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 87 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
1-465-465.104-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.104	$0$	✓	✓			$0.113$	$0$	$1.17900$	Character $\chi_{465}(104, \cdot)$
1-465-465.107-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.107	$0$	✓	✓			$-0.115$	$0$	$0.581408$	Character $\chi_{465}(107, \cdot)$
1-465-465.113-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.113	$0$	✓	✓			$0.115$	$0$	$1.36814$	Character $\chi_{465}(113, \cdot)$
1-465-465.119-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.119	$0$	✓	✓			$0.127$	$0$	$1.89247$	Character $\chi_{465}(119, \cdot)$
1-465-465.128-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.128	$0$	✓	✓			$-0.294$	$0$	$0.563482$	Character $\chi_{465}(128, \cdot)$
1-465-465.143-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.143	$0$	✓	✓			$0.187$	$0$	$1.02662$	Character $\chi_{465}(143, \cdot)$
1-465-465.152-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.152	$0$	✓	✓			$-0.295$	$0$	$0.435686$	Character $\chi_{465}(152, \cdot)$
1-465-465.173-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.173	$0$	✓	✓			$0.136$	$0$	$1.63590$	Character $\chi_{465}(173, \cdot)$
1-465-465.179-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.179	$0$	✓	✓			$-0.425$	$0$	$0.0321805$	Character $\chi_{465}(179, \cdot)$
1-465-465.188-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.188	$0$	✓	✓			$0.0595$	$0$	$1.07379$	Character $\chi_{465}(188, \cdot)$
1-465-465.2-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.2	$0$	✓	✓			$-0.264$	$0$	$0.883133$	Character $\chi_{465}(2, \cdot)$
1-465-465.209-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.209	$0$	✓	✓			$0.241$	$0$	$1.44554$	Character $\chi_{465}(209, \cdot)$
1-465-465.227-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.227	$0$	✓	✓			$-0.0286$	$0$	$1.43380$	Character $\chi_{465}(227, \cdot)$
1-465-465.233-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.233	$0$	✓	✓			$0.264$	$0$	$1.93283$	Character $\chi_{465}(233, \cdot)$
1-465-465.239-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.239	$0$	✓	✓			$0.425$	$0$	$1.67404$	Character $\chi_{465}(239, \cdot)$
1-465-465.242-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.242	$0$	✓	✓			$-0.0980$	$0$	$1.05603$	Character $\chi_{465}(242, \cdot)$
1-465-465.254-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.254	$0$	✓	✓			$-0.127$	$0$	$1.10228$	Character $\chi_{465}(254, \cdot)$
1-465-465.257-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.257	$0$	✓	✓			$0.237$	$0$	$1.24951$	Character $\chi_{465}(257, \cdot)$
1-465-465.269-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.269	$0$	✓	✓			$0.0671$	$0$	$0.741612$	Character $\chi_{465}(269, \cdot)$
1-465-465.287-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.287	$0$	✓	✓			$0.294$	$0$	$1.13268$	Character $\chi_{465}(287, \cdot)$
1-465-465.29-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.29	$0$	✓	✓			$0.246$	$0$	$1.23077$	Character $\chi_{465}(29, \cdot)$
1-465-465.293-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.293	$0$	✓	✓			$0.208$	$0$	$1.98683$	Character $\chi_{465}(293, \cdot)$
1-465-465.317-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.317	$0$	✓	✓			$0.438$	$0$	$1.83946$	Character $\chi_{465}(317, \cdot)$
1-465-465.338-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.338	$0$	✓	✓			$0.0286$	$0$	$1.24691$	Character $\chi_{465}(338, \cdot)$
1-465-465.344-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.344	$0$	✓	✓			$-0.0671$	$0$	$1.17649$	Character $\chi_{465}(344, \cdot)$
1-465-465.377-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.377	$0$	✓	✓			$-0.225$	$0$	$1.07260$	Character $\chi_{465}(377, \cdot)$
1-465-465.38-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.38	$0$	✓	✓			$-0.237$	$0$	$0.858828$	Character $\chi_{465}(38, \cdot)$
1-465-465.389-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.389	$0$	✓	✓			$-0.113$	$0$	$1.03098$	Character $\chi_{465}(389, \cdot)$
1-465-465.392-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.392	$0$	✓	✓			$-0.208$	$0$	$0.299131$	Character $\chi_{465}(392, \cdot)$
1-465-465.407-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.407	$0$	✓	✓			$0.382$	$0$	$1.81683$	Character $\chi_{465}(407, \cdot)$
1-465-465.413-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.413	$0$	✓	✓			$0.295$	$0$	$1.42297$	Character $\chi_{465}(413, \cdot)$
1-465-465.422-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.422	$0$	✓	✓			$-0.136$	$0$	$1.26153$	Character $\chi_{465}(422, \cdot)$
1-465-465.428-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.428	$0$	✓	✓			$0.225$	$0$	$1.16309$	Character $\chi_{465}(428, \cdot)$
1-465-465.44-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.44	$0$	✓	✓			$0.471$	$0$	$0.480467$	Character $\chi_{465}(44, \cdot)$
1-465-465.443-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.443	$0$	✓	✓			$-0.438$	$0$	$0.646614$	Character $\chi_{465}(443, \cdot)$
1-465-465.449-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.449	$0$	✓	✓			$-0.246$	$0$	$0.956334$	Character $\chi_{465}(449, \cdot)$
1-465-465.452-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.452	$0$	✓	✓			$-0.187$	$0$	$0.549935$	Character $\chi_{465}(452, \cdot)$
1-465-465.464-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.464	$0$	✓	✓	✓	✓	$0$	$0$	$1.34858$	Character $\chi_{465}(464, \cdot)$
1-465-465.47-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.47	$0$	✓	✓			$-0.0595$	$0$	$1.08736$	Character $\chi_{465}(47, \cdot)$
1-465-465.74-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.74	$0$	✓	✓			$-0.471$	$0$	$1.91873$	Character $\chi_{465}(74, \cdot)$
1-465-465.8-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.8	$0$	✓	✓			$-0.382$	$0$	$0.806317$	Character $\chi_{465}(8, \cdot)$
1-465-465.89-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.89	$0$	✓	✓			$-0.241$	$0$	$0.287056$	Character $\chi_{465}(89, \cdot)$
1-465-465.98-r0-0-0	$2.15$	$2.15$	$1$	$3 \cdot 5 \cdot 31$	465.98	$0$	✓	✓			$0.0980$	$0$	$0.738432$	Character $\chi_{465}(98, \cdot)$
1-465-465.122-r1-0-0	$49.9$	$49.9$	$1$	$3 \cdot 5 \cdot 31$	465.122	$1$	✓	✓			$-0.415$	$0$	$0.417173$	Character $\chi_{465}(122, \cdot)$
1-465-465.134-r1-0-0	$49.9$	$49.9$	$1$	$3 \cdot 5 \cdot 31$	465.134	$1$	✓	✓			$0.133$	$0$	$0.525660$	Character $\chi_{465}(134, \cdot)$
1-465-465.137-r1-0-0	$49.9$	$49.9$	$1$	$3 \cdot 5 \cdot 31$	465.137	$1$	✓	✓			$-0.190$	$0$	$0.501322$	Character $\chi_{465}(137, \cdot)$
1-465-465.14-r1-0-0	$49.9$	$49.9$	$1$	$3 \cdot 5 \cdot 31$	465.14	$1$	✓	✓			$0.0467$	$0$	$0.913728$	Character $\chi_{465}(14, \cdot)$
1-465-465.149-r1-0-0	$49.9$	$49.9$	$1$	$3 \cdot 5 \cdot 31$	465.149	$1$	✓	✓			$0.0638$	$0$	$1.32706$	Character $\chi_{465}(149, \cdot)$
1-465-465.158-r1-0-0	$49.9$	$49.9$	$1$	$3 \cdot 5 \cdot 31$	465.158	$1$	✓	✓			$-0.405$	$0$	$0.0476147$	Character $\chi_{465}(158, \cdot)$
1-465-465.164-r1-0-0	$49.9$	$49.9$	$1$	$3 \cdot 5 \cdot 31$	465.164	$1$	✓	✓			$0.399$	$0$	$1.40720$	Character $\chi_{465}(164, \cdot)$

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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
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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.