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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1699.1.b.a	$1699$	$1$	1699.b	1699.b	$2$	$5$	$5$	$0.848$	\(\Q(\zeta_{22})^+\)	$D_{11}$	\(\Q(\sqrt{-1699}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q+q^{4}+\beta _{4}q^{5}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)