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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 17
7497.2.a.a 7497.a 1.a $1$ $59.864$ \(\Q\) None \(-2\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-3q^{11}+\cdots\)
7497.2.a.b 7497.a 1.a $1$ $59.864$ \(\Q\) None \(-2\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-q^{11}+\cdots\)
7497.2.a.c 7497.a 1.a $1$ $59.864$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-3q^{5}+3q^{8}+3q^{10}+\cdots\)
7497.2.a.d 7497.a 1.a $1$ $59.864$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots\)
7497.2.a.e 7497.a 1.a $1$ $59.864$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-2q^{10}+\cdots\)
7497.2.a.f 7497.a 1.a $1$ $59.864$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{5}+3q^{8}-3q^{10}+\cdots\)
7497.2.a.g 7497.a 1.a $1$ $59.864$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-4q^{5}-4q^{11}+q^{13}+4q^{16}+\cdots\)
7497.2.a.h 7497.a 1.a $1$ $59.864$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-3q^{11}-3q^{13}+4q^{16}+\cdots\)
7497.2.a.i 7497.a 1.a $1$ $59.864$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+5q^{11}+5q^{13}+4q^{16}+\cdots\)
7497.2.a.j 7497.a 1.a $1$ $59.864$ \(\Q\) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}+3q^{11}+q^{13}+4q^{16}+\cdots\)
7497.2.a.k 7497.a 1.a $1$ $59.864$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+4q^{5}-4q^{11}-q^{13}+4q^{16}+\cdots\)
7497.2.a.l 7497.a 1.a $1$ $59.864$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
7497.2.a.m 7497.a 1.a $1$ $59.864$ \(\Q\) None \(1\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+2q^{11}+\cdots\)
7497.2.a.n 7497.a 1.a $1$ $59.864$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+2q^{11}+\cdots\)
7497.2.a.o 7497.a 1.a $1$ $59.864$ \(\Q\) None \(2\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{5}-6q^{10}+3q^{11}+\cdots\)
7497.2.a.p 7497.a 1.a $1$ $59.864$ \(\Q\) None \(2\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+3q^{11}+\cdots\)
7497.2.a.q 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
7497.2.a.r 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
7497.2.a.s 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{5}-2\beta q^{8}+(2-\beta )q^{10}+\cdots\)
7497.2.a.t 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{5}-2\beta q^{8}+(2-\beta )q^{10}+\cdots\)
7497.2.a.u 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{5}-2\beta q^{8}+(-2+\beta )q^{10}+\cdots\)
7497.2.a.v 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}+(1+\beta )q^{5}+(4+\beta )q^{8}+\cdots\)
7497.2.a.w 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
7497.2.a.x 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2\beta q^{5}+(3+\cdots)q^{8}+\cdots\)
7497.2.a.y 7497.a 1.a $2$ $59.864$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
7497.2.a.z 7497.a 1.a $3$ $59.864$ 3.3.148.1 None \(-2\) \(0\) \(5\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
7497.2.a.ba 7497.a 1.a $3$ $59.864$ 3.3.316.1 None \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
7497.2.a.bb 7497.a 1.a $3$ $59.864$ \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1})q^{5}+(1+\cdots)q^{8}+\cdots\)
7497.2.a.bc 7497.a 1.a $3$ $59.864$ \(\Q(\zeta_{14})^+\) None \(1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1})q^{5}+(1-2\beta _{1}+\cdots)q^{8}+\cdots\)
7497.2.a.bd 7497.a 1.a $3$ $59.864$ 3.3.148.1 None \(2\) \(0\) \(-5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
7497.2.a.be 7497.a 1.a $4$ $59.864$ 4.4.7232.1 None \(-2\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(1-\beta _{2}-\beta _{3})q^{4}+\beta _{1}q^{5}+\cdots\)
7497.2.a.bf 7497.a 1.a $4$ $59.864$ \(\Q(\sqrt{2}, \sqrt{39})\) None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{5}+2\beta _{2}q^{8}+\beta _{2}q^{10}+\cdots\)
7497.2.a.bg 7497.a 1.a $4$ $59.864$ \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
7497.2.a.bh 7497.a 1.a $4$ $59.864$ \(\Q(\sqrt{2}, \sqrt{39})\) None \(0\) \(0\) \(4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{5}+2\beta _{2}q^{8}-\beta _{2}q^{10}+\cdots\)
7497.2.a.bi 7497.a 1.a $4$ $59.864$ \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
7497.2.a.bj 7497.a 1.a $4$ $59.864$ 4.4.1957.1 None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
7497.2.a.bk 7497.a 1.a $4$ $59.864$ 4.4.1957.1 None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bl 7497.a 1.a $4$ $59.864$ 4.4.9301.1 None \(1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
7497.2.a.bm 7497.a 1.a $4$ $59.864$ 4.4.14013.1 None \(1\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7497.2.a.bn 7497.a 1.a $4$ $59.864$ 4.4.14013.1 None \(1\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
7497.2.a.bo 7497.a 1.a $4$ $59.864$ 4.4.9301.1 None \(3\) \(0\) \(-6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
7497.2.a.bp 7497.a 1.a $4$ $59.864$ 4.4.9301.1 None \(3\) \(0\) \(6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
7497.2.a.bq 7497.a 1.a $5$ $59.864$ 5.5.1224176.1 None \(-2\) \(0\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
7497.2.a.br 7497.a 1.a $5$ $59.864$ 5.5.453749.1 None \(-2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(2-\beta _{3})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bs 7497.a 1.a $5$ $59.864$ 5.5.885424.1 None \(-1\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(2-\beta _{3})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots\)
7497.2.a.bt 7497.a 1.a $5$ $59.864$ 5.5.885424.1 None \(-1\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(2-\beta _{3})q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots\)
7497.2.a.bu 7497.a 1.a $5$ $59.864$ 5.5.1224176.1 None \(2\) \(0\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
7497.2.a.bv 7497.a 1.a $5$ $59.864$ 5.5.1383597.1 None \(2\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bw 7497.a 1.a $5$ $59.864$ 5.5.1383597.1 None \(2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
7497.2.a.bx 7497.a 1.a $6$ $59.864$ 6.6.29722117.1 None \(-2\) \(0\) \(-7\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
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