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 55 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
1-113-113.100-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.100	$0$	✓	✓			$-0.385$	$0$	$0.392941$	Character $\chi_{113}(100, \cdot)$
1-113-113.102-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.102	$0$	✓	✓			$0.0734$	$0$	$2.59427$	Character $\chi_{113}(102, \cdot)$
1-113-113.104-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.104	$0$	✓	✓			$0.343$	$0$	$2.01539$	Character $\chi_{113}(104, \cdot)$
1-113-113.105-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.105	$0$	✓	✓			$-0.320$	$0$	$1.38817$	Character $\chi_{113}(105, \cdot)$
1-113-113.106-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.106	$0$	✓	✓			$0.392$	$0$	$0.250470$	Character $\chi_{113}(106, \cdot)$
1-113-113.109-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.109	$0$	✓	✓			$-0.405$	$0$	$0.583025$	Character $\chi_{113}(109, \cdot)$
1-113-113.11-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.11	$0$	✓	✓			$-0.284$	$0$	$1.40108$	Character $\chi_{113}(11, \cdot)$
1-113-113.111-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.111	$0$	✓	✓			$0.115$	$0$	$1.12914$	Character $\chi_{113}(111, \cdot)$
1-113-113.112-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.112	$0$	✓	✓	✓	✓	$0$	$0$	$1.62199$	Character $\chi_{113}(112, \cdot)$
1-113-113.13-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.13	$0$	✓	✓			$-0.444$	$0$	$2.75499$	Character $\chi_{113}(13, \cdot)$
1-113-113.14-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.14	$0$	✓	✓			$0.320$	$0$	$2.72303$	Character $\chi_{113}(14, \cdot)$
1-113-113.15-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.15	$0$	✓	✓			$-0.0677$	$0$	$2.03889$	Character $\chi_{113}(15, \cdot)$
1-113-113.16-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.16	$0$	✓	✓			$-0.392$	$0$	$3.35230$	Character $\chi_{113}(16, \cdot)$
1-113-113.18-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.18	$0$	✓	✓			$0.239$	$0$	$2.07103$	Character $\chi_{113}(18, \cdot)$
1-113-113.2-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.2	$0$	✓	✓			$0.182$	$0$	$1.74761$	Character $\chi_{113}(2, \cdot)$
1-113-113.22-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.22	$0$	✓	✓			$-0.0472$	$0$	$1.17313$	Character $\chi_{113}(22, \cdot)$
1-113-113.25-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.25	$0$	✓	✓			$-0.343$	$0$	$0.949567$	Character $\chi_{113}(25, \cdot)$
1-113-113.26-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.26	$0$	✓	✓			$0.385$	$0$	$2.62200$	Character $\chi_{113}(26, \cdot)$
1-113-113.28-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.28	$0$	✓	✓			$0.405$	$0$	$1.97509$	Character $\chi_{113}(28, \cdot)$
1-113-113.30-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.30	$0$	✓	✓			$0.0630$	$0$	$1.51694$	Character $\chi_{113}(30, \cdot)$
1-113-113.31-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.31	$0$	✓	✓			$0.198$	$0$	$1.32065$	Character $\chi_{113}(31, \cdot)$
1-113-113.32-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.32	$0$	✓	✓			$-0.131$	$0$	$0.557077$	Character $\chi_{113}(32, \cdot)$
1-113-113.36-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.36	$0$	✓	✓			$0.0472$	$0$	$1.97291$	Character $\chi_{113}(36, \cdot)$
1-113-113.4-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.4	$0$	✓	✓			$-0.130$	$0$	$1.02861$	Character $\chi_{113}(4, \cdot)$
1-113-113.41-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.41	$0$	✓	✓			$-0.0734$	$0$	$1.64593$	Character $\chi_{113}(41, \cdot)$
1-113-113.44-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.44	$0$	✓	✓			$-0.239$	$0$	$1.05691$	Character $\chi_{113}(44, \cdot)$
1-113-113.49-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.49	$0$	✓	✓			$-0.0630$	$0$	$1.79695$	Character $\chi_{113}(49, \cdot)$
1-113-113.50-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.50	$0$	✓	✓			$-0.0252$	$0$	$1.53140$	Character $\chi_{113}(50, \cdot)$
1-113-113.51-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.51	$0$	✓	✓			$0.0954$	$0$	$1.94729$	Character $\chi_{113}(51, \cdot)$
1-113-113.52-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.52	$0$	✓	✓			$0.0252$	$0$	$1.99031$	Character $\chi_{113}(52, \cdot)$
1-113-113.53-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.53	$0$	✓	✓			$0.131$	$0$	$1.25134$	Character $\chi_{113}(53, \cdot)$
1-113-113.56-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.56	$0$	✓	✓			$-0.115$	$0$	$1.10018$	Character $\chi_{113}(56, \cdot)$
1-113-113.57-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.57	$0$	✓	✓			$-0.182$	$0$	$1.86968$	Character $\chi_{113}(57, \cdot)$
1-113-113.60-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.60	$0$	✓	✓			$-0.104$	$0$	$1.62335$	Character $\chi_{113}(60, \cdot)$
1-113-113.61-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.61	$0$	✓	✓			$-0.202$	$0$	$1.71782$	Character $\chi_{113}(61, \cdot)$
1-113-113.62-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.62	$0$	✓	✓			$-0.198$	$0$	$1.08232$	Character $\chi_{113}(62, \cdot)$
1-113-113.63-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.63	$0$	✓	✓			$0.202$	$0$	$2.77922$	Character $\chi_{113}(63, \cdot)$
1-113-113.64-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.64	$0$	✓	✓			$0.0398$	$0$	$1.69765$	Character $\chi_{113}(64, \cdot)$
1-113-113.69-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.69	$0$	✓	✓			$0.171$	$0$	$1.56980$	Character $\chi_{113}(69, \cdot)$
1-113-113.7-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.7	$0$	✓	✓			$-0.170$	$0$	$1.84042$	Character $\chi_{113}(7, \cdot)$
1-113-113.72-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.72	$0$	✓	✓			$0.284$	$0$	$2.67420$	Character $\chi_{113}(72, \cdot)$
1-113-113.77-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.77	$0$	✓	✓			$-0.486$	$0$	$1.07808$	Character $\chi_{113}(77, \cdot)$
1-113-113.8-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.8	$0$	✓	✓			$-0.354$	$0$	$0.743223$	Character $\chi_{113}(8, \cdot)$
1-113-113.81-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.81	$0$	✓	✓			$0.104$	$0$	$1.82447$	Character $\chi_{113}(81, \cdot)$
1-113-113.82-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.82	$0$	✓	✓			$-0.0954$	$0$	$0.951959$	Character $\chi_{113}(82, \cdot)$
1-113-113.83-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.83	$0$	✓	✓			$-0.0398$	$0$	$0.611910$	Character $\chi_{113}(83, \cdot)$
1-113-113.85-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.85	$0$	✓	✓			$0.130$	$0$	$1.76259$	Character $\chi_{113}(85, \cdot)$
1-113-113.87-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.87	$0$	✓	✓			$0.444$	$0$	$0.506416$	Character $\chi_{113}(87, \cdot)$
1-113-113.88-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.88	$0$	✓	✓			$-0.332$	$0$	$1.18348$	Character $\chi_{113}(88, \cdot)$
1-113-113.9-r0-0-0	$0.524$	$0.524$	$1$	$113$	113.9	$0$	✓	✓			$0.332$	$0$	$2.52807$	Character $\chi_{113}(9, \cdot)$

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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.