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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1775.1.c.a 1775.c 355.c $6$ $0.886$ 6.0.153664.1 \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1775.1.d.a 1775.d 71.b $1$ $0.886$ \(\Q\) \(\Q(\sqrt{-71}) \), \(\Q(\sqrt{-355}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-q^{9}+q^{16}+2q^{19}+2q^{29}+\cdots\)
1775.1.d.b 1775.d 71.b $3$ $0.886$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-71}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1775.1.d.c 1775.d 71.b $6$ $0.886$ \(\Q(\zeta_{28})^+\) \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(1-2\beta _{2}+\cdots)q^{6}+\cdots\)
1775.1.p.a 1775.p 1775.p $4$ $0.886$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-71}) \) None \(3\) \(-2\) \(-1\) \(0\) \(q+(1-\zeta_{10}^{3})q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\cdots\)
1775.1.p.b 1775.p 1775.p $24$ $0.886$ \(\Q(\zeta_{35})\) \(\Q(\sqrt{-71}) \) None \(-3\) \(2\) \(1\) \(0\) \(q+(-\zeta_{70}+\zeta_{70}^{20})q^{2}+(\zeta_{70}^{18}+\zeta_{70}^{24}+\cdots)q^{3}+\cdots\)
1775.1.bb.a 1775.bb 1775.ab $4$ $0.886$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-71}) \) None \(5\) \(0\) \(1\) \(0\) \(q+(1-\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{2})q^{3}+\cdots\)
1775.1.bb.b 1775.bb 1775.ab $24$ $0.886$ \(\Q(\zeta_{35})\) \(\Q(\sqrt{-71}) \) None \(-5\) \(0\) \(-1\) \(0\) \(q+(\zeta_{70}^{17}-\zeta_{70}^{25})q^{2}+(-\zeta_{70}^{23}+\cdots)q^{3}+\cdots\)
1775.2.a.a 1775.a 1.a $1$ $14.173$ \(\Q\) None None \(-2\) \(0\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{7}-3q^{9}+2q^{11}+\cdots\)
1775.2.a.b 1775.a 1.a $1$ $14.173$ \(\Q\) None None \(0\) \(2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}+q^{7}+q^{9}-4q^{12}+\cdots\)
1775.2.a.c 1775.a 1.a $1$ $14.173$ \(\Q\) None None \(2\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{7}-3q^{9}+2q^{11}+\cdots\)
1775.2.a.d 1775.a 1.a $3$ $14.173$ 3.3.169.1 None None \(-1\) \(-2\) \(0\) \(-9\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1775.2.a.e 1775.a 1.a $3$ $14.173$ 3.3.257.1 None None \(0\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
1775.2.a.f 1775.a 1.a $3$ $14.173$ 3.3.257.1 None None \(1\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-3+\cdots)q^{6}+\cdots\)
1775.2.a.g 1775.a 1.a $3$ $14.173$ 3.3.169.1 None None \(1\) \(2\) \(0\) \(9\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
1775.2.a.h 1775.a 1.a $4$ $14.173$ 4.4.725.1 None None \(2\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1775.2.a.i 1775.a 1.a $4$ $14.173$ 4.4.1957.1 None None \(4\) \(3\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
1775.2.a.j 1775.a 1.a $6$ $14.173$ 6.6.62581037.1 None None \(-3\) \(-3\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
1775.2.a.k 1775.a 1.a $8$ $14.173$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-4\) \(1\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{4})q^{2}+\beta _{6}q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
1775.2.a.l 1775.a 1.a $8$ $14.173$ 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{3}+(-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
1775.2.a.m 1775.a 1.a $9$ $14.173$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(-2\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1775.2.a.n 1775.a 1.a $9$ $14.173$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(2\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1775.2.a.o 1775.a 1.a $12$ $14.173$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-1\) \(-4\) \(0\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
1775.2.a.p 1775.a 1.a $12$ $14.173$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(1\) \(4\) \(0\) \(14\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
1775.2.a.q 1775.a 1.a $24$ $14.173$ None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$
1775.4.a.a 1775.a 1.a $1$ $104.728$ \(\Q\) None None \(-1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-7q^{4}+q^{6}+q^{7}+15q^{8}+\cdots\)
1775.4.a.b 1775.a 1.a $4$ $104.728$ 4.4.135041.1 None None \(3\) \(6\) \(0\) \(35\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
1775.4.a.c 1775.a 1.a $12$ $104.728$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(-7\) \(0\) \(-48\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{1}+\beta _{7}+\cdots)q^{4}+\cdots\)
1775.4.a.d 1775.a 1.a $15$ $104.728$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(3\) \(4\) \(0\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(3+\beta _{2})q^{4}+(-2+\cdots)q^{6}+\cdots\)
1775.4.a.e 1775.a 1.a $16$ $104.728$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(11\) \(10\) \(0\) \(86\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{6})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
1775.4.a.f 1775.a 1.a $19$ $104.728$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None None \(-9\) \(4\) \(0\) \(18\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(5+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{6}+\cdots\)
1775.4.a.g 1775.a 1.a $20$ $104.728$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-9\) \(-14\) \(0\) \(-40\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{5})q^{3}+(5+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1775.4.a.h 1775.a 1.a $35$ $104.728$ None None \(-6\) \(-19\) \(0\) \(-76\) $-$ $\mathrm{SU}(2)$
1775.4.a.i 1775.a 1.a $35$ $104.728$ None None \(-2\) \(-5\) \(0\) \(-92\) $-$ $\mathrm{SU}(2)$
1775.4.a.j 1775.a 1.a $35$ $104.728$ None None \(2\) \(5\) \(0\) \(92\) $+$ $\mathrm{SU}(2)$
1775.4.a.k 1775.a 1.a $35$ $104.728$ None None \(6\) \(19\) \(0\) \(76\) $+$ $\mathrm{SU}(2)$
1775.4.a.l 1775.a 1.a $46$ $104.728$ None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$
1775.4.a.m 1775.a 1.a $60$ $104.728$ None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$
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