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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.1.e.a 304.e 19.b $1$ $0.152$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
304.2.a.a 304.a 1.a $1$ $2.427$ \(\Q\) None None \(0\) \(-2\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
304.2.a.b 304.a 1.a $1$ $2.427$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
304.2.a.c 304.a 1.a $1$ $2.427$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots\)
304.2.a.d 304.a 1.a $1$ $2.427$ \(\Q\) None None \(0\) \(1\) \(-4\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
304.2.a.e 304.a 1.a $1$ $2.427$ \(\Q\) None None \(0\) \(2\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
304.2.a.f 304.a 1.a $1$ $2.427$ \(\Q\) None None \(0\) \(2\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
304.2.a.g 304.a 1.a $3$ $2.427$ 3.3.961.1 None None \(0\) \(-1\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
304.2.h.a 304.h 76.d $2$ $2.427$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b 304.h 76.d $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c 304.h 76.d $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
304.2.i.a 304.i 19.c $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.b 304.i 19.c $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.c 304.i 19.c $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
304.2.i.d 304.i 19.c $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.e 304.i 19.c $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
304.2.i.f 304.i 19.c $6$ $2.427$ 6.0.2696112.1 None None \(0\) \(1\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
304.2.k.a 304.k 16.e $4$ $2.427$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
304.2.k.b 304.k 16.e $68$ $2.427$ None None \(0\) \(4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
304.2.m.a 304.m 304.m $76$ $2.427$ None None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
304.2.n.a 304.n 76.f $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
304.2.n.b 304.n 76.f $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
304.2.n.c 304.n 76.f $4$ $2.427$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
304.2.n.d 304.n 76.f $6$ $2.427$ 6.0.31726512.1 None None \(0\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
304.2.n.e 304.n 76.f $6$ $2.427$ 6.0.31726512.1 None None \(0\) \(1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
304.2.u.a 304.u 19.e $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(-9\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
304.2.u.b 304.u 19.e $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots\)
304.2.u.c 304.u 19.e $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots\)
304.2.u.d 304.u 19.e $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(6\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots\)
304.2.u.e 304.u 19.e $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
304.2.u.f 304.u 19.e $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
304.2.v.a 304.v 304.v $152$ $2.427$ None None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$
304.2.x.a 304.x 304.x $4$ $2.427$ \(\Q(\zeta_{12})\) None None \(-2\) \(2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.b 304.x 304.x $4$ $2.427$ \(\Q(\zeta_{12})\) None None \(2\) \(4\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.c 304.x 304.x $144$ $2.427$ None None \(-6\) \(-12\) \(2\) \(-8\) $\mathrm{SU}(2)[C_{12}]$
304.2.be.a 304.be 76.k $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.b 304.be 76.k $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
304.2.be.c 304.be 76.k $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$ \(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.d 304.be 76.k $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{18}]$ \(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.bg.a 304.bg 304.ag $456$ $2.427$ None None \(-12\) \(-12\) \(-12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
304.2.bi.a 304.bi 304.ai $456$ $2.427$ None None \(-12\) \(-12\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{36}]$
304.3.d.a 304.d 4.b $6$ $8.283$ 6.0.210056875.1 None None \(0\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)
304.3.d.b 304.d 4.b $12$ $8.283$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots\)
304.3.e.a 304.e 19.b $1$ $8.283$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-9\) \(5\) $\mathrm{U}(1)[D_{2}]$ \(q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots\)
304.3.e.b 304.e 19.b $2$ $8.283$ \(\Q(\sqrt{-29}) \) None None \(0\) \(0\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots\)
304.3.e.c 304.e 19.b $2$ $8.283$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots\)
304.3.e.d 304.e 19.b $2$ $8.283$ \(\Q(\sqrt{-13}) \) None None \(0\) \(0\) \(8\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots\)
304.3.e.e 304.e 19.b $2$ $8.283$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(-5\) $\mathrm{U}(1)[D_{2}]$ \(q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots\)
304.3.e.f 304.e 19.b $2$ $8.283$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(14\) \(-22\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots\)
304.3.e.g 304.e 19.b $8$ $8.283$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(-14\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
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