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 197 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-199-199.10-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.10	$0$	✓	✓	$0.0490$	$0$	$1.52908$	Character $\chi_{199}(10, \cdot)$
1-199-199.100-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.100	$0$	✓	✓	$0.234$	$0$	$1.27029$	Character $\chi_{199}(100, \cdot)$
1-199-199.102-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.102	$0$	✓	✓	$0.396$	$0$	$2.78568$	Character $\chi_{199}(102, \cdot)$
1-199-199.103-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.103	$0$	✓	✓	$0.423$	$0$	$2.07739$	Character $\chi_{199}(103, \cdot)$
1-199-199.104-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.104	$0$	✓	✓	$0.158$	$0$	$0.726313$	Character $\chi_{199}(104, \cdot)$
1-199-199.106-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.106	$0$	✓	✓	$0.437$	$0$	$1.75711$	Character $\chi_{199}(106, \cdot)$
1-199-199.111-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.111	$0$	✓	✓	$0.453$	$0$	$2.15441$	Character $\chi_{199}(111, \cdot)$
1-199-199.112-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.112	$0$	✓	✓	$-0.111$	$0$	$1.57829$	Character $\chi_{199}(112, \cdot)$
1-199-199.114-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.114	$0$	✓	✓	$-0.423$	$0$	$0.995764$	Character $\chi_{199}(114, \cdot)$
1-199-199.115-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.115	$0$	✓	✓	$0.436$	$0$	$2.78287$	Character $\chi_{199}(115, \cdot)$
1-199-199.116-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.116	$0$	✓	✓	$0.0907$	$0$	$1.60206$	Character $\chi_{199}(116, \cdot)$
1-199-199.117-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.117	$0$	✓	✓	$0.176$	$0$	$1.87838$	Character $\chi_{199}(117, \cdot)$
1-199-199.121-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.121	$0$	✓	✓	$0.0321$	$0$	$1.18111$	Character $\chi_{199}(121, \cdot)$
1-199-199.122-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.122	$0$	✓	✓	$-0.418$	$0$	$2.74888$	Character $\chi_{199}(122, \cdot)$
1-199-199.123-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.123	$0$	✓	✓	$-0.192$	$0$	$1.65742$	Character $\chi_{199}(123, \cdot)$
1-199-199.124-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.124	$0$	✓	✓	$-0.0184$	$0$	$1.12605$	Character $\chi_{199}(124, \cdot)$
1-199-199.125-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.125	$0$	✓	✓	$-0.0321$	$0$	$1.35999$	Character $\chi_{199}(125, \cdot)$
1-199-199.126-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.126	$0$	✓	✓	$0.220$	$0$	$2.28054$	Character $\chi_{199}(126, \cdot)$
1-199-199.128-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.128	$0$	✓	✓	$0.269$	$0$	$1.79526$	Character $\chi_{199}(128, \cdot)$
1-199-199.13-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.13	$0$	✓	✓	$0.0348$	$0$	$1.96720$	Character $\chi_{199}(13, \cdot)$
1-199-199.130-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.130	$0$	✓	✓	$0.0184$	$0$	$1.93701$	Character $\chi_{199}(130, \cdot)$
1-199-199.131-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.131	$0$	✓	✓	$-0.397$	$0$	$2.33294$	Character $\chi_{199}(131, \cdot)$
1-199-199.132-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.132	$0$	✓	✓	$0.373$	$0$	$2.46661$	Character $\chi_{199}(132, \cdot)$
1-199-199.139-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.139	$0$	✓	✓	$-0.278$	$0$	$0.809401$	Character $\chi_{199}(139, \cdot)$
1-199-199.14-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.14	$0$	✓	✓	$-0.269$	$0$	$0.942369$	Character $\chi_{199}(14, \cdot)$
1-199-199.140-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.140	$0$	✓	✓	$-0.194$	$0$	$0.605192$	Character $\chi_{199}(140, \cdot)$
1-199-199.144-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.144	$0$	✓	✓	$0.192$	$0$	$2.29214$	Character $\chi_{199}(144, \cdot)$
1-199-199.145-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.145	$0$	✓	✓	$0.188$	$0$	$1.70878$	Character $\chi_{199}(145, \cdot)$
1-199-199.151-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.151	$0$	✓	✓	$0.0909$	$0$	$1.41879$	Character $\chi_{199}(151, \cdot)$
1-199-199.155-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.155	$0$	✓	✓	$-0.158$	$0$	$0.708226$	Character $\chi_{199}(155, \cdot)$
1-199-199.157-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.157	$0$	✓	✓	$0.389$	$0$	$1.51668$	Character $\chi_{199}(157, \cdot)$
1-199-199.158-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.158	$0$	✓	✓	$0.202$	$0$	$1.02139$	Character $\chi_{199}(158, \cdot)$
1-199-199.16-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.16	$0$	✓	✓	$0.111$	$0$	$2.13662$	Character $\chi_{199}(16, \cdot)$
1-199-199.160-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.160	$0$	✓	✓	$0.109$	$0$	$1.17175$	Character $\chi_{199}(160, \cdot)$
1-199-199.161-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.161	$0$	✓	✓	$-0.369$	$0$	$2.99071$	Character $\chi_{199}(161, \cdot)$
1-199-199.162-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.162	$0$	✓	✓	$-0.453$	$0$	$0.796319$	Character $\chi_{199}(162, \cdot)$
1-199-199.165-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.165	$0$	✓	✓	$-0.202$	$0$	$0.917119$	Character $\chi_{199}(165, \cdot)$
1-199-199.169-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.169	$0$	✓	✓	$-0.220$	$0$	$0.674976$	Character $\chi_{199}(169, \cdot)$
1-199-199.172-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.172	$0$	✓	✓	$0.194$	$0$	$1.71218$	Character $\chi_{199}(172, \cdot)$
1-199-199.175-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.175	$0$	✓	✓	$-0.0442$	$0$	$1.57470$	Character $\chi_{199}(175, \cdot)$
1-199-199.177-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.177	$0$	✓	✓	$-0.211$	$0$	$1.40210$	Character $\chi_{199}(177, \cdot)$
1-199-199.178-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.178	$0$	✓	✓	$0.304$	$0$	$1.62405$	Character $\chi_{199}(178, \cdot)$
1-199-199.18-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.18	$0$	✓	✓	$-0.0277$	$0$	$1.33490$	Character $\chi_{199}(18, \cdot)$
1-199-199.180-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.180	$0$	✓	✓	$-0.304$	$0$	$0.456065$	Character $\chi_{199}(180, \cdot)$
1-199-199.182-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.182	$0$	✓	✓	$-0.176$	$0$	$1.42087$	Character $\chi_{199}(182, \cdot)$
1-199-199.184-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.184	$0$	✓	✓	$0.0836$	$0$	$1.14133$	Character $\chi_{199}(184, \cdot)$
1-199-199.187-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.187	$0$	✓	✓	$-0.0907$	$0$	$1.09598$	Character $\chi_{199}(187, \cdot)$
1-199-199.188-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.188	$0$	✓	✓	$0.0277$	$0$	$0.745948$	Character $\chi_{199}(188, \cdot)$
1-199-199.193-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.193	$0$	✓	✓	$0.0294$	$0$	$0.966040$	Character $\chi_{199}(193, \cdot)$
1-199-199.196-r0-0-0	$0.924$	$0.924$	$1$	$199$	199.196	$0$	✓	✓	$0.494$	$0$	$0.300487$	Character $\chi_{199}(196, \cdot)$

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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.