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 750 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4235-4235.1004-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1004	$1$	✓	✓	$0.195$	$0$	$0.693998$	Character $\chi_{4235}(1004, \cdot)$
1-4235-4235.1007-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1007	$1$	✓	✓	$-0.269$	$0$	$0.491511$	Character $\chi_{4235}(1007, \cdot)$
1-4235-4235.1017-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1017	$1$	✓	✓	$0.284$	$0$	$0.646269$	Character $\chi_{4235}(1017, \cdot)$
1-4235-4235.1018-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1018	$1$	✓	✓	$-0.00815$	$0$	$0.260994$	Character $\chi_{4235}(1018, \cdot)$
1-4235-4235.1019-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1019	$1$	✓	✓	$0.363$	$0$	$1.05642$	Character $\chi_{4235}(1019, \cdot)$
1-4235-4235.102-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.102	$1$	✓	✓	$-0.295$	$0$	$0.571542$	Character $\chi_{4235}(102, \cdot)$
1-4235-4235.1038-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1038	$1$	✓	✓	$0.295$	$0$	$0.403290$	Character $\chi_{4235}(1038, \cdot)$
1-4235-4235.1039-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1039	$1$	✓	✓	$0.0799$	$0$	$0.0166201$	Character $\chi_{4235}(1039, \cdot)$
1-4235-4235.104-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.104	$1$	✓	✓	$-0.426$	$0$	$0.837519$	Character $\chi_{4235}(104, \cdot)$
1-4235-4235.1042-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1042	$1$	✓	✓	$-0.373$	$0$	$0.317187$	Character $\chi_{4235}(1042, \cdot)$
1-4235-4235.1053-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1053	$1$	✓	✓	$0.107$	$0$	$0.545592$	Character $\chi_{4235}(1053, \cdot)$
1-4235-4235.1063-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1063	$1$	✓	✓	$0.0978$	$0$	$0.214586$	Character $\chi_{4235}(1063, \cdot)$
1-4235-4235.1068-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1068	$1$	✓	✓	$-0.118$	$0$	$0.579239$	Character $\chi_{4235}(1068, \cdot)$
1-4235-4235.1077-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1077	$1$	✓	✓	$-0.469$	$0$	$0.836911$	Character $\chi_{4235}(1077, \cdot)$
1-4235-4235.1082-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1082	$1$	✓	✓	$0.357$	$0$	$0.771683$	Character $\chi_{4235}(1082, \cdot)$
1-4235-4235.1087-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1087	$1$	✓	✓	$0.360$	$0$	$0.963956$	Character $\chi_{4235}(1087, \cdot)$
1-4235-4235.109-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.109	$1$	✓	✓	$0.432$	$0$	$0.654519$	Character $\chi_{4235}(109, \cdot)$
1-4235-4235.1097-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1097	$1$	✓	✓	$-0.0794$	$0$	$1.03079$	Character $\chi_{4235}(1097, \cdot)$
1-4235-4235.1102-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1102	$1$	✓	✓	$0.183$	$0$	$0.712216$	Character $\chi_{4235}(1102, \cdot)$
1-4235-4235.1103-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1103	$1$	✓	✓	$-0.284$	$0$	$0.786259$	Character $\chi_{4235}(1103, \cdot)$
1-4235-4235.1104-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1104	$1$	✓	✓	$0.460$	$0$	$0.186538$	Character $\chi_{4235}(1104, \cdot)$
1-4235-4235.1109-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1109	$1$	✓	✓	$0.491$	$0$	$0.0171533$	Character $\chi_{4235}(1109, \cdot)$
1-4235-4235.1118-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1118	$1$	✓	✓	$0.0848$	$0$	$0.718748$	Character $\chi_{4235}(1118, \cdot)$
1-4235-4235.1124-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1124	$1$	✓	✓	$-0.0894$	$0$	$0.606978$	Character $\chi_{4235}(1124, \cdot)$
1-4235-4235.1132-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1132	$1$	✓	✓	$-0.0794$	$0$	$1.50944$	Character $\chi_{4235}(1132, \cdot)$
1-4235-4235.1138-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1138	$1$	✓	✓	$0.0877$	$0$	$0.171827$	Character $\chi_{4235}(1138, \cdot)$
1-4235-4235.1168-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1168	$1$	✓	✓	$0.225$	$0$	$0.422780$	Character $\chi_{4235}(1168, \cdot)$
1-4235-4235.117-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.117	$1$	✓	✓	$0.276$	$0$	$0.339567$	Character $\chi_{4235}(117, \cdot)$
1-4235-4235.1172-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1172	$1$	✓	✓	$-0.479$	$0$	$0.129600$	Character $\chi_{4235}(1172, \cdot)$
1-4235-4235.1178-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1178	$1$	✓	✓	$0.0955$	$0$	$0.804982$	Character $\chi_{4235}(1178, \cdot)$
1-4235-4235.1189-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1189	$1$	✓	✓	$0.479$	$0$	$0.467617$	Character $\chi_{4235}(1189, \cdot)$
1-4235-4235.1192-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1192	$1$	✓	✓	$-0.439$	$0$	$0.173619$	Character $\chi_{4235}(1192, \cdot)$
1-4235-4235.1194-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1194	$1$	✓	✓	$0.110$	$0$	$0.328442$	Character $\chi_{4235}(1194, \cdot)$
1-4235-4235.1208-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1208	$1$	✓	✓	$0.163$	$0$	$0.737940$	Character $\chi_{4235}(1208, \cdot)$
1-4235-4235.1214-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1214	$1$	✓	✓	$0.395$	$0$	$0.0285804$	Character $\chi_{4235}(1214, \cdot)$
1-4235-4235.1217-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1217	$1$	✓	✓	$-0.132$	$0$	$0.470293$	Character $\chi_{4235}(1217, \cdot)$
1-4235-4235.1222-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1222	$1$	✓	✓	$0.0201$	$0$	$0.315519$	Character $\chi_{4235}(1222, \cdot)$
1-4235-4235.1223-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1223	$1$	✓	✓	$-0.199$	$0$	$0.384540$	Character $\chi_{4235}(1223, \cdot)$
1-4235-4235.1224-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1224	$1$	✓	✓	$0.314$	$0$	$0.508468$	Character $\chi_{4235}(1224, \cdot)$
1-4235-4235.1228-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1228	$1$	✓	✓	$0.227$	$0$	$1.01393$	Character $\chi_{4235}(1228, \cdot)$
1-4235-4235.1229-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1229	$1$	✓	✓	$0.116$	$0$	$0.581741$	Character $\chi_{4235}(1229, \cdot)$
1-4235-4235.1234-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1234	$1$	✓	✓	$0.196$	$0$	$1.07629$	Character $\chi_{4235}(1234, \cdot)$
1-4235-4235.1238-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1238	$1$	✓	✓	$-0.330$	$0$	$0.659116$	Character $\chi_{4235}(1238, \cdot)$
1-4235-4235.1242-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1242	$1$	✓	✓	$0.115$	$0$	$0.926569$	Character $\chi_{4235}(1242, \cdot)$
1-4235-4235.1244-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1244	$1$	✓	✓	$-0.0270$	$0$	$0.610365$	Character $\chi_{4235}(1244, \cdot)$
1-4235-4235.1248-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1248	$1$	✓	✓	$0.00132$	$0$	$0.139587$	Character $\chi_{4235}(1248, \cdot)$
1-4235-4235.1257-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1257	$1$	✓	✓	$0.116$	$0$	$0.559562$	Character $\chi_{4235}(1257, \cdot)$
1-4235-4235.1259-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1259	$1$	✓	✓	$-0.314$	$0$	$0.0539832$	Character $\chi_{4235}(1259, \cdot)$
1-4235-4235.1264-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1264	$1$	✓	✓	$-0.448$	$0$	$0.784034$	Character $\chi_{4235}(1264, \cdot)$
1-4235-4235.1272-r1-0-0	$455.$	$455.$	$1$	$5 \cdot 7 \cdot 11^{2}$	4235.1272	$1$	✓	✓	$-0.427$	$0$	$0.0964539$	Character $\chi_{4235}(1272, \cdot)$

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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.