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 530 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1063-1063.100-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.100	$0$	✓	✓	$0.129$	$0$	$0.146383$	Character $\chi_{1063}(100, \cdot)$
1-1063-1063.1001-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1001	$0$	✓	✓	$0.0509$	$0$	$1.60749$	Character $\chi_{1063}(1001, \cdot)$
1-1063-1063.1002-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1002	$0$	✓	✓	$0.411$	$0$	$0.585294$	Character $\chi_{1063}(1002, \cdot)$
1-1063-1063.1004-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1004	$0$	✓	✓	$0.00562$	$0$	$1.42096$	Character $\chi_{1063}(1004, \cdot)$
1-1063-1063.1005-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1005	$0$	✓	✓	$0.474$	$0$	$0.531925$	Character $\chi_{1063}(1005, \cdot)$
1-1063-1063.1006-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1006	$0$	✓	✓	$0.425$	$0$	$1.75378$	Character $\chi_{1063}(1006, \cdot)$
1-1063-1063.1008-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1008	$0$	✓	✓	$-0.474$	$0$	$1.91162$	Character $\chi_{1063}(1008, \cdot)$
1-1063-1063.1009-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1009	$0$	✓	✓	$-0.328$	$0$	$0.199982$	Character $\chi_{1063}(1009, \cdot)$
1-1063-1063.1010-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1010	$0$	✓	✓	$0.0784$	$0$	$1.24812$	Character $\chi_{1063}(1010, \cdot)$
1-1063-1063.1012-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1012	$0$	✓	✓	$-0.408$	$0$	$1.95270$	Character $\chi_{1063}(1012, \cdot)$
1-1063-1063.1015-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1015	$0$	✓	✓	$-0.441$	$0$	$0.692155$	Character $\chi_{1063}(1015, \cdot)$
1-1063-1063.1018-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1018	$0$	✓	✓	$0.0832$	$0$	$0.434834$	Character $\chi_{1063}(1018, \cdot)$
1-1063-1063.1020-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1020	$0$	✓	✓	$0.459$	$0$	$1.98652$	Character $\chi_{1063}(1020, \cdot)$
1-1063-1063.1021-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1021	$0$	✓	✓	$-0.305$	$0$	$0.407555$	Character $\chi_{1063}(1021, \cdot)$
1-1063-1063.1022-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1022	$0$	✓	✓	$0.0985$	$0$	$1.59773$	Character $\chi_{1063}(1022, \cdot)$
1-1063-1063.1023-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1023	$0$	✓	✓	$0.269$	$0$	$0.572574$	Character $\chi_{1063}(1023, \cdot)$
1-1063-1063.1024-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1024	$0$	✓	✓	$0.179$	$0$	$1.65704$	Character $\chi_{1063}(1024, \cdot)$
1-1063-1063.1028-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1028	$0$	✓	✓	$0.434$	$0$	$1.64754$	Character $\chi_{1063}(1028, \cdot)$
1-1063-1063.1030-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1030	$0$	✓	✓	$0.394$	$0$	$1.63081$	Character $\chi_{1063}(1030, \cdot)$
1-1063-1063.1032-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1032	$0$	✓	✓	$-0.434$	$0$	$1.81090$	Character $\chi_{1063}(1032, \cdot)$
1-1063-1063.1034-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1034	$0$	✓	✓	$0.448$	$0$	$0.336999$	Character $\chi_{1063}(1034, \cdot)$
1-1063-1063.1036-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1036	$0$	✓	✓	$0.0913$	$0$	$1.32497$	Character $\chi_{1063}(1036, \cdot)$
1-1063-1063.1039-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1039	$0$	✓	✓	$0.285$	$0$	$1.00690$	Character $\chi_{1063}(1039, \cdot)$
1-1063-1063.104-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.104	$0$	✓	✓	$-0.118$	$0$	$0.455646$	Character $\chi_{1063}(104, \cdot)$
1-1063-1063.1042-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1042	$0$	✓	✓	$0.110$	$0$	$0.788498$	Character $\chi_{1063}(1042, \cdot)$
1-1063-1063.1043-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1043	$0$	✓	✓	$0.0849$	$0$	$1.24294$	Character $\chi_{1063}(1043, \cdot)$
1-1063-1063.105-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.105	$0$	✓	✓	$0.353$	$0$	$1.80090$	Character $\chi_{1063}(105, \cdot)$
1-1063-1063.1051-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1051	$0$	✓	✓	$0.134$	$0$	$0.983393$	Character $\chi_{1063}(1051, \cdot)$
1-1063-1063.1053-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1053	$0$	✓	✓	$0.278$	$0$	$1.07688$	Character $\chi_{1063}(1053, \cdot)$
1-1063-1063.1057-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1057	$0$	✓	✓	$0.313$	$0$	$1.04251$	Character $\chi_{1063}(1057, \cdot)$
1-1063-1063.1058-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1058	$0$	✓	✓	$-0.398$	$0$	$0.393455$	Character $\chi_{1063}(1058, \cdot)$
1-1063-1063.1060-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.1060	$0$	✓	✓	$0.0329$	$0$	$0.977793$	Character $\chi_{1063}(1060, \cdot)$
1-1063-1063.109-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.109	$0$	✓	✓	$-0.179$	$0$	$0.174198$	Character $\chi_{1063}(109, \cdot)$
1-1063-1063.11-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.11	$0$	✓	✓	$0.201$	$0$	$0.0474113$	Character $\chi_{1063}(11, \cdot)$
1-1063-1063.112-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.112	$0$	✓	✓	$0.0851$	$0$	$1.00369$	Character $\chi_{1063}(112, \cdot)$
1-1063-1063.117-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.117	$0$	✓	✓	$-0.438$	$0$	$0.436858$	Character $\chi_{1063}(117, \cdot)$
1-1063-1063.119-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.119	$0$	✓	✓	$0.00865$	$0$	$1.40048$	Character $\chi_{1063}(119, \cdot)$
1-1063-1063.120-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.120	$0$	✓	✓	$-0.0509$	$0$	$0.942353$	Character $\chi_{1063}(120, \cdot)$
1-1063-1063.121-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.121	$0$	✓	✓	$0.438$	$0$	$1.35325$	Character $\chi_{1063}(121, \cdot)$
1-1063-1063.123-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.123	$0$	✓	✓	$-0.438$	$0$	$0.364702$	Character $\chi_{1063}(123, \cdot)$
1-1063-1063.126-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.126	$0$	✓	✓	$-0.309$	$0$	$0.646951$	Character $\chi_{1063}(126, \cdot)$
1-1063-1063.128-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.128	$0$	✓	✓	$0.0558$	$0$	$0.842553$	Character $\chi_{1063}(128, \cdot)$
1-1063-1063.129-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.129	$0$	✓	✓	$-0.157$	$0$	$0.0479534$	Character $\chi_{1063}(129, \cdot)$
1-1063-1063.13-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.13	$0$	✓	✓	$0.258$	$0$	$1.33425$	Character $\chi_{1063}(13, \cdot)$
1-1063-1063.133-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.133	$0$	✓	✓	$0.322$	$0$	$1.40137$	Character $\chi_{1063}(133, \cdot)$
1-1063-1063.134-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.134	$0$	✓	✓	$-0.00865$	$0$	$1.13225$	Character $\chi_{1063}(134, \cdot)$
1-1063-1063.135-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.135	$0$	✓	✓	$-0.419$	$0$	$0.790031$	Character $\chi_{1063}(135, \cdot)$
1-1063-1063.136-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.136	$0$	✓	✓	$-0.475$	$0$	$0.483463$	Character $\chi_{1063}(136, \cdot)$
1-1063-1063.139-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.139	$0$	✓	✓	$0.108$	$0$	$0.848571$	Character $\chi_{1063}(139, \cdot)$
1-1063-1063.14-r0-0-0	$4.93$	$4.93$	$1$	$1063$	1063.14	$0$	✓	✓	$0.198$	$0$	$1.50203$	Character $\chi_{1063}(14, \cdot)$

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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.