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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad \(p\)	Root analytic conductor	Motivic weight	Spectral label

Root number	Primitive	Origin	Exclude origin

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Columns to display		Euler factor constraints
	e.g. 3,7,19		e.g. F3=1-T,F5=1+T+5T^2

Results (4 matches)

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		$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label	Origin	\(F_{ 2 }(T)\)	\(F_{ 3 }(T)\)	\(F_{ 5 }(T)\)	\(F_{ 7 }(T)\)	\(F_{ 71 }(T)\)
4-3328e2-1.1-c1e2-0-16	Modular form 3328.2.a.ba	$1$	$( 1 - T + 3 T^{2} )^{2}$	$1 - 2 T + 3 T^{2} - 10 T^{3} + 25 T^{4}$	$1 + 2 T + 7 T^{2} + 14 T^{3} + 49 T^{4}$	$1 - 26 T + 303 T^{2} - 1846 T^{3} + 5041 T^{4}$
4-3328e2-1.1-c1e2-0-27	Modular form 3328.2.a.o	$1$	$( 1 + T + 3 T^{2} )^{2}$	$1 + 2 T + 3 T^{2} + 10 T^{3} + 25 T^{4}$	$1 + 2 T + 7 T^{2} + 14 T^{3} + 49 T^{4}$	$1 - 26 T + 303 T^{2} - 1846 T^{3} + 5041 T^{4}$
4-6928e2-1.1-c1e2-0-0	Modular form 6928.2.a.f	$1$	$1 + 4 T^{2} + 9 T^{4}$	$1 + 8 T^{2} + 25 T^{4}$	$1 + 2 T + 7 T^{2} + 14 T^{3} + 49 T^{4}$	$1 - 26 T + 303 T^{2} - 1846 T^{3} + 5041 T^{4}$
4-7257e2-1.1-c1e2-0-0	Modular form 7257.2.a.p	$( 1 - T + 2 T^{2} )^{2}$	$( 1 - T )^{2}$	$1 - 2 T + 3 T^{2} - 10 T^{3} + 25 T^{4}$	$( 1 + 3 T + 7 T^{2} )^{2}$	$1 - 26 T + 303 T^{2} - 1846 T^{3} + 5041 T^{4}$