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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1571.1.b.a	$1571$	$1$	1571.b	1571.b	$2$	$8$	$8$	$0.784$	\(\Q(\zeta_{34})^+\)	$D_{17}$	\(\Q(\sqrt{-1571}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q+\beta _{6}q^{3}+q^{4}-\beta _{7}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)