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 380 matches)

Next Download displayed columns for results to

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\nu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
2-3549-21.11-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$-0.489$	$0$	$0.0438219$	Modular form 3549.1.bk.d.1691.1
2-3549-21.11-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$-0.406$	$0$	$0.564586$	Artin representation 2.3549.6t5.a.a Modular form 3549.1.bk.b.1691.1
2-3549-21.11-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$-0.489$	$0$	$0.618397$	Modular form 3549.1.bk.c.1691.1
2-3549-21.11-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$-0.156$	$0$	$0.697332$	Modular form 3549.1.bk.e.1691.2
2-3549-21.11-c0-0-4	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$0.0100$	$0$	$0.944096$	Modular form 3549.1.bk.c.1691.2
2-3549-21.11-c0-0-5	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$0.0934$	$0$	$1.07980$	Artin representation 2.3549.12t18.f.b Modular form 3549.1.bk.a.1691.1
2-3549-21.11-c0-0-6	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$0.0100$	$0$	$1.40031$	Modular form 3549.1.bk.d.1691.2
2-3549-21.11-c0-0-7	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.11	$0.0$	✓	✓	$0.343$	$0$	$1.70800$	Modular form 3549.1.bk.e.1691.1
2-3549-21.2-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$-0.0934$	$0$	$0.307844$	Artin representation 2.3549.12t18.f.a Modular form 3549.1.bk.a.170.1
2-3549-21.2-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$-0.343$	$0$	$0.502833$	Modular form 3549.1.bk.e.170.2
2-3549-21.2-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$0.489$	$0$	$1.04276$	Modular form 3549.1.bk.d.170.1
2-3549-21.2-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$0.156$	$0$	$1.42382$	Modular form 3549.1.bk.e.170.1
2-3549-21.2-c0-0-4	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$-0.0100$	$0$	$1.44005$	Modular form 3549.1.bk.c.170.2
2-3549-21.2-c0-0-5	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$0.406$	$0$	$1.48809$	Artin representation 2.3549.6t5.a.b Modular form 3549.1.bk.b.170.1
2-3549-21.2-c0-0-6	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$-0.0100$	$0$	$1.58650$	Modular form 3549.1.bk.d.170.2
2-3549-21.2-c0-0-7	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	21.2	$0.0$	✓	✓	$0.489$	$0$	$1.65992$	Modular form 3549.1.bk.c.170.1
2-3549-273.107-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.107	$0.0$	✓	✓	$-0.424$	$0$	$0.480056$	Modular form 3549.1.s.b.653.2
2-3549-273.107-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.107	$0.0$	✓	✓	$-0.00804$	$0$	$1.31611$	Artin representation 2.3549.12t18.g.b Modular form 3549.1.s.a.653.1
2-3549-273.107-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.107	$0.0$	✓	✓	$0.103$	$0$	$1.47581$	Modular form 3549.1.s.c.653.2
2-3549-273.107-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.107	$0.0$	✓	✓	$0.0752$	$0$	$1.55626$	Modular form 3549.1.s.b.653.1
2-3549-273.107-c0-0-4	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.107	$0.0$	✓	✓	$0.290$	$0$	$1.83657$	Modular form 3549.1.s.c.653.1
2-3549-273.110-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.110	$0.0$	✓	✓	$-0.0184$	$0$	$0.905001$	Modular form 3549.1.ch.b.1202.1
2-3549-273.110-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.110	$0.0$	✓	✓	$-0.317$	$0$	$0.960738$	Modular form 3549.1.ch.c.1202.1
2-3549-273.110-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.110	$0.0$	✓	✓	$0.182$	$0$	$1.51885$	Modular form 3549.1.ch.a.1202.1
2-3549-273.116-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$0.166$	$0$	$0.485144$	Modular form 3549.1.w.c.2027.1
2-3549-273.116-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$-0.0629$	$0$	$1.00531$	Modular form 3549.1.w.d.2027.2
2-3549-273.116-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$-0.146$	$0$	$1.18664$	Modular form 3549.1.w.e.2027.1
2-3549-273.116-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$-0.333$	$0$	$1.21389$	Modular form 3549.1.w.e.2027.2
2-3549-273.116-c0-0-4	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$0.249$	$0$	$1.60006$	Modular form 3549.1.w.d.2027.1
2-3549-273.116-c0-0-5	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$0.353$	$0$	$1.60349$	Modular form 3549.1.w.c.2027.2
2-3549-273.116-c0-0-6	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$0.298$	$0$	$1.84470$	Modular form 3549.1.w.b.2027.1
2-3549-273.116-c0-0-7	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.116	$0.0$	✓	✓	$0.388$	$0$	$1.87761$	Modular form 3549.1.w.a.2027.1
2-3549-273.122-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.122	$0.0$	✓	✓	$-0.272$	$0$	$0.432201$	Modular form 3549.1.cb.a.1760.1
2-3549-273.122-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.122	$0.0$	✓	✓	$-0.223$	$0$	$1.16201$	Modular form 3549.1.cb.c.1760.1
2-3549-273.122-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.122	$0.0$	✓	✓	$0.0266$	$0$	$1.19598$	Modular form 3549.1.cb.d.1760.1
2-3549-273.122-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.122	$0.0$	✓	✓	$-0.111$	$0$	$1.29292$	Modular form 3549.1.cb.b.1760.1
2-3549-273.125-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.125	$0.0$	✓	✓	$0.453$	$0$	$0.483028$	Artin representation 2.3549.8t17.c.a Modular form 3549.1.o.b.944.1
2-3549-273.125-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.125	$0.0$	✓	✓	$0.203$	$0$	$1.19689$	Artin representation 2.3549.8t17.d.b Modular form 3549.1.o.a.944.1
2-3549-273.164-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.164	$0.0$	✓	✓	$-0.178$	$0$	$0.687044$	Modular form 3549.1.cb.a.437.1
2-3549-273.164-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.164	$0.0$	✓	✓	$0.183$	$0$	$0.926874$	Modular form 3549.1.cb.c.437.1
2-3549-273.164-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.164	$0.0$	✓	✓	$-0.0669$	$0$	$1.09270$	Modular form 3549.1.cb.d.437.1
2-3549-273.164-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.164	$0.0$	✓	✓	$0.481$	$0$	$1.32447$	Modular form 3549.1.cb.b.437.1
2-3549-273.167-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.167	$0.0$	✓	✓	$-0.128$	$0$	$0.587876$	Modular form 3549.1.ca.a.2624.1
2-3549-273.167-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.167	$0.0$	✓	✓	$0.170$	$0$	$1.10202$	Modular form 3549.1.ca.d.2624.1
2-3549-273.167-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.167	$0.0$	✓	✓	$0.121$	$0$	$1.25940$	Modular form 3549.1.ca.b.2624.1
2-3549-273.167-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.167	$0.0$	✓	✓	$0.420$	$0$	$1.82681$	Modular form 3549.1.ca.c.2624.1
2-3549-273.179-c0-0-0	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.179	$0.0$	✓	✓	$-0.115$	$0$	$0.889713$	Modular form 3549.1.x.a.1544.1
2-3549-273.179-c0-0-1	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.179	$0.0$	✓	✓	$-0.199$	$0$	$0.896601$	Modular form 3549.1.x.b.1544.2
2-3549-273.179-c0-0-2	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.179	$0.0$	✓	✓	$-0.199$	$0$	$0.989478$	Modular form 3549.1.x.d.1544.2
2-3549-273.179-c0-0-3	$1.33$	$1.77$	$2$	$3 \cdot 7 \cdot 13^{2}$	273.179	$0.0$	✓	✓	$-0.115$	$0$	$1.10542$	Modular form 3549.1.x.c.1544.1

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 380 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.