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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
475.1.c.a \(1\) \(0.237\) \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-2q^{11}+q^{16}-q^{19}+\cdots\)
475.1.c.b \(2\) \(0.237\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-\beta q^{3}-q^{4}-2q^{6}-q^{9}+\beta q^{12}+\cdots\)
475.1.m.a \(4\) \(0.237\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{10}^{3}q^{4}-\zeta_{10}q^{5}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
475.1.o.a \(4\) \(0.237\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(-\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
475.2.a.a \(1\) \(3.793\) \(\Q\) None None \(-1\) \(0\) \(0\) \(2\) \(+\) \(q-q^{2}-q^{4}+2q^{7}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
475.2.a.b \(1\) \(3.793\) \(\Q\) None None \(0\) \(2\) \(0\) \(1\) \(-\) \(q+2q^{3}-2q^{4}+q^{7}+q^{9}+3q^{11}+\cdots\)
475.2.a.c \(1\) \(3.793\) \(\Q\) None None \(1\) \(0\) \(0\) \(-2\) \(+\) \(q+q^{2}-q^{4}-2q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
475.2.a.d \(3\) \(3.793\) \(\Q(\zeta_{14})^+\) None None \(-4\) \(-2\) \(0\) \(0\) \(+\) \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
475.2.a.e \(3\) \(3.793\) 3.3.169.1 None None \(-2\) \(-2\) \(0\) \(-4\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
475.2.a.f \(3\) \(3.793\) 3.3.148.1 None None \(-1\) \(-2\) \(0\) \(0\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.g \(3\) \(3.793\) 3.3.169.1 None None \(2\) \(2\) \(0\) \(4\) \(-\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.h \(3\) \(3.793\) \(\Q(\zeta_{14})^+\) None None \(4\) \(2\) \(0\) \(0\) \(-\) \(q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.i \(4\) \(3.793\) 4.4.11344.1 None None \(2\) \(-2\) \(0\) \(-4\) \(-\) \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
475.2.a.j \(6\) \(3.793\) 6.6.66064384.1 None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
475.2.b.a \(2\) \(3.793\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+2q^{4}-iq^{7}-q^{9}+3q^{11}+\cdots\)
475.2.b.b \(6\) \(3.793\) 6.0.1827904.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{1}+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
475.2.b.c \(6\) \(3.793\) 6.0.153664.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
475.2.b.d \(6\) \(3.793\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots\)
475.2.b.e \(8\) \(3.793\) 8.0.2058981376.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{1}q^{3}+(-2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
475.2.e.a \(2\) \(3.793\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(-8\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-4q^{7}+\cdots\)
475.2.e.b \(2\) \(3.793\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(8\) \(q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+4q^{7}+\cdots\)
475.2.e.c \(2\) \(3.793\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(8\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+4q^{7}+3\zeta_{6}q^{9}+\cdots\)
475.2.e.d \(6\) \(3.793\) 6.0.3518667.1 None None \(1\) \(1\) \(0\) \(-4\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
475.2.e.e \(8\) \(3.793\) 8.0.4601315889.1 None None \(1\) \(3\) \(0\) \(8\) \(q-\beta _{7}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
475.2.e.f \(12\) \(3.793\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(-3\) \(0\) \(4\) \(q+(\beta _{7}+\beta _{8})q^{2}+(1-\beta _{1}+\beta _{2}+\beta _{9}+\cdots)q^{3}+\cdots\)
475.2.e.g \(12\) \(3.793\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\beta _{8}+\cdots)q^{4}+\cdots\)
475.2.e.h \(12\) \(3.793\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(2\) \(3\) \(0\) \(-4\) \(q+(-\beta _{7}-\beta _{8})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
475.2.g.a \(4\) \(3.793\) \(\Q(i, \sqrt{19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(0\) \(-6\) \(q-2\beta _{1}q^{4}+(-2+2\beta _{1}+\beta _{3})q^{7}+3\beta _{1}q^{9}+\cdots\)
475.2.g.b \(12\) \(3.793\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots\)
475.2.g.c \(16\) \(3.793\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2\beta _{7}-\beta _{10})q^{4}+\cdots\)
475.2.g.d \(24\) \(3.793\) None None \(0\) \(0\) \(0\) \(0\)
475.2.h.a \(84\) \(3.793\) None None \(-1\) \(-2\) \(2\) \(0\)
475.2.h.b \(100\) \(3.793\) None None \(-1\) \(-2\) \(1\) \(-10\)
475.2.j.a \(4\) \(3.793\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{4}+2\zeta_{12}^{3}q^{7}+\cdots\)
475.2.j.b \(12\) \(3.793\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
475.2.j.c \(16\) \(3.793\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{14}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
475.2.j.d \(24\) \(3.793\) None None \(0\) \(0\) \(0\) \(0\)
475.2.l.a \(6\) \(3.793\) \(\Q(\zeta_{18})\) None None \(6\) \(3\) \(0\) \(0\) \(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots\)
475.2.l.b \(18\) \(3.793\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(-3\) \(3\) \(0\) \(0\) \(q+\beta _{14}q^{2}+(\beta _{4}-\beta _{6}+\beta _{7}+\beta _{15})q^{3}+\cdots\)
475.2.l.c \(18\) \(3.793\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(3\) \(3\) \(0\) \(0\) \(q+(\beta _{4}-\beta _{15})q^{2}+(-\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{3}+\cdots\)
475.2.l.d \(42\) \(3.793\) None None \(0\) \(-3\) \(0\) \(0\)
475.2.l.e \(42\) \(3.793\) None None \(0\) \(3\) \(0\) \(0\)
475.2.l.f \(48\) \(3.793\) None None \(0\) \(0\) \(0\) \(0\)
475.2.n.a \(80\) \(3.793\) None None \(0\) \(0\) \(-3\) \(0\)
475.2.n.b \(96\) \(3.793\) None None \(0\) \(0\) \(-4\) \(0\)
475.2.p.a \(4\) \(3.793\) \(\Q(\zeta_{12})\) None None \(-2\) \(4\) \(0\) \(0\) \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(2+2\zeta_{12}+\cdots)q^{3}+\cdots\)
475.2.p.b \(4\) \(3.793\) \(\Q(\zeta_{12})\) None None \(0\) \(6\) \(0\) \(-8\) \(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(2\zeta_{12}+\cdots)q^{4}+\cdots\)
475.2.p.c \(4\) \(3.793\) \(\Q(\zeta_{12})\) None None \(2\) \(-4\) \(0\) \(0\) \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2-2\zeta_{12}+\cdots)q^{3}+\cdots\)
475.2.p.d \(4\) \(3.793\) \(\Q(\zeta_{12})\) None None \(6\) \(6\) \(0\) \(8\) \(q+(1-\zeta_{12}+\zeta_{12}^{2}+2\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\)
475.2.p.e \(16\) \(3.793\) 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{14}q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{6}+\cdots\)
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