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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3648.1.b.a 3648.b 228.b $1$ $1.821$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-57}) \) \(\Q(\sqrt{19}) \) 912.1.b.a \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+q^{19}+q^{25}-q^{27}-2q^{31}+\cdots\)
3648.1.b.b 3648.b 228.b $1$ $1.821$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-57}) \) \(\Q(\sqrt{19}) \) 912.1.b.a \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-q^{19}+q^{25}+q^{27}+2q^{31}+\cdots\)
3648.1.l.a 3648.l 456.l $2$ $1.821$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-38}) \) \(\Q(\sqrt{114}) \) 3648.1.l.a \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}-q^{13}+iq^{19}+\cdots\)
3648.1.l.b 3648.l 456.l $2$ $1.821$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-38}) \) \(\Q(\sqrt{114}) \) 3648.1.l.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{9}+q^{13}-iq^{19}+\cdots\)
3648.1.l.c 3648.l 456.l $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-38}) \) None 3648.1.l.c \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}-q^{13}+\cdots\)
3648.1.l.d 3648.l 456.l $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-38}) \) None 3648.1.l.c \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)
3648.1.ba.a 3648.ba 456.s $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3648.1.ba.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)
3648.1.ba.b 3648.ba 456.s $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3648.1.ba.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{2}q^{13}+\cdots\)
3648.1.bf.a 3648.bf 456.x $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None 3648.1.bf.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}-q^{9}+(\zeta_{12}-\zeta_{12}^{5})q^{11}+\cdots\)
3648.1.bf.b 3648.bf 456.x $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3648.1.bf.b \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+(-\zeta_{12}+\zeta_{12}^{5})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
3648.1.bf.c 3648.bf 456.x $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None 3648.1.bf.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{9}+(-\zeta_{12}+\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)
3648.1.bf.d 3648.bf 456.x $4$ $1.821$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3648.1.bf.b \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-\zeta_{12}+\zeta_{12}^{5})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
3648.1.bj.a 3648.bj 228.n $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 912.1.bj.a \(0\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}q^{3}+(-\zeta_{6}-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
3648.1.bj.b 3648.bj 228.n $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 912.1.bj.a \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
3648.1.bl.a 3648.bl 57.h $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(-1\) \(0\) \(2\) \(q+\zeta_{6}^{2}q^{3}+q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots\)
3648.1.bl.b 3648.bl 57.h $2$ $1.821$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(1\) \(0\) \(-2\) \(q-\zeta_{6}^{2}q^{3}-q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots\)
3648.1.cn.a 3648.cn 456.ah $12$ $1.821$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None 3648.1.cn.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{7}q^{3}+(-\zeta_{36}^{13}+\zeta_{36}^{17})q^{7}+\cdots\)
3648.1.cn.b 3648.cn 456.ah $12$ $1.821$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None 3648.1.cn.b \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{3}-\zeta_{36}^{4}q^{9}+(\zeta_{36}-\zeta_{36}^{5}+\cdots)q^{11}+\cdots\)
3648.1.cn.c 3648.cn 456.ah $12$ $1.821$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None 3648.1.cn.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{7}q^{3}+(-\zeta_{36}^{13}+\zeta_{36}^{17})q^{7}+\cdots\)
3648.1.cn.d 3648.cn 456.ah $12$ $1.821$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None 3648.1.cn.b \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{3}q^{3}+\zeta_{36}^{6}q^{9}+(-\zeta_{36}+\zeta_{36}^{5}+\cdots)q^{11}+\cdots\)
3648.1.cr.a 3648.cr 57.l $6$ $1.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None 228.1.s.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{4}q^{3}+(\zeta_{18}-\zeta_{18}^{2})q^{7}+\zeta_{18}^{8}q^{9}+\cdots\)
3648.1.cr.b 3648.cr 57.l $6$ $1.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None 228.1.s.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{3}+(-\zeta_{18}+\zeta_{18}^{2})q^{7}+\zeta_{18}^{8}q^{9}+\cdots\)
3648.1.cu.a 3648.cu 228.u $6$ $1.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None 912.1.ce.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{3}+(\zeta_{18}+\zeta_{18}^{2})q^{7}+\zeta_{18}^{8}q^{9}+\cdots\)
3648.1.cu.b 3648.cu 228.u $6$ $1.821$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None 912.1.ce.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{4}q^{3}+(-\zeta_{18}-\zeta_{18}^{2})q^{7}+\zeta_{18}^{8}q^{9}+\cdots\)
3648.1.cz.a 3648.cz 456.at $12$ $1.821$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None 3648.1.cz.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{3}+(-\zeta_{36}-\zeta_{36}^{5})q^{7}+\cdots\)
3648.1.cz.b 3648.cz 456.at $12$ $1.821$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None 3648.1.cz.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{3}+(\zeta_{36}+\zeta_{36}^{5})q^{7}-\zeta_{36}^{4}q^{9}+\cdots\)
3648.2.a.a 3648.a 1.a $1$ $29.129$ \(\Q\) None None 456.2.a.b \(0\) \(-1\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
3648.2.a.b 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.f \(0\) \(-1\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
3648.2.a.c 3648.a 1.a $1$ $29.129$ \(\Q\) None None 114.2.a.b \(0\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
3648.2.a.d 3648.a 1.a $1$ $29.129$ \(\Q\) None None 456.2.a.d \(0\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
3648.2.a.e 3648.a 1.a $1$ $29.129$ \(\Q\) None None 228.2.a.b \(0\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3648.2.a.f 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.e \(0\) \(-1\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots\)
3648.2.a.g 3648.a 1.a $1$ $29.129$ \(\Q\) None None 456.2.a.a \(0\) \(-1\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
3648.2.a.h 3648.a 1.a $1$ $29.129$ \(\Q\) None None 57.2.a.b \(0\) \(-1\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+6q^{13}+\cdots\)
3648.2.a.i 3648.a 1.a $1$ $29.129$ \(\Q\) None None 114.2.a.c \(0\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
3648.2.a.j 3648.a 1.a $1$ $29.129$ \(\Q\) None None 114.2.a.a \(0\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{17}+\cdots\)
3648.2.a.k 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.d \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-2q^{17}-q^{19}+6q^{23}+\cdots\)
3648.2.a.l 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.c \(0\) \(-1\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+5q^{11}-4q^{13}+\cdots\)
3648.2.a.m 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.b \(0\) \(-1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-q^{15}+\cdots\)
3648.2.a.n 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.a \(0\) \(-1\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
3648.2.a.o 3648.a 1.a $1$ $29.129$ \(\Q\) None None 57.2.a.c \(0\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-6q^{13}-2q^{15}+\cdots\)
3648.2.a.p 3648.a 1.a $1$ $29.129$ \(\Q\) None None 456.2.a.c \(0\) \(-1\) \(3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-3q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
3648.2.a.q 3648.a 1.a $1$ $29.129$ \(\Q\) None None 228.2.a.a \(0\) \(-1\) \(3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-q^{7}+q^{9}-5q^{11}+6q^{13}+\cdots\)
3648.2.a.r 3648.a 1.a $1$ $29.129$ \(\Q\) None None 57.2.a.a \(0\) \(-1\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+5q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
3648.2.a.s 3648.a 1.a $1$ $29.129$ \(\Q\) None None 456.2.a.b \(0\) \(1\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
3648.2.a.t 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.f \(0\) \(1\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
3648.2.a.u 3648.a 1.a $1$ $29.129$ \(\Q\) None None 1824.2.a.e \(0\) \(1\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots\)
3648.2.a.v 3648.a 1.a $1$ $29.129$ \(\Q\) None None 228.2.a.b \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3648.2.a.w 3648.a 1.a $1$ $29.129$ \(\Q\) None None 456.2.a.d \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
3648.2.a.x 3648.a 1.a $1$ $29.129$ \(\Q\) None None 114.2.a.b \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
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