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 503 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1009-1009.10-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.10	$0$	✓	✓			$0.395$	$0$	$0.492267$	Character $\chi_{1009}(10, \cdot)$
1-1009-1009.100-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.100	$0$	✓	✓			$-0.429$	$0$	$0.345625$	Character $\chi_{1009}(100, \cdot)$
1-1009-1009.1000-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1000	$0$	✓	✓			$-0.429$	$0$	$0.128689$	Character $\chi_{1009}(1000, \cdot)$
1-1009-1009.1001-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1001	$0$	✓	✓			$0.111$	$0$	$1.33354$	Character $\chi_{1009}(1001, \cdot)$
1-1009-1009.1002-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1002	$0$	✓	✓			$0.424$	$0$	$0.286286$	Character $\chi_{1009}(1002, \cdot)$
1-1009-1009.1003-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1003	$0$	✓	✓			$-0.437$	$0$	$1.92788$	Character $\chi_{1009}(1003, \cdot)$
1-1009-1009.1004-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1004	$0$	✓	✓			$0.211$	$0$	$1.51139$	Character $\chi_{1009}(1004, \cdot)$
1-1009-1009.1005-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1005	$0$	✓	✓			$0.334$	$0$	$1.34274$	Character $\chi_{1009}(1005, \cdot)$
1-1009-1009.1006-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1006	$0$	✓	✓			$0.207$	$0$	$0.914651$	Character $\chi_{1009}(1006, \cdot)$
1-1009-1009.1007-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1007	$0$	✓	✓			$-0.217$	$0$	$0.837615$	Character $\chi_{1009}(1007, \cdot)$
1-1009-1009.1008-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.1008	$0$	✓	✓	✓	✓	$0$	$0$	$1.71950$	Character $\chi_{1009}(1008, \cdot)$
1-1009-1009.101-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.101	$0$	✓	✓			$-0.395$	$0$	$1.84937$	Character $\chi_{1009}(101, \cdot)$
1-1009-1009.103-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.103	$0$	✓	✓			$0.242$	$0$	$1.16112$	Character $\chi_{1009}(103, \cdot)$
1-1009-1009.105-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.105	$0$	✓	✓			$0.467$	$0$	$0.943520$	Character $\chi_{1009}(105, \cdot)$
1-1009-1009.108-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.108	$0$	✓	✓			$-0.0421$	$0$	$0.534459$	Character $\chi_{1009}(108, \cdot)$
1-1009-1009.109-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.109	$0$	✓	✓			$-0.384$	$0$	$0.615837$	Character $\chi_{1009}(109, \cdot)$
1-1009-1009.111-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.111	$0$	✓	✓			$0.429$	$0$	$1.06811$	Character $\chi_{1009}(111, \cdot)$
1-1009-1009.112-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.112	$0$	✓	✓			$0.429$	$0$	$1.21207$	Character $\chi_{1009}(112, \cdot)$
1-1009-1009.113-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.113	$0$	✓	✓			$-0.284$	$0$	$0.182183$	Character $\chi_{1009}(113, \cdot)$
1-1009-1009.116-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.116	$0$	✓	✓			$0.466$	$0$	$1.27140$	Character $\chi_{1009}(116, \cdot)$
1-1009-1009.12-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.12	$0$	✓	✓			$-0.237$	$0$	$0.166322$	Character $\chi_{1009}(12, \cdot)$
1-1009-1009.120-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.120	$0$	✓	✓			$0.0942$	$0$	$1.56890$	Character $\chi_{1009}(120, \cdot)$
1-1009-1009.121-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.121	$0$	✓	✓			$0.00223$	$0$	$0.763926$	Character $\chi_{1009}(121, \cdot)$
1-1009-1009.123-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.123	$0$	✓	✓			$-0.0352$	$0$	$0.767166$	Character $\chi_{1009}(123, \cdot)$
1-1009-1009.125-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.125	$0$	✓	✓			$-0.189$	$0$	$0.697403$	Character $\chi_{1009}(125, \cdot)$
1-1009-1009.126-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.126	$0$	✓	✓			$-0.111$	$0$	$1.28253$	Character $\chi_{1009}(126, \cdot)$
1-1009-1009.127-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.127	$0$	✓	✓			$0.337$	$0$	$1.18533$	Character $\chi_{1009}(127, \cdot)$
1-1009-1009.128-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.128	$0$	✓	✓			$-0.0645$	$0$	$0.496674$	Character $\chi_{1009}(128, \cdot)$
1-1009-1009.134-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.134	$0$	✓	✓			$-0.460$	$0$	$0.258479$	Character $\chi_{1009}(134, \cdot)$
1-1009-1009.135-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.135	$0$	✓	✓			$0.0541$	$0$	$1.15582$	Character $\chi_{1009}(135, \cdot)$
1-1009-1009.137-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.137	$0$	✓	✓			$0.351$	$0$	$1.12458$	Character $\chi_{1009}(137, \cdot)$
1-1009-1009.139-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.139	$0$	✓	✓			$0.345$	$0$	$1.10856$	Character $\chi_{1009}(139, \cdot)$
1-1009-1009.14-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.14	$0$	✓	✓			$-0.273$	$0$	$0.324049$	Character $\chi_{1009}(14, \cdot)$
1-1009-1009.140-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.140	$0$	✓	✓			$-0.150$	$0$	$2.28273$	Character $\chi_{1009}(140, \cdot)$
1-1009-1009.142-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.142	$0$	✓	✓			$0.176$	$0$	$1.47473$	Character $\chi_{1009}(142, \cdot)$
1-1009-1009.143-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.143	$0$	✓	✓			$-0.208$	$0$	$0.419228$	Character $\chi_{1009}(143, \cdot)$
1-1009-1009.144-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.144	$0$	✓	✓			$-0.424$	$0$	$1.24805$	Character $\chi_{1009}(144, \cdot)$
1-1009-1009.145-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.145	$0$	✓	✓			$-0.407$	$0$	$0.280430$	Character $\chi_{1009}(145, \cdot)$
1-1009-1009.147-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.147	$0$	✓	✓			$0.443$	$0$	$0.452949$	Character $\chi_{1009}(147, \cdot)$
1-1009-1009.148-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.148	$0$	✓	✓			$-0.268$	$0$	$2.01394$	Character $\chi_{1009}(148, \cdot)$
1-1009-1009.15-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.15	$0$	✓	✓			$-0.266$	$0$	$0.633488$	Character $\chi_{1009}(15, \cdot)$
1-1009-1009.150-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.150	$0$	✓	✓			$-0.230$	$0$	$0.159362$	Character $\chi_{1009}(150, \cdot)$
1-1009-1009.151-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.151	$0$	✓	✓			$0.415$	$0$	$1.68198$	Character $\chi_{1009}(151, \cdot)$
1-1009-1009.157-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.157	$0$	✓	✓			$0.447$	$0$	$0.490848$	Character $\chi_{1009}(157, \cdot)$
1-1009-1009.16-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.16	$0$	✓	✓			$0.157$	$0$	$1.25531$	Character $\chi_{1009}(16, \cdot)$
1-1009-1009.160-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.160	$0$	✓	✓			$0.453$	$0$	$0.656993$	Character $\chi_{1009}(160, \cdot)$
1-1009-1009.162-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.162	$0$	✓	✓			$-0.186$	$0$	$0.610339$	Character $\chi_{1009}(162, \cdot)$
1-1009-1009.164-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.164	$0$	✓	✓			$-0.249$	$0$	$0.484954$	Character $\chi_{1009}(164, \cdot)$
1-1009-1009.167-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.167	$0$	✓	✓			$0.175$	$0$	$0.790522$	Character $\chi_{1009}(167, \cdot)$
1-1009-1009.168-r0-0-0	$4.68$	$4.68$	$1$	$1009$	1009.168	$0$	✓	✓			$0.437$	$0$	$0.206829$	Character $\chi_{1009}(168, \cdot)$

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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.