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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
361.2.a.a 361.a 1.a $1$ $2.883$ \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-1\) \(3\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-q^{5}+3q^{7}-3q^{9}-5q^{11}+\cdots\)
361.2.a.b 361.a 1.a $1$ $2.883$ \(\Q\) None \(0\) \(2\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
361.2.a.c 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
361.2.a.d 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None \(0\) \(-4\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}-2q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
361.2.a.e 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None \(0\) \(4\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+2q^{3}+3q^{4}+\beta q^{5}+\cdots\)
361.2.a.f 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None \(1\) \(3\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+2\beta q^{5}+\cdots\)
361.2.a.g 361.a 1.a $3$ $2.883$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
361.2.a.h 361.a 1.a $3$ $2.883$ \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
361.2.a.i 361.a 1.a $4$ $2.883$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(-4\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
361.2.c.a 361.c 19.c $2$ $2.883$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
361.2.c.b 361.c 19.c $2$ $2.883$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(1\) \(6\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+3q^{7}+3\zeta_{6}q^{9}+\cdots\)
361.2.c.c 361.c 19.c $2$ $2.883$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
361.2.c.d 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(-3\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-2+\beta _{1}-2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
361.2.c.e 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(-4\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{3})q^{3}+\cdots\)
361.2.c.f 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(4\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\beta _{1}+\beta _{3})q^{2}+(2+2\beta _{3})q^{3}+\cdots\)
361.2.c.g 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(1\) \(3\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(2-\beta _{1}+2\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
361.2.c.h 361.c 19.c $6$ $2.883$ \(\Q(\zeta_{18})\) None \(-3\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-1+\zeta_{18}+\cdots)q^{3}+\cdots\)
361.2.c.i 361.c 19.c $6$ $2.883$ \(\Q(\zeta_{18})\) None \(3\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
361.2.c.j 361.c 19.c $8$ $2.883$ 8.0.324000000.2 None \(0\) \(0\) \(4\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}-\beta _{3}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
361.2.e.a 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) None \(-3\) \(-6\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+\cdots\)
361.2.e.b 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) None \(-3\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
361.2.e.c 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(-9\) $\mathrm{U}(1)[D_{9}]$ \(q+2\zeta_{18}^{5}q^{4}-\zeta_{18}^{4}q^{5}+(-3+3\zeta_{18}^{3}+\cdots)q^{7}+\cdots\)
361.2.e.d 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+2\zeta_{18}q^{3}+2\zeta_{18}^{5}q^{4}+3\zeta_{18}^{4}q^{5}+\cdots\)
361.2.e.e 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q-2\zeta_{18}q^{3}+2\zeta_{18}^{5}q^{4}+3\zeta_{18}^{4}q^{5}+\cdots\)
361.2.e.f 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) None \(3\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
361.2.e.g 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) None \(3\) \(6\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
361.2.e.h 361.e 19.e $6$ $2.883$ \(\Q(\zeta_{18})\) None \(6\) \(3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots\)
361.2.e.i 361.e 19.e $12$ $2.883$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{7}q^{2}+(-\beta _{1}-2\beta _{3})q^{3}+(\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots\)
361.2.e.j 361.e 19.e $12$ $2.883$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{7}-2\beta _{9})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
361.2.e.k 361.e 19.e $12$ $2.883$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{5}-2\beta _{10}+\beta _{11})q^{2}+2\beta _{5}q^{3}+\cdots\)
361.2.e.l 361.e 19.e $12$ $2.883$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{5}-2\beta _{10}+\beta _{11})q^{2}-2\beta _{5}q^{3}+\cdots\)
361.2.e.m 361.e 19.e $24$ $2.883$ None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{9}]$
361.2.g.a 361.g 361.g $540$ $2.883$ None \(-16\) \(-32\) \(-17\) \(-11\) $\mathrm{SU}(2)[C_{19}]$
361.2.i.a 361.i 361.i $1080$ $2.883$ None \(-38\) \(-19\) \(-37\) \(-40\) $\mathrm{SU}(2)[C_{57}]$
361.2.k.a 361.k 361.k $3348$ $2.883$ None \(-108\) \(-111\) \(-108\) \(-111\) $\mathrm{SU}(2)[C_{171}]$
361.3.b.a 361.b 19.b $6$ $9.837$ 6.0.42172928.2 None \(0\) \(0\) \(-14\) \(22\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{4}q^{3}+(-2-\beta _{3}+\cdots)q^{4}+\cdots\)
361.3.b.b 361.b 19.b $6$ $9.837$ 6.0.6967728.1 None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{5})q^{3}+(-1+2\beta _{1}+\cdots)q^{4}+\cdots\)
361.3.b.c 361.b 19.b $12$ $9.837$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(6\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{6}-\beta _{8})q^{3}+(\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
361.3.b.d 361.b 19.b $24$ $9.837$ None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{2}]$
361.3.d.a 361.d 19.d $2$ $9.837$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(9\) \(-10\) $\mathrm{U}(1)[D_{6}]$ \(q-4\zeta_{6}q^{4}+(9-9\zeta_{6})q^{5}-5q^{7}-9\zeta_{6}q^{9}+\cdots\)
361.3.d.b 361.d 19.d $4$ $9.837$ \(\Q(\sqrt{-3}, \sqrt{-13})\) None \(0\) \(0\) \(-8\) \(-20\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+9\beta _{2}q^{4}+(-4+4\beta _{2}+\cdots)q^{5}+\cdots\)
361.3.d.c 361.d 19.d $6$ $9.837$ 6.0.6967728.1 None \(3\) \(9\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{5})q^{2}+(-\beta _{1}-2\beta _{2}-\beta _{3}-\beta _{5})q^{3}+\cdots\)
361.3.d.d 361.d 19.d $12$ $9.837$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-9\) \(-3\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{4}+\beta _{5}+\beta _{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
361.3.d.e 361.d 19.d $12$ $9.837$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(14\) \(44\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{4}+\beta _{6})q^{2}+(\beta _{9}+\beta _{11})q^{3}+(2+\cdots)q^{4}+\cdots\)
361.3.d.f 361.d 19.d $12$ $9.837$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(9\) \(-3\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{4}+\beta _{6}+\beta _{8})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
361.3.d.g 361.d 19.d $48$ $9.837$ None \(0\) \(0\) \(-4\) \(16\) $\mathrm{SU}(2)[C_{6}]$
361.3.f.a 361.f 19.f $6$ $9.837$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(15\) $\mathrm{U}(1)[D_{18}]$ \(q-4\zeta_{18}q^{4}+(9\zeta_{18}^{2}-9\zeta_{18}^{5})q^{5}+\cdots\)
361.3.f.b 361.f 19.f $12$ $9.837$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-3\) \(-9\) \(3\) \(6\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)
361.3.f.c 361.f 19.f $12$ $9.837$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-3\) \(9\) \(3\) \(6\) $\mathrm{SU}(2)[C_{18}]$ \(q+(1+\beta _{3}-\beta _{9}+\beta _{11})q^{2}+(1+\beta _{1}+\cdots)q^{3}+\cdots\)
361.3.f.d 361.f 19.f $12$ $9.837$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(30\) $\mathrm{SU}(2)[C_{18}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{7})q^{3}+9\beta _{2}q^{4}+(-4\beta _{4}+\cdots)q^{5}+\cdots\)
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