LMFDB - L-function search results

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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad $p$	Root analytic conductor	Motivic weight	Spectral label

Root angle	Primitive	Origin	Exclude origin	Self-dual

Arithmetic

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Results (1-50 of at least 1000)

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	$\nu$	$w$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
2-648-648.211-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.211	$$	$0.0$	$0$	✓	✓			$-0.382$	$0$	$0.621897$	Modular form 648.1.bf.a.211.1
2-648-216.187-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	216.187	$$	$0.0$	$0$	✓	✓			$-0.240$	$0$	$1.20756$	Modular form 648.1.r.a.235.1
2-648-216.139-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	216.139	$$	$0.0$	$0$	✓	✓			$-0.0925$	$0$	$1.89428$	Modular form 648.1.r.a.307.1
2-648-648.643-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.643	$$	$0.0$	$0$	✓	✓			$-0.0493$	$0$	$2.05103$	Modular form 648.1.bf.a.643.1
2-648-216.115-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	216.115	$$	$0.0$	$0$	✓	✓			$0.0925$	$0$	$2.15089$	Modular form 648.1.r.a.19.1
2-648-648.187-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.187	$$	$0.0$	$0$	✓	✓			$0.0493$	$0$	$1.80172$	Modular form 648.1.bf.a.187.1
2-648-648.571-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.571	$$	$0.0$	$0$	✓	✓			$0.0617$	$0$	$1.38273$	Modular form 648.1.bf.a.571.1
2-648-648.403-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.403	$$	$0.0$	$0$	✓	✓			$0.0493$	$0$	$1.76495$	Modular form 648.1.bf.a.403.1
2-648-72.29-c0-0-1	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	72.29	$$	$0.0$	$0$	✓	✓			$0.361$	$0$	$2.68129$	Modular form 648.1.j.b.269.1
2-648-216.67-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	216.67	$$	$0.0$	$0$	✓	✓			$0.240$	$0$	$1.70823$	Modular form 648.1.r.a.91.1
2-648-648.475-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.475	$$	$0.0$	$0$	✓	✓			$-0.283$	$0$	$1.19277$	Modular form 648.1.bf.a.475.1
2-648-648.43-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.43	$$	$0.0$	$0$	✓	✓			$0.382$	$0$	$1.74783$	Modular form 648.1.bf.a.43.1
2-648-648.499-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.499	$$	$0.0$	$0$	✓	✓			$-0.0493$	$0$	$1.66458$	Modular form 648.1.bf.a.499.1
2-648-648.115-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.115	$$	$0.0$	$0$	✓	✓			$0.271$	$0$	$2.43172$	Modular form 648.1.bf.a.115.1
2-648-648.331-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.331	$$	$0.0$	$0$	✓	✓			$-0.395$	$0$	$1.18272$	Modular form 648.1.bf.a.331.1
2-648-648.259-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.259	$$	$0.0$	$0$	✓	✓			$0.0493$	$0$	$2.41066$	Modular form 648.1.bf.a.259.1
2-648-648.427-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.427	$$	$0.0$	$0$	✓	✓			$0.283$	$0$	$1.94171$	Modular form 648.1.bf.a.427.1
2-648-648.619-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.619	$$	$0.0$	$0$	✓	✓			$0.0493$	$0$	$1.62119$	Modular form 648.1.bf.a.619.1
2-648-648.283-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.283	$$	$0.0$	$0$	✓	✓			$-0.0493$	$0$	$1.02034$	Modular form 648.1.bf.a.283.1
2-648-216.211-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	216.211	$$	$0.0$	$0$	✓	✓			$-0.0925$	$0$	$1.34644$	Modular form 648.1.r.a.523.1
2-648-216.43-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	216.43	$$	$0.0$	$0$	✓	✓			$0.0925$	$0$	$1.37093$	Modular form 648.1.r.a.451.1
2-648-648.67-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.67	$$	$0.0$	$0$	✓	✓			$-0.0493$	$0$	$1.63438$	Modular form 648.1.bf.a.67.1
2-648-648.547-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.547	$$	$0.0$	$0$	✓	✓			$-0.0617$	$0$	$0.936710$	Modular form 648.1.bf.a.547.1
2-648-8.3-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	8.3	$$	$0.0$	$0$	✓	✓	✓	✓	$0$	$0$	$1.36724$	Artin representation 2.648.6t3.b Artin representation 2.648.6t3.b.a Modular form 648.1.b.a Modular form 648.1.b.a.163.1
2-648-72.5-c0-0-1	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	72.5	$$	$0.0$	$0$	✓	✓			$0.138$	$0$	$1.48015$	Artin representation 2.648.6t5.b.a Modular form 648.1.j.a.53.1
2-648-72.5-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	72.5	$$	$0.0$	$0$	✓	✓			$-0.361$	$0$	$1.09986$	Modular form 648.1.j.b.53.1
2-648-8.3-c0-0-1	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	8.3	$$	$0.0$	$0$	✓	✓	✓	✓	$0$	$0$	$2.07086$	Artin representation 2.648.3t2.b Artin representation 2.648.3t2.b.a Modular form 648.1.b.b Modular form 648.1.b.b.163.1
2-648-72.29-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	72.29	$$	$0.0$	$0$	✓	✓			$-0.138$	$0$	$1.54583$	Artin representation 2.648.6t5.b.b Modular form 648.1.j.a.269.1
2-648-648.139-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.139	$$	$0.0$	$0$	✓	✓			$0.395$	$0$	$2.86034$	Modular form 648.1.bf.a.139.1
2-648-648.355-c0-0-0	$0.568$	$0.323$	$2$	$2^{3} \cdot 3^{4}$	648.355	$$	$0.0$	$0$	✓	✓			$-0.271$	$0$	$1.67990$	Modular form 648.1.bf.a.355.1
2-648-648.155-c1-0-45	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.0485$	$0$	$1.06947$	Modular form 648.2.bb.b.155.28
2-648-648.155-c1-0-43	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.325$	$0$	$1.03619$	Modular form 648.2.bb.b.155.79
2-648-648.155-c1-0-46	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.319$	$0$	$1.08925$	Modular form 648.2.bb.b.155.70
2-648-648.155-c1-0-41	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.278$	$0$	$1.02971$	Modular form 648.2.bb.b.155.101
2-648-648.133-c1-0-17	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.133	$$	$1.0$	$1$	✓	✓			$0.367$	$0$	$0.367794$	Modular form 648.2.bd.a.133.76
2-648-648.155-c1-0-42	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.437$	$0$	$1.03012$	Modular form 648.2.bb.b.155.64
2-648-648.155-c1-0-47	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.0565$	$0$	$1.10740$	Modular form 648.2.bb.b.155.31
2-648-648.155-c1-0-38	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.0627$	$0$	$0.954777$	Modular form 648.2.bb.b.155.17
2-648-648.155-c1-0-36	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$0.0523$	$0$	$0.939173$	Modular form 648.2.bb.b.155.4
2-648-648.155-c1-0-39	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.161$	$0$	$0.985788$	Modular form 648.2.bb.b.155.43
2-648-648.155-c1-0-32	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.272$	$0$	$0.893997$	Modular form 648.2.bb.b.155.25
2-648-648.131-c1-0-94	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.131	$$	$1.0$	$1$	✓	✓			$0.358$	$0$	$2.30222$	Modular form 648.2.bb.b.131.91
2-648-648.155-c1-0-33	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$0.144$	$0$	$0.914430$	Modular form 648.2.bb.b.155.32
2-648-648.155-c1-0-4	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$0.196$	$0$	$0.0266888$	Modular form 648.2.bb.b.155.59
2-648-648.155-c1-0-48	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.228$	$0$	$1.11858$	Modular form 648.2.bb.b.155.103
2-648-648.155-c1-0-102	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.281$	$0$	$2.61572$	Modular form 648.2.bb.b.155.41
2-648-648.131-c1-0-47	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.131	$$	$1.0$	$1$	✓	✓			$-0.165$	$0$	$1.10116$	Modular form 648.2.bb.b.131.20
2-648-648.131-c1-0-91	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.131	$$	$1.0$	$1$	✓	✓			$0.131$	$0$	$2.23342$	Modular form 648.2.bb.b.131.96
2-648-648.155-c1-0-16	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$-0.437$	$0$	$0.561710$	Modular form 648.2.bb.b.155.87
2-648-648.155-c1-0-31	$2.27$	$5.17$	$2$	$2^{3} \cdot 3^{4}$	648.155	$$	$1.0$	$1$	✓	✓			$0.0145$	$0$	$0.868898$	Modular form 648.2.bb.b.155.23

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.