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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3420.1.h.a 3420.h 95.d $2$ $1.707$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{11}+(\zeta_{6}+\cdots)q^{17}+\cdots\)
3420.1.h.b 3420.h 95.d $4$ $1.707$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{5}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{7}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)
3420.1.u.a 3420.u 285.j $8$ $1.707$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{24}q^{5}+(\zeta_{24}^{8}-\zeta_{24}^{10})q^{7}+(-\zeta_{24}+\cdots)q^{11}+\cdots\)
3420.1.u.b 3420.u 285.j $8$ $1.707$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{24}^{7}q^{5}+(-\zeta_{24}^{8}+\zeta_{24}^{10})q^{7}+\cdots\)
3420.1.bh.a 3420.bh 95.h $2$ $1.707$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{5}-q^{11}-\zeta_{6}q^{19}-\zeta_{6}q^{25}+\cdots\)
3420.1.bn.a 3420.bn 3420.an $16$ $1.707$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{5}q^{2}+\zeta_{48}q^{3}+\zeta_{48}^{10}q^{4}+\cdots\)
3420.1.bn.b 3420.bn 3420.an $16$ $1.707$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{9}q^{2}+\zeta_{48}^{19}q^{3}+\zeta_{48}^{18}q^{4}+\cdots\)
3420.1.df.a 3420.df 380.p $4$ $1.707$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3420.1.df.b 3420.df 380.p $4$ $1.707$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
3420.1.es.a 3420.es 95.m $4$ $1.707$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(-4\) \(q-\zeta_{12}^{2}q^{5}+(-1+\zeta_{12}^{3})q^{7}+q^{11}+\cdots\)
3420.1.es.b 3420.es 95.m $4$ $1.707$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{2}q^{5}-q^{11}+(-\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{13}+\cdots\)
3420.1.es.c 3420.es 95.m $4$ $1.707$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(-4\) \(q+\zeta_{12}^{2}q^{5}+(-1+\zeta_{12}^{3})q^{7}-q^{11}+\cdots\)
3420.1.fk.a 3420.fk 380.aa $12$ $1.707$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{5}q^{2}+\zeta_{36}^{10}q^{4}+\zeta_{36}q^{5}+\cdots\)
3420.1.fk.b 3420.fk 380.aa $12$ $1.707$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{3}q^{2}+\zeta_{36}^{6}q^{4}-\zeta_{36}q^{5}+\zeta_{36}^{9}q^{8}+\cdots\)
3420.2.a.a 3420.a 1.a $1$ $27.309$ \(\Q\) None None \(0\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-2q^{11}+6q^{13}+2q^{17}+\cdots\)
3420.2.a.b 3420.a 1.a $1$ $27.309$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-4q^{11}+2q^{17}+q^{19}+\cdots\)
3420.2.a.c 3420.a 1.a $1$ $27.309$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-4q^{13}+2q^{17}-q^{19}+\cdots\)
3420.2.a.d 3420.a 1.a $1$ $27.309$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+4q^{11}-4q^{13}-6q^{17}+\cdots\)
3420.2.a.e 3420.a 1.a $1$ $27.309$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-4q^{13}-6q^{17}+q^{19}+\cdots\)
3420.2.a.f 3420.a 1.a $1$ $27.309$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+6q^{13}-2q^{17}-q^{19}+\cdots\)
3420.2.a.g 3420.a 1.a $2$ $27.309$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-2+2\beta )q^{7}+2q^{11}+(-2+\cdots)q^{13}+\cdots\)
3420.2.a.h 3420.a 1.a $2$ $27.309$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2\beta q^{11}+(-1+\beta )q^{13}+\cdots\)
3420.2.a.i 3420.a 1.a $2$ $27.309$ \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
3420.2.a.j 3420.a 1.a $3$ $27.309$ 3.3.404.1 None None \(0\) \(0\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta _{2})q^{7}+(1-\beta _{1}+2\beta _{2})q^{11}+\cdots\)
3420.2.a.k 3420.a 1.a $3$ $27.309$ 3.3.1524.1 None None \(0\) \(0\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta _{1}q^{7}+(1+\beta _{2})q^{11}+(2-\beta _{1}+\cdots)q^{13}+\cdots\)
3420.2.a.l 3420.a 1.a $3$ $27.309$ 3.3.564.1 None None \(0\) \(0\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
3420.2.a.m 3420.a 1.a $3$ $27.309$ 3.3.564.1 None None \(0\) \(0\) \(-3\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1-\beta _{2})q^{7}+(-2-\beta _{1}+\beta _{2})q^{11}+\cdots\)
3420.2.a.n 3420.a 1.a $3$ $27.309$ 3.3.404.1 None None \(0\) \(0\) \(3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta _{2})q^{7}+(-1+\beta _{1}-2\beta _{2})q^{11}+\cdots\)
3420.2.a.o 3420.a 1.a $3$ $27.309$ 3.3.564.1 None None \(0\) \(0\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{1})q^{11}+\cdots\)
3420.2.e.a 3420.e 285.b $16$ $27.309$ 16.0.\(\cdots\).1 \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{5}+(-\beta _{11}+\beta _{12})q^{7}+(-\beta _{9}+\cdots)q^{11}+\cdots\)
3420.2.e.b 3420.e 285.b $24$ $27.309$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
3420.2.f.a 3420.f 5.b $4$ $27.309$ \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(3-\beta _{2})q^{11}+\cdots\)
3420.2.f.b 3420.f 5.b $6$ $27.309$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{4})q^{5}-\beta _{5}q^{7}+(1-\beta _{2})q^{11}+\cdots\)
3420.2.f.c 3420.f 5.b $6$ $27.309$ 6.0.14077504.2 None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-3-\beta _{1}+\cdots)q^{11}+\cdots\)
3420.2.f.d 3420.f 5.b $8$ $27.309$ 8.0.796594176.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}-\beta _{5}q^{7}-\beta _{1}q^{11}-\beta _{5}q^{13}+\cdots\)
3420.2.f.e 3420.f 5.b $10$ $27.309$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{5}+\beta _{4}q^{7}+(-1+\beta _{5})q^{11}+\cdots\)
3420.2.f.f 3420.f 5.b $12$ $27.309$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}+\beta _{5}q^{7}+\beta _{3}q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
3420.2.j.a 3420.j 57.d $24$ $27.309$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
3420.2.t.a 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}-5q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots\)
3420.2.t.b 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}-4q^{7}+3q^{11}-6\zeta_{6}q^{13}+\cdots\)
3420.2.t.c 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}-3q^{7}+2q^{11}+\zeta_{6}q^{13}+\cdots\)
3420.2.t.d 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}-2q^{7}-2q^{11}+4\zeta_{6}q^{13}+\cdots\)
3420.2.t.e 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+2q^{7}-3q^{11}+6\zeta_{6}q^{13}+\cdots\)
3420.2.t.f 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+2q^{7}+q^{11}-6\zeta_{6}q^{13}+\cdots\)
3420.2.t.g 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+2q^{7}+6q^{11}+(5+\cdots)q^{17}+\cdots\)
3420.2.t.h 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+2q^{7}+6q^{11}+4\zeta_{6}q^{13}+\cdots\)
3420.2.t.i 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+4q^{7}+2q^{11}-6\zeta_{6}q^{13}+\cdots\)
3420.2.t.j 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{5}-2q^{7}-3q^{11}+(-4+\cdots)q^{17}+\cdots\)
3420.2.t.k 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{5}-2q^{7}+q^{11}-4\zeta_{6}q^{13}+\cdots\)
3420.2.t.l 3420.t 19.c $2$ $27.309$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{5}-2q^{7}+2q^{11}+(1-\zeta_{6})q^{17}+\cdots\)
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