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
1-71e2-5041.10-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.10	$0$	✓	✓	$0.435$	$0$	$0.888277$	Character $\chi_{5041}(10, \cdot)$
1-71e2-5041.100-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.100	$0$	✓	✓	$-0.314$	$0$	$0.914002$	Character $\chi_{5041}(100, \cdot)$
1-71e2-5041.1000-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1000	$0$	✓	✓	$-0.145$	$0$	$0.0897028$	Character $\chi_{5041}(1000, \cdot)$
1-71e2-5041.1002-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1002	$0$	✓	✓	$0.350$	$0$	$1.22158$	Character $\chi_{5041}(1002, \cdot)$
1-71e2-5041.1003-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1003	$0$	✓	✓	$-0.398$	$0$	$0.210825$	Character $\chi_{5041}(1003, \cdot)$
1-71e2-5041.1004-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1004	$0$	✓	✓	$0.218$	$0$	$1.20024$	Character $\chi_{5041}(1004, \cdot)$
1-71e2-5041.1006-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1006	$0$	✓	✓	$0.401$	$0$	$1.07564$	Character $\chi_{5041}(1006, \cdot)$
1-71e2-5041.1009-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1009	$0$	✓	✓	$-0.277$	$0$	$0.702788$	Character $\chi_{5041}(1009, \cdot)$
1-71e2-5041.101-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.101	$0$	✓	✓	$0.189$	$0$	$1.28535$	Character $\chi_{5041}(101, \cdot)$
1-71e2-5041.1010-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1010	$0$	✓	✓	$-0.276$	$0$	$0.203014$	Character $\chi_{5041}(1010, \cdot)$
1-71e2-5041.1012-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1012	$0$	✓	✓	$0.343$	$0$	$1.24281$	Character $\chi_{5041}(1012, \cdot)$
1-71e2-5041.1013-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1013	$0$	✓	✓	$0.370$	$0$	$0.895489$	Character $\chi_{5041}(1013, \cdot)$
1-71e2-5041.1014-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1014	$0$	✓	✓	$0.192$	$0$	$0.0495532$	Character $\chi_{5041}(1014, \cdot)$
1-71e2-5041.1018-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1018	$0$	✓	✓	$-0.459$	$0$	$0.314914$	Character $\chi_{5041}(1018, \cdot)$
1-71e2-5041.1019-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1019	$0$	✓	✓	$-0.335$	$0$	$0.0276618$	Character $\chi_{5041}(1019, \cdot)$
1-71e2-5041.1021-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1021	$0$	✓	✓	$-0.489$	$0$	$0.0108334$	Character $\chi_{5041}(1021, \cdot)$
1-71e2-5041.1023-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1023	$0$	✓	✓	$0.0648$	$0$	$0.873608$	Character $\chi_{5041}(1023, \cdot)$
1-71e2-5041.1024-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1024	$0$	✓	✓	$0.0275$	$0$	$0.434971$	Character $\chi_{5041}(1024, \cdot)$
1-71e2-5041.1026-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1026	$0$	✓	✓	$0.372$	$0$	$1.50096$	Character $\chi_{5041}(1026, \cdot)$
1-71e2-5041.103-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.103	$0$	✓	✓	$0.370$	$0$	$0.986109$	Character $\chi_{5041}(103, \cdot)$
1-71e2-5041.1030-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1030	$0$	✓	✓	$0.135$	$0$	$1.48503$	Character $\chi_{5041}(1030, \cdot)$
1-71e2-5041.1031-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1031	$0$	✓	✓	$-0.493$	$0$	$0.958493$	Character $\chi_{5041}(1031, \cdot)$
1-71e2-5041.1032-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1032	$0$	✓	✓	$-0.0575$	$0$	$1.08807$	Character $\chi_{5041}(1032, \cdot)$
1-71e2-5041.1034-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1034	$0$	✓	✓	$0.0644$	$0$	$0.00181862$	Character $\chi_{5041}(1034, \cdot)$
1-71e2-5041.1037-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1037	$0$	✓	✓	$-0.223$	$0$	$0.477746$	Character $\chi_{5041}(1037, \cdot)$
1-71e2-5041.1039-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1039	$0$	✓	✓	$0.366$	$0$	$0.00246362$	Character $\chi_{5041}(1039, \cdot)$
1-71e2-5041.1042-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1042	$0$	✓	✓	$0.345$	$0$	$0.917046$	Character $\chi_{5041}(1042, \cdot)$
1-71e2-5041.1043-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1043	$0$	✓	✓	$0.0398$	$0$	$1.32451$	Character $\chi_{5041}(1043, \cdot)$
1-71e2-5041.1044-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1044	$0$	✓	✓	$-0.426$	$0$	$0.234140$	Character $\chi_{5041}(1044, \cdot)$
1-71e2-5041.1048-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1048	$0$	✓	✓	$-0.152$	$0$	$0.372905$	Character $\chi_{5041}(1048, \cdot)$
1-71e2-5041.1051-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1051	$0$	✓	✓	$-0.229$	$0$	$0.399627$	Character $\chi_{5041}(1051, \cdot)$
1-71e2-5041.1052-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1052	$0$	✓	✓	$0.0502$	$0$	$0.301308$	Character $\chi_{5041}(1052, \cdot)$
1-71e2-5041.1054-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1054	$0$	✓	✓	$-0.181$	$0$	$1.62789$	Character $\chi_{5041}(1054, \cdot)$
1-71e2-5041.1058-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1058	$0$	✓	✓	$-0.370$	$0$	$0.281032$	Character $\chi_{5041}(1058, \cdot)$
1-71e2-5041.1066-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1066	$0$	✓	✓	$0.0517$	$0$	$0.745019$	Character $\chi_{5041}(1066, \cdot)$
1-71e2-5041.1067-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1067	$0$	✓	✓	$-0.00777$	$0$	$0.997704$	Character $\chi_{5041}(1067, \cdot)$
1-71e2-5041.1068-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1068	$0$	✓	✓	$0.122$	$0$	$0.453857$	Character $\chi_{5041}(1068, \cdot)$
1-71e2-5041.1069-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1069	$0$	✓	✓	$0.352$	$0$	$1.08148$	Character $\chi_{5041}(1069, \cdot)$
1-71e2-5041.107-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.107	$0$	✓	✓	$-0.248$	$0$	$0.682288$	Character $\chi_{5041}(107, \cdot)$
1-71e2-5041.1070-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1070	$0$	✓	✓	$0.343$	$0$	$0.878502$	Character $\chi_{5041}(1070, \cdot)$
1-71e2-5041.1071-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1071	$0$	✓	✓	$0.169$	$0$	$1.23608$	Character $\chi_{5041}(1071, \cdot)$
1-71e2-5041.1073-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1073	$0$	✓	✓	$0.000198$	$0$	$0.861747$	Character $\chi_{5041}(1073, \cdot)$
1-71e2-5041.1074-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1074	$0$	✓	✓	$0.0910$	$0$	$0.690227$	Character $\chi_{5041}(1074, \cdot)$
1-71e2-5041.1075-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1075	$0$	✓	✓	$0.000198$	$0$	$1.05999$	Character $\chi_{5041}(1075, \cdot)$
1-71e2-5041.1077-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1077	$0$	✓	✓	$0.423$	$0$	$0.0825420$	Character $\chi_{5041}(1077, \cdot)$
1-71e2-5041.108-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.108	$0$	✓	✓	$-0.200$	$0$	$0.470205$	Character $\chi_{5041}(108, \cdot)$
1-71e2-5041.1080-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1080	$0$	✓	✓	$0.245$	$0$	$1.29469$	Character $\chi_{5041}(1080, \cdot)$
1-71e2-5041.1081-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1081	$0$	✓	✓	$0.366$	$0$	$0.117556$	Character $\chi_{5041}(1081, \cdot)$
1-71e2-5041.1083-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1083	$0$	✓	✓	$-0.181$	$0$	$0.570443$	Character $\chi_{5041}(1083, \cdot)$
1-71e2-5041.1084-r0-0-0	$23.4$	$23.4$	$1$	$71^{2}$	5041.1084	$0$	✓	✓	$0.000175$	$0$	$0.994543$	Character $\chi_{5041}(1084, \cdot)$

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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.