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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
71.1.b.a 71.b 71.b $3$ $0.035$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-71}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
41.2.a.a 41.a 1.a $3$ $0.327$ 3.3.148.1 None None \(-1\) \(0\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
53.2.a.b 53.a 1.a $3$ $0.423$ 3.3.148.1 None None \(-1\) \(3\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
61.2.a.b 61.a 1.a $3$ $0.487$ 3.3.148.1 None None \(1\) \(2\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
71.2.a.a 71.a 1.a $3$ $0.567$ 3.3.257.1 None None \(-1\) \(1\) \(5\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
71.2.a.b 71.a 1.a $3$ $0.567$ 3.3.257.1 None None \(0\) \(-1\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
23.3.b.a 23.b 23.b $3$ $0.627$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
87.2.a.b 87.a 1.a $3$ $0.695$ 3.3.229.1 None None \(2\) \(-3\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}-2\beta _{1}q^{5}+\cdots\)
91.2.a.d 91.a 1.a $3$ $0.727$ 3.3.316.1 None None \(1\) \(-2\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
93.2.a.b 93.a 1.a $3$ $0.743$ 3.3.229.1 None None \(0\) \(3\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
95.2.a.a 95.a 1.a $3$ $0.759$ 3.3.148.1 None None \(1\) \(2\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
97.2.a.a 97.a 1.a $3$ $0.775$ \(\Q(\zeta_{14})^+\) None None \(-4\) \(-4\) \(-3\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots\)
31.3.b.b 31.b 31.b $3$ $0.845$ 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
17.4.a.b 17.a 1.a $3$ $1.003$ 3.3.2636.1 None None \(1\) \(4\) \(-8\) \(22\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
19.4.a.b 19.a 1.a $3$ $1.121$ 3.3.3144.1 None None \(3\) \(1\) \(14\) \(-35\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
59.3.b.a 59.b 59.b $3$ $1.608$ 3.3.1593.1 \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+\cdots\)
11.6.a.b 11.a 1.a $3$ $1.764$ 3.3.54492.1 None None \(0\) \(34\) \(24\) \(84\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots\)
35.4.a.c 35.a 1.a $3$ $2.065$ 3.3.14360.1 None None \(-3\) \(2\) \(15\) \(21\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
13.6.a.b 13.a 1.a $3$ $2.085$ 3.3.168897.1 None None \(7\) \(8\) \(56\) \(-60\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(3-\beta _{1}-\beta _{2})q^{3}+(40+\cdots)q^{4}+\cdots\)
83.3.b.a 83.b 83.b $3$ $2.262$ 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-3\beta _{1}-2\beta _{2})q^{7}+\cdots\)
39.4.a.c 39.a 1.a $3$ $2.301$ 3.3.3144.1 None None \(2\) \(9\) \(4\) \(30\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(3+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
87.3.d.a 87.d 87.d $3$ $2.371$ 3.3.2349.1 \(\Q(\sqrt{-87}) \) None \(0\) \(-9\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-3q^{3}+(4+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
87.3.d.b 87.d 87.d $3$ $2.371$ 3.3.2349.1 \(\Q(\sqrt{-87}) \) None \(0\) \(9\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+3q^{3}+(4+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
23.5.b.a 23.b 23.b $3$ $2.378$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
41.4.a.a 41.a 1.a $3$ $2.419$ 3.3.404.1 None None \(-3\) \(-8\) \(-10\) \(-50\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-3-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
47.4.a.a 47.a 1.a $3$ $2.773$ 3.3.1101.1 None None \(-5\) \(-5\) \(-6\) \(-45\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
51.4.a.e 51.a 1.a $3$ $3.009$ 3.3.5912.1 None None \(5\) \(9\) \(8\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+3q^{3}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
31.5.b.a 31.b 31.b $3$ $3.204$ 3.3.837.1 \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots\)
55.4.a.c 55.a 1.a $3$ $3.245$ 3.3.568.1 None None \(5\) \(-3\) \(-15\) \(-15\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-2-3\beta _{2})q^{3}+\cdots\)
57.4.a.c 57.a 1.a $3$ $3.363$ 3.3.2700.1 None None \(-3\) \(-9\) \(-12\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}-3q^{3}+(3+4\beta _{1}+\beta _{2})q^{4}+\cdots\)
58.4.a.d 58.a 1.a $3$ $3.422$ 3.3.19816.1 None None \(6\) \(2\) \(20\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(6+2\beta _{1}+\cdots)q^{5}+\cdots\)
62.4.a.c 62.a 1.a $3$ $3.658$ 3.3.4364.1 None None \(-6\) \(4\) \(1\) \(17\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+4q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
62.4.a.d 62.a 1.a $3$ $3.658$ 3.3.23964.1 None None \(6\) \(4\) \(17\) \(21\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(6-\beta _{1}+\cdots)q^{5}+\cdots\)
23.6.a.a 23.a 1.a $3$ $3.689$ 3.3.7925.1 None None \(-4\) \(-20\) \(-58\) \(-282\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-7-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
68.4.a.b 68.a 1.a $3$ $4.012$ 3.3.1524.1 None None \(0\) \(4\) \(26\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(9-\beta _{1})q^{5}+(2+3\beta _{1}+\cdots)q^{7}+\cdots\)
74.4.a.c 74.a 1.a $3$ $4.366$ 3.3.15629.1 None None \(-6\) \(4\) \(7\) \(7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+(2+\cdots)q^{5}+\cdots\)
76.4.a.b 76.a 1.a $3$ $4.484$ 3.3.35529.1 None None \(0\) \(1\) \(9\) \(44\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots\)
82.4.a.d 82.a 1.a $3$ $4.838$ 3.3.6452.1 None None \(-6\) \(-4\) \(-2\) \(-26\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1-\beta _{2})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
82.4.a.e 82.a 1.a $3$ $4.838$ 3.3.564.1 None None \(6\) \(-2\) \(18\) \(36\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2+3\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
85.4.a.e 85.a 1.a $3$ $5.015$ 3.3.1304.1 None None \(-6\) \(-4\) \(-15\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
85.4.a.f 85.a 1.a $3$ $5.015$ 3.3.568.1 None None \(3\) \(9\) \(-15\) \(34\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-3\beta _{1})q^{3}+(-1+\cdots)q^{4}+\cdots\)
86.4.a.d 86.a 1.a $3$ $5.074$ 3.3.85685.1 None None \(-6\) \(-9\) \(-5\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
88.4.a.d 88.a 1.a $3$ $5.192$ 3.3.11109.1 None None \(0\) \(2\) \(8\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(3+\beta _{2})q^{5}+(8-\beta _{1}+\cdots)q^{7}+\cdots\)
17.8.a.b 17.a 1.a $3$ $5.311$ 3.3.694349.1 None None \(1\) \(-86\) \(-198\) \(-1558\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-28-\beta _{1}-2\beta _{2})q^{3}+(78+\cdots)q^{4}+\cdots\)
91.4.a.a 91.a 1.a $3$ $5.369$ 3.3.1384.1 None None \(1\) \(1\) \(-22\) \(-21\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
92.4.a.a 92.a 1.a $3$ $5.428$ 3.3.1229.1 None None \(0\) \(-4\) \(-10\) \(-46\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-4-\beta _{1}+3\beta _{2})q^{5}+\cdots\)
92.4.a.b 92.a 1.a $3$ $5.428$ 3.3.28669.1 None None \(0\) \(8\) \(0\) \(42\) $+$ $\mathrm{SU}(2)$ \(q+(3+\beta _{2})q^{3}+\beta _{1}q^{5}+(14-\beta _{1})q^{7}+\cdots\)
34.6.a.d 34.a 1.a $3$ $5.453$ 3.3.1505580.1 None None \(12\) \(4\) \(144\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(1+\beta _{2})q^{3}+2^{4}q^{4}+(7^{2}+\beta _{1}+\cdots)q^{5}+\cdots\)
93.4.a.e 93.a 1.a $3$ $5.487$ 3.3.2089.1 None None \(3\) \(-9\) \(8\) \(19\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}-3q^{3}+(1+3\beta _{1}+2\beta _{2})q^{4}+\cdots\)
95.4.a.e 95.a 1.a $3$ $5.605$ 3.3.1304.1 None None \(-3\) \(-11\) \(15\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{2})q^{3}+\cdots\)
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