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 160 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-403-403.10-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.10	$0$	✓	✓	$-0.118$	$0$	$1.38348$	Character $\chi_{403}(10, \cdot)$
1-403-403.100-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.100	$0$	✓	✓	$0.0576$	$0$	$1.14722$	Character $\chi_{403}(100, \cdot)$
1-403-403.101-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.101	$0$	✓	✓	$-0.129$	$0$	$0.616896$	Character $\chi_{403}(101, \cdot)$
1-403-403.103-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.103	$0$	✓	✓	$-0.0334$	$0$	$1.02268$	Character $\chi_{403}(103, \cdot)$
1-403-403.106-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.106	$0$	✓	✓	$-0.282$	$0$	$1.20103$	Character $\chi_{403}(106, \cdot)$
1-403-403.107-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.107	$0$	✓	✓	$-0.0772$	$0$	$1.57392$	Character $\chi_{403}(107, \cdot)$
1-403-403.11-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.11	$0$	✓	✓	$-0.0470$	$0$	$1.38946$	Character $\chi_{403}(11, \cdot)$
1-403-403.110-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.110	$0$	✓	✓	$0.0470$	$0$	$1.84998$	Character $\chi_{403}(110, \cdot)$
1-403-403.113-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.113	$0$	✓	✓	$0.0772$	$0$	$1.62056$	Character $\chi_{403}(113, \cdot)$
1-403-403.115-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.115	$0$	✓	✓	$0.264$	$0$	$1.53589$	Character $\chi_{403}(115, \cdot)$
1-403-403.119-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.119	$0$	✓	✓	$0.373$	$0$	$1.85007$	Character $\chi_{403}(119, \cdot)$
1-403-403.121-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.121	$0$	✓	✓	$0.118$	$0$	$1.80462$	Character $\chi_{403}(121, \cdot)$
1-403-403.122-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.122	$0$	✓	✓	$-0.206$	$0$	$0.837420$	Character $\chi_{403}(122, \cdot)$
1-403-403.123-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.123	$0$	✓	✓	$0.493$	$0$	$1.62550$	Character $\chi_{403}(123, \cdot)$
1-403-403.126-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.126	$0$	✓	✓	$-0.311$	$0$	$0.927416$	Character $\chi_{403}(126, \cdot)$
1-403-403.129-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.129	$0$	✓	✓	$-0.230$	$0$	$0.857575$	Character $\chi_{403}(129, \cdot)$
1-403-403.133-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.133	$0$	✓	✓	$-0.0576$	$0$	$0.964597$	Character $\chi_{403}(133, \cdot)$
1-403-403.134-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.134	$0$	✓	✓	$0.0519$	$0$	$1.05437$	Character $\chi_{403}(134, \cdot)$
1-403-403.135-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.135	$0$	✓	✓	$-0.00638$	$0$	$1.08877$	Character $\chi_{403}(135, \cdot)$
1-403-403.136-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.136	$0$	✓	✓	$-0.311$	$0$	$2.30359$	Character $\chi_{403}(136, \cdot)$
1-403-403.137-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.137	$0$	✓	✓	$-0.107$	$0$	$1.13456$	Character $\chi_{403}(137, \cdot)$
1-403-403.140-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.140	$0$	✓	✓	$-0.483$	$0$	$0.304985$	Character $\chi_{403}(140, \cdot)$
1-403-403.141-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.141	$0$	✓	✓	$0.0593$	$0$	$0.958238$	Character $\chi_{403}(141, \cdot)$
1-403-403.142-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.142	$0$	✓	✓	$-0.191$	$0$	$0.802151$	Character $\chi_{403}(142, \cdot)$
1-403-403.145-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.145	$0$	✓	✓	$0.313$	$0$	$1.23485$	Character $\chi_{403}(145, \cdot)$
1-403-403.148-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.148	$0$	✓	✓	$-0.212$	$0$	$2.62208$	Character $\chi_{403}(148, \cdot)$
1-403-403.15-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.15	$0$	✓	✓	$-0.333$	$0$	$0.984862$	Character $\chi_{403}(15, \cdot)$
1-403-403.150-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.150	$0$	✓	✓	$-0.451$	$0$	$0.888927$	Character $\chi_{403}(150, \cdot)$
1-403-403.151-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.151	$0$	✓	✓	$0.211$	$0$	$1.69950$	Character $\chi_{403}(151, \cdot)$
1-403-403.152-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.152	$0$	✓	✓	$0.324$	$0$	$1.38833$	Character $\chi_{403}(152, \cdot)$
1-403-403.154-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.154	$0$	✓	✓	$-0.493$	$0$	$0.225938$	Character $\chi_{403}(154, \cdot)$
1-403-403.158-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.158	$0$	✓	✓	$-0.487$	$0$	$0.192312$	Character $\chi_{403}(158, \cdot)$
1-403-403.159-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.159	$0$	✓	✓	$-0.246$	$0$	$1.21794$	Character $\chi_{403}(159, \cdot)$
1-403-403.16-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.16	$0$	✓	✓	$0.311$	$0$	$1.62076$	Character $\chi_{403}(16, \cdot)$
1-403-403.160-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.160	$0$	✓	✓	$-0.145$	$0$	$0.183567$	Character $\chi_{403}(160, \cdot)$
1-403-403.161-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.161	$0$	✓	✓	$0.0857$	$0$	$1.36935$	Character $\chi_{403}(161, \cdot)$
1-403-403.165-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.165	$0$	✓	✓	$0.257$	$0$	$2.20996$	Character $\chi_{403}(165, \cdot)$
1-403-403.167-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.167	$0$	✓	✓	$-0.299$	$0$	$1.21477$	Character $\chi_{403}(167, \cdot)$
1-403-403.173-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.173	$0$	✓	✓	$-0.106$	$0$	$1.46463$	Character $\chi_{403}(173, \cdot)$
1-403-403.176-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.176	$0$	✓	✓	$0.487$	$0$	$1.88917$	Character $\chi_{403}(176, \cdot)$
1-403-403.177-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.177	$0$	✓	✓	$0.212$	$0$	$0.178638$	Character $\chi_{403}(177, \cdot)$
1-403-403.184-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.184	$0$	✓	✓	$0.158$	$0$	$0.909009$	Character $\chi_{403}(184, \cdot)$
1-403-403.189-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.189	$0$	✓	✓	$-0.313$	$0$	$1.19047$	Character $\chi_{403}(189, \cdot)$
1-403-403.191-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.191	$0$	✓	✓	$0.0601$	$0$	$1.07361$	Character $\chi_{403}(191, \cdot)$
1-403-403.194-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.194	$0$	✓	✓	$-0.0439$	$0$	$0.509595$	Character $\chi_{403}(194, \cdot)$
1-403-403.197-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.197	$0$	✓	✓	$0.359$	$0$	$2.13559$	Character $\chi_{403}(197, \cdot)$
1-403-403.201-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.201	$0$	✓	✓	$0.247$	$0$	$1.00001$	Character $\chi_{403}(201, \cdot)$
1-403-403.203-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.203	$0$	✓	✓	$0.00638$	$0$	$1.54610$	Character $\chi_{403}(203, \cdot)$
1-403-403.204-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.204	$0$	✓	✓	$0.0988$	$0$	$0.693379$	Character $\chi_{403}(204, \cdot)$
1-403-403.205-r0-0-0	$1.87$	$1.87$	$1$	$13 \cdot 31$	403.205	$0$	✓	✓	$0.106$	$0$	$1.43280$	Character $\chi_{403}(205, \cdot)$

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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.