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 2250 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6223-6223.10-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.10	$0$	✓	✓	$0.245$	$0$	$0.159377$	Character $\chi_{6223}(10, \cdot)$
1-6223-6223.100-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.100	$0$	✓	✓	$-0.332$	$0$	$0.188498$	Character $\chi_{6223}(100, \cdot)$
1-6223-6223.1000-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1000	$0$	✓	✓	$-0.122$	$0$	$0.366351$	Character $\chi_{6223}(1000, \cdot)$
1-6223-6223.1002-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1002	$0$	✓	✓	$0.0168$	$0$	$0.627613$	Character $\chi_{6223}(1002, \cdot)$
1-6223-6223.1007-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1007	$0$	✓	✓	$-0.131$	$0$	$0.975240$	Character $\chi_{6223}(1007, \cdot)$
1-6223-6223.1009-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1009	$0$	✓	✓	$-0.264$	$0$	$0.663949$	Character $\chi_{6223}(1009, \cdot)$
1-6223-6223.101-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.101	$0$	✓	✓	$0.331$	$0$	$0.439525$	Character $\chi_{6223}(101, \cdot)$
1-6223-6223.1014-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1014	$0$	✓	✓	$-0.439$	$0$	$0.113854$	Character $\chi_{6223}(1014, \cdot)$
1-6223-6223.1021-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1021	$0$	✓	✓	$0.293$	$0$	$1.37150$	Character $\chi_{6223}(1021, \cdot)$
1-6223-6223.1024-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1024	$0$	✓	✓	$-0.175$	$0$	$0.548483$	Character $\chi_{6223}(1024, \cdot)$
1-6223-6223.1031-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1031	$0$	✓	✓	$0.485$	$0$	$1.10585$	Character $\chi_{6223}(1031, \cdot)$
1-6223-6223.1033-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1033	$0$	✓	✓	$0.297$	$0$	$1.31363$	Character $\chi_{6223}(1033, \cdot)$
1-6223-6223.1037-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1037	$0$	✓	✓	$0.277$	$0$	$0.0823658$	Character $\chi_{6223}(1037, \cdot)$
1-6223-6223.1038-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1038	$0$	✓	✓	$-0.301$	$0$	$1.40505$	Character $\chi_{6223}(1038, \cdot)$
1-6223-6223.1039-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1039	$0$	✓	✓	$-0.337$	$0$	$0.810424$	Character $\chi_{6223}(1039, \cdot)$
1-6223-6223.1049-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1049	$0$	✓	✓	$0.125$	$0$	$0.512243$	Character $\chi_{6223}(1049, \cdot)$
1-6223-6223.1051-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1051	$0$	✓	✓	$-0.393$	$0$	$1.11634$	Character $\chi_{6223}(1051, \cdot)$
1-6223-6223.1052-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1052	$0$	✓	✓	$-0.0749$	$0$	$1.09265$	Character $\chi_{6223}(1052, \cdot)$
1-6223-6223.1054-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1054	$0$	✓	✓	$-0.00882$	$0$	$0.695561$	Character $\chi_{6223}(1054, \cdot)$
1-6223-6223.1055-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1055	$0$	✓	✓	$-0.178$	$0$	$0.252270$	Character $\chi_{6223}(1055, \cdot)$
1-6223-6223.1056-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1056	$0$	✓	✓	$-0.487$	$0$	$1.31937$	Character $\chi_{6223}(1056, \cdot)$
1-6223-6223.1058-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1058	$0$	✓	✓	$-0.184$	$0$	$0.405944$	Character $\chi_{6223}(1058, \cdot)$
1-6223-6223.1062-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1062	$0$	✓	✓	$0.126$	$0$	$0.689574$	Character $\chi_{6223}(1062, \cdot)$
1-6223-6223.1065-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1065	$0$	✓	✓	$0.176$	$0$	$1.25192$	Character $\chi_{6223}(1065, \cdot)$
1-6223-6223.1066-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1066	$0$	✓	✓	$0.227$	$0$	$0.919754$	Character $\chi_{6223}(1066, \cdot)$
1-6223-6223.1067-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1067	$0$	✓	✓	$0.0195$	$0$	$1.10612$	Character $\chi_{6223}(1067, \cdot)$
1-6223-6223.1068-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1068	$0$	✓	✓	$-0.0114$	$0$	$1.10692$	Character $\chi_{6223}(1068, \cdot)$
1-6223-6223.1069-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1069	$0$	✓	✓	$-0.435$	$0$	$0.214733$	Character $\chi_{6223}(1069, \cdot)$
1-6223-6223.107-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.107	$0$	✓	✓	$-0.0560$	$0$	$0.166334$	Character $\chi_{6223}(107, \cdot)$
1-6223-6223.1070-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1070	$0$	✓	✓	$-0.144$	$0$	$0.310240$	Character $\chi_{6223}(1070, \cdot)$
1-6223-6223.1074-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1074	$0$	✓	✓	$-0.490$	$0$	$1.79872$	Character $\chi_{6223}(1074, \cdot)$
1-6223-6223.108-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.108	$0$	✓	✓	$-0.0831$	$0$	$0.520990$	Character $\chi_{6223}(108, \cdot)$
1-6223-6223.1080-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1080	$0$	✓	✓	$-0.115$	$0$	$0.800804$	Character $\chi_{6223}(1080, \cdot)$
1-6223-6223.1081-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1081	$0$	✓	✓	$0.127$	$0$	$0.727936$	Character $\chi_{6223}(1081, \cdot)$
1-6223-6223.1083-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1083	$0$	✓	✓	$-0.355$	$0$	$0.418295$	Character $\chi_{6223}(1083, \cdot)$
1-6223-6223.1086-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1086	$0$	✓	✓	$-0.196$	$0$	$0.908640$	Character $\chi_{6223}(1086, \cdot)$
1-6223-6223.1087-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1087	$0$	✓	✓	$-0.364$	$0$	$0.982939$	Character $\chi_{6223}(1087, \cdot)$
1-6223-6223.1089-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1089	$0$	✓	✓	$-0.296$	$0$	$0.405750$	Character $\chi_{6223}(1089, \cdot)$
1-6223-6223.1091-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1091	$0$	✓	✓	$-0.472$	$0$	$1.00700$	Character $\chi_{6223}(1091, \cdot)$
1-6223-6223.11-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.11	$0$	✓	✓	$-0.318$	$0$	$0.210122$	Character $\chi_{6223}(11, \cdot)$
1-6223-6223.110-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.110	$0$	✓	✓	$0.212$	$0$	$0.964953$	Character $\chi_{6223}(110, \cdot)$
1-6223-6223.1100-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1100	$0$	✓	✓	$-0.296$	$0$	$0.202196$	Character $\chi_{6223}(1100, \cdot)$
1-6223-6223.1102-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1102	$0$	✓	✓	$0.270$	$0$	$1.12866$	Character $\chi_{6223}(1102, \cdot)$
1-6223-6223.1103-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1103	$0$	✓	✓	$-0.0364$	$0$	$0.542851$	Character $\chi_{6223}(1103, \cdot)$
1-6223-6223.1105-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1105	$0$	✓	✓	$-0.276$	$0$	$0.559127$	Character $\chi_{6223}(1105, \cdot)$
1-6223-6223.111-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.111	$0$	✓	✓	$-0.173$	$0$	$0.603984$	Character $\chi_{6223}(111, \cdot)$
1-6223-6223.1110-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1110	$0$	✓	✓	$-0.0640$	$0$	$0.978506$	Character $\chi_{6223}(1110, \cdot)$
1-6223-6223.1111-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1111	$0$	✓	✓	$-0.312$	$0$	$1.24472$	Character $\chi_{6223}(1111, \cdot)$
1-6223-6223.1112-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1112	$0$	✓	✓	$0.497$	$0$	$0.0364148$	Character $\chi_{6223}(1112, \cdot)$
1-6223-6223.1114-r0-0-0	$28.8$	$28.8$	$1$	$7^{2} \cdot 127$	6223.1114	$0$	✓	✓	$-0.157$	$0$	$0.867247$	Character $\chi_{6223}(1114, \cdot)$

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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.