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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1075.1.c.a 1075.c 43.b $1$ $0.536$ \(\Q\) \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-q^{11}-q^{13}+q^{16}+2q^{17}+\cdots\)
1075.1.c.b 1075.c 43.b $1$ $0.536$ \(\Q\) \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-q^{11}+q^{13}+q^{16}-2q^{17}+\cdots\)
1075.1.c.c 1075.c 43.b $6$ $0.536$ 6.0.153664.1 \(\Q(\sqrt{-215}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1075.1.d.a 1075.d 215.d $2$ $0.536$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-43}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-q^{9}-q^{11}-iq^{13}+q^{16}+\cdots\)
1075.2.a.a 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(-2\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{3}+2q^{4}-4q^{6}-2q^{7}+\cdots\)
1075.2.a.b 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(-1\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-2q^{6}+4q^{7}+3q^{8}+\cdots\)
1075.2.a.c 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(0\) \(-2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+4q^{7}+q^{9}+q^{11}+\cdots\)
1075.2.a.d 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+2q^{7}-3q^{9}-q^{11}+q^{13}+\cdots\)
1075.2.a.e 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(0\) \(2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-4q^{7}+q^{9}+q^{11}+\cdots\)
1075.2.a.f 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(1\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}-2q^{6}-4q^{7}-3q^{8}+\cdots\)
1075.2.a.g 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(2\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}-4q^{6}+2q^{7}+\cdots\)
1075.2.a.h 1075.a 1.a $1$ $8.584$ \(\Q\) None None \(2\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}+4q^{6}+q^{9}+\cdots\)
1075.2.a.i 1075.a 1.a $2$ $8.584$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}-2q^{6}+(2+\beta )q^{7}-2\beta q^{8}+\cdots\)
1075.2.a.j 1075.a 1.a $3$ $8.584$ 3.3.169.1 None None \(-1\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1075.2.a.k 1075.a 1.a $3$ $8.584$ 3.3.169.1 None None \(1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2-2\beta _{1}+\cdots)q^{4}+\cdots\)
1075.2.a.l 1075.a 1.a $3$ $8.584$ 3.3.321.1 None None \(2\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1075.2.a.m 1075.a 1.a $5$ $8.584$ 5.5.1933097.1 None None \(-2\) \(1\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1075.2.a.n 1075.a 1.a $5$ $8.584$ 5.5.24217.1 None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
1075.2.a.o 1075.a 1.a $5$ $8.584$ 5.5.24217.1 None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
1075.2.a.p 1075.a 1.a $6$ $8.584$ 6.6.32503921.1 None None \(-3\) \(-4\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots\)
1075.2.a.q 1075.a 1.a $6$ $8.584$ 6.6.282109865.1 None None \(-1\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(2+\beta _{4}+\cdots)q^{6}+\cdots\)
1075.2.a.r 1075.a 1.a $6$ $8.584$ 6.6.282109865.1 None None \(1\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(2+\beta _{4}+\cdots)q^{6}+\cdots\)
1075.2.a.s 1075.a 1.a $7$ $8.584$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-4\) \(-5\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
1075.2.a.t 1075.a 1.a $7$ $8.584$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(4\) \(5\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)
1075.2.b.a 1075.b 5.b $2$ $8.584$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+2iq^{3}-2q^{4}-4q^{6}+2iq^{7}+\cdots\)
1075.2.b.b 1075.b 5.b $2$ $8.584$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2iq^{3}-2q^{4}+4q^{6}-q^{9}+\cdots\)
1075.2.b.c 1075.b 5.b $2$ $8.584$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-4iq^{7}+\cdots\)
1075.2.b.d 1075.b 5.b $2$ $8.584$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+2q^{4}+4iq^{7}-q^{9}+q^{11}+\cdots\)
1075.2.b.e 1075.b 5.b $2$ $8.584$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+2iq^{7}+3q^{9}-q^{11}-iq^{13}+\cdots\)
1075.2.b.f 1075.b 5.b $4$ $8.584$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{2}q^{3}-2q^{6}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1075.2.b.g 1075.b 5.b $6$ $8.584$ 6.0.6594624.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
1075.2.b.h 1075.b 5.b $10$ $8.584$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
1075.2.b.i 1075.b 5.b $10$ $8.584$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{3})q^{2}-\beta _{4}q^{3}+(\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots\)
1075.2.b.j 1075.b 5.b $12$ $8.584$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-2+\beta _{2})q^{4}+(2+\cdots)q^{6}+\cdots\)
1075.2.b.k 1075.b 5.b $12$ $8.584$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{7})q^{2}+(-\beta _{7}-\beta _{10})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1075.4.a.a 1075.a 1.a $4$ $63.427$ 4.4.45868.1 None None \(4\) \(11\) \(0\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{2}+(3-\beta _{2}+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
1075.4.a.b 1075.a 1.a $6$ $63.427$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(-6\) \(-7\) \(0\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
1075.4.a.c 1075.a 1.a $6$ $63.427$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(5\) \(5\) \(0\) \(34\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{5})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
1075.4.a.d 1075.a 1.a $8$ $63.427$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(7\) \(0\) \(36\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
1075.4.a.e 1075.a 1.a $13$ $63.427$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(-5\) \(-5\) \(0\) \(-34\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(5+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
1075.4.a.f 1075.a 1.a $15$ $63.427$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(-1\) \(-7\) \(0\) \(-36\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(6+\beta _{2})q^{4}+(3+\beta _{5}+\cdots)q^{6}+\cdots\)
1075.4.a.g 1075.a 1.a $19$ $63.427$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
1075.4.a.h 1075.a 1.a $19$ $63.427$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
1075.4.a.i 1075.a 1.a $23$ $63.427$ None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$
1075.4.a.j 1075.a 1.a $23$ $63.427$ None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$
1075.4.a.k 1075.a 1.a $32$ $63.427$ None None \(-10\) \(-18\) \(0\) \(-28\) $-$ $\mathrm{SU}(2)$
1075.4.a.l 1075.a 1.a $32$ $63.427$ None None \(10\) \(18\) \(0\) \(28\) $+$ $\mathrm{SU}(2)$
1075.6.a.a 1075.a 1.a $8$ $172.413$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(12\) \(26\) \(0\) \(136\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(2+\beta _{1}-\beta _{4}+\beta _{7})q^{3}+\cdots\)
1075.6.a.b 1075.a 1.a $10$ $172.413$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-8\) \(-28\) \(0\) \(-60\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-3-\beta _{6})q^{3}+(21+\cdots)q^{4}+\cdots\)
1075.6.a.c 1075.a 1.a $13$ $172.413$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(7\) \(16\) \(0\) \(372\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\)
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