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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
585.1.o.a \(8\) \(0.292\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)
585.2.a.a \(1\) \(4.671\) \(\Q\) None None \(-2\) \(0\) \(-1\) \(-3\) \(+\) \(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
585.2.a.b \(1\) \(4.671\) \(\Q\) None None \(-2\) \(0\) \(-1\) \(3\) \(-\) \(q-2q^{2}+2q^{4}-q^{5}+3q^{7}+2q^{10}+\cdots\)
585.2.a.c \(1\) \(4.671\) \(\Q\) None None \(-2\) \(0\) \(1\) \(-1\) \(+\) \(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
585.2.a.d \(1\) \(4.671\) \(\Q\) None None \(-1\) \(0\) \(-1\) \(2\) \(+\) \(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
585.2.a.e \(1\) \(4.671\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(q-2q^{4}-q^{5}-q^{7}+3q^{11}+q^{13}+\cdots\)
585.2.a.f \(1\) \(4.671\) \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) \(+\) \(q-2q^{4}+q^{5}-q^{7}-3q^{11}+q^{13}+\cdots\)
585.2.a.g \(1\) \(4.671\) \(\Q\) None None \(1\) \(0\) \(-1\) \(0\) \(+\) \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-4q^{11}+\cdots\)
585.2.a.h \(1\) \(4.671\) \(\Q\) None None \(1\) \(0\) \(1\) \(-4\) \(+\) \(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
585.2.a.i \(1\) \(4.671\) \(\Q\) None None \(1\) \(0\) \(1\) \(2\) \(-\) \(q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots\)
585.2.a.j \(2\) \(4.671\) \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(-2\) \(-5\) \(+\) \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-3+\beta )q^{7}+\cdots\)
585.2.a.k \(2\) \(4.671\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(4\) \(-\) \(q+\beta q^{2}+q^{4}+q^{5}+2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
585.2.a.l \(2\) \(4.671\) \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(2\) \(-5\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(-3+\beta )q^{7}+\cdots\)
585.2.a.m \(2\) \(4.671\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-2\) \(4\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(2+2\beta )q^{7}+\cdots\)
585.2.a.n \(3\) \(4.671\) 3.3.316.1 None None \(0\) \(0\) \(3\) \(1\) \(-\) \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+q^{5}-\beta _{2}q^{7}+\cdots\)
585.2.b.a \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+iq^{5}+2iq^{7}+3iq^{8}+\cdots\)
585.2.b.b \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+iq^{5}+4iq^{7}+3iq^{8}+\cdots\)
585.2.b.c \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+iq^{5}-4iq^{7}+3iq^{8}+\cdots\)
585.2.b.d \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+iq^{5}-3iq^{7}-3iq^{11}+(2+\cdots)q^{13}+\cdots\)
585.2.b.e \(4\) \(4.671\) \(\Q(i, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
585.2.b.f \(4\) \(4.671\) \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{1}q^{2}-2q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
585.2.b.g \(6\) \(4.671\) 6.0.5089536.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
585.2.c.a \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+2q^{4}+(1+2i)q^{5}-iq^{7}+q^{11}+\cdots\)
585.2.c.b \(6\) \(4.671\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots\)
585.2.c.c \(10\) \(4.671\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
585.2.c.d \(12\) \(4.671\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{2}+(-1-\beta _{9})q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)
585.2.h.a \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(-4\) \(0\) \(-4\) \(-6\) \(q-2q^{2}+2q^{4}+(-2+i)q^{5}-3q^{7}+\cdots\)
585.2.h.b \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(-2\) \(0\) \(q-q^{2}-q^{4}+(-1-i)q^{5}+3q^{8}+(1+\cdots)q^{10}+\cdots\)
585.2.h.c \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(2\) \(0\) \(q+q^{2}-q^{4}+(1+i)q^{5}-3q^{8}+(1+i)q^{10}+\cdots\)
585.2.h.d \(2\) \(4.671\) \(\Q(\sqrt{-1}) \) None None \(4\) \(0\) \(4\) \(6\) \(q+2q^{2}+2q^{4}+(2-i)q^{5}+3q^{7}+(4+\cdots)q^{10}+\cdots\)
585.2.h.e \(4\) \(4.671\) \(\Q(\sqrt{-5}, \sqrt{13})\) \(\Q(\sqrt{-195}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\cdots\)
585.2.h.f \(8\) \(4.671\) 8.0.\(\cdots\).21 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(2-\beta _{2})q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots\)
585.2.h.g \(12\) \(4.671\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}+(1+\beta _{5}-\beta _{11})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
585.2.i.a \(2\) \(4.671\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-1\) \(4\) \(q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
585.2.i.b \(2\) \(4.671\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(1\) \(-2\) \(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
585.2.i.c \(2\) \(4.671\) \(\Q(\sqrt{-3}) \) None None \(1\) \(3\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
585.2.i.d \(2\) \(4.671\) \(\Q(\sqrt{-3}) \) None None \(2\) \(-3\) \(1\) \(0\) \(q+(2-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
585.2.i.e \(16\) \(4.671\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(1\) \(8\) \(11\) \(q-\beta _{6}q^{2}+(-\beta _{7}+\beta _{14})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
585.2.i.f \(16\) \(4.671\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(-2\) \(-8\) \(6\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
585.2.i.g \(26\) \(4.671\) None None \(1\) \(1\) \(-13\) \(-10\)
585.2.i.h \(30\) \(4.671\) None None \(1\) \(1\) \(15\) \(-10\)
585.2.j.a \(2\) \(4.671\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(1\) \(q+2\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
585.2.j.b \(2\) \(4.671\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(2\) \(-5\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+q^{5}-5\zeta_{6}q^{7}+\cdots\)
585.2.j.c \(4\) \(4.671\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(-4\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
585.2.j.d \(4\) \(4.671\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-1\) \(0\) \(4\) \(2\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
585.2.j.e \(4\) \(4.671\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(1\) \(0\) \(-4\) \(-4\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots\)
585.2.j.f \(6\) \(4.671\) 6.0.1714608.1 None None \(0\) \(0\) \(-6\) \(-3\) \(q+(\beta _{3}-\beta _{5})q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
585.2.j.g \(6\) \(4.671\) 6.0.591408.1 None None \(0\) \(0\) \(6\) \(5\) \(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
585.2.j.h \(10\) \(4.671\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-2\) \(0\) \(10\) \(-1\) \(q+(\beta _{1}+\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8})q^{4}+\cdots\)
585.2.j.i \(10\) \(4.671\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(2\) \(0\) \(-10\) \(-1\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)
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