## Results (1-50 of 110 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.1.c.a $1$ $0.038$ $$\Q$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$-1$$ $$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$$
76.2.a.a $1$ $0.607$ $$\Q$$ None None $$0$$ $$2$$ $$-1$$ $$-3$$ $-$ $$q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots$$
76.2.d.a $8$ $0.607$ 8.0.$$\cdots$$.1 None None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$$
76.2.e.a $2$ $0.607$ $$\Q(\sqrt{-3})$$ None None $$0$$ $$1$$ $$1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$$
76.2.f.a $16$ $0.607$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None None $$-3$$ $$0$$ $$-2$$ $$0$$ $$q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots$$
76.2.i.a $12$ $0.607$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-3$$ $$0$$ $$3$$ $$q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots$$
76.2.k.a $48$ $0.607$ None None $$-6$$ $$0$$ $$-12$$ $$0$$
76.3.b.a $4$ $2.071$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None None $$-4$$ $$0$$ $$-4$$ $$0$$ $$q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots$$
76.3.b.b $14$ $2.071$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots$$
76.3.c.a $2$ $2.071$ $$\Q(\sqrt{-29})$$ None None $$0$$ $$0$$ $$-8$$ $$-2$$ $$q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots$$
76.3.c.b $2$ $2.071$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$9$$ $$5$$ $$q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots$$
76.3.g.a $4$ $2.071$ $$\Q(\sqrt{-3}, \sqrt{-10})$$ None None $$-4$$ $$6$$ $$-4$$ $$0$$ $$q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots$$
76.3.g.b $4$ $2.071$ $$\Q(\sqrt{-3}, \sqrt{-10})$$ None None $$8$$ $$-6$$ $$-4$$ $$0$$ $$q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots$$
76.3.g.c $28$ $2.071$ None None $$-5$$ $$0$$ $$6$$ $$0$$
76.3.h.a $8$ $2.071$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None None $$0$$ $$6$$ $$-1$$ $$-12$$ $$q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
76.3.j.a $18$ $2.071$ $$\mathbb{Q}[x]/(x^{18} + \cdots)$$ None None $$0$$ $$-6$$ $$0$$ $$9$$ $$q+(-\beta _{4}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{12})q^{3}+\cdots$$
76.3.l.a $108$ $2.071$ None None $$-6$$ $$0$$ $$-12$$ $$0$$
76.4.a.a $2$ $4.484$ $$\Q(\sqrt{33})$$ None None $$0$$ $$-5$$ $$-5$$ $$-30$$ $-$ $$q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots$$
76.4.a.b $3$ $4.484$ 3.3.35529.1 None None $$0$$ $$1$$ $$9$$ $$44$$ $+$ $$q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots$$
76.4.d.a $28$ $4.484$ None None $$0$$ $$0$$ $$-4$$ $$0$$
76.4.e.a $10$ $4.484$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None None $$0$$ $$7$$ $$-4$$ $$-20$$ $$q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots$$
76.4.f.a $56$ $4.484$ None None $$-3$$ $$0$$ $$-2$$ $$0$$
76.4.i.a $30$ $4.484$ None None $$0$$ $$-3$$ $$0$$ $$6$$
76.4.k.a $168$ $4.484$ None None $$-6$$ $$0$$ $$-12$$ $$0$$
76.5.b.a $36$ $7.856$ None None $$6$$ $$0$$ $$24$$ $$0$$
76.5.c.a $2$ $7.856$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-31$$ $$73$$ $$q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots$$
76.5.c.b $4$ $7.856$ $$\mathbb{Q}[x]/(x^{4} + \cdots)$$ None None $$0$$ $$0$$ $$22$$ $$24$$ $$q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots$$
76.5.g.a $76$ $7.856$ None None $$-1$$ $$0$$ $$-2$$ $$0$$
76.5.h.a $12$ $7.856$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None None $$0$$ $$-12$$ $$9$$ $$-52$$ $$q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$
76.5.j.a $42$ $7.856$ None None $$0$$ $$12$$ $$0$$ $$-45$$
76.5.l.a $228$ $7.856$ None None $$-6$$ $$0$$ $$-12$$ $$0$$
76.6.a.a $3$ $12.189$ 3.3.272193.1 None None $$0$$ $$-8$$ $$-9$$ $$-13$$ $+$ $$q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots$$
76.6.a.b $4$ $12.189$ $$\mathbb{Q}[x]/(x^{4} - \cdots)$$ None None $$0$$ $$10$$ $$-110$$ $$30$$ $-$ $$q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots$$
76.6.d.a $48$ $12.189$ None None $$0$$ $$0$$ $$-4$$ $$0$$
76.6.e.a $18$ $12.189$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None None $$0$$ $$-11$$ $$11$$ $$336$$ $$q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots$$
76.6.f.a $96$ $12.189$ None None $$-3$$ $$0$$ $$-2$$ $$0$$
76.6.i.a $48$ $12.189$ None None $$0$$ $$33$$ $$0$$ $$-177$$
76.6.k.a $288$ $12.189$ None None $$-6$$ $$0$$ $$-12$$ $$0$$
76.7.b.a $54$ $17.484$ None None $$-10$$ $$0$$ $$-44$$ $$0$$
76.7.c.a $2$ $17.484$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$54$$ $$-610$$ $$q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots$$
76.7.c.b $8$ $17.484$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None None $$0$$ $$0$$ $$2$$ $$362$$ $$q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$$
76.7.g.a $116$ $17.484$ None None $$-1$$ $$0$$ $$-2$$ $$0$$
76.7.h.a $20$ $17.484$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None None $$0$$ $$-30$$ $$-56$$ $$464$$ $$q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots$$
76.7.j.a $60$ $17.484$ None None $$0$$ $$30$$ $$0$$ $$-216$$
76.7.l.a $348$ $17.484$ None None $$-6$$ $$0$$ $$-12$$ $$0$$
76.8.a.a $5$ $23.741$ $$\mathbb{Q}[x]/(x^{5} - \cdots)$$ None None $$0$$ $$-14$$ $$-280$$ $$414$$ $-$ $$q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$$
76.8.a.b $6$ $23.741$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None None $$0$$ $$40$$ $$279$$ $$-1565$$ $+$ $$q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots$$
76.8.d.a $68$ $23.741$ None None $$0$$ $$0$$ $$-4$$ $$0$$
76.8.e.a $22$ $23.741$ None None $$0$$ $$13$$ $$1$$ $$560$$
76.8.f.a $136$ $23.741$ None None $$-3$$ $$0$$ $$-2$$ $$0$$