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 243 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-319-319.10-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.10	$0$	✓	✓	$0.412$	$0$	$1.93348$	Character $\chi_{319}(10, \cdot)$
1-319-319.101-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.101	$0$	✓	✓	$0.395$	$0$	$1.93286$	Character $\chi_{319}(101, \cdot)$
1-319-319.103-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.103	$0$	✓	✓	$0.161$	$0$	$1.01842$	Character $\chi_{319}(103, \cdot)$
1-319-319.105-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.105	$0$	✓	✓	$0.459$	$0$	$1.89123$	Character $\chi_{319}(105, \cdot)$
1-319-319.106-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.106	$0$	✓	✓	$0.0892$	$0$	$1.68546$	Character $\chi_{319}(106, \cdot)$
1-319-319.115-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.115	$0$	✓	✓	$0.442$	$0$	$0.665860$	Character $\chi_{319}(115, \cdot)$
1-319-319.118-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.118	$0$	✓	✓	$-0.0182$	$0$	$0.777114$	Character $\chi_{319}(118, \cdot)$
1-319-319.125-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.125	$0$	✓	✓	$0.397$	$0$	$0.0269031$	Character $\chi_{319}(125, \cdot)$
1-319-319.127-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.127	$0$	✓	✓	$-0.287$	$0$	$1.01808$	Character $\chi_{319}(127, \cdot)$
1-319-319.128-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.128	$0$	✓	✓	$-0.180$	$0$	$1.49334$	Character $\chi_{319}(128, \cdot)$
1-319-319.131-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.131	$0$	✓	✓	$-0.0207$	$0$	$1.22749$	Character $\chi_{319}(131, \cdot)$
1-319-319.134-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.134	$0$	✓	✓	$-0.0474$	$0$	$1.15617$	Character $\chi_{319}(134, \cdot)$
1-319-319.136-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.136	$0$	✓	✓	$-0.154$	$0$	$1.12945$	Character $\chi_{319}(136, \cdot)$
1-319-319.141-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.141	$0$	✓	✓	$0.129$	$0$	$1.36698$	Character $\chi_{319}(141, \cdot)$
1-319-319.142-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.142	$0$	✓	✓	$-0.0503$	$0$	$0.507172$	Character $\chi_{319}(142, \cdot)$
1-319-319.152-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.152	$0$	✓	✓	$-0.0147$	$0$	$1.88093$	Character $\chi_{319}(152, \cdot)$
1-319-319.153-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.153	$0$	✓	✓	$0.0407$	$0$	$0.948296$	Character $\chi_{319}(153, \cdot)$
1-319-319.156-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.156	$0$	✓	✓	$0.205$	$0$	$2.10089$	Character $\chi_{319}(156, \cdot)$
1-319-319.158-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.158	$0$	✓	✓	$-0.390$	$0$	$1.22611$	Character $\chi_{319}(158, \cdot)$
1-319-319.16-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.16	$0$	✓	✓	$-0.399$	$0$	$0.626975$	Character $\chi_{319}(16, \cdot)$
1-319-319.160-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.160	$0$	✓	✓	$-0.267$	$0$	$1.51827$	Character $\chi_{319}(160, \cdot)$
1-319-319.162-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.162	$0$	✓	✓	$0.180$	$0$	$1.94281$	Character $\chi_{319}(162, \cdot)$
1-319-319.164-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.164	$0$	✓	✓	$0.0503$	$0$	$1.71823$	Character $\chi_{319}(164, \cdot)$
1-319-319.168-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.168	$0$	✓	✓	$-0.0534$	$0$	$1.40219$	Character $\chi_{319}(168, \cdot)$
1-319-319.169-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.169	$0$	✓	✓	$0.0534$	$0$	$1.48622$	Character $\chi_{319}(169, \cdot)$
1-319-319.17-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.17	$0$	✓	✓	$-0.0267$	$0$	$1.58630$	Character $\chi_{319}(17, \cdot)$
1-319-319.170-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.170	$0$	✓	✓	$0.0147$	$0$	$1.88233$	Character $\chi_{319}(170, \cdot)$
1-319-319.171-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.171	$0$	✓	✓	$-0.296$	$0$	$0.411903$	Character $\chi_{319}(171, \cdot)$
1-319-319.172-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.172	$0$	✓	✓	$-0.110$	$0$	$0.0620899$	Character $\chi_{319}(172, \cdot)$
1-319-319.179-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.179	$0$	✓	✓	$-0.0527$	$0$	$0.714357$	Character $\chi_{319}(179, \cdot)$
1-319-319.18-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.18	$0$	✓	✓	$-0.255$	$0$	$0.267959$	Character $\chi_{319}(18, \cdot)$
1-319-319.180-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.180	$0$	✓	✓	$0.0527$	$0$	$1.03562$	Character $\chi_{319}(180, \cdot)$
1-319-319.181-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.181	$0$	✓	✓	$-0.129$	$0$	$1.21127$	Character $\chi_{319}(181, \cdot)$
1-319-319.182-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.182	$0$	✓	✓	$-0.205$	$0$	$1.24142$	Character $\chi_{319}(182, \cdot)$
1-319-319.184-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.184	$0$	✓	✓	$0.373$	$0$	$1.79603$	Character $\chi_{319}(184, \cdot)$
1-319-319.186-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.186	$0$	✓	✓	$-0.219$	$0$	$0.560257$	Character $\chi_{319}(186, \cdot)$
1-319-319.189-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.189	$0$	✓	✓	$0.225$	$0$	$1.65339$	Character $\chi_{319}(189, \cdot)$
1-319-319.19-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.19	$0$	✓	✓	$0.0113$	$0$	$1.56215$	Character $\chi_{319}(19, \cdot)$
1-319-319.190-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.190	$0$	✓	✓	$0.154$	$0$	$2.26938$	Character $\chi_{319}(190, \cdot)$
1-319-319.193-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.193	$0$	✓	✓	$-0.196$	$0$	$0.577526$	Character $\chi_{319}(193, \cdot)$
1-319-319.195-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.195	$0$	✓	✓	$0.255$	$0$	$1.61884$	Character $\chi_{319}(195, \cdot)$
1-319-319.196-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.196	$0$	✓	✓	$0.114$	$0$	$1.07301$	Character $\chi_{319}(196, \cdot)$
1-319-319.2-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.2	$0$	✓	✓	$0.267$	$0$	$2.31395$	Character $\chi_{319}(2, \cdot)$
1-319-319.20-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.20	$0$	✓	✓	$0.399$	$0$	$1.93227$	Character $\chi_{319}(20, \cdot)$
1-319-319.200-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.200	$0$	✓	✓	$0.196$	$0$	$1.81360$	Character $\chi_{319}(200, \cdot)$
1-319-319.202-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.202	$0$	✓	✓	$0.00378$	$0$	$1.49799$	Character $\chi_{319}(202, \cdot)$
1-319-319.205-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.205	$0$	✓	✓	$0.0596$	$0$	$1.41994$	Character $\chi_{319}(205, \cdot)$
1-319-319.206-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.206	$0$	✓	✓	$-0.451$	$0$	$2.15179$	Character $\chi_{319}(206, \cdot)$
1-319-319.207-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.207	$0$	✓	✓	$0.000443$	$0$	$1.54420$	Character $\chi_{319}(207, \cdot)$
1-319-319.21-r0-0-0	$1.48$	$1.48$	$1$	$11 \cdot 29$	319.21	$0$	✓	✓	$0.293$	$0$	$2.15602$	Character $\chi_{319}(21, \cdot)$

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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.