LMFDB - L-function search results

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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

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6037-6037.10-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.10	$0$	✓	✓	$-0.377$	$0$	$0.116757$	Character $\chi_{6037}(10, \cdot)$
1-6037-6037.100-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.100	$0$	✓	✓	$-0.0757$	$0$	$0.499922$	Character $\chi_{6037}(100, \cdot)$
1-6037-6037.1000-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1000	$0$	✓	✓	$-0.326$	$0$	$0.358193$	Character $\chi_{6037}(1000, \cdot)$
1-6037-6037.1001-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1001	$0$	✓	✓	$-0.332$	$0$	$0.602371$	Character $\chi_{6037}(1001, \cdot)$
1-6037-6037.1003-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1003	$0$	✓	✓	$0.498$	$0$	$1.76620$	Character $\chi_{6037}(1003, \cdot)$
1-6037-6037.1004-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1004	$0$	✓	✓	$-0.299$	$0$	$0.850958$	Character $\chi_{6037}(1004, \cdot)$
1-6037-6037.1005-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1005	$0$	✓	✓	$-0.0752$	$0$	$0.115282$	Character $\chi_{6037}(1005, \cdot)$
1-6037-6037.1007-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1007	$0$	✓	✓	$-0.298$	$0$	$0.461326$	Character $\chi_{6037}(1007, \cdot)$
1-6037-6037.101-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.101	$0$	✓	✓	$0.476$	$0$	$1.12332$	Character $\chi_{6037}(101, \cdot)$
1-6037-6037.1010-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1010	$0$	✓	✓	$-0.147$	$0$	$0.706007$	Character $\chi_{6037}(1010, \cdot)$
1-6037-6037.1015-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1015	$0$	✓	✓	$0.124$	$0$	$0.496534$	Character $\chi_{6037}(1015, \cdot)$
1-6037-6037.1019-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1019	$0$	✓	✓	$0.116$	$0$	$0.853787$	Character $\chi_{6037}(1019, \cdot)$
1-6037-6037.1021-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1021	$0$	✓	✓	$-0.0482$	$0$	$0.665777$	Character $\chi_{6037}(1021, \cdot)$
1-6037-6037.1024-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1024	$0$	✓	✓	$-0.104$	$0$	$0.250366$	Character $\chi_{6037}(1024, \cdot)$
1-6037-6037.1025-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1025	$0$	✓	✓	$0.157$	$0$	$0.739768$	Character $\chi_{6037}(1025, \cdot)$
1-6037-6037.1026-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1026	$0$	✓	✓	$-0.312$	$0$	$0.487606$	Character $\chi_{6037}(1026, \cdot)$
1-6037-6037.1027-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1027	$0$	✓	✓	$-0.361$	$0$	$0.551226$	Character $\chi_{6037}(1027, \cdot)$
1-6037-6037.103-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.103	$0$	✓	✓	$0.276$	$0$	$1.25775$	Character $\chi_{6037}(103, \cdot)$
1-6037-6037.1030-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1030	$0$	✓	✓	$0.499$	$0$	$0.644544$	Character $\chi_{6037}(1030, \cdot)$
1-6037-6037.1031-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1031	$0$	✓	✓	$0.206$	$0$	$0.787321$	Character $\chi_{6037}(1031, \cdot)$
1-6037-6037.1035-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1035	$0$	✓	✓	$0.201$	$0$	$1.42161$	Character $\chi_{6037}(1035, \cdot)$
1-6037-6037.1036-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1036	$0$	✓	✓	$-0.368$	$0$	$1.76354$	Character $\chi_{6037}(1036, \cdot)$
1-6037-6037.1038-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1038	$0$	✓	✓	$0.346$	$0$	$0.557078$	Character $\chi_{6037}(1038, \cdot)$
1-6037-6037.104-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.104	$0$	✓	✓	$-0.296$	$0$	$0.898094$	Character $\chi_{6037}(104, \cdot)$
1-6037-6037.1040-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1040	$0$	✓	✓	$-0.311$	$0$	$0.973280$	Character $\chi_{6037}(1040, \cdot)$
1-6037-6037.1041-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1041	$0$	✓	✓	$0.298$	$0$	$1.51603$	Character $\chi_{6037}(1041, \cdot)$
1-6037-6037.1042-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1042	$0$	✓	✓	$0.386$	$0$	$1.35018$	Character $\chi_{6037}(1042, \cdot)$
1-6037-6037.1043-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1043	$0$	✓	✓	$0.233$	$0$	$0.709386$	Character $\chi_{6037}(1043, \cdot)$
1-6037-6037.1044-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1044	$0$	✓	✓	$0.336$	$0$	$0.992433$	Character $\chi_{6037}(1044, \cdot)$
1-6037-6037.1045-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1045	$0$	✓	✓	$0.0966$	$0$	$0.413178$	Character $\chi_{6037}(1045, \cdot)$
1-6037-6037.1047-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1047	$0$	✓	✓	$-0.172$	$0$	$0.290747$	Character $\chi_{6037}(1047, \cdot)$
1-6037-6037.1049-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1049	$0$	✓	✓	$0.496$	$0$	$0.211733$	Character $\chi_{6037}(1049, \cdot)$
1-6037-6037.105-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.105	$0$	✓	✓	$0.369$	$0$	$1.19710$	Character $\chi_{6037}(105, \cdot)$
1-6037-6037.1050-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1050	$0$	✓	✓	$-0.337$	$0$	$0.163987$	Character $\chi_{6037}(1050, \cdot)$
1-6037-6037.1054-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1054	$0$	✓	✓	$0.417$	$0$	$1.31856$	Character $\chi_{6037}(1054, \cdot)$
1-6037-6037.1055-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1055	$0$	✓	✓	$-0.419$	$0$	$0.0980719$	Character $\chi_{6037}(1055, \cdot)$
1-6037-6037.1059-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1059	$0$	✓	✓	$0.284$	$0$	$0.903434$	Character $\chi_{6037}(1059, \cdot)$
1-6037-6037.106-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.106	$0$	✓	✓	$0.112$	$0$	$1.04361$	Character $\chi_{6037}(106, \cdot)$
1-6037-6037.1060-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1060	$0$	✓	✓	$-0.469$	$0$	$1.61961$	Character $\chi_{6037}(1060, \cdot)$
1-6037-6037.1061-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1061	$0$	✓	✓	$-0.332$	$0$	$0.156903$	Character $\chi_{6037}(1061, \cdot)$
1-6037-6037.1063-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1063	$0$	✓	✓	$0.470$	$0$	$0.128421$	Character $\chi_{6037}(1063, \cdot)$
1-6037-6037.1066-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1066	$0$	✓	✓	$-0.310$	$0$	$0.450553$	Character $\chi_{6037}(1066, \cdot)$
1-6037-6037.1069-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1069	$0$	✓	✓	$0.479$	$0$	$1.30284$	Character $\chi_{6037}(1069, \cdot)$
1-6037-6037.1074-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1074	$0$	✓	✓	$-0.218$	$0$	$0.254762$	Character $\chi_{6037}(1074, \cdot)$
1-6037-6037.1075-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1075	$0$	✓	✓	$-0.419$	$0$	$1.39273$	Character $\chi_{6037}(1075, \cdot)$
1-6037-6037.1076-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1076	$0$	✓	✓	$-0.317$	$0$	$0.258640$	Character $\chi_{6037}(1076, \cdot)$
1-6037-6037.108-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.108	$0$	✓	✓	$0.248$	$0$	$1.07394$	Character $\chi_{6037}(108, \cdot)$
1-6037-6037.1080-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1080	$0$	✓	✓	$-0.159$	$0$	$0.744236$	Character $\chi_{6037}(1080, \cdot)$
1-6037-6037.1082-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1082	$0$	✓	✓	$-0.133$	$0$	$0.621982$	Character $\chi_{6037}(1082, \cdot)$
1-6037-6037.1083-r0-0-0	$28.0$	$28.0$	$1$	$6037$	6037.1083	$0$	✓	✓	$-0.485$	$0$	$1.17959$	Character $\chi_{6037}(1083, \cdot)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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