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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
429.1.v.a \(4\) \(0.214\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None \(-3\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
429.1.v.b \(4\) \(0.214\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-39}) \) None \(3\) \(-1\) \(-2\) \(0\) \(q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
429.1.v.c \(8\) \(0.214\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-39}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
429.2.a.a \(1\) \(3.426\) \(\Q\) None None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
429.2.a.b \(1\) \(3.426\) \(\Q\) None None \(-1\) \(1\) \(-2\) \(0\) \(+\) \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots\)
429.2.a.c \(2\) \(3.426\) \(\Q(\sqrt{2}) \) None None \(-2\) \(2\) \(-4\) \(-4\) \(+\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
429.2.a.d \(2\) \(3.426\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(-4\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
429.2.a.e \(3\) \(3.426\) 3.3.564.1 None None \(-1\) \(-3\) \(-2\) \(2\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
429.2.a.f \(3\) \(3.426\) 3.3.148.1 None None \(1\) \(3\) \(0\) \(-2\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots\)
429.2.a.g \(3\) \(3.426\) 3.3.148.1 None None \(3\) \(3\) \(4\) \(-2\) \(-\) \(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
429.2.a.h \(4\) \(3.426\) 4.4.8468.1 None None \(-2\) \(-4\) \(0\) \(2\) \(-\) \(q+\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
429.2.b.a \(10\) \(3.426\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(-10\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
429.2.b.b \(14\) \(3.426\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(14\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-1-\beta _{5}+\beta _{6})q^{4}+\cdots\)
429.2.e.a \(8\) \(3.426\) 8.0.\(\cdots\).21 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(-2-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
429.2.e.b \(8\) \(3.426\) 8.0.3317760000.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{4}q^{6}+\cdots\)
429.2.e.c \(16\) \(3.426\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{5}q^{3}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
429.2.e.d \(20\) \(3.426\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) \(\Q(\sqrt{-143}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(-2+\beta _{8})q^{4}+\beta _{7}q^{6}+\cdots\)
429.2.f.a \(48\) \(3.426\) None None \(0\) \(-6\) \(0\) \(0\)
429.2.i.a \(2\) \(3.426\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(4\) \(-1\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+2q^{5}-\zeta_{6}q^{7}+\cdots\)
429.2.i.b \(2\) \(3.426\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(4\) \(3\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+2q^{5}+3\zeta_{6}q^{7}+\cdots\)
429.2.i.c \(10\) \(3.426\) 10.0.\(\cdots\).1 None None \(-2\) \(-5\) \(16\) \(-9\) \(q+\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{6})q^{4}+\cdots\)
429.2.i.d \(10\) \(3.426\) 10.0.\(\cdots\).1 None None \(0\) \(5\) \(-4\) \(-7\) \(q+(\beta _{2}+\beta _{7}-\beta _{8}+\beta _{9})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
429.2.i.e \(10\) \(3.426\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(2\) \(5\) \(4\) \(9\) \(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
429.2.i.f \(10\) \(3.426\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(4\) \(-5\) \(-8\) \(3\) \(q+(1-\beta _{1}-\beta _{6})q^{2}+(-1+\beta _{6})q^{3}+\cdots\)
429.2.j.a \(96\) \(3.426\) None None \(0\) \(0\) \(0\) \(-16\)
429.2.m.a \(28\) \(3.426\) None None \(0\) \(-28\) \(4\) \(0\)
429.2.m.b \(28\) \(3.426\) None None \(0\) \(28\) \(-4\) \(0\)
429.2.n.a \(12\) \(3.426\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(3\) \(-3\) \(8\) \(5\) \(q-\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
429.2.n.b \(20\) \(3.426\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(1\) \(5\) \(4\) \(-3\) \(q+\beta _{5}q^{2}-\beta _{9}q^{3}+(-\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
429.2.n.c \(28\) \(3.426\) None None \(1\) \(7\) \(-4\) \(1\)
429.2.n.d \(36\) \(3.426\) None None \(3\) \(-9\) \(0\) \(1\)
429.2.p.a \(8\) \(3.426\) 8.0.\(\cdots\).7 None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\beta _{2}+\beta _{3})q^{3}+2\beta _{2}q^{4}-2\beta _{6}q^{5}+\cdots\)
429.2.p.b \(96\) \(3.426\) None None \(0\) \(2\) \(0\) \(0\)
429.2.s.a \(24\) \(3.426\) None None \(0\) \(12\) \(0\) \(6\)
429.2.s.b \(28\) \(3.426\) None None \(0\) \(-14\) \(0\) \(0\)
429.2.t.a \(104\) \(3.426\) None None \(0\) \(-2\) \(0\) \(0\)
429.2.x.a \(192\) \(3.426\) None None \(0\) \(6\) \(0\) \(0\)
429.2.y.a \(32\) \(3.426\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\)
429.2.y.b \(176\) \(3.426\) None None \(0\) \(-6\) \(0\) \(0\)
429.2.bb.a \(56\) \(3.426\) None None \(0\) \(-14\) \(0\) \(0\)
429.2.bb.b \(56\) \(3.426\) None None \(0\) \(14\) \(0\) \(0\)
429.2.bd.a \(56\) \(3.426\) None None \(0\) \(-28\) \(4\) \(0\)
429.2.bd.b \(56\) \(3.426\) None None \(0\) \(28\) \(-4\) \(0\)
429.2.be.a \(184\) \(3.426\) None None \(0\) \(0\) \(0\) \(12\)
429.2.bg.a \(112\) \(3.426\) None None \(0\) \(-14\) \(6\) \(0\)
429.2.bg.b \(112\) \(3.426\) None None \(0\) \(14\) \(-6\) \(0\)
429.2.bi.a \(416\) \(3.426\) None None \(0\) \(-12\) \(0\) \(-12\)
429.2.bj.a \(112\) \(3.426\) None None \(0\) \(-28\) \(-6\) \(0\)
429.2.bj.b \(112\) \(3.426\) None None \(0\) \(28\) \(6\) \(0\)
429.2.bm.a \(416\) \(3.426\) None None \(0\) \(-3\) \(0\) \(-30\)
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