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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3192.1.m.a 3192.m 3192.m $1$ $1.593$ \(\Q\) \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(-1\) \(-1\) \(0\) \(-1\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
3192.1.m.b 3192.m 3192.m $1$ $1.593$ \(\Q\) \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3192.1.m.c 3192.m 3192.m $1$ $1.593$ \(\Q\) \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
3192.1.m.d 3192.m 3192.m $1$ $1.593$ \(\Q\) \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(1\) \(1\) \(0\) \(-1\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
3192.1.m.e 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{114}) \) 3192.1.m.e \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-iq^{3}+q^{4}-iq^{5}+iq^{6}+q^{7}+\cdots\)
3192.1.m.f 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-38}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{42}) \) 3192.1.m.f \(0\) \(0\) \(0\) \(2\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+q^{7}+iq^{8}+\cdots\)
3192.1.m.g 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-38}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{42}) \) 3192.1.m.f \(0\) \(0\) \(0\) \(2\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+q^{7}-iq^{8}+\cdots\)
3192.1.m.h 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{114}) \) 3192.1.m.e \(2\) \(0\) \(0\) \(2\) \(q+q^{2}-iq^{3}+q^{4}+iq^{5}-iq^{6}+q^{7}+\cdots\)
3192.1.m.i 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-38}) \) None 3192.1.m.i \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{4}q^{6}+\cdots\)
3192.1.m.j 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-38}) \) None 3192.1.m.i \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
3192.1.m.k 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-399}) \) None 3192.1.m.k \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
3192.1.m.l 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-399}) \) None 3192.1.m.k \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{8}^{3}q^{2}+\zeta_{8}^{2}q^{3}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
3192.1.bu.a 3192.bu 399.n $4$ $1.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None 3192.1.bu.a \(0\) \(2\) \(0\) \(2\) \(q+(1-\beta _{2})q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-\beta _{2}q^{9}+\cdots\)
3192.1.eb.a 3192.eb 3192.db $12$ $1.593$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-38}) \) None 3192.1.eb.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{15}q^{2}-\zeta_{36}q^{3}-\zeta_{36}^{12}q^{4}+\cdots\)
3192.1.eb.b 3192.eb 3192.db $12$ $1.593$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-38}) \) None 3192.1.eb.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{3}q^{2}-\zeta_{36}q^{3}+\zeta_{36}^{6}q^{4}+\zeta_{36}^{4}q^{6}+\cdots\)
3192.1.ev.a 3192.ev 399.ai $4$ $1.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None 3192.1.bu.a \(0\) \(-4\) \(0\) \(2\) \(q-q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots\)
3192.1.fm.a 3192.fm 3192.em $2$ $1.593$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None 3192.1.fm.a \(-1\) \(-1\) \(3\) \(-2\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(1-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
3192.1.fm.b 3192.fm 3192.em $2$ $1.593$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None 3192.1.fm.a \(-1\) \(1\) \(-3\) \(-2\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(-1+\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
3192.1.fm.c 3192.fm 3192.em $2$ $1.593$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None 3192.1.fm.a \(1\) \(-1\) \(3\) \(-2\) \(q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(1-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
3192.1.fm.d 3192.fm 3192.em $2$ $1.593$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None 3192.1.fm.a \(1\) \(1\) \(-3\) \(-2\) \(q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(-1+\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
3192.1.fm.e 3192.fm 3192.em $4$ $1.593$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None 3192.1.fm.e \(-2\) \(0\) \(0\) \(4\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+\cdots\)
3192.1.fm.f 3192.fm 3192.em $4$ $1.593$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None 3192.1.fm.e \(2\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}+\cdots\)
3192.1.hj.a 3192.hj 3192.gj $6$ $1.593$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None 3192.1.hj.a \(0\) \(0\) \(-3\) \(3\) \(q-\zeta_{18}^{7}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
3192.1.hj.b 3192.hj 3192.gj $6$ $1.593$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None 3192.1.hj.a \(0\) \(0\) \(-3\) \(3\) \(q+\zeta_{18}^{7}q^{2}-\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
3192.1.hj.c 3192.hj 3192.gj $6$ $1.593$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None 3192.1.hj.a \(0\) \(0\) \(3\) \(3\) \(q-\zeta_{18}^{7}q^{2}-\zeta_{18}^{4}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
3192.1.hj.d 3192.hj 3192.gj $6$ $1.593$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-14}) \) None 3192.1.hj.a \(0\) \(0\) \(3\) \(3\) \(q+\zeta_{18}^{7}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
3192.1.hj.e 3192.hj 3192.gj $12$ $1.593$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-14}) \) None 3192.1.hj.e \(0\) \(0\) \(0\) \(-6\) \(q-\zeta_{36}^{14}q^{2}+\zeta_{36}^{5}q^{3}-\zeta_{36}^{10}q^{4}+\cdots\)
3192.1.hj.f 3192.hj 3192.gj $12$ $1.593$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-14}) \) None 3192.1.hj.e \(0\) \(0\) \(0\) \(-6\) \(q+\zeta_{36}^{14}q^{2}-\zeta_{36}^{17}q^{3}-\zeta_{36}^{10}q^{4}+\cdots\)
3192.2.a.a 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.a \(0\) \(-1\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}-q^{7}+q^{9}-2q^{13}+4q^{15}+\cdots\)
3192.2.a.b 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.b \(0\) \(-1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3192.2.a.c 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.c \(0\) \(-1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
3192.2.a.d 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.d \(0\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
3192.2.a.e 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.e \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-2q^{13}+q^{19}+q^{21}+\cdots\)
3192.2.a.f 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.f \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3192.2.a.g 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.g \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
3192.2.a.h 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.h \(0\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
3192.2.a.i 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.i \(0\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
3192.2.a.j 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.j \(0\) \(-1\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
3192.2.a.k 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.k \(0\) \(1\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3192.2.a.l 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.l \(0\) \(1\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
3192.2.a.m 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.m \(0\) \(1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3192.2.a.n 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.n \(0\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
3192.2.a.o 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.o \(0\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-2q^{13}-8q^{17}+\cdots\)
3192.2.a.p 3192.a 1.a $1$ $25.488$ \(\Q\) None None 3192.2.a.p \(0\) \(1\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
3192.2.a.q 3192.a 1.a $2$ $25.488$ \(\Q(\sqrt{3}) \) None None 3192.2.a.q \(0\) \(-2\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
3192.2.a.r 3192.a 1.a $2$ $25.488$ \(\Q(\sqrt{2}) \) None None 3192.2.a.r \(0\) \(2\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2+\beta )q^{5}-q^{7}+q^{9}+2\beta q^{11}+\cdots\)
3192.2.a.s 3192.a 1.a $2$ $25.488$ \(\Q(\sqrt{3}) \) None None 3192.2.a.s \(0\) \(2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}-4q^{11}+\cdots\)
3192.2.a.t 3192.a 1.a $2$ $25.488$ \(\Q(\sqrt{3}) \) None None 3192.2.a.t \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{13}+\beta q^{15}+\cdots\)
3192.2.a.u 3192.a 1.a $3$ $25.488$ 3.3.568.1 None None 3192.2.a.u \(0\) \(-3\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
3192.2.a.v 3192.a 1.a $3$ $25.488$ 3.3.316.1 None None 3192.2.a.v \(0\) \(3\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+(-1+\beta _{1})q^{11}+\cdots\)
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