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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
950.2.a.a 950.a 1.a $1$ $7.586$ \(\Q\) None 190.2.a.c \(-1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
950.2.a.b 950.a 1.a $1$ $7.586$ \(\Q\) None 38.2.a.b \(-1\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
950.2.a.c 950.a 1.a $1$ $7.586$ \(\Q\) None 190.2.a.b \(-1\) \(3\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+5q^{7}-q^{8}+\cdots\)
950.2.a.d 950.a 1.a $1$ $7.586$ \(\Q\) None 38.2.a.a \(1\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
950.2.a.e 950.a 1.a $1$ $7.586$ \(\Q\) None 190.2.a.a \(1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
950.2.a.f 950.a 1.a $2$ $7.586$ \(\Q(\sqrt{2}) \) None 190.2.b.a \(-2\) \(2\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
950.2.a.g 950.a 1.a $2$ $7.586$ \(\Q(\sqrt{2}) \) None 190.2.b.a \(2\) \(-2\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
950.2.a.h 950.a 1.a $2$ $7.586$ \(\Q(\sqrt{17}) \) None 190.2.a.d \(2\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}+q^{8}+\cdots\)
950.2.a.i 950.a 1.a $3$ $7.586$ 3.3.568.1 None 190.2.b.b \(-3\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.j 950.a 1.a $3$ $7.586$ 3.3.993.1 None 950.2.a.j \(-3\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.k 950.a 1.a $3$ $7.586$ 3.3.257.1 None 950.2.a.k \(-3\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(1+\cdots)q^{6}+\cdots\)
950.2.a.l 950.a 1.a $3$ $7.586$ 3.3.993.1 None 950.2.a.j \(3\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
950.2.a.m 950.a 1.a $3$ $7.586$ 3.3.257.1 None 950.2.a.k \(3\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.a.n 950.a 1.a $3$ $7.586$ 3.3.568.1 None 190.2.b.b \(3\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
950.2.b.a 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None 190.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-5iq^{7}+\cdots\)
950.2.b.b 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None 38.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
950.2.b.c 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None 38.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
950.2.b.d 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None 190.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
950.2.b.e 950.b 5.b $2$ $7.586$ \(\Q(\sqrt{-1}) \) None 190.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
950.2.b.f 950.b 5.b $4$ $7.586$ \(\Q(i, \sqrt{17})\) None 190.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
950.2.b.g 950.b 5.b $6$ $7.586$ 6.0.4227136.2 None 950.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4})q^{3}-q^{4}+\cdots\)
950.2.b.h 950.b 5.b $6$ $7.586$ 6.0.63107136.1 None 950.2.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.a 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 190.2.e.b \(-1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.b 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.b \(-1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.c 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.c \(-1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{7}+q^{8}+\cdots\)
950.2.e.d 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 38.2.c.a \(-1\) \(1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.e 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.c \(1\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}-q^{8}+\cdots\)
950.2.e.f 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 190.2.e.a \(1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{7}-q^{8}+3\zeta_{6}q^{9}+\cdots\)
950.2.e.g 950.e 19.c $2$ $7.586$ \(\Q(\sqrt{-3}) \) None 950.2.e.b \(1\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.h 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 190.2.e.c \(-2\) \(-1\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.i 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 950.2.e.i \(-2\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.j 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 950.2.e.i \(2\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.k 950.e 19.c $4$ $7.586$ \(\Q(\sqrt{-3}, \sqrt{7})\) None 38.2.c.b \(2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.l 950.e 19.c $8$ $7.586$ 8.0.\(\cdots\).1 None 950.2.e.l \(-4\) \(1\) \(0\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.m 950.e 19.c $8$ $7.586$ 8.0.\(\cdots\).1 None 950.2.e.l \(4\) \(-1\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.n 950.e 19.c $10$ $7.586$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 190.2.i.a \(-5\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.o 950.e 19.c $10$ $7.586$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 190.2.i.a \(5\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.f.a 950.f 95.g $4$ $7.586$ \(\Q(\zeta_{8})\) None 190.2.f.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{7}+\cdots\)
950.2.f.b 950.f 95.g $8$ $7.586$ 8.0.3317760000.4 None 950.2.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+q^{6}+\beta _{3}q^{7}+\cdots\)
950.2.f.c 950.f 95.g $16$ $7.586$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 190.2.f.b \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{9}q^{2}+\beta _{13}q^{3}+\beta _{1}q^{4}+\beta _{2}q^{6}+\cdots\)
950.2.f.d 950.f 95.g $32$ $7.586$ None 950.2.f.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
950.2.h.a 950.h 25.d $4$ $7.586$ \(\Q(\zeta_{10})\) None 950.2.h.a \(1\) \(4\) \(5\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots\)
950.2.h.b 950.h 25.d $40$ $7.586$ None 950.2.h.b \(-10\) \(5\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{5}]$
950.2.h.c 950.h 25.d $44$ $7.586$ None 950.2.h.c \(-11\) \(1\) \(-1\) \(18\) $\mathrm{SU}(2)[C_{5}]$
950.2.h.d 950.h 25.d $44$ $7.586$ None 950.2.h.d \(11\) \(-1\) \(-11\) \(-10\) $\mathrm{SU}(2)[C_{5}]$
950.2.h.e 950.h 25.d $44$ $7.586$ None 950.2.h.e \(11\) \(-1\) \(-5\) \(28\) $\mathrm{SU}(2)[C_{5}]$
950.2.j.a 950.j 95.i $4$ $7.586$ \(\Q(\zeta_{12})\) None 190.2.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.b 950.j 95.i $4$ $7.586$ \(\Q(\zeta_{12})\) None 950.2.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.c 950.j 95.i $4$ $7.586$ \(\Q(\zeta_{12})\) None 950.2.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+4\zeta_{12}^{3}q^{7}+\cdots\)
950.2.j.d 950.j 95.i $4$ $7.586$ \(\Q(\zeta_{12})\) None 190.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
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