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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1000.1.e.a \(2\) \(0.499\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-10}) \) None \(-2\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{4}+(1-\beta )q^{7}-q^{8}+q^{9}+\cdots\)
1000.1.e.b \(2\) \(0.499\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-10}) \) None \(2\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+q^{9}+\cdots\)
1000.1.g.a \(4\) \(0.499\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-q^{4}-\beta _{1}q^{7}+\beta _{3}q^{8}-q^{9}+\cdots\)
1000.2.a.a \(2\) \(7.985\) \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(q-\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
1000.2.a.b \(2\) \(7.985\) \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(0\) \(4\) \(+\) \(q-\beta q^{3}+(1+2\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
1000.2.a.c \(2\) \(7.985\) \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(0\) \(-4\) \(+\) \(q+\beta q^{3}+(-1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
1000.2.a.d \(2\) \(7.985\) \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(0\) \(1\) \(-\) \(q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots\)
1000.2.a.e \(4\) \(7.985\) 4.4.4400.1 None None \(0\) \(-4\) \(0\) \(-6\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{2}-\beta _{3})q^{7}+\cdots\)
1000.2.a.f \(4\) \(7.985\) 4.4.10025.1 None None \(0\) \(-1\) \(0\) \(-9\) \(-\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
1000.2.a.g \(4\) \(7.985\) 4.4.10025.1 None None \(0\) \(1\) \(0\) \(9\) \(-\) \(q+\beta _{1}q^{3}+(2+\beta _{3})q^{7}+(2-\beta _{2}+\beta _{3})q^{9}+\cdots\)
1000.2.a.h \(4\) \(7.985\) 4.4.4400.1 None None \(0\) \(4\) \(0\) \(6\) \(-\) \(q+(1+\beta _{1})q^{3}+(2+\beta _{2}-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
1000.2.c.a \(4\) \(7.985\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1000.2.c.b \(4\) \(7.985\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1000.2.c.c \(8\) \(7.985\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(3\beta _{2}+\beta _{3}-\beta _{7})q^{7}+(-3+\cdots)q^{9}+\cdots\)
1000.2.c.d \(8\) \(7.985\) 8.0.309760000.3 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1000.2.d.a \(4\) \(7.985\) \(\Q(i, \sqrt{5})\) None None \(-4\) \(0\) \(0\) \(2\) \(q+(-1+\beta _{3})q^{2}+2\beta _{1}q^{3}-2\beta _{3}q^{4}+\cdots\)
1000.2.d.b \(4\) \(7.985\) \(\Q(i, \sqrt{5})\) None None \(4\) \(0\) \(0\) \(-2\) \(q+(1+\beta _{3})q^{2}+2\beta _{1}q^{3}+2\beta _{3}q^{4}+(2\beta _{1}+\cdots)q^{6}+\cdots\)
1000.2.d.c \(40\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.d.d \(48\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.f.a \(4\) \(7.985\) \(\Q(i, \sqrt{5})\) None None \(-4\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{3})q^{2}+(-2-2\beta _{2})q^{3}+2\beta _{3}q^{4}+\cdots\)
1000.2.f.b \(4\) \(7.985\) \(\Q(i, \sqrt{5})\) None None \(4\) \(4\) \(0\) \(0\) \(q+(1-\beta _{3})q^{2}+(2+2\beta _{2})q^{3}-2\beta _{3}q^{4}+\cdots\)
1000.2.f.c \(20\) \(7.985\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(4\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{14}q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
1000.2.f.d \(20\) \(7.985\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(3\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{14}q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
1000.2.f.e \(48\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.k.a \(8\) \(7.985\) 8.0.1024000000.2 \(\Q(\sqrt{-10}) \) None \(-8\) \(0\) \(0\) \(4\) \(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+\beta _{3}q^{7}+\cdots\)
1000.2.k.b \(8\) \(7.985\) 8.0.1024000000.2 \(\Q(\sqrt{-10}) \) None \(8\) \(0\) \(0\) \(-4\) \(q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}-\beta _{3}q^{7}+(-2+\cdots)q^{8}+\cdots\)
1000.2.k.c \(16\) \(7.985\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-4\) \(4\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{7}+\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1000.2.k.d \(16\) \(7.985\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{15}q^{2}+(\beta _{1}+\beta _{14})q^{3}+(-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
1000.2.k.e \(16\) \(7.985\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(4\) \(-4\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(\beta _{3}+\beta _{7}-\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1000.2.k.f \(64\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.k.g \(64\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.m.a \(4\) \(7.985\) \(\Q(\zeta_{10})\) None None \(0\) \(-5\) \(0\) \(-6\) \(q+(-2+2\zeta_{10}+\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1000.2.m.b \(8\) \(7.985\) 8.0.58140625.2 None None \(0\) \(6\) \(0\) \(-4\) \(q+(1-\beta _{2})q^{3}+(-\beta _{1}+\beta _{4}+\beta _{5})q^{7}+\cdots\)
1000.2.m.c \(16\) \(7.985\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-1\) \(0\) \(6\) \(q-\beta _{1}q^{3}-\beta _{10}q^{7}+(\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
1000.2.m.d \(32\) \(7.985\) None None \(0\) \(-2\) \(0\) \(16\)
1000.2.m.e \(32\) \(7.985\) None None \(0\) \(2\) \(0\) \(-16\)
1000.2.o.a \(112\) \(7.985\) None None \(5\) \(0\) \(0\) \(0\)
1000.2.o.b \(224\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.q.a \(8\) \(7.985\) \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+\cdots\)
1000.2.q.b \(16\) \(7.985\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{9}+\beta _{10})q^{3}+(-\beta _{5}+\beta _{9}+\beta _{11}+\cdots)q^{7}+\cdots\)
1000.2.q.c \(32\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.q.d \(32\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.t.a \(112\) \(7.985\) None None \(3\) \(0\) \(0\) \(16\)
1000.2.t.b \(224\) \(7.985\) None None \(0\) \(0\) \(0\) \(0\)
1000.2.v.a \(8\) \(7.985\) \(\Q(\zeta_{20})\) None None \(-8\) \(0\) \(0\) \(4\) \(q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
1000.2.v.b \(8\) \(7.985\) \(\Q(\zeta_{20})\) None None \(-2\) \(0\) \(0\) \(-4\) \(q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
1000.2.v.c \(8\) \(7.985\) \(\Q(\zeta_{20})\) None None \(2\) \(0\) \(0\) \(4\) \(q+(\zeta_{20}+\zeta_{20}^{6})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
1000.2.v.d \(8\) \(7.985\) \(\Q(\zeta_{20})\) None None \(2\) \(0\) \(0\) \(4\) \(q+(\zeta_{20}+\zeta_{20}^{6})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
1000.2.v.e \(8\) \(7.985\) \(\Q(\zeta_{20})\) None None \(8\) \(0\) \(0\) \(-4\) \(q+(1-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
1000.2.v.f \(8\) \(7.985\) \(\Q(\zeta_{20})\) None None \(8\) \(0\) \(0\) \(-4\) \(q+(1-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
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