## Results (displaying matches 1-50 of 359) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
320.1.h.a $$1$$ $$0.160$$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$1$$ $$0$$ $$q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots$$
320.1.p.a $$2$$ $$0.160$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{5}+iq^{9}+(1-i)q^{13}+(-1-i+\cdots)q^{17}+\cdots$$
320.2.a.a $$1$$ $$2.555$$ $$\Q$$ None None $$0$$ $$-2$$ $$1$$ $$-2$$ $$+$$ $$q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots$$
320.2.a.b $$1$$ $$2.555$$ $$\Q$$ None None $$0$$ $$-2$$ $$1$$ $$2$$ $$-$$ $$q-2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$$
320.2.a.c $$1$$ $$2.555$$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$-4$$ $$+$$ $$q-q^{5}-4q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots$$
320.2.a.d $$1$$ $$2.555$$ $$\Q$$ None None $$0$$ $$0$$ $$-1$$ $$4$$ $$-$$ $$q-q^{5}+4q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots$$
320.2.a.e $$1$$ $$2.555$$ $$\Q$$ None None $$0$$ $$2$$ $$1$$ $$-2$$ $$-$$ $$q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots$$
320.2.a.f $$1$$ $$2.555$$ $$\Q$$ None None $$0$$ $$2$$ $$1$$ $$2$$ $$-$$ $$q+2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots$$
320.2.a.g $$2$$ $$2.555$$ $$\Q(\sqrt{2})$$ None None $$0$$ $$0$$ $$-2$$ $$0$$ $$-$$ $$q+\beta q^{3}-q^{5}+\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots$$
320.2.c.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}+3q^{9}+2iq^{13}+4iq^{17}+\cdots$$
320.2.c.b $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1+i)q^{5}+iq^{7}-q^{9}-4q^{11}+\cdots$$
320.2.c.c $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots$$
320.2.c.d $$4$$ $$2.555$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots$$
320.2.d.a $$4$$ $$2.555$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$-12$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(-3+\cdots)q^{7}+\cdots$$
320.2.d.b $$4$$ $$2.555$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$12$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots$$
320.2.f.a $$4$$ $$2.555$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-10})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{1}q^{11}+\cdots$$
320.2.f.b $$8$$ $$2.555$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{4}q^{3}-\zeta_{24}^{6}q^{5}+\zeta_{24}^{2}q^{7}+\cdots$$
320.2.j.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$2$$ $$6$$ $$q-2iq^{3}+(1+2i)q^{5}+(3+3i)q^{7}+\cdots$$
320.2.j.b $$18$$ $$2.555$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$0$$ $$-4$$ $$-2$$ $$q-\beta _{12}q^{3}-\beta _{4}q^{5}+\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots$$
320.2.l.a $$16$$ $$2.555$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{5}+\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$$
320.2.n.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-4$$ $$4$$ $$4$$ $$q+(-2-2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots$$
320.2.n.b $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$-2$$ $$-6$$ $$q+(-1-i)q^{3}+(-1-2i)q^{5}+(-3+\cdots)q^{7}+\cdots$$
320.2.n.c $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$-2$$ $$2$$ $$q+(-1-i)q^{3}+(-1+2i)q^{5}+(1-i)q^{7}+\cdots$$
320.2.n.d $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2-i)q^{5}-3iq^{9}+(5-5i)q^{13}+\cdots$$
320.2.n.e $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2-i)q^{5}-3iq^{9}+(1-i)q^{13}+(3+\cdots)q^{17}+\cdots$$
320.2.n.f $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$-2$$ $$-2$$ $$q+(1+i)q^{3}+(-1+2i)q^{5}+(-1+i)q^{7}+\cdots$$
320.2.n.g $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$-2$$ $$6$$ $$q+(1+i)q^{3}+(-1-2i)q^{5}+(3-3i)q^{7}+\cdots$$
320.2.n.h $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$4$$ $$4$$ $$-4$$ $$q+(2+2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots$$
320.2.n.i $$4$$ $$2.555$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$4$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+(1+2\zeta_{12})q^{5}-\zeta_{12}^{3}q^{7}+\cdots$$
320.2.o.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$-2$$ $$-2$$ $$q+(-1+i)q^{3}+(-1-2i)q^{5}+(-1+\cdots)q^{7}+\cdots$$
320.2.o.b $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$2$$ $$2$$ $$q+(-1+i)q^{3}+(1+2i)q^{5}+(1-i)q^{7}+\cdots$$
320.2.o.c $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$-2$$ $$2$$ $$q+(1-i)q^{3}+(-1-2i)q^{5}+(1-i)q^{7}+\cdots$$
320.2.o.d $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$2$$ $$-2$$ $$q+(1-i)q^{3}+(1+2i)q^{5}+(-1+i)q^{7}+\cdots$$
320.2.o.e $$8$$ $$2.555$$ 8.0.49787136.1 None None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{2}-\beta _{7})q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots$$
320.2.o.f $$8$$ $$2.555$$ 8.0.49787136.1 None None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots$$
320.2.q.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$-2$$ $$2$$ $$0$$ $$q+(-1-i)q^{3}+(1+2i)q^{5}-iq^{9}+\cdots$$
320.2.q.b $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$2$$ $$4$$ $$0$$ $$q+(1+i)q^{3}+(2+i)q^{5}-iq^{9}+(3+3i)q^{11}+\cdots$$
320.2.q.c $$16$$ $$2.555$$ 16.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\beta _{11}q^{3}+(-1-\beta _{6}-\beta _{10})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$$
320.2.s.a $$2$$ $$2.555$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$4$$ $$-4$$ $$6$$ $$q+2q^{3}+(-2+i)q^{5}+(3+3i)q^{7}+\cdots$$
320.2.s.b $$18$$ $$2.555$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$-2$$ $$q-\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$$
320.2.bd.a $$368$$ $$2.555$$ None None $$-8$$ $$-8$$ $$-8$$ $$-8$$
320.2.be.a $$256$$ $$2.555$$ None None $$0$$ $$0$$ $$0$$ $$0$$
320.2.bf.a $$368$$ $$2.555$$ None None $$0$$ $$0$$ $$-8$$ $$0$$
320.2.bj.a $$368$$ $$2.555$$ None None $$-8$$ $$-8$$ $$-8$$ $$-8$$
320.3.b.a $$4$$ $$8.719$$ $$\Q(\sqrt{-3}, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots$$
320.3.b.b $$4$$ $$8.719$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-4\beta _{2})q^{7}+(-5+\cdots)q^{9}+\cdots$$
320.3.b.c $$4$$ $$8.719$$ $$\Q(\zeta_{10})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{7}+\cdots$$
320.3.b.d $$4$$ $$8.719$$ $$\Q(i, \sqrt{5})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots$$
320.3.e.a $$8$$ $$8.719$$ 8.0.$$\cdots$$.3 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+(-\beta _{4}-\beta _{6})q^{5}+\beta _{2}q^{7}+\cdots$$
320.3.e.b $$16$$ $$8.719$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(-6-\beta _{5}+\cdots)q^{9}+\cdots$$
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