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
1-5245-5245.1007-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1007	$1$	✓	✓	$-0.0252$	$0$	$0.847189$	Character $\chi_{5245}(1007, \cdot)$
1-5245-5245.1013-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1013	$1$	✓	✓	$0.118$	$0$	$0.235490$	Character $\chi_{5245}(1013, \cdot)$
1-5245-5245.1014-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1014	$1$	✓	✓	$-0.487$	$0$	$0.678044$	Character $\chi_{5245}(1014, \cdot)$
1-5245-5245.1017-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1017	$1$	✓	✓	$-0.122$	$0$	$0.668679$	Character $\chi_{5245}(1017, \cdot)$
1-5245-5245.1019-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1019	$1$	✓	✓	$0.487$	$0$	$0.150289$	Character $\chi_{5245}(1019, \cdot)$
1-5245-5245.102-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.102	$1$	✓	✓	$0.479$	$0$	$0.918598$	Character $\chi_{5245}(102, \cdot)$
1-5245-5245.1023-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1023	$1$	✓	✓	$-0.464$	$0$	$0.582905$	Character $\chi_{5245}(1023, \cdot)$
1-5245-5245.1027-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1027	$1$	✓	✓	$-0.451$	$0$	$1.16490$	Character $\chi_{5245}(1027, \cdot)$
1-5245-5245.1028-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1028	$1$	✓	✓	$0.114$	$0$	$0.506341$	Character $\chi_{5245}(1028, \cdot)$
1-5245-5245.103-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.103	$1$	✓	✓	$0.302$	$0$	$0.498304$	Character $\chi_{5245}(103, \cdot)$
1-5245-5245.1033-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1033	$1$	✓	✓	$-0.403$	$0$	$0.0107121$	Character $\chi_{5245}(1033, \cdot)$
1-5245-5245.1034-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1034	$1$	✓	✓	$-0.479$	$0$	$0.0620242$	Character $\chi_{5245}(1034, \cdot)$
1-5245-5245.1038-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1038	$1$	✓	✓	$0.227$	$0$	$0.770351$	Character $\chi_{5245}(1038, \cdot)$
1-5245-5245.1047-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1047	$1$	✓	✓	$0.0178$	$0$	$0.470963$	Character $\chi_{5245}(1047, \cdot)$
1-5245-5245.1048-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1048	$1$	✓	✓	$0.411$	$0$	$1.29082$	Character $\chi_{5245}(1048, \cdot)$
1-5245-5245.1053-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1053	$1$	✓	✓	$-0.00859$	$0$	$0.220630$	Character $\chi_{5245}(1053, \cdot)$
1-5245-5245.1057-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1057	$1$	✓	✓	$-0.347$	$0$	$0.960483$	Character $\chi_{5245}(1057, \cdot)$
1-5245-5245.1058-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1058	$1$	✓	✓	$0.0686$	$0$	$0.528282$	Character $\chi_{5245}(1058, \cdot)$
1-5245-5245.1062-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1062	$1$	✓	✓	$-0.154$	$0$	$0.710518$	Character $\chi_{5245}(1062, \cdot)$
1-5245-5245.1064-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1064	$1$	✓	✓	$0.0425$	$0$	$0.0482291$	Character $\chi_{5245}(1064, \cdot)$
1-5245-5245.1067-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1067	$1$	✓	✓	$0.422$	$0$	$0.578229$	Character $\chi_{5245}(1067, \cdot)$
1-5245-5245.1068-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1068	$1$	✓	✓	$-0.0231$	$0$	$0.193788$	Character $\chi_{5245}(1068, \cdot)$
1-5245-5245.107-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.107	$1$	✓	✓	$-0.191$	$0$	$0.915300$	Character $\chi_{5245}(107, \cdot)$
1-5245-5245.1078-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1078	$1$	✓	✓	$-0.375$	$0$	$0.342909$	Character $\chi_{5245}(1078, \cdot)$
1-5245-5245.1079-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1079	$1$	✓	✓	$-0.0507$	$0$	$0.371151$	Character $\chi_{5245}(1079, \cdot)$
1-5245-5245.1084-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1084	$1$	✓	✓	$0.0507$	$0$	$0.403452$	Character $\chi_{5245}(1084, \cdot)$
1-5245-5245.1087-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1087	$1$	✓	✓	$-0.474$	$0$	$0.897316$	Character $\chi_{5245}(1087, \cdot)$
1-5245-5245.109-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.109	$1$	✓	✓	$-0.211$	$0$	$0.335587$	Character $\chi_{5245}(109, \cdot)$
1-5245-5245.1092-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1092	$1$	✓	✓	$-0.282$	$0$	$0.172387$	Character $\chi_{5245}(1092, \cdot)$
1-5245-5245.1093-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1093	$1$	✓	✓	$-0.0169$	$0$	$0.522500$	Character $\chi_{5245}(1093, \cdot)$
1-5245-5245.1098-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1098	$1$	✓	✓	$0.326$	$0$	$0.122533$	Character $\chi_{5245}(1098, \cdot)$
1-5245-5245.1102-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1102	$1$	✓	✓	$-0.423$	$0$	$1.34042$	Character $\chi_{5245}(1102, \cdot)$
1-5245-5245.1107-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1107	$1$	✓	✓	$-0.0391$	$0$	$0.951966$	Character $\chi_{5245}(1107, \cdot)$
1-5245-5245.1108-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1108	$1$	✓	✓	$-0.242$	$0$	$0.0927240$	Character $\chi_{5245}(1108, \cdot)$
1-5245-5245.1109-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1109	$1$	✓	✓	$-0.217$	$0$	$0.768838$	Character $\chi_{5245}(1109, \cdot)$
1-5245-5245.1113-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1113	$1$	✓	✓	$-0.433$	$0$	$0.392287$	Character $\chi_{5245}(1113, \cdot)$
1-5245-5245.1118-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1118	$1$	✓	✓	$0.489$	$0$	$0.0250716$	Character $\chi_{5245}(1118, \cdot)$
1-5245-5245.1119-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1119	$1$	✓	✓	$-0.0425$	$0$	$0.986924$	Character $\chi_{5245}(1119, \cdot)$
1-5245-5245.1122-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1122	$1$	✓	✓	$-0.255$	$0$	$0.122176$	Character $\chi_{5245}(1122, \cdot)$
1-5245-5245.1124-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1124	$1$	✓	✓	$0.118$	$0$	$0.512757$	Character $\chi_{5245}(1124, \cdot)$
1-5245-5245.1128-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1128	$1$	✓	✓	$0.137$	$0$	$0.859954$	Character $\chi_{5245}(1128, \cdot)$
1-5245-5245.113-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.113	$1$	✓	✓	$0.367$	$0$	$0.878858$	Character $\chi_{5245}(113, \cdot)$
1-5245-5245.1133-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1133	$1$	✓	✓	$0.0882$	$0$	$0.400563$	Character $\chi_{5245}(1133, \cdot)$
1-5245-5245.1134-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1134	$1$	✓	✓	$0.111$	$0$	$0.694005$	Character $\chi_{5245}(1134, \cdot)$
1-5245-5245.1137-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1137	$1$	✓	✓	$-0.170$	$0$	$0.696952$	Character $\chi_{5245}(1137, \cdot)$
1-5245-5245.114-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.114	$1$	✓	✓	$-0.114$	$0$	$0.338005$	Character $\chi_{5245}(114, \cdot)$
1-5245-5245.1142-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1142	$1$	✓	✓	$-0.347$	$0$	$1.17723$	Character $\chi_{5245}(1142, \cdot)$
1-5245-5245.1147-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1147	$1$	✓	✓	$0.126$	$0$	$0.429527$	Character $\chi_{5245}(1147, \cdot)$
1-5245-5245.1148-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1148	$1$	✓	✓	$-0.0228$	$0$	$0.548135$	Character $\chi_{5245}(1148, \cdot)$
1-5245-5245.1152-r1-0-0	$563.$	$563.$	$1$	$5 \cdot 1049$	5245.1152	$1$	✓	✓	$0.478$	$0$	$0.218847$	Character $\chi_{5245}(1152, \cdot)$

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 $\F_{q}$
Belyi maps

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.