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 184 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-473-473.10-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.10	$1$	✓	✓	$-0.126$	$0$	$0.962626$	Character $\chi_{473}(10, \cdot)$
1-473-473.101-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.101	$1$	✓	✓	$-0.418$	$0$	$0.408781$	Character $\chi_{473}(101, \cdot)$
1-473-473.104-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.104	$1$	✓	✓	$-0.117$	$0$	$1.19122$	Character $\chi_{473}(104, \cdot)$
1-473-473.107-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.107	$1$	✓	✓	$-0.318$	$0$	$1.38719$	Character $\chi_{473}(107, \cdot)$
1-473-473.108-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.108	$1$	✓	✓	$0.155$	$0$	$0.472384$	Character $\chi_{473}(108, \cdot)$
1-473-473.109-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.109	$1$	✓	✓	$0.464$	$0$	$0.352768$	Character $\chi_{473}(109, \cdot)$
1-473-473.113-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.113	$1$	✓	✓	$-0.0723$	$0$	$1.00620$	Character $\chi_{473}(113, \cdot)$
1-473-473.114-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.114	$1$	✓	✓	$0.0138$	$0$	$0.845623$	Character $\chi_{473}(114, \cdot)$
1-473-473.115-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.115	$1$	✓	✓	$-0.279$	$0$	$0.586627$	Character $\chi_{473}(115, \cdot)$
1-473-473.117-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.117	$1$	✓	✓	$0.199$	$0$	$0.917585$	Character $\chi_{473}(117, \cdot)$
1-473-473.119-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.119	$1$	✓	✓	$-0.333$	$0$	$0.396112$	Character $\chi_{473}(119, \cdot)$
1-473-473.125-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.125	$1$	✓	✓	$0.370$	$0$	$0.691305$	Character $\chi_{473}(125, \cdot)$
1-473-473.127-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.127	$1$	✓	✓	$-0.366$	$0$	$1.96148$	Character $\chi_{473}(127, \cdot)$
1-473-473.13-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.13	$1$	✓	✓	$0.172$	$0$	$0.719821$	Character $\chi_{473}(13, \cdot)$
1-473-473.136-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.136	$1$	✓	✓	$-0.132$	$0$	$0.365046$	Character $\chi_{473}(136, \cdot)$
1-473-473.137-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.137	$1$	✓	✓	$0.111$	$0$	$0.893588$	Character $\chi_{473}(137, \cdot)$
1-473-473.138-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.138	$1$	✓	✓	$0.121$	$0$	$0.576982$	Character $\chi_{473}(138, \cdot)$
1-473-473.139-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.139	$1$	✓	✓	$-0.487$	$0$	$1.79470$	Character $\chi_{473}(139, \cdot)$
1-473-473.140-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.140	$1$	✓	✓	$0.265$	$0$	$1.59021$	Character $\chi_{473}(140, \cdot)$
1-473-473.141-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.141	$1$	✓	✓	$0.117$	$0$	$1.65707$	Character $\chi_{473}(141, \cdot)$
1-473-473.142-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.142	$1$	✓	✓	$0.126$	$0$	$1.41407$	Character $\chi_{473}(142, \cdot)$
1-473-473.145-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.145	$1$	✓	✓	$-0.162$	$0$	$0.397780$	Character $\chi_{473}(145, \cdot)$
1-473-473.147-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.147	$1$	✓	✓	$-0.156$	$0$	$0.628462$	Character $\chi_{473}(147, \cdot)$
1-473-473.148-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.148	$1$	✓	✓	$0.406$	$0$	$0.448896$	Character $\chi_{473}(148, \cdot)$
1-473-473.150-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.150	$1$	✓	✓	$-0.0406$	$0$	$0.918517$	Character $\chi_{473}(150, \cdot)$
1-473-473.153-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.153	$1$	✓	✓	$-0.167$	$0$	$0.595978$	Character $\chi_{473}(153, \cdot)$
1-473-473.157-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.157	$1$	✓	✓	$-0.193$	$0$	$0.532482$	Character $\chi_{473}(157, \cdot)$
1-473-473.158-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.158	$1$	✓	✓	$-0.318$	$0$	$0.137053$	Character $\chi_{473}(158, \cdot)$
1-473-473.159-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.159	$1$	✓	✓	$0.333$	$0$	$1.07845$	Character $\chi_{473}(159, \cdot)$
1-473-473.160-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.160	$1$	✓	✓	$-0.485$	$0$	$0.651923$	Character $\chi_{473}(160, \cdot)$
1-473-473.163-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.163	$1$	✓	✓	$-0.406$	$0$	$1.32535$	Character $\chi_{473}(163, \cdot)$
1-473-473.164-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.164	$1$	✓	✓	$0.208$	$0$	$0.837712$	Character $\chi_{473}(164, \cdot)$
1-473-473.167-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.167	$1$	✓	✓	$-0.478$	$0$	$0.591230$	Character $\chi_{473}(167, \cdot)$
1-473-473.168-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.168	$1$	✓	✓	$0.163$	$0$	$1.49483$	Character $\chi_{473}(168, \cdot)$
1-473-473.17-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.17	$1$	✓	✓	$0.478$	$0$	$1.41164$	Character $\chi_{473}(17, \cdot)$
1-473-473.174-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.174	$1$	✓	✓	$-0.441$	$0$	$0.239889$	Character $\chi_{473}(174, \cdot)$
1-473-473.178-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.178	$1$	✓	✓	$0.428$	$0$	$1.52685$	Character $\chi_{473}(178, \cdot)$
1-473-473.179-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.179	$1$	✓	✓	$-0.340$	$0$	$1.44336$	Character $\chi_{473}(179, \cdot)$
1-473-473.180-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.180	$1$	✓	✓	$0.0723$	$0$	$0.785263$	Character $\chi_{473}(180, \cdot)$
1-473-473.182-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.182	$1$	✓	✓	$-0.172$	$0$	$0.165804$	Character $\chi_{473}(182, \cdot)$
1-473-473.183-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.183	$1$	✓	✓	$-0.456$	$0$	$0.103605$	Character $\chi_{473}(183, \cdot)$
1-473-473.186-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.186	$1$	✓	✓	$-0.459$	$0$	$1.15660$	Character $\chi_{473}(186, \cdot)$
1-473-473.189-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.189	$1$	✓	✓	$-0.428$	$0$	$0.177295$	Character $\chi_{473}(189, \cdot)$
1-473-473.190-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.190	$1$	✓	✓	$-0.363$	$0$	$0.0483148$	Character $\chi_{473}(190, \cdot)$
1-473-473.191-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.191	$1$	✓	✓	$0.368$	$0$	$1.46511$	Character $\chi_{473}(191, \cdot)$
1-473-473.192-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.192	$1$	✓	✓	$0.232$	$0$	$0.807567$	Character $\chi_{473}(192, \cdot)$
1-473-473.193-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.193	$1$	✓	✓	$0.273$	$0$	$2.01560$	Character $\chi_{473}(193, \cdot)$
1-473-473.195-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.195	$1$	✓	✓	$-0.174$	$0$	$0.649619$	Character $\chi_{473}(195, \cdot)$
1-473-473.197-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.197	$1$	✓	✓	$0.439$	$0$	$1.47282$	Character $\chi_{473}(197, \cdot)$
1-473-473.20-r1-0-0	$50.8$	$50.8$	$1$	$11 \cdot 43$	473.20	$1$	✓	✓	$-0.0527$	$0$	$0.545672$	Character $\chi_{473}(20, \cdot)$

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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.