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 132 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-351-351.103-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.103	$0$	✓	✓	$0.00925$	$0$	$0.621252$	Character $\chi_{351}(103, \cdot)$
1-351-351.11-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.11	$0$	✓	✓	$0.00311$	$0$	$0.907107$	Character $\chi_{351}(11, \cdot)$
1-351-351.110-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.110	$0$	✓	✓	$-0.182$	$0$	$0.588083$	Character $\chi_{351}(110, \cdot)$
1-351-351.119-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.119	$0$	✓	✓	$-0.0966$	$0$	$1.08520$	Character $\chi_{351}(119, \cdot)$
1-351-351.121-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.121	$0$	✓	✓	$-0.238$	$0$	$0.992720$	Character $\chi_{351}(121, \cdot)$
1-351-351.122-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.122	$0$	✓	✓	$-0.277$	$0$	$0.513437$	Character $\chi_{351}(122, \cdot)$
1-351-351.128-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.128	$0$	✓	✓	$0.00311$	$0$	$1.54583$	Character $\chi_{351}(128, \cdot)$
1-351-351.133-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.133	$0$	✓	✓	$-0.466$	$0$	$0.641574$	Character $\chi_{351}(133, \cdot)$
1-351-351.137-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.137	$0$	✓	✓	$-0.0884$	$0$	$1.31064$	Character $\chi_{351}(137, \cdot)$
1-351-351.139-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.139	$0$	✓	✓	$-0.200$	$0$	$1.02262$	Character $\chi_{351}(139, \cdot)$
1-351-351.142-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.142	$0$	✓	✓	$-0.00925$	$0$	$1.03400$	Character $\chi_{351}(142, \cdot)$
1-351-351.149-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.149	$0$	✓	✓	$-0.330$	$0$	$0.117182$	Character $\chi_{351}(149, \cdot)$
1-351-351.158-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.158	$0$	✓	✓	$0.421$	$0$	$0.374086$	Character $\chi_{351}(158, \cdot)$
1-351-351.16-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.16	$0$	✓	✓	$0.200$	$0$	$1.71472$	Character $\chi_{351}(16, \cdot)$
1-351-351.160-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.160	$0$	✓	✓	$0.409$	$0$	$0.0872012$	Character $\chi_{351}(160, \cdot)$
1-351-351.164-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.164	$0$	✓	✓	$0.277$	$0$	$0.995251$	Character $\chi_{351}(164, \cdot)$
1-351-351.166-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.166	$0$	✓	✓	$-0.0761$	$0$	$1.76948$	Character $\chi_{351}(166, \cdot)$
1-351-351.167-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.167	$0$	✓	✓	$-0.484$	$0$	$0.673722$	Character $\chi_{351}(167, \cdot)$
1-351-351.176-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.176	$0$	✓	✓	$-0.236$	$0$	$1.21361$	Character $\chi_{351}(176, \cdot)$
1-351-351.178-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.178	$0$	✓	✓	$-0.218$	$0$	$1.21782$	Character $\chi_{351}(178, \cdot)$
1-351-351.2-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.2	$0$	✓	✓	$0.236$	$0$	$1.67423$	Character $\chi_{351}(2, \cdot)$
1-351-351.20-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.20	$0$	✓	✓	$-0.421$	$0$	$2.00921$	Character $\chi_{351}(20, \cdot)$
1-351-351.200-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.200	$0$	✓	✓	$-0.462$	$0$	$0.0138615$	Character $\chi_{351}(200, \cdot)$
1-351-351.203-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.203	$0$	✓	✓	$0.129$	$0$	$1.22620$	Character $\chi_{351}(203, \cdot)$
1-351-351.205-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.205	$0$	✓	✓	$-0.0946$	$0$	$0.950493$	Character $\chi_{351}(205, \cdot)$
1-351-351.211-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.211	$0$	✓	✓	$0.218$	$0$	$1.81170$	Character $\chi_{351}(211, \cdot)$
1-351-351.22-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.22	$0$	✓	✓	$-0.200$	$0$	$0.799938$	Character $\chi_{351}(22, \cdot)$
1-351-351.220-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.220	$0$	✓	✓	$0.00925$	$0$	$1.30809$	Character $\chi_{351}(220, \cdot)$
1-351-351.227-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.227	$0$	✓	✓	$0.484$	$0$	$2.31848$	Character $\chi_{351}(227, \cdot)$
1-351-351.236-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.236	$0$	✓	✓	$-0.0966$	$0$	$0.844207$	Character $\chi_{351}(236, \cdot)$
1-351-351.238-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.238	$0$	✓	✓	$0.0946$	$0$	$1.73423$	Character $\chi_{351}(238, \cdot)$
1-351-351.239-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.239	$0$	✓	✓	$0.0560$	$0$	$1.13209$	Character $\chi_{351}(239, \cdot)$
1-351-351.245-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.245	$0$	✓	✓	$0.330$	$0$	$1.55951$	Character $\chi_{351}(245, \cdot)$
1-351-351.25-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.25	$0$	✓	✓	$0.324$	$0$	$2.19610$	Character $\chi_{351}(25, \cdot)$
1-351-351.250-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.250	$0$	✓	✓	$0.200$	$0$	$1.06163$	Character $\chi_{351}(250, \cdot)$
1-351-351.254-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.254	$0$	✓	✓	$-0.421$	$0$	$0.609279$	Character $\chi_{351}(254, \cdot)$
1-351-351.256-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.256	$0$	✓	✓	$0.466$	$0$	$2.52920$	Character $\chi_{351}(256, \cdot)$
1-351-351.259-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.259	$0$	✓	✓	$-0.00925$	$0$	$1.29679$	Character $\chi_{351}(259, \cdot)$
1-351-351.266-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.266	$0$	✓	✓	$0.00311$	$0$	$1.44316$	Character $\chi_{351}(266, \cdot)$
1-351-351.275-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.275	$0$	✓	✓	$0.421$	$0$	$1.72380$	Character $\chi_{351}(275, \cdot)$
1-351-351.277-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.277	$0$	✓	✓	$0.0761$	$0$	$1.72290$	Character $\chi_{351}(277, \cdot)$
1-351-351.281-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.281	$0$	✓	✓	$-0.0560$	$0$	$1.59761$	Character $\chi_{351}(281, \cdot)$
1-351-351.283-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.283	$0$	✓	✓	$-0.409$	$0$	$1.76719$	Character $\chi_{351}(283, \cdot)$
1-351-351.284-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.284	$0$	✓	✓	$0.182$	$0$	$1.44383$	Character $\chi_{351}(284, \cdot)$
1-351-351.293-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.293	$0$	✓	✓	$0.0966$	$0$	$1.17068$	Character $\chi_{351}(293, \cdot)$
1-351-351.295-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.295	$0$	✓	✓	$0.114$	$0$	$1.02275$	Character $\chi_{351}(295, \cdot)$
1-351-351.317-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.317	$0$	✓	✓	$-0.462$	$0$	$2.15397$	Character $\chi_{351}(317, \cdot)$
1-351-351.32-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.32	$0$	✓	✓	$0.00311$	$0$	$1.45705$	Character $\chi_{351}(32, \cdot)$
1-351-351.320-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.320	$0$	✓	✓	$0.462$	$0$	$0.252700$	Character $\chi_{351}(320, \cdot)$
1-351-351.322-r0-0-0	$1.63$	$1.63$	$1$	$3^{3} \cdot 13$	351.322	$0$	✓	✓	$0.238$	$0$	$1.35420$	Character $\chi_{351}(322, \cdot)$

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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.