\( 1 - 4 T + 4 T^{2} - 8 T^{3} + 39 T^{4} - 40 T^{5} + 100 T^{6} - 500 T^{7} + 625 T^{8} \))(\( 1 + 4 T + 4 T^{2} + 8 T^{3} + 39 T^{4} + 40 T^{5} + 100 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 + 4 T + 4 T^{2} + 8 T^{3} + 39 T^{4} + 40 T^{5} + 100 T^{6} + 500 T^{7} + 625 T^{8} \))(\( ( 1 + T + 5 T^{2} )^{2}( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} ) \))(\( 1 - 4 T + 4 T^{2} - 8 T^{3} + 39 T^{4} - 40 T^{5} + 100 T^{6} - 500 T^{7} + 625 T^{8} \))
$7$ 1
$11$ (\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 + 4 T - 2 T^{2} - 16 T^{3} + 27 T^{4} - 176 T^{5} - 242 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( ( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} )^{2} \))(\( 1 - 4 T - 2 T^{2} + 16 T^{3} + 27 T^{4} + 176 T^{5} - 242 T^{6} - 5324 T^{7} + 14641 T^{8} \))(\( ( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} )^{2} \))(\( 1 - 4 T - 2 T^{2} + 16 T^{3} + 27 T^{4} + 176 T^{5} - 242 T^{6} - 5324 T^{7} + 14641 T^{8} \))(\( 1 + T - 7 T^{2} - 14 T^{3} - 68 T^{4} - 154 T^{5} - 847 T^{6} + 1331 T^{7} + 14641 T^{8} \))(\( 1 + 4 T - 2 T^{2} - 16 T^{3} + 27 T^{4} - 176 T^{5} - 242 T^{6} + 5324 T^{7} + 14641 T^{8} \))
$13$ (\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 3 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 - 3 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 8 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 8 T + 40 T^{2} + 104 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 + 24 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 8 T + 40 T^{2} - 104 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 + 24 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 5 T + 18 T^{2} + 65 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 + 8 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 12 T + 76 T^{2} + 408 T^{3} + 1887 T^{4} + 6936 T^{5} + 21964 T^{6} + 58956 T^{7} + 83521 T^{8} \))(\( 1 - 4 T - 4 T^{2} + 56 T^{3} - 161 T^{4} + 952 T^{5} - 1156 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( 1 + 4 T - 4 T^{2} - 56 T^{3} - 161 T^{4} - 952 T^{5} - 1156 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 + 4 T - 4 T^{2} - 56 T^{3} - 161 T^{4} - 952 T^{5} - 1156 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 - 4 T - 4 T^{2} + 56 T^{3} - 161 T^{4} + 952 T^{5} - 1156 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( ( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} )^{2} \))(\( 1 - 12 T + 76 T^{2} - 408 T^{3} + 1887 T^{4} - 6936 T^{5} + 21964 T^{6} - 58956 T^{7} + 83521 T^{8} \))
$19$ (\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 - T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 8 T + 18 T^{2} - 64 T^{3} + 539 T^{4} - 1216 T^{5} + 6498 T^{6} - 54872 T^{7} + 130321 T^{8} \))(\( 1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8} \))(\( 1 + 8 T + 18 T^{2} + 64 T^{3} + 539 T^{4} + 1216 T^{5} + 6498 T^{6} + 54872 T^{7} + 130321 T^{8} \))(\( 1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8} \))(\( 1 - 8 T + 18 T^{2} - 64 T^{3} + 539 T^{4} - 1216 T^{5} + 6498 T^{6} - 54872 T^{7} + 130321 T^{8} \))(\( 1 - 5 T - 5 T^{2} + 40 T^{3} + 64 T^{4} + 760 T^{5} - 1805 T^{6} - 34295 T^{7} + 130321 T^{8} \))(\( 1 + 8 T + 18 T^{2} + 64 T^{3} + 539 T^{4} + 1216 T^{5} + 6498 T^{6} + 54872 T^{7} + 130321 T^{8} \))
$23$ (\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 26 T^{2} - 16 T^{3} + 867 T^{4} - 368 T^{5} - 13754 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 + 4 T - 2 T^{2} - 112 T^{3} - 573 T^{4} - 2576 T^{5} - 1058 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 - 4 T - 26 T^{2} + 16 T^{3} + 867 T^{4} + 368 T^{5} - 13754 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 + 4 T - 2 T^{2} - 112 T^{3} - 573 T^{4} - 2576 T^{5} - 1058 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 - 4 T - 26 T^{2} + 16 T^{3} + 867 T^{4} + 368 T^{5} - 13754 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( ( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \))(\( 1 + 4 T - 26 T^{2} - 16 T^{3} + 867 T^{4} - 368 T^{5} - 13754 T^{6} + 48668 T^{7} + 279841 T^{8} \))
$29$ (\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 9 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 5 T + 29 T^{2} )^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 50 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 8 T + 66 T^{2} + 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 8 T + 66 T^{2} + 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 3 T + 46 T^{2} - 87 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 50 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 279 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 5 T - 6 T^{2} - 155 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( 1 + 3 T - 22 T^{2} + 93 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 + 3 T - 22 T^{2} + 93 T^{3} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 54 T^{2} + 1955 T^{4} - 51894 T^{6} + 923521 T^{8} \))(\( 1 - 8 T - 6 T^{2} - 64 T^{3} + 1955 T^{4} - 1984 T^{5} - 5766 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( 1 + 16 T + 138 T^{2} + 896 T^{3} + 5027 T^{4} + 27776 T^{5} + 132618 T^{6} + 476656 T^{7} + 923521 T^{8} \))(\( 1 + 8 T - 6 T^{2} + 64 T^{3} + 1955 T^{4} + 1984 T^{5} - 5766 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 - 16 T + 138 T^{2} - 896 T^{3} + 5027 T^{4} - 27776 T^{5} + 132618 T^{6} - 476656 T^{7} + 923521 T^{8} \))(\( ( 1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4} )^{2} \))(\( 1 - 54 T^{2} + 1955 T^{4} - 51894 T^{6} + 923521 T^{8} \))
$37$ (\( 1 - 6 T - T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 6 T - T^{2} - 222 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 6 T - T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 9 T + 44 T^{2} - 333 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 6 T - T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 6 T^{2} - 128 T^{3} - 373 T^{4} - 4736 T^{5} + 8214 T^{6} + 405224 T^{7} + 1874161 T^{8} \))(\( ( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 8 T + 6 T^{2} + 128 T^{3} - 373 T^{4} + 4736 T^{5} + 8214 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( ( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 8 T + 6 T^{2} + 128 T^{3} - 373 T^{4} + 4736 T^{5} + 8214 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 + 3 T - 53 T^{2} - 36 T^{3} + 2142 T^{4} - 1332 T^{5} - 72557 T^{6} + 151959 T^{7} + 1874161 T^{8} \))(\( 1 + 8 T + 6 T^{2} - 128 T^{3} - 373 T^{4} - 4736 T^{5} + 8214 T^{6} + 405224 T^{7} + 1874161 T^{8} \))
$41$ (\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 100 T^{2} - 492 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 4 T + 68 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 4 T + 84 T^{2} - 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 4 T + 68 T^{2} - 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 4 T + 84 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 6 T + 34 T^{2} + 246 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 12 T + 100 T^{2} + 492 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 5 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 6 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 10 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 11 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 2 T + 43 T^{2} )^{2} \))(\( ( 1 - T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 42 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 54 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{4} \))(\( ( 1 + 54 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{4} \))(\( ( 1 - 7 T + 84 T^{2} - 301 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 42 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 10 T + 53 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 26 T^{2} + 448 T^{3} - 3773 T^{4} + 21056 T^{5} + 57434 T^{6} - 830584 T^{7} + 4879681 T^{8} \))(\( 1 - 86 T^{2} + 5187 T^{4} - 189974 T^{6} + 4879681 T^{8} \))(\( 1 + 8 T - 38 T^{2} + 64 T^{3} + 5187 T^{4} + 3008 T^{5} - 83942 T^{6} + 830584 T^{7} + 4879681 T^{8} \))(\( 1 - 86 T^{2} + 5187 T^{4} - 189974 T^{6} + 4879681 T^{8} \))(\( 1 - 8 T - 38 T^{2} - 64 T^{3} + 5187 T^{4} - 3008 T^{5} - 83942 T^{6} - 830584 T^{7} + 4879681 T^{8} \))(\( ( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} )^{2} \))(\( 1 + 8 T + 26 T^{2} - 448 T^{3} - 3773 T^{4} - 21056 T^{5} + 57434 T^{6} + 830584 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 9 T + 28 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 2 T - 49 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 - 3 T - 44 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 2 T - 49 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 91 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 28 T^{2} - 477 T^{3} + 2809 T^{4} \))(\( 1 + 8 T + 11 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( ( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} )^{2} \))(\( 1 - 4 T + 34 T^{2} + 496 T^{3} - 3333 T^{4} + 26288 T^{5} + 95506 T^{6} - 595508 T^{7} + 7890481 T^{8} \))(\( ( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} )^{2} \))(\( 1 - 4 T + 34 T^{2} + 496 T^{3} - 3333 T^{4} + 26288 T^{5} + 95506 T^{6} - 595508 T^{7} + 7890481 T^{8} \))(\( 1 + 11 T - T^{2} + 176 T^{3} + 5662 T^{4} + 9328 T^{5} - 2809 T^{6} + 1637647 T^{7} + 7890481 T^{8} \))(\( ( 1 - 2 T - 49 T^{2} - 106 T^{3} + 2809 T^{4} )^{2} \))
$59$ (\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 5 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 5 T - 34 T^{2} - 295 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 11 T + 62 T^{2} - 649 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 5 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 - 46 T^{2} - 1365 T^{4} - 160126 T^{6} + 12117361 T^{8} \))(\( 1 - 8 T - 62 T^{2} - 64 T^{3} + 8619 T^{4} - 3776 T^{5} - 215822 T^{6} - 1643032 T^{7} + 12117361 T^{8} \))(\( 1 + 16 T + 82 T^{2} + 896 T^{3} + 11691 T^{4} + 52864 T^{5} + 285442 T^{6} + 3286064 T^{7} + 12117361 T^{8} \))(\( 1 + 8 T - 62 T^{2} + 64 T^{3} + 8619 T^{4} + 3776 T^{5} - 215822 T^{6} + 1643032 T^{7} + 12117361 T^{8} \))(\( 1 - 16 T + 82 T^{2} - 896 T^{3} + 11691 T^{4} - 52864 T^{5} + 285442 T^{6} - 3286064 T^{7} + 12117361 T^{8} \))(\( 1 + 5 T - 85 T^{2} - 40 T^{3} + 7144 T^{4} - 2360 T^{5} - 295885 T^{6} + 1026895 T^{7} + 12117361 T^{8} \))(\( 1 - 46 T^{2} - 1365 T^{4} - 160126 T^{6} + 12117361 T^{8} \))
$61$ (\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 45 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 45 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 + 8 T - 24 T^{2} - 272 T^{3} + 119 T^{4} - 16592 T^{5} - 89304 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 16 T + 88 T^{2} - 736 T^{3} + 8887 T^{4} - 44896 T^{5} + 327448 T^{6} - 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T + 24 T^{2} + 656 T^{3} - 6025 T^{4} + 40016 T^{5} + 89304 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 + 16 T + 88 T^{2} + 736 T^{3} + 8887 T^{4} + 44896 T^{5} + 327448 T^{6} + 3631696 T^{7} + 13845841 T^{8} \))(\( 1 + 8 T + 24 T^{2} - 656 T^{3} - 6025 T^{4} - 40016 T^{5} + 89304 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( ( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} )^{2} \))(\( 1 - 8 T - 24 T^{2} + 272 T^{3} + 119 T^{4} + 16592 T^{5} - 89304 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 6 T - 31 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 10 T + 33 T^{2} + 670 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 15 T + 158 T^{2} + 1005 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 77 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 6 T^{2} - 4453 T^{4} - 26934 T^{6} + 20151121 T^{8} \))(\( 1 - 102 T^{2} + 5915 T^{4} - 457878 T^{6} + 20151121 T^{8} \))(\( ( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} )^{2} \))(\( 1 - 102 T^{2} + 5915 T^{4} - 457878 T^{6} + 20151121 T^{8} \))(\( ( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} )^{2} \))(\( 1 - 7 T - 83 T^{2} + 14 T^{3} + 9652 T^{4} + 938 T^{5} - 372587 T^{6} - 2105341 T^{7} + 20151121 T^{8} \))(\( 1 - 6 T^{2} - 4453 T^{4} - 26934 T^{6} + 20151121 T^{8} \))
$71$ (\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 14 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 71 T^{2} )^{2} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 14 T + 71 T^{2} )^{2} \))(\( ( 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 4 T + 18 T^{2} - 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 4 T + 138 T^{2} + 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 4 T + 18 T^{2} - 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 4 T + 138 T^{2} + 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 2 T + 71 T^{2} )^{4} \))(\( ( 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} )^{2} \))
$73$ (\( 1 - 16 T + 183 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 3 T - 64 T^{2} + 219 T^{3} + 5329 T^{4} \))(\( 1 - 14 T + 123 T^{2} - 1022 T^{3} + 5329 T^{4} \))(\( 1 + 6 T - 37 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 8 T - 9 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 4 T - 57 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 4 T - 57 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 8 T - 9 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 + 14 T + 123 T^{2} + 1022 T^{3} + 5329 T^{4} \))(\( 1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 24 T + 304 T^{2} + 3024 T^{3} + 26607 T^{4} + 220752 T^{5} + 1620016 T^{6} + 9336408 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T + 656 T^{3} - 5905 T^{4} + 47888 T^{5} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + 8 T - 48 T^{2} - 272 T^{3} + 2543 T^{4} - 19856 T^{5} - 255792 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + 8 T - 656 T^{3} - 5905 T^{4} - 47888 T^{5} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T - 48 T^{2} + 272 T^{3} + 2543 T^{4} + 19856 T^{5} - 255792 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 + T - 131 T^{2} - 14 T^{3} + 12022 T^{4} - 1022 T^{5} - 698099 T^{6} + 389017 T^{7} + 28398241 T^{8} \))(\( 1 - 24 T + 304 T^{2} - 3024 T^{3} + 26607 T^{4} - 220752 T^{5} + 1620016 T^{6} - 9336408 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 65 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 79 T^{2} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 - 79 T^{2} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 + 3 T - 70 T^{2} + 237 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 3 T - 70 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 65 T^{2} - 948 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 66 T^{2} - 512 T^{3} + 9635 T^{4} - 40448 T^{5} + 411906 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 66 T^{2} - 512 T^{3} + 9635 T^{4} - 40448 T^{5} + 411906 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 16 T + 66 T^{2} + 512 T^{3} + 9635 T^{4} + 40448 T^{5} + 411906 T^{6} + 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 66 T^{2} - 512 T^{3} + 9635 T^{4} - 40448 T^{5} + 411906 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 16 T + 66 T^{2} + 512 T^{3} + 9635 T^{4} + 40448 T^{5} + 411906 T^{6} + 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 8 T - 53 T^{2} + 328 T^{3} + 2392 T^{4} + 25912 T^{5} - 330773 T^{6} - 3944312 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 66 T^{2} - 512 T^{3} + 9635 T^{4} - 40448 T^{5} + 411906 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))
$83$ (\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 7 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 9 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 2 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 7 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{4} \))(\( ( 1 + 8 T + 54 T^{2} + 664 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 8 T + 54 T^{2} - 664 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 8 T + 54 T^{2} - 664 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 8 T + 54 T^{2} + 664 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 7 T + 164 T^{2} - 581 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{4} \))
$89$ (\( 1 + 8 T - 25 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 16 T + 167 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 - 2 T - 85 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 14 T + 107 T^{2} + 1246 T^{3} + 7921 T^{4} \))(\( 1 + 18 T + 235 T^{2} + 1602 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 4 T - 73 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 14 T + 107 T^{2} + 1246 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 55 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 4 T - 73 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 8 T - 25 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 + 2 T - 85 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 - 8 T - 25 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 20 T + 140 T^{2} + 1640 T^{3} + 24079 T^{4} + 145960 T^{5} + 1108940 T^{6} + 14099380 T^{7} + 62742241 T^{8} \))(\( 1 + 20 T + 140 T^{2} + 1640 T^{3} + 24079 T^{4} + 145960 T^{5} + 1108940 T^{6} + 14099380 T^{7} + 62742241 T^{8} \))(\( 1 - 4 T - 4 T^{2} + 632 T^{3} - 8945 T^{4} + 56248 T^{5} - 31684 T^{6} - 2819876 T^{7} + 62742241 T^{8} \))(\( 1 - 20 T + 140 T^{2} - 1640 T^{3} + 24079 T^{4} - 145960 T^{5} + 1108940 T^{6} - 14099380 T^{7} + 62742241 T^{8} \))(\( 1 + 4 T - 4 T^{2} - 632 T^{3} - 8945 T^{4} - 56248 T^{5} - 31684 T^{6} + 2819876 T^{7} + 62742241 T^{8} \))(\( 1 + 6 T - 94 T^{2} - 288 T^{3} + 5775 T^{4} - 25632 T^{5} - 744574 T^{6} + 4229814 T^{7} + 62742241 T^{8} \))(\( 1 - 20 T + 140 T^{2} - 1640 T^{3} + 24079 T^{4} - 145960 T^{5} + 1108940 T^{6} - 14099380 T^{7} + 62742241 T^{8} \))
$97$ (\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 18 T + 97 T^{2} )^{2} \))(\( ( 1 - 17 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 16 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 4 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 16 T + 97 T^{2} )^{2} \))(\( ( 1 + 7 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 192 T^{2} - 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 8 T + 208 T^{2} + 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 8 T + 208 T^{2} - 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 25 T + 336 T^{2} + 2425 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 8 T + 192 T^{2} + 776 T^{3} + 9409 T^{4} )^{2} \))
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