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 1209 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2623-2623.10-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.10	$1$	✓	✓	$-0.438$	$0$	$0.272533$	Character $\chi_{2623}(10, \cdot)$
1-2623-2623.1000-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1000	$1$	✓	✓	$0.446$	$0$	$0.839267$	Character $\chi_{2623}(1000, \cdot)$
1-2623-2623.1001-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1001	$1$	✓	✓	$0.439$	$0$	$1.31624$	Character $\chi_{2623}(1001, \cdot)$
1-2623-2623.1002-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1002	$1$	✓	✓	$0.335$	$0$	$1.19829$	Character $\chi_{2623}(1002, \cdot)$
1-2623-2623.1004-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1004	$1$	✓	✓	$-0.340$	$0$	$0.0258050$	Character $\chi_{2623}(1004, \cdot)$
1-2623-2623.1005-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1005	$1$	✓	✓	$0.126$	$0$	$1.01372$	Character $\chi_{2623}(1005, \cdot)$
1-2623-2623.1006-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1006	$1$	✓	✓	$0.479$	$0$	$0.116119$	Character $\chi_{2623}(1006, \cdot)$
1-2623-2623.101-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.101	$1$	✓	✓	$0.00986$	$0$	$0.299957$	Character $\chi_{2623}(101, \cdot)$
1-2623-2623.1013-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1013	$1$	✓	✓	$0.0510$	$0$	$0.563500$	Character $\chi_{2623}(1013, \cdot)$
1-2623-2623.1014-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1014	$1$	✓	✓	$-0.130$	$0$	$0.539425$	Character $\chi_{2623}(1014, \cdot)$
1-2623-2623.1015-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1015	$1$	✓	✓	$0.261$	$0$	$0.0773212$	Character $\chi_{2623}(1015, \cdot)$
1-2623-2623.1017-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1017	$1$	✓	✓	$0.346$	$0$	$0.843243$	Character $\chi_{2623}(1017, \cdot)$
1-2623-2623.1018-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1018	$1$	✓	✓	$0.463$	$0$	$0.985655$	Character $\chi_{2623}(1018, \cdot)$
1-2623-2623.1020-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1020	$1$	✓	✓	$-0.214$	$0$	$1.16007$	Character $\chi_{2623}(1020, \cdot)$
1-2623-2623.1021-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1021	$1$	✓	✓	$-0.476$	$0$	$0.346892$	Character $\chi_{2623}(1021, \cdot)$
1-2623-2623.1022-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1022	$1$	✓	✓	$-0.468$	$0$	$0.296557$	Character $\chi_{2623}(1022, \cdot)$
1-2623-2623.1023-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1023	$1$	✓	✓	$-0.225$	$0$	$0.0116652$	Character $\chi_{2623}(1023, \cdot)$
1-2623-2623.1027-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1027	$1$	✓	✓	$0.175$	$0$	$0.688282$	Character $\chi_{2623}(1027, \cdot)$
1-2623-2623.1028-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1028	$1$	✓	✓	$-0.246$	$0$	$0.974277$	Character $\chi_{2623}(1028, \cdot)$
1-2623-2623.1029-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1029	$1$	✓	✓	$0.315$	$0$	$0.0330906$	Character $\chi_{2623}(1029, \cdot)$
1-2623-2623.1030-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1030	$1$	✓	✓	$-0.434$	$0$	$1.04927$	Character $\chi_{2623}(1030, \cdot)$
1-2623-2623.1034-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1034	$1$	✓	✓	$-0.0995$	$0$	$0.372981$	Character $\chi_{2623}(1034, \cdot)$
1-2623-2623.1040-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1040	$1$	✓	✓	$0.484$	$0$	$0.475718$	Character $\chi_{2623}(1040, \cdot)$
1-2623-2623.1043-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1043	$1$	✓	✓	$0.394$	$0$	$0.401118$	Character $\chi_{2623}(1043, \cdot)$
1-2623-2623.1045-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1045	$1$	✓	✓	$0.329$	$0$	$1.20264$	Character $\chi_{2623}(1045, \cdot)$
1-2623-2623.1047-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1047	$1$	✓	✓	$-0.157$	$0$	$0.384505$	Character $\chi_{2623}(1047, \cdot)$
1-2623-2623.1048-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1048	$1$	✓	✓	$0.399$	$0$	$1.38387$	Character $\chi_{2623}(1048, \cdot)$
1-2623-2623.1050-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1050	$1$	✓	✓	$0.462$	$0$	$0.329100$	Character $\chi_{2623}(1050, \cdot)$
1-2623-2623.1051-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1051	$1$	✓	✓	$0.471$	$0$	$0.940143$	Character $\chi_{2623}(1051, \cdot)$
1-2623-2623.1052-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1052	$1$	✓	✓	$0.176$	$0$	$0.268647$	Character $\chi_{2623}(1052, \cdot)$
1-2623-2623.1055-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1055	$1$	✓	✓	$-0.320$	$0$	$0.459540$	Character $\chi_{2623}(1055, \cdot)$
1-2623-2623.1059-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1059	$1$	✓	✓	$0.470$	$0$	$0.892058$	Character $\chi_{2623}(1059, \cdot)$
1-2623-2623.106-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.106	$1$	✓	✓	$0.214$	$0$	$0.396182$	Character $\chi_{2623}(106, \cdot)$
1-2623-2623.1062-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1062	$1$	✓	✓	$0.418$	$0$	$0.377903$	Character $\chi_{2623}(1062, \cdot)$
1-2623-2623.1063-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1063	$1$	✓	✓	$-0.277$	$0$	$0.419386$	Character $\chi_{2623}(1063, \cdot)$
1-2623-2623.1064-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1064	$1$	✓	✓	$0.246$	$0$	$1.31431$	Character $\chi_{2623}(1064, \cdot)$
1-2623-2623.1067-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1067	$1$	✓	✓	$-0.360$	$0$	$1.18395$	Character $\chi_{2623}(1067, \cdot)$
1-2623-2623.1068-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1068	$1$	✓	✓	$-0.0803$	$0$	$0.819037$	Character $\chi_{2623}(1068, \cdot)$
1-2623-2623.1070-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1070	$1$	✓	✓	$0.208$	$0$	$1.14493$	Character $\chi_{2623}(1070, \cdot)$
1-2623-2623.1071-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1071	$1$	✓	✓	$0.495$	$0$	$1.18630$	Character $\chi_{2623}(1071, \cdot)$
1-2623-2623.1072-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1072	$1$	✓	✓	$-0.368$	$0$	$0.935024$	Character $\chi_{2623}(1072, \cdot)$
1-2623-2623.1078-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1078	$1$	✓	✓	$-0.0463$	$0$	$0.419214$	Character $\chi_{2623}(1078, \cdot)$
1-2623-2623.108-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.108	$1$	✓	✓	$-0.472$	$0$	$0.0373134$	Character $\chi_{2623}(108, \cdot)$
1-2623-2623.1081-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1081	$1$	✓	✓	$-0.249$	$0$	$0.998028$	Character $\chi_{2623}(1081, \cdot)$
1-2623-2623.1082-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1082	$1$	✓	✓	$-0.0646$	$0$	$2.16319$	Character $\chi_{2623}(1082, \cdot)$
1-2623-2623.1083-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1083	$1$	✓	✓	$0.499$	$0$	$0.121297$	Character $\chi_{2623}(1083, \cdot)$
1-2623-2623.1088-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1088	$1$	✓	✓	$0.159$	$0$	$0.653664$	Character $\chi_{2623}(1088, \cdot)$
1-2623-2623.1090-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1090	$1$	✓	✓	$0.295$	$0$	$0.711064$	Character $\chi_{2623}(1090, \cdot)$
1-2623-2623.1091-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1091	$1$	✓	✓	$0.248$	$0$	$0.817353$	Character $\chi_{2623}(1091, \cdot)$
1-2623-2623.1092-r1-0-0	$281.$	$281.$	$1$	$43 \cdot 61$	2623.1092	$1$	✓	✓	$-0.305$	$0$	$0.0700262$	Character $\chi_{2623}(1092, \cdot)$

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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.