## Results (displaying matches 1-50 of 401) Next

Label Dim. $$A$$ Field CM RM Traces Fricke sign $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
400.1.b.a $$1$$ $$0.200$$ $$\Q$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+q^{9}-2q^{29}-2q^{41}+q^{49}-2q^{61}+\cdots$$
400.1.x.a $$4$$ $$0.200$$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q+\zeta_{10}^{3}q^{5}-\zeta_{10}^{4}q^{9}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots$$
400.2.a.a $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$-3$$ $$0$$ $$2$$ $$+$$ $$q-3q^{3}+2q^{7}+6q^{9}-q^{11}-4q^{13}+\cdots$$
400.2.a.b $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$-2$$ $$-$$ $$q-2q^{3}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$$
400.2.a.c $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$-2$$ $$0$$ $$2$$ $$-$$ $$q-2q^{3}+2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots$$
400.2.a.d $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$-1$$ $$0$$ $$-2$$ $$+$$ $$q-q^{3}-2q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots$$
400.2.a.e $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$0$$ $$0$$ $$-4$$ $$+$$ $$q-4q^{7}-3q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots$$
400.2.a.f $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$1$$ $$0$$ $$2$$ $$-$$ $$q+q^{3}+2q^{7}-2q^{9}+3q^{11}+4q^{13}+\cdots$$
400.2.a.g $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$2$$ $$0$$ $$2$$ $$-$$ $$q+2q^{3}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots$$
400.2.a.h $$1$$ $$3.194$$ $$\Q$$ None None $$0$$ $$3$$ $$0$$ $$-2$$ $$-$$ $$q+3q^{3}-2q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots$$
400.2.c.a $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}+2iq^{7}-6q^{9}-q^{11}+4iq^{13}+\cdots$$
400.2.c.b $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}+iq^{13}+3iq^{17}+\cdots$$
400.2.c.c $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-2iq^{7}+2q^{9}+3q^{11}+4iq^{13}+\cdots$$
400.2.c.d $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{7}+3q^{9}-4q^{11}+iq^{13}+iq^{17}+\cdots$$
400.2.j.a $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$0$$ $$0$$ $$6$$ $$q+(-1+i)q^{2}-2iq^{3}-2iq^{4}+(2+\cdots)q^{6}+\cdots$$
400.2.j.b $$8$$ $$3.194$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}-\zeta_{24}^{5})q^{2}+(\zeta_{24}^{4}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots$$
400.2.j.c $$16$$ $$3.194$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{12}q^{2}-\beta _{8}q^{3}+\beta _{15}q^{4}+(-1+\cdots)q^{6}+\cdots$$
400.2.j.d $$18$$ $$3.194$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$4$$ $$0$$ $$0$$ $$-2$$ $$q-\beta _{7}q^{2}+\beta _{16}q^{3}+\beta _{14}q^{4}+(-1+\cdots)q^{6}+\cdots$$
400.2.j.e $$24$$ $$3.194$$ None None $$0$$ $$0$$ $$0$$ $$0$$
400.2.l.a $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$0$$ $$0$$ $$q+(-1+i)q^{2}+(-1+i)q^{3}-2iq^{4}+\cdots$$
400.2.l.b $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$2$$ $$0$$ $$0$$ $$q+(1-i)q^{2}+(1-i)q^{3}-2iq^{4}-2iq^{6}+\cdots$$
400.2.l.c $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$2$$ $$0$$ $$0$$ $$q+(1+i)q^{2}+(1-i)q^{3}+2iq^{4}+2q^{6}+\cdots$$
400.2.l.d $$4$$ $$3.194$$ $$\Q(i, \sqrt{11})$$ None None $$-4$$ $$-2$$ $$0$$ $$0$$ $$q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$$
400.2.l.e $$4$$ $$3.194$$ $$\Q(i, \sqrt{11})$$ None None $$4$$ $$2$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$$
400.2.l.f $$12$$ $$3.194$$ 12.0.$$\cdots$$.1 None None $$-4$$ $$-2$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}-\beta _{6}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$$
400.2.l.g $$12$$ $$3.194$$ 12.0.$$\cdots$$.1 None None $$4$$ $$2$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots$$
400.2.l.h $$16$$ $$3.194$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+(\beta _{4}+\beta _{11})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$$
400.2.l.i $$16$$ $$3.194$$ 16.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+(-\beta _{2}+\beta _{9}+\beta _{12}-\beta _{14}+\cdots)q^{3}+\cdots$$
400.2.n.a $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-3iq^{9}+(5-5i)q^{13}+(5+5i)q^{17}+\cdots$$
400.2.n.b $$4$$ $$3.194$$ $$\Q(\zeta_{12})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+\zeta_{12}^{3}q^{7}+3\zeta_{12}q^{9}+\cdots$$
400.2.n.c $$4$$ $$3.194$$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{3}q^{3}+\beta _{2}q^{7}-7\beta _{1}q^{9}+10q^{21}+\cdots$$
400.2.n.d $$8$$ $$3.194$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{3}+4\zeta_{24}^{5}q^{7}-2\zeta_{24}^{3}q^{9}+\cdots$$
400.2.q.a $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$-2$$ $$-2$$ $$0$$ $$-4$$ $$q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots$$
400.2.q.b $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$2$$ $$0$$ $$4$$ $$q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+2q^{6}+\cdots$$
400.2.q.c $$4$$ $$3.194$$ $$\Q(i, \sqrt{11})$$ None None $$-4$$ $$2$$ $$0$$ $$-4$$ $$q+(-1-\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$$
400.2.q.d $$4$$ $$3.194$$ $$\Q(i, \sqrt{11})$$ None None $$4$$ $$-2$$ $$0$$ $$4$$ $$q+(1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+2\beta _{1}q^{4}+\cdots$$
400.2.q.e $$12$$ $$3.194$$ 12.0.$$\cdots$$.1 None None $$-2$$ $$2$$ $$0$$ $$-12$$ $$q-\beta _{6}q^{2}-\beta _{7}q^{3}+\beta _{10}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$$
400.2.q.f $$12$$ $$3.194$$ 12.0.$$\cdots$$.1 None None $$2$$ $$-2$$ $$0$$ $$12$$ $$q+\beta _{6}q^{2}+\beta _{7}q^{3}+\beta _{10}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$$
400.2.q.g $$16$$ $$3.194$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-4$$ $$0$$ $$0$$ $$-8$$ $$q+\beta _{2}q^{2}+(-\beta _{6}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$$
400.2.q.h $$16$$ $$3.194$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$4$$ $$0$$ $$0$$ $$8$$ $$q-\beta _{2}q^{2}+(\beta _{6}+\beta _{11})q^{3}+(-\beta _{2}-\beta _{12}+\cdots)q^{4}+\cdots$$
400.2.s.a $$2$$ $$3.194$$ $$\Q(\sqrt{-1})$$ None None $$2$$ $$4$$ $$0$$ $$6$$ $$q+(1-i)q^{2}+2q^{3}-2iq^{4}+(2-2i)q^{6}+\cdots$$
400.2.s.b $$8$$ $$3.194$$ $$\Q(\zeta_{24})$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{24}-\zeta_{24}^{5})q^{2}+\zeta_{24}^{7}q^{3}-2q^{4}+\cdots$$
400.2.s.c $$16$$ $$3.194$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}+\beta _{5}q^{3}-\beta _{15}q^{4}+(-1-\beta _{11}+\cdots)q^{6}+\cdots$$
400.2.s.d $$18$$ $$3.194$$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+\beta _{2}q^{2}+\beta _{4}q^{3}-\beta _{14}q^{4}+(-1-\beta _{3}+\cdots)q^{6}+\cdots$$
400.2.s.e $$24$$ $$3.194$$ None None $$0$$ $$0$$ $$0$$ $$0$$
400.2.u.a $$4$$ $$3.194$$ $$\Q(\zeta_{10})$$ None None $$0$$ $$-5$$ $$-5$$ $$-6$$ $$q+(-2+2\zeta_{10}+\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots$$
400.2.u.b $$4$$ $$3.194$$ $$\Q(\zeta_{10})$$ None None $$0$$ $$1$$ $$-5$$ $$2$$ $$q+\zeta_{10}^{3}q^{3}+(-2+\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{5}+\cdots$$
400.2.u.c $$4$$ $$3.194$$ $$\Q(\zeta_{10})$$ None None $$0$$ $$1$$ $$5$$ $$12$$ $$q+(1-\zeta_{10}-2\zeta_{10}^{3})q^{3}+(2-2\zeta_{10}+\cdots)q^{5}+\cdots$$
400.2.u.d $$8$$ $$3.194$$ 8.0.58140625.2 None None $$0$$ $$3$$ $$0$$ $$-4$$ $$q+(\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$$
400.2.u.e $$8$$ $$3.194$$ 8.0.58140625.2 None None $$0$$ $$6$$ $$5$$ $$-4$$ $$q+(1-\beta _{3})q^{3}+(-\beta _{4}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$$
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