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 1047 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
1-1049-1049.10-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.10	$0$	✓	✓			$0.390$	$0$	$0.503484$	Character $\chi_{1049}(10, \cdot)$
1-1049-1049.100-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.100	$0$	✓	✓			$0.450$	$0$	$0.905757$	Character $\chi_{1049}(100, \cdot)$
1-1049-1049.1000-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1000	$0$	✓	✓			$-0.0529$	$0$	$1.12217$	Character $\chi_{1049}(1000, \cdot)$
1-1049-1049.1004-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1004	$0$	✓	✓			$0.325$	$0$	$0.178819$	Character $\chi_{1049}(1004, \cdot)$
1-1049-1049.1005-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1005	$0$	✓	✓			$0.276$	$0$	$1.62096$	Character $\chi_{1049}(1005, \cdot)$
1-1049-1049.1006-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1006	$0$	✓	✓			$0.327$	$0$	$1.69750$	Character $\chi_{1049}(1006, \cdot)$
1-1049-1049.1007-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1007	$0$	✓	✓			$-0.285$	$0$	$0.581894$	Character $\chi_{1049}(1007, \cdot)$
1-1049-1049.1009-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1009	$0$	✓	✓			$0.00378$	$0$	$0.415843$	Character $\chi_{1049}(1009, \cdot)$
1-1049-1049.1011-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1011	$0$	✓	✓			$-0.161$	$0$	$0.210696$	Character $\chi_{1049}(1011, \cdot)$
1-1049-1049.1013-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1013	$0$	✓	✓			$0.0534$	$0$	$1.33725$	Character $\chi_{1049}(1013, \cdot)$
1-1049-1049.1017-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1017	$0$	✓	✓			$-0.375$	$0$	$0.402709$	Character $\chi_{1049}(1017, \cdot)$
1-1049-1049.102-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.102	$0$	✓	✓			$0.276$	$0$	$1.27594$	Character $\chi_{1049}(102, \cdot)$
1-1049-1049.1020-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1020	$0$	✓	✓			$-0.248$	$0$	$0.706749$	Character $\chi_{1049}(1020, \cdot)$
1-1049-1049.1023-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1023	$0$	✓	✓			$0.299$	$0$	$1.14396$	Character $\chi_{1049}(1023, \cdot)$
1-1049-1049.1024-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1024	$0$	✓	✓			$0.285$	$0$	$1.27973$	Character $\chi_{1049}(1024, \cdot)$
1-1049-1049.1027-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1027	$0$	✓	✓			$0.139$	$0$	$1.08678$	Character $\chi_{1049}(1027, \cdot)$
1-1049-1049.1028-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1028	$0$	✓	✓			$-0.235$	$0$	$1.04759$	Character $\chi_{1049}(1028, \cdot)$
1-1049-1049.1029-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1029	$0$	✓	✓			$-0.330$	$0$	$0.424903$	Character $\chi_{1049}(1029, \cdot)$
1-1049-1049.103-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.103	$0$	✓	✓			$-0.426$	$0$	$0.500309$	Character $\chi_{1049}(103, \cdot)$
1-1049-1049.1030-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1030	$0$	✓	✓			$-0.349$	$0$	$0.0254006$	Character $\chi_{1049}(1030, \cdot)$
1-1049-1049.1031-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1031	$0$	✓	✓			$0.187$	$0$	$1.67519$	Character $\chi_{1049}(1031, \cdot)$
1-1049-1049.1033-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1033	$0$	✓	✓			$0.246$	$0$	$0.389739$	Character $\chi_{1049}(1033, \cdot)$
1-1049-1049.1036-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1036	$0$	✓	✓			$0.448$	$0$	$0.272923$	Character $\chi_{1049}(1036, \cdot)$
1-1049-1049.1038-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1038	$0$	✓	✓			$-0.272$	$0$	$0.942419$	Character $\chi_{1049}(1038, \cdot)$
1-1049-1049.1039-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1039	$0$	✓	✓			$-0.299$	$0$	$0.497220$	Character $\chi_{1049}(1039, \cdot)$
1-1049-1049.104-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.104	$0$	✓	✓			$-0.324$	$0$	$0.326173$	Character $\chi_{1049}(104, \cdot)$
1-1049-1049.1040-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1040	$0$	✓	✓			$0.350$	$0$	$1.28391$	Character $\chi_{1049}(1040, \cdot)$
1-1049-1049.1041-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1041	$0$	✓	✓			$0.211$	$0$	$1.46228$	Character $\chi_{1049}(1041, \cdot)$
1-1049-1049.1044-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1044	$0$	✓	✓			$0.191$	$0$	$1.53644$	Character $\chi_{1049}(1044, \cdot)$
1-1049-1049.1045-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1045	$0$	✓	✓			$-0.0520$	$0$	$0.817661$	Character $\chi_{1049}(1045, \cdot)$
1-1049-1049.1047-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1047	$0$	✓	✓			$-0.303$	$0$	$0.736377$	Character $\chi_{1049}(1047, \cdot)$
1-1049-1049.1048-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.1048	$0$	✓	✓	✓	✓	$0$	$0$	$1.14742$	Character $\chi_{1049}(1048, \cdot)$
1-1049-1049.105-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.105	$0$	✓	✓			$-0.390$	$0$	$1.55609$	Character $\chi_{1049}(105, \cdot)$
1-1049-1049.106-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.106	$0$	✓	✓			$-0.0226$	$0$	$1.30438$	Character $\chi_{1049}(106, \cdot)$
1-1049-1049.107-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.107	$0$	✓	✓			$0.178$	$0$	$1.48858$	Character $\chi_{1049}(107, \cdot)$
1-1049-1049.11-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.11	$0$	✓	✓			$-0.461$	$0$	$0.366654$	Character $\chi_{1049}(11, \cdot)$
1-1049-1049.110-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.110	$0$	✓	✓			$0.266$	$0$	$1.22580$	Character $\chi_{1049}(110, \cdot)$
1-1049-1049.111-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.111	$0$	✓	✓			$-0.0566$	$0$	$0.379785$	Character $\chi_{1049}(111, \cdot)$
1-1049-1049.113-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.113	$0$	✓	✓			$0.478$	$0$	$1.17235$	Character $\chi_{1049}(113, \cdot)$
1-1049-1049.116-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.116	$0$	✓	✓			$-0.322$	$0$	$0.691569$	Character $\chi_{1049}(116, \cdot)$
1-1049-1049.117-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.117	$0$	✓	✓			$-0.264$	$0$	$0.420726$	Character $\chi_{1049}(117, \cdot)$
1-1049-1049.118-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.118	$0$	✓	✓			$-0.0230$	$0$	$0.772589$	Character $\chi_{1049}(118, \cdot)$
1-1049-1049.119-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.119	$0$	✓	✓			$-0.0762$	$0$	$0.905910$	Character $\chi_{1049}(119, \cdot)$
1-1049-1049.121-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.121	$0$	✓	✓			$-0.299$	$0$	$0.290697$	Character $\chi_{1049}(121, \cdot)$
1-1049-1049.122-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.122	$0$	✓	✓			$0.366$	$0$	$0.306753$	Character $\chi_{1049}(122, \cdot)$
1-1049-1049.123-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.123	$0$	✓	✓			$0.0318$	$0$	$1.11869$	Character $\chi_{1049}(123, \cdot)$
1-1049-1049.125-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.125	$0$	✓	✓			$0.0747$	$0$	$0.0990797$	Character $\chi_{1049}(125, \cdot)$
1-1049-1049.128-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.128	$0$	✓	✓			$0.0259$	$0$	$1.43577$	Character $\chi_{1049}(128, \cdot)$
1-1049-1049.13-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.13	$0$	✓	✓			$0.165$	$0$	$1.50711$	Character $\chi_{1049}(13, \cdot)$
1-1049-1049.130-r0-0-0	$4.87$	$4.87$	$1$	$1049$	1049.130	$0$	✓	✓			$-0.213$	$0$	$0.596149$	Character $\chi_{1049}(130, \cdot)$

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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.