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 405 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-517-517.10-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.10	$0$	✓	✓	$0.0145$	$0$	$1.14523$	Character $\chi_{517}(10, \cdot)$
1-517-517.102-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.102	$0$	✓	✓	$-0.201$	$0$	$1.21841$	Character $\chi_{517}(102, \cdot)$
1-517-517.103-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.103	$0$	✓	✓	$-0.370$	$0$	$0.895401$	Character $\chi_{517}(103, \cdot)$
1-517-517.105-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.105	$0$	✓	✓	$-0.394$	$0$	$0.216842$	Character $\chi_{517}(105, \cdot)$
1-517-517.107-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.107	$0$	✓	✓	$-0.315$	$0$	$0.260896$	Character $\chi_{517}(107, \cdot)$
1-517-517.108-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.108	$0$	✓	✓	$0.0436$	$0$	$0.600921$	Character $\chi_{517}(108, \cdot)$
1-517-517.109-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.109	$0$	✓	✓	$0.228$	$0$	$1.64450$	Character $\chi_{517}(109, \cdot)$
1-517-517.115-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.115	$0$	✓	✓	$0.417$	$0$	$0.751711$	Character $\chi_{517}(115, \cdot)$
1-517-517.116-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.116	$0$	✓	✓	$-0.0749$	$0$	$1.20087$	Character $\chi_{517}(116, \cdot)$
1-517-517.117-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.117	$0$	✓	✓	$-0.422$	$0$	$0.730224$	Character $\chi_{517}(117, \cdot)$
1-517-517.119-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.119	$0$	✓	✓	$-0.293$	$0$	$0.309920$	Character $\chi_{517}(119, \cdot)$
1-517-517.120-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.120	$0$	✓	✓	$0.168$	$0$	$0.170658$	Character $\chi_{517}(120, \cdot)$
1-517-517.123-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.123	$0$	✓	✓	$-0.0768$	$0$	$1.61683$	Character $\chi_{517}(123, \cdot)$
1-517-517.126-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.126	$0$	✓	✓	$0.293$	$0$	$1.09157$	Character $\chi_{517}(126, \cdot)$
1-517-517.127-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.127	$0$	✓	✓	$0.138$	$0$	$1.54951$	Character $\chi_{517}(127, \cdot)$
1-517-517.129-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.129	$0$	✓	✓	$0.0962$	$0$	$1.26056$	Character $\chi_{517}(129, \cdot)$
1-517-517.13-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.13	$0$	✓	✓	$-0.230$	$0$	$0.402501$	Character $\chi_{517}(13, \cdot)$
1-517-517.130-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.130	$0$	✓	✓	$0.00532$	$0$	$1.18232$	Character $\chi_{517}(130, \cdot)$
1-517-517.134-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.134	$0$	✓	✓	$-0.187$	$0$	$1.05383$	Character $\chi_{517}(134, \cdot)$
1-517-517.136-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.136	$0$	✓	✓	$0.110$	$0$	$1.49567$	Character $\chi_{517}(136, \cdot)$
1-517-517.138-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.138	$0$	✓	✓	$-0.245$	$0$	$0.968051$	Character $\chi_{517}(138, \cdot)$
1-517-517.139-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.139	$0$	✓	✓	$-0.100$	$0$	$0.688718$	Character $\chi_{517}(139, \cdot)$
1-517-517.14-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.14	$0$	✓	✓	$-0.317$	$0$	$2.17007$	Character $\chi_{517}(14, \cdot)$
1-517-517.140-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.140	$0$	✓	✓	$-0.238$	$0$	$0.178810$	Character $\chi_{517}(140, \cdot)$
1-517-517.147-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.147	$0$	✓	✓	$0.201$	$0$	$1.62145$	Character $\chi_{517}(147, \cdot)$
1-517-517.148-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.148	$0$	✓	✓	$0.0647$	$0$	$1.82700$	Character $\chi_{517}(148, \cdot)$
1-517-517.151-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.151	$0$	✓	✓	$-0.224$	$0$	$0.789954$	Character $\chi_{517}(151, \cdot)$
1-517-517.156-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.156	$0$	✓	✓	$0.0749$	$0$	$1.21784$	Character $\chi_{517}(156, \cdot)$
1-517-517.157-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.157	$0$	✓	✓	$-0.385$	$0$	$0.948037$	Character $\chi_{517}(157, \cdot)$
1-517-517.158-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.158	$0$	✓	✓	$0.355$	$0$	$1.32740$	Character $\chi_{517}(158, \cdot)$
1-517-517.159-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.159	$0$	✓	✓	$0.281$	$0$	$1.52029$	Character $\chi_{517}(159, \cdot)$
1-517-517.16-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.16	$0$	✓	✓	$-0.338$	$0$	$0.379196$	Character $\chi_{517}(16, \cdot)$
1-517-517.160-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.160	$0$	✓	✓	$0.292$	$0$	$0.189577$	Character $\chi_{517}(160, \cdot)$
1-517-517.161-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.161	$0$	✓	✓	$0.272$	$0$	$1.04596$	Character $\chi_{517}(161, \cdot)$
1-517-517.164-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.164	$0$	✓	✓	$0.338$	$0$	$1.67419$	Character $\chi_{517}(164, \cdot)$
1-517-517.167-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.167	$0$	✓	✓	$0.0147$	$0$	$0.905352$	Character $\chi_{517}(167, \cdot)$
1-517-517.168-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.168	$0$	✓	✓	$-0.425$	$0$	$1.29735$	Character $\chi_{517}(168, \cdot)$
1-517-517.169-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.169	$0$	✓	✓	$0.297$	$0$	$1.90265$	Character $\chi_{517}(169, \cdot)$
1-517-517.171-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.171	$0$	✓	✓	$-0.298$	$0$	$2.74297$	Character $\chi_{517}(171, \cdot)$
1-517-517.172-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.172	$0$	✓	✓	$-0.353$	$0$	$1.39231$	Character $\chi_{517}(172, \cdot)$
1-517-517.182-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.182	$0$	✓	✓	$0.264$	$0$	$0.313183$	Character $\chi_{517}(182, \cdot)$
1-517-517.184-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.184	$0$	✓	✓	$0.425$	$0$	$1.68086$	Character $\chi_{517}(184, \cdot)$
1-517-517.186-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.186	$0$	✓	✓	$-0.338$	$0$	$0.795784$	Character $\chi_{517}(186, \cdot)$
1-517-517.19-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.19	$0$	✓	✓	$-0.0997$	$0$	$1.56034$	Character $\chi_{517}(19, \cdot)$
1-517-517.190-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.190	$0$	✓	✓	$0.0281$	$0$	$1.28081$	Character $\chi_{517}(190, \cdot)$
1-517-517.191-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.191	$0$	✓	✓	$0.385$	$0$	$2.13942$	Character $\chi_{517}(191, \cdot)$
1-517-517.192-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.192	$0$	✓	✓	$-0.177$	$0$	$0.837371$	Character $\chi_{517}(192, \cdot)$
1-517-517.193-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.193	$0$	✓	✓	$0.0142$	$0$	$0.796031$	Character $\chi_{517}(193, \cdot)$
1-517-517.196-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.196	$0$	✓	✓	$0.159$	$0$	$1.08022$	Character $\chi_{517}(196, \cdot)$
1-517-517.202-r0-0-0	$2.40$	$2.40$	$1$	$11 \cdot 47$	517.202	$0$	✓	✓	$0.0901$	$0$	$1.40667$	Character $\chi_{517}(202, \cdot)$

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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.