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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
667.1.b.a \(1\) \(0.333\) \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-667}) \) \(\Q(\sqrt{29}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}-2q^{13}+q^{16}-q^{23}+\cdots\)
667.1.b.b \(2\) \(0.333\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
667.1.i.a \(6\) \(0.333\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-23}) \) None \(5\) \(-2\) \(0\) \(0\) \(q+(1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}-\zeta_{14}^{5})q^{3}+\cdots\)
667.1.i.b \(12\) \(0.333\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-23}) \) None \(-5\) \(2\) \(0\) \(0\) \(q+(-\zeta_{42}+\zeta_{42}^{14})q^{2}+(\zeta_{42}^{16}-\zeta_{42}^{17}+\cdots)q^{3}+\cdots\)
667.1.k.a \(6\) \(0.333\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-23}) \) None \(-7\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}+\zeta_{14}^{5}+\cdots)q^{3}+\cdots\)
667.1.k.b \(12\) \(0.333\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-23}) \) None \(7\) \(0\) \(0\) \(0\) \(q+(\zeta_{42}^{7}+\zeta_{42}^{8})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{10}+\cdots)q^{3}+\cdots\)
667.2.a.a \(10\) \(5.326\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-3\) \(-9\) \(-10\) \(1\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
667.2.a.b \(12\) \(5.326\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-3\) \(-3\) \(-16\) \(-7\) \(+\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)
667.2.a.c \(13\) \(5.326\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(4\) \(3\) \(16\) \(1\) \(-\) \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
667.2.a.d \(16\) \(5.326\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(3\) \(5\) \(16\) \(1\) \(-\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
667.2.c.a \(24\) \(5.326\) None None \(0\) \(0\) \(6\) \(-14\)
667.2.c.b \(30\) \(5.326\) None None \(0\) \(0\) \(-2\) \(6\)
667.2.f.a \(12\) \(5.326\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{9}-\beta _{10})q^{2}+(-\beta _{3}+\beta _{8}+\cdots)q^{3}+\cdots\)
667.2.f.b \(104\) \(5.326\) None None \(-8\) \(-4\) \(0\) \(0\)
667.2.g.a \(6\) \(5.326\) \(\Q(\zeta_{14})\) None None \(-2\) \(1\) \(2\) \(-13\) \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
667.2.g.b \(144\) \(5.326\) None None \(1\) \(-1\) \(-2\) \(19\)
667.2.g.c \(186\) \(5.326\) None None \(-1\) \(0\) \(-8\) \(-14\)
667.2.h.a \(280\) \(5.326\) None None \(0\) \(-2\) \(-8\) \(-10\)
667.2.h.b \(280\) \(5.326\) None None \(0\) \(-2\) \(0\) \(6\)
667.2.j.a \(144\) \(5.326\) None None \(0\) \(0\) \(-6\) \(14\)
667.2.j.b \(180\) \(5.326\) None None \(0\) \(0\) \(2\) \(-6\)
667.2.m.a \(580\) \(5.326\) None None \(0\) \(0\) \(-14\) \(-22\)
667.2.o.a \(72\) \(5.326\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\)
667.2.o.b \(624\) \(5.326\) None None \(-20\) \(-24\) \(0\) \(0\)
667.2.q.a \(1160\) \(5.326\) None None \(-14\) \(-18\) \(0\) \(-44\)
667.2.s.a \(3480\) \(5.326\) None None \(-49\) \(-45\) \(-49\) \(-49\)
667.2.u.a \(3480\) \(5.326\) None None \(-63\) \(-63\) \(-49\) \(-41\)
667.2.x.a \(6960\) \(5.326\) None None \(-112\) \(-108\) \(-154\) \(-110\)
667.4.a.a \(35\) \(39.354\) None None \(-6\) \(-22\) \(-80\) \(-38\) \(-\)
667.4.a.b \(38\) \(39.354\) None None \(-8\) \(-16\) \(-80\) \(-38\) \(-\)
667.4.a.c \(39\) \(39.354\) None None \(6\) \(2\) \(80\) \(18\) \(+\)
667.4.a.d \(42\) \(39.354\) None None \(12\) \(32\) \(80\) \(18\) \(+\)
667.6.a.a \(61\) \(106.976\) None None \(-24\) \(-97\) \(-400\) \(-243\) \(+\)
667.6.a.b \(64\) \(106.976\) None None \(-12\) \(-7\) \(-400\) \(-243\) \(+\)
667.6.a.c \(65\) \(106.976\) None None \(16\) \(47\) \(400\) \(149\) \(-\)
667.6.a.d \(68\) \(106.976\) None None \(12\) \(65\) \(400\) \(149\) \(-\)
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