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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
87.1.d.a \(1\) \(0.043\) \(\Q\) \(\Q(\sqrt{-87}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
87.1.d.b \(1\) \(0.043\) \(\Q\) \(\Q(\sqrt{-87}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)
87.2.a.a \(2\) \(0.695\) \(\Q(\sqrt{5}) \) None None \(1\) \(2\) \(2\) \(-4\) \(-\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots\)
87.2.a.b \(3\) \(0.695\) 3.3.229.1 None None \(2\) \(-3\) \(0\) \(4\) \(-\) \(q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}-2\beta _{1}q^{5}+\cdots\)
87.2.c.a \(4\) \(0.695\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(4\) \(-8\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-2\beta _{2}q^{5}+\cdots\)
87.2.f.a \(4\) \(0.695\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(8\) \(-4\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
87.2.f.b \(4\) \(0.695\) \(\Q(\zeta_{12})\) None None \(2\) \(6\) \(-8\) \(-4\) \(q+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\)
87.2.f.c \(8\) \(0.695\) 8.0.1871773696.1 None None \(0\) \(-8\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(2\beta _{3}+\cdots)q^{4}+\cdots\)
87.2.g.a \(18\) \(0.695\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-4\) \(-3\) \(-1\) \(-4\) \(q+(-\beta _{3}+\beta _{9})q^{2}-\beta _{10}q^{3}+(2\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)
87.2.g.b \(18\) \(0.695\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-2\) \(3\) \(-7\) \(-4\) \(q-\beta _{3}q^{2}+\beta _{14}q^{3}+(-\beta _{10}-\beta _{16}+\cdots)q^{4}+\cdots\)
87.2.i.a \(24\) \(0.695\) None None \(0\) \(0\) \(-4\) \(8\)
87.2.k.a \(96\) \(0.695\) None None \(0\) \(-12\) \(0\) \(-20\)
87.3.b.a \(18\) \(2.371\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(-2\) \(0\) \(-12\) \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
87.3.d.a \(3\) \(2.371\) 3.3.2349.1 \(\Q(\sqrt{-87}) \) None \(0\) \(-9\) \(0\) \(0\) \(q+\beta _{1}q^{2}-3q^{3}+(4+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
87.3.d.b \(3\) \(2.371\) 3.3.2349.1 \(\Q(\sqrt{-87}) \) None \(0\) \(9\) \(0\) \(0\) \(q-\beta _{1}q^{2}+3q^{3}+(4+2\beta _{1}+\beta _{2})q^{4}+\cdots\)
87.3.d.c \(12\) \(2.371\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{8}q^{2}+\beta _{6}q^{3}+\beta _{5}q^{4}-\beta _{9}q^{5}+\cdots\)
87.3.e.a \(8\) \(2.371\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-8\) \(0\) \(0\) \(12\) \(q+(-1-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
87.3.e.b \(12\) \(2.371\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) \(q+(\beta _{3}-\beta _{6})q^{2}+\beta _{6}q^{3}+(\beta _{2}+\beta _{6}-3\beta _{7}+\cdots)q^{4}+\cdots\)
87.3.h.a \(108\) \(2.371\) None None \(0\) \(-7\) \(0\) \(-18\)
87.3.j.a \(108\) \(2.371\) None None \(0\) \(-5\) \(0\) \(-2\)
87.3.l.a \(120\) \(2.371\) None None \(8\) \(0\) \(0\) \(0\)
87.4.a.a \(2\) \(5.133\) \(\Q(\sqrt{17}) \) None None \(-5\) \(6\) \(-11\) \(-24\) \(-\) \(q+(-2-\beta )q^{2}+3q^{3}+5\beta q^{4}+(-4+\cdots)q^{5}+\cdots\)
87.4.a.b \(2\) \(5.133\) \(\Q(\sqrt{41}) \) None None \(-1\) \(-6\) \(-1\) \(-24\) \(-\) \(q-\beta q^{2}-3q^{3}+(2+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots\)
87.4.a.c \(5\) \(5.133\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(3\) \(-15\) \(-1\) \(4\) \(+\) \(q+(1-\beta _{1})q^{2}-3q^{3}+(6-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
87.4.a.d \(5\) \(5.133\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(3\) \(15\) \(29\) \(4\) \(+\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
87.4.c.a \(16\) \(5.133\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-28\) \(40\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
87.4.f.a \(56\) \(5.133\) None None \(0\) \(-2\) \(0\) \(-8\)
87.4.g.a \(42\) \(5.133\) None None \(-2\) \(21\) \(-47\) \(20\)
87.4.g.b \(42\) \(5.133\) None None \(2\) \(-21\) \(31\) \(20\)
87.4.i.a \(96\) \(5.133\) None None \(0\) \(0\) \(28\) \(-40\)
87.4.k.a \(336\) \(5.133\) None None \(0\) \(-12\) \(0\) \(-20\)
87.5.b.a \(38\) \(8.993\) None None \(0\) \(-2\) \(0\) \(76\)
87.5.d.a \(3\) \(8.993\) 3.3.2349.1 \(\Q(\sqrt{-87}) \) None \(0\) \(-27\) \(0\) \(0\) \(q+(-2\beta _{1}-\beta _{2})q^{2}-9q^{3}+(2^{4}+5\beta _{1}+\cdots)q^{4}+\cdots\)
87.5.d.b \(3\) \(8.993\) 3.3.2349.1 \(\Q(\sqrt{-87}) \) None \(0\) \(27\) \(0\) \(0\) \(q+(2\beta _{1}+\beta _{2})q^{2}+9q^{3}+(2^{4}+5\beta _{1}+\cdots)q^{4}+\cdots\)
87.5.d.c \(32\) \(8.993\) None None \(0\) \(0\) \(0\) \(-84\)
87.5.e.a \(40\) \(8.993\) None None \(12\) \(0\) \(0\) \(0\)
87.5.h.a \(228\) \(8.993\) None None \(0\) \(-7\) \(0\) \(70\)
87.5.j.a \(228\) \(8.993\) None None \(0\) \(-5\) \(0\) \(-90\)
87.5.l.a \(240\) \(8.993\) None None \(-12\) \(0\) \(0\) \(0\)
87.6.a.a \(4\) \(13.953\) 4.4.8167381.1 None None \(-3\) \(36\) \(-136\) \(-28\) \(+\) \(q+(-1-\beta _{1})q^{2}+9q^{3}+(14+6\beta _{1}+\cdots)q^{4}+\cdots\)
87.6.a.b \(5\) \(13.953\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-9\) \(-45\) \(14\) \(-68\) \(+\) \(q+(-2+\beta _{1})q^{2}-9q^{3}+(11-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
87.6.a.c \(7\) \(13.953\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(13\) \(63\) \(64\) \(168\) \(-\) \(q+(2-\beta _{1})q^{2}+9q^{3}+(21-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
87.6.a.d \(8\) \(13.953\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-1\) \(-72\) \(14\) \(128\) \(-\) \(q-\beta _{1}q^{2}-9q^{3}+(19+\beta _{1}+\beta _{2})q^{4}+\cdots\)
87.6.c.a \(24\) \(13.953\) None None \(0\) \(0\) \(-196\) \(-120\)
87.6.f.a \(96\) \(13.953\) None None \(0\) \(-2\) \(0\) \(-8\)
87.6.g.a \(78\) \(13.953\) None None \(2\) \(-117\) \(-17\) \(-60\)
87.6.g.b \(78\) \(13.953\) None None \(10\) \(117\) \(49\) \(-60\)
87.6.i.a \(144\) \(13.953\) None None \(0\) \(0\) \(196\) \(120\)
87.6.k.a \(576\) \(13.953\) None None \(0\) \(-12\) \(0\) \(-20\)
87.7.b.a \(56\) \(20.015\) None None \(0\) \(52\) \(0\) \(160\)
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