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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
760.1.b.a \(8\) \(0.379\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)
760.1.bm.a \(2\) \(0.379\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+q^{8}+\cdots\)
760.1.bm.b \(2\) \(0.379\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(1\) \(2\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}-q^{8}+\cdots\)
760.1.bt.a \(4\) \(0.379\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}+\cdots\)
760.1.bz.a \(6\) \(0.379\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}-\zeta_{18}^{5}q^{5}+\cdots\)
760.1.bz.b \(6\) \(0.379\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{5}q^{5}+\cdots\)
760.2.a.a \(1\) \(6.069\) \(\Q\) None None \(0\) \(-2\) \(1\) \(0\) \(+\) \(q-2q^{3}+q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots\)
760.2.a.b \(1\) \(6.069\) \(\Q\) None None \(0\) \(-2\) \(1\) \(4\) \(-\) \(q-2q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
760.2.a.c \(1\) \(6.069\) \(\Q\) None None \(0\) \(0\) \(1\) \(0\) \(+\) \(q+q^{5}-3q^{9}-4q^{11}-6q^{13}-6q^{17}+\cdots\)
760.2.a.d \(1\) \(6.069\) \(\Q\) None None \(0\) \(2\) \(1\) \(4\) \(-\) \(q+2q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
760.2.a.e \(1\) \(6.069\) \(\Q\) None None \(0\) \(3\) \(1\) \(-1\) \(-\) \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+4q^{11}+\cdots\)
760.2.a.f \(2\) \(6.069\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) \(-\) \(q+\beta q^{3}-q^{5}+2\beta q^{7}-q^{9}+(2+2\beta )q^{11}+\cdots\)
760.2.a.g \(2\) \(6.069\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(0\) \(-\) \(q+(1+\beta )q^{3}-q^{5}+(1+2\beta )q^{9}+2q^{11}+\cdots\)
760.2.a.h \(3\) \(6.069\) 3.3.568.1 None None \(0\) \(-1\) \(-3\) \(-5\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(-2-\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
760.2.a.i \(3\) \(6.069\) 3.3.316.1 None None \(0\) \(-1\) \(-3\) \(-1\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
760.2.a.j \(3\) \(6.069\) 3.3.229.1 None None \(0\) \(-1\) \(3\) \(-1\) \(-\) \(q+\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots\)
760.2.d.a \(2\) \(6.069\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots\)
760.2.d.b \(4\) \(6.069\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
760.2.d.c \(4\) \(6.069\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
760.2.d.d \(4\) \(6.069\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(1+\zeta_{8})q^{5}+(-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
760.2.d.e \(12\) \(6.069\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{11}q^{3}-\beta _{1}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots\)
760.2.e.a \(80\) \(6.069\) None None \(0\) \(0\) \(0\) \(0\)
760.2.f.a \(28\) \(6.069\) None None \(2\) \(0\) \(0\) \(4\)
760.2.f.b \(44\) \(6.069\) None None \(2\) \(0\) \(0\) \(4\)
760.2.k.a \(108\) \(6.069\) None None \(0\) \(0\) \(0\) \(0\)
760.2.p.a \(4\) \(6.069\) \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{5}+2\beta _{3}q^{7}+\cdots\)
760.2.p.b \(4\) \(6.069\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.c \(4\) \(6.069\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.d \(8\) \(6.069\) 8.0.1499238400.2 None None \(-8\) \(-8\) \(0\) \(0\) \(q+(-1-\beta _{5})q^{2}-q^{3}+2\beta _{5}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
760.2.p.e \(8\) \(6.069\) 8.0.5473632256.3 None None \(-4\) \(8\) \(0\) \(0\) \(q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.f \(8\) \(6.069\) 8.0.5473632256.3 None None \(4\) \(-8\) \(0\) \(0\) \(q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.g \(8\) \(6.069\) 8.0.1499238400.2 None None \(8\) \(8\) \(0\) \(0\) \(q+(1+\beta _{5})q^{2}+q^{3}+2\beta _{5}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
760.2.p.h \(16\) \(6.069\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}+\cdots\)
760.2.p.i \(56\) \(6.069\) None None \(0\) \(0\) \(0\) \(0\)
760.2.q.a \(2\) \(6.069\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(-4\) \(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots\)
760.2.q.b \(2\) \(6.069\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(-1\) \(8\) \(q+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+4q^{7}+\cdots\)
760.2.q.c \(2\) \(6.069\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(1\) \(0\) \(q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
760.2.q.d \(8\) \(6.069\) 8.0.\(\cdots\).1 None None \(0\) \(-1\) \(-4\) \(-6\) \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots\)
760.2.q.e \(8\) \(6.069\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(4\) \(-4\) \(q+\beta _{1}q^{3}+(1-\beta _{5})q^{5}+(-1-\beta _{4}+2\beta _{7})q^{7}+\cdots\)
760.2.q.f \(8\) \(6.069\) 8.0.4601315889.1 None None \(0\) \(1\) \(-4\) \(4\) \(q-\beta _{7}q^{3}-\beta _{5}q^{5}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
760.2.q.g \(10\) \(6.069\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(1\) \(5\) \(10\) \(q+\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(1+\beta _{5})q^{7}+\cdots\)
760.2.t.a \(232\) \(6.069\) None None \(0\) \(0\) \(0\) \(-8\)
760.2.v.a \(12\) \(6.069\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(-12\) \(-4\) \(q+\beta _{10}q^{3}+(-1-2\beta _{5})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
760.2.v.b \(48\) \(6.069\) None None \(0\) \(0\) \(12\) \(4\)
760.2.w.a \(2\) \(6.069\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(4\) \(2\) \(-6\) \(q+(-1+i)q^{2}+(2-2i)q^{3}-2iq^{4}+\cdots\)
760.2.w.b \(2\) \(6.069\) \(\Q(\sqrt{-1}) \) None None \(2\) \(4\) \(-2\) \(6\) \(q+(1-i)q^{2}+(2-2i)q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
760.2.w.c \(104\) \(6.069\) None None \(0\) \(-8\) \(0\) \(0\)
760.2.w.d \(108\) \(6.069\) None None \(0\) \(0\) \(0\) \(0\)
760.2.z.a \(232\) \(6.069\) None None \(0\) \(0\) \(0\) \(0\)
760.2.bf.a \(8\) \(6.069\) 8.0.207360000.2 \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(2+2\beta _{4})q^{4}-\beta _{6}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
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