LMFDB - L-function search results

Refine search

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

		Sort order	Select

Results (1-50 of 72 matches)

Next Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-507-507.11-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.11	$0$	✓	✓	$-0.0813$	$0$	$0.369435$	Character $\chi_{507}(11, \cdot)$
1-507-507.110-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.110	$0$	✓	✓	$0.373$	$0$	$1.47411$	Character $\chi_{507}(110, \cdot)$
1-507-507.119-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.119	$0$	✓	✓	$0.462$	$0$	$2.11454$	Character $\chi_{507}(119, \cdot)$
1-507-507.122-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.122	$0$	✓	✓	$0.491$	$0$	$0.121848$	Character $\chi_{507}(122, \cdot)$
1-507-507.125-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.125	$0$	✓	✓	$0.0813$	$0$	$1.32399$	Character $\chi_{507}(125, \cdot)$
1-507-507.128-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.128	$0$	✓	✓	$-0.129$	$0$	$1.10611$	Character $\chi_{507}(128, \cdot)$
1-507-507.137-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.137	$0$	✓	✓	$0.195$	$0$	$1.82773$	Character $\chi_{507}(137, \cdot)$
1-507-507.149-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.149	$0$	✓	✓	$0.157$	$0$	$1.49099$	Character $\chi_{507}(149, \cdot)$
1-507-507.158-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.158	$0$	✓	✓	$-0.0813$	$0$	$1.30758$	Character $\chi_{507}(158, \cdot)$
1-507-507.161-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.161	$0$	✓	✓	$0.128$	$0$	$1.62071$	Character $\chi_{507}(161, \cdot)$
1-507-507.164-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.164	$0$	✓	✓	$0.0399$	$0$	$1.09418$	Character $\chi_{507}(164, \cdot)$
1-507-507.167-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.167	$0$	✓	✓	$0.0813$	$0$	$1.76836$	Character $\chi_{507}(167, \cdot)$
1-507-507.176-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.176	$0$	✓	✓	$-0.204$	$0$	$0.189626$	Character $\chi_{507}(176, \cdot)$
1-507-507.197-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.197	$0$	✓	✓	$-0.304$	$0$	$0.174398$	Character $\chi_{507}(197, \cdot)$
1-507-507.2-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.2	$0$	✓	✓	$0.0813$	$0$	$0.917545$	Character $\chi_{507}(2, \cdot)$
1-507-507.20-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.20	$0$	✓	✓	$-0.342$	$0$	$0.362752$	Character $\chi_{507}(20, \cdot)$
1-507-507.200-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.200	$0$	✓	✓	$-0.195$	$0$	$0.702190$	Character $\chi_{507}(200, \cdot)$
1-507-507.203-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.203	$0$	✓	✓	$-0.0399$	$0$	$0.987347$	Character $\chi_{507}(203, \cdot)$
1-507-507.206-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.206	$0$	✓	✓	$0.304$	$0$	$1.33974$	Character $\chi_{507}(206, \cdot)$
1-507-507.215-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.215	$0$	✓	✓	$0.0813$	$0$	$1.07610$	Character $\chi_{507}(215, \cdot)$
1-507-507.227-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.227	$0$	✓	✓	$-0.324$	$0$	$0.875738$	Character $\chi_{507}(227, \cdot)$
1-507-507.236-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.236	$0$	✓	✓	$-0.175$	$0$	$0.870334$	Character $\chi_{507}(236, \cdot)$
1-507-507.242-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.242	$0$	✓	✓	$-0.0813$	$0$	$1.22950$	Character $\chi_{507}(242, \cdot)$
1-507-507.245-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.245	$0$	✓	✓	$-0.157$	$0$	$1.09485$	Character $\chi_{507}(245, \cdot)$
1-507-507.254-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.254	$0$	✓	✓	$-0.0813$	$0$	$0.543370$	Character $\chi_{507}(254, \cdot)$
1-507-507.266-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.266	$0$	✓	✓	$0.293$	$0$	$1.19303$	Character $\chi_{507}(266, \cdot)$
1-507-507.275-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.275	$0$	✓	✓	$-0.373$	$0$	$1.67692$	Character $\chi_{507}(275, \cdot)$
1-507-507.278-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.278	$0$	✓	✓	$-0.304$	$0$	$1.08267$	Character $\chi_{507}(278, \cdot)$
1-507-507.281-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.281	$0$	✓	✓	$0.204$	$0$	$1.23475$	Character $\chi_{507}(281, \cdot)$
1-507-507.284-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.284	$0$	✓	✓	$-0.293$	$0$	$0.0574064$	Character $\chi_{507}(284, \cdot)$
1-507-507.293-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.293	$0$	✓	✓	$-0.462$	$0$	$0.595347$	Character $\chi_{507}(293, \cdot)$
1-507-507.305-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.305	$0$	✓	✓	$0.129$	$0$	$1.23895$	Character $\chi_{507}(305, \cdot)$
1-507-507.314-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.314	$0$	✓	✓	$0.204$	$0$	$1.49671$	Character $\chi_{507}(314, \cdot)$
1-507-507.317-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.317	$0$	✓	✓	$-0.128$	$0$	$0.571128$	Character $\chi_{507}(317, \cdot)$
1-507-507.32-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.32	$0$	✓	✓	$-0.304$	$0$	$0.530304$	Character $\chi_{507}(32, \cdot)$
1-507-507.320-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.320	$0$	✓	✓	$-0.491$	$0$	$1.92858$	Character $\chi_{507}(320, \cdot)$
1-507-507.323-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.323	$0$	✓	✓	$0.462$	$0$	$0.638667$	Character $\chi_{507}(323, \cdot)$
1-507-507.332-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.332	$0$	✓	✓	$0.304$	$0$	$2.09079$	Character $\chi_{507}(332, \cdot)$
1-507-507.344-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.344	$0$	✓	✓	$-0.195$	$0$	$0.508623$	Character $\chi_{507}(344, \cdot)$
1-507-507.353-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.353	$0$	✓	✓	$0.462$	$0$	$1.72835$	Character $\chi_{507}(353, \cdot)$
1-507-507.356-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.356	$0$	✓	✓	$0.00887$	$0$	$1.15405$	Character $\chi_{507}(356, \cdot)$
1-507-507.359-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.359	$0$	✓	✓	$-0.128$	$0$	$1.19590$	Character $\chi_{507}(359, \cdot)$
1-507-507.362-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.362	$0$	✓	✓	$0.204$	$0$	$1.21357$	Character $\chi_{507}(362, \cdot)$
1-507-507.371-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.371	$0$	✓	✓	$-0.370$	$0$	$0.616244$	Character $\chi_{507}(371, \cdot)$
1-507-507.383-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.383	$0$	✓	✓	$-0.462$	$0$	$2.18701$	Character $\chi_{507}(383, \cdot)$
1-507-507.392-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.392	$0$	✓	✓	$-0.293$	$0$	$1.08299$	Character $\chi_{507}(392, \cdot)$
1-507-507.395-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.395	$0$	✓	✓	$-0.295$	$0$	$0.498009$	Character $\chi_{507}(395, \cdot)$
1-507-507.398-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.398	$0$	✓	✓	$0.195$	$0$	$0.878936$	Character $\chi_{507}(398, \cdot)$
1-507-507.401-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.401	$0$	✓	✓	$-0.373$	$0$	$0.729908$	Character $\chi_{507}(401, \cdot)$
1-507-507.41-r0-0-0	$2.35$	$2.35$	$1$	$3 \cdot 13^{2}$	507.41	$0$	✓	✓	$0.370$	$0$	$2.03795$	Character $\chi_{507}(41, \cdot)$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 72 matches)

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