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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
363.1.b.a 363.b 3.b $1$ $0.181$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{33}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots\)
363.1.h.a 363.h 33.h $4$ $0.181$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{33}) \) \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{9}-q^{12}+\cdots\)
363.2.a.a 363.a 1.a $1$ $2.899$ \(\Q\) None None \(-2\) \(-1\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
363.2.a.b 363.a 1.a $1$ $2.899$ \(\Q\) None None \(-1\) \(-1\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
363.2.a.c 363.a 1.a $1$ $2.899$ \(\Q\) None None \(2\) \(-1\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots\)
363.2.a.d 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None None \(-3\) \(-2\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1-\beta )q^{5}+\cdots\)
363.2.a.e 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None None \(-1\) \(2\) \(-3\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
363.2.a.f 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-3q^{5}-\beta q^{6}-2\beta q^{7}+\cdots\)
363.2.a.g 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+3q^{4}+2q^{5}-\beta q^{6}+\cdots\)
363.2.a.h 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None None \(1\) \(2\) \(-3\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
363.2.a.i 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None None \(3\) \(-2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(1-\beta )q^{5}+\cdots\)
363.2.a.j 363.a 1.a $4$ $2.899$ \(\Q(\sqrt{3}, \sqrt{11})\) None None \(0\) \(4\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots\)
363.2.d.a 363.d 33.d $2$ $2.899$ \(\Q(\sqrt{-2}) \) None None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
363.2.d.b 363.d 33.d $2$ $2.899$ \(\Q(\sqrt{-2}) \) None None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
363.2.d.c 363.d 33.d $4$ $2.899$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+\cdots\)
363.2.d.d 363.d 33.d $4$ $2.899$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}-2q^{4}-\beta _{2}q^{7}+3q^{9}+2\beta _{1}q^{12}+\cdots\)
363.2.d.e 363.d 33.d $8$ $2.899$ 8.0.3588489216.5 None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(-1-\beta _{7})q^{3}+(2-\beta _{4}-\beta _{7})q^{4}+\cdots\)
363.2.d.f 363.d 33.d $8$ $2.899$ \(\Q(\zeta_{20})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{20}^{6}q^{2}+(1-\zeta_{20}+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots\)
363.2.e.a 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(-5\) \(-1\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.b 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(-4\) \(1\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.c 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(-2\) \(-1\) \(4\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
363.2.e.d 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(-2\) \(1\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.e 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(-1\) \(1\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.f 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(1\) \(1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.g 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(1\) \(1\) \(2\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.h 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(2\) \(-1\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
363.2.e.i 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(2\) \(1\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
363.2.e.j 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(3\) \(-1\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
363.2.e.k 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(4\) \(1\) \(2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.l 363.e 11.c $4$ $2.899$ \(\Q(\zeta_{10})\) None None \(5\) \(-1\) \(-2\) \(10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
363.2.e.m 363.e 11.c $8$ $2.899$ 8.0.324000000.3 None None \(0\) \(2\) \(6\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(3+3\beta _{2}+\cdots)q^{5}+\cdots\)
363.2.e.n 363.e 11.c $16$ $2.899$ 16.0.\(\cdots\).3 None None \(0\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{12}q^{2}+\beta _{4}q^{3}+(\beta _{3}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)
363.2.f.a 363.f 33.f $8$ $2.899$ 8.0.64000000.1 None None \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{6}q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
363.2.f.b 363.f 33.f $8$ $2.899$ \(\Q(\zeta_{20})\) None None \(0\) \(-6\) \(0\) \(10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1-\zeta_{20}+\cdots)q^{3}+\cdots\)
363.2.f.c 363.f 33.f $8$ $2.899$ 8.0.228765625.1 \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q-\beta _{1}q^{3}-2\beta _{7}q^{4}+(-\beta _{4}-2\beta _{5})q^{5}+\cdots\)
363.2.f.d 363.f 33.f $8$ $2.899$ \(\Q(\zeta_{20})\) None None \(0\) \(4\) \(0\) \(10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(1+\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
363.2.f.e 363.f 33.f $8$ $2.899$ \(\Q(\zeta_{20})\) None None \(0\) \(4\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}-\zeta_{20}^{7})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
363.2.f.f 363.f 33.f $8$ $2.899$ 8.0.64000000.1 None None \(2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
363.2.f.g 363.f 33.f $16$ $2.899$ 16.0.\(\cdots\).7 \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+(\beta _{1}+\beta _{5}-\beta _{10}-\beta _{13})q^{3}+2\beta _{4}q^{4}+\cdots\)
363.2.f.h 363.f 33.f $16$ $2.899$ 16.0.\(\cdots\).1 None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{2}-2\beta _{6}-\beta _{8}+\beta _{12}+\beta _{13})q^{2}+\cdots\)
363.2.f.i 363.f 33.f $32$ $2.899$ None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
363.2.i.a 363.i 121.e $110$ $2.899$ None None \(-3\) \(110\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{11}]$
363.2.i.b 363.i 121.e $110$ $2.899$ None None \(-1\) \(-110\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{11}]$
363.2.j.a 363.j 363.j $420$ $2.899$ None None \(0\) \(-22\) \(0\) \(-22\) $\mathrm{SU}(2)[C_{22}]$
363.2.m.a 363.m 121.g $440$ $2.899$ None None \(1\) \(110\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{55}]$
363.2.m.b 363.m 121.g $440$ $2.899$ None None \(3\) \(-110\) \(1\) \(3\) $\mathrm{SU}(2)[C_{55}]$
363.2.p.a 363.p 363.p $1680$ $2.899$ None None \(0\) \(-28\) \(0\) \(-78\) $\mathrm{SU}(2)[C_{110}]$
363.3.b.a 363.b 3.b $1$ $9.891$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-11\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+4q^{4}-11q^{7}+9q^{9}-12q^{12}+\cdots\)
363.3.b.b 363.b 3.b $1$ $9.891$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(11\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+4q^{4}+11q^{7}+9q^{9}-12q^{12}+\cdots\)
363.3.b.c 363.b 3.b $2$ $9.891$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(5\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(3-\beta )q^{3}+4q^{4}+(-3+6\beta )q^{5}+\cdots\)
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