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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
169.2.a.a \(2\) \(1.349\) \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+2q^{3}+q^{4}-\beta q^{5}+2\beta q^{6}+\cdots\)
169.2.a.b \(3\) \(1.349\) \(\Q(\zeta_{14})^+\) None \(-2\) \(-2\) \(-4\) \(-3\) \(+\) \(q+(-1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
169.2.a.c \(3\) \(1.349\) \(\Q(\zeta_{14})^+\) None \(2\) \(-2\) \(4\) \(3\) \(-\) \(q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
169.2.b.a \(2\) \(1.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+2q^{3}-q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{6}+\cdots\)
169.2.b.b \(6\) \(1.349\) 6.0.153664.1 None \(0\) \(-4\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{5})q^{2}+(-1+\beta _{4})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
169.2.c.a \(4\) \(1.349\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}-2\zeta_{12}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
169.2.c.b \(6\) \(1.349\) 6.0.64827.1 None \(-2\) \(2\) \(8\) \(-3\) \(q+(-1+\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+\cdots\)
169.2.c.c \(6\) \(1.349\) 6.0.64827.1 None \(2\) \(2\) \(-8\) \(3\) \(q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
169.2.e.a \(2\) \(1.349\) \(\Q(\sqrt{-3}) \) None \(3\) \(-2\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
169.2.e.b \(12\) \(1.349\) 12.0.\(\cdots\).1 None \(0\) \(4\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{8}+\beta _{10})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
169.2.g.a \(156\) \(1.349\) None \(-10\) \(-9\) \(-7\) \(-5\)
169.2.h.a \(168\) \(1.349\) None \(-13\) \(-13\) \(-13\) \(-13\)
169.2.i.a \(336\) \(1.349\) None \(-26\) \(-26\) \(-26\) \(-26\)
169.2.k.a \(360\) \(1.349\) None \(-23\) \(-24\) \(-26\) \(-26\)
169.3.d.a \(4\) \(4.605\) \(\Q(\zeta_{12})\) None \(-2\) \(4\) \(-14\) \(4\) \(q+\zeta_{12}^{3}q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
169.3.d.b \(4\) \(4.605\) \(\Q(i, \sqrt{22})\) None \(0\) \(-12\) \(0\) \(0\) \(q+\beta _{1}q^{2}-3q^{3}+7\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots\)
169.3.d.c \(4\) \(4.605\) \(\Q(\zeta_{12})\) None \(2\) \(4\) \(14\) \(-4\) \(q+(1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
169.3.d.d \(4\) \(4.605\) \(\Q(i, \sqrt{10})\) None \(4\) \(-4\) \(-8\) \(12\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
169.3.d.e \(24\) \(4.605\) None \(0\) \(12\) \(0\) \(0\)
169.3.f.a \(4\) \(4.605\) \(\Q(\zeta_{12})\) None \(-4\) \(-2\) \(14\) \(20\) \(q+(-1-\zeta_{12})q^{2}+(-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
169.3.f.b \(4\) \(4.605\) \(\Q(\zeta_{12})\) None \(2\) \(-2\) \(14\) \(-16\) \(q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
169.3.f.c \(4\) \(4.605\) \(\Q(\zeta_{12})\) None \(4\) \(-2\) \(-14\) \(-20\) \(q+(1+\zeta_{12})q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
169.3.f.d \(8\) \(4.605\) 8.0.3317760000.2 None \(-4\) \(4\) \(-16\) \(-12\) \(q+(-1-\beta _{2}-\beta _{3}+\beta _{4}+\beta _{7})q^{2}+(1+\cdots)q^{3}+\cdots\)
169.3.f.e \(8\) \(4.605\) 8.0.\(\cdots\).9 None \(0\) \(12\) \(0\) \(0\) \(q+\beta _{1}q^{2}+3\beta _{4}q^{3}+7\beta _{2}q^{4}+(\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
169.3.f.f \(8\) \(4.605\) 8.0.3317760000.2 None \(4\) \(4\) \(16\) \(12\) \(q+(1+\beta _{2}-\beta _{3}-\beta _{4}+\beta _{7})q^{2}+(1+\beta _{3}+\cdots)q^{3}+\cdots\)
169.3.f.g \(48\) \(4.605\) None \(0\) \(-12\) \(0\) \(0\)
169.3.j.a \(720\) \(4.605\) None \(-22\) \(-22\) \(-34\) \(-14\)
169.3.l.a \(1392\) \(4.605\) None \(-50\) \(-50\) \(-38\) \(-68\)
169.4.a.a \(1\) \(9.971\) \(\Q\) None \(-4\) \(2\) \(-17\) \(-20\) \(+\) \(q-4q^{2}+2q^{3}+8q^{4}-17q^{5}-8q^{6}+\cdots\)
169.4.a.b \(1\) \(9.971\) \(\Q\) None \(-3\) \(-1\) \(9\) \(-15\) \(-\) \(q-3q^{2}-q^{3}+q^{4}+9q^{5}+3q^{6}-15q^{7}+\cdots\)
169.4.a.c \(1\) \(9.971\) \(\Q\) None \(3\) \(-1\) \(-9\) \(15\) \(-\) \(q+3q^{2}-q^{3}+q^{4}-9q^{5}-3q^{6}+15q^{7}+\cdots\)
169.4.a.d \(1\) \(9.971\) \(\Q\) None \(4\) \(2\) \(17\) \(20\) \(+\) \(q+4q^{2}+2q^{3}+8q^{4}+17q^{5}+8q^{6}+\cdots\)
169.4.a.e \(1\) \(9.971\) \(\Q\) None \(5\) \(-7\) \(7\) \(13\) \(+\) \(q+5q^{2}-7q^{3}+17q^{4}+7q^{5}-35q^{6}+\cdots\)
169.4.a.f \(2\) \(9.971\) \(\Q(\sqrt{17}) \) None \(-5\) \(5\) \(-15\) \(15\) \(+\) \(q+(-2-\beta )q^{2}+(1+3\beta )q^{3}+5\beta q^{4}+\cdots\)
169.4.a.g \(2\) \(9.971\) \(\Q(\sqrt{17}) \) None \(-1\) \(5\) \(3\) \(9\) \(+\) \(q-\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
169.4.a.h \(2\) \(9.971\) \(\Q(\sqrt{3}) \) None \(0\) \(-14\) \(0\) \(0\) \(-\) \(q+2\beta q^{2}-7q^{3}+4q^{4}+8\beta q^{5}-14\beta q^{6}+\cdots\)
169.4.a.i \(2\) \(9.971\) \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+2q^{3}-5q^{4}+\beta q^{5}+2\beta q^{6}+\cdots\)
169.4.a.j \(2\) \(9.971\) \(\Q(\sqrt{17}) \) None \(5\) \(5\) \(15\) \(-15\) \(+\) \(q+(3-\beta )q^{2}+(4-3\beta )q^{3}+(5-5\beta )q^{4}+\cdots\)
169.4.a.k \(9\) \(9.971\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-5\) \(1\) \(-30\) \(-38\) \(-\) \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(5+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
169.4.a.l \(9\) \(9.971\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(5\) \(1\) \(30\) \(38\) \(+\) \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(5+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
169.4.b.a \(2\) \(9.971\) \(\Q(\sqrt{-1}) \) None \(0\) \(-14\) \(0\) \(0\) \(q+5iq^{2}-7q^{3}-17q^{4}+7iq^{5}-35iq^{6}+\cdots\)
169.4.b.b \(2\) \(9.971\) \(\Q(\sqrt{-3}) \) None \(0\) \(-14\) \(0\) \(0\) \(q-2\zeta_{6}q^{2}-7q^{3}-4q^{4}-8\zeta_{6}q^{5}+\cdots\)
169.4.b.c \(2\) \(9.971\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+4iq^{2}+2q^{3}-8q^{4}+17iq^{5}+8iq^{6}+\cdots\)
169.4.b.d \(2\) \(9.971\) \(\Q(\sqrt{-3}) \) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+2q^{3}+5q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{6}+\cdots\)
169.4.b.e \(4\) \(9.971\) \(\Q(i, \sqrt{17})\) None \(0\) \(10\) \(0\) \(0\) \(q+(\beta _{1}+3\beta _{2})q^{2}+(1+3\beta _{3})q^{3}-5\beta _{3}q^{4}+\cdots\)
169.4.b.f \(4\) \(9.971\) \(\Q(i, \sqrt{17})\) None \(0\) \(10\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+3\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
169.4.b.g \(18\) \(9.971\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{9}q^{2}-\beta _{2}q^{3}+(-4+\beta _{1})q^{4}+(-\beta _{9}+\cdots)q^{5}+\cdots\)
169.4.c.a \(2\) \(9.971\) \(\Q(\sqrt{-3}) \) None \(-5\) \(7\) \(14\) \(-13\) \(q+(-5+5\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}-17\zeta_{6}q^{4}+\cdots\)
169.4.c.b \(2\) \(9.971\) \(\Q(\sqrt{-3}) \) None \(-3\) \(1\) \(-18\) \(-15\) \(q+(-3+3\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
169.4.c.c \(2\) \(9.971\) \(\Q(\sqrt{-3}) \) None \(3\) \(1\) \(18\) \(15\) \(q+(3-3\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
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