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 64 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2e9-512.101-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.101	$0$	✓	✓	$0.0644$	$0$	$1.33512$	Character $\chi_{512}(101, \cdot)$
1-2e9-512.109-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.109	$0$	✓	✓	$-0.0644$	$0$	$1.20688$	Character $\chi_{512}(109, \cdot)$
1-2e9-512.117-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.117	$0$	✓	✓	$0.298$	$0$	$1.12710$	Character $\chi_{512}(117, \cdot)$
1-2e9-512.125-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.125	$0$	✓	✓	$-0.298$	$0$	$0.855126$	Character $\chi_{512}(125, \cdot)$
1-2e9-512.13-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.13	$0$	✓	✓	$0.123$	$0$	$1.15280$	Character $\chi_{512}(13, \cdot)$
1-2e9-512.133-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.133	$0$	✓	✓	$0.126$	$0$	$1.28422$	Character $\chi_{512}(133, \cdot)$
1-2e9-512.141-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.141	$0$	✓	✓	$0.123$	$0$	$0.933321$	Character $\chi_{512}(141, \cdot)$
1-2e9-512.149-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.149	$0$	✓	✓	$-0.0761$	$0$	$0.885281$	Character $\chi_{512}(149, \cdot)$
1-2e9-512.157-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.157	$0$	✓	✓	$-0.423$	$0$	$0.575833$	Character $\chi_{512}(157, \cdot)$
1-2e9-512.165-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.165	$0$	✓	✓	$0.0644$	$0$	$1.58168$	Character $\chi_{512}(165, \cdot)$
1-2e9-512.173-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.173	$0$	✓	✓	$0.435$	$0$	$0.0224163$	Character $\chi_{512}(173, \cdot)$
1-2e9-512.181-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.181	$0$	✓	✓	$-0.0761$	$0$	$0.963444$	Character $\chi_{512}(181, \cdot)$
1-2e9-512.189-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.189	$0$	✓	✓	$0.0761$	$0$	$1.26495$	Character $\chi_{512}(189, \cdot)$
1-2e9-512.197-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.197	$0$	✓	✓	$-0.123$	$0$	$0.942936$	Character $\chi_{512}(197, \cdot)$
1-2e9-512.205-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.205	$0$	✓	✓	$-0.126$	$0$	$0.972499$	Character $\chi_{512}(205, \cdot)$
1-2e9-512.21-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.21	$0$	✓	✓	$-0.326$	$0$	$0.801100$	Character $\chi_{512}(21, \cdot)$
1-2e9-512.213-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.213	$0$	✓	✓	$0.298$	$0$	$1.93101$	Character $\chi_{512}(213, \cdot)$
1-2e9-512.221-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.221	$0$	✓	✓	$0.201$	$0$	$1.91281$	Character $\chi_{512}(221, \cdot)$
1-2e9-512.229-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.229	$0$	✓	✓	$-0.435$	$0$	$2.09940$	Character $\chi_{512}(229, \cdot)$
1-2e9-512.237-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.237	$0$	✓	✓	$0.435$	$0$	$0.225992$	Character $\chi_{512}(237, \cdot)$
1-2e9-512.245-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.245	$0$	✓	✓	$0.0488$	$0$	$1.43974$	Character $\chi_{512}(245, \cdot)$
1-2e9-512.253-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.253	$0$	✓	✓	$-0.0488$	$0$	$1.09862$	Character $\chi_{512}(253, \cdot)$
1-2e9-512.261-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.261	$0$	✓	✓	$0.126$	$0$	$1.17098$	Character $\chi_{512}(261, \cdot)$
1-2e9-512.269-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.269	$0$	✓	✓	$0.123$	$0$	$1.47900$	Character $\chi_{512}(269, \cdot)$
1-2e9-512.277-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.277	$0$	✓	✓	$0.173$	$0$	$1.12417$	Character $\chi_{512}(277, \cdot)$
1-2e9-512.285-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.285	$0$	✓	✓	$0.326$	$0$	$1.79644$	Character $\chi_{512}(285, \cdot)$
1-2e9-512.29-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.29	$0$	✓	✓	$-0.173$	$0$	$0.926755$	Character $\chi_{512}(29, \cdot)$
1-2e9-512.293-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.293	$0$	✓	✓	$-0.435$	$0$	$1.69010$	Character $\chi_{512}(293, \cdot)$
1-2e9-512.301-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.301	$0$	✓	✓	$-0.0644$	$0$	$1.42028$	Character $\chi_{512}(301, \cdot)$
1-2e9-512.309-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.309	$0$	✓	✓	$-0.326$	$0$	$0.771537$	Character $\chi_{512}(309, \cdot)$
1-2e9-512.317-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.317	$0$	✓	✓	$0.326$	$0$	$1.83724$	Character $\chi_{512}(317, \cdot)$
1-2e9-512.325-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.325	$0$	✓	✓	$-0.123$	$0$	$1.25209$	Character $\chi_{512}(325, \cdot)$
1-2e9-512.333-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.333	$0$	✓	✓	$-0.126$	$0$	$1.27302$	Character $\chi_{512}(333, \cdot)$
1-2e9-512.341-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.341	$0$	✓	✓	$-0.451$	$0$	$0.319201$	Character $\chi_{512}(341, \cdot)$
1-2e9-512.349-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.349	$0$	✓	✓	$-0.0488$	$0$	$0.927238$	Character $\chi_{512}(349, \cdot)$
1-2e9-512.357-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.357	$0$	✓	✓	$0.0644$	$0$	$1.10149$	Character $\chi_{512}(357, \cdot)$
1-2e9-512.365-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.365	$0$	✓	✓	$-0.0644$	$0$	$0.920197$	Character $\chi_{512}(365, \cdot)$
1-2e9-512.37-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.37	$0$	✓	✓	$-0.435$	$0$	$0.259219$	Character $\chi_{512}(37, \cdot)$
1-2e9-512.373-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.373	$0$	✓	✓	$-0.201$	$0$	$0.919552$	Character $\chi_{512}(373, \cdot)$
1-2e9-512.381-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.381	$0$	✓	✓	$0.201$	$0$	$0.953944$	Character $\chi_{512}(381, \cdot)$
1-2e9-512.389-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.389	$0$	✓	✓	$0.126$	$0$	$1.59985$	Character $\chi_{512}(389, \cdot)$
1-2e9-512.397-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.397	$0$	✓	✓	$0.123$	$0$	$1.46987$	Character $\chi_{512}(397, \cdot)$
1-2e9-512.405-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.405	$0$	✓	✓	$0.423$	$0$	$1.62113$	Character $\chi_{512}(405, \cdot)$
1-2e9-512.413-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.413	$0$	✓	✓	$0.0761$	$0$	$0.841967$	Character $\chi_{512}(413, \cdot)$
1-2e9-512.421-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.421	$0$	✓	✓	$0.0644$	$0$	$1.00461$	Character $\chi_{512}(421, \cdot)$
1-2e9-512.429-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.429	$0$	✓	✓	$0.435$	$0$	$1.89057$	Character $\chi_{512}(429, \cdot)$
1-2e9-512.437-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.437	$0$	✓	✓	$0.423$	$0$	$2.06087$	Character $\chi_{512}(437, \cdot)$
1-2e9-512.445-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.445	$0$	✓	✓	$-0.423$	$0$	$0.138765$	Character $\chi_{512}(445, \cdot)$
1-2e9-512.45-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.45	$0$	✓	✓	$-0.0644$	$0$	$0.635731$	Character $\chi_{512}(45, \cdot)$
1-2e9-512.453-r0-0-0	$2.37$	$2.37$	$1$	$2^{9}$	512.453	$0$	✓	✓	$-0.123$	$0$	$0.753126$	Character $\chi_{512}(453, \cdot)$

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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.