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 (37 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
1-119-119.101-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.101	$1$	✓	✓			$-0.146$	$0$	$0.367484$	Character $\chi_{119}(101, \cdot)$
1-119-119.104-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.104	$1$	✓	✓			$0.242$	$0$	$1.02842$	Character $\chi_{119}(104, \cdot)$
1-119-119.107-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.107	$1$	✓	✓			$0.233$	$0$	$1.93143$	Character $\chi_{119}(107, \cdot)$
1-119-119.109-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.109	$1$	✓	✓			$-0.233$	$0$	$0.746558$	Character $\chi_{119}(109, \cdot)$
1-119-119.11-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.11	$1$	✓	✓			$-0.175$	$0$	$0.435027$	Character $\chi_{119}(11, \cdot)$
1-119-119.110-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.110	$1$	✓	✓			$0.283$	$0$	$1.02571$	Character $\chi_{119}(110, \cdot)$
1-119-119.111-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.111	$1$	✓	✓			$-0.242$	$0$	$0.969200$	Character $\chi_{119}(111, \cdot)$
1-119-119.114-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.114	$1$	✓	✓			$0.173$	$0$	$1.89935$	Character $\chi_{119}(114, \cdot)$
1-119-119.115-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.115	$1$	✓	✓			$0.248$	$0$	$1.76711$	Character $\chi_{119}(115, \cdot)$
1-119-119.116-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.116	$1$	✓	✓			$-0.344$	$0$	$2.79917$	Character $\chi_{119}(116, \cdot)$
1-119-119.117-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.117	$1$	✓	✓			$0.00940$	$0$	$1.66964$	Character $\chi_{119}(117, \cdot)$
1-119-119.118-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.118	$1$	✓	✓	✓	✓	$0$	$0$	$1.98378$	Character $\chi_{119}(118, \cdot)$
1-119-119.13-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.13	$1$	✓	✓			$0.394$	$0$	$0.272423$	Character $\chi_{119}(13, \cdot)$
1-119-119.19-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.19	$1$	✓	✓			$0.389$	$0$	$0.350221$	Character $\chi_{119}(19, \cdot)$
1-119-119.23-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.23	$1$	✓	✓			$-0.332$	$0$	$0.391700$	Character $\chi_{119}(23, \cdot)$
1-119-119.26-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.26	$1$	✓	✓			$-0.0961$	$0$	$1.02326$	Character $\chi_{119}(26, \cdot)$
1-119-119.33-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.33	$1$	✓	✓			$0.146$	$0$	$1.07786$	Character $\chi_{119}(33, \cdot)$
1-119-119.37-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.37	$1$	✓	✓			$-0.147$	$0$	$0.610097$	Character $\chi_{119}(37, \cdot)$
1-119-119.38-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.38	$1$	✓	✓			$0.459$	$0$	$0.608195$	Character $\chi_{119}(38, \cdot)$
1-119-119.39-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.39	$1$	✓	✓			$-0.286$	$0$	$1.12447$	Character $\chi_{119}(39, \cdot)$
1-119-119.44-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.44	$1$	✓	✓			$0.346$	$0$	$0.920305$	Character $\chi_{119}(44, \cdot)$
1-119-119.46-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.46	$1$	✓	✓			$-0.346$	$0$	$0.252771$	Character $\chi_{119}(46, \cdot)$
1-119-119.47-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.47	$1$	✓	✓			$-0.459$	$0$	$2.71334$	Character $\chi_{119}(47, \cdot)$
1-119-119.55-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.55	$1$	✓	✓			$-0.394$	$0$	$2.25624$	Character $\chi_{119}(55, \cdot)$
1-119-119.58-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.58	$1$	✓	✓			$0.286$	$0$	$1.65407$	Character $\chi_{119}(58, \cdot)$
1-119-119.59-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.59	$1$	✓	✓			$-0.00940$	$0$	$1.50730$	Character $\chi_{119}(59, \cdot)$
1-119-119.65-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.65	$1$	✓	✓			$0.175$	$0$	$1.44677$	Character $\chi_{119}(65, \cdot)$
1-119-119.66-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.66	$1$	✓	✓			$-0.283$	$0$	$0.592002$	Character $\chi_{119}(66, \cdot)$
1-119-119.74-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.74	$1$	✓	✓			$0.147$	$0$	$1.22307$	Character $\chi_{119}(74, \cdot)$
1-119-119.76-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.76	$1$	✓	✓			$0.137$	$0$	$1.60008$	Character $\chi_{119}(76, \cdot)$
1-119-119.79-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.79	$1$	✓	✓			$0.344$	$0$	$0.506743$	Character $\chi_{119}(79, \cdot)$
1-119-119.83-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.83	$1$	✓	✓			$-0.137$	$0$	$0.497859$	Character $\chi_{119}(83, \cdot)$
1-119-119.87-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.87	$1$	✓	✓			$0.0961$	$0$	$1.51299$	Character $\chi_{119}(87, \cdot)$
1-119-119.88-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.88	$1$	✓	✓			$0.332$	$0$	$1.40771$	Character $\chi_{119}(88, \cdot)$
1-119-119.89-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.89	$1$	✓	✓			$-0.248$	$0$	$0.280576$	Character $\chi_{119}(89, \cdot)$
1-119-119.94-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.94	$1$	✓	✓			$-0.389$	$0$	$3.00986$	Character $\chi_{119}(94, \cdot)$
1-119-119.95-r1-0-0	$12.7$	$12.7$	$1$	$7 \cdot 17$	119.95	$1$	✓	✓			$-0.173$	$0$	$1.36330$	Character $\chi_{119}(95, \cdot)$

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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.