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 108 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-980-980.107-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.107	$0$	✓	✓	$-0.275$	$0$	$0.0691067$	Character $\chi_{980}(107, \cdot)$
1-980-980.123-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.123	$0$	✓	✓	$0.214$	$0$	$1.29419$	Character $\chi_{980}(123, \cdot)$
1-980-980.127-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.127	$0$	✓	✓	$-0.330$	$0$	$0.555523$	Character $\chi_{980}(127, \cdot)$
1-980-980.139-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.139	$0$	✓	✓	$0.198$	$0$	$0.948503$	Character $\chi_{980}(139, \cdot)$
1-980-980.159-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.159	$0$	✓	✓	$0.164$	$0$	$1.02763$	Character $\chi_{980}(159, \cdot)$
1-980-980.163-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.163	$0$	✓	✓	$-0.0370$	$0$	$0.599523$	Character $\chi_{980}(163, \cdot)$
1-980-980.183-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.183	$0$	✓	✓	$-0.0574$	$0$	$0.976243$	Character $\chi_{980}(183, \cdot)$
1-980-980.199-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.199	$0$	✓	✓	$0.198$	$0$	$1.49685$	Character $\chi_{980}(199, \cdot)$
1-980-980.207-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.207	$0$	✓	✓	$0.452$	$0$	$1.62114$	Character $\chi_{980}(207, \cdot)$
1-980-980.23-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.23	$0$	✓	✓	$-0.336$	$0$	$0.451241$	Character $\chi_{980}(23, \cdot)$
1-980-980.247-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.247	$0$	✓	✓	$-0.214$	$0$	$0.762104$	Character $\chi_{980}(247, \cdot)$
1-980-980.267-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.267	$0$	✓	✓	$-0.493$	$0$	$0.259498$	Character $\chi_{980}(267, \cdot)$
1-980-980.279-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.279	$0$	✓	✓	$0.219$	$0$	$1.15277$	Character $\chi_{980}(279, \cdot)$
1-980-980.299-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.299	$0$	✓	✓	$0.198$	$0$	$1.32010$	Character $\chi_{980}(299, \cdot)$
1-980-980.303-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.303	$0$	✓	✓	$-0.452$	$0$	$0.372775$	Character $\chi_{980}(303, \cdot)$
1-980-980.323-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.323	$0$	✓	✓	$0.493$	$0$	$1.71053$	Character $\chi_{980}(323, \cdot)$
1-980-980.339-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.339	$0$	✓	✓	$-0.164$	$0$	$0.923473$	Character $\chi_{980}(339, \cdot)$
1-980-980.347-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.347	$0$	✓	✓	$0.173$	$0$	$1.04653$	Character $\chi_{980}(347, \cdot)$
1-980-980.387-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.387	$0$	✓	✓	$0.0370$	$0$	$0.848622$	Character $\chi_{980}(387, \cdot)$
1-980-980.403-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.403	$0$	✓	✓	$0.275$	$0$	$1.19990$	Character $\chi_{980}(403, \cdot)$
1-980-980.407-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.407	$0$	✓	✓	$0.0574$	$0$	$1.39575$	Character $\chi_{980}(407, \cdot)$
1-980-980.419-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.419	$0$	✓	✓	$0.168$	$0$	$1.34137$	Character $\chi_{980}(419, \cdot)$
1-980-980.43-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.43	$0$	✓	✓	$-0.0370$	$0$	$1.21700$	Character $\chi_{980}(43, \cdot)$
1-980-980.439-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.439	$0$	✓	✓	$0.447$	$0$	$1.90477$	Character $\chi_{980}(439, \cdot)$
1-980-980.443-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.443	$0$	✓	✓	$-0.390$	$0$	$1.59701$	Character $\chi_{980}(443, \cdot)$
1-980-980.463-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.463	$0$	✓	✓	$0.330$	$0$	$1.22847$	Character $\chi_{980}(463, \cdot)$
1-980-980.479-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.479	$0$	✓	✓	$0.113$	$0$	$0.803255$	Character $\chi_{980}(479, \cdot)$
1-980-980.487-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.487	$0$	✓	✓	$0.0370$	$0$	$1.13492$	Character $\chi_{980}(487, \cdot)$
1-980-980.527-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.527	$0$	✓	✓	$0.00307$	$0$	$1.18507$	Character $\chi_{980}(527, \cdot)$
1-980-980.543-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.543	$0$	✓	✓	$0.00307$	$0$	$1.20566$	Character $\chi_{980}(543, \cdot)$
1-980-980.547-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.547	$0$	✓	✓	$0.0370$	$0$	$1.01737$	Character $\chi_{980}(547, \cdot)$
1-980-980.559-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.559	$0$	✓	✓	$-0.168$	$0$	$0.870808$	Character $\chi_{980}(559, \cdot)$
1-980-980.579-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.579	$0$	✓	✓	$-0.113$	$0$	$0.567740$	Character $\chi_{980}(579, \cdot)$
1-980-980.583-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.583	$0$	✓	✓	$-0.139$	$0$	$0.874466$	Character $\chi_{980}(583, \cdot)$
1-980-980.59-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.59	$0$	✓	✓	$-0.198$	$0$	$0.338741$	Character $\chi_{980}(59, \cdot)$
1-980-980.603-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.603	$0$	✓	✓	$-0.118$	$0$	$0.631956$	Character $\chi_{980}(603, \cdot)$
1-980-980.627-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.627	$0$	✓	✓	$0.139$	$0$	$1.29573$	Character $\chi_{980}(627, \cdot)$
1-980-980.683-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.683	$0$	✓	✓	$-0.139$	$0$	$0.330704$	Character $\chi_{980}(683, \cdot)$
1-980-980.699-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.699	$0$	✓	✓	$-0.219$	$0$	$0.811677$	Character $\chi_{980}(699, \cdot)$
1-980-980.719-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.719	$0$	✓	✓	$-0.198$	$0$	$0.722429$	Character $\chi_{980}(719, \cdot)$
1-980-980.723-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.723	$0$	✓	✓	$-0.173$	$0$	$0.554660$	Character $\chi_{980}(723, \cdot)$
1-980-980.743-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.743	$0$	✓	✓	$-0.139$	$0$	$0.705220$	Character $\chi_{980}(743, \cdot)$
1-980-980.759-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.759	$0$	✓	✓	$-0.447$	$0$	$0.355267$	Character $\chi_{980}(759, \cdot)$
1-980-980.767-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.767	$0$	✓	✓	$0.336$	$0$	$1.17806$	Character $\chi_{980}(767, \cdot)$
1-980-980.807-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.807	$0$	✓	✓	$-0.160$	$0$	$0.472871$	Character $\chi_{980}(807, \cdot)$
1-980-980.823-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.823	$0$	✓	✓	$-0.0370$	$0$	$0.912706$	Character $\chi_{980}(823, \cdot)$
1-980-980.827-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.827	$0$	✓	✓	$0.139$	$0$	$0.867355$	Character $\chi_{980}(827, \cdot)$
1-980-980.839-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.839	$0$	✓	✓	$-0.198$	$0$	$0.611272$	Character $\chi_{980}(839, \cdot)$
1-980-980.859-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.859	$0$	✓	✓	$0.498$	$0$	$0.00137950$	Character $\chi_{980}(859, \cdot)$
1-980-980.899-r0-0-0	$4.55$	$4.55$	$1$	$2^{2} \cdot 5 \cdot 7^{2}$	980.899	$0$	✓	✓	$0.498$	$0$	$1.69321$	Character $\chi_{980}(899, \cdot)$

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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.