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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
59.2.a.a 59.a 1.a $5$ $0.471$ 5.5.138136.1 None \(0\) \(-2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots\)
79.2.a.b 79.a 1.a $5$ $0.631$ 5.5.81589.1 None \(0\) \(1\) \(7\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
89.2.a.c 89.a 1.a $5$ $0.711$ 5.5.535120.1 None \(-1\) \(-3\) \(-1\) \(8\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(3-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
47.3.b.b 47.b 47.b $5$ $1.281$ 5.5.6903125.1 \(\Q(\sqrt{-47}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(4+2\beta _{1}+\cdots)q^{4}+\cdots\)
29.4.a.b 29.a 1.a $5$ $1.711$ 5.5.13458092.1 None \(0\) \(8\) \(10\) \(40\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)
31.4.a.b 31.a 1.a $5$ $1.829$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(3\) \(4\) \(15\) \(9\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
79.3.b.a 79.b 79.b $5$ $2.153$ 5.5.19503125.1 \(\Q(\sqrt{-79}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(4+2\beta _{1}+\beta _{4})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
37.4.a.b 37.a 1.a $5$ $2.183$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(4\) \(13\) \(11\) \(24\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3-\beta _{2})q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\)
65.4.a.e 65.a 1.a $5$ $3.835$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(8\) \(25\) \(38\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+(7-\beta _{2}+\cdots)q^{4}+\cdots\)
77.4.a.e 77.a 1.a $5$ $4.543$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(2\) \(-24\) \(35\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(9+\beta _{1}+\beta _{2})q^{4}+\cdots\)
79.4.a.b 79.a 1.a $5$ $4.661$ 5.5.4787257.1 None \(-3\) \(-8\) \(-41\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{4})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots\)
47.5.b.a 47.b 47.b $5$ $4.858$ 5.5.6903125.1 \(\Q(\sqrt{-47}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2\beta _{1}+\beta _{4})q^{2}+(-2\beta _{2}+5\beta _{3})q^{3}+\cdots\)
31.6.a.a 31.a 1.a $5$ $4.972$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-9\) \(-20\) \(-72\) \(-108\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots\)
85.4.a.g 85.a 1.a $5$ $5.015$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(2\) \(-1\) \(25\) \(10\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(6-2\beta _{1}+\beta _{3})q^{4}+\cdots\)
87.4.a.c 87.a 1.a $5$ $5.133$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(3\) \(-15\) \(-1\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-3q^{3}+(6-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
87.4.a.d 87.a 1.a $5$ $5.133$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(3\) \(15\) \(29\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
91.4.a.c 91.a 1.a $5$ $5.369$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(7\) \(-5\) \(16\) \(-35\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{4})q^{2}+(-1-\beta _{3})q^{3}+(10-\beta _{2}+\cdots)q^{4}+\cdots\)
95.4.a.f 95.a 1.a $5$ $5.605$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-3\) \(-4\) \(25\) \(72\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots\)
11.10.a.b 11.a 1.a $5$ $5.665$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(16\) \(112\) \(1594\) \(8400\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{2}+(22+3\beta _{1}+\beta _{4})q^{3}+\cdots\)
13.10.a.b 13.a 1.a $5$ $6.695$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(15\) \(161\) \(1803\) \(10099\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{2}+(2^{5}+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.8.a.a 23.a 1.a $5$ $7.185$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-16\) \(-68\) \(-56\) \(-1156\) $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+(-14+\beta _{2})q^{3}+(51+\cdots)q^{4}+\cdots\)
79.5.b.a 79.b 79.b $5$ $8.166$ 5.5.19503125.1 \(\Q(\sqrt{-79}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(2^{4}+2\beta _{1}-5\beta _{3})q^{4}+(5\beta _{1}+\cdots)q^{5}+\cdots\)
51.6.a.d 51.a 1.a $5$ $8.180$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(-45\) \(4\) \(-40\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-9q^{3}+(24+\beta _{1}+2\beta _{2}+\beta _{4})q^{4}+\cdots\)
11.12.a.b 11.a 1.a $5$ $8.452$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(32\) \(160\) \(-8398\) \(79040\) $+$ $\mathrm{SU}(2)$ \(q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots\)
17.10.a.a 17.a 1.a $5$ $8.756$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-33\) \(-236\) \(1480\) \(-13202\) $+$ $\mathrm{SU}(2)$ \(q+(-7+\beta _{1})q^{2}+(-48+2\beta _{1}+\beta _{4})q^{3}+\cdots\)
55.6.a.c 55.a 1.a $5$ $8.821$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(9\) \(0\) \(125\) \(70\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(24-3\beta _{1}+\cdots)q^{4}+\cdots\)
13.12.a.a 13.a 1.a $5$ $9.988$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-41\) \(-496\) \(-2542\) \(-36296\) $-$ $\mathrm{SU}(2)$ \(q+(-8-\beta _{1})q^{2}+(-99-2\beta _{1}-\beta _{4})q^{3}+\cdots\)
47.7.b.a 47.b 47.b $5$ $10.813$ 5.5.6903125.1 \(\Q(\sqrt{-47}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-2\beta _{3})q^{2}+(5\beta _{2}-4\beta _{4})q^{3}+(2^{6}+\cdots)q^{4}+\cdots\)
35.8.a.d 35.a 1.a $5$ $10.933$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(11\) \(65\) \(625\) \(1715\) $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{2}+(13-\beta _{2})q^{3}+(111-\beta _{1}+\cdots)q^{4}+\cdots\)
69.6.a.e 69.a 1.a $5$ $11.066$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(8\) \(45\) \(94\) \(272\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{2})q^{2}+9q^{3}+(24-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
11.14.a.a 11.a 1.a $5$ $11.795$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-64\) \(480\) \(-454\) \(-313920\) $+$ $\mathrm{SU}(2)$ \(q+(-13-\beta _{1})q^{2}+(96-2\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
74.6.a.d 74.a 1.a $5$ $11.868$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(19\) \(-67\) \(182\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(4+\beta _{2})q^{3}+2^{4}q^{4}+(-14+\cdots)q^{5}+\cdots\)
74.6.a.e 74.a 1.a $5$ $11.868$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(19\) \(95\) \(170\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+(4-\beta _{1})q^{3}+2^{4}q^{4}+(19+\beta _{2}+\cdots)q^{5}+\cdots\)
39.8.a.d 39.a 1.a $5$ $12.183$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(135\) \(774\) \(1420\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3^{3}q^{3}+(91+\beta _{1}+\beta _{2})q^{4}+\cdots\)
77.6.a.c 77.a 1.a $5$ $12.350$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(17\) \(119\) \(-245\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(3+\beta _{1}-\beta _{4})q^{3}+(23+\cdots)q^{4}+\cdots\)
82.6.a.c 82.a 1.a $5$ $13.151$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(-10\) \(-38\) \(-38\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-2-\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{5}+\cdots\)
85.6.a.a 85.a 1.a $5$ $13.633$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-7\) \(-36\) \(125\) \(-204\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-8+\beta _{1}-\beta _{3})q^{3}+\cdots\)
86.6.a.c 86.a 1.a $5$ $13.793$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(-1\) \(61\) \(122\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+(12-2\beta _{1}+\cdots)q^{5}+\cdots\)
87.6.a.b 87.a 1.a $5$ $13.953$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-9\) \(-45\) \(14\) \(-68\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}-9q^{3}+(11-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
93.6.a.b 93.a 1.a $5$ $14.916$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(9\) \(-45\) \(36\) \(108\) $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}-9q^{3}+(11+\beta _{2}-\beta _{4})q^{4}+\cdots\)
95.6.a.b 95.a 1.a $5$ $15.236$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-7\) \(-16\) \(125\) \(-312\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-4+\beta _{1}+\beta _{4})q^{3}+\cdots\)
11.16.a.a 11.a 1.a $5$ $15.696$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-128\) \(-5424\) \(-458990\) \(-2203600\) $-$ $\mathrm{SU}(2)$ \(q+(-26+\beta _{1})q^{2}+(-1085+\beta _{2})q^{3}+\cdots\)
99.6.a.h 99.a 1.a $5$ $15.878$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-4\) \(0\) \(-100\) \(-18\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(21-3\beta _{1}+\beta _{4})q^{4}+\cdots\)
99.6.a.i 99.a 1.a $5$ $15.878$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(4\) \(0\) \(100\) \(-18\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(21-3\beta _{1}+\beta _{4})q^{4}+\cdots\)
51.8.a.e 51.a 1.a $5$ $15.932$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-15\) \(-135\) \(173\) \(400\) $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}-3^{3}q^{3}+(110-4\beta _{1}+\cdots)q^{4}+\cdots\)
55.8.a.b 55.a 1.a $5$ $17.181$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-3\) \(0\) \(625\) \(-890\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
57.8.a.b 57.a 1.a $5$ $17.806$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(-135\) \(138\) \(670\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3^{3}q^{3}+(111+\beta _{4})q^{4}+(29+\cdots)q^{5}+\cdots\)
35.10.a.d 35.a 1.a $5$ $18.026$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(2\) \(140\) \(-3125\) \(12005\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(28+\beta _{2})q^{3}+(168-4\beta _{1}+\cdots)q^{4}+\cdots\)
58.8.a.d 58.a 1.a $5$ $18.118$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(40\) \(56\) \(570\) \(920\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+(11+\beta _{1})q^{3}+2^{6}q^{4}+(114+\cdots)q^{5}+\cdots\)
79.7.b.a 79.b 79.b $5$ $18.174$ 5.5.19503125.1 \(\Q(\sqrt{-79}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(3\beta _{1}-2\beta _{4})q^{2}+(2^{6}-11\beta _{2}-28\beta _{3}+\cdots)q^{4}+\cdots\)
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