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Results (47 matches)

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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1045.1.k.a \(2\) \(0.522\) \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{209}) \) \(-2\) \(0\) \(0\) \(0\) \(q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots\)
1045.1.k.b \(2\) \(0.522\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(-2\) \(q-iq^{4}+q^{5}+(-1+i)q^{7}-iq^{9}+\cdots\)
1045.1.k.c \(2\) \(0.522\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(2\) \(q-iq^{4}+q^{5}+(1-i)q^{7}-iq^{9}+iq^{11}+\cdots\)
1045.1.k.d \(2\) \(0.522\) \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{209}) \) \(2\) \(0\) \(0\) \(0\) \(q+(1+i)q^{2}+iq^{4}-iq^{5}+q^{8}-iq^{9}+\cdots\)
1045.1.w.a \(4\) \(0.522\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-95}) \) None \(-2\) \(-2\) \(-1\) \(0\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
1045.1.w.b \(4\) \(0.522\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-5\) \(q+\zeta_{10}q^{4}-\zeta_{10}q^{5}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1045.1.w.c \(4\) \(0.522\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(5\) \(q+\zeta_{10}q^{4}-\zeta_{10}^{3}q^{5}+(1-\zeta_{10}^{2})q^{7}+\cdots\)
1045.1.w.d \(4\) \(0.522\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-95}) \) None \(2\) \(2\) \(-1\) \(0\) \(q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
1045.1.w.e \(8\) \(0.522\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{3}+\cdots\)
1045.1.w.f \(16\) \(0.522\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots\)
1045.1.br.a \(8\) \(0.522\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-8\) \(q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots\)
1045.1.br.b \(8\) \(0.522\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-2\) \(q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots\)
1045.2.a.a \(1\) \(8.344\) \(\Q\) None None \(-1\) \(-2\) \(-1\) \(-2\) \(+\) \(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
1045.2.a.b \(1\) \(8.344\) \(\Q\) None None \(1\) \(0\) \(1\) \(0\) \(+\) \(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
1045.2.a.c \(2\) \(8.344\) \(\Q(\sqrt{2}) \) None None \(2\) \(4\) \(2\) \(0\) \(-\) \(q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
1045.2.a.d \(5\) \(8.344\) \(\Q(\zeta_{22})^+\) None None \(-3\) \(-7\) \(5\) \(-11\) \(+\) \(q+(-1+\beta _{1}-\beta _{4})q^{2}+(-2-\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
1045.2.a.e \(5\) \(8.344\) 5.5.36497.1 None None \(-1\) \(-3\) \(-5\) \(3\) \(+\) \(q+\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+\beta _{3}q^{4}-q^{5}+\cdots\)
1045.2.a.f \(6\) \(8.344\) 6.6.7281497.1 None None \(-2\) \(-1\) \(-6\) \(5\) \(+\) \(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(\beta _{4}+\beta _{5})q^{4}-q^{5}+\cdots\)
1045.2.a.g \(6\) \(8.344\) 6.6.131947641.1 None None \(0\) \(3\) \(6\) \(5\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1045.2.a.h \(7\) \(8.344\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(1\) \(3\) \(-7\) \(-1\) \(-\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1045.2.a.i \(8\) \(8.344\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-6\) \(-7\) \(8\) \(-11\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{6})q^{3}+(2+\cdots)q^{4}+\cdots\)
1045.2.a.j \(9\) \(8.344\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(3\) \(3\) \(-9\) \(-9\) \(-\) \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{8})q^{4}+\cdots\)
1045.2.a.k \(9\) \(8.344\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(3\) \(3\) \(9\) \(13\) \(-\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
1045.2.b.a \(4\) \(8.344\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
1045.2.b.b \(16\) \(8.344\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(3\) \(0\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{13}+\cdots)q^{5}+\cdots\)
1045.2.b.c \(20\) \(8.344\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots\)
1045.2.b.d \(22\) \(8.344\) None None \(0\) \(0\) \(7\) \(0\)
1045.2.b.e \(30\) \(8.344\) None None \(0\) \(0\) \(0\) \(0\)
1045.2.f.a \(40\) \(8.344\) None None \(0\) \(0\) \(-40\) \(0\)
1045.2.f.b \(40\) \(8.344\) None None \(0\) \(0\) \(40\) \(0\)
1045.4.a.a \(1\) \(61.657\) \(\Q\) None None \(-5\) \(-1\) \(-5\) \(-2\) \(-\) \(q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots\)
1045.4.a.b \(20\) \(61.657\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-12\) \(-21\) \(100\) \(-131\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(4+\cdots)q^{4}+\cdots\)
1045.4.a.c \(20\) \(61.657\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-1\) \(-8\) \(-100\) \(49\) \(-\) \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)
1045.4.a.d \(22\) \(61.657\) None None \(-4\) \(-21\) \(110\) \(-41\) \(-\)
1045.4.a.e \(22\) \(61.657\) None None \(12\) \(21\) \(110\) \(93\) \(+\)
1045.4.a.f \(23\) \(61.657\) None None \(-2\) \(-9\) \(-115\) \(13\) \(-\)
1045.4.a.g \(23\) \(61.657\) None None \(6\) \(9\) \(-115\) \(-37\) \(+\)
1045.4.a.h \(24\) \(61.657\) None None \(4\) \(21\) \(120\) \(71\) \(+\)
1045.4.a.i \(25\) \(61.657\) None None \(2\) \(9\) \(-125\) \(-15\) \(+\)
1045.6.a.a \(35\) \(167.601\) None None \(-4\) \(-27\) \(-875\) \(117\) \(+\)
1045.6.a.b \(36\) \(167.601\) None None \(-8\) \(-63\) \(900\) \(-509\) \(+\)
1045.6.a.c \(37\) \(167.601\) None None \(-12\) \(-27\) \(-925\) \(337\) \(+\)
1045.6.a.d \(37\) \(167.601\) None None \(4\) \(27\) \(-925\) \(-79\) \(-\)
1045.6.a.e \(38\) \(167.601\) None None \(-24\) \(-63\) \(950\) \(-729\) \(+\)
1045.6.a.f \(38\) \(167.601\) None None \(8\) \(63\) \(950\) \(275\) \(-\)
1045.6.a.g \(39\) \(167.601\) None None \(12\) \(27\) \(-975\) \(-251\) \(-\)
1045.6.a.h \(40\) \(167.601\) None None \(24\) \(63\) \(1000\) \(839\) \(-\)
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