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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
460.1.d.a \(1\) \(0.230\) \(\Q\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-q^{5}+q^{7}+q^{9}+q^{17}-q^{23}+q^{25}+\cdots\)
460.1.d.b \(1\) \(0.230\) \(\Q\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+q^{5}-q^{7}+q^{9}-q^{17}+q^{23}+q^{25}+\cdots\)
460.1.n.a \(10\) \(0.230\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(-1\) \(9\) \(q+\zeta_{22}^{10}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{4})q^{3}-\zeta_{22}^{9}q^{4}+\cdots\)
460.1.n.b \(10\) \(0.230\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(-1\) \(-9\) \(q-\zeta_{22}^{10}q^{2}+(-\zeta_{22}^{2}-\zeta_{22}^{4})q^{3}+\cdots\)
460.2.a.a \(1\) \(3.673\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-2\) \(+\) \(q-q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
460.2.a.b \(1\) \(3.673\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(q-q^{5}-q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots\)
460.2.a.c \(1\) \(3.673\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-4\) \(+\) \(q+q^{3}-q^{5}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
460.2.a.d \(1\) \(3.673\) \(\Q\) None None \(0\) \(3\) \(-1\) \(2\) \(-\) \(q+3q^{3}-q^{5}+2q^{7}+6q^{9}-3q^{13}+\cdots\)
460.2.a.e \(2\) \(3.673\) \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(2\) \(1\) \(-\) \(q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
460.2.c.a \(12\) \(3.673\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{6})q^{3}+\beta _{9}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
460.2.e.a \(16\) \(3.673\) 16.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{2}+\beta _{8})q^{4}+\cdots\)
460.2.e.b \(32\) \(3.673\) None None \(4\) \(0\) \(0\) \(0\)
460.2.g.a \(4\) \(3.673\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+2q^{6}+\cdots\)
460.2.g.b \(8\) \(3.673\) 8.0.207360000.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
460.2.g.c \(56\) \(3.673\) None None \(0\) \(0\) \(0\) \(0\)
460.2.i.a \(8\) \(3.673\) 8.0.\(\cdots\).3 None None \(0\) \(-8\) \(0\) \(0\) \(q+(-1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{6})q^{5}-\beta _{2}q^{7}+\cdots\)
460.2.i.b \(16\) \(3.673\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{15})q^{7}+\cdots\)
460.2.j.a \(132\) \(3.673\) None None \(0\) \(0\) \(0\) \(0\)
460.2.m.a \(30\) \(3.673\) None None \(0\) \(0\) \(-3\) \(1\)
460.2.m.b \(50\) \(3.673\) None None \(0\) \(0\) \(5\) \(-1\)
460.2.o.a \(40\) \(3.673\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\)
460.2.o.b \(640\) \(3.673\) None None \(0\) \(0\) \(-22\) \(0\)
460.2.q.a \(480\) \(3.673\) None None \(-4\) \(0\) \(0\) \(0\)
460.2.s.a \(120\) \(3.673\) None None \(0\) \(0\) \(0\) \(0\)
460.2.w.a \(1360\) \(3.673\) None None \(-18\) \(0\) \(-36\) \(0\)
460.2.x.a \(240\) \(3.673\) None None \(0\) \(4\) \(0\) \(0\)
460.3.b.a \(88\) \(12.534\) None None \(0\) \(0\) \(0\) \(0\)
460.3.d.a \(2\) \(12.534\) \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-10\) \(-9\) \(q-5q^{5}+(-4-\beta )q^{7}+9q^{9}+(4+3\beta )q^{17}+\cdots\)
460.3.d.b \(2\) \(12.534\) \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(10\) \(9\) \(q+5q^{5}+(4+\beta )q^{7}+9q^{9}+(-4-3\beta )q^{17}+\cdots\)
460.3.d.c \(20\) \(12.534\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{1}q^{5}-\beta _{16}q^{7}+(-4+\beta _{11}+\cdots)q^{9}+\cdots\)
460.3.f.a \(16\) \(12.534\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(4+\beta _{2}+\cdots)q^{9}+\cdots\)
460.3.l.a \(44\) \(12.534\) None None \(0\) \(0\) \(8\) \(16\)
460.4.a.a \(5\) \(27.141\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-7\) \(25\) \(-20\) \(-\) \(q+(-1-\beta _{3})q^{3}+5q^{5}+(-5-\beta _{1}+\cdots)q^{7}+\cdots\)
460.4.a.b \(5\) \(27.141\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-3\) \(-25\) \(8\) \(-\) \(q+(-1+\beta _{1})q^{3}-5q^{5}+(2-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
460.4.a.c \(6\) \(27.141\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-1\) \(30\) \(24\) \(+\) \(q-\beta _{1}q^{3}+5q^{5}+(4+\beta _{3}-\beta _{4})q^{7}+\cdots\)
460.4.a.d \(6\) \(27.141\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(3\) \(-30\) \(20\) \(+\) \(q+(1-\beta _{1})q^{3}-5q^{5}+(3+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
460.4.c.a \(32\) \(27.141\) None None \(0\) \(0\) \(-12\) \(0\)
460.4.i.a \(72\) \(27.141\) None None \(0\) \(8\) \(0\) \(0\)
460.5.d.a \(2\) \(47.550\) \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-50\) \(-17\) \(q-5^{2}q^{5}+(-10-3\beta )q^{7}+3^{4}q^{9}+\cdots\)
460.5.d.b \(2\) \(47.550\) \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(50\) \(17\) \(q+5^{2}q^{5}+(10+3\beta )q^{7}+3^{4}q^{9}+(234+\cdots)q^{17}+\cdots\)
460.5.d.c \(44\) \(47.550\) None None \(0\) \(0\) \(0\) \(0\)
460.5.f.a \(32\) \(47.550\) None None \(0\) \(0\) \(0\) \(0\)
460.5.l.a \(88\) \(47.550\) None None \(0\) \(0\) \(48\) \(-160\)
460.6.a.a \(9\) \(73.777\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-31\) \(-225\) \(-319\) \(+\) \(q+(-3-\beta _{1})q^{3}-5^{2}q^{5}+(-35-\beta _{1}+\cdots)q^{7}+\cdots\)
460.6.a.b \(9\) \(73.777\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-9\) \(225\) \(-95\) \(+\) \(q+(-1-\beta _{1})q^{3}+5^{2}q^{5}+(-11+2\beta _{1}+\cdots)q^{7}+\cdots\)
460.6.a.c \(10\) \(73.777\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(-13\) \(-250\) \(-28\) \(-\) \(q+(-1-\beta _{1})q^{3}-5^{2}q^{5}+(-3+2\beta _{1}+\cdots)q^{7}+\cdots\)
460.6.a.d \(10\) \(73.777\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(9\) \(250\) \(6\) \(-\) \(q+(1-\beta _{1})q^{3}+5^{2}q^{5}+(1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
460.6.c.a \(56\) \(73.777\) None None \(0\) \(0\) \(-60\) \(0\)
460.7.d.a \(2\) \(105.825\) \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-250\) \(594\) \(q-5^{3}q^{5}+(297-4\beta )q^{7}+3^{6}q^{9}+(-4103+\cdots)q^{17}+\cdots\)
460.7.d.b \(2\) \(105.825\) \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(250\) \(-594\) \(q+5^{3}q^{5}+(-297-4\beta )q^{7}+3^{6}q^{9}+\cdots\)
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