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 105 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
1-185-185.103-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.103	$0$	✓	✓			$0.000341$	$0$	$0.529446$	Character $\chi_{185}(103, \cdot)$
1-185-185.104-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.104	$0$	✓	✓			$-0.390$	$0$	$0.959546$	Character $\chi_{185}(104, \cdot)$
1-185-185.113-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.113	$0$	✓	✓			$-0.363$	$0$	$1.03031$	Character $\chi_{185}(113, \cdot)$
1-185-185.114-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.114	$0$	✓	✓			$-0.245$	$0$	$3.17484$	Character $\chi_{185}(114, \cdot)$
1-185-185.117-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.117	$0$	✓	✓			$0.199$	$0$	$2.36880$	Character $\chi_{185}(117, \cdot)$
1-185-185.128-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.128	$0$	✓	✓			$0.000994$	$0$	$1.62780$	Character $\chi_{185}(128, \cdot)$
1-185-185.13-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.13	$0$	✓	✓			$0.278$	$0$	$2.55139$	Character $\chi_{185}(13, \cdot)$
1-185-185.133-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.133	$0$	✓	✓			$-0.404$	$0$	$0.524165$	Character $\chi_{185}(133, \cdot)$
1-185-185.139-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.139	$0$	✓	✓			$0.0684$	$0$	$1.36911$	Character $\chi_{185}(139, \cdot)$
1-185-185.142-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.142	$0$	✓	✓			$0.476$	$0$	$2.20156$	Character $\chi_{185}(142, \cdot)$
1-185-185.143-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.143	$0$	✓	✓			$-0.271$	$0$	$1.51643$	Character $\chi_{185}(143, \cdot)$
1-185-185.144-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.144	$0$	✓	✓			$0.0776$	$0$	$2.24700$	Character $\chi_{185}(144, \cdot)$
1-185-185.153-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.153	$0$	✓	✓			$0.0721$	$0$	$1.49274$	Character $\chi_{185}(153, \cdot)$
1-185-185.159-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.159	$0$	✓	✓			$0.380$	$0$	$1.89489$	Character $\chi_{185}(159, \cdot)$
1-185-185.162-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.162	$0$	✓	✓			$-0.276$	$0$	$0.206349$	Character $\chi_{185}(162, \cdot)$
1-185-185.163-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.163	$0$	✓	✓			$0.248$	$0$	$1.93560$	Character $\chi_{185}(163, \cdot)$
1-185-185.164-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.164	$0$	✓	✓			$0.120$	$0$	$1.35965$	Character $\chi_{185}(164, \cdot)$
1-185-185.167-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.167	$0$	✓	✓			$0.363$	$0$	$2.25424$	Character $\chi_{185}(167, \cdot)$
1-185-185.168-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.168	$0$	✓	✓			$0.0456$	$0$	$0.960848$	Character $\chi_{185}(168, \cdot)$
1-185-185.169-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.169	$0$	✓	✓			$0.390$	$0$	$2.27448$	Character $\chi_{185}(169, \cdot)$
1-185-185.17-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.17	$0$	✓	✓			$-0.324$	$0$	$0.585917$	Character $\chi_{185}(17, \cdot)$
1-185-185.172-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.172	$0$	✓	✓			$0.000994$	$0$	$1.68816$	Character $\chi_{185}(172, \cdot)$
1-185-185.174-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.174	$0$	✓	✓			$-0.0234$	$0$	$1.81223$	Character $\chi_{185}(174, \cdot)$
1-185-185.177-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.177	$0$	✓	✓			$-0.323$	$0$	$1.37702$	Character $\chi_{185}(177, \cdot)$
1-185-185.18-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.18	$0$	✓	✓			$0.260$	$0$	$1.34236$	Character $\chi_{185}(18, \cdot)$
1-185-185.183-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.183	$0$	✓	✓			$0.0633$	$0$	$1.21825$	Character $\chi_{185}(183, \cdot)$
1-185-185.184-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.184	$0$	✓	✓	✓	✓	$0$	$0$	$1.42759$	Character $\chi_{185}(184, \cdot)$
1-185-185.2-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.2	$0$	✓	✓			$0.312$	$0$	$1.35770$	Character $\chi_{185}(2, \cdot)$
1-185-185.22-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.22	$0$	✓	✓			$0.271$	$0$	$2.30630$	Character $\chi_{185}(22, \cdot)$
1-185-185.23-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.23	$0$	✓	✓			$0.323$	$0$	$2.39480$	Character $\chi_{185}(23, \cdot)$
1-185-185.32-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.32	$0$	✓	✓			$0.404$	$0$	$1.51536$	Character $\chi_{185}(32, \cdot)$
1-185-185.34-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.34	$0$	✓	✓			$-0.267$	$0$	$0.665749$	Character $\chi_{185}(34, \cdot)$
1-185-185.4-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.4	$0$	✓	✓			$-0.0684$	$0$	$1.37107$	Character $\chi_{185}(4, \cdot)$
1-185-185.42-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.42	$0$	✓	✓			$-0.248$	$0$	$0.899826$	Character $\chi_{185}(42, \cdot)$
1-185-185.43-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.43	$0$	✓	✓			$-0.476$	$0$	$0.406150$	Character $\chi_{185}(43, \cdot)$
1-185-185.44-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.44	$0$	✓	✓			$-0.120$	$0$	$0.801330$	Character $\chi_{185}(44, \cdot)$
1-185-185.49-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.49	$0$	✓	✓			$0.267$	$0$	$1.48742$	Character $\chi_{185}(49, \cdot)$
1-185-185.52-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.52	$0$	✓	✓			$-0.0721$	$0$	$1.20440$	Character $\chi_{185}(52, \cdot)$
1-185-185.57-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.57	$0$	✓	✓			$-0.278$	$0$	$1.28007$	Character $\chi_{185}(57, \cdot)$
1-185-185.64-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.64	$0$	✓	✓			$-0.380$	$0$	$0.999005$	Character $\chi_{185}(64, \cdot)$
1-185-185.68-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.68	$0$	✓	✓			$-0.199$	$0$	$1.34997$	Character $\chi_{185}(68, \cdot)$
1-185-185.72-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.72	$0$	✓	✓			$-0.260$	$0$	$0.893920$	Character $\chi_{185}(72, \cdot)$
1-185-185.8-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.8	$0$	✓	✓			$0.276$	$0$	$1.96157$	Character $\chi_{185}(8, \cdot)$
1-185-185.82-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.82	$0$	✓	✓			$-0.0471$	$0$	$1.08990$	Character $\chi_{185}(82, \cdot)$
1-185-185.84-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.84	$0$	✓	✓			$0.0234$	$0$	$1.37727$	Character $\chi_{185}(84, \cdot)$
1-185-185.87-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.87	$0$	✓	✓			$-0.0456$	$0$	$1.44003$	Character $\chi_{185}(87, \cdot)$
1-185-185.88-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.88	$0$	✓	✓			$0.0471$	$0$	$1.86759$	Character $\chi_{185}(88, \cdot)$
1-185-185.9-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.9	$0$	✓	✓			$-0.0776$	$0$	$1.85944$	Character $\chi_{185}(9, \cdot)$
1-185-185.92-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.92	$0$	✓	✓			$-0.0633$	$0$	$1.65998$	Character $\chi_{185}(92, \cdot)$
1-185-185.93-r0-0-0	$0.859$	$0.859$	$1$	$5 \cdot 37$	185.93	$0$	✓	✓			$-0.312$	$0$	$0.858477$	Character $\chi_{185}(93, \cdot)$

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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.