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 165 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
1-221-221.100-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.100	$0$	✓	✓			$-0.138$	$0$	$1.75440$	Character $\chi_{221}(100, \cdot)$
1-221-221.101-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.101	$0$	✓	✓			$-0.418$	$0$	$1.12679$	Character $\chi_{221}(101, \cdot)$
1-221-221.109-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.109	$0$	✓	✓			$0.0104$	$0$	$1.09356$	Character $\chi_{221}(109, \cdot)$
1-221-221.11-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.11	$0$	✓	✓			$-0.0549$	$0$	$1.39507$	Character $\chi_{221}(11, \cdot)$
1-221-221.112-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.112	$0$	✓	✓			$-0.0225$	$0$	$1.72986$	Character $\chi_{221}(112, \cdot)$
1-221-221.121-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.121	$0$	✓	✓			$0.0363$	$0$	$0.968955$	Character $\chi_{221}(121, \cdot)$
1-221-221.122-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.122	$0$	✓	✓			$-0.0485$	$0$	$1.58735$	Character $\chi_{221}(122, \cdot)$
1-221-221.124-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.124	$0$	✓	✓			$-0.0429$	$0$	$0.948765$	Character $\chi_{221}(124, \cdot)$
1-221-221.125-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.125	$0$	✓	✓			$0.0485$	$0$	$1.61671$	Character $\chi_{221}(125, \cdot)$
1-221-221.127-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.127	$0$	✓	✓			$-0.156$	$0$	$1.24548$	Character $\chi_{221}(127, \cdot)$
1-221-221.134-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.134	$0$	✓	✓			$0.156$	$0$	$1.45793$	Character $\chi_{221}(134, \cdot)$
1-221-221.140-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.140	$0$	✓	✓			$0.436$	$0$	$2.11801$	Character $\chi_{221}(140, \cdot)$
1-221-221.141-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.141	$0$	✓	✓			$-0.290$	$0$	$1.28353$	Character $\chi_{221}(141, \cdot)$
1-221-221.148-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.148	$0$	✓	✓			$0.0225$	$0$	$1.55903$	Character $\chi_{221}(148, \cdot)$
1-221-221.150-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.150	$0$	✓	✓			$0.148$	$0$	$2.17128$	Character $\chi_{221}(150, \cdot)$
1-221-221.152-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.152	$0$	✓	✓			$0.123$	$0$	$1.54026$	Character $\chi_{221}(152, \cdot)$
1-221-221.155-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.155	$0$	✓	✓			$-0.382$	$0$	$1.17991$	Character $\chi_{221}(155, \cdot)$
1-221-221.158-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.158	$0$	✓	✓			$-0.384$	$0$	$0.154331$	Character $\chi_{221}(158, \cdot)$
1-221-221.16-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.16	$0$	✓	✓			$-0.123$	$0$	$0.757229$	Character $\chi_{221}(16, \cdot)$
1-221-221.163-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.163	$0$	✓	✓			$-0.0550$	$0$	$1.39051$	Character $\chi_{221}(163, \cdot)$
1-221-221.164-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.164	$0$	✓	✓			$0.225$	$0$	$0.856302$	Character $\chi_{221}(164, \cdot)$
1-221-221.166-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.166	$0$	✓	✓			$-0.274$	$0$	$0.518218$	Character $\chi_{221}(166, \cdot)$
1-221-221.167-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.167	$0$	✓	✓			$-0.0994$	$0$	$1.19532$	Character $\chi_{221}(167, \cdot)$
1-221-221.168-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.168	$0$	✓	✓			$-0.262$	$0$	$0.542690$	Character $\chi_{221}(168, \cdot)$
1-221-221.172-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.172	$0$	✓	✓			$0.493$	$0$	$2.47547$	Character $\chi_{221}(172, \cdot)$
1-221-221.175-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.175	$0$	✓	✓			$-0.136$	$0$	$1.66446$	Character $\chi_{221}(175, \cdot)$
1-221-221.176-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.176	$0$	✓	✓			$0.0161$	$0$	$1.58235$	Character $\chi_{221}(176, \cdot)$
1-221-221.177-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.177	$0$	✓	✓			$0.416$	$0$	$0.543054$	Character $\chi_{221}(177, \cdot)$
1-221-221.178-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.178	$0$	✓	✓			$0.386$	$0$	$1.78756$	Character $\chi_{221}(178, \cdot)$
1-221-221.179-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.179	$0$	✓	✓			$-0.0363$	$0$	$0.897459$	Character $\chi_{221}(179, \cdot)$
1-221-221.180-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.180	$0$	✓	✓			$-0.302$	$0$	$2.55217$	Character $\chi_{221}(180, \cdot)$
1-221-221.184-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.184	$0$	✓	✓			$-0.193$	$0$	$1.49485$	Character $\chi_{221}(184, \cdot)$
1-221-221.185-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.185	$0$	✓	✓			$-0.386$	$0$	$0.965469$	Character $\chi_{221}(185, \cdot)$
1-221-221.186-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.186	$0$	✓	✓			$0.418$	$0$	$2.60704$	Character $\chi_{221}(186, \cdot)$
1-221-221.190-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.190	$0$	✓	✓			$0.357$	$0$	$2.43980$	Character $\chi_{221}(190, \cdot)$
1-221-221.191-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.191	$0$	✓	✓			$-0.0205$	$0$	$0.641470$	Character $\chi_{221}(191, \cdot)$
1-221-221.193-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.193	$0$	✓	✓			$-0.231$	$0$	$0.849904$	Character $\chi_{221}(193, \cdot)$
1-221-221.197-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.197	$0$	✓	✓			$-0.396$	$0$	$0.764563$	Character $\chi_{221}(197, \cdot)$
1-221-221.20-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.20	$0$	✓	✓			$0.325$	$0$	$0.503636$	Character $\chi_{221}(20, \cdot)$
1-221-221.201-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.201	$0$	✓	✓			$0.0549$	$0$	$0.682723$	Character $\chi_{221}(201, \cdot)$
1-221-221.210-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.210	$0$	✓	✓			$-0.325$	$0$	$2.89513$	Character $\chi_{221}(210, \cdot)$
1-221-221.212-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.212	$0$	✓	✓			$-0.319$	$0$	$0.654862$	Character $\chi_{221}(212, \cdot)$
1-221-221.214-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.214	$0$	✓	✓			$-0.148$	$0$	$1.33496$	Character $\chi_{221}(214, \cdot)$
1-221-221.215-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.215	$0$	✓	✓			$0.193$	$0$	$2.27676$	Character $\chi_{221}(215, \cdot)$
1-221-221.216-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.216	$0$	✓	✓			$0.428$	$0$	$0.263582$	Character $\chi_{221}(216, \cdot)$
1-221-221.217-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.217	$0$	✓	✓			$0.268$	$0$	$2.22710$	Character $\chi_{221}(217, \cdot)$
1-221-221.220-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.220	$0$	✓	✓	✓	✓	$0$	$0$	$1.21257$	Character $\chi_{221}(220, \cdot)$
1-221-221.24-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.24	$0$	✓	✓			$0.136$	$0$	$1.45708$	Character $\chi_{221}(24, \cdot)$
1-221-221.25-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.25	$0$	✓	✓			$0.262$	$0$	$1.15318$	Character $\chi_{221}(25, \cdot)$
1-221-221.28-r0-0-0	$1.02$	$1.02$	$1$	$13 \cdot 17$	221.28	$0$	✓	✓			$-0.148$	$0$	$0.819294$	Character $\chi_{221}(28, \cdot)$

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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.