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 63 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
1-460-460.123-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.123	$0$	✓	✓			$0.213$	$0$	$1.56288$	Character $\chi_{460}(123, \cdot)$
1-460-460.127-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.127	$0$	✓	✓			$-0.350$	$0$	$0.630806$	Character $\chi_{460}(127, \cdot)$
1-460-460.147-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.147	$0$	✓	✓			$-0.415$	$0$	$0.105131$	Character $\chi_{460}(147, \cdot)$
1-460-460.159-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.159	$0$	✓	✓			$-0.0558$	$0$	$0.730701$	Character $\chi_{460}(159, \cdot)$
1-460-460.163-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.163	$0$	✓	✓			$0.350$	$0$	$1.82900$	Character $\chi_{460}(163, \cdot)$
1-460-460.167-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.167	$0$	✓	✓			$0.342$	$0$	$1.48150$	Character $\chi_{460}(167, \cdot)$
1-460-460.187-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.187	$0$	✓	✓			$-0.213$	$0$	$0.915702$	Character $\chi_{460}(187, \cdot)$
1-460-460.19-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.19	$0$	✓	✓			$-0.156$	$0$	$1.12804$	Character $\chi_{460}(19, \cdot)$
1-460-460.199-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.199	$0$	✓	✓			$0.111$	$0$	$0.924238$	Character $\chi_{460}(199, \cdot)$
1-460-460.223-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.223	$0$	✓	✓			$0.228$	$0$	$1.41666$	Character $\chi_{460}(223, \cdot)$
1-460-460.243-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.243	$0$	✓	✓			$0.0955$	$0$	$1.59575$	Character $\chi_{460}(243, \cdot)$
1-460-460.27-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.27	$0$	✓	✓			$0.334$	$0$	$1.97745$	Character $\chi_{460}(27, \cdot)$
1-460-460.3-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.3	$0$	✓	✓			$0.110$	$0$	$1.09026$	Character $\chi_{460}(3, \cdot)$
1-460-460.303-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.303	$0$	✓	✓			$-0.342$	$0$	$0.603546$	Character $\chi_{460}(303, \cdot)$
1-460-460.307-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.307	$0$	✓	✓			$-0.110$	$0$	$1.01167$	Character $\chi_{460}(307, \cdot)$
1-460-460.319-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.319	$0$	✓	✓			$-0.111$	$0$	$0.765565$	Character $\chi_{460}(319, \cdot)$
1-460-460.339-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.339	$0$	✓	✓			$0.156$	$0$	$1.64284$	Character $\chi_{460}(339, \cdot)$
1-460-460.347-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.347	$0$	✓	✓			$0.0263$	$0$	$1.10998$	Character $\chi_{460}(347, \cdot)$
1-460-460.359-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.359	$0$	✓	✓			$0.247$	$0$	$1.45070$	Character $\chi_{460}(359, \cdot)$
1-460-460.363-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.363	$0$	✓	✓			$0.415$	$0$	$1.39961$	Character $\chi_{460}(363, \cdot)$
1-460-460.379-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.379	$0$	✓	✓			$0.0558$	$0$	$1.09673$	Character $\chi_{460}(379, \cdot)$
1-460-460.403-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.403	$0$	✓	✓			$-0.0263$	$0$	$0.668735$	Character $\chi_{460}(403, \cdot)$
1-460-460.407-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.407	$0$	✓	✓			$-0.0955$	$0$	$0.935607$	Character $\chi_{460}(407, \cdot)$
1-460-460.419-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.419	$0$	✓	✓			$-0.247$	$0$	$0.943085$	Character $\chi_{460}(419, \cdot)$
1-460-460.423-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.423	$0$	✓	✓			$-0.0917$	$0$	$1.08049$	Character $\chi_{460}(423, \cdot)$
1-460-460.427-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.427	$0$	✓	✓			$-0.228$	$0$	$0.483585$	Character $\chi_{460}(427, \cdot)$
1-460-460.443-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.443	$0$	✓	✓			$-0.334$	$0$	$0.773373$	Character $\chi_{460}(443, \cdot)$
1-460-460.459-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.459	$0$	✓	✓	✓	✓	$0$	$0$	$1.22799$	Character $\chi_{460}(459, \cdot)$
1-460-460.79-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.79	$0$	✓	✓			$-0.427$	$0$	$2.16198$	Character $\chi_{460}(79, \cdot)$
1-460-460.87-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.87	$0$	✓	✓			$0.0917$	$0$	$1.66198$	Character $\chi_{460}(87, \cdot)$
1-460-460.99-r0-0-0	$2.13$	$2.13$	$1$	$2^{2} \cdot 5 \cdot 23$	460.99	$0$	✓	✓			$0.427$	$0$	$0.0530336$	Character $\chi_{460}(99, \cdot)$
1-460-460.103-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.103	$1$	✓	✓			$0.217$	$0$	$1.02911$	Character $\chi_{460}(103, \cdot)$
1-460-460.107-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.107	$1$	✓	✓			$-0.0504$	$0$	$0.406661$	Character $\chi_{460}(107, \cdot)$
1-460-460.119-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.119	$1$	✓	✓			$0.00398$	$0$	$1.00136$	Character $\chi_{460}(119, \cdot)$
1-460-460.143-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.143	$1$	✓	✓			$-0.0853$	$0$	$0.661757$	Character $\chi_{460}(143, \cdot)$
1-460-460.179-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.179	$1$	✓	✓			$-0.246$	$0$	$0.381247$	Character $\chi_{460}(179, \cdot)$
1-460-460.183-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.183	$1$	✓	✓			$0.161$	$0$	$1.19542$	Character $\chi_{460}(183, \cdot)$
1-460-460.203-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.203	$1$	✓	✓			$0.00491$	$0$	$0.754803$	Character $\chi_{460}(203, \cdot)$
1-460-460.219-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.219	$1$	✓	✓			$0.311$	$0$	$1.09707$	Character $\chi_{460}(219, \cdot)$
1-460-460.227-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.227	$1$	✓	✓			$-0.273$	$0$	$0.637977$	Character $\chi_{460}(227, \cdot)$
1-460-460.239-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.239	$1$	✓	✓			$0.246$	$0$	$0.807328$	Character $\chi_{460}(239, \cdot)$
1-460-460.247-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.247	$1$	✓	✓			$0.00491$	$0$	$0.523064$	Character $\chi_{460}(247, \cdot)$
1-460-460.259-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.259	$1$	✓	✓			$0.00398$	$0$	$0.806504$	Character $\chi_{460}(259, \cdot)$
1-460-460.263-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.263	$1$	✓	✓			$-0.265$	$0$	$0.731543$	Character $\chi_{460}(263, \cdot)$
1-460-460.267-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.267	$1$	✓	✓			$0.0853$	$0$	$1.02812$	Character $\chi_{460}(267, \cdot)$
1-460-460.279-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.279	$1$	✓	✓			$0.448$	$0$	$0.205815$	Character $\chi_{460}(279, \cdot)$
1-460-460.283-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.283	$1$	✓	✓			$-0.410$	$0$	$0.200552$	Character $\chi_{460}(283, \cdot)$
1-460-460.287-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.287	$1$	✓	✓			$-0.106$	$0$	$0.725893$	Character $\chi_{460}(287, \cdot)$
1-460-460.327-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.327	$1$	✓	✓			$-0.409$	$0$	$0.286572$	Character $\chi_{460}(327, \cdot)$
1-460-460.343-r1-0-0	$49.4$	$49.4$	$1$	$2^{2} \cdot 5 \cdot 23$	460.343	$1$	✓	✓			$0.106$	$0$	$0.694877$	Character $\chi_{460}(343, \cdot)$

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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.