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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
58.2.a.a 58.a 1.a $1$ $0.463$ \(\Q\) None 58.2.a.a \(-1\) \(-3\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}-3q^{5}+3q^{6}-2q^{7}+\cdots\)
58.2.a.b 58.a 1.a $1$ $0.463$ \(\Q\) None 58.2.a.b \(1\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
58.2.b.a 58.b 29.b $2$ $0.463$ \(\Q(\sqrt{-1}) \) None 58.2.b.a \(0\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
58.2.d.a 58.d 29.d $6$ $0.463$ \(\Q(\zeta_{14})\) None 58.2.d.a \(1\) \(3\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{7}]$ \(q-\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+\cdots\)
58.2.d.b 58.d 29.d $12$ $0.463$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 58.2.d.b \(-2\) \(-3\) \(0\) \(1\) $\mathrm{SU}(2)[C_{7}]$ \(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{6}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
58.2.e.a 58.e 29.e $12$ $0.463$ \(\Q(\zeta_{28})\) None 58.2.e.a \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{14}]$ \(q-\zeta_{28}^{9}q^{2}+(-\zeta_{28}-\zeta_{28}^{3}-\zeta_{28}^{5}+\cdots)q^{3}+\cdots\)
58.3.c.a 58.c 29.c $4$ $1.580$ \(\Q(i, \sqrt{6})\) None 58.3.c.a \(4\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots\)
58.3.c.b 58.c 29.c $6$ $1.580$ 6.0.9296045056.1 None 58.3.c.b \(-6\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+\cdots\)
58.3.f.a 58.f 29.f $24$ $1.580$ None 58.3.f.a \(-4\) \(-4\) \(28\) \(34\) $\mathrm{SU}(2)[C_{28}]$
58.3.f.b 58.f 29.f $36$ $1.580$ None 58.3.f.b \(6\) \(4\) \(-28\) \(-34\) $\mathrm{SU}(2)[C_{28}]$
58.4.a.a 58.a 1.a $1$ $3.422$ \(\Q\) None 58.4.a.a \(-2\) \(7\) \(5\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots\)
58.4.a.b 58.a 1.a $1$ $3.422$ \(\Q\) None 58.4.a.b \(2\) \(-7\) \(-15\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-7q^{3}+4q^{4}-15q^{5}-14q^{6}+\cdots\)
58.4.a.c 58.a 1.a $2$ $3.422$ \(\Q(\sqrt{6}) \) None 58.4.a.c \(-4\) \(-2\) \(-10\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-5+\cdots)q^{5}+\cdots\)
58.4.a.d 58.a 1.a $3$ $3.422$ 3.3.19816.1 None 58.4.a.d \(6\) \(2\) \(20\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(6+2\beta _{1}+\cdots)q^{5}+\cdots\)
58.4.b.a 58.b 29.b $8$ $3.422$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 58.4.b.a \(0\) \(0\) \(-22\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{1}q^{3}-4q^{4}+(-3-\beta _{4}+\cdots)q^{5}+\cdots\)
58.4.d.a 58.d 29.d $18$ $3.422$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 58.4.d.a \(6\) \(-5\) \(-16\) \(-59\) $\mathrm{SU}(2)[C_{7}]$ \(q+2\beta _{8}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots\)
58.4.d.b 58.d 29.d $24$ $3.422$ None 58.4.d.b \(-8\) \(5\) \(16\) \(71\) $\mathrm{SU}(2)[C_{7}]$
58.4.e.a 58.e 29.e $48$ $3.422$ None 58.4.e.a \(0\) \(0\) \(22\) \(-12\) $\mathrm{SU}(2)[C_{14}]$
58.5.c.a 58.c 29.c $10$ $5.995$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 58.5.c.a \(-20\) \(16\) \(0\) \(-96\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2\beta _{3})q^{2}+(2-\beta _{1}+2\beta _{3})q^{3}+\cdots\)
58.5.c.b 58.c 29.c $10$ $5.995$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 58.5.c.b \(20\) \(-16\) \(0\) \(96\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2\beta _{5})q^{2}+(-2+\beta _{1}+2\beta _{5})q^{3}+\cdots\)
58.5.f.a 58.f 29.f $60$ $5.995$ None 58.5.f.a \(-20\) \(16\) \(-56\) \(72\) $\mathrm{SU}(2)[C_{28}]$
58.5.f.b 58.f 29.f $60$ $5.995$ None 58.5.f.b \(20\) \(-16\) \(56\) \(-72\) $\mathrm{SU}(2)[C_{28}]$
58.6.a.a 58.a 1.a $2$ $9.302$ \(\Q(\sqrt{22}) \) None 58.6.a.a \(8\) \(-14\) \(-82\) \(-160\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(-7+\beta )q^{3}+2^{4}q^{4}+(-41+\cdots)q^{5}+\cdots\)
58.6.a.b 58.a 1.a $3$ $9.302$ 3.3.431464.1 None 58.6.a.b \(-12\) \(14\) \(68\) \(24\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(4+\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
58.6.a.c 58.a 1.a $4$ $9.302$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 58.6.a.c \(-16\) \(-13\) \(-7\) \(-74\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-3-\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
58.6.a.d 58.a 1.a $4$ $9.302$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 58.6.a.d \(16\) \(13\) \(93\) \(134\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(3+\beta _{1})q^{3}+2^{4}q^{4}+(23-\beta _{2}+\cdots)q^{5}+\cdots\)
58.6.b.a 58.b 29.b $12$ $9.302$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 58.6.b.a \(0\) \(0\) \(-10\) \(76\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(\beta _{6}+\beta _{7})q^{3}-2^{4}q^{4}+(-1+\cdots)q^{5}+\cdots\)
58.6.d.a 58.d 29.d $36$ $9.302$ None 58.6.d.a \(-24\) \(1\) \(-228\) \(-9\) $\mathrm{SU}(2)[C_{7}]$
58.6.d.b 58.d 29.d $42$ $9.302$ None 58.6.d.b \(28\) \(-1\) \(156\) \(85\) $\mathrm{SU}(2)[C_{7}]$
58.6.e.a 58.e 29.e $72$ $9.302$ None 58.6.e.a \(0\) \(0\) \(10\) \(-76\) $\mathrm{SU}(2)[C_{14}]$
58.7.c.a 58.c 29.c $14$ $13.343$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 58.7.c.a \(-56\) \(-28\) \(0\) \(776\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-4-4\beta _{2})q^{2}+(-2-\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
58.7.c.b 58.c 29.c $16$ $13.343$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 58.7.c.b \(64\) \(28\) \(0\) \(-776\) $\mathrm{SU}(2)[C_{4}]$ \(q+(4+4\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
58.7.f.a 58.f 29.f $84$ $13.343$ None 58.7.f.a \(56\) \(28\) \(588\) \(610\) $\mathrm{SU}(2)[C_{28}]$
58.7.f.b 58.f 29.f $96$ $13.343$ None 58.7.f.b \(-64\) \(-28\) \(-588\) \(-610\) $\mathrm{SU}(2)[C_{28}]$
58.8.a.a 58.a 1.a $3$ $18.118$ 3.3.1792765.1 None 58.8.a.a \(-24\) \(13\) \(195\) \(110\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+(4-\beta _{1}-\beta _{2})q^{3}+2^{6}q^{4}+\cdots\)
58.8.a.b 58.a 1.a $3$ $18.118$ 3.3.732765.1 None 58.8.a.b \(24\) \(-25\) \(-305\) \(-1138\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+(-8+\beta _{2})q^{3}+2^{6}q^{4}+(-104+\cdots)q^{5}+\cdots\)
58.8.a.c 58.a 1.a $4$ $18.118$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 58.8.a.c \(-32\) \(-68\) \(-180\) \(-576\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+(-17+\beta _{2})q^{3}+2^{6}q^{4}+(-45+\cdots)q^{5}+\cdots\)
58.8.a.d 58.a 1.a $5$ $18.118$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 58.8.a.d \(40\) \(56\) \(570\) \(920\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+(11+\beta _{1})q^{3}+2^{6}q^{4}+(114+\cdots)q^{5}+\cdots\)
58.8.b.a 58.b 29.b $18$ $18.118$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 58.8.b.a \(0\) \(0\) \(-82\) \(-1348\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{10}q^{2}+(-\beta _{9}+\beta _{10})q^{3}-2^{6}q^{4}+\cdots\)
58.8.d.a 58.d 29.d $48$ $18.118$ None 58.8.d.a \(-64\) \(-31\) \(-356\) \(-3695\) $\mathrm{SU}(2)[C_{7}]$
58.8.d.b 58.d 29.d $54$ $18.118$ None 58.8.d.b \(72\) \(31\) \(496\) \(2347\) $\mathrm{SU}(2)[C_{7}]$
58.8.e.a 58.e 29.e $108$ $18.118$ None 58.8.e.a \(0\) \(0\) \(82\) \(1348\) $\mathrm{SU}(2)[C_{14}]$
58.9.c.a 58.c 29.c $20$ $23.628$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 58.9.c.a \(-160\) \(-32\) \(0\) \(1728\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-8+8\beta _{1})q^{2}+(-2+2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
58.9.c.b 58.c 29.c $20$ $23.628$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 58.9.c.b \(160\) \(32\) \(0\) \(-1728\) $\mathrm{SU}(2)[C_{4}]$ \(q+(8+8\beta _{3})q^{2}+(2-\beta _{2}+2\beta _{3})q^{3}+\cdots\)
58.9.f.a 58.f 29.f $120$ $23.628$ None 58.9.f.a \(-160\) \(-32\) \(2576\) \(-12048\) $\mathrm{SU}(2)[C_{28}]$
58.9.f.b 58.f 29.f $120$ $23.628$ None 58.9.f.b \(160\) \(32\) \(-2576\) \(12048\) $\mathrm{SU}(2)[C_{28}]$
58.10.a.a 58.a 1.a $4$ $29.872$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 58.10.a.a \(64\) \(4\) \(-3012\) \(-12576\) $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+(1+\beta _{2})q^{3}+2^{8}q^{4}+(-753+\cdots)q^{5}+\cdots\)
58.10.a.b 58.a 1.a $5$ $29.872$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 58.10.a.b \(-80\) \(152\) \(738\) \(3848\) $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(30+\beta _{4})q^{3}+2^{8}q^{4}+(147+\cdots)q^{5}+\cdots\)
58.10.a.c 58.a 1.a $6$ $29.872$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 58.10.a.c \(-96\) \(-91\) \(-1137\) \(-954\) $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(-15+\beta _{1})q^{3}+2^{8}q^{4}+\cdots\)
58.10.a.d 58.a 1.a $6$ $29.872$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 58.10.a.d \(96\) \(247\) \(1363\) \(1830\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+(41+\beta _{1})q^{3}+2^{8}q^{4}+(226+\cdots)q^{5}+\cdots\)
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