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 232 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1984-1984.1003-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1003	$0$	✓	✓	$0.179$	$0$	$1.28679$	Character $\chi_{1984}(1003, \cdot)$
1-1984-1984.101-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.101	$0$	✓	✓	$-0.203$	$0$	$0.551695$	Character $\chi_{1984}(101, \cdot)$
1-1984-1984.1019-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1019	$0$	✓	✓	$-0.0510$	$0$	$1.25131$	Character $\chi_{1984}(1019, \cdot)$
1-1984-1984.1035-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1035	$0$	✓	✓	$0.193$	$0$	$1.25711$	Character $\chi_{1984}(1035, \cdot)$
1-1984-1984.1037-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1037	$0$	✓	✓	$-0.393$	$0$	$0.297466$	Character $\chi_{1984}(1037, \cdot)$
1-1984-1984.1061-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1061	$0$	✓	✓	$-0.459$	$0$	$0.0971524$	Character $\chi_{1984}(1061, \cdot)$
1-1984-1984.1067-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1067	$0$	✓	✓	$0.337$	$0$	$1.26265$	Character $\chi_{1984}(1067, \cdot)$
1-1984-1984.1075-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1075	$0$	✓	✓	$0.0765$	$0$	$0.626900$	Character $\chi_{1984}(1075, \cdot)$
1-1984-1984.1083-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1083	$0$	✓	✓	$0.0369$	$0$	$1.08632$	Character $\chi_{1984}(1083, \cdot)$
1-1984-1984.109-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.109	$0$	✓	✓	$-0.438$	$0$	$0.262914$	Character $\chi_{1984}(109, \cdot)$
1-1984-1984.1091-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1091	$0$	✓	✓	$-0.393$	$0$	$0.689789$	Character $\chi_{1984}(1091, \cdot)$
1-1984-1984.1093-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1093	$0$	✓	✓	$0.296$	$0$	$1.23094$	Character $\chi_{1984}(1093, \cdot)$
1-1984-1984.11-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.11	$0$	✓	✓	$0.179$	$0$	$0.957124$	Character $\chi_{1984}(11, \cdot)$
1-1984-1984.1101-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1101	$0$	✓	✓	$0.0617$	$0$	$1.34767$	Character $\chi_{1984}(1101, \cdot)$
1-1984-1984.1107-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1107	$0$	✓	✓	$-0.265$	$0$	$0.766126$	Character $\chi_{1984}(1107, \cdot)$
1-1984-1984.1115-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1115	$0$	✓	✓	$-0.109$	$0$	$0.771852$	Character $\chi_{1984}(1115, \cdot)$
1-1984-1984.1125-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1125	$0$	✓	✓	$-0.259$	$0$	$0.570283$	Character $\chi_{1984}(1125, \cdot)$
1-1984-1984.1131-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1131	$0$	✓	✓	$-0.380$	$0$	$0.493317$	Character $\chi_{1984}(1131, \cdot)$
1-1984-1984.1139-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1139	$0$	✓	✓	$0.0510$	$0$	$0.937719$	Character $\chi_{1984}(1139, \cdot)$
1-1984-1984.1141-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1141	$0$	✓	✓	$-0.420$	$0$	$1.64792$	Character $\chi_{1984}(1141, \cdot)$
1-1984-1984.1149-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1149	$0$	✓	✓	$-0.217$	$0$	$1.86118$	Character $\chi_{1984}(1149, \cdot)$
1-1984-1984.115-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.115	$0$	✓	✓	$0.234$	$0$	$1.41116$	Character $\chi_{1984}(115, \cdot)$
1-1984-1984.1157-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1157	$0$	✓	✓	$0.173$	$0$	$1.03086$	Character $\chi_{1984}(1157, \cdot)$
1-1984-1984.1165-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1165	$0$	✓	✓	$-0.0657$	$0$	$0.547360$	Character $\chi_{1984}(1165, \cdot)$
1-1984-1984.1171-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1171	$0$	✓	✓	$0.483$	$0$	$1.63901$	Character $\chi_{1984}(1171, \cdot)$
1-1984-1984.1195-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1195	$0$	✓	✓	$0.352$	$0$	$1.21781$	Character $\chi_{1984}(1195, \cdot)$
1-1984-1984.1197-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1197	$0$	✓	✓	$0.284$	$0$	$1.27529$	Character $\chi_{1984}(1197, \cdot)$
1-1984-1984.1213-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1213	$0$	✓	✓	$-0.171$	$0$	$0.277683$	Character $\chi_{1984}(1213, \cdot)$
1-1984-1984.1229-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1229	$0$	✓	✓	$0.112$	$0$	$1.08890$	Character $\chi_{1984}(1229, \cdot)$
1-1984-1984.123-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.123	$0$	✓	✓	$0.390$	$0$	$1.61018$	Character $\chi_{1984}(123, \cdot)$
1-1984-1984.1235-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1235	$0$	✓	✓	$0.237$	$0$	$1.25972$	Character $\chi_{1984}(1235, \cdot)$
1-1984-1984.1237-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1237	$0$	✓	✓	$-0.0175$	$0$	$0.888588$	Character $\chi_{1984}(1237, \cdot)$
1-1984-1984.1243-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1243	$0$	✓	✓	$0.423$	$0$	$1.46709$	Character $\chi_{1984}(1243, \cdot)$
1-1984-1984.1245-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1245	$0$	✓	✓	$0.420$	$0$	$0.238877$	Character $\chi_{1984}(1245, \cdot)$
1-1984-1984.1251-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1251	$0$	✓	✓	$-0.352$	$0$	$0.190325$	Character $\chi_{1984}(1251, \cdot)$
1-1984-1984.1267-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1267	$0$	✓	✓	$0.167$	$0$	$0.933950$	Character $\chi_{1984}(1267, \cdot)$
1-1984-1984.1283-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1283	$0$	✓	✓	$-0.337$	$0$	$0.606821$	Character $\chi_{1984}(1283, \cdot)$
1-1984-1984.1285-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1285	$0$	✓	✓	$-0.112$	$0$	$1.02630$	Character $\chi_{1984}(1285, \cdot)$
1-1984-1984.1309-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1309	$0$	✓	✓	$-0.115$	$0$	$0.717564$	Character $\chi_{1984}(1309, \cdot)$
1-1984-1984.1315-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1315	$0$	✓	✓	$-0.193$	$0$	$0.762383$	Character $\chi_{1984}(1315, \cdot)$
1-1984-1984.1323-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1323	$0$	✓	✓	$-0.267$	$0$	$0.702065$	Character $\chi_{1984}(1323, \cdot)$
1-1984-1984.133-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.133	$0$	✓	✓	$0.240$	$0$	$0.657382$	Character $\chi_{1984}(133, \cdot)$
1-1984-1984.1331-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1331	$0$	✓	✓	$0.255$	$0$	$1.35844$	Character $\chi_{1984}(1331, \cdot)$
1-1984-1984.1339-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1339	$0$	✓	✓	$0.262$	$0$	$1.05860$	Character $\chi_{1984}(1339, \cdot)$
1-1984-1984.1341-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1341	$0$	✓	✓	$0.140$	$0$	$1.58847$	Character $\chi_{1984}(1341, \cdot)$
1-1984-1984.1349-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1349	$0$	✓	✓	$0.342$	$0$	$1.37330$	Character $\chi_{1984}(1349, \cdot)$
1-1984-1984.1355-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1355	$0$	✓	✓	$-0.108$	$0$	$0.814059$	Character $\chi_{1984}(1355, \cdot)$
1-1984-1984.1363-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1363	$0$	✓	✓	$0.109$	$0$	$0.688671$	Character $\chi_{1984}(1363, \cdot)$
1-1984-1984.1373-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1373	$0$	✓	✓	$0.0840$	$0$	$1.16454$	Character $\chi_{1984}(1373, \cdot)$
1-1984-1984.1379-r0-0-0	$9.21$	$9.21$	$1$	$2^{6} \cdot 31$	1984.1379	$0$	✓	✓	$0.0880$	$0$	$1.00008$	Character $\chi_{1984}(1379, \cdot)$

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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 $\F_{q}$
Belyi maps

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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.