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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
320.1.h.a \(1\) \(0.160\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots\)
320.1.p.a \(2\) \(0.160\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+iq^{9}+(1-i)q^{13}+(-1-i+\cdots)q^{17}+\cdots\)
320.2.a.a \(1\) \(2.555\) \(\Q\) None None \(0\) \(-2\) \(1\) \(-2\) \(+\) \(q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots\)
320.2.a.b \(1\) \(2.555\) \(\Q\) None None \(0\) \(-2\) \(1\) \(2\) \(-\) \(q-2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
320.2.a.c \(1\) \(2.555\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-4\) \(+\) \(q-q^{5}-4q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots\)
320.2.a.d \(1\) \(2.555\) \(\Q\) None None \(0\) \(0\) \(-1\) \(4\) \(-\) \(q-q^{5}+4q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots\)
320.2.a.e \(1\) \(2.555\) \(\Q\) None None \(0\) \(2\) \(1\) \(-2\) \(-\) \(q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
320.2.a.f \(1\) \(2.555\) \(\Q\) None None \(0\) \(2\) \(1\) \(2\) \(-\) \(q+2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
320.2.a.g \(2\) \(2.555\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) \(-\) \(q+\beta q^{3}-q^{5}+\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)
320.2.c.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}+3q^{9}+2iq^{13}+4iq^{17}+\cdots\)
320.2.c.b \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+i)q^{5}+iq^{7}-q^{9}-4q^{11}+\cdots\)
320.2.c.c \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots\)
320.2.c.d \(4\) \(2.555\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\)
320.2.d.a \(4\) \(2.555\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-12\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(-3+\cdots)q^{7}+\cdots\)
320.2.d.b \(4\) \(2.555\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(12\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots\)
320.2.f.a \(4\) \(2.555\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{1}q^{11}+\cdots\)
320.2.f.b \(8\) \(2.555\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{3}-\zeta_{24}^{6}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)
320.2.j.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(6\) \(q-2iq^{3}+(1+2i)q^{5}+(3+3i)q^{7}+\cdots\)
320.2.j.b \(18\) \(2.555\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(-4\) \(-2\) \(q-\beta _{12}q^{3}-\beta _{4}q^{5}+\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots\)
320.2.l.a \(16\) \(2.555\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{5}+\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
320.2.n.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(4\) \(4\) \(q+(-2-2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots\)
320.2.n.b \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-2\) \(-6\) \(q+(-1-i)q^{3}+(-1-2i)q^{5}+(-3+\cdots)q^{7}+\cdots\)
320.2.n.c \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-2\) \(2\) \(q+(-1-i)q^{3}+(-1+2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.n.d \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(-2-i)q^{5}-3iq^{9}+(5-5i)q^{13}+\cdots\)
320.2.n.e \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(2-i)q^{5}-3iq^{9}+(1-i)q^{13}+(3+\cdots)q^{17}+\cdots\)
320.2.n.f \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-2\) \(-2\) \(q+(1+i)q^{3}+(-1+2i)q^{5}+(-1+i)q^{7}+\cdots\)
320.2.n.g \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-2\) \(6\) \(q+(1+i)q^{3}+(-1-2i)q^{5}+(3-3i)q^{7}+\cdots\)
320.2.n.h \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(4\) \(-4\) \(q+(2+2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots\)
320.2.n.i \(4\) \(2.555\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{12}^{2}q^{3}+(1+2\zeta_{12})q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
320.2.o.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-2\) \(-2\) \(q+(-1+i)q^{3}+(-1-2i)q^{5}+(-1+\cdots)q^{7}+\cdots\)
320.2.o.b \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(2\) \(q+(-1+i)q^{3}+(1+2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.o.c \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-2\) \(2\) \(q+(1-i)q^{3}+(-1-2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.o.d \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(-2\) \(q+(1-i)q^{3}+(1+2i)q^{5}+(-1+i)q^{7}+\cdots\)
320.2.o.e \(8\) \(2.555\) 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(-4\) \(q+(-\beta _{2}-\beta _{7})q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots\)
320.2.o.f \(8\) \(2.555\) 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(4\) \(q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)
320.2.q.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(0\) \(q+(-1-i)q^{3}+(1+2i)q^{5}-iq^{9}+\cdots\)
320.2.q.b \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(4\) \(0\) \(q+(1+i)q^{3}+(2+i)q^{5}-iq^{9}+(3+3i)q^{11}+\cdots\)
320.2.q.c \(16\) \(2.555\) 16.0.\(\cdots\).1 None None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{11}q^{3}+(-1-\beta _{6}-\beta _{10})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
320.2.s.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(-4\) \(6\) \(q+2q^{3}+(-2+i)q^{5}+(3+3i)q^{7}+\cdots\)
320.2.s.b \(18\) \(2.555\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(2\) \(-2\) \(q-\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
320.2.bd.a \(368\) \(2.555\) None None \(-8\) \(-8\) \(-8\) \(-8\)
320.2.be.a \(256\) \(2.555\) None None \(0\) \(0\) \(0\) \(0\)
320.2.bf.a \(368\) \(2.555\) None None \(0\) \(0\) \(-8\) \(0\)
320.2.bj.a \(368\) \(2.555\) None None \(-8\) \(-8\) \(-8\) \(-8\)
320.3.b.a \(4\) \(8.719\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots\)
320.3.b.b \(4\) \(8.719\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-4\beta _{2})q^{7}+(-5+\cdots)q^{9}+\cdots\)
320.3.b.c \(4\) \(8.719\) \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{7}+\cdots\)
320.3.b.d \(4\) \(8.719\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots\)
320.3.e.a \(8\) \(8.719\) 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-\beta _{4}-\beta _{6})q^{5}+\beta _{2}q^{7}+\cdots\)
320.3.e.b \(16\) \(8.719\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(-6-\beta _{5}+\cdots)q^{9}+\cdots\)
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