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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1734.2.a.a 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.a \(-1\) \(-1\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
1734.2.a.b 1734.a 1.a $1$ $13.846$ \(\Q\) None 102.2.a.b \(-1\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
1734.2.a.c 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.c \(-1\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
1734.2.a.d 1734.a 1.a $1$ $13.846$ \(\Q\) None 102.2.b.a \(-1\) \(-1\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots\)
1734.2.a.e 1734.a 1.a $1$ $13.846$ \(\Q\) None 102.2.b.a \(-1\) \(1\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1734.2.a.f 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.c \(-1\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1734.2.a.g 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.a \(-1\) \(1\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
1734.2.a.h 1734.a 1.a $1$ $13.846$ \(\Q\) None 102.2.a.a \(-1\) \(1\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+2q^{7}+\cdots\)
1734.2.a.i 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.i \(1\) \(-1\) \(-4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
1734.2.a.j 1734.a 1.a $1$ $13.846$ \(\Q\) None 102.2.a.c \(1\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
1734.2.a.k 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.k \(1\) \(-1\) \(3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+4q^{7}+\cdots\)
1734.2.a.l 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.k \(1\) \(1\) \(-3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
1734.2.a.m 1734.a 1.a $1$ $13.846$ \(\Q\) None 1734.2.a.i \(1\) \(1\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+3q^{7}+\cdots\)
1734.2.a.n 1734.a 1.a $2$ $13.846$ \(\Q(\sqrt{2}) \) None 102.2.f.a \(2\) \(-2\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
1734.2.a.o 1734.a 1.a $2$ $13.846$ \(\Q(\sqrt{2}) \) None 102.2.f.a \(2\) \(2\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
1734.2.a.p 1734.a 1.a $3$ $13.846$ \(\Q(\zeta_{18})^+\) None 1734.2.a.p \(-3\) \(-3\) \(-6\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
1734.2.a.q 1734.a 1.a $3$ $13.846$ \(\Q(\zeta_{18})^+\) None 1734.2.a.p \(-3\) \(3\) \(6\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(2-\beta _{1})q^{5}-q^{6}+\cdots\)
1734.2.a.r 1734.a 1.a $3$ $13.846$ \(\Q(\zeta_{18})^+\) None 1734.2.a.r \(3\) \(-3\) \(-6\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}-q^{6}+\cdots\)
1734.2.a.s 1734.a 1.a $3$ $13.846$ \(\Q(\zeta_{18})^+\) None 1734.2.a.r \(3\) \(3\) \(6\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2-\beta _{1})q^{5}+q^{6}+\cdots\)
1734.2.a.t 1734.a 1.a $4$ $13.846$ \(\Q(\zeta_{16})^+\) None 102.2.h.b \(-4\) \(-4\) \(8\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(2+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1734.2.a.u 1734.a 1.a $4$ $13.846$ \(\Q(\zeta_{16})^+\) None 102.2.h.b \(-4\) \(4\) \(-8\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1734.2.a.v 1734.a 1.a $4$ $13.846$ \(\Q(\zeta_{16})^+\) None 102.2.h.a \(4\) \(-4\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1734.2.a.w 1734.a 1.a $4$ $13.846$ \(\Q(\zeta_{16})^+\) None 102.2.h.a \(4\) \(4\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+q^{6}+\cdots\)
1734.2.b.a 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.i \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+iq^{3}+q^{4}+4iq^{5}-iq^{6}+\cdots\)
1734.2.b.b 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 102.2.a.c \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-iq^{3}+q^{4}+2iq^{5}+iq^{6}+\cdots\)
1734.2.b.c 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.k \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-iq^{3}+q^{4}+3iq^{5}+iq^{6}+\cdots\)
1734.2.b.d 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 102.2.a.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+4iq^{5}+iq^{6}+\cdots\)
1734.2.b.e 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.c \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+iq^{6}+iq^{7}+q^{8}+\cdots\)
1734.2.b.f 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 102.2.a.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-iq^{3}+q^{4}-iq^{6}+2iq^{7}+\cdots\)
1734.2.b.g 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots\)
1734.2.b.h 1734.b 17.b $4$ $13.846$ \(\Q(\zeta_{8})\) None 102.2.f.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\zeta_{8}q^{3}+q^{4}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
1734.2.b.i 1734.b 17.b $6$ $13.846$ 6.0.419904.1 None 1734.2.a.r \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots\)
1734.2.b.j 1734.b 17.b $6$ $13.846$ 6.0.419904.1 None 1734.2.a.p \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots\)
1734.2.b.k 1734.b 17.b $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.a \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\zeta_{16}q^{3}+q^{4}+(\zeta_{16}^{2}+\zeta_{16}^{3}+\cdots)q^{5}+\cdots\)
1734.2.b.l 1734.b 17.b $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.b \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\zeta_{16}q^{3}+q^{4}+(2\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{5}+\cdots\)
1734.2.f.a 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 1734.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots\)
1734.2.f.b 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 102.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\zeta_{8}q^{6}+\cdots\)
1734.2.f.c 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 1734.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+3\zeta_{8}q^{5}+\cdots\)
1734.2.f.d 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 1734.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}-\zeta_{8}q^{6}+\cdots\)
1734.2.f.e 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 102.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+2\zeta_{8}q^{5}+\cdots\)
1734.2.f.f 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 1734.2.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+4\zeta_{8}q^{5}+\cdots\)
1734.2.f.g 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 102.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+4\zeta_{8}q^{5}+\cdots\)
1734.2.f.h 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 102.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+2\zeta_{8}q^{5}+\cdots\)
1734.2.f.i 1734.f 17.c $4$ $13.846$ \(\Q(\zeta_{8})\) None 102.2.f.a \(0\) \(0\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1734.2.f.j 1734.f 17.c $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.a \(0\) \(0\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{5}q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
1734.2.f.k 1734.f 17.c $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.b \(0\) \(0\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}q^{3}-q^{4}+(-1+2\zeta_{16}+\cdots)q^{5}+\cdots\)
1734.2.f.l 1734.f 17.c $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.b \(0\) \(0\) \(8\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}q^{3}-q^{4}+(1+2\zeta_{16}+\cdots)q^{5}+\cdots\)
1734.2.f.m 1734.f 17.c $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.a \(0\) \(0\) \(8\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{16}^{3}q^{2}-\zeta_{16}q^{3}-q^{4}+(1+\zeta_{16}^{3}+\cdots)q^{5}+\cdots\)
1734.2.f.n 1734.f 17.c $12$ $13.846$ 12.0.\(\cdots\).1 None 1734.2.a.p \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{7}q^{2}-\beta _{10}q^{3}-q^{4}+(2\beta _{10}-\beta _{11})q^{5}+\cdots\)
1734.2.f.o 1734.f 17.c $12$ $13.846$ 12.0.\(\cdots\).1 None 1734.2.a.r \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}-\beta _{10}q^{3}-q^{4}+(2\beta _{10}-\beta _{11})q^{5}+\cdots\)
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