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 at least 1000)

Next To download results, determine the number of results.

Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1259-1259.100-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.100	$0$	✓	✓	$-0.460$	$0$	$1.96003$	Character $\chi_{1259}(100, \cdot)$
1-1259-1259.1001-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1001	$0$	✓	✓	$-0.353$	$0$	$0.349064$	Character $\chi_{1259}(1001, \cdot)$
1-1259-1259.1005-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1005	$0$	✓	✓	$0.0505$	$0$	$0.929651$	Character $\chi_{1259}(1005, \cdot)$
1-1259-1259.1006-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1006	$0$	✓	✓	$0.155$	$0$	$0.572977$	Character $\chi_{1259}(1006, \cdot)$
1-1259-1259.1008-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1008	$0$	✓	✓	$-0.291$	$0$	$0.536507$	Character $\chi_{1259}(1008, \cdot)$
1-1259-1259.1009-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1009	$0$	✓	✓	$-0.470$	$0$	$0.519223$	Character $\chi_{1259}(1009, \cdot)$
1-1259-1259.101-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.101	$0$	✓	✓	$-0.0664$	$0$	$0.959871$	Character $\chi_{1259}(101, \cdot)$
1-1259-1259.1017-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1017	$0$	✓	✓	$0.209$	$0$	$0.533483$	Character $\chi_{1259}(1017, \cdot)$
1-1259-1259.1020-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1020	$0$	✓	✓	$-0.107$	$0$	$1.48947$	Character $\chi_{1259}(1020, \cdot)$
1-1259-1259.1021-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1021	$0$	✓	✓	$0.222$	$0$	$1.28934$	Character $\chi_{1259}(1021, \cdot)$
1-1259-1259.1023-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1023	$0$	✓	✓	$-0.0451$	$0$	$1.03524$	Character $\chi_{1259}(1023, \cdot)$
1-1259-1259.1024-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1024	$0$	✓	✓	$-0.163$	$0$	$1.04175$	Character $\chi_{1259}(1024, \cdot)$
1-1259-1259.1026-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1026	$0$	✓	✓	$-0.0468$	$0$	$0.0224149$	Character $\chi_{1259}(1026, \cdot)$
1-1259-1259.1028-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1028	$0$	✓	✓	$0.378$	$0$	$1.21286$	Character $\chi_{1259}(1028, \cdot)$
1-1259-1259.1029-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1029	$0$	✓	✓	$0.390$	$0$	$0.224482$	Character $\chi_{1259}(1029, \cdot)$
1-1259-1259.1030-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1030	$0$	✓	✓	$0.447$	$0$	$1.39161$	Character $\chi_{1259}(1030, \cdot)$
1-1259-1259.1031-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1031	$0$	✓	✓	$-0.398$	$0$	$1.85021$	Character $\chi_{1259}(1031, \cdot)$
1-1259-1259.1033-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1033	$0$	✓	✓	$0.499$	$0$	$1.63156$	Character $\chi_{1259}(1033, \cdot)$
1-1259-1259.1035-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1035	$0$	✓	✓	$-0.0899$	$0$	$1.10817$	Character $\chi_{1259}(1035, \cdot)$
1-1259-1259.1036-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1036	$0$	✓	✓	$-0.323$	$0$	$0.613720$	Character $\chi_{1259}(1036, \cdot)$
1-1259-1259.1037-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1037	$0$	✓	✓	$-0.338$	$0$	$0.750399$	Character $\chi_{1259}(1037, \cdot)$
1-1259-1259.1038-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1038	$0$	✓	✓	$-0.481$	$0$	$0.240343$	Character $\chi_{1259}(1038, \cdot)$
1-1259-1259.1039-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1039	$0$	✓	✓	$-0.0547$	$0$	$0.721669$	Character $\chi_{1259}(1039, \cdot)$
1-1259-1259.104-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.104	$0$	✓	✓	$-0.390$	$0$	$1.99222$	Character $\chi_{1259}(104, \cdot)$
1-1259-1259.1041-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1041	$0$	✓	✓	$-0.136$	$0$	$0.993894$	Character $\chi_{1259}(1041, \cdot)$
1-1259-1259.1042-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1042	$0$	✓	✓	$-0.141$	$0$	$1.12446$	Character $\chi_{1259}(1042, \cdot)$
1-1259-1259.1043-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1043	$0$	✓	✓	$-0.0524$	$0$	$0.427759$	Character $\chi_{1259}(1043, \cdot)$
1-1259-1259.1045-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1045	$0$	✓	✓	$0.263$	$0$	$0.156464$	Character $\chi_{1259}(1045, \cdot)$
1-1259-1259.1048-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1048	$0$	✓	✓	$-0.237$	$0$	$0.768743$	Character $\chi_{1259}(1048, \cdot)$
1-1259-1259.1049-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1049	$0$	✓	✓	$0.257$	$0$	$0.909945$	Character $\chi_{1259}(1049, \cdot)$
1-1259-1259.105-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.105	$0$	✓	✓	$-0.0616$	$0$	$0.161654$	Character $\chi_{1259}(105, \cdot)$
1-1259-1259.1051-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1051	$0$	✓	✓	$0.355$	$0$	$1.97437$	Character $\chi_{1259}(1051, \cdot)$
1-1259-1259.1054-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1054	$0$	✓	✓	$0.0688$	$0$	$1.11487$	Character $\chi_{1259}(1054, \cdot)$
1-1259-1259.1056-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1056	$0$	✓	✓	$-0.0247$	$0$	$1.31903$	Character $\chi_{1259}(1056, \cdot)$
1-1259-1259.1057-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1057	$0$	✓	✓	$0.0639$	$0$	$0.999544$	Character $\chi_{1259}(1057, \cdot)$
1-1259-1259.1059-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1059	$0$	✓	✓	$0.324$	$0$	$1.55793$	Character $\chi_{1259}(1059, \cdot)$
1-1259-1259.1060-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1060	$0$	✓	✓	$0.194$	$0$	$1.69847$	Character $\chi_{1259}(1060, \cdot)$
1-1259-1259.1062-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1062	$0$	✓	✓	$-0.388$	$0$	$1.22813$	Character $\chi_{1259}(1062, \cdot)$
1-1259-1259.1064-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1064	$0$	✓	✓	$-0.331$	$0$	$0.888316$	Character $\chi_{1259}(1064, \cdot)$
1-1259-1259.1065-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1065	$0$	✓	✓	$0.115$	$0$	$1.46143$	Character $\chi_{1259}(1065, \cdot)$
1-1259-1259.107-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.107	$0$	✓	✓	$-0.356$	$0$	$0.246725$	Character $\chi_{1259}(107, \cdot)$
1-1259-1259.1071-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1071	$0$	✓	✓	$0.481$	$0$	$2.21437$	Character $\chi_{1259}(1071, \cdot)$
1-1259-1259.1072-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1072	$0$	✓	✓	$-0.0821$	$0$	$0.599141$	Character $\chi_{1259}(1072, \cdot)$
1-1259-1259.1075-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1075	$0$	✓	✓	$-0.233$	$0$	$1.60413$	Character $\chi_{1259}(1075, \cdot)$
1-1259-1259.1078-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1078	$0$	✓	✓	$-0.0367$	$0$	$1.95986$	Character $\chi_{1259}(1078, \cdot)$
1-1259-1259.108-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.108	$0$	✓	✓	$0.464$	$0$	$0.00680783$	Character $\chi_{1259}(108, \cdot)$
1-1259-1259.1082-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1082	$0$	✓	✓	$-0.163$	$0$	$1.18346$	Character $\chi_{1259}(1082, \cdot)$
1-1259-1259.1083-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1083	$0$	✓	✓	$-0.175$	$0$	$0.462952$	Character $\chi_{1259}(1083, \cdot)$
1-1259-1259.1086-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1086	$0$	✓	✓	$-0.249$	$0$	$0.730902$	Character $\chi_{1259}(1086, \cdot)$
1-1259-1259.1088-r0-0-0	$5.84$	$5.84$	$1$	$1259$	1259.1088	$0$	✓	✓	$0.216$	$0$	$1.34638$	Character $\chi_{1259}(1088, \cdot)$

Next To download results, determine the number of results.

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 at least 1000)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.