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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
600.1.n.a \(1\) \(0.299\) \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
600.1.n.b \(1\) \(0.299\) \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
600.1.q.a \(4\) \(0.299\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots\)
600.1.q.b \(8\) \(0.299\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}^{4}q^{6}+\cdots\)
600.1.z.a \(8\) \(0.299\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}+\cdots\)
600.1.bj.a \(4\) \(0.299\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(-1\) \(-2\) \(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{5}+\cdots\)
600.1.bj.b \(4\) \(0.299\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(1\) \(-2\) \(q+\zeta_{10}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}q^{5}+\cdots\)
600.2.a.a \(1\) \(4.791\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-4\) \(-\) \(q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
600.2.a.b \(1\) \(4.791\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-3\) \(+\) \(q-q^{3}-3q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots\)
600.2.a.c \(1\) \(4.791\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{3}+q^{9}-4q^{11}-6q^{13}+6q^{17}+\cdots\)
600.2.a.d \(1\) \(4.791\) \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) \(-\) \(q-q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
600.2.a.e \(1\) \(4.791\) \(\Q\) None None \(0\) \(-1\) \(0\) \(5\) \(-\) \(q-q^{3}+5q^{7}+q^{9}-6q^{11}+3q^{13}+\cdots\)
600.2.a.f \(1\) \(4.791\) \(\Q\) None None \(0\) \(1\) \(0\) \(-5\) \(+\) \(q+q^{3}-5q^{7}+q^{9}-6q^{11}-3q^{13}+\cdots\)
600.2.a.g \(1\) \(4.791\) \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) \(-\) \(q+q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
600.2.a.h \(1\) \(4.791\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(-\) \(q+q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
600.2.a.i \(1\) \(4.791\) \(\Q\) None None \(0\) \(1\) \(0\) \(3\) \(-\) \(q+q^{3}+3q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots\)
600.2.b.a \(2\) \(4.791\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\beta q^{2}+(1-\beta )q^{3}-2q^{4}+(2+\beta )q^{6}+\cdots\)
600.2.b.b \(4\) \(4.791\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.b.c \(4\) \(4.791\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots\)
600.2.b.d \(4\) \(4.791\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.b.e \(8\) \(4.791\) 8.0.1649659456.5 None None \(-1\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
600.2.b.f \(8\) \(4.791\) 8.0.1649659456.5 None None \(1\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
600.2.b.g \(12\) \(4.791\) 12.0.\(\cdots\).1 None None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1+\beta _{4})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots\)
600.2.b.h \(12\) \(4.791\) 12.0.\(\cdots\).1 None None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
600.2.b.i \(16\) \(4.791\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{10}q^{2}+\beta _{5}q^{3}-\beta _{14}q^{4}+(\beta _{7}+\beta _{12}+\cdots)q^{6}+\cdots\)
600.2.d.a \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(0\) \(0\) \(q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots\)
600.2.d.b \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(0\) \(0\) \(q+(-1+i)q^{2}+q^{3}-2iq^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.d.c \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(0\) \(0\) \(q+(1+i)q^{2}-q^{3}+2iq^{4}+(-1-i)q^{6}+\cdots\)
600.2.d.d \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(0\) \(0\) \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
600.2.d.e \(6\) \(4.791\) 6.0.399424.1 None None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
600.2.d.f \(6\) \(4.791\) 6.0.399424.1 None None \(0\) \(6\) \(0\) \(0\) \(q-\beta _{2}q^{2}+q^{3}-\beta _{1}q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
600.2.d.g \(8\) \(4.791\) 8.0.214798336.3 None None \(-2\) \(-8\) \(0\) \(0\) \(q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.d.h \(8\) \(4.791\) 8.0.214798336.3 None None \(2\) \(8\) \(0\) \(0\) \(q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.f.a \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots\)
600.2.f.b \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}-4q^{11}+6iq^{13}+6iq^{17}+\cdots\)
600.2.f.c \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots\)
600.2.f.d \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-3iq^{7}-q^{9}+2q^{11}-3iq^{13}+\cdots\)
600.2.f.e \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
600.2.k.a \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(-4\) \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots\)
600.2.k.b \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(4\) \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-1+i)q^{6}+\cdots\)
600.2.k.c \(6\) \(4.791\) 6.0.399424.1 None None \(-2\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+\beta _{4}q^{6}+\cdots\)
600.2.k.d \(8\) \(4.791\) 8.0.214798336.3 None None \(-2\) \(0\) \(0\) \(8\) \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.k.e \(8\) \(4.791\) 8.0.214798336.3 None None \(2\) \(0\) \(0\) \(-8\) \(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.k.f \(12\) \(4.791\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{6}+\cdots\)
600.2.m.a \(4\) \(4.791\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\)
600.2.m.b \(8\) \(4.791\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{3}q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.m.c \(16\) \(4.791\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-1+\beta _{11}+\cdots)q^{6}+\cdots\)
600.2.m.d \(16\) \(4.791\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}-\beta _{14}q^{6}+\cdots\)
600.2.m.e \(24\) \(4.791\) None None \(0\) \(0\) \(0\) \(0\)
600.2.r.a \(4\) \(4.791\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(-8\) \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
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