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Results (11 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
695.1.d.a	$695$	$1$	695.d	695.d	$2$	$1$	$1$	$0.347$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-695}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-q^{2}-q^{3}+q^{5}+q^{6}+q^{8}-q^{10}+\cdots\)
695.1.d.b	$695$	$1$	695.d	695.d	$2$	$1$	$1$	$0.347$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-139}) \), \(\Q(\sqrt{-695}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{4}+q^{5}-q^{9}+2q^{11}+q^{16}-q^{20}+\cdots\)
695.1.d.c	$695$	$1$	695.d	695.d	$2$	$1$	$1$	$0.347$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-695}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(1\)	\(0\)	$1$		\(q+q^{2}+q^{3}+q^{5}+q^{6}-q^{8}+q^{10}+\cdots\)
695.1.d.e	$695$	$1$	695.d	695.d	$2$	$2$	$2$	$0.347$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-695}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{2}-\beta q^{3}+q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
695.1.d.f	$695$	$1$	695.d	695.d	$2$	$2$	$2$	$0.347$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-695}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta q^{2}+\beta q^{3}+2q^{4}+q^{5}-3q^{6}+\cdots\)
695.1.d.g	$695$	$1$	695.d	695.d	$2$	$4$	$4$	$0.347$	\(\Q(\zeta_{24})^+\)	$D_{12}$	\(\Q(\sqrt{-695}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
3475.1.c.a	$3475$	$1$	3475.c	139.b	$2$	$1$	$1$	$1.734$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-139}) \), \(\Q(\sqrt{-695}) \)	\(\Q(\sqrt{5}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{9}+2q^{11}+q^{16}-2q^{29}+\cdots\)
3475.1.c.c	$3475$	$1$	3475.c	139.b	$2$	$2$	$2$	$1.734$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-695}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
3475.1.c.d	$3475$	$1$	3475.c	139.b	$2$	$2$	$2$	$1.734$	\(\Q(\sqrt{-2}) \)	$D_{4}$	\(\Q(\sqrt{-695}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+\beta q^{3}-q^{4}+2q^{6}-q^{9}-2q^{11}+\cdots\)
3475.1.c.e	$3475$	$1$	3475.c	139.b	$2$	$2$	$2$	$1.734$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-695}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}+iq^{3}+q^{6}-iq^{8}-q^{11}+\cdots\)
3475.1.c.g	$3475$	$1$	3475.c	139.b	$2$	$4$	$4$	$1.734$	\(\Q(\sqrt{-2}, \sqrt{3})\)	$D_{12}$	\(\Q(\sqrt{-695}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-q^{6}+\cdots\)