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 4019 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4021-4021.100-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.100	$0$	✓	✓	$0.267$	$0$	$0.736042$	Character $\chi_{4021}(100, \cdot)$
1-4021-4021.1001-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1001	$0$	✓	✓	$0.436$	$0$	$0.981803$	Character $\chi_{4021}(1001, \cdot)$
1-4021-4021.1002-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1002	$0$	✓	✓	$-0.346$	$0$	$0.0258501$	Character $\chi_{4021}(1002, \cdot)$
1-4021-4021.1003-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1003	$0$	✓	✓	$0.405$	$0$	$1.21441$	Character $\chi_{4021}(1003, \cdot)$
1-4021-4021.1004-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1004	$0$	✓	✓	$0.287$	$0$	$1.14819$	Character $\chi_{4021}(1004, \cdot)$
1-4021-4021.1005-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1005	$0$	✓	✓	$0.382$	$0$	$1.03458$	Character $\chi_{4021}(1005, \cdot)$
1-4021-4021.1006-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1006	$0$	✓	✓	$-0.402$	$0$	$0.340196$	Character $\chi_{4021}(1006, \cdot)$
1-4021-4021.1009-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1009	$0$	✓	✓	$-0.339$	$0$	$0.864740$	Character $\chi_{4021}(1009, \cdot)$
1-4021-4021.101-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.101	$0$	✓	✓	$-0.192$	$0$	$0.696213$	Character $\chi_{4021}(101, \cdot)$
1-4021-4021.1012-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1012	$0$	✓	✓	$0.0167$	$0$	$0.304222$	Character $\chi_{4021}(1012, \cdot)$
1-4021-4021.1015-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1015	$0$	✓	✓	$0.495$	$0$	$1.23467$	Character $\chi_{4021}(1015, \cdot)$
1-4021-4021.1018-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1018	$0$	✓	✓	$-0.192$	$0$	$0.733669$	Character $\chi_{4021}(1018, \cdot)$
1-4021-4021.1020-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1020	$0$	✓	✓	$-0.287$	$0$	$0.467044$	Character $\chi_{4021}(1020, \cdot)$
1-4021-4021.1022-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1022	$0$	✓	✓	$0.225$	$0$	$1.04725$	Character $\chi_{4021}(1022, \cdot)$
1-4021-4021.1023-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1023	$0$	✓	✓	$-0.188$	$0$	$1.14235$	Character $\chi_{4021}(1023, \cdot)$
1-4021-4021.1024-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1024	$0$	✓	✓	$0.0730$	$0$	$0.506815$	Character $\chi_{4021}(1024, \cdot)$
1-4021-4021.1026-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1026	$0$	✓	✓	$0.389$	$0$	$0.895910$	Character $\chi_{4021}(1026, \cdot)$
1-4021-4021.103-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.103	$0$	✓	✓	$0.286$	$0$	$0.0420057$	Character $\chi_{4021}(103, \cdot)$
1-4021-4021.1031-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1031	$0$	✓	✓	$0.463$	$0$	$1.39831$	Character $\chi_{4021}(1031, \cdot)$
1-4021-4021.1032-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1032	$0$	✓	✓	$0.297$	$0$	$0.914961$	Character $\chi_{4021}(1032, \cdot)$
1-4021-4021.1033-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1033	$0$	✓	✓	$0.346$	$0$	$1.31390$	Character $\chi_{4021}(1033, \cdot)$
1-4021-4021.1037-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1037	$0$	✓	✓	$0.101$	$0$	$1.18115$	Character $\chi_{4021}(1037, \cdot)$
1-4021-4021.1038-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1038	$0$	✓	✓	$-0.131$	$0$	$0.778755$	Character $\chi_{4021}(1038, \cdot)$
1-4021-4021.1039-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1039	$0$	✓	✓	$0.154$	$0$	$0.721796$	Character $\chi_{4021}(1039, \cdot)$
1-4021-4021.1040-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1040	$0$	✓	✓	$0.263$	$0$	$0.287510$	Character $\chi_{4021}(1040, \cdot)$
1-4021-4021.1042-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1042	$0$	✓	✓	$0.0564$	$0$	$1.22925$	Character $\chi_{4021}(1042, \cdot)$
1-4021-4021.1043-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1043	$0$	✓	✓	$-0.264$	$0$	$0.792193$	Character $\chi_{4021}(1043, \cdot)$
1-4021-4021.1045-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1045	$0$	✓	✓	$0.137$	$0$	$0.878247$	Character $\chi_{4021}(1045, \cdot)$
1-4021-4021.1050-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1050	$0$	✓	✓	$0.108$	$0$	$0.0375029$	Character $\chi_{4021}(1050, \cdot)$
1-4021-4021.1051-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1051	$0$	✓	✓	$-0.440$	$0$	$0.346797$	Character $\chi_{4021}(1051, \cdot)$
1-4021-4021.1053-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1053	$0$	✓	✓	$-0.430$	$0$	$0.635597$	Character $\chi_{4021}(1053, \cdot)$
1-4021-4021.1054-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1054	$0$	✓	✓	$-0.242$	$0$	$0.346205$	Character $\chi_{4021}(1054, \cdot)$
1-4021-4021.1056-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1056	$0$	✓	✓	$-0.108$	$0$	$0.878471$	Character $\chi_{4021}(1056, \cdot)$
1-4021-4021.1060-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1060	$0$	✓	✓	$0.0667$	$0$	$2.15276$	Character $\chi_{4021}(1060, \cdot)$
1-4021-4021.1061-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1061	$0$	✓	✓	$0.0314$	$0$	$1.83836$	Character $\chi_{4021}(1061, \cdot)$
1-4021-4021.1063-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1063	$0$	✓	✓	$0.397$	$0$	$1.04893$	Character $\chi_{4021}(1063, \cdot)$
1-4021-4021.1065-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1065	$0$	✓	✓	$-0.397$	$0$	$0.582529$	Character $\chi_{4021}(1065, \cdot)$
1-4021-4021.1066-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1066	$0$	✓	✓	$0.225$	$0$	$0.170836$	Character $\chi_{4021}(1066, \cdot)$
1-4021-4021.1068-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1068	$0$	✓	✓	$0.379$	$0$	$1.03011$	Character $\chi_{4021}(1068, \cdot)$
1-4021-4021.1069-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1069	$0$	✓	✓	$-0.0965$	$0$	$0.740838$	Character $\chi_{4021}(1069, \cdot)$
1-4021-4021.107-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.107	$0$	✓	✓	$-0.0691$	$0$	$0.693562$	Character $\chi_{4021}(107, \cdot)$
1-4021-4021.1072-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1072	$0$	✓	✓	$-0.155$	$0$	$0.480261$	Character $\chi_{4021}(1072, \cdot)$
1-4021-4021.1076-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1076	$0$	✓	✓	$0.297$	$0$	$1.10872$	Character $\chi_{4021}(1076, \cdot)$
1-4021-4021.1077-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1077	$0$	✓	✓	$0.423$	$0$	$1.65221$	Character $\chi_{4021}(1077, \cdot)$
1-4021-4021.1078-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1078	$0$	✓	✓	$-0.249$	$0$	$0.982357$	Character $\chi_{4021}(1078, \cdot)$
1-4021-4021.1079-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1079	$0$	✓	✓	$0.475$	$0$	$1.50706$	Character $\chi_{4021}(1079, \cdot)$
1-4021-4021.108-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.108	$0$	✓	✓	$-0.371$	$0$	$1.16226$	Character $\chi_{4021}(108, \cdot)$
1-4021-4021.1081-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1081	$0$	✓	✓	$-0.349$	$0$	$0.660225$	Character $\chi_{4021}(1081, \cdot)$
1-4021-4021.1083-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1083	$0$	✓	✓	$-0.265$	$0$	$0.510474$	Character $\chi_{4021}(1083, \cdot)$
1-4021-4021.1085-r0-0-0	$18.6$	$18.6$	$1$	$4021$	4021.1085	$0$	✓	✓	$-0.0193$	$0$	$0.921935$	Character $\chi_{4021}(1085, \cdot)$

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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.