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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.1.c.a \(1\) \(0.038\) \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
76.2.a.a \(1\) \(0.607\) \(\Q\) None None \(0\) \(2\) \(-1\) \(-3\) \(-\) \(q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
76.2.d.a \(8\) \(0.607\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
76.2.e.a \(2\) \(0.607\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(0\) \(q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
76.2.f.a \(16\) \(0.607\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(0\) \(-2\) \(0\) \(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)
76.2.i.a \(12\) \(0.607\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-3\) \(0\) \(3\) \(q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots\)
76.2.k.a \(48\) \(0.607\) None None \(-6\) \(0\) \(-12\) \(0\)
76.3.b.a \(4\) \(2.071\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(-4\) \(0\) \(-4\) \(0\) \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
76.3.b.b \(14\) \(2.071\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots\)
76.3.c.a \(2\) \(2.071\) \(\Q(\sqrt{-29}) \) None None \(0\) \(0\) \(-8\) \(-2\) \(q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots\)
76.3.c.b \(2\) \(2.071\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(5\) \(q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots\)
76.3.g.a \(4\) \(2.071\) \(\Q(\sqrt{-3}, \sqrt{-10})\) None None \(-4\) \(6\) \(-4\) \(0\) \(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
76.3.g.b \(4\) \(2.071\) \(\Q(\sqrt{-3}, \sqrt{-10})\) None None \(8\) \(-6\) \(-4\) \(0\) \(q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
76.3.g.c \(28\) \(2.071\) None None \(-5\) \(0\) \(6\) \(0\)
76.3.h.a \(8\) \(2.071\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(6\) \(-1\) \(-12\) \(q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
76.3.j.a \(18\) \(2.071\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(-6\) \(0\) \(9\) \(q+(-\beta _{4}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{12})q^{3}+\cdots\)
76.3.l.a \(108\) \(2.071\) None None \(-6\) \(0\) \(-12\) \(0\)
76.4.a.a \(2\) \(4.484\) \(\Q(\sqrt{33}) \) None None \(0\) \(-5\) \(-5\) \(-30\) \(-\) \(q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
76.4.a.b \(3\) \(4.484\) 3.3.35529.1 None None \(0\) \(1\) \(9\) \(44\) \(+\) \(q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots\)
76.4.d.a \(28\) \(4.484\) None None \(0\) \(0\) \(-4\) \(0\)
76.4.e.a \(10\) \(4.484\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(7\) \(-4\) \(-20\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.4.f.a \(56\) \(4.484\) None None \(-3\) \(0\) \(-2\) \(0\)
76.4.i.a \(30\) \(4.484\) None None \(0\) \(-3\) \(0\) \(6\)
76.4.k.a \(168\) \(4.484\) None None \(-6\) \(0\) \(-12\) \(0\)
76.5.b.a \(36\) \(7.856\) None None \(6\) \(0\) \(24\) \(0\)
76.5.c.a \(2\) \(7.856\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-31\) \(73\) \(q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots\)
76.5.c.b \(4\) \(7.856\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None None \(0\) \(0\) \(22\) \(24\) \(q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots\)
76.5.g.a \(76\) \(7.856\) None None \(-1\) \(0\) \(-2\) \(0\)
76.5.h.a \(12\) \(7.856\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-12\) \(9\) \(-52\) \(q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
76.5.j.a \(42\) \(7.856\) None None \(0\) \(12\) \(0\) \(-45\)
76.5.l.a \(228\) \(7.856\) None None \(-6\) \(0\) \(-12\) \(0\)
76.6.a.a \(3\) \(12.189\) 3.3.272193.1 None None \(0\) \(-8\) \(-9\) \(-13\) \(+\) \(q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots\)
76.6.a.b \(4\) \(12.189\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(10\) \(-110\) \(30\) \(-\) \(q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots\)
76.6.d.a \(48\) \(12.189\) None None \(0\) \(0\) \(-4\) \(0\)
76.6.e.a \(18\) \(12.189\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(-11\) \(11\) \(336\) \(q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.6.f.a \(96\) \(12.189\) None None \(-3\) \(0\) \(-2\) \(0\)
76.6.i.a \(48\) \(12.189\) None None \(0\) \(33\) \(0\) \(-177\)
76.6.k.a \(288\) \(12.189\) None None \(-6\) \(0\) \(-12\) \(0\)
76.7.b.a \(54\) \(17.484\) None None \(-10\) \(0\) \(-44\) \(0\)
76.7.c.a \(2\) \(17.484\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(54\) \(-610\) \(q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots\)
76.7.c.b \(8\) \(17.484\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(2\) \(362\) \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
76.7.g.a \(116\) \(17.484\) None None \(-1\) \(0\) \(-2\) \(0\)
76.7.h.a \(20\) \(17.484\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-30\) \(-56\) \(464\) \(q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots\)
76.7.j.a \(60\) \(17.484\) None None \(0\) \(30\) \(0\) \(-216\)
76.7.l.a \(348\) \(17.484\) None None \(-6\) \(0\) \(-12\) \(0\)
76.8.a.a \(5\) \(23.741\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-14\) \(-280\) \(414\) \(-\) \(q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
76.8.a.b \(6\) \(23.741\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(40\) \(279\) \(-1565\) \(+\) \(q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots\)
76.8.d.a \(68\) \(23.741\) None None \(0\) \(0\) \(-4\) \(0\)
76.8.e.a \(22\) \(23.741\) None None \(0\) \(13\) \(1\) \(560\)
76.8.f.a \(136\) \(23.741\) None None \(-3\) \(0\) \(-2\) \(0\)
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