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 320 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4000-4000.1011-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1011	$1$	✓	✓	$0.0627$	$0$	$0.720656$	Character $\chi_{4000}(1011, \cdot)$
1-4000-4000.1013-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1013	$1$	✓	✓	$-0.112$	$0$	$0.460836$	Character $\chi_{4000}(1013, \cdot)$
1-4000-4000.1019-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1019	$1$	✓	✓	$-0.326$	$0$	$0.144064$	Character $\chi_{4000}(1019, \cdot)$
1-4000-4000.1037-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1037	$1$	✓	✓	$0.174$	$0$	$0.421729$	Character $\chi_{4000}(1037, \cdot)$
1-4000-4000.1053-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1053	$1$	✓	✓	$0.226$	$0$	$0.227516$	Character $\chi_{4000}(1053, \cdot)$
1-4000-4000.1059-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1059	$1$	✓	✓	$0.324$	$0$	$1.29105$	Character $\chi_{4000}(1059, \cdot)$
1-4000-4000.1077-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1077	$1$	✓	✓	$-0.324$	$0$	$1.46350$	Character $\chi_{4000}(1077, \cdot)$
1-4000-4000.1091-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1091	$1$	✓	✓	$0.124$	$0$	$0.551078$	Character $\chi_{4000}(1091, \cdot)$
1-4000-4000.11-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.11	$1$	✓	✓	$-0.124$	$0$	$0.442535$	Character $\chi_{4000}(11, \cdot)$
1-4000-4000.1117-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1117	$1$	✓	✓	$0.210$	$0$	$1.00897$	Character $\chi_{4000}(1117, \cdot)$
1-4000-4000.1131-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1131	$1$	✓	✓	$0.0232$	$0$	$0.545567$	Character $\chi_{4000}(1131, \cdot)$
1-4000-4000.1133-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1133	$1$	✓	✓	$-0.0392$	$0$	$0.423269$	Character $\chi_{4000}(1133, \cdot)$
1-4000-4000.1139-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1139	$1$	✓	✓	$-0.137$	$0$	$0.0609932$	Character $\chi_{4000}(1139, \cdot)$
1-4000-4000.117-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.117	$1$	✓	✓	$-0.226$	$0$	$0.185787$	Character $\chi_{4000}(117, \cdot)$
1-4000-4000.1171-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1171	$1$	✓	✓	$-0.173$	$0$	$0.0616207$	Character $\chi_{4000}(1171, \cdot)$
1-4000-4000.1173-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1173	$1$	✓	✓	$-0.324$	$0$	$0.0829172$	Character $\chi_{4000}(1173, \cdot)$
1-4000-4000.1179-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1179	$1$	✓	✓	$0.289$	$0$	$0.538485$	Character $\chi_{4000}(1179, \cdot)$
1-4000-4000.1197-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1197	$1$	✓	✓	$-0.0232$	$0$	$0.637869$	Character $\chi_{4000}(1197, \cdot)$
1-4000-4000.1211-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1211	$1$	✓	✓	$-0.174$	$0$	$0.272598$	Character $\chi_{4000}(1211, \cdot)$
1-4000-4000.1213-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1213	$1$	✓	✓	$-0.0752$	$0$	$0.793904$	Character $\chi_{4000}(1213, \cdot)$
1-4000-4000.1219-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1219	$1$	✓	✓	$0.260$	$0$	$0.795033$	Character $\chi_{4000}(1219, \cdot)$
1-4000-4000.1237-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1237	$1$	✓	✓	$-0.112$	$0$	$0.414407$	Character $\chi_{4000}(1237, \cdot)$
1-4000-4000.1253-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1253	$1$	✓	✓	$0.139$	$0$	$0.893922$	Character $\chi_{4000}(1253, \cdot)$
1-4000-4000.1259-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1259	$1$	✓	✓	$0.387$	$0$	$0.0237395$	Character $\chi_{4000}(1259, \cdot)$
1-4000-4000.1277-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1277	$1$	✓	✓	$-0.487$	$0$	$0.400330$	Character $\chi_{4000}(1277, \cdot)$
1-4000-4000.1291-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1291	$1$	✓	✓	$-0.0127$	$0$	$0.402529$	Character $\chi_{4000}(1291, \cdot)$
1-4000-4000.13-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.13	$1$	✓	✓	$-0.425$	$0$	$1.15472$	Character $\chi_{4000}(13, \cdot)$
1-4000-4000.131-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.131	$1$	✓	✓	$-0.0392$	$0$	$0.249790$	Character $\chi_{4000}(131, \cdot)$
1-4000-4000.1317-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1317	$1$	✓	✓	$0.323$	$0$	$0.626028$	Character $\chi_{4000}(1317, \cdot)$
1-4000-4000.133-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.133	$1$	✓	✓	$0.0232$	$0$	$0.685199$	Character $\chi_{4000}(133, \cdot)$
1-4000-4000.1331-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1331	$1$	✓	✓	$0.210$	$0$	$0.998881$	Character $\chi_{4000}(1331, \cdot)$
1-4000-4000.1333-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1333	$1$	✓	✓	$-0.326$	$0$	$0.625544$	Character $\chi_{4000}(1333, \cdot)$
1-4000-4000.1339-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1339	$1$	✓	✓	$0.425$	$0$	$0.819015$	Character $\chi_{4000}(1339, \cdot)$
1-4000-4000.1371-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1371	$1$	✓	✓	$-0.0107$	$0$	$0.374773$	Character $\chi_{4000}(1371, \cdot)$
1-4000-4000.1373-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1373	$1$	✓	✓	$0.312$	$0$	$0.0687114$	Character $\chi_{4000}(1373, \cdot)$
1-4000-4000.1379-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1379	$1$	✓	✓	$-0.323$	$0$	$0.380601$	Character $\chi_{4000}(1379, \cdot)$
1-4000-4000.139-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.139	$1$	✓	✓	$-0.324$	$0$	$0.189472$	Character $\chi_{4000}(139, \cdot)$
1-4000-4000.1397-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1397	$1$	✓	✓	$0.489$	$0$	$0.0982199$	Character $\chi_{4000}(1397, \cdot)$
1-4000-4000.1411-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1411	$1$	✓	✓	$-0.387$	$0$	$0.439271$	Character $\chi_{4000}(1411, \cdot)$
1-4000-4000.1413-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1413	$1$	✓	✓	$0.237$	$0$	$0.775330$	Character $\chi_{4000}(1413, \cdot)$
1-4000-4000.1419-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1419	$1$	✓	✓	$-0.476$	$0$	$0.291303$	Character $\chi_{4000}(1419, \cdot)$
1-4000-4000.1437-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1437	$1$	✓	✓	$0.124$	$0$	$0.376950$	Character $\chi_{4000}(1437, \cdot)$
1-4000-4000.1453-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1453	$1$	✓	✓	$0.476$	$0$	$0.307464$	Character $\chi_{4000}(1453, \cdot)$
1-4000-4000.1459-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1459	$1$	✓	✓	$0.174$	$0$	$0.806069$	Character $\chi_{4000}(1459, \cdot)$
1-4000-4000.1477-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1477	$1$	✓	✓	$-0.174$	$0$	$0.272990$	Character $\chi_{4000}(1477, \cdot)$
1-4000-4000.1491-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1491	$1$	✓	✓	$-0.425$	$0$	$1.17868$	Character $\chi_{4000}(1491, \cdot)$
1-4000-4000.1517-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1517	$1$	✓	✓	$0.260$	$0$	$0.114193$	Character $\chi_{4000}(1517, \cdot)$
1-4000-4000.1531-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1531	$1$	✓	✓	$-0.426$	$0$	$0.0169985$	Character $\chi_{4000}(1531, \cdot)$
1-4000-4000.1533-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1533	$1$	✓	✓	$-0.289$	$0$	$0.381938$	Character $\chi_{4000}(1533, \cdot)$
1-4000-4000.1539-r1-0-0	$429.$	$429.$	$1$	$2^{5} \cdot 5^{3}$	4000.1539	$1$	✓	✓	$0.0127$	$0$	$0.460511$	Character $\chi_{4000}(1539, \cdot)$

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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.