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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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1033-1033.100-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.100	$0$	✓	✓			$0.491$	$0$	$0.437451$	Character $\chi_{1033}(100, \cdot)$
1-1033-1033.1001-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1001	$0$	✓	✓			$0.273$	$0$	$1.71386$	Character $\chi_{1033}(1001, \cdot)$
1-1033-1033.1002-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1002	$0$	✓	✓			$-0.443$	$0$	$0.0376292$	Character $\chi_{1033}(1002, \cdot)$
1-1033-1033.1005-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1005	$0$	✓	✓			$0.199$	$0$	$1.68551$	Character $\chi_{1033}(1005, \cdot)$
1-1033-1033.1006-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1006	$0$	✓	✓			$-0.224$	$0$	$0.759636$	Character $\chi_{1033}(1006, \cdot)$
1-1033-1033.1008-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1008	$0$	✓	✓			$-0.0985$	$0$	$0.965120$	Character $\chi_{1033}(1008, \cdot)$
1-1033-1033.1009-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1009	$0$	✓	✓			$0.0113$	$0$	$0.953652$	Character $\chi_{1033}(1009, \cdot)$
1-1033-1033.101-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.101	$0$	✓	✓			$0.0565$	$0$	$0.899461$	Character $\chi_{1033}(101, \cdot)$
1-1033-1033.1012-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1012	$0$	✓	✓			$-0.285$	$0$	$1.97536$	Character $\chi_{1033}(1012, \cdot)$
1-1033-1033.1014-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1014	$0$	✓	✓			$0.338$	$0$	$1.26948$	Character $\chi_{1033}(1014, \cdot)$
1-1033-1033.1015-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1015	$0$	✓	✓			$0.246$	$0$	$0.946720$	Character $\chi_{1033}(1015, \cdot)$
1-1033-1033.1016-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1016	$0$	✓	✓			$0.122$	$0$	$0.913755$	Character $\chi_{1033}(1016, \cdot)$
1-1033-1033.1017-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1017	$0$	✓	✓			$-0.174$	$0$	$1.01351$	Character $\chi_{1033}(1017, \cdot)$
1-1033-1033.1019-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1019	$0$	✓	✓			$-0.433$	$0$	$0.855039$	Character $\chi_{1033}(1019, \cdot)$
1-1033-1033.102-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.102	$0$	✓	✓			$0.221$	$0$	$1.33323$	Character $\chi_{1033}(102, \cdot)$
1-1033-1033.1021-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1021	$0$	✓	✓			$0.380$	$0$	$1.82173$	Character $\chi_{1033}(1021, \cdot)$
1-1033-1033.1024-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1024	$0$	✓	✓			$0.483$	$0$	$0.439929$	Character $\chi_{1033}(1024, \cdot)$
1-1033-1033.1025-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1025	$0$	✓	✓			$-0.411$	$0$	$0.136721$	Character $\chi_{1033}(1025, \cdot)$
1-1033-1033.1026-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1026	$0$	✓	✓			$0.363$	$0$	$1.13746$	Character $\chi_{1033}(1026, \cdot)$
1-1033-1033.1027-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1027	$0$	✓	✓			$0.458$	$0$	$1.61502$	Character $\chi_{1033}(1027, \cdot)$
1-1033-1033.1029-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1029	$0$	✓	✓			$-0.282$	$0$	$0.854438$	Character $\chi_{1033}(1029, \cdot)$
1-1033-1033.1030-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1030	$0$	✓	✓			$-0.00846$	$0$	$1.10750$	Character $\chi_{1033}(1030, \cdot)$
1-1033-1033.1031-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1031	$0$	✓	✓			$-0.0901$	$0$	$0.904400$	Character $\chi_{1033}(1031, \cdot)$
1-1033-1033.1032-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.1032	$0$	✓	✓	✓	✓	$0$	$0$	$1.32333$	Character $\chi_{1033}(1032, \cdot)$
1-1033-1033.108-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.108	$0$	✓	✓			$0.222$	$0$	$1.02810$	Character $\chi_{1033}(108, \cdot)$
1-1033-1033.110-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.110	$0$	✓	✓			$-0.0696$	$0$	$1.01387$	Character $\chi_{1033}(110, \cdot)$
1-1033-1033.111-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.111	$0$	✓	✓			$-0.344$	$0$	$0.577748$	Character $\chi_{1033}(111, \cdot)$
1-1033-1033.112-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.112	$0$	✓	✓			$-0.274$	$0$	$0.501608$	Character $\chi_{1033}(112, \cdot)$
1-1033-1033.113-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.113	$0$	✓	✓			$0.0652$	$0$	$0.930901$	Character $\chi_{1033}(113, \cdot)$
1-1033-1033.114-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.114	$0$	✓	✓			$-0.298$	$0$	$1.37336$	Character $\chi_{1033}(114, \cdot)$
1-1033-1033.115-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.115	$0$	✓	✓			$0.224$	$0$	$0.973963$	Character $\chi_{1033}(115, \cdot)$
1-1033-1033.119-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.119	$0$	✓	✓			$-0.107$	$0$	$0.932612$	Character $\chi_{1033}(119, \cdot)$
1-1033-1033.12-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.12	$0$	✓	✓			$-0.289$	$0$	$0.642347$	Character $\chi_{1033}(12, \cdot)$
1-1033-1033.121-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.121	$0$	✓	✓			$-0.0580$	$0$	$0.531969$	Character $\chi_{1033}(121, \cdot)$
1-1033-1033.122-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.122	$0$	✓	✓			$0.0415$	$0$	$1.22902$	Character $\chi_{1033}(122, \cdot)$
1-1033-1033.123-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.123	$0$	✓	✓			$-0.0907$	$0$	$0.697524$	Character $\chi_{1033}(123, \cdot)$
1-1033-1033.124-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.124	$0$	✓	✓			$0.0272$	$0$	$1.10594$	Character $\chi_{1033}(124, \cdot)$
1-1033-1033.126-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.126	$0$	✓	✓			$0.125$	$0$	$0.678555$	Character $\chi_{1033}(126, \cdot)$
1-1033-1033.127-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.127	$0$	✓	✓			$0.133$	$0$	$0.805004$	Character $\chi_{1033}(127, \cdot)$
1-1033-1033.128-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.128	$0$	✓	✓			$-0.0184$	$0$	$0.974956$	Character $\chi_{1033}(128, \cdot)$
1-1033-1033.129-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.129	$0$	✓	✓			$0.411$	$0$	$1.77997$	Character $\chi_{1033}(129, \cdot)$
1-1033-1033.130-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.130	$0$	✓	✓			$0.379$	$0$	$1.93596$	Character $\chi_{1033}(130, \cdot)$
1-1033-1033.133-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.133	$0$	✓	✓			$0.0784$	$0$	$0.245278$	Character $\chi_{1033}(133, \cdot)$
1-1033-1033.136-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.136	$0$	✓	✓			$0.0997$	$0$	$1.01114$	Character $\chi_{1033}(136, \cdot)$
1-1033-1033.137-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.137	$0$	✓	✓			$0.0528$	$0$	$1.22887$	Character $\chi_{1033}(137, \cdot)$
1-1033-1033.14-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.14	$0$	✓	✓			$-0.168$	$0$	$0.589414$	Character $\chi_{1033}(14, \cdot)$
1-1033-1033.143-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.143	$0$	✓	✓			$-0.0326$	$0$	$1.19958$	Character $\chi_{1033}(143, \cdot)$
1-1033-1033.144-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.144	$0$	✓	✓			$-0.482$	$0$	$1.43550$	Character $\chi_{1033}(144, \cdot)$
1-1033-1033.145-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.145	$0$	✓	✓			$-0.137$	$0$	$1.11218$	Character $\chi_{1033}(145, \cdot)$
1-1033-1033.147-r0-0-0	$4.79$	$4.79$	$1$	$1033$	1033.147	$0$	✓	✓			$0.155$	$0$	$1.40090$	Character $\chi_{1033}(147, \cdot)$

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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.