## Results (displaying matches 1-50 of 266) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
200.1.e.a $$2$$ $$0.100$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots$$
200.1.g.a $$1$$ $$0.100$$ $$\Q$$ $$\Q(\sqrt{-2})$$ None $$-1$$ $$1$$ $$0$$ $$0$$ $$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$$
200.1.g.b $$1$$ $$0.100$$ $$\Q$$ $$\Q(\sqrt{-2})$$ None $$1$$ $$-1$$ $$0$$ $$0$$ $$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots$$
200.2.a.a $$1$$ $$1.597$$ $$\Q$$ None None $$0$$ $$-3$$ $$0$$ $$2$$ $$-$$ $$q-3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots$$
200.2.a.b $$1$$ $$1.597$$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$-2$$ $$+$$ $$q-2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$$
200.2.a.c $$1$$ $$1.597$$ $$\Q$$ None None $$0$$ $$0$$ $$0$$ $$4$$ $$-$$ $$q+4q^{7}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$$
200.2.a.d $$1$$ $$1.597$$ $$\Q$$ None None $$0$$ $$2$$ $$0$$ $$2$$ $$-$$ $$q+2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$$
200.2.a.e $$1$$ $$1.597$$ $$\Q$$ None None $$0$$ $$3$$ $$0$$ $$-2$$ $$-$$ $$q+3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots$$
200.2.c.a $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}+2iq^{7}-6q^{9}+q^{11}-4iq^{13}+\cdots$$
200.2.c.b $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+3q^{9}+4q^{11}-iq^{13}-iq^{17}+\cdots$$
200.2.d.a $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots$$
200.2.d.b $$2$$ $$1.597$$ $$\Q(\sqrt{-7})$$ None None $$-1$$ $$0$$ $$0$$ $$-8$$ $$q-\beta q^{2}+(1-2\beta )q^{3}+(-2+\beta )q^{4}+\cdots$$
200.2.d.c $$2$$ $$1.597$$ $$\Q(\sqrt{-7})$$ None None $$1$$ $$0$$ $$0$$ $$8$$ $$q+\beta q^{2}+(-1+2\beta )q^{3}+(-2+\beta )q^{4}+\cdots$$
200.2.d.d $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(1+i)q^{2}-iq^{3}+2iq^{4}+(1-i)q^{6}+\cdots$$
200.2.d.e $$4$$ $$1.597$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$$
200.2.d.f $$4$$ $$1.597$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
200.2.f.a $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots$$
200.2.f.b $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$2$$ $$0$$ $$0$$ $$q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots$$
200.2.f.c $$4$$ $$1.597$$ $$\Q(\zeta_{12})$$ None None $$-2$$ $$4$$ $$0$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
200.2.f.d $$4$$ $$1.597$$ $$\Q(i, \sqrt{7})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$$
200.2.f.e $$4$$ $$1.597$$ $$\Q(\zeta_{12})$$ None None $$2$$ $$-4$$ $$0$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$
200.2.k.a $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$-2$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots$$
200.2.k.b $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-10})$$ None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+i)q^{2}-2iq^{4}+(-2+2i)q^{7}+\cdots$$
200.2.k.c $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-10})$$ None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(1-i)q^{2}-2iq^{4}+(2-2i)q^{7}+(-2+\cdots)q^{8}+\cdots$$
200.2.k.d $$2$$ $$1.597$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$2$$ $$4$$ $$0$$ $$0$$ $$q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots$$
200.2.k.e $$4$$ $$1.597$$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-2})$$ None $$-4$$ $$4$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+\cdots$$
200.2.k.f $$4$$ $$1.597$$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-2})$$ None $$4$$ $$-4$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+\cdots$$
200.2.k.g $$8$$ $$1.597$$ 8.0.3317760000.5 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots$$
200.2.k.h $$8$$ $$1.597$$ $$\Q(\zeta_{20})$$ None None $$2$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{20}^{7}q^{2}+(1-\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots$$
200.2.m.a $$4$$ $$1.597$$ $$\Q(\zeta_{10})$$ None None $$0$$ $$5$$ $$-5$$ $$6$$ $$q+(2-2\zeta_{10}-\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots$$
200.2.m.b $$8$$ $$1.597$$ 8.0.58140625.2 None None $$0$$ $$-6$$ $$5$$ $$4$$ $$q+(-1+\beta _{2})q^{3}+(1+\beta _{5})q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$$
200.2.m.c $$16$$ $$1.597$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$1$$ $$-1$$ $$-6$$ $$q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{14}+\cdots)q^{5}+\cdots$$
200.2.o.a $$112$$ $$1.597$$ None None $$-5$$ $$0$$ $$0$$ $$0$$
200.2.q.a $$32$$ $$1.597$$ None None $$0$$ $$0$$ $$2$$ $$0$$
200.2.t.a $$112$$ $$1.597$$ None None $$-3$$ $$0$$ $$0$$ $$-16$$
200.2.v.a $$8$$ $$1.597$$ $$\Q(\zeta_{20})$$ None None $$-8$$ $$0$$ $$10$$ $$4$$ $$q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
200.2.v.b $$8$$ $$1.597$$ $$\Q(\zeta_{20})$$ None None $$-2$$ $$0$$ $$-10$$ $$-4$$ $$q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
200.2.v.c $$208$$ $$1.597$$ None None $$2$$ $$-16$$ $$0$$ $$0$$
200.3.e.a $$2$$ $$5.450$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-iq^{3}-4q^{4}+4q^{6}-4iq^{8}+\cdots$$
200.3.e.b $$4$$ $$5.450$$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots$$
200.3.e.c $$12$$ $$5.450$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{6}+\beta _{9})q^{4}+\cdots$$
200.3.e.d $$16$$ $$5.450$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{2}q^{3}+(1+\beta _{11})q^{4}+(-2+\cdots)q^{6}+\cdots$$
200.3.g.a $$1$$ $$5.450$$ $$\Q$$ $$\Q(\sqrt{-2})$$ None $$2$$ $$2$$ $$0$$ $$0$$ $$q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+8q^{8}+\cdots$$
200.3.g.b $$2$$ $$5.450$$ $$\Q(\sqrt{6})$$ $$\Q(\sqrt{-2})$$ None $$-4$$ $$2$$ $$0$$ $$0$$ $$q-2q^{2}+(1+\beta )q^{3}+4q^{4}+(-2-2\beta )q^{6}+\cdots$$
200.3.g.c $$2$$ $$5.450$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-4q^{4}-3iq^{7}-4iq^{8}-9q^{9}+\cdots$$
200.3.g.d $$2$$ $$5.450$$ $$\Q(\sqrt{6})$$ $$\Q(\sqrt{-2})$$ None $$4$$ $$-2$$ $$0$$ $$0$$ $$q+2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$$
200.3.g.e $$6$$ $$5.450$$ 6.0.189974000.1 None None $$-3$$ $$2$$ $$0$$ $$0$$ $$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
200.3.g.f $$6$$ $$5.450$$ 6.0.189974000.1 None None $$3$$ $$-2$$ $$0$$ $$0$$ $$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$$
200.3.g.g $$8$$ $$5.450$$ 8.0.$$\cdots$$.1 None None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}+\beta _{6}q^{3}+(-1+\beta _{1})q^{4}+(-1+\cdots)q^{6}+\cdots$$
200.3.g.h $$8$$ $$5.450$$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{6}q^{3}+(2+\beta _{5})q^{4}+(2-\beta _{2}+\cdots)q^{6}+\cdots$$
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