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Results (40 matches)

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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
799.1.c.a \(1\) \(0.399\) \(\Q\) \(\Q(\sqrt{-47}) \), \(\Q(\sqrt{-799}) \) \(\Q(\sqrt{17}) \) \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+3q^{4}-4q^{8}+q^{9}+5q^{16}+\cdots\)
799.1.c.b \(2\) \(0.399\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-799}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-\beta q^{5}+q^{9}+\beta q^{11}+q^{16}+\cdots\)
799.1.c.c \(4\) \(0.399\) \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-799}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{3})q^{10}+\cdots\)
799.1.c.d \(4\) \(0.399\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-47}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{3}+\cdots\)
799.1.e.a \(2\) \(0.399\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-47}) \) None \(0\) \(2\) \(0\) \(-2\) \(q-iq^{2}+(1-i)q^{3}-3q^{4}+(-2-2i+\cdots)q^{6}+\cdots\)
799.1.e.b \(8\) \(0.399\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-47}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}+(-\zeta_{20}+\zeta_{20}^{4}+\cdots)q^{3}+\cdots\)
799.1.h.a \(4\) \(0.399\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-47}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
799.1.h.b \(16\) \(0.399\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-47}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(\zeta_{40}^{11}-\zeta_{40}^{19})q^{2}+(-\zeta_{40}^{7}+\zeta_{40}^{8}+\cdots)q^{3}+\cdots\)
799.2.a.a \(1\) \(6.380\) \(\Q\) None None \(-1\) \(2\) \(0\) \(-2\) \(+\) \(q-q^{2}+2q^{3}-q^{4}-2q^{6}-2q^{7}+3q^{8}+\cdots\)
799.2.a.b \(1\) \(6.380\) \(\Q\) None None \(-1\) \(2\) \(4\) \(-2\) \(-\) \(q-q^{2}+2q^{3}-q^{4}+4q^{5}-2q^{6}-2q^{7}+\cdots\)
799.2.a.c \(2\) \(6.380\) \(\Q(\sqrt{5}) \) None None \(-3\) \(0\) \(-1\) \(-2\) \(+\) \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
799.2.a.d \(8\) \(6.380\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(-7\) \(-10\) \(-9\) \(+\) \(q-\beta _{6}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{7})q^{4}+\cdots\)
799.2.a.e \(12\) \(6.380\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-4\) \(-1\) \(-11\) \(1\) \(+\) \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
799.2.a.f \(17\) \(6.380\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(3\) \(1\) \(11\) \(1\) \(-\) \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots\)
799.2.a.g \(20\) \(6.380\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(3\) \(13\) \(-3\) \(-\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{17}+\cdots)q^{5}+\cdots\)
799.2.b.a \(2\) \(6.380\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+iq^{3}-q^{4}-iq^{5}+iq^{6}-iq^{7}+\cdots\)
799.2.b.b \(28\) \(6.380\) None None \(0\) \(0\) \(0\) \(0\)
799.2.b.c \(40\) \(6.380\) None None \(-6\) \(0\) \(0\) \(0\)
799.2.f.a \(60\) \(6.380\) None None \(0\) \(-2\) \(-4\) \(0\)
799.2.f.b \(80\) \(6.380\) None None \(0\) \(-2\) \(-4\) \(0\)
799.2.g.a \(4\) \(6.380\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-4\) \(-8\) \(q+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
799.2.g.b \(4\) \(6.380\) \(\Q(\zeta_{8})\) None None \(4\) \(0\) \(0\) \(-4\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
799.2.g.c \(112\) \(6.380\) None None \(4\) \(4\) \(4\) \(8\)
799.2.g.d \(152\) \(6.380\) None None \(-4\) \(0\) \(0\) \(4\)
799.2.j.a \(80\) \(6.380\) \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\)
799.2.j.b \(480\) \(6.380\) None None \(-16\) \(-16\) \(0\) \(-16\)
799.2.k.a \(704\) \(6.380\) None None \(0\) \(-2\) \(-6\) \(21\)
799.2.k.b \(704\) \(6.380\) None None \(0\) \(-2\) \(-2\) \(-21\)
799.2.n.a \(1540\) \(6.380\) None None \(-42\) \(0\) \(0\) \(0\)
799.2.o.a \(3080\) \(6.380\) None None \(0\) \(-42\) \(-38\) \(-46\)
799.2.r.a \(6160\) \(6.380\) None None \(-84\) \(-84\) \(-92\) \(-84\)
799.2.s.a \(12320\) \(6.380\) None None \(-168\) \(-168\) \(-184\) \(-168\)
799.4.a.a \(41\) \(47.143\) None None \(-9\) \(-12\) \(-48\) \(-18\) \(-\)
799.4.a.b \(43\) \(47.143\) None None \(-5\) \(-12\) \(-92\) \(-32\) \(-\)
799.4.a.c \(49\) \(47.143\) None None \(7\) \(0\) \(72\) \(-46\) \(+\)
799.4.a.d \(51\) \(47.143\) None None \(11\) \(24\) \(68\) \(108\) \(+\)
799.6.a.a \(72\) \(128.147\) None None \(-19\) \(-81\) \(-459\) \(-793\) \(+\)
799.6.a.b \(74\) \(128.147\) None None \(-11\) \(-9\) \(-241\) \(285\) \(+\)
799.6.a.c \(80\) \(128.147\) None None \(13\) \(27\) \(341\) \(187\) \(-\)
799.6.a.d \(82\) \(128.147\) None None \(21\) \(27\) \(359\) \(89\) \(-\)
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