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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
99.1.h.a \(2\) \(0.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)
99.2.a.a \(1\) \(0.791\) \(\Q\) None None \(-1\) \(0\) \(-4\) \(-2\) \(+\) \(q-q^{2}-q^{4}-4q^{5}-2q^{7}+3q^{8}+4q^{10}+\cdots\)
99.2.a.b \(1\) \(0.791\) \(\Q\) None None \(-1\) \(0\) \(2\) \(4\) \(-\) \(q-q^{2}-q^{4}+2q^{5}+4q^{7}+3q^{8}-2q^{10}+\cdots\)
99.2.a.c \(1\) \(0.791\) \(\Q\) None None \(1\) \(0\) \(4\) \(-2\) \(-\) \(q+q^{2}-q^{4}+4q^{5}-2q^{7}-3q^{8}+4q^{10}+\cdots\)
99.2.a.d \(1\) \(0.791\) \(\Q\) None None \(2\) \(0\) \(-1\) \(-2\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}-2q^{7}-2q^{10}+\cdots\)
99.2.d.a \(4\) \(0.791\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{8}+\cdots\)
99.2.e.a \(2\) \(0.791\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-1\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
99.2.e.b \(2\) \(0.791\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(3\) \(4\) \(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
99.2.e.c \(2\) \(0.791\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(2\) \(-4\) \(q+(2-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
99.2.e.d \(6\) \(0.791\) \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(-3\) \(3\) \(q+(\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
99.2.e.e \(8\) \(0.791\) 8.0.508277025.1 None None \(-1\) \(5\) \(-4\) \(-1\) \(q+(-\beta _{2}-\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)
99.2.f.a \(4\) \(0.791\) \(\Q(\zeta_{10})\) None None \(1\) \(0\) \(3\) \(1\) \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
99.2.f.b \(4\) \(0.791\) \(\Q(\zeta_{10})\) None None \(3\) \(0\) \(1\) \(-3\) \(q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10})q^{4}+(1-2\zeta_{10}+\cdots)q^{5}+\cdots\)
99.2.f.c \(8\) \(0.791\) 8.0.484000000.9 None None \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{1}q^{2}+(1+2\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+\beta _{7})q^{5}+\cdots\)
99.2.g.a \(4\) \(0.791\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-9\) \(0\) \(q-\beta _{1}q^{3}+(2-2\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
99.2.g.b \(16\) \(0.791\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{6}-\beta _{7}+\beta _{9}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots\)
99.2.j.a \(16\) \(0.791\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{8}-\beta _{10}-\beta _{11}+\beta _{12}-\beta _{14}+2\beta _{15})q^{2}+\cdots\)
99.2.m.a \(8\) \(0.791\) \(\Q(\zeta_{15})\) None None \(-4\) \(3\) \(6\) \(-1\) \(q+(1-2\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
99.2.m.b \(72\) \(0.791\) None None \(-1\) \(-12\) \(-8\) \(-2\)
99.2.p.a \(80\) \(0.791\) None None \(-15\) \(-3\) \(-6\) \(-5\)
99.3.b.a \(8\) \(2.698\) 8.0.\(\cdots\).6 None None \(0\) \(0\) \(0\) \(16\) \(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
99.3.c.a \(1\) \(2.698\) \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(1\) \(0\) \(q+4q^{4}+q^{5}+11q^{11}+2^{4}q^{16}+4q^{20}+\cdots\)
99.3.c.b \(4\) \(2.698\) 4.0.39744.5 None None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{3}q^{2}+(-5-2\beta _{1})q^{4}+(-1-3\beta _{1}+\cdots)q^{5}+\cdots\)
99.3.c.c \(4\) \(2.698\) \(\Q(\sqrt{-3}, \sqrt{46})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}-5\beta _{2}q^{8}+\cdots\)
99.3.h.a \(4\) \(2.698\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(5\) \(-1\) \(0\) \(q+(2\beta _{2}-\beta _{3})q^{3}-4\beta _{2}q^{4}+(3-6\beta _{1}+\cdots)q^{5}+\cdots\)
99.3.h.b \(40\) \(2.698\) None None \(0\) \(-6\) \(2\) \(0\)
99.3.i.a \(40\) \(2.698\) None None \(0\) \(-1\) \(-9\) \(2\)
99.3.k.a \(4\) \(2.698\) \(\Q(\zeta_{10})\) None None \(5\) \(0\) \(4\) \(10\) \(q+(2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-4+\cdots)q^{4}+\cdots\)
99.3.k.b \(16\) \(2.698\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(30\) \(q+\beta _{5}q^{2}+(-1-3\beta _{2}-\beta _{4}-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\)
99.3.k.c \(16\) \(2.698\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(4\) \(-30\) \(q+(-1-\beta _{2}+\beta _{5}-\beta _{7}-\beta _{8})q^{2}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
99.3.l.a \(32\) \(2.698\) None None \(0\) \(0\) \(0\) \(-16\)
99.3.n.a \(176\) \(2.698\) None None \(-9\) \(-3\) \(-18\) \(-3\)
99.3.o.a \(176\) \(2.698\) None None \(-5\) \(-9\) \(-6\) \(-5\)
99.4.a.a \(1\) \(5.841\) \(\Q\) None None \(1\) \(0\) \(4\) \(-26\) \(-\) \(q+q^{2}-7q^{4}+4q^{5}-26q^{7}-15q^{8}+\cdots\)
99.4.a.b \(1\) \(5.841\) \(\Q\) None None \(5\) \(0\) \(14\) \(-32\) \(+\) \(q+5q^{2}+17q^{4}+14q^{5}-2^{5}q^{7}+45q^{8}+\cdots\)
99.4.a.c \(2\) \(5.841\) \(\Q(\sqrt{3}) \) None None \(-2\) \(0\) \(-2\) \(20\) \(+\) \(q+(-1+\beta )q^{2}+(-4-2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
99.4.a.d \(2\) \(5.841\) \(\Q(\sqrt{3}) \) None None \(-2\) \(0\) \(-20\) \(-16\) \(-\) \(q+(-1+\beta )q^{2}+(5-2\beta )q^{4}+(-10+\cdots)q^{5}+\cdots\)
99.4.a.e \(2\) \(5.841\) \(\Q(\sqrt{33}) \) None None \(-1\) \(0\) \(-16\) \(2\) \(-\) \(q-\beta q^{2}+\beta q^{4}+(-10+4\beta )q^{5}+(2+\cdots)q^{7}+\cdots\)
99.4.a.f \(2\) \(5.841\) \(\Q(\sqrt{97}) \) None None \(-1\) \(0\) \(14\) \(24\) \(+\) \(q-\beta q^{2}+(2^{4}+\beta )q^{4}+(6+2\beta )q^{5}+(14+\cdots)q^{7}+\cdots\)
99.4.a.g \(2\) \(5.841\) \(\Q(\sqrt{3}) \) None None \(2\) \(0\) \(20\) \(-16\) \(+\) \(q+(1+\beta )q^{2}+(5+2\beta )q^{4}+(10-\beta )q^{5}+\cdots\)
99.4.d.a \(2\) \(5.841\) \(\Q(\sqrt{-2}) \) None None \(-6\) \(0\) \(0\) \(0\) \(q-3q^{2}+q^{4}+14\beta q^{5}-12\beta q^{7}+21q^{8}+\cdots\)
99.4.d.b \(2\) \(5.841\) \(\Q(\sqrt{-2}) \) None None \(6\) \(0\) \(0\) \(0\) \(q+3q^{2}+q^{4}+14\beta q^{5}+12\beta q^{7}-21q^{8}+\cdots\)
99.4.d.c \(8\) \(5.841\) 8.0.\(\cdots\).4 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(5+\beta _{3})q^{4}-5\beta _{6}q^{5}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)
99.4.e.a \(2\) \(5.841\) \(\Q(\sqrt{-3}) \) None None \(4\) \(-9\) \(19\) \(26\) \(q+(4-4\zeta_{6})q^{2}+(-6+3\zeta_{6})q^{3}-8\zeta_{6}q^{4}+\cdots\)
99.4.e.b \(24\) \(5.841\) None None \(-4\) \(6\) \(2\) \(8\)
99.4.e.c \(34\) \(5.841\) None None \(0\) \(5\) \(3\) \(-22\)
99.4.f.a \(4\) \(5.841\) \(\Q(\zeta_{10})\) None None \(-10\) \(0\) \(21\) \(37\) \(q+(-2-2\zeta_{10}+2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
99.4.f.b \(8\) \(5.841\) 8.0.682515625.5 None None \(6\) \(0\) \(-9\) \(3\) \(q+(\beta _{1}+2\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(2+\cdots)q^{4}+\cdots\)
99.4.f.c \(8\) \(5.841\) 8.0.\(\cdots\).1 None None \(7\) \(0\) \(7\) \(-35\) \(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(3-2\beta _{1}+\cdots)q^{4}+\cdots\)
99.4.f.d \(12\) \(5.841\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-28\) \(12\) \(q+(1+\beta _{3}+\beta _{5}+\beta _{6}+\beta _{7})q^{2}+(-1+\cdots)q^{4}+\cdots\)
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