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 615 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-731-731.100-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.100	$0$	✓	✓	$-0.162$	$0$	$0.953456$	Character $\chi_{731}(100, \cdot)$
1-731-731.101-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.101	$0$	✓	✓	$-0.0122$	$0$	$1.41922$	Character $\chi_{731}(101, \cdot)$
1-731-731.105-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.105	$0$	✓	✓	$0.412$	$0$	$1.33454$	Character $\chi_{731}(105, \cdot)$
1-731-731.108-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.108	$0$	✓	✓	$-0.374$	$0$	$0.426330$	Character $\chi_{731}(108, \cdot)$
1-731-731.110-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.110	$0$	✓	✓	$-0.0364$	$0$	$0.998056$	Character $\chi_{731}(110, \cdot)$
1-731-731.111-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.111	$0$	✓	✓	$-0.404$	$0$	$0.217324$	Character $\chi_{731}(111, \cdot)$
1-731-731.112-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.112	$0$	✓	✓	$0.315$	$0$	$1.47829$	Character $\chi_{731}(112, \cdot)$
1-731-731.113-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.113	$0$	✓	✓	$0.249$	$0$	$1.65943$	Character $\chi_{731}(113, \cdot)$
1-731-731.114-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.114	$0$	✓	✓	$-0.0368$	$0$	$1.54141$	Character $\chi_{731}(114, \cdot)$
1-731-731.116-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.116	$0$	✓	✓	$-0.360$	$0$	$0.676465$	Character $\chi_{731}(116, \cdot)$
1-731-731.117-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.117	$0$	✓	✓	$-0.475$	$0$	$2.41790$	Character $\chi_{731}(117, \cdot)$
1-731-731.12-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.12	$0$	✓	✓	$-0.162$	$0$	$1.17075$	Character $\chi_{731}(12, \cdot)$
1-731-731.121-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.121	$0$	✓	✓	$0.00515$	$0$	$1.12180$	Character $\chi_{731}(121, \cdot)$
1-731-731.125-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.125	$0$	✓	✓	$0.0229$	$0$	$0.842753$	Character $\chi_{731}(125, \cdot)$
1-731-731.127-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.127	$0$	✓	✓	$0.334$	$0$	$0.382405$	Character $\chi_{731}(127, \cdot)$
1-731-731.13-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.13	$0$	✓	✓	$0.365$	$0$	$2.17522$	Character $\chi_{731}(13, \cdot)$
1-731-731.131-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.131	$0$	✓	✓	$-0.0546$	$0$	$0.854350$	Character $\chi_{731}(131, \cdot)$
1-731-731.135-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.135	$0$	✓	✓	$0.215$	$0$	$1.89715$	Character $\chi_{731}(135, \cdot)$
1-731-731.138-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.138	$0$	✓	✓	$-0.0838$	$0$	$0.882065$	Character $\chi_{731}(138, \cdot)$
1-731-731.140-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.140	$0$	✓	✓	$0.474$	$0$	$0.318467$	Character $\chi_{731}(140, \cdot)$
1-731-731.141-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.141	$0$	✓	✓	$0.397$	$0$	$1.76666$	Character $\chi_{731}(141, \cdot)$
1-731-731.144-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.144	$0$	✓	✓	$0.000170$	$0$	$0.455275$	Character $\chi_{731}(144, \cdot)$
1-731-731.145-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.145	$0$	✓	✓	$-0.00515$	$0$	$0.803720$	Character $\chi_{731}(145, \cdot)$
1-731-731.147-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.147	$0$	✓	✓	$-0.0891$	$0$	$1.00987$	Character $\chi_{731}(147, \cdot)$
1-731-731.148-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.148	$0$	✓	✓	$-0.0159$	$0$	$0.594546$	Character $\chi_{731}(148, \cdot)$
1-731-731.15-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.15	$0$	✓	✓	$-0.0243$	$0$	$1.53051$	Character $\chi_{731}(15, \cdot)$
1-731-731.152-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.152	$0$	✓	✓	$0.0122$	$0$	$1.18597$	Character $\chi_{731}(152, \cdot)$
1-731-731.156-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.156	$0$	✓	✓	$0.132$	$0$	$1.72168$	Character $\chi_{731}(156, \cdot)$
1-731-731.158-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.158	$0$	✓	✓	$0.0489$	$0$	$0.991650$	Character $\chi_{731}(158, \cdot)$
1-731-731.159-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.159	$0$	✓	✓	$-0.243$	$0$	$2.46270$	Character $\chi_{731}(159, \cdot)$
1-731-731.16-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.16	$0$	✓	✓	$-0.137$	$0$	$0.577714$	Character $\chi_{731}(16, \cdot)$
1-731-731.163-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.163	$0$	✓	✓	$0.0159$	$0$	$0.855096$	Character $\chi_{731}(163, \cdot)$
1-731-731.169-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.169	$0$	✓	✓	$0.150$	$0$	$1.18658$	Character $\chi_{731}(169, \cdot)$
1-731-731.175-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.175	$0$	✓	✓	$0.273$	$0$	$1.65984$	Character $\chi_{731}(175, \cdot)$
1-731-731.177-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.177	$0$	✓	✓	$-0.0779$	$0$	$0.516271$	Character $\chi_{731}(177, \cdot)$
1-731-731.178-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.178	$0$	✓	✓	$0.227$	$0$	$1.38663$	Character $\chi_{731}(178, \cdot)$
1-731-731.180-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.180	$0$	✓	✓	$0.296$	$0$	$1.85971$	Character $\chi_{731}(180, \cdot)$
1-731-731.183-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.183	$0$	✓	✓	$-0.236$	$0$	$1.29382$	Character $\chi_{731}(183, \cdot)$
1-731-731.184-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.184	$0$	✓	✓	$0.0891$	$0$	$0.984133$	Character $\chi_{731}(184, \cdot)$
1-731-731.185-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.185	$0$	✓	✓	$-0.290$	$0$	$0.891754$	Character $\chi_{731}(185, \cdot)$
1-731-731.186-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.186	$0$	✓	✓	$-0.150$	$0$	$1.22895$	Character $\chi_{731}(186, \cdot)$
1-731-731.189-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.189	$0$	✓	✓	$0.130$	$0$	$1.60008$	Character $\chi_{731}(189, \cdot)$
1-731-731.190-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.190	$0$	✓	✓	$-0.206$	$0$	$0.851529$	Character $\chi_{731}(190, \cdot)$
1-731-731.192-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.192	$0$	✓	✓	$-0.201$	$0$	$2.56372$	Character $\chi_{731}(192, \cdot)$
1-731-731.194-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.194	$0$	✓	✓	$0.494$	$0$	$1.69606$	Character $\chi_{731}(194, \cdot)$
1-731-731.195-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.195	$0$	✓	✓	$0.0243$	$0$	$1.40037$	Character $\chi_{731}(195, \cdot)$
1-731-731.196-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.196	$0$	✓	✓	$0.0838$	$0$	$0.857352$	Character $\chi_{731}(196, \cdot)$
1-731-731.198-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.198	$0$	✓	✓	$0.0638$	$0$	$1.49922$	Character $\chi_{731}(198, \cdot)$
1-731-731.199-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.199	$0$	✓	✓	$-0.296$	$0$	$0.441963$	Character $\chi_{731}(199, \cdot)$
1-731-731.20-r0-0-0	$3.39$	$3.39$	$1$	$17 \cdot 43$	731.20	$0$	✓	✓	$-0.332$	$0$	$0.536196$	Character $\chi_{731}(20, \cdot)$

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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.