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 675 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-799-799.10-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.10	$0$	✓	✓	$-0.493$	$0$	$1.91284$	Character $\chi_{799}(10, \cdot)$
1-799-799.100-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.100	$0$	✓	✓	$-0.329$	$0$	$0.297996$	Character $\chi_{799}(100, \cdot)$
1-799-799.101-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.101	$0$	✓	✓	$-0.0170$	$0$	$0.576235$	Character $\chi_{799}(101, \cdot)$
1-799-799.105-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.105	$0$	✓	✓	$-0.0241$	$0$	$0.711043$	Character $\chi_{799}(105, \cdot)$
1-799-799.106-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.106	$0$	✓	✓	$0.332$	$0$	$1.66903$	Character $\chi_{799}(106, \cdot)$
1-799-799.107-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.107	$0$	✓	✓	$-0.138$	$0$	$1.17177$	Character $\chi_{799}(107, \cdot)$
1-799-799.109-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.109	$0$	✓	✓	$-0.449$	$0$	$0.985047$	Character $\chi_{799}(109, \cdot)$
1-799-799.11-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.11	$0$	✓	✓	$-0.156$	$0$	$0.747826$	Character $\chi_{799}(11, \cdot)$
1-799-799.110-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.110	$0$	✓	✓	$-0.332$	$0$	$1.16651$	Character $\chi_{799}(110, \cdot)$
1-799-799.111-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.111	$0$	✓	✓	$0.164$	$0$	$2.08020$	Character $\chi_{799}(111, \cdot)$
1-799-799.113-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.113	$0$	✓	✓	$-0.0341$	$0$	$1.49444$	Character $\chi_{799}(113, \cdot)$
1-799-799.114-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.114	$0$	✓	✓	$0.498$	$0$	$0.834580$	Character $\chi_{799}(114, \cdot)$
1-799-799.115-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.115	$0$	✓	✓	$0.392$	$0$	$0.397221$	Character $\chi_{799}(115, \cdot)$
1-799-799.116-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.116	$0$	✓	✓	$-0.359$	$0$	$0.142342$	Character $\chi_{799}(116, \cdot)$
1-799-799.118-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.118	$0$	✓	✓	$-0.246$	$0$	$1.04709$	Character $\chi_{799}(118, \cdot)$
1-799-799.121-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.121	$0$	✓	✓	$-0.365$	$0$	$0.727473$	Character $\chi_{799}(121, \cdot)$
1-799-799.124-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.124	$0$	✓	✓	$-0.0348$	$0$	$0.470737$	Character $\chi_{799}(124, \cdot)$
1-799-799.125-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.125	$0$	✓	✓	$-0.159$	$0$	$0.0956548$	Character $\chi_{799}(125, \cdot)$
1-799-799.128-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.128	$0$	✓	✓	$0.0962$	$0$	$1.56891$	Character $\chi_{799}(128, \cdot)$
1-799-799.129-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.129	$0$	✓	✓	$-0.434$	$0$	$0.273248$	Character $\chi_{799}(129, \cdot)$
1-799-799.133-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.133	$0$	✓	✓	$-0.0681$	$0$	$1.07246$	Character $\chi_{799}(133, \cdot)$
1-799-799.139-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.139	$0$	✓	✓	$-0.162$	$0$	$1.35464$	Character $\chi_{799}(139, \cdot)$
1-799-799.144-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.144	$0$	✓	✓	$-0.143$	$0$	$0.376109$	Character $\chi_{799}(144, \cdot)$
1-799-799.145-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.145	$0$	✓	✓	$-0.0941$	$0$	$1.01795$	Character $\chi_{799}(145, \cdot)$
1-799-799.146-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.146	$0$	✓	✓	$-0.169$	$0$	$1.03769$	Character $\chi_{799}(146, \cdot)$
1-799-799.149-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.149	$0$	✓	✓	$0.211$	$0$	$1.23025$	Character $\chi_{799}(149, \cdot)$
1-799-799.155-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.155	$0$	✓	✓	$-0.213$	$0$	$0.574743$	Character $\chi_{799}(155, \cdot)$
1-799-799.156-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.156	$0$	✓	✓	$0.491$	$0$	$2.07139$	Character $\chi_{799}(156, \cdot)$
1-799-799.157-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.157	$0$	✓	✓	$0.261$	$0$	$1.76727$	Character $\chi_{799}(157, \cdot)$
1-799-799.16-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.16	$0$	✓	✓	$0.405$	$0$	$1.63813$	Character $\chi_{799}(16, \cdot)$
1-799-799.160-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.160	$0$	✓	✓	$0.157$	$0$	$0.473210$	Character $\chi_{799}(160, \cdot)$
1-799-799.162-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.162	$0$	✓	✓	$-0.369$	$0$	$0.395055$	Character $\chi_{799}(162, \cdot)$
1-799-799.163-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.163	$0$	✓	✓	$0.437$	$0$	$1.38555$	Character $\chi_{799}(163, \cdot)$
1-799-799.164-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.164	$0$	✓	✓	$0.339$	$0$	$1.54003$	Character $\chi_{799}(164, \cdot)$
1-799-799.166-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.166	$0$	✓	✓	$-0.414$	$0$	$1.85957$	Character $\chi_{799}(166, \cdot)$
1-799-799.167-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.167	$0$	✓	✓	$-0.180$	$0$	$2.36092$	Character $\chi_{799}(167, \cdot)$
1-799-799.168-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.168	$0$	✓	✓	$-0.245$	$0$	$0.740563$	Character $\chi_{799}(168, \cdot)$
1-799-799.169-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.169	$0$	✓	✓	$-0.101$	$0$	$1.16295$	Character $\chi_{799}(169, \cdot)$
1-799-799.176-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.176	$0$	✓	✓	$-0.362$	$0$	$2.51262$	Character $\chi_{799}(176, \cdot)$
1-799-799.178-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.178	$0$	✓	✓	$0.0931$	$0$	$1.18176$	Character $\chi_{799}(178, \cdot)$
1-799-799.180-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.180	$0$	✓	✓	$-0.271$	$0$	$0.921965$	Character $\chi_{799}(180, \cdot)$
1-799-799.181-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.181	$0$	✓	✓	$-0.249$	$0$	$0.271395$	Character $\chi_{799}(181, \cdot)$
1-799-799.182-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.182	$0$	✓	✓	$0.271$	$0$	$0.612562$	Character $\chi_{799}(182, \cdot)$
1-799-799.183-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.183	$0$	✓	✓	$0.246$	$0$	$0.231675$	Character $\chi_{799}(183, \cdot)$
1-799-799.184-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.184	$0$	✓	✓	$0.186$	$0$	$1.83795$	Character $\chi_{799}(184, \cdot)$
1-799-799.191-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.191	$0$	✓	✓	$0.449$	$0$	$1.23068$	Character $\chi_{799}(191, \cdot)$
1-799-799.193-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.193	$0$	✓	✓	$-0.0982$	$0$	$0.755617$	Character $\chi_{799}(193, \cdot)$
1-799-799.195-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.195	$0$	✓	✓	$0.245$	$0$	$1.10695$	Character $\chi_{799}(195, \cdot)$
1-799-799.196-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.196	$0$	✓	✓	$0.449$	$0$	$0.593683$	Character $\chi_{799}(196, \cdot)$
1-799-799.198-r0-0-0	$3.71$	$3.71$	$1$	$17 \cdot 47$	799.198	$0$	✓	✓	$-0.245$	$0$	$0.756572$	Character $\chi_{799}(198, \cdot)$

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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.