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

Arithmetic

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Results (1-50 of 4285 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6013-6013.10-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.10	$0$	✓	✓	$-0.157$	$0$	$0.565528$	Character $\chi_{6013}(10, \cdot)$
1-6013-6013.100-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.100	$0$	✓	✓	$-0.131$	$0$	$0.724454$	Character $\chi_{6013}(100, \cdot)$
1-6013-6013.1000-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1000	$0$	✓	✓	$-0.307$	$0$	$0.0727499$	Character $\chi_{6013}(1000, \cdot)$
1-6013-6013.1003-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1003	$0$	✓	✓	$-0.408$	$0$	$0.831754$	Character $\chi_{6013}(1003, \cdot)$
1-6013-6013.1004-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1004	$0$	✓	✓	$-0.401$	$0$	$1.46280$	Character $\chi_{6013}(1004, \cdot)$
1-6013-6013.1005-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1005	$0$	✓	✓	$-0.388$	$0$	$1.68518$	Character $\chi_{6013}(1005, \cdot)$
1-6013-6013.1006-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1006	$0$	✓	✓	$0.410$	$0$	$0.645538$	Character $\chi_{6013}(1006, \cdot)$
1-6013-6013.1007-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1007	$0$	✓	✓	$-0.275$	$0$	$0.913888$	Character $\chi_{6013}(1007, \cdot)$
1-6013-6013.101-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.101	$0$	✓	✓	$0.391$	$0$	$0.0523787$	Character $\chi_{6013}(101, \cdot)$
1-6013-6013.1010-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1010	$0$	✓	✓	$0.446$	$0$	$0.918254$	Character $\chi_{6013}(1010, \cdot)$
1-6013-6013.1012-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1012	$0$	✓	✓	$-0.451$	$0$	$0.182384$	Character $\chi_{6013}(1012, \cdot)$
1-6013-6013.1018-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1018	$0$	✓	✓	$-0.282$	$0$	$0.123542$	Character $\chi_{6013}(1018, \cdot)$
1-6013-6013.102-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.102	$0$	✓	✓	$0.335$	$0$	$0.475401$	Character $\chi_{6013}(102, \cdot)$
1-6013-6013.1020-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1020	$0$	✓	✓	$0.0464$	$0$	$0.605420$	Character $\chi_{6013}(1020, \cdot)$
1-6013-6013.1021-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1021	$0$	✓	✓	$0.384$	$0$	$0.0151848$	Character $\chi_{6013}(1021, \cdot)$
1-6013-6013.1024-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1024	$0$	✓	✓	$0.425$	$0$	$0.533463$	Character $\chi_{6013}(1024, \cdot)$
1-6013-6013.1031-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1031	$0$	✓	✓	$0.245$	$0$	$0.929960$	Character $\chi_{6013}(1031, \cdot)$
1-6013-6013.1035-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1035	$0$	✓	✓	$0.0382$	$0$	$0.635083$	Character $\chi_{6013}(1035, \cdot)$
1-6013-6013.1038-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1038	$0$	✓	✓	$0.235$	$0$	$0.597251$	Character $\chi_{6013}(1038, \cdot)$
1-6013-6013.104-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.104	$0$	✓	✓	$0.0531$	$0$	$1.25323$	Character $\chi_{6013}(104, \cdot)$
1-6013-6013.1040-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1040	$0$	✓	✓	$0.0479$	$0$	$0.907388$	Character $\chi_{6013}(1040, \cdot)$
1-6013-6013.1041-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1041	$0$	✓	✓	$-0.317$	$0$	$1.39763$	Character $\chi_{6013}(1041, \cdot)$
1-6013-6013.1042-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1042	$0$	✓	✓	$-0.309$	$0$	$0.0986722$	Character $\chi_{6013}(1042, \cdot)$
1-6013-6013.1045-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1045	$0$	✓	✓	$0.474$	$0$	$1.06607$	Character $\chi_{6013}(1045, \cdot)$
1-6013-6013.1046-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1046	$0$	✓	✓	$-0.410$	$0$	$0.618674$	Character $\chi_{6013}(1046, \cdot)$
1-6013-6013.1047-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1047	$0$	✓	✓	$0.0268$	$0$	$0.484532$	Character $\chi_{6013}(1047, \cdot)$
1-6013-6013.1048-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1048	$0$	✓	✓	$0.407$	$0$	$1.13588$	Character $\chi_{6013}(1048, \cdot)$
1-6013-6013.1056-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1056	$0$	✓	✓	$0.498$	$0$	$1.10449$	Character $\chi_{6013}(1056, \cdot)$
1-6013-6013.1061-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1061	$0$	✓	✓	$-0.416$	$0$	$0.193883$	Character $\chi_{6013}(1061, \cdot)$
1-6013-6013.1062-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1062	$0$	✓	✓	$-0.288$	$0$	$1.04466$	Character $\chi_{6013}(1062, \cdot)$
1-6013-6013.1063-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1063	$0$	✓	✓	$-0.423$	$0$	$1.51342$	Character $\chi_{6013}(1063, \cdot)$
1-6013-6013.1068-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1068	$0$	✓	✓	$-0.0326$	$0$	$0.821728$	Character $\chi_{6013}(1068, \cdot)$
1-6013-6013.1073-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1073	$0$	✓	✓	$-0.423$	$0$	$1.31903$	Character $\chi_{6013}(1073, \cdot)$
1-6013-6013.1075-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1075	$0$	✓	✓	$0.407$	$0$	$1.40776$	Character $\chi_{6013}(1075, \cdot)$
1-6013-6013.108-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.108	$0$	✓	✓	$-0.401$	$0$	$0.478168$	Character $\chi_{6013}(108, \cdot)$
1-6013-6013.1080-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1080	$0$	✓	✓	$0.263$	$0$	$0.627652$	Character $\chi_{6013}(1080, \cdot)$
1-6013-6013.1081-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1081	$0$	✓	✓	$-0.0548$	$0$	$0.721435$	Character $\chi_{6013}(1081, \cdot)$
1-6013-6013.1082-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1082	$0$	✓	✓	$-0.235$	$0$	$0.860576$	Character $\chi_{6013}(1082, \cdot)$
1-6013-6013.1083-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1083	$0$	✓	✓	$-0.142$	$0$	$0.234921$	Character $\chi_{6013}(1083, \cdot)$
1-6013-6013.1087-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1087	$0$	✓	✓	$0.466$	$0$	$0.0274586$	Character $\chi_{6013}(1087, \cdot)$
1-6013-6013.1089-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1089	$0$	✓	✓	$0.270$	$0$	$1.17174$	Character $\chi_{6013}(1089, \cdot)$
1-6013-6013.1094-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1094	$0$	✓	✓	$-0.446$	$0$	$1.23619$	Character $\chi_{6013}(1094, \cdot)$
1-6013-6013.1097-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1097	$0$	✓	✓	$0.305$	$0$	$0.972082$	Character $\chi_{6013}(1097, \cdot)$
1-6013-6013.1098-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1098	$0$	✓	✓	$0.499$	$0$	$0.928079$	Character $\chi_{6013}(1098, \cdot)$
1-6013-6013.1102-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1102	$0$	✓	✓	$-0.118$	$0$	$0.870727$	Character $\chi_{6013}(1102, \cdot)$
1-6013-6013.1103-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1103	$0$	✓	✓	$-0.103$	$0$	$0.701045$	Character $\chi_{6013}(1103, \cdot)$
1-6013-6013.1108-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1108	$0$	✓	✓	$0.314$	$0$	$0.494247$	Character $\chi_{6013}(1108, \cdot)$
1-6013-6013.1109-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1109	$0$	✓	✓	$0.388$	$0$	$0.262959$	Character $\chi_{6013}(1109, \cdot)$
1-6013-6013.1115-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1115	$0$	✓	✓	$-0.259$	$0$	$0.492657$	Character $\chi_{6013}(1115, \cdot)$
1-6013-6013.1117-r0-0-0	$27.9$	$27.9$	$1$	$7 \cdot 859$	6013.1117	$0$	✓	✓	$0.137$	$0$	$0.936738$	Character $\chi_{6013}(1117, \cdot)$

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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.