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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
975.1.e.a 975.e 195.e $2$ $0.487$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) 39.1.d.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-q^{9}-iq^{12}-iq^{13}+\cdots\)
975.1.g.a 975.g 39.d $1$ $0.487$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) 39.1.d.a \(0\) \(1\) \(0\) \(0\) \(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
975.1.g.b 975.g 39.d $2$ $0.487$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-39}) \) None 195.1.e.a \(0\) \(-2\) \(0\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}-\beta q^{11}+\cdots\)
975.1.g.c 975.g 39.d $2$ $0.487$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-39}) \) None 195.1.e.a \(0\) \(2\) \(0\) \(0\) \(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+\beta q^{11}+\cdots\)
975.1.j.a 975.j 195.j $4$ $0.487$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None 975.1.j.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
975.1.u.a 975.u 195.u $4$ $0.487$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None 975.1.j.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}-q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
975.1.x.a 975.x 39.h $2$ $0.487$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 975.1.x.a \(0\) \(-1\) \(0\) \(-3\) \(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(-1-\zeta_{6})q^{7}+\cdots\)
975.1.x.b 975.x 39.h $2$ $0.487$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 975.1.x.a \(0\) \(1\) \(0\) \(3\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
975.1.y.a 975.y 195.x $4$ $0.487$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 975.1.ba.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)
975.1.z.a 975.z 195.y $4$ $0.487$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 975.1.x.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{7}+\cdots\)
975.1.ba.a 975.ba 39.i $2$ $0.487$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 975.1.ba.a \(0\) \(-1\) \(0\) \(1\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
975.1.ba.b 975.ba 39.i $2$ $0.487$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 975.1.ba.a \(0\) \(1\) \(0\) \(-1\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
975.1.bd.a 975.bd 975.ad $4$ $0.487$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None 975.1.bd.a \(-3\) \(-1\) \(1\) \(0\) \(q+(-1+\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
975.1.bd.b 975.bd 975.ad $4$ $0.487$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None 975.1.bd.a \(3\) \(-1\) \(-1\) \(0\) \(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
975.1.bd.c 975.bd 975.ad $8$ $0.487$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-39}) \) None 975.1.bd.c \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.1.bi.a 975.bi 975.ai $16$ $0.487$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-39}) \) None 975.1.bi.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{40}^{9}-\zeta_{40}^{15})q^{2}-\zeta_{40}^{14}q^{3}+\cdots\)
975.1.bk.a 975.bk 195.ac $8$ $0.487$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None 975.1.bk.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{9}-\zeta_{24}^{11}+\cdots)q^{7}+\cdots\)
975.1.bv.a 975.bv 195.an $8$ $0.487$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None 975.1.bk.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{3}-\zeta_{24}^{4}q^{4}+(\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
975.1.cj.a 975.cj 975.bj $16$ $0.487$ \(\Q(\zeta_{60})\) None None 975.1.cj.a \(0\) \(0\) \(0\) \(-8\) \(q+(-\zeta_{60}^{11}+\zeta_{60}^{17})q^{2}+\zeta_{60}^{23}q^{3}+\cdots\)
975.2.a.a 975.a 1.a $1$ $7.785$ \(\Q\) None None 195.2.a.c \(-2\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
975.2.a.b 975.a 1.a $1$ $7.785$ \(\Q\) None None 195.2.a.d \(-2\) \(-1\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
975.2.a.c 975.a 1.a $1$ $7.785$ \(\Q\) None None 195.2.a.b \(-2\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
975.2.a.d 975.a 1.a $1$ $7.785$ \(\Q\) None None 975.2.a.d \(-1\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{7}+3q^{8}+\cdots\)
975.2.a.e 975.a 1.a $1$ $7.785$ \(\Q\) None None 975.2.a.e \(-1\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
975.2.a.f 975.a 1.a $1$ $7.785$ \(\Q\) None None 39.2.a.a \(-1\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots\)
975.2.a.g 975.a 1.a $1$ $7.785$ \(\Q\) None None 195.2.c.a \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}+2q^{12}+\cdots\)
975.2.a.h 975.a 1.a $1$ $7.785$ \(\Q\) None None 195.2.c.a \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}-2q^{12}+\cdots\)
975.2.a.i 975.a 1.a $1$ $7.785$ \(\Q\) None None 195.2.a.a \(1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
975.2.a.j 975.a 1.a $1$ $7.785$ \(\Q\) None None 975.2.a.e \(1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
975.2.a.k 975.a 1.a $1$ $7.785$ \(\Q\) None None 975.2.a.d \(1\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{7}-3q^{8}+\cdots\)
975.2.a.l 975.a 1.a $2$ $7.785$ \(\Q(\sqrt{2}) \) None None 39.2.a.b \(2\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
975.2.a.m 975.a 1.a $3$ $7.785$ 3.3.148.1 None None 975.2.a.m \(-3\) \(-3\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
975.2.a.n 975.a 1.a $3$ $7.785$ 3.3.564.1 None None 975.2.a.n \(-1\) \(-3\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.a.o 975.a 1.a $3$ $7.785$ 3.3.316.1 None None 195.2.a.e \(0\) \(3\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(3+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.a.p 975.a 1.a $3$ $7.785$ 3.3.564.1 None None 975.2.a.n \(1\) \(3\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.a.q 975.a 1.a $3$ $7.785$ 3.3.148.1 None None 975.2.a.m \(3\) \(3\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
975.2.a.r 975.a 1.a $5$ $7.785$ 5.5.1821184.1 None None 195.2.c.b \(0\) \(-5\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.a.s 975.a 1.a $5$ $7.785$ 5.5.1821184.1 None None 195.2.c.b \(0\) \(5\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.b.a 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None None 195.2.h.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-q^{3}-2q^{4}-2iq^{6}-3iq^{7}+\cdots\)
975.2.b.b 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None None 195.2.b.b \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}+q^{4}-iq^{6}-2iq^{7}+\cdots\)
975.2.b.c 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None None 195.2.h.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+q^{3}-2q^{4}+2iq^{6}-3iq^{7}+\cdots\)
975.2.b.d 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-3}) \) None None 39.2.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+q^{3}-q^{4}-\zeta_{6}q^{6}+2\zeta_{6}q^{7}+\cdots\)
975.2.b.e 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None None 195.2.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2q^{4}-iq^{7}+q^{9}-iq^{11}+\cdots\)
975.2.b.f 975.b 13.b $4$ $7.785$ \(\Q(i, \sqrt{17})\) None None 195.2.b.c \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-3+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.b.g 975.b 13.b $4$ $7.785$ 4.0.27648.1 None None 975.2.b.g \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.b.h 975.b 13.b $4$ $7.785$ 4.0.27648.1 None None 975.2.b.g \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.b.i 975.b 13.b $6$ $7.785$ 6.0.559227904.1 None None 975.2.b.i \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.b.j 975.b 13.b $6$ $7.785$ 6.0.50922496.1 None None 195.2.h.c \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{3}+(-1-\beta _{5})q^{4}-\beta _{2}q^{6}+\cdots\)
975.2.b.k 975.b 13.b $6$ $7.785$ 6.0.559227904.1 None None 975.2.b.i \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.b.l 975.b 13.b $6$ $7.785$ 6.0.50922496.1 None None 195.2.h.c \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+q^{3}+(-1-\beta _{5})q^{4}+\beta _{2}q^{6}+\cdots\)
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