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Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
41.2.c.a 41.c 41.c $6$ $0.327$ 6.0.5089536.1 None \(0\) \(-4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
16.3.f.a 16.f 16.f $6$ $0.436$ 6.0.399424.1 None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
146.2.d.b 146.d 73.d $6$ $1.166$ 6.0.18524416.1 None \(-6\) \(0\) \(-8\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
146.2.d.c 146.d 73.d $6$ $1.166$ 6.0.5089536.1 None \(6\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(\beta _{4}-\beta _{5})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
164.2.f.a 164.f 41.c $6$ $1.310$ 6.0.5089536.1 None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
13.5.d.a 13.d 13.d $6$ $1.344$ 6.0.\(\cdots\).1 None \(-2\) \(-4\) \(-14\) \(48\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
52.3.g.a 52.g 13.d $6$ $1.417$ 6.0.\(\cdots\).3 None \(0\) \(0\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
178.2.c.d 178.c 89.c $6$ $1.421$ 6.0.8248384.1 None \(-6\) \(-4\) \(0\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+(-1+\beta _{2}+\beta _{5})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots\)
185.2.f.c 185.f 185.f $6$ $1.477$ 6.0.350464.1 None \(0\) \(-2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.k.c 185.k 185.k $6$ $1.477$ 6.0.350464.1 None \(-2\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
58.3.c.b 58.c 29.c $6$ $1.580$ 6.0.9296045056.1 None \(-6\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+\cdots\)
64.3.f.a 64.f 16.f $6$ $1.744$ 6.0.399424.1 None \(0\) \(2\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{5})q^{5}+\cdots\)
226.2.c.d 226.c 113.c $6$ $1.805$ 6.0.153664.1 None \(6\) \(2\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{4}-\beta _{5})q^{5}+\cdots\)
240.2.y.d 240.y 80.s $6$ $1.916$ 6.0.399424.1 None \(0\) \(6\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+q^{3}+(-\beta _{1}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
240.2.bc.d 240.bc 80.j $6$ $1.916$ 6.0.399424.1 None \(-2\) \(0\) \(12\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
34.4.c.b 34.c 17.c $6$ $2.006$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(4\) \(-12\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}-4q^{4}+\cdots\)
5.9.c.a 5.c 5.c $6$ $2.037$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-2\) \(-72\) \(220\) \(-2352\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\)
26.5.d.a 26.d 13.d $6$ $2.688$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(-12\) \(0\) \(18\) \(-42\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+\cdots\)
26.5.d.b 26.d 13.d $6$ $2.688$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(12\) \(0\) \(-30\) \(-90\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2\beta _{2})q^{2}-\beta _{3}q^{3}+8\beta _{2}q^{4}+(-5+\cdots)q^{5}+\cdots\)
104.3.l.b 104.l 13.d $6$ $2.834$ 6.0.891380736.2 None \(0\) \(-4\) \(-14\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
104.3.l.c 104.l 13.d $6$ $2.834$ 6.0.195552256.1 None \(0\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}-\beta _{4}q^{5}+(2+\beta _{1}-2\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
369.2.f.c 369.f 41.c $6$ $2.946$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{1}+\beta _{3})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\)
128.3.f.a 128.f 16.f $6$ $3.488$ 6.0.399424.1 None \(0\) \(-2\) \(2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
128.3.f.b 128.f 16.f $6$ $3.488$ 6.0.399424.1 None \(0\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
438.2.f.i 438.f 73.d $6$ $3.497$ 6.0.399424.1 None \(-6\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
144.3.m.a 144.m 16.f $6$ $3.924$ 6.0.399424.1 None \(2\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(-1-\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
68.4.e.b 68.e 17.c $6$ $4.012$ 6.0.27793984.1 None \(0\) \(6\) \(0\) \(44\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{2}+\beta _{3}-3\beta _{5})q^{5}+\cdots\)
514.2.c.c 514.c 257.c $6$ $4.104$ 6.0.433305856.1 None \(6\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
40.5.l.c 40.l 5.c $6$ $4.135$ 6.0.313431616.3 None \(0\) \(-8\) \(-4\) \(-40\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{3}+(-1+7\beta _{1}+\cdots)q^{5}+\cdots\)
544.2.o.g 544.o 17.c $6$ $4.344$ 6.0.419904.1 None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}+(1+\beta _{2})q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
544.2.o.h 544.o 17.c $6$ $4.344$ 6.0.419904.1 None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{3}+(1+\beta _{1})q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
545.2.f.b 545.f 545.f $6$ $4.352$ 6.0.350464.1 None \(0\) \(2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
545.2.k.b 545.k 545.k $6$ $4.352$ 6.0.350464.1 None \(-2\) \(2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
160.3.p.e 160.p 5.c $6$ $4.360$ 6.0.3534400.1 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 \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(2+2\beta _{3}+\cdots)q^{7}+\cdots\)
20.7.f.a 20.f 5.c $6$ $4.601$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(32\) \(-156\) \(-264\) $\mathrm{SU}(2)[C_{4}]$ \(q+(5+5\beta _{1}+\beta _{4})q^{3}+(-5^{2}+20\beta _{1}+\cdots)q^{5}+\cdots\)
582.2.f.j 582.f 97.d $6$ $4.647$ 6.0.81577024.1 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
646.2.g.l 646.g 17.c $6$ $5.158$ 6.0.350464.1 None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+\beta _{5}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
656.2.l.f 656.l 41.c $6$ $5.238$ 6.0.5089536.1 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
656.2.l.g 656.l 41.c $6$ $5.238$ 6.0.5089536.1 None \(0\) \(4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3}-\beta _{4})q^{3}+(-\beta _{4}-\beta _{5})q^{5}+\cdots\)
34.6.c.a 34.c 17.c $6$ $5.453$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(12\) \(-26\) \(140\) $\mathrm{SU}(2)[C_{4}]$ \(q-4\beta _{1}q^{2}+(2-2\beta _{1}-\beta _{2})q^{3}-2^{4}q^{4}+\cdots\)
208.3.t.d 208.t 13.d $6$ $5.668$ 6.0.\(\cdots\).3 None \(0\) \(0\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
208.3.t.e 208.t 13.d $6$ $5.668$ 6.0.195552256.1 None \(0\) \(0\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}-\beta _{4}q^{5}+(-2-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
208.3.t.f 208.t 13.d $6$ $5.668$ 6.0.891380736.2 None \(0\) \(4\) \(-14\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}-\beta _{2})q^{3}+(-2-\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
720.2.z.e 720.z 80.s $6$ $5.749$ 6.0.399424.1 None \(0\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(-1+2\beta _{3}+\cdots)q^{5}+\cdots\)
720.2.bd.e 720.bd 80.j $6$ $5.749$ 6.0.399424.1 None \(2\) \(0\) \(-12\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{5})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
740.2.l.a 740.l 185.f $6$ $5.909$ 6.0.79423744.1 None \(0\) \(2\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-1-2\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
740.2.o.a 740.o 185.k $6$ $5.909$ 6.0.79423744.1 None \(0\) \(-2\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(2+\beta _{4})q^{5}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
26.7.d.a 26.d 13.d $6$ $5.981$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(24\) \(0\) \(-150\) \(150\) $\mathrm{SU}(2)[C_{4}]$ \(q+(4+4\beta _{2})q^{2}+\beta _{3}q^{3}+2^{5}\beta _{2}q^{4}+\cdots\)
785.2.f.d 785.f 785.f $6$ $6.268$ 6.0.3356224.1 None \(0\) \(0\) \(12\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{4})q^{4}+(2-\beta _{3}+\cdots)q^{5}+\cdots\)
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