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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
170.2.a.a \(1\) \(1.357\) \(\Q\) None \(-1\) \(-2\) \(-1\) \(2\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\)
170.2.a.b \(1\) \(1.357\) \(\Q\) None \(-1\) \(-2\) \(1\) \(-2\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
170.2.a.c \(1\) \(1.357\) \(\Q\) None \(-1\) \(1\) \(1\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
170.2.a.d \(1\) \(1.357\) \(\Q\) None \(-1\) \(3\) \(-1\) \(2\) \(-\) \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+2q^{7}+\cdots\)
170.2.a.e \(1\) \(1.357\) \(\Q\) None \(1\) \(1\) \(-1\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
170.2.a.f \(2\) \(1.357\) \(\Q(\sqrt{17}) \) None \(2\) \(-1\) \(2\) \(2\) \(-\) \(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+2\beta q^{7}+\cdots\)
170.2.b.a \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+iq^{3}+q^{4}+iq^{5}-iq^{6}-q^{8}+\cdots\)
170.2.b.b \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+3iq^{3}+q^{4}+iq^{5}+3iq^{6}+\cdots\)
170.2.b.c \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+iq^{5}+2iq^{7}+q^{8}+3q^{9}+\cdots\)
170.2.c.a \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}-q^{6}+\cdots\)
170.2.c.b \(6\) \(1.357\) 6.0.5161984.1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}-q^{4}+\cdots\)
170.2.d.a \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(-4\) \(-4\) \(q+iq^{2}-q^{3}-q^{4}+(-2+i)q^{5}-iq^{6}+\cdots\)
170.2.d.b \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(4\) \(4\) \(q+iq^{2}+q^{3}-q^{4}+(2-i)q^{5}+iq^{6}+\cdots\)
170.2.d.c \(4\) \(1.357\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(-2\zeta_{8}+2\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
170.2.g.a \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(-2\) \(2\) \(2\) \(-6\) \(q-q^{2}+(1-i)q^{3}+q^{4}+(1-2i)q^{5}+\cdots\)
170.2.g.b \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(-2\) \(2\) \(2\) \(2\) \(q-q^{2}+(1-i)q^{3}+q^{4}+(1+2i)q^{5}+\cdots\)
170.2.g.c \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(2\) \(-2\) \(-4\) \(6\) \(q+q^{2}+(-1+i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
170.2.g.d \(2\) \(1.357\) \(\Q(\sqrt{-1}) \) None \(2\) \(-2\) \(4\) \(-2\) \(q+q^{2}+(-1+i)q^{3}+q^{4}+(2+i)q^{5}+\cdots\)
170.2.g.e \(4\) \(1.357\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(4\) \(q-q^{2}+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+\cdots\)
170.2.g.f \(4\) \(1.357\) \(\Q(\zeta_{8})\) None \(4\) \(4\) \(0\) \(-4\) \(q+q^{2}+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+(\zeta_{8}+\cdots)q^{5}+\cdots\)
170.2.h.a \(4\) \(1.357\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) \(q-\zeta_{8}^{2}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}-q^{4}+\cdots\)
170.2.h.b \(8\) \(1.357\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{2}-\beta _{7}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{6}q^{6}+\cdots\)
170.2.k.a \(8\) \(1.357\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{2}+(\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{3}+\cdots)q^{3}+\cdots\)
170.2.k.b \(16\) \(1.357\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(-\beta _{6}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots\)
170.2.n.a \(20\) \(1.357\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{10}q^{4}+\beta _{14}q^{5}+\cdots\)
170.2.n.b \(20\) \(1.357\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{8}q^{2}+\beta _{5}q^{3}+\beta _{10}q^{4}-\beta _{16}q^{5}+\cdots\)
170.2.o.a \(32\) \(1.357\) None \(0\) \(0\) \(0\) \(0\)
170.2.o.b \(40\) \(1.357\) None \(0\) \(0\) \(0\) \(0\)
170.2.r.a \(32\) \(1.357\) None \(0\) \(0\) \(0\) \(0\)
170.2.r.b \(40\) \(1.357\) None \(0\) \(0\) \(0\) \(0\)
170.3.e.a \(2\) \(4.632\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-i)q^{2}+4iq^{3}+2iq^{4}-5iq^{5}+\cdots\)
170.3.e.b \(16\) \(4.632\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(-2\) \(0\) \(q+(1-\beta _{5})q^{2}-\beta _{1}q^{3}-2\beta _{5}q^{4}-\beta _{12}q^{5}+\cdots\)
170.3.e.c \(18\) \(4.632\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-18\) \(0\) \(8\) \(0\) \(q+(-1-\beta _{4})q^{2}-\beta _{1}q^{3}+2\beta _{4}q^{4}+\cdots\)
170.3.f.a \(16\) \(4.632\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-16\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{3})q^{2}+\beta _{1}q^{3}-2\beta _{3}q^{4}+\cdots\)
170.3.f.b \(20\) \(4.632\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(20\) \(0\) \(0\) \(0\) \(q+(1+\beta _{5})q^{2}+\beta _{8}q^{3}+2\beta _{5}q^{4}+\beta _{9}q^{5}+\cdots\)
170.3.i.a \(16\) \(4.632\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(8\) \(-8\) \(4\) \(q+(-1-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{4})q^{3}+\cdots\)
170.3.i.b \(16\) \(4.632\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(8\) \(12\) \(q+(1+\beta _{3})q^{2}-\beta _{1}q^{3}+2\beta _{3}q^{4}-\beta _{10}q^{5}+\cdots\)
170.3.j.a \(2\) \(4.632\) \(\Q(\sqrt{-1}) \) None \(2\) \(8\) \(-10\) \(16\) \(q+(1-i)q^{2}+4q^{3}-2iq^{4}-5q^{5}+\cdots\)
170.3.j.b \(16\) \(4.632\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-16\) \(0\) \(2\) \(-12\) \(q+(-1-\beta _{5})q^{2}+\beta _{3}q^{3}+2\beta _{5}q^{4}+\cdots\)
170.3.j.c \(18\) \(4.632\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(18\) \(-8\) \(18\) \(-28\) \(q+(1+\beta _{4})q^{2}-\beta _{3}q^{3}+2\beta _{4}q^{4}+(1+\cdots)q^{5}+\cdots\)
170.3.l.a \(36\) \(4.632\) None \(0\) \(0\) \(-4\) \(-12\)
170.3.l.b \(36\) \(4.632\) None \(0\) \(0\) \(0\) \(-12\)
170.3.m.a \(36\) \(4.632\) None \(0\) \(0\) \(-8\) \(12\)
170.3.m.b \(36\) \(4.632\) None \(0\) \(0\) \(-4\) \(12\)
170.3.p.a \(48\) \(4.632\) None \(0\) \(-16\) \(0\) \(-16\)
170.3.p.b \(48\) \(4.632\) None \(0\) \(16\) \(0\) \(16\)
170.3.q.a \(72\) \(4.632\) None \(0\) \(0\) \(0\) \(0\)
170.3.q.b \(72\) \(4.632\) None \(0\) \(0\) \(0\) \(0\)
170.4.a.a \(1\) \(10.030\) \(\Q\) None \(-2\) \(4\) \(-5\) \(-4\) \(-\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
170.4.a.b \(1\) \(10.030\) \(\Q\) None \(2\) \(7\) \(5\) \(-10\) \(+\) \(q+2q^{2}+7q^{3}+4q^{4}+5q^{5}+14q^{6}+\cdots\)
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