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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4001.2.a.a 4001.a 1.a $149$ $31.948$ None \(-6\) \(-28\) \(-19\) \(-47\) $+$ $\mathrm{SU}(2)$
4001.2.a.b 4001.a 1.a $184$ $31.948$ None \(3\) \(28\) \(15\) \(49\) $-$ $\mathrm{SU}(2)$
4002.2.a.a 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
4002.2.a.b 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots\)
4002.2.a.c 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(-1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
4002.2.a.d 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
4002.2.a.e 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.f 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.g 4002.a 1.a $1$ $31.956$ \(\Q\) None \(-1\) \(1\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4002.2.a.h 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
4002.2.a.i 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots\)
4002.2.a.j 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
4002.2.a.k 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
4002.2.a.l 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(-1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
4002.2.a.m 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(-3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.n 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
4002.2.a.o 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
4002.2.a.p 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4002.2.a.q 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
4002.2.a.r 4002.a 1.a $1$ $31.956$ \(\Q\) None \(1\) \(1\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
4002.2.a.s 4002.a 1.a $2$ $31.956$ \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
4002.2.a.t 4002.a 1.a $2$ $31.956$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+\beta q^{7}+\cdots\)
4002.2.a.u 4002.a 1.a $2$ $31.956$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots\)
4002.2.a.v 4002.a 1.a $2$ $31.956$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4002.2.a.w 4002.a 1.a $2$ $31.956$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(6\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots\)
4002.2.a.x 4002.a 1.a $2$ $31.956$ \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(8\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+(2-\beta )q^{7}+\cdots\)
4002.2.a.y 4002.a 1.a $3$ $31.956$ 3.3.1772.1 None \(-3\) \(-3\) \(-1\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots\)
4002.2.a.z 4002.a 1.a $3$ $31.956$ 3.3.316.1 None \(3\) \(-3\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.ba 4002.a 1.a $4$ $31.956$ 4.4.16448.2 None \(-4\) \(-4\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)
4002.2.a.bb 4002.a 1.a $4$ $31.956$ 4.4.23252.1 None \(-4\) \(4\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots\)
4002.2.a.bc 4002.a 1.a $4$ $31.956$ 4.4.11324.1 None \(4\) \(4\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
4002.2.a.bd 4002.a 1.a $4$ $31.956$ 4.4.19796.1 None \(4\) \(4\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4002.2.a.be 4002.a 1.a $5$ $31.956$ 5.5.2389280.1 None \(-5\) \(-5\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bf 4002.a 1.a $6$ $31.956$ 6.6.61157024.1 None \(-6\) \(6\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots\)
4002.2.a.bg 4002.a 1.a $7$ $31.956$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-7\) \(2\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bh 4002.a 1.a $7$ $31.956$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}-\beta _{6}q^{7}+\cdots\)
4002.2.a.bi 4002.a 1.a $8$ $31.956$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(-3\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bj 4002.a 1.a $8$ $31.956$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots\)
4002.2.a.bk 4002.a 1.a $8$ $31.956$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-8\) \(2\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
4003.2.a.a 4003.a 1.a $2$ $31.964$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+\beta q^{5}+2q^{6}-q^{7}+\cdots\)
4003.2.a.b 4003.a 1.a $152$ $31.964$ None \(-22\) \(-18\) \(-59\) \(-19\) $+$ $\mathrm{SU}(2)$
4003.2.a.c 4003.a 1.a $179$ $31.964$ None \(22\) \(16\) \(61\) \(21\) $-$ $\mathrm{SU}(2)$
4004.2.a.a 4004.a 1.a $1$ $31.972$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots\)
4004.2.a.b 4004.a 1.a $1$ $31.972$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
4004.2.a.c 4004.a 1.a $1$ $31.972$ \(\Q\) None \(0\) \(2\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
4004.2.a.d 4004.a 1.a $4$ $31.972$ 4.4.3981.1 None \(0\) \(-3\) \(-1\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
4004.2.a.e 4004.a 1.a $4$ $31.972$ \(\Q(\zeta_{15})^+\) None \(0\) \(1\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
4004.2.a.f 4004.a 1.a $5$ $31.972$ 5.5.463341.1 None \(0\) \(3\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
4004.2.a.g 4004.a 1.a $6$ $31.972$ 6.6.246302029.1 None \(0\) \(-2\) \(-3\) \(6\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
4004.2.a.h 4004.a 1.a $9$ $31.972$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(0\) \(9\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
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