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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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