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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.1.p.a 160.p 5.c $2$ $0.080$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\)
160.2.a.a 160.a 1.a $1$ $1.278$ \(\Q\) None None \(0\) \(-2\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
160.2.a.b 160.a 1.a $1$ $1.278$ \(\Q\) None None \(0\) \(2\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
160.2.a.c 160.a 1.a $2$ $1.278$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)
160.2.c.a 160.c 5.b $2$ $1.278$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1+i)q^{5}+3q^{9}+2iq^{13}-4iq^{17}+\cdots\)
160.2.c.b 160.c 5.b $4$ $1.278$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\)
160.2.d.a 160.d 8.b $4$ $1.278$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(1+\zeta_{12}^{3})q^{7}+\cdots\)
160.2.f.a 160.f 40.f $4$ $1.278$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
160.2.n.a 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{3}+(-2+i)q^{5}+(-2+\cdots)q^{7}+\cdots\)
160.2.n.b 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(1-2i)q^{5}+(-1+i)q^{7}+\cdots\)
160.2.n.c 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(1+2i)q^{5}+(3-3i)q^{7}+\cdots\)
160.2.n.d 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1+2i)q^{5}+(-3+3i)q^{7}+\cdots\)
160.2.n.e 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1-2i)q^{5}+(1-i)q^{7}+\cdots\)
160.2.n.f 160.n 20.e $2$ $1.278$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{3}+(-2+i)q^{5}+(2-2i)q^{7}+\cdots\)
160.2.o.a 160.o 40.k $8$ $1.278$ \(\Q(\zeta_{20})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{20}^{3}q^{3}+\zeta_{20}^{5}q^{5}-\zeta_{20}^{6}q^{7}+\cdots\)
160.2.u.a 160.u 160.u $88$ $1.278$ None None \(-4\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$
160.2.x.a 160.x 32.g $64$ $1.278$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
160.2.z.a 160.z 160.z $88$ $1.278$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$
160.2.ba.a 160.ba 160.aa $88$ $1.278$ None None \(-4\) \(-4\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{8}]$
160.3.b.a 160.b 4.b $4$ $4.360$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+4\beta _{2})q^{7}+\cdots\)
160.3.b.b 160.b 4.b $4$ $4.360$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots\)
160.3.e.a 160.e 40.e $1$ $4.360$ \(\Q\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(-5\) \(6\) $\mathrm{U}(1)[D_{2}]$ \(q-5q^{5}+6q^{7}+9q^{9}+18q^{11}+6q^{13}+\cdots\)
160.3.e.b 160.e 40.e $1$ $4.360$ \(\Q\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(5\) \(-6\) $\mathrm{U}(1)[D_{2}]$ \(q+5q^{5}-6q^{7}+9q^{9}+18q^{11}-6q^{13}+\cdots\)
160.3.e.c 160.e 40.e $8$ $4.360$ 8.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
160.3.g.a 160.g 8.d $8$ $4.360$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(3+\beta _{3}+\cdots)q^{9}+\cdots\)
160.3.h.a 160.h 20.d $6$ $4.360$ 6.0.1827904.1 None None \(0\) \(-4\) \(-2\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{3}-\beta _{4}q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.h.b 160.h 20.d $6$ $4.360$ 6.0.1827904.1 None None \(0\) \(4\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{4})q^{5}+\cdots\)
160.3.m.a 160.m 40.i $20$ $4.360$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{8}q^{3}+\beta _{9}q^{5}-\beta _{4}q^{7}+(2\beta _{2}-\beta _{13}+\cdots)q^{9}+\cdots\)
160.3.p.a 160.p 5.c $2$ $4.360$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-4+3i)q^{5}+9iq^{9}+(-17+17i)q^{13}+\cdots\)
160.3.p.b 160.p 5.c $2$ $4.360$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(8\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(4+3i)q^{5}+9iq^{9}+(7-7i)q^{13}+\cdots\)
160.3.p.c 160.p 5.c $4$ $4.360$ \(\Q(i, \sqrt{15})\) None None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}-5q^{5}+\beta _{3}q^{7}+21\beta _{1}q^{9}+\cdots\)
160.3.p.d 160.p 5.c $4$ $4.360$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(3+4\beta _{1})q^{5}-3\beta _{3}q^{7}+5\beta _{1}q^{9}+\cdots\)
160.3.p.e 160.p 5.c $6$ $4.360$ 6.0.3534400.1 None None \(0\) \(0\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.p.f 160.p 5.c $6$ $4.360$ 6.0.3534400.1 None None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots\)
160.3.v.a 160.v 160.v $184$ $4.360$ None None \(-4\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$
160.3.w.a 160.w 32.h $128$ $4.360$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
160.3.y.a 160.y 160.y $184$ $4.360$ None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$
160.3.bb.a 160.bb 160.ab $184$ $4.360$ None None \(-4\) \(-4\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{8}]$
160.4.a.a 160.a 1.a $1$ $9.440$ \(\Q\) None None \(0\) \(-2\) \(-5\) \(6\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-5q^{5}+6q^{7}-23q^{9}+60q^{11}+\cdots\)
160.4.a.b 160.a 1.a $1$ $9.440$ \(\Q\) None None \(0\) \(2\) \(-5\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-5q^{5}-6q^{7}-23q^{9}-60q^{11}+\cdots\)
160.4.a.c 160.a 1.a $2$ $9.440$ \(\Q(\sqrt{6}) \) None None \(0\) \(-8\) \(10\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(-4+\beta )q^{3}+5q^{5}+(-4-5\beta )q^{7}+\cdots\)
160.4.a.d 160.a 1.a $2$ $9.440$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-10\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-5q^{5}+7\beta q^{7}-7q^{9}+2\beta q^{11}+\cdots\)
160.4.a.e 160.a 1.a $2$ $9.440$ \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(-10\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-5q^{5}-\beta q^{7}+5^{2}q^{9}-6\beta q^{11}+\cdots\)
160.4.a.f 160.a 1.a $2$ $9.440$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(10\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+5q^{5}+3\beta q^{7}+13q^{9}-2\beta q^{11}+\cdots\)
160.4.a.g 160.a 1.a $2$ $9.440$ \(\Q(\sqrt{6}) \) None None \(0\) \(8\) \(10\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(4+\beta )q^{3}+5q^{5}+(4-5\beta )q^{7}+(13+\cdots)q^{9}+\cdots\)
160.4.c.a 160.c 5.b $2$ $9.440$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-22\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-11+i)q^{5}+3^{3}q^{9}-46iq^{13}+\cdots\)
160.4.c.b 160.c 5.b $4$ $9.440$ \(\Q(i, \sqrt{29})\) None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-3+\beta _{1})q^{5}+\beta _{2}q^{7}+11q^{9}+\cdots\)
160.4.c.c 160.c 5.b $4$ $9.440$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+2\beta _{3})q^{3}-5\beta _{2}q^{5}+(-6\beta _{1}+\cdots)q^{7}+\cdots\)
160.4.c.d 160.c 5.b $8$ $9.440$ 8.0.\(\cdots\).22 None None \(0\) \(0\) \(32\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(4-\beta _{4})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
160.4.d.a 160.d 8.b $12$ $9.440$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+(-9+\cdots)q^{9}+\cdots\)
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