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 51 matches)

Next Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-760-760.107-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.107	$1$	✓	✓			$-0.0941$	$0$	$0.651023$	Character $\chi_{760}(107, \cdot)$
1-760-760.109-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.109	$1$	✓	✓			$0.130$	$0$	$1.18112$	Character $\chi_{760}(109, \cdot)$
1-760-760.139-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.139	$1$	✓	✓			$-0.335$	$0$	$0.312903$	Character $\chi_{760}(139, \cdot)$
1-760-760.147-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.147	$1$	✓	✓			$-0.0316$	$0$	$0.948113$	Character $\chi_{760}(147, \cdot)$
1-760-760.157-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.157	$1$	✓	✓			$0.0943$	$0$	$0.913609$	Character $\chi_{760}(157, \cdot)$
1-760-760.189-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.189	$1$	✓	✓	✓	✓	$0$	$0$	$0.215803$	Character $\chi_{760}(189, \cdot)$
1-760-760.197-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.197	$1$	✓	✓			$-0.0291$	$0$	$0.508682$	Character $\chi_{760}(197, \cdot)$
1-760-760.203-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.203	$1$	✓	✓			$-0.449$	$0$	$0.287318$	Character $\chi_{760}(203, \cdot)$
1-760-760.213-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.213	$1$	✓	✓			$-0.0943$	$0$	$0.294346$	Character $\chi_{760}(213, \cdot)$
1-760-760.227-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.227	$1$	✓	✓			$-0.161$	$0$	$0.358551$	Character $\chi_{760}(227, \cdot)$
1-760-760.237-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.237	$1$	✓	✓			$-0.270$	$0$	$0.476279$	Character $\chi_{760}(237, \cdot)$
1-760-760.243-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.243	$1$	✓	✓			$0.0316$	$0$	$0.680463$	Character $\chi_{760}(243, \cdot)$
1-760-760.253-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.253	$1$	✓	✓			$0.326$	$0$	$0.0187062$	Character $\chi_{760}(253, \cdot)$
1-760-760.269-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.269	$1$	✓	✓			$-0.388$	$0$	$0.172355$	Character $\chi_{760}(269, \cdot)$
1-760-760.27-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.27	$1$	✓	✓			$-0.229$	$0$	$0.816130$	Character $\chi_{760}(27, \cdot)$
1-760-760.277-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.277	$1$	✓	✓			$-0.294$	$0$	$0.397436$	Character $\chi_{760}(277, \cdot)$
1-760-760.29-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.29	$1$	✓	✓			$0.475$	$0$	$1.20829$	Character $\chi_{760}(29, \cdot)$
1-760-760.3-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.3	$1$	✓	✓			$-0.226$	$0$	$0.396105$	Character $\chi_{760}(3, \cdot)$
1-760-760.307-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.307	$1$	✓	✓			$0.449$	$0$	$1.44627$	Character $\chi_{760}(307, \cdot)$
1-760-760.339-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.339	$1$	✓	✓			$0.335$	$0$	$0.837446$	Character $\chi_{760}(339, \cdot)$
1-760-760.363-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.363	$1$	✓	✓			$-0.314$	$0$	$0.434898$	Character $\chi_{760}(363, \cdot)$
1-760-760.397-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.397	$1$	✓	✓			$-0.0533$	$0$	$0.536080$	Character $\chi_{760}(397, \cdot)$
1-760-760.453-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.453	$1$	✓	✓			$0.00235$	$0$	$0.880047$	Character $\chi_{760}(453, \cdot)$
1-760-760.469-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.469	$1$	✓	✓			$0.388$	$0$	$1.28524$	Character $\chi_{760}(469, \cdot)$
1-760-760.483-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.483	$1$	✓	✓			$0.0941$	$0$	$0.611564$	Character $\chi_{760}(483, \cdot)$
1-760-760.499-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.499	$1$	✓	✓			$-0.243$	$0$	$0.226958$	Character $\chi_{760}(499, \cdot)$
1-760-760.507-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.507	$1$	✓	✓			$0.226$	$0$	$0.616368$	Character $\chi_{760}(507, \cdot)$
1-760-760.509-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.509	$1$	✓	✓			$-0.130$	$0$	$0.789999$	Character $\chi_{760}(509, \cdot)$
1-760-760.517-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.517	$1$	✓	✓			$-0.418$	$0$	$0.489328$	Character $\chi_{760}(517, \cdot)$
1-760-760.523-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.523	$1$	✓	✓			$-0.362$	$0$	$0.161862$	Character $\chi_{760}(523, \cdot)$
1-760-760.539-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.539	$1$	✓	✓			$-0.367$	$0$	$0.557328$	Character $\chi_{760}(539, \cdot)$
1-760-760.547-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.547	$1$	✓	✓			$-0.292$	$0$	$0.110429$	Character $\chi_{760}(547, \cdot)$
1-760-760.557-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.557	$1$	✓	✓			$0.00235$	$0$	$0.686798$	Character $\chi_{760}(557, \cdot)$
1-760-760.563-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.563	$1$	✓	✓			$0.229$	$0$	$1.24850$	Character $\chi_{760}(563, \cdot)$
1-760-760.579-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.579	$1$	✓	✓			$0.391$	$0$	$1.00803$	Character $\chi_{760}(579, \cdot)$
1-760-760.603-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.603	$1$	✓	✓			$0.292$	$0$	$0.592145$	Character $\chi_{760}(603, \cdot)$
1-760-760.613-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.613	$1$	✓	✓			$0.418$	$0$	$1.24280$	Character $\chi_{760}(613, \cdot)$
1-760-760.619-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.619	$1$	✓	✓			$0.367$	$0$	$1.41404$	Character $\chi_{760}(619, \cdot)$
1-760-760.629-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.629	$1$	✓	✓			$-0.475$	$0$	$0.246754$	Character $\chi_{760}(629, \cdot)$
1-760-760.653-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.653	$1$	✓	✓			$0.294$	$0$	$1.17922$	Character $\chi_{760}(653, \cdot)$
1-760-760.667-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.667	$1$	✓	✓			$0.362$	$0$	$0.977299$	Character $\chi_{760}(667, \cdot)$
1-760-760.67-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.67	$1$	✓	✓			$0.314$	$0$	$1.29247$	Character $\chi_{760}(67, \cdot)$
1-760-760.683-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.683	$1$	✓	✓			$0.161$	$0$	$1.05458$	Character $\chi_{760}(683, \cdot)$
1-760-760.69-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.69	$1$	✓	✓			$0.0677$	$0$	$0.828710$	Character $\chi_{760}(69, \cdot)$
1-760-760.693-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.693	$1$	✓	✓			$0.0533$	$0$	$0.676388$	Character $\chi_{760}(693, \cdot)$
1-760-760.733-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.733	$1$	✓	✓			$0.0291$	$0$	$0.528766$	Character $\chi_{760}(733, \cdot)$
1-760-760.739-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.739	$1$	✓	✓			$-0.391$	$0$	$0.328414$	Character $\chi_{760}(739, \cdot)$
1-760-760.749-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.749	$1$	✓	✓			$-0.0677$	$0$	$0.351444$	Character $\chi_{760}(749, \cdot)$
1-760-760.757-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.757	$1$	✓	✓			$-0.326$	$0$	$1.79819$	Character $\chi_{760}(757, \cdot)$
1-760-760.93-r1-0-0	$81.6$	$81.6$	$1$	$2^{3} \cdot 5 \cdot 19$	760.93	$1$	✓	✓			$0.270$	$0$	$1.56226$	Character $\chi_{760}(93, \cdot)$

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 51 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.