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Results (displaying matches 1-50 of 322) Next

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
50.2.a.a \(1\) \(0.399\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
50.2.a.b \(1\) \(0.399\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
50.2.b.a \(2\) \(0.399\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots\)
50.2.d.a \(4\) \(0.399\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(5\) \(-12\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\)
50.2.d.b \(8\) \(0.399\) 8.0.58140625.2 None \(-2\) \(-3\) \(0\) \(4\) \(q+(-1+\beta _{2}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+\cdots\)
50.2.e.a \(8\) \(0.399\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(-10\) \(0\) \(q+\zeta_{20}q^{2}+(-1+\zeta_{20}^{2}-\zeta_{20}^{4}+2\zeta_{20}^{6}+\cdots)q^{3}+\cdots\)
50.3.c.a \(2\) \(1.362\) \(\Q(\sqrt{-1}) \) None \(-2\) \(6\) \(0\) \(-6\) \(q+(-1-i)q^{2}+(3-3i)q^{3}+2iq^{4}+\cdots\)
50.3.c.b \(2\) \(1.362\) \(\Q(\sqrt{-1}) \) None \(2\) \(-6\) \(0\) \(6\) \(q+(1+i)q^{2}+(-3+3i)q^{3}+2iq^{4}+\cdots\)
50.3.c.c \(2\) \(1.362\) \(\Q(\sqrt{-1}) \) None \(2\) \(4\) \(0\) \(-4\) \(q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots\)
50.3.f.a \(16\) \(1.362\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-4\) \(2\) \(0\) \(-2\) \(q+(\beta _{1}+\beta _{9})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7}+\cdots)q^{3}+\cdots\)
50.3.f.b \(24\) \(1.362\) None \(6\) \(2\) \(0\) \(-2\)
50.4.a.a \(1\) \(2.950\) \(\Q\) None \(-2\) \(-7\) \(0\) \(34\) \(+\) \(q-2q^{2}-7q^{3}+4q^{4}+14q^{6}+34q^{7}+\cdots\)
50.4.a.b \(1\) \(2.950\) \(\Q\) None \(-2\) \(-2\) \(0\) \(-26\) \(-\) \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-26q^{7}+\cdots\)
50.4.a.c \(1\) \(2.950\) \(\Q\) None \(-2\) \(8\) \(0\) \(4\) \(+\) \(q-2q^{2}+8q^{3}+4q^{4}-2^{4}q^{6}+4q^{7}+\cdots\)
50.4.a.d \(1\) \(2.950\) \(\Q\) None \(2\) \(2\) \(0\) \(26\) \(+\) \(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+26q^{7}+\cdots\)
50.4.a.e \(1\) \(2.950\) \(\Q\) None \(2\) \(7\) \(0\) \(-34\) \(+\) \(q+2q^{2}+7q^{3}+4q^{4}+14q^{6}-34q^{7}+\cdots\)
50.4.b.a \(2\) \(2.950\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+4iq^{3}-4q^{4}-2^{4}q^{6}-2iq^{7}+\cdots\)
50.4.b.b \(2\) \(2.950\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-7iq^{3}-4q^{4}+14q^{6}-34iq^{7}+\cdots\)
50.4.d.a \(12\) \(2.950\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(1\) \(20\) \(58\) \(q+2\beta _{5}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
50.4.d.b \(16\) \(2.950\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-8\) \(7\) \(15\) \(-54\) \(q+2\beta _{6}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
50.4.e.a \(32\) \(2.950\) None \(0\) \(0\) \(-30\) \(0\)
50.5.c.a \(2\) \(5.168\) \(\Q(\sqrt{-1}) \) None \(-4\) \(-2\) \(0\) \(38\) \(q+(-2-2i)q^{2}+(-1+i)q^{3}+8iq^{4}+\cdots\)
50.5.c.b \(2\) \(5.168\) \(\Q(\sqrt{-1}) \) None \(4\) \(-18\) \(0\) \(-58\) \(q+(2+2i)q^{2}+(-9+9i)q^{3}+8iq^{4}+\cdots\)
50.5.c.c \(4\) \(5.168\) \(\Q(i, \sqrt{6})\) None \(-8\) \(-24\) \(0\) \(-144\) \(q+(-2+2\beta _{2})q^{2}+(-6+\beta _{1}-6\beta _{2}+\cdots)q^{3}+\cdots\)
50.5.c.d \(4\) \(5.168\) \(\Q(i, \sqrt{6})\) None \(8\) \(24\) \(0\) \(144\) \(q+(2-2\beta _{2})q^{2}+(6+\beta _{1}+6\beta _{2})q^{3}+\cdots\)
50.5.f.a \(40\) \(5.168\) None \(-20\) \(-10\) \(30\) \(-10\)
50.5.f.b \(40\) \(5.168\) None \(20\) \(-10\) \(30\) \(-10\)
50.6.a.a \(1\) \(8.019\) \(\Q\) None \(-4\) \(-11\) \(0\) \(-142\) \(-\) \(q-4q^{2}-11q^{3}+2^{4}q^{4}+44q^{6}-142q^{7}+\cdots\)
50.6.a.b \(1\) \(8.019\) \(\Q\) None \(-4\) \(-6\) \(0\) \(118\) \(+\) \(q-4q^{2}-6q^{3}+2^{4}q^{4}+24q^{6}+118q^{7}+\cdots\)
50.6.a.c \(1\) \(8.019\) \(\Q\) None \(-4\) \(14\) \(0\) \(158\) \(-\) \(q-4q^{2}+14q^{3}+2^{4}q^{4}-56q^{6}+158q^{7}+\cdots\)
50.6.a.d \(1\) \(8.019\) \(\Q\) None \(4\) \(-24\) \(0\) \(172\) \(-\) \(q+4q^{2}-24q^{3}+2^{4}q^{4}-96q^{6}+172q^{7}+\cdots\)
50.6.a.e \(1\) \(8.019\) \(\Q\) None \(4\) \(-14\) \(0\) \(-158\) \(+\) \(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}-158q^{7}+\cdots\)
50.6.a.f \(1\) \(8.019\) \(\Q\) None \(4\) \(11\) \(0\) \(142\) \(-\) \(q+4q^{2}+11q^{3}+2^{4}q^{4}+44q^{6}+142q^{7}+\cdots\)
50.6.a.g \(1\) \(8.019\) \(\Q\) None \(4\) \(26\) \(0\) \(22\) \(-\) \(q+4q^{2}+26q^{3}+2^{4}q^{4}+104q^{6}+\cdots\)
50.6.b.a \(2\) \(8.019\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+12iq^{3}-2^{4}q^{4}-96q^{6}+\cdots\)
50.6.b.b \(2\) \(8.019\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-2^{4}q^{4}+24q^{6}+\cdots\)
50.6.b.c \(2\) \(8.019\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{2}-11iq^{3}-2^{4}q^{4}+44q^{6}+\cdots\)
50.6.b.d \(2\) \(8.019\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-13iq^{3}-2^{4}q^{4}+104q^{6}+\cdots\)
50.6.d.a \(24\) \(8.019\) None \(-24\) \(-11\) \(-120\) \(548\)
50.6.d.b \(28\) \(8.019\) None \(28\) \(7\) \(-145\) \(-236\)
50.6.e.a \(48\) \(8.019\) None \(0\) \(0\) \(180\) \(0\)
50.7.c.a \(2\) \(11.503\) \(\Q(\sqrt{-1}) \) None \(-8\) \(-6\) \(0\) \(-234\) \(q+(-4-4i)q^{2}+(-3+3i)q^{3}+2^{5}iq^{4}+\cdots\)
50.7.c.b \(2\) \(11.503\) \(\Q(\sqrt{-1}) \) None \(8\) \(6\) \(0\) \(234\) \(q+(4+4i)q^{2}+(3-3i)q^{3}+2^{5}iq^{4}+\cdots\)
50.7.c.c \(2\) \(11.503\) \(\Q(\sqrt{-1}) \) None \(8\) \(46\) \(0\) \(494\) \(q+(4+4i)q^{2}+(23-23i)q^{3}+2^{5}iq^{4}+\cdots\)
50.7.c.d \(4\) \(11.503\) \(\Q(i, \sqrt{129})\) None \(-16\) \(18\) \(0\) \(202\) \(q+(-4+4\beta _{1})q^{2}+(5+5\beta _{1}-\beta _{2})q^{3}+\cdots\)
50.7.c.e \(4\) \(11.503\) \(\Q(i, \sqrt{6})\) None \(-16\) \(48\) \(0\) \(672\) \(q+(-4-4\beta _{2})q^{2}+(12-12\beta _{2}-\beta _{3})q^{3}+\cdots\)
50.7.c.f \(4\) \(11.503\) \(\Q(i, \sqrt{6})\) None \(16\) \(-48\) \(0\) \(-672\) \(q+(4+4\beta _{2})q^{2}+(-12+12\beta _{2}-\beta _{3})q^{3}+\cdots\)
50.7.f.a \(56\) \(11.503\) None \(56\) \(32\) \(150\) \(348\)
50.7.f.b \(64\) \(11.503\) None \(-64\) \(32\) \(-330\) \(348\)
50.8.a.a \(1\) \(15.619\) \(\Q\) None \(-8\) \(-43\) \(0\) \(-974\) \(+\) \(q-8q^{2}-43q^{3}+2^{6}q^{4}+344q^{6}+\cdots\)
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