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 (28 matches)

Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-273-273.107-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.107	$1$	✓	✓	$0.469$	$0$	$1.67776$	Character $\chi_{273}(107, \cdot)$
1-273-273.110-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.110	$1$	✓	✓	$-0.359$	$0$	$0.203925$	Character $\chi_{273}(110, \cdot)$
1-273-273.116-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.116	$1$	✓	✓	$0.239$	$0$	$0.797297$	Character $\chi_{273}(116, \cdot)$
1-273-273.122-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.122	$1$	✓	✓	$0.400$	$0$	$1.66489$	Character $\chi_{273}(122, \cdot)$
1-273-273.125-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.125	$1$	✓	✓	$0.453$	$0$	$0.0523030$	Character $\chi_{273}(125, \cdot)$
1-273-273.164-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.164	$1$	✓	✓	$0.306$	$0$	$1.43496$	Character $\chi_{273}(164, \cdot)$
1-273-273.167-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.167	$1$	✓	✓	$-0.493$	$0$	$2.15547$	Character $\chi_{273}(167, \cdot)$
1-273-273.179-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.179	$1$	✓	✓	$0.154$	$0$	$1.13986$	Character $\chi_{273}(179, \cdot)$
1-273-273.188-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.188	$1$	✓	✓	$0.493$	$0$	$0.438641$	Character $\chi_{273}(188, \cdot)$
1-273-273.191-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.191	$1$	✓	✓	$0.0507$	$0$	$1.31371$	Character $\chi_{273}(191, \cdot)$
1-273-273.20-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.20	$1$	✓	✓	$0.0874$	$0$	$0.774240$	Character $\chi_{273}(20, \cdot)$
1-273-273.206-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.206	$1$	✓	✓	$0.359$	$0$	$1.03854$	Character $\chi_{273}(206, \cdot)$
1-273-273.212-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.212	$1$	✓	✓	$-0.154$	$0$	$0.438691$	Character $\chi_{273}(212, \cdot)$
1-273-273.215-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.215	$1$	✓	✓	$0.233$	$0$	$1.57533$	Character $\chi_{273}(215, \cdot)$
1-273-273.227-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.227	$1$	✓	✓	$0.347$	$0$	$1.24438$	Character $\chi_{273}(227, \cdot)$
1-273-273.23-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.23	$1$	✓	✓	$-0.325$	$0$	$0.517953$	Character $\chi_{273}(23, \cdot)$
1-273-273.233-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.233	$1$	✓	✓	$-0.239$	$0$	$0.621773$	Character $\chi_{273}(233, \cdot)$
1-273-273.236-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.236	$1$	✓	✓	$0.0590$	$0$	$0.365099$	Character $\chi_{273}(236, \cdot)$
1-273-273.263-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.263	$1$	✓	✓	$-0.0507$	$0$	$0.561228$	Character $\chi_{273}(263, \cdot)$
1-273-273.41-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.41	$1$	✓	✓	$-0.0874$	$0$	$0.905026$	Character $\chi_{273}(41, \cdot)$
1-273-273.47-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.47	$1$	✓	✓	$-0.400$	$0$	$0.167599$	Character $\chi_{273}(47, \cdot)$
1-273-273.5-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.5	$1$	✓	✓	$-0.306$	$0$	$0.613415$	Character $\chi_{273}(5, \cdot)$
1-273-273.59-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.59	$1$	✓	✓	$-0.0590$	$0$	$0.784285$	Character $\chi_{273}(59, \cdot)$
1-273-273.74-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.74	$1$	✓	✓	$-0.469$	$0$	$0.241226$	Character $\chi_{273}(74, \cdot)$
1-273-273.80-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.80	$1$	✓	✓	$-0.233$	$0$	$0.923329$	Character $\chi_{273}(80, \cdot)$
1-273-273.83-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.83	$1$	✓	✓	$-0.453$	$0$	$1.32131$	Character $\chi_{273}(83, \cdot)$
1-273-273.89-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.89	$1$	✓	✓	$-0.347$	$0$	$0.755263$	Character $\chi_{273}(89, \cdot)$
1-273-273.95-r1-0-0	$29.3$	$29.3$	$1$	$3 \cdot 7 \cdot 13$	273.95	$1$	✓	✓	$0.325$	$0$	$1.87142$	Character $\chi_{273}(95, \cdot)$

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 (28 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.