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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4000.1.b.a \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{3}-\beta _{3}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
4000.1.b.b \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-\beta _{3}q^{11}+\cdots\)
4000.1.e.a \(2\) \(1.996\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\beta q^{7}+q^{9}+(1-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
4000.1.e.b \(2\) \(1.996\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\beta q^{7}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots\)
4000.1.g.a \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{7}-q^{9}-\beta _{2}q^{11}-\beta _{1}q^{13}+\cdots\)
4000.1.h.a \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(0\) \(4\) \(q+(-1-\beta _{2})q^{3}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
4000.1.h.b \(4\) \(1.996\) \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(0\) \(-4\) \(q+(1+\beta _{2})q^{3}-q^{7}+(1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
4000.1.p.a \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(-\zeta_{20}+\zeta_{20}^{4})q^{3}+(\zeta_{20}^{7}-\zeta_{20}^{8}+\cdots)q^{7}+\cdots\)
4000.1.p.b \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{2}-\zeta_{20}^{3}+\cdots)q^{7}+\cdots\)
4000.1.bf.a \(8\) \(1.996\) \(\Q(\zeta_{20})\) None None \(0\) \(-2\) \(0\) \(4\) \(q-\zeta_{20}^{2}q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6})q^{7}+\cdots\)
4000.1.bf.b \(8\) \(1.996\) \(\Q(\zeta_{20})\) None None \(0\) \(2\) \(0\) \(-4\) \(q+\zeta_{20}^{2}q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{7}+(-\zeta_{20}^{3}+\cdots)q^{13}+\cdots\)
4000.1.bh.a \(8\) \(1.996\) \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{3}+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{13}+\cdots\)
4000.1.bo.a \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{9}+(-\zeta_{20}^{6}-\zeta_{20}^{7})q^{13}+\cdots\)
4000.1.bo.b \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2})q^{13}+(\zeta_{20}^{4}+\cdots)q^{17}+\cdots\)
4000.1.bo.c \(8\) \(1.996\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{9}+(\zeta_{20}^{6}+\zeta_{20}^{7})q^{13}+(\zeta_{20}^{2}+\cdots)q^{17}+\cdots\)
4000.1.cq.a \(40\) \(1.996\) \(\Q(\zeta_{100})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{100}^{13}q^{5}-\zeta_{100}^{49}q^{9}+(\zeta_{100}^{2}-\zeta_{100}^{21}+\cdots)q^{13}+\cdots\)
4000.2.a.a \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-5}) \) None \(0\) \(-6\) \(0\) \(-8\) \(+\) \(q+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
4000.2.a.b \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(-2\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots\)
4000.2.a.c \(4\) \(31.940\) 4.4.16400.1 None None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(q+\beta _{2}q^{3}+(-1-\beta _{2})q^{7}+(-2-\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.a.d \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
4000.2.a.e \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}-2\beta _{3}q^{11}+\cdots\)
4000.2.a.f \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{3}+\beta _{3}q^{7}+\beta _{2}q^{9}+2\beta _{3}q^{11}+\cdots\)
4000.2.a.g \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
4000.2.a.h \(4\) \(31.940\) 4.4.16400.1 None None \(0\) \(2\) \(0\) \(2\) \(+\) \(q-\beta _{2}q^{3}+(1+\beta _{2})q^{7}+(-2-\beta _{2})q^{9}+\cdots\)
4000.2.a.i \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(2\) \(-\) \(q+(1+\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
4000.2.a.j \(4\) \(31.940\) \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-5}) \) None \(0\) \(6\) \(0\) \(8\) \(-\) \(q+(2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1+2\beta _{1}+\cdots)q^{7}+\cdots\)
4000.2.a.k \(6\) \(31.940\) 6.6.30040000.1 None None \(0\) \(0\) \(0\) \(-3\) \(+\) \(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.l \(6\) \(31.940\) 6.6.30040000.1 None None \(0\) \(0\) \(0\) \(-3\) \(-\) \(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.m \(6\) \(31.940\) 6.6.30040000.1 None None \(0\) \(0\) \(0\) \(3\) \(+\) \(q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.n \(6\) \(31.940\) 6.6.30040000.1 None None \(0\) \(0\) \(0\) \(3\) \(-\) \(q-\beta _{1}q^{3}+(1-\beta _{5})q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
4000.2.a.o \(8\) \(31.940\) 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots\)
4000.2.a.p \(8\) \(31.940\) 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{4}q^{3}-\beta _{6}q^{7}+(1-\beta _{5})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
4000.2.a.q \(8\) \(31.940\) 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
4000.2.a.r \(8\) \(31.940\) 8.8.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
4000.2.c.a \(8\) \(31.940\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{3}+(\zeta_{20}^{2}-2\zeta_{20}^{3}+\cdots)q^{7}+\cdots\)
4000.2.c.b \(8\) \(31.940\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{3}q^{3}+(\zeta_{20}^{3}-\zeta_{20}^{7})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4000.2.c.c \(8\) \(31.940\) \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{3}+(\zeta_{20}^{2}-\zeta_{20}^{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
4000.2.c.d \(8\) \(31.940\) \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{2}q^{3}-\zeta_{20}^{7}q^{7}-\zeta_{20}^{5}q^{9}+\cdots\)
4000.2.c.e \(8\) \(31.940\) 8.0.268960000.3 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.c.f \(12\) \(31.940\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots\)
4000.2.c.g \(12\) \(31.940\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{11}q^{7}+(\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{9}+\cdots\)
4000.2.c.h \(16\) \(31.940\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{15}q^{7}+(-2+\beta _{4})q^{9}+\cdots\)
4000.2.c.i \(16\) \(31.940\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{12}q^{7}+(-1+\beta _{6})q^{9}+\cdots\)
4000.2.d.a \(4\) \(31.940\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-2\) \(q+2\beta _{1}q^{3}+(1+3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.d.b \(4\) \(31.940\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(2\) \(q+2\beta _{1}q^{3}+(-1-3\beta _{2})q^{7}+(-1+4\beta _{2}+\cdots)q^{9}+\cdots\)
4000.2.d.c \(40\) \(31.940\) None None \(0\) \(0\) \(0\) \(0\)
4000.2.d.d \(48\) \(31.940\) None None \(0\) \(0\) \(0\) \(0\)
4000.2.f.a \(4\) \(31.940\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-2-2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots\)
4000.2.f.b \(4\) \(31.940\) \(\Q(i, \sqrt{5})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(2+2\beta _{2})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(5+\cdots)q^{9}+\cdots\)
4000.2.f.c \(20\) \(31.940\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{9}q^{3}+\beta _{5}q^{7}+(\beta _{1}-\beta _{7}+\beta _{10}+\cdots)q^{9}+\cdots\)
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