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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
60.2.d.a \(2\) \(0.479\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+2i)q^{5}-4iq^{7}-q^{9}+\cdots\)
60.2.e.a \(8\) \(0.479\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-\beta _{4}-\beta _{7})q^{3}+(\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
60.2.h.a \(4\) \(0.479\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots\)
60.2.h.b \(4\) \(0.479\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)
60.2.i.a \(4\) \(0.479\) \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(-4\) \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
60.2.j.a \(12\) \(0.479\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{2}+\beta _{4}-\beta _{7})q^{4}+\cdots\)
60.3.b.a \(4\) \(1.635\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
60.3.c.a \(8\) \(1.635\) 8.0.85100625.1 None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
60.3.f.a \(4\) \(1.635\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
60.3.f.b \(8\) \(1.635\) 8.0.\(\cdots\).4 None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
60.3.g.a \(2\) \(1.635\) \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(4\) \(q+(2+\beta )q^{3}+\beta q^{5}+2q^{7}+(-1+4\beta )q^{9}+\cdots\)
60.3.k.a \(4\) \(1.635\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(12\) \(20\) \(q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
60.3.l.a \(40\) \(1.635\) None \(0\) \(0\) \(0\) \(0\)
60.4.a.a \(1\) \(3.540\) \(\Q\) None \(0\) \(-3\) \(-5\) \(-28\) \(-\) \(q-3q^{3}-5q^{5}-28q^{7}+9q^{9}-24q^{11}+\cdots\)
60.4.a.b \(1\) \(3.540\) \(\Q\) None \(0\) \(-3\) \(5\) \(32\) \(+\) \(q-3q^{3}+5q^{5}+2^{5}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
60.4.d.a \(2\) \(3.540\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-20\) \(0\) \(q+3iq^{3}+(-10+5i)q^{5}+22iq^{7}+\cdots\)
60.4.e.a \(24\) \(3.540\) None \(0\) \(0\) \(0\) \(0\)
60.4.h.a \(4\) \(3.540\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{2}q^{2}+(\beta _{1}-4\beta _{2})q^{3}-8q^{4}-5\beta _{3}q^{5}+\cdots\)
60.4.h.b \(4\) \(3.540\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
60.4.h.c \(24\) \(3.540\) None \(0\) \(0\) \(0\) \(0\)
60.4.i.a \(4\) \(3.540\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(92\) \(q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
60.4.i.b \(8\) \(3.540\) 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(-80\) \(q-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
60.4.j.a \(8\) \(3.540\) 8.0.157351936.1 None \(0\) \(0\) \(-24\) \(0\) \(q+(\beta _{2}+\beta _{4})q^{2}+3\beta _{5}q^{3}+(6\beta _{3}+2\beta _{6}+\cdots)q^{4}+\cdots\)
60.4.j.b \(28\) \(3.540\) None \(0\) \(0\) \(24\) \(0\)
60.5.b.a \(8\) \(6.202\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(6+\beta _{2}+\cdots)q^{9}+\cdots\)
60.5.c.a \(16\) \(6.202\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-12\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{3})q^{2}+\beta _{2}q^{3}+(2+\beta _{3}+\beta _{7}+\cdots)q^{4}+\cdots\)
60.5.f.a \(24\) \(6.202\) None \(0\) \(0\) \(-24\) \(0\)
60.5.g.a \(2\) \(6.202\) \(\Q(\sqrt{-5}) \) None \(0\) \(12\) \(0\) \(148\) \(q+(6+3\beta )q^{3}-5\beta q^{5}+74q^{7}+(-9+\cdots)q^{9}+\cdots\)
60.5.g.b \(4\) \(6.202\) \(\Q(\sqrt{-5}, \sqrt{34})\) None \(0\) \(-20\) \(0\) \(-40\) \(q+(-5+\beta _{1})q^{3}-\beta _{3}q^{5}+(-10-\beta _{1}+\cdots)q^{7}+\cdots\)
60.5.k.a \(8\) \(6.202\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(12\) \(-140\) \(q+\beta _{2}q^{3}+(2+2\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
60.5.l.a \(88\) \(6.202\) None \(0\) \(0\) \(0\) \(0\)
60.6.a.a \(1\) \(9.623\) \(\Q\) None \(0\) \(-9\) \(-25\) \(44\) \(-\) \(q-9q^{3}-5^{2}q^{5}+44q^{7}+3^{4}q^{9}+6^{3}q^{11}+\cdots\)
60.6.a.b \(1\) \(9.623\) \(\Q\) None \(0\) \(-9\) \(25\) \(-16\) \(+\) \(q-9q^{3}+5^{2}q^{5}-2^{4}q^{7}+3^{4}q^{9}-564q^{11}+\cdots\)
60.6.a.c \(1\) \(9.623\) \(\Q\) None \(0\) \(9\) \(-25\) \(-244\) \(+\) \(q+9q^{3}-5^{2}q^{5}-244q^{7}+3^{4}q^{9}+\cdots\)
60.6.a.d \(1\) \(9.623\) \(\Q\) None \(0\) \(9\) \(25\) \(56\) \(-\) \(q+9q^{3}+5^{2}q^{5}+56q^{7}+3^{4}q^{9}+156q^{11}+\cdots\)
60.6.d.a \(6\) \(9.623\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-38\) \(0\) \(q+\beta _{1}q^{3}+(-6-\beta _{1}-\beta _{2})q^{5}+(-3\beta _{1}+\cdots)q^{7}+\cdots\)
60.6.e.a \(40\) \(9.623\) None \(0\) \(0\) \(0\) \(0\)
60.6.h.a \(4\) \(9.623\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+4\beta _{1}q^{2}+(10\beta _{1}+\beta _{2})q^{3}-2^{5}q^{4}+\cdots\)
60.6.h.b \(4\) \(9.623\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+9\beta _{1}q^{3}+(31-\beta _{3})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
60.6.h.c \(48\) \(9.623\) None \(0\) \(0\) \(0\) \(0\)
60.6.i.a \(20\) \(9.623\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(2\) \(0\) \(76\) \(q-\beta _{6}q^{3}-\beta _{5}q^{5}+(4+4\beta _{1}+\beta _{8})q^{7}+\cdots\)
60.6.j.a \(60\) \(9.623\) None \(0\) \(0\) \(0\) \(0\)
60.7.b.a \(12\) \(13.803\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
60.7.c.a \(24\) \(13.803\) None \(20\) \(0\) \(0\) \(0\)
60.7.f.a \(36\) \(13.803\) None \(0\) \(0\) \(44\) \(0\)
60.7.g.a \(8\) \(13.803\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-20\) \(0\) \(-560\) \(q+(-3-\beta _{1})q^{3}+\beta _{2}q^{5}+(-71-\beta _{4}+\cdots)q^{7}+\cdots\)
60.7.k.a \(12\) \(13.803\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(312\) \(120\) \(q+\beta _{2}q^{3}+(26-4\beta _{1}+\beta _{2}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
60.7.l.a \(136\) \(13.803\) None \(0\) \(0\) \(0\) \(0\)
60.8.a.a \(1\) \(18.743\) \(\Q\) None \(0\) \(-27\) \(-125\) \(1028\) \(-\) \(q-3^{3}q^{3}-5^{3}q^{5}+1028q^{7}+3^{6}q^{9}+\cdots\)
60.8.a.b \(1\) \(18.743\) \(\Q\) None \(0\) \(-27\) \(125\) \(-832\) \(+\) \(q-3^{3}q^{3}+5^{3}q^{5}-832q^{7}+3^{6}q^{9}+\cdots\)
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