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 641 matches)

Next Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-643-643.10-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.10	$0$	✓	✓	$0.109$	$0$	$1.69959$	Character $\chi_{643}(10, \cdot)$
1-643-643.100-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.100	$0$	✓	✓	$-0.201$	$0$	$0.137426$	Character $\chi_{643}(100, \cdot)$
1-643-643.101-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.101	$0$	✓	✓	$0.0437$	$0$	$1.80612$	Character $\chi_{643}(101, \cdot)$
1-643-643.104-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.104	$0$	✓	✓	$0.463$	$0$	$2.08947$	Character $\chi_{643}(104, \cdot)$
1-643-643.105-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.105	$0$	✓	✓	$0.0128$	$0$	$1.30290$	Character $\chi_{643}(105, \cdot)$
1-643-643.111-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.111	$0$	✓	✓	$0.460$	$0$	$2.23653$	Character $\chi_{643}(111, \cdot)$
1-643-643.112-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.112	$0$	✓	✓	$-0.0784$	$0$	$0.331373$	Character $\chi_{643}(112, \cdot)$
1-643-643.116-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.116	$0$	✓	✓	$-0.124$	$0$	$0.624767$	Character $\chi_{643}(116, \cdot)$
1-643-643.118-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.118	$0$	✓	✓	$0.388$	$0$	$1.65517$	Character $\chi_{643}(118, \cdot)$
1-643-643.121-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.121	$0$	✓	✓	$-0.0183$	$0$	$1.08496$	Character $\chi_{643}(121, \cdot)$
1-643-643.122-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.122	$0$	✓	✓	$0.226$	$0$	$0.919944$	Character $\chi_{643}(122, \cdot)$
1-643-643.123-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.123	$0$	✓	✓	$0.0834$	$0$	$1.32339$	Character $\chi_{643}(123, \cdot)$
1-643-643.124-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.124	$0$	✓	✓	$-0.483$	$0$	$1.65237$	Character $\chi_{643}(124, \cdot)$
1-643-643.129-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.129	$0$	✓	✓	$-0.238$	$0$	$0.839471$	Character $\chi_{643}(129, \cdot)$
1-643-643.131-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.131	$0$	✓	✓	$-0.219$	$0$	$0.659605$	Character $\chi_{643}(131, \cdot)$
1-643-643.132-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.132	$0$	✓	✓	$0.202$	$0$	$1.61745$	Character $\chi_{643}(132, \cdot)$
1-643-643.134-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.134	$0$	✓	✓	$0.222$	$0$	$1.92976$	Character $\chi_{643}(134, \cdot)$
1-643-643.135-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.135	$0$	✓	✓	$-0.435$	$0$	$2.27719$	Character $\chi_{643}(135, \cdot)$
1-643-643.136-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.136	$0$	✓	✓	$0.196$	$0$	$1.43078$	Character $\chi_{643}(136, \cdot)$
1-643-643.138-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.138	$0$	✓	✓	$-0.102$	$0$	$0.825684$	Character $\chi_{643}(138, \cdot)$
1-643-643.139-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.139	$0$	✓	✓	$0.429$	$0$	$1.73102$	Character $\chi_{643}(139, \cdot)$
1-643-643.141-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.141	$0$	✓	✓	$-0.150$	$0$	$0.585721$	Character $\chi_{643}(141, \cdot)$
1-643-643.142-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.142	$0$	✓	✓	$-0.181$	$0$	$0.353800$	Character $\chi_{643}(142, \cdot)$
1-643-643.143-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.143	$0$	✓	✓	$-0.224$	$0$	$1.27963$	Character $\chi_{643}(143, \cdot)$
1-643-643.144-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.144	$0$	✓	✓	$-0.0889$	$0$	$0.968105$	Character $\chi_{643}(144, \cdot)$
1-643-643.146-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.146	$0$	✓	✓	$-0.258$	$0$	$2.19825$	Character $\chi_{643}(146, \cdot)$
1-643-643.149-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.149	$0$	✓	✓	$-0.0961$	$0$	$1.29255$	Character $\chi_{643}(149, \cdot)$
1-643-643.15-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.15	$0$	✓	✓	$0.316$	$0$	$1.89328$	Character $\chi_{643}(15, \cdot)$
1-643-643.150-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.150	$0$	✓	✓	$-0.182$	$0$	$0.936470$	Character $\chi_{643}(150, \cdot)$
1-643-643.152-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.152	$0$	✓	✓	$-0.0995$	$0$	$0.690197$	Character $\chi_{643}(152, \cdot)$
1-643-643.154-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.154	$0$	✓	✓	$-0.372$	$0$	$1.48376$	Character $\chi_{643}(154, \cdot)$
1-643-643.156-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.156	$0$	✓	✓	$-0.137$	$0$	$1.19499$	Character $\chi_{643}(156, \cdot)$
1-643-643.158-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.158	$0$	✓	✓	$-0.237$	$0$	$1.26122$	Character $\chi_{643}(158, \cdot)$
1-643-643.16-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.16	$0$	✓	✓	$0.130$	$0$	$1.31713$	Character $\chi_{643}(16, \cdot)$
1-643-643.160-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.160	$0$	✓	✓	$-0.269$	$0$	$2.18750$	Character $\chi_{643}(160, \cdot)$
1-643-643.161-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.161	$0$	✓	✓	$-0.382$	$0$	$0.897894$	Character $\chi_{643}(161, \cdot)$
1-643-643.163-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.163	$0$	✓	✓	$0.306$	$0$	$1.52538$	Character $\chi_{643}(163, \cdot)$
1-643-643.167-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.167	$0$	✓	✓	$0.499$	$0$	$0.561683$	Character $\chi_{643}(167, \cdot)$
1-643-643.168-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.168	$0$	✓	✓	$-0.460$	$0$	$0.514163$	Character $\chi_{643}(168, \cdot)$
1-643-643.169-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.169	$0$	✓	✓	$0.137$	$0$	$1.35721$	Character $\chi_{643}(169, \cdot)$
1-643-643.173-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.173	$0$	✓	✓	$0.352$	$0$	$1.88157$	Character $\chi_{643}(173, \cdot)$
1-643-643.174-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.174	$0$	✓	✓	$0.243$	$0$	$0.285681$	Character $\chi_{643}(174, \cdot)$
1-643-643.175-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.175	$0$	✓	✓	$0.237$	$0$	$1.70672$	Character $\chi_{643}(175, \cdot)$
1-643-643.177-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.177	$0$	✓	✓	$0.0351$	$0$	$1.85522$	Character $\chi_{643}(177, \cdot)$
1-643-643.181-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.181	$0$	✓	✓	$0.435$	$0$	$0.693059$	Character $\chi_{643}(181, \cdot)$
1-643-643.182-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.182	$0$	✓	✓	$-0.399$	$0$	$0.215406$	Character $\chi_{643}(182, \cdot)$
1-643-643.183-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.183	$0$	✓	✓	$0.314$	$0$	$0.990103$	Character $\chi_{643}(183, \cdot)$
1-643-643.185-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.185	$0$	✓	✓	$0.386$	$0$	$1.42680$	Character $\chi_{643}(185, \cdot)$
1-643-643.186-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.186	$0$	✓	✓	$0.0183$	$0$	$1.46775$	Character $\chi_{643}(186, \cdot)$
1-643-643.187-r0-0-0	$2.98$	$2.98$	$1$	$643$	643.187	$0$	✓	✓	$0.274$	$0$	$0.124668$	Character $\chi_{643}(187, \cdot)$

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 641 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.