## Results (47 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1045.1.k.a $2$ $0.522$ $$\Q(\sqrt{-1})$$ None $$\Q(\sqrt{209})$$ $$-2$$ $$0$$ $$0$$ $$0$$ $$q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots$$
1045.1.k.b $2$ $0.522$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$-2$$ $$q-iq^{4}+q^{5}+(-1+i)q^{7}-iq^{9}+\cdots$$
1045.1.k.c $2$ $0.522$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$2$$ $$2$$ $$q-iq^{4}+q^{5}+(1-i)q^{7}-iq^{9}+iq^{11}+\cdots$$
1045.1.k.d $2$ $0.522$ $$\Q(\sqrt{-1})$$ None $$\Q(\sqrt{209})$$ $$2$$ $$0$$ $$0$$ $$0$$ $$q+(1+i)q^{2}+iq^{4}-iq^{5}+q^{8}-iq^{9}+\cdots$$
1045.1.w.a $4$ $0.522$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-95})$$ None $$-2$$ $$-2$$ $$-1$$ $$0$$ $$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$$
1045.1.w.b $4$ $0.522$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$-5$$ $$q+\zeta_{10}q^{4}-\zeta_{10}q^{5}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$$
1045.1.w.c $4$ $0.522$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$5$$ $$q+\zeta_{10}q^{4}-\zeta_{10}^{3}q^{5}+(1-\zeta_{10}^{2})q^{7}+\cdots$$
1045.1.w.d $4$ $0.522$ $$\Q(\zeta_{10})$$ $$\Q(\sqrt{-95})$$ None $$2$$ $$2$$ $$-1$$ $$0$$ $$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$$
1045.1.w.e $8$ $0.522$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{3}+\cdots$$
1045.1.w.f $16$ $0.522$ $$\Q(\zeta_{40})$$ $$\Q(\sqrt{-95})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots$$
1045.1.br.a $8$ $0.522$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$-8$$ $$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots$$
1045.1.br.b $8$ $0.522$ $$\Q(\zeta_{20})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$-2$$ $$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots$$
1045.2.a.a $1$ $8.344$ $$\Q$$ None None $$-1$$ $$-2$$ $$-1$$ $$-2$$ $+$ $$q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots$$
1045.2.a.b $1$ $8.344$ $$\Q$$ None None $$1$$ $$0$$ $$1$$ $$0$$ $+$ $$q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots$$
1045.2.a.c $2$ $8.344$ $$\Q(\sqrt{2})$$ None None $$2$$ $$4$$ $$2$$ $$0$$ $-$ $$q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots$$
1045.2.a.d $5$ $8.344$ $$\Q(\zeta_{22})^+$$ None None $$-3$$ $$-7$$ $$5$$ $$-11$$ $+$ $$q+(-1+\beta _{1}-\beta _{4})q^{2}+(-2-\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$$
1045.2.a.e $5$ $8.344$ 5.5.36497.1 None None $$-1$$ $$-3$$ $$-5$$ $$3$$ $+$ $$q+\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+\beta _{3}q^{4}-q^{5}+\cdots$$
1045.2.a.f $6$ $8.344$ 6.6.7281497.1 None None $$-2$$ $$-1$$ $$-6$$ $$5$$ $+$ $$q-\beta _{4}q^{2}+\beta _{3}q^{3}+(\beta _{4}+\beta _{5})q^{4}-q^{5}+\cdots$$
1045.2.a.g $6$ $8.344$ 6.6.131947641.1 None None $$0$$ $$3$$ $$6$$ $$5$$ $-$ $$q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$
1045.2.a.h $7$ $8.344$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$1$$ $$3$$ $$-7$$ $$-1$$ $-$ $$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$$
1045.2.a.i $8$ $8.344$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$-6$$ $$-7$$ $$8$$ $$-11$$ $+$ $$q+(-1+\beta _{1})q^{2}+(-1-\beta _{6})q^{3}+(2+\cdots)q^{4}+\cdots$$
1045.2.a.j $9$ $8.344$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$3$$ $$3$$ $$-9$$ $$-9$$ $-$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{8})q^{4}+\cdots$$
1045.2.a.k $9$ $8.344$ $$\mathbb{Q}[x]/(x^{9} - \cdots)$$ None None $$3$$ $$3$$ $$9$$ $$13$$ $-$ $$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$$
1045.2.b.a $4$ $8.344$ $$\Q(\zeta_{8})$$ None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$$
1045.2.b.b $16$ $8.344$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None None $$0$$ $$0$$ $$3$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{13}+\cdots)q^{5}+\cdots$$
1045.2.b.c $20$ $8.344$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots$$
1045.2.b.d $22$ $8.344$ None None $$0$$ $$0$$ $$7$$ $$0$$
1045.2.b.e $30$ $8.344$ None None $$0$$ $$0$$ $$0$$ $$0$$
1045.2.f.a $40$ $8.344$ None None $$0$$ $$0$$ $$-40$$ $$0$$
1045.2.f.b $40$ $8.344$ None None $$0$$ $$0$$ $$40$$ $$0$$
1045.4.a.a $1$ $61.657$ $$\Q$$ None None $$-5$$ $$-1$$ $$-5$$ $$-2$$ $-$ $$q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots$$
1045.4.a.b $20$ $61.657$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$-12$$ $$-21$$ $$100$$ $$-131$$ $-$ $$q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(4+\cdots)q^{4}+\cdots$$
1045.4.a.c $20$ $61.657$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$-1$$ $$-8$$ $$-100$$ $$49$$ $-$ $$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots$$
1045.4.a.d $22$ $61.657$ None None $$-4$$ $$-21$$ $$110$$ $$-41$$ $-$
1045.4.a.e $22$ $61.657$ None None $$12$$ $$21$$ $$110$$ $$93$$ $+$
1045.4.a.f $23$ $61.657$ None None $$-2$$ $$-9$$ $$-115$$ $$13$$ $-$
1045.4.a.g $23$ $61.657$ None None $$6$$ $$9$$ $$-115$$ $$-37$$ $+$
1045.4.a.h $24$ $61.657$ None None $$4$$ $$21$$ $$120$$ $$71$$ $+$
1045.4.a.i $25$ $61.657$ None None $$2$$ $$9$$ $$-125$$ $$-15$$ $+$
1045.6.a.a $35$ $167.601$ None None $$-4$$ $$-27$$ $$-875$$ $$117$$ $+$
1045.6.a.b $36$ $167.601$ None None $$-8$$ $$-63$$ $$900$$ $$-509$$ $+$
1045.6.a.c $37$ $167.601$ None None $$-12$$ $$-27$$ $$-925$$ $$337$$ $+$
1045.6.a.d $37$ $167.601$ None None $$4$$ $$27$$ $$-925$$ $$-79$$ $-$
1045.6.a.e $38$ $167.601$ None None $$-24$$ $$-63$$ $$950$$ $$-729$$ $+$
1045.6.a.f $38$ $167.601$ None None $$8$$ $$63$$ $$950$$ $$275$$ $-$
1045.6.a.g $39$ $167.601$ None None $$12$$ $$27$$ $$-975$$ $$-251$$ $-$
1045.6.a.h $40$ $167.601$ None None $$24$$ $$63$$ $$1000$$ $$839$$ $-$