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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
325.1.u.a \(8\) \(0.162\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}-\zeta_{24}^{11}q^{3}-\zeta_{24}^{4}q^{6}+\cdots\)
325.2.a.a \(1\) \(2.595\) \(\Q\) None None \(-2\) \(-1\) \(0\) \(-2\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}-2q^{7}+\cdots\)
325.2.a.b \(1\) \(2.595\) \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) \(+\) \(q-q^{3}-2q^{4}+4q^{7}-2q^{9}-6q^{11}+\cdots\)
325.2.a.c \(1\) \(2.595\) \(\Q\) None None \(0\) \(1\) \(0\) \(-4\) \(+\) \(q+q^{3}-2q^{4}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
325.2.a.d \(1\) \(2.595\) \(\Q\) None None \(1\) \(2\) \(0\) \(4\) \(-\) \(q+q^{2}+2q^{3}-q^{4}+2q^{6}+4q^{7}-3q^{8}+\cdots\)
325.2.a.e \(1\) \(2.595\) \(\Q\) None None \(2\) \(1\) \(0\) \(2\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots\)
325.2.a.f \(2\) \(2.595\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(-2\) \(-\) \(q+(-1+\beta )q^{2}-2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
325.2.a.g \(2\) \(2.595\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-4\) \(+\) \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}+(-3-\beta )q^{6}+\cdots\)
325.2.a.h \(2\) \(2.595\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(2\) \(-\) \(q+(1+\beta )q^{2}-2\beta q^{3}+(1+2\beta )q^{4}+(-4+\cdots)q^{6}+\cdots\)
325.2.a.i \(2\) \(2.595\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(-4\) \(-\) \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(2+\cdots)q^{6}+\cdots\)
325.2.a.j \(3\) \(2.595\) 3.3.148.1 None None \(-3\) \(-4\) \(0\) \(-2\) \(+\) \(q+(-1-\beta _{2})q^{2}+(-1-\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots\)
325.2.a.k \(3\) \(2.595\) 3.3.148.1 None None \(3\) \(4\) \(0\) \(2\) \(-\) \(q+(1+\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
325.2.b.a \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
325.2.b.b \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}+4iq^{7}+\cdots\)
325.2.b.c \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2q^{4}+4iq^{7}+2q^{9}-6q^{11}+\cdots\)
325.2.b.d \(4\) \(2.595\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
325.2.b.e \(4\) \(2.595\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
325.2.b.f \(4\) \(2.595\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
325.2.c.a \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}-2iq^{6}-5iq^{7}+\cdots\)
325.2.c.b \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}-2iq^{6}+3iq^{8}+\cdots\)
325.2.c.c \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-2q^{4}-iq^{6}+iq^{7}+\cdots\)
325.2.c.d \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-2q^{4}+iq^{6}+iq^{7}+\cdots\)
325.2.c.e \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(0\) \(0\) \(q+iq^{2}+2q^{3}+q^{4}+2iq^{6}+3iq^{8}+\cdots\)
325.2.c.f \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(0\) \(0\) \(q+iq^{2}+2q^{3}+q^{4}+2iq^{6}-5iq^{7}+\cdots\)
325.2.c.g \(6\) \(2.595\) 6.0.5089536.1 None None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(1+\beta _{1})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)
325.2.d.a \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(-4\) \(0\) \(0\) \(-4\) \(q-2q^{2}+iq^{3}+2q^{4}-2iq^{6}-2q^{7}+\cdots\)
325.2.d.b \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(10\) \(q-q^{2}+2iq^{3}-q^{4}-2iq^{6}+5q^{7}+\cdots\)
325.2.d.c \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(-10\) \(q+q^{2}+2iq^{3}-q^{4}+2iq^{6}-5q^{7}+\cdots\)
325.2.d.d \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(4\) \(0\) \(0\) \(4\) \(q+2q^{2}+iq^{3}+2q^{4}+2iq^{6}+2q^{7}+\cdots\)
325.2.d.e \(6\) \(2.595\) 6.0.5089536.1 None None \(-2\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
325.2.d.f \(6\) \(2.595\) 6.0.5089536.1 None None \(2\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
325.2.e.a \(4\) \(2.595\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-1\) \(2\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.b \(4\) \(2.595\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(1\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{2}+(1-2\beta _{1}+\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.c \(10\) \(2.595\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(-3\) \(0\) \(2\) \(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{8})q^{3}+\cdots\)
325.2.e.d \(10\) \(2.595\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(3\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{8})q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\)
325.2.e.e \(12\) \(2.595\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(\beta _{6}-\beta _{11})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.f.a \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(4\) \(q-iq^{2}+(-1+i)q^{3}+q^{4}+(1+i)q^{6}+\cdots\)
325.2.f.b \(8\) \(2.595\) 8.0.619810816.2 None None \(0\) \(6\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
325.2.f.c \(12\) \(2.595\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}-\beta _{4}q^{3}+(-2+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
325.2.f.d \(16\) \(2.595\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{13}q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(1+\beta _{4}+\cdots)q^{6}+\cdots\)
325.2.k.a \(2\) \(2.595\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(0\) \(0\) \(q-q^{2}+(-1-i)q^{3}-q^{4}+(1+i)q^{6}+\cdots\)
325.2.k.b \(8\) \(2.595\) 8.0.619810816.2 None None \(4\) \(6\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
325.2.k.c \(12\) \(2.595\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(2-\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
325.2.k.d \(16\) \(2.595\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{1}q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)
325.2.l.a \(4\) \(2.595\) \(\Q(\zeta_{10})\) None None \(3\) \(4\) \(-5\) \(-2\) \(q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots\)
325.2.l.b \(56\) \(2.595\) None None \(0\) \(-2\) \(9\) \(-20\)
325.2.l.c \(60\) \(2.595\) None None \(-3\) \(-6\) \(2\) \(10\)
325.2.m.a \(4\) \(2.595\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
325.2.m.b \(8\) \(2.595\) 8.0.22581504.2 None None \(-2\) \(6\) \(0\) \(10\) \(q+(1-\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
325.2.m.c \(8\) \(2.595\) 8.0.22581504.2 None None \(2\) \(-6\) \(0\) \(-10\) \(q+(-1+\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-2+\beta _{3}+\cdots)q^{3}+\cdots\)
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