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 309 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-311-311.10-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.10	$0$	✓	✓	$-0.130$	$0$	$0.525055$	Character $\chi_{311}(10, \cdot)$
1-311-311.100-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.100	$0$	✓	✓	$-0.406$	$0$	$0.946238$	Character $\chi_{311}(100, \cdot)$
1-311-311.104-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.104	$0$	✓	✓	$-0.288$	$0$	$2.22983$	Character $\chi_{311}(104, \cdot)$
1-311-311.105-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.105	$0$	✓	✓	$-0.134$	$0$	$0.749232$	Character $\chi_{311}(105, \cdot)$
1-311-311.106-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.106	$0$	✓	✓	$0.195$	$0$	$0.979841$	Character $\chi_{311}(106, \cdot)$
1-311-311.107-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.107	$0$	✓	✓	$-0.0327$	$0$	$1.34244$	Character $\chi_{311}(107, \cdot)$
1-311-311.108-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.108	$0$	✓	✓	$0.0395$	$0$	$1.58999$	Character $\chi_{311}(108, \cdot)$
1-311-311.109-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.109	$0$	✓	✓	$-0.443$	$0$	$0.759528$	Character $\chi_{311}(109, \cdot)$
1-311-311.112-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.112	$0$	✓	✓	$0.297$	$0$	$1.58636$	Character $\chi_{311}(112, \cdot)$
1-311-311.113-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.113	$0$	✓	✓	$-0.0259$	$0$	$0.931861$	Character $\chi_{311}(113, \cdot)$
1-311-311.117-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.117	$0$	✓	✓	$-0.190$	$0$	$1.67479$	Character $\chi_{311}(117, \cdot)$
1-311-311.12-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.12	$0$	✓	✓	$-0.338$	$0$	$0.815779$	Character $\chi_{311}(12, \cdot)$
1-311-311.120-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.120	$0$	✓	✓	$-0.104$	$0$	$3.02491$	Character $\chi_{311}(120, \cdot)$
1-311-311.121-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.121	$0$	✓	✓	$-0.142$	$0$	$0.856527$	Character $\chi_{311}(121, \cdot)$
1-311-311.125-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.125	$0$	✓	✓	$-0.310$	$0$	$0.894709$	Character $\chi_{311}(125, \cdot)$
1-311-311.126-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.126	$0$	✓	✓	$0.249$	$0$	$1.95931$	Character $\chi_{311}(126, \cdot)$
1-311-311.127-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.127	$0$	✓	✓	$0.104$	$0$	$0.0390710$	Character $\chi_{311}(127, \cdot)$
1-311-311.128-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.128	$0$	✓	✓	$-0.314$	$0$	$0.550255$	Character $\chi_{311}(128, \cdot)$
1-311-311.13-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.13	$0$	✓	✓	$0.0526$	$0$	$1.04758$	Character $\chi_{311}(13, \cdot)$
1-311-311.130-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.130	$0$	✓	✓	$-0.0582$	$0$	$0.628429$	Character $\chi_{311}(130, \cdot)$
1-311-311.134-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.134	$0$	✓	✓	$0.202$	$0$	$1.90506$	Character $\chi_{311}(134, \cdot)$
1-311-311.135-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.135	$0$	✓	✓	$-0.338$	$0$	$1.17878$	Character $\chi_{311}(135, \cdot)$
1-311-311.137-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.137	$0$	✓	✓	$-0.0280$	$0$	$1.15334$	Character $\chi_{311}(137, \cdot)$
1-311-311.139-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.139	$0$	✓	✓	$0.173$	$0$	$1.74889$	Character $\chi_{311}(139, \cdot)$
1-311-311.14-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.14	$0$	✓	✓	$-0.180$	$0$	$0.631326$	Character $\chi_{311}(14, \cdot)$
1-311-311.140-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.140	$0$	✓	✓	$0.0229$	$0$	$1.87216$	Character $\chi_{311}(140, \cdot)$
1-311-311.141-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.141	$0$	✓	✓	$-0.360$	$0$	$0.652980$	Character $\chi_{311}(141, \cdot)$
1-311-311.144-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.144	$0$	✓	✓	$0.0864$	$0$	$1.71639$	Character $\chi_{311}(144, \cdot)$
1-311-311.146-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.146	$0$	✓	✓	$0.0535$	$0$	$1.50313$	Character $\chi_{311}(146, \cdot)$
1-311-311.147-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.147	$0$	✓	✓	$0.436$	$0$	$0.202089$	Character $\chi_{311}(147, \cdot)$
1-311-311.15-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.15	$0$	✓	✓	$0.452$	$0$	$0.152828$	Character $\chi_{311}(15, \cdot)$
1-311-311.150-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.150	$0$	✓	✓	$-0.0993$	$0$	$1.35470$	Character $\chi_{311}(150, \cdot)$
1-311-311.156-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.156	$0$	✓	✓	$0.366$	$0$	$1.57880$	Character $\chi_{311}(156, \cdot)$
1-311-311.157-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.157	$0$	✓	✓	$0.190$	$0$	$1.99252$	Character $\chi_{311}(157, \cdot)$
1-311-311.158-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.158	$0$	✓	✓	$0.102$	$0$	$1.21448$	Character $\chi_{311}(158, \cdot)$
1-311-311.159-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.159	$0$	✓	✓	$-0.0387$	$0$	$0.363177$	Character $\chi_{311}(159, \cdot)$
1-311-311.16-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.16	$0$	✓	✓	$0.457$	$0$	$1.24677$	Character $\chi_{311}(16, \cdot)$
1-311-311.160-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.160	$0$	✓	✓	$-0.138$	$0$	$1.28902$	Character $\chi_{311}(160, \cdot)$
1-311-311.162-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.162	$0$	✓	✓	$0.165$	$0$	$1.49860$	Character $\chi_{311}(162, \cdot)$
1-311-311.163-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.163	$0$	✓	✓	$-0.288$	$0$	$1.15502$	Character $\chi_{311}(163, \cdot)$
1-311-311.166-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.166	$0$	✓	✓	$0.288$	$0$	$2.42068$	Character $\chi_{311}(166, \cdot)$
1-311-311.168-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.168	$0$	✓	✓	$0.0706$	$0$	$1.26280$	Character $\chi_{311}(168, \cdot)$
1-311-311.169-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.169	$0$	✓	✓	$0.424$	$0$	$1.65355$	Character $\chi_{311}(169, \cdot)$
1-311-311.173-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.173	$0$	✓	✓	$0.138$	$0$	$0.962049$	Character $\chi_{311}(173, \cdot)$
1-311-311.175-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.175	$0$	✓	✓	$-0.457$	$0$	$0.129853$	Character $\chi_{311}(175, \cdot)$
1-311-311.178-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.178	$0$	✓	✓	$0.0387$	$0$	$0.885036$	Character $\chi_{311}(178, \cdot)$
1-311-311.179-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.179	$0$	✓	✓	$-0.173$	$0$	$0.555929$	Character $\chi_{311}(179, \cdot)$
1-311-311.18-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.18	$0$	✓	✓	$0.142$	$0$	$2.12420$	Character $\chi_{311}(18, \cdot)$
1-311-311.180-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.180	$0$	✓	✓	$-0.205$	$0$	$0.112315$	Character $\chi_{311}(180, \cdot)$
1-311-311.182-r0-0-0	$1.44$	$1.44$	$1$	$311$	311.182	$0$	✓	✓	$0.338$	$0$	$2.37494$	Character $\chi_{311}(182, \cdot)$

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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.