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 321 matches)

Next Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-643-643.102-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.102	$1$	✓	✓	$0.138$	$0$	$1.34113$	Character $\chi_{643}(102, \cdot)$
1-643-643.103-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.103	$1$	✓	✓	$0.150$	$0$	$0.0588810$	Character $\chi_{643}(103, \cdot)$
1-643-643.106-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.106	$1$	✓	✓	$-0.0965$	$0$	$1.04080$	Character $\chi_{643}(106, \cdot)$
1-643-643.107-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.107	$1$	✓	✓	$-0.283$	$0$	$0.691436$	Character $\chi_{643}(107, \cdot)$
1-643-643.108-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.108	$1$	✓	✓	$0.346$	$0$	$0.927332$	Character $\chi_{643}(108, \cdot)$
1-643-643.109-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.109	$1$	✓	✓	$-0.300$	$0$	$0.716770$	Character $\chi_{643}(109, \cdot)$
1-643-643.11-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.11	$1$	✓	✓	$-0.243$	$0$	$0.920214$	Character $\chi_{643}(11, \cdot)$
1-643-643.110-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.110	$1$	✓	✓	$-0.365$	$0$	$1.33160$	Character $\chi_{643}(110, \cdot)$
1-643-643.113-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.113	$1$	✓	✓	$-0.372$	$0$	$0.0633524$	Character $\chi_{643}(113, \cdot)$
1-643-643.114-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.114	$1$	✓	✓	$0.0559$	$0$	$1.14098$	Character $\chi_{643}(114, \cdot)$
1-643-643.115-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.115	$1$	✓	✓	$0.202$	$0$	$0.500474$	Character $\chi_{643}(115, \cdot)$
1-643-643.117-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.117	$1$	✓	✓	$0.243$	$0$	$1.08257$	Character $\chi_{643}(117, \cdot)$
1-643-643.119-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.119	$1$	✓	✓	$0.333$	$0$	$0.906446$	Character $\chi_{643}(119, \cdot)$
1-643-643.12-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.12	$1$	✓	✓	$0.316$	$0$	$1.28038$	Character $\chi_{643}(12, \cdot)$
1-643-643.120-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.120	$1$	✓	✓	$-0.202$	$0$	$0.644581$	Character $\chi_{643}(120, \cdot)$
1-643-643.125-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.125	$1$	✓	✓	$0.129$	$0$	$0.864365$	Character $\chi_{643}(125, \cdot)$
1-643-643.126-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.126	$1$	✓	✓	$0.106$	$0$	$0.621278$	Character $\chi_{643}(126, \cdot)$
1-643-643.127-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.127	$1$	✓	✓	$-0.355$	$0$	$0.204239$	Character $\chi_{643}(127, \cdot)$
1-643-643.128-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.128	$1$	✓	✓	$0.00986$	$0$	$0.332906$	Character $\chi_{643}(128, \cdot)$
1-643-643.13-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.13	$1$	✓	✓	$0.282$	$0$	$1.20552$	Character $\chi_{643}(13, \cdot)$
1-643-643.130-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.130	$1$	✓	✓	$0.0736$	$0$	$1.39682$	Character $\chi_{643}(130, \cdot)$
1-643-643.133-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.133	$1$	✓	✓	$0.491$	$0$	$0.837385$	Character $\chi_{643}(133, \cdot)$
1-643-643.137-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.137	$1$	✓	✓	$0.273$	$0$	$1.43547$	Character $\chi_{643}(137, \cdot)$
1-643-643.14-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.14	$1$	✓	✓	$-0.342$	$0$	$1.80886$	Character $\chi_{643}(14, \cdot)$
1-643-643.140-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.140	$1$	✓	✓	$0.0510$	$0$	$0.236753$	Character $\chi_{643}(140, \cdot)$
1-643-643.145-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.145	$1$	✓	✓	$-0.138$	$0$	$0.637852$	Character $\chi_{643}(145, \cdot)$
1-643-643.147-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.147	$1$	✓	✓	$-0.124$	$0$	$1.09256$	Character $\chi_{643}(147, \cdot)$
1-643-643.148-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.148	$1$	✓	✓	$-0.106$	$0$	$0.116889$	Character $\chi_{643}(148, \cdot)$
1-643-643.151-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.151	$1$	✓	✓	$0.188$	$0$	$0.606022$	Character $\chi_{643}(151, \cdot)$
1-643-643.153-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.153	$1$	✓	✓	$-0.206$	$0$	$0.0680223$	Character $\chi_{643}(153, \cdot)$
1-643-643.155-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.155	$1$	✓	✓	$-0.120$	$0$	$0.671665$	Character $\chi_{643}(155, \cdot)$
1-643-643.157-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.157	$1$	✓	✓	$0.481$	$0$	$0.872686$	Character $\chi_{643}(157, \cdot)$
1-643-643.159-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.159	$1$	✓	✓	$-0.230$	$0$	$0.308263$	Character $\chi_{643}(159, \cdot)$
1-643-643.162-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.162	$1$	✓	✓	$-0.164$	$0$	$0.979303$	Character $\chi_{643}(162, \cdot)$
1-643-643.164-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.164	$1$	✓	✓	$-0.214$	$0$	$1.04854$	Character $\chi_{643}(164, \cdot)$
1-643-643.165-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.165	$1$	✓	✓	$0.419$	$0$	$1.73745$	Character $\chi_{643}(165, \cdot)$
1-643-643.166-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.166	$1$	✓	✓	$0.203$	$0$	$0.121243$	Character $\chi_{643}(166, \cdot)$
1-643-643.17-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.17	$1$	✓	✓	$-0.260$	$0$	$2.42255$	Character $\chi_{643}(17, \cdot)$
1-643-643.170-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.170	$1$	✓	✓	$0.171$	$0$	$0.548961$	Character $\chi_{643}(170, \cdot)$
1-643-643.171-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.171	$1$	✓	✓	$-0.105$	$0$	$0.698727$	Character $\chi_{643}(171, \cdot)$
1-643-643.172-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.172	$1$	✓	✓	$0.241$	$0$	$0.0137671$	Character $\chi_{643}(172, \cdot)$
1-643-643.176-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.176	$1$	✓	✓	$-0.0591$	$0$	$0.422760$	Character $\chi_{643}(176, \cdot)$
1-643-643.178-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.178	$1$	✓	✓	$0.0702$	$0$	$0.611019$	Character $\chi_{643}(178, \cdot)$
1-643-643.179-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.179	$1$	✓	✓	$0.105$	$0$	$0.315989$	Character $\chi_{643}(179, \cdot)$
1-643-643.18-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.18	$1$	✓	✓	$-0.472$	$0$	$0.0909291$	Character $\chi_{643}(18, \cdot)$
1-643-643.180-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.180	$1$	✓	✓	$0.210$	$0$	$0.480765$	Character $\chi_{643}(180, \cdot)$
1-643-643.184-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.184	$1$	✓	✓	$0.408$	$0$	$0.291960$	Character $\chi_{643}(184, \cdot)$
1-643-643.188-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.188	$1$	✓	✓	$-0.163$	$0$	$0.786257$	Character $\chi_{643}(188, \cdot)$
1-643-643.189-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.189	$1$	✓	✓	$-0.414$	$0$	$1.82732$	Character $\chi_{643}(189, \cdot)$
1-643-643.19-r1-0-0	$69.0$	$69.0$	$1$	$643$	643.19	$1$	✓	✓	$0.210$	$0$	$0.640221$	Character $\chi_{643}(19, \cdot)$

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 321 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.