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

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4729-4729.10-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.10	$0$	✓	✓	$-0.484$	$0$	$0.169462$	Character $\chi_{4729}(10, \cdot)$
1-4729-4729.100-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.100	$0$	✓	✓	$0.00976$	$0$	$0.246081$	Character $\chi_{4729}(100, \cdot)$
1-4729-4729.1000-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1000	$0$	✓	✓	$-0.192$	$0$	$0.639523$	Character $\chi_{4729}(1000, \cdot)$
1-4729-4729.1004-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1004	$0$	✓	✓	$0.114$	$0$	$0.527869$	Character $\chi_{4729}(1004, \cdot)$
1-4729-4729.1005-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1005	$0$	✓	✓	$-0.00664$	$0$	$1.67750$	Character $\chi_{4729}(1005, \cdot)$
1-4729-4729.1008-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1008	$0$	✓	✓	$0.404$	$0$	$1.15592$	Character $\chi_{4729}(1008, \cdot)$
1-4729-4729.1012-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1012	$0$	✓	✓	$-0.382$	$0$	$0.153305$	Character $\chi_{4729}(1012, \cdot)$
1-4729-4729.1013-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1013	$0$	✓	✓	$-0.173$	$0$	$0.758826$	Character $\chi_{4729}(1013, \cdot)$
1-4729-4729.1014-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1014	$0$	✓	✓	$-0.212$	$0$	$0.305157$	Character $\chi_{4729}(1014, \cdot)$
1-4729-4729.1016-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1016	$0$	✓	✓	$0.0479$	$0$	$0.673757$	Character $\chi_{4729}(1016, \cdot)$
1-4729-4729.1018-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1018	$0$	✓	✓	$-0.176$	$0$	$0.455207$	Character $\chi_{4729}(1018, \cdot)$
1-4729-4729.1022-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1022	$0$	✓	✓	$-0.273$	$0$	$0.794491$	Character $\chi_{4729}(1022, \cdot)$
1-4729-4729.1023-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1023	$0$	✓	✓	$0.318$	$0$	$1.36311$	Character $\chi_{4729}(1023, \cdot)$
1-4729-4729.1024-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1024	$0$	✓	✓	$0.274$	$0$	$1.05284$	Character $\chi_{4729}(1024, \cdot)$
1-4729-4729.1026-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1026	$0$	✓	✓	$-0.244$	$0$	$0.0480943$	Character $\chi_{4729}(1026, \cdot)$
1-4729-4729.1029-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1029	$0$	✓	✓	$-0.210$	$0$	$0.372349$	Character $\chi_{4729}(1029, \cdot)$
1-4729-4729.1031-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1031	$0$	✓	✓	$0.0947$	$0$	$1.00305$	Character $\chi_{4729}(1031, \cdot)$
1-4729-4729.1034-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1034	$0$	✓	✓	$-0.449$	$0$	$1.28533$	Character $\chi_{4729}(1034, \cdot)$
1-4729-4729.1036-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1036	$0$	✓	✓	$-0.340$	$0$	$1.52518$	Character $\chi_{4729}(1036, \cdot)$
1-4729-4729.1037-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1037	$0$	✓	✓	$-0.0892$	$0$	$1.02519$	Character $\chi_{4729}(1037, \cdot)$
1-4729-4729.104-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.104	$0$	✓	✓	$0.0650$	$0$	$1.08906$	Character $\chi_{4729}(104, \cdot)$
1-4729-4729.1040-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1040	$0$	✓	✓	$0.471$	$0$	$0.155317$	Character $\chi_{4729}(1040, \cdot)$
1-4729-4729.1042-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1042	$0$	✓	✓	$-0.275$	$0$	$0.961889$	Character $\chi_{4729}(1042, \cdot)$
1-4729-4729.1043-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1043	$0$	✓	✓	$-0.0135$	$0$	$0.519488$	Character $\chi_{4729}(1043, \cdot)$
1-4729-4729.1047-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1047	$0$	✓	✓	$0.150$	$0$	$0.730518$	Character $\chi_{4729}(1047, \cdot)$
1-4729-4729.1048-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1048	$0$	✓	✓	$-0.105$	$0$	$0.637779$	Character $\chi_{4729}(1048, \cdot)$
1-4729-4729.105-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.105	$0$	✓	✓	$0.0312$	$0$	$0.927449$	Character $\chi_{4729}(105, \cdot)$
1-4729-4729.1050-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1050	$0$	✓	✓	$0.170$	$0$	$0.783840$	Character $\chi_{4729}(1050, \cdot)$
1-4729-4729.1051-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1051	$0$	✓	✓	$0.00814$	$0$	$1.81709$	Character $\chi_{4729}(1051, \cdot)$
1-4729-4729.1052-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1052	$0$	✓	✓	$0.000267$	$0$	$1.12912$	Character $\chi_{4729}(1052, \cdot)$
1-4729-4729.1053-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1053	$0$	✓	✓	$0.457$	$0$	$1.21027$	Character $\chi_{4729}(1053, \cdot)$
1-4729-4729.1054-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1054	$0$	✓	✓	$-0.273$	$0$	$0.0935577$	Character $\chi_{4729}(1054, \cdot)$
1-4729-4729.1055-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1055	$0$	✓	✓	$-0.163$	$0$	$0.0284639$	Character $\chi_{4729}(1055, \cdot)$
1-4729-4729.1058-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1058	$0$	✓	✓	$0.143$	$0$	$0.712355$	Character $\chi_{4729}(1058, \cdot)$
1-4729-4729.1059-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1059	$0$	✓	✓	$0.489$	$0$	$1.21775$	Character $\chi_{4729}(1059, \cdot)$
1-4729-4729.1061-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1061	$0$	✓	✓	$-0.344$	$0$	$1.65364$	Character $\chi_{4729}(1061, \cdot)$
1-4729-4729.1062-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1062	$0$	✓	✓	$0.171$	$0$	$0.933640$	Character $\chi_{4729}(1062, \cdot)$
1-4729-4729.1064-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1064	$0$	✓	✓	$0.0152$	$0$	$0.915654$	Character $\chi_{4729}(1064, \cdot)$
1-4729-4729.1065-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1065	$0$	✓	✓	$0.420$	$0$	$0.670548$	Character $\chi_{4729}(1065, \cdot)$
1-4729-4729.1072-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1072	$0$	✓	✓	$-0.425$	$0$	$0.814758$	Character $\chi_{4729}(1072, \cdot)$
1-4729-4729.1074-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1074	$0$	✓	✓	$-0.111$	$0$	$0.136299$	Character $\chi_{4729}(1074, \cdot)$
1-4729-4729.1079-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1079	$0$	✓	✓	$-0.0574$	$0$	$0.456305$	Character $\chi_{4729}(1079, \cdot)$
1-4729-4729.108-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.108	$0$	✓	✓	$0.108$	$0$	$0.755555$	Character $\chi_{4729}(108, \cdot)$
1-4729-4729.1080-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1080	$0$	✓	✓	$0.255$	$0$	$0.111214$	Character $\chi_{4729}(1080, \cdot)$
1-4729-4729.1081-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1081	$0$	✓	✓	$-0.430$	$0$	$1.25661$	Character $\chi_{4729}(1081, \cdot)$
1-4729-4729.1082-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1082	$0$	✓	✓	$-0.340$	$0$	$1.32236$	Character $\chi_{4729}(1082, \cdot)$
1-4729-4729.1083-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1083	$0$	✓	✓	$0.300$	$0$	$0.673938$	Character $\chi_{4729}(1083, \cdot)$
1-4729-4729.1084-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1084	$0$	✓	✓	$0.474$	$0$	$0.489154$	Character $\chi_{4729}(1084, \cdot)$
1-4729-4729.1087-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1087	$0$	✓	✓	$-0.235$	$0$	$1.61104$	Character $\chi_{4729}(1087, \cdot)$
1-4729-4729.1089-r0-0-0	$21.9$	$21.9$	$1$	$4729$	4729.1089	$0$	✓	✓	$0.498$	$0$	$1.08302$	Character $\chi_{4729}(1089, \cdot)$

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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.