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 230 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1045-1045.1003-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.1003	$1$	✓	✓	$-0.471$	$0$	$1.49666$	Character $\chi_{1045}(1003, \cdot)$
1-1045-1045.1014-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.1014	$1$	✓	✓	$0.379$	$0$	$0.0649483$	Character $\chi_{1045}(1014, \cdot)$
1-1045-1045.102-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.102	$1$	✓	✓	$-0.282$	$0$	$0.236783$	Character $\chi_{1045}(102, \cdot)$
1-1045-1045.1022-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.1022	$1$	✓	✓	$0.457$	$0$	$0.953951$	Character $\chi_{1045}(1022, \cdot)$
1-1045-1045.1032-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.1032	$1$	✓	✓	$0.309$	$0$	$1.25100$	Character $\chi_{1045}(1032, \cdot)$
1-1045-1045.1037-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.1037	$1$	✓	✓	$0.451$	$0$	$0.556760$	Character $\chi_{1045}(1037, \cdot)$
1-1045-1045.1039-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.1039	$1$	✓	✓	$0.331$	$0$	$0.688795$	Character $\chi_{1045}(1039, \cdot)$
1-1045-1045.1043-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.1043	$1$	✓	✓	$0.0777$	$0$	$0.777163$	Character $\chi_{1045}(1043, \cdot)$
1-1045-1045.107-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.107	$1$	✓	✓	$-0.383$	$0$	$1.55722$	Character $\chi_{1045}(107, \cdot)$
1-1045-1045.117-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.117	$1$	✓	✓	$0.238$	$0$	$0.0662944$	Character $\chi_{1045}(117, \cdot)$
1-1045-1045.124-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.124	$1$	✓	✓	$-0.0278$	$0$	$0.231826$	Character $\chi_{1045}(124, \cdot)$
1-1045-1045.127-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.127	$1$	✓	✓	$-0.269$	$0$	$0.0845548$	Character $\chi_{1045}(127, \cdot)$
1-1045-1045.128-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.128	$1$	✓	✓	$-0.418$	$0$	$0.892924$	Character $\chi_{1045}(128, \cdot)$
1-1045-1045.13-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.13	$1$	✓	✓	$0.0471$	$0$	$0.576617$	Character $\chi_{1045}(13, \cdot)$
1-1045-1045.137-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.137	$1$	✓	✓	$-0.225$	$0$	$0.603906$	Character $\chi_{1045}(137, \cdot)$
1-1045-1045.139-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.139	$1$	✓	✓	$0.203$	$0$	$1.25780$	Character $\chi_{1045}(139, \cdot)$
1-1045-1045.14-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.14	$1$	✓	✓	$-0.373$	$0$	$0.339186$	Character $\chi_{1045}(14, \cdot)$
1-1045-1045.149-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.149	$1$	✓	✓	$-0.410$	$0$	$0.246431$	Character $\chi_{1045}(149, \cdot)$
1-1045-1045.157-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.157	$1$	✓	✓	$-0.159$	$0$	$0.893213$	Character $\chi_{1045}(157, \cdot)$
1-1045-1045.158-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.158	$1$	✓	✓	$-0.420$	$0$	$0.524698$	Character $\chi_{1045}(158, \cdot)$
1-1045-1045.162-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.162	$1$	✓	✓	$0.0250$	$0$	$0.545300$	Character $\chi_{1045}(162, \cdot)$
1-1045-1045.163-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.163	$1$	✓	✓	$-0.163$	$0$	$0.823635$	Character $\chi_{1045}(163, \cdot)$
1-1045-1045.167-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.167	$1$	✓	✓	$-0.295$	$0$	$0.533538$	Character $\chi_{1045}(167, \cdot)$
1-1045-1045.168-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.168	$1$	✓	✓	$0.243$	$0$	$0.0144370$	Character $\chi_{1045}(168, \cdot)$
1-1045-1045.173-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.173	$1$	✓	✓	$-0.102$	$0$	$0.104813$	Character $\chi_{1045}(173, \cdot)$
1-1045-1045.174-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.174	$1$	✓	✓	$-0.331$	$0$	$0.718967$	Character $\chi_{1045}(174, \cdot)$
1-1045-1045.179-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.179	$1$	✓	✓	$0.428$	$0$	$1.44243$	Character $\chi_{1045}(179, \cdot)$
1-1045-1045.18-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.18	$1$	✓	✓	$0.450$	$0$	$0.0308912$	Character $\chi_{1045}(18, \cdot)$
1-1045-1045.183-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.183	$1$	✓	✓	$-0.481$	$0$	$0.0631284$	Character $\chi_{1045}(183, \cdot)$
1-1045-1045.193-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.193	$1$	✓	✓	$-0.223$	$0$	$0.392831$	Character $\chi_{1045}(193, \cdot)$
1-1045-1045.194-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.194	$1$	✓	✓	$-0.217$	$0$	$0.332938$	Character $\chi_{1045}(194, \cdot)$
1-1045-1045.2-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.2	$1$	✓	✓	$0.358$	$0$	$0.718365$	Character $\chi_{1045}(2, \cdot)$
1-1045-1045.207-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.207	$1$	✓	✓	$0.246$	$0$	$1.08298$	Character $\chi_{1045}(207, \cdot)$
1-1045-1045.208-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.208	$1$	✓	✓	$0.411$	$0$	$0.0837040$	Character $\chi_{1045}(208, \cdot)$
1-1045-1045.213-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.213	$1$	✓	✓	$0.159$	$0$	$0.763896$	Character $\chi_{1045}(213, \cdot)$
1-1045-1045.217-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.217	$1$	✓	✓	$0.481$	$0$	$1.12471$	Character $\chi_{1045}(217, \cdot)$
1-1045-1045.218-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.218	$1$	✓	✓	$-0.139$	$0$	$0.882291$	Character $\chi_{1045}(218, \cdot)$
1-1045-1045.222-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.222	$1$	✓	✓	$0.223$	$0$	$0.893360$	Character $\chi_{1045}(222, \cdot)$
1-1045-1045.224-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.224	$1$	✓	✓	$0.373$	$0$	$0.864849$	Character $\chi_{1045}(224, \cdot)$
1-1045-1045.227-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.227	$1$	✓	✓	$-0.372$	$0$	$0.314538$	Character $\chi_{1045}(227, \cdot)$
1-1045-1045.238-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.238	$1$	✓	✓	$-0.0732$	$0$	$0.139334$	Character $\chi_{1045}(238, \cdot)$
1-1045-1045.239-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.239	$1$	✓	✓	$-0.171$	$0$	$0.435677$	Character $\chi_{1045}(239, \cdot)$
1-1045-1045.24-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.24	$1$	✓	✓	$0.497$	$0$	$0.181465$	Character $\chi_{1045}(24, \cdot)$
1-1045-1045.244-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.244	$1$	✓	✓	$0.0822$	$0$	$0.721026$	Character $\chi_{1045}(244, \cdot)$
1-1045-1045.258-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.258	$1$	✓	✓	$-0.278$	$0$	$0.480880$	Character $\chi_{1045}(258, \cdot)$
1-1045-1045.269-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.269	$1$	✓	✓	$-0.446$	$0$	$0.0833667$	Character $\chi_{1045}(269, \cdot)$
1-1045-1045.273-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.273	$1$	✓	✓	$0.101$	$0$	$0.696076$	Character $\chi_{1045}(273, \cdot)$
1-1045-1045.279-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.279	$1$	✓	✓	$-0.107$	$0$	$0.938129$	Character $\chi_{1045}(279, \cdot)$
1-1045-1045.284-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.284	$1$	✓	✓	$0.0572$	$0$	$0.777743$	Character $\chi_{1045}(284, \cdot)$
1-1045-1045.288-r1-0-0	$112.$	$112.$	$1$	$5 \cdot 11 \cdot 19$	1045.288	$1$	✓	✓	$0.269$	$0$	$0.838577$	Character $\chi_{1045}(288, \cdot)$

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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.