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 1404 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2009-2009.100-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.100	$0$	✓	✓	$-0.444$	$0$	$0.436488$	Character $\chi_{2009}(100, \cdot)$
1-2009-2009.1002-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1002	$0$	✓	✓	$0.419$	$0$	$0.901541$	Character $\chi_{2009}(1002, \cdot)$
1-2009-2009.1005-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1005	$0$	✓	✓	$0.161$	$0$	$1.43637$	Character $\chi_{2009}(1005, \cdot)$
1-2009-2009.1006-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1006	$0$	✓	✓	$0.0507$	$0$	$0.452221$	Character $\chi_{2009}(1006, \cdot)$
1-2009-2009.1009-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1009	$0$	✓	✓	$-0.383$	$0$	$0.695797$	Character $\chi_{2009}(1009, \cdot)$
1-2009-2009.101-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.101	$0$	✓	✓	$-0.0995$	$0$	$0.655953$	Character $\chi_{2009}(101, \cdot)$
1-2009-2009.1013-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1013	$0$	✓	✓	$-0.464$	$0$	$0.346438$	Character $\chi_{2009}(1013, \cdot)$
1-2009-2009.1014-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1014	$0$	✓	✓	$-0.438$	$0$	$0.488593$	Character $\chi_{2009}(1014, \cdot)$
1-2009-2009.1016-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1016	$0$	✓	✓	$-0.130$	$0$	$1.31078$	Character $\chi_{2009}(1016, \cdot)$
1-2009-2009.1017-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1017	$0$	✓	✓	$-0.134$	$0$	$0.782523$	Character $\chi_{2009}(1017, \cdot)$
1-2009-2009.1018-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1018	$0$	✓	✓	$-0.102$	$0$	$0.324561$	Character $\chi_{2009}(1018, \cdot)$
1-2009-2009.102-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.102	$0$	✓	✓	$0.179$	$0$	$1.02313$	Character $\chi_{2009}(102, \cdot)$
1-2009-2009.1023-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1023	$0$	✓	✓	$-0.186$	$0$	$0.180008$	Character $\chi_{2009}(1023, \cdot)$
1-2009-2009.1024-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1024	$0$	✓	✓	$-0.122$	$0$	$1.05887$	Character $\chi_{2009}(1024, \cdot)$
1-2009-2009.1032-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1032	$0$	✓	✓	$-0.169$	$0$	$0.993043$	Character $\chi_{2009}(1032, \cdot)$
1-2009-2009.1033-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1033	$0$	✓	✓	$-0.0862$	$0$	$0.974405$	Character $\chi_{2009}(1033, \cdot)$
1-2009-2009.1039-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1039	$0$	✓	✓	$-0.115$	$0$	$0.426957$	Character $\chi_{2009}(1039, \cdot)$
1-2009-2009.104-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.104	$0$	✓	✓	$-0.364$	$0$	$0.528978$	Character $\chi_{2009}(104, \cdot)$
1-2009-2009.1042-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1042	$0$	✓	✓	$-0.239$	$0$	$0.801597$	Character $\chi_{2009}(1042, \cdot)$
1-2009-2009.1045-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1045	$0$	✓	✓	$0.431$	$0$	$0.949849$	Character $\chi_{2009}(1045, \cdot)$
1-2009-2009.1049-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1049	$0$	✓	✓	$-0.192$	$0$	$0.905034$	Character $\chi_{2009}(1049, \cdot)$
1-2009-2009.1053-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1053	$0$	✓	✓	$0.146$	$0$	$1.31210$	Character $\chi_{2009}(1053, \cdot)$
1-2009-2009.1055-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1055	$0$	✓	✓	$0.272$	$0$	$1.25203$	Character $\chi_{2009}(1055, \cdot)$
1-2009-2009.1058-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1058	$0$	✓	✓	$-0.467$	$0$	$0.0101624$	Character $\chi_{2009}(1058, \cdot)$
1-2009-2009.1061-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1061	$0$	✓	✓	$0.419$	$0$	$0.732060$	Character $\chi_{2009}(1061, \cdot)$
1-2009-2009.1063-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1063	$0$	✓	✓	$0.392$	$0$	$0.737071$	Character $\chi_{2009}(1063, \cdot)$
1-2009-2009.1065-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1065	$0$	✓	✓	$-0.326$	$0$	$0.363546$	Character $\chi_{2009}(1065, \cdot)$
1-2009-2009.1068-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1068	$0$	✓	✓	$-0.379$	$0$	$0.651080$	Character $\chi_{2009}(1068, \cdot)$
1-2009-2009.1069-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1069	$0$	✓	✓	$0.231$	$0$	$1.61671$	Character $\chi_{2009}(1069, \cdot)$
1-2009-2009.107-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.107	$0$	✓	✓	$-0.186$	$0$	$0.579922$	Character $\chi_{2009}(107, \cdot)$
1-2009-2009.1075-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1075	$0$	✓	✓	$-0.318$	$0$	$0.318469$	Character $\chi_{2009}(1075, \cdot)$
1-2009-2009.108-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.108	$0$	✓	✓	$-0.112$	$0$	$0.366581$	Character $\chi_{2009}(108, \cdot)$
1-2009-2009.1081-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1081	$0$	✓	✓	$-0.178$	$0$	$1.07450$	Character $\chi_{2009}(1081, \cdot)$
1-2009-2009.1082-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1082	$0$	✓	✓	$-0.344$	$0$	$0.218772$	Character $\chi_{2009}(1082, \cdot)$
1-2009-2009.1083-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1083	$0$	✓	✓	$0.464$	$0$	$1.54094$	Character $\chi_{2009}(1083, \cdot)$
1-2009-2009.1086-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1086	$0$	✓	✓	$0.186$	$0$	$0.650544$	Character $\chi_{2009}(1086, \cdot)$
1-2009-2009.1087-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1087	$0$	✓	✓	$0.495$	$0$	$1.08477$	Character $\chi_{2009}(1087, \cdot)$
1-2009-2009.1088-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1088	$0$	✓	✓	$-0.364$	$0$	$0.462196$	Character $\chi_{2009}(1088, \cdot)$
1-2009-2009.1089-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1089	$0$	✓	✓	$0.186$	$0$	$0.373077$	Character $\chi_{2009}(1089, \cdot)$
1-2009-2009.1090-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1090	$0$	✓	✓	$0.140$	$0$	$0.616121$	Character $\chi_{2009}(1090, \cdot)$
1-2009-2009.1095-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1095	$0$	✓	✓	$0.375$	$0$	$1.72826$	Character $\chi_{2009}(1095, \cdot)$
1-2009-2009.110-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.110	$0$	✓	✓	$-0.384$	$0$	$0.284973$	Character $\chi_{2009}(110, \cdot)$
1-2009-2009.1103-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1103	$0$	✓	✓	$-0.145$	$0$	$0.485603$	Character $\chi_{2009}(1103, \cdot)$
1-2009-2009.1104-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1104	$0$	✓	✓	$0.103$	$0$	$0.778921$	Character $\chi_{2009}(1104, \cdot)$
1-2009-2009.111-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.111	$0$	✓	✓	$0.0864$	$0$	$1.03459$	Character $\chi_{2009}(111, \cdot)$
1-2009-2009.1115-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1115	$0$	✓	✓	$0.172$	$0$	$1.28533$	Character $\chi_{2009}(1115, \cdot)$
1-2009-2009.1117-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1117	$0$	✓	✓	$-0.0724$	$0$	$1.05607$	Character $\chi_{2009}(1117, \cdot)$
1-2009-2009.1118-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1118	$0$	✓	✓	$-0.450$	$0$	$1.18351$	Character $\chi_{2009}(1118, \cdot)$
1-2009-2009.1119-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.1119	$0$	✓	✓	$0.366$	$0$	$1.36282$	Character $\chi_{2009}(1119, \cdot)$
1-2009-2009.113-r0-0-0	$9.32$	$9.32$	$1$	$7^{2} \cdot 41$	2009.113	$0$	✓	✓	$0.337$	$0$	$1.50635$	Character $\chi_{2009}(113, \cdot)$

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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.