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 185 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-373-373.10-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.10	$0$	✓	✓	$0.263$	$0$	$1.46826$	Character $\chi_{373}(10, \cdot)$
1-373-373.100-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.100	$0$	✓	✓	$-0.257$	$0$	$0.896649$	Character $\chi_{373}(100, \cdot)$
1-373-373.101-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.101	$0$	✓	✓	$0.0780$	$0$	$1.60273$	Character $\chi_{373}(101, \cdot)$
1-373-373.103-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.103	$0$	✓	✓	$-0.484$	$0$	$0.501864$	Character $\chi_{373}(103, \cdot)$
1-373-373.106-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.106	$0$	✓	✓	$0.448$	$0$	$0.169471$	Character $\chi_{373}(106, \cdot)$
1-373-373.107-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.107	$0$	✓	✓	$0.446$	$0$	$2.25192$	Character $\chi_{373}(107, \cdot)$
1-373-373.108-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.108	$0$	✓	✓	$0.0598$	$0$	$2.08607$	Character $\chi_{373}(108, \cdot)$
1-373-373.109-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.109	$0$	✓	✓	$-0.484$	$0$	$0.583781$	Character $\chi_{373}(109, \cdot)$
1-373-373.111-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.111	$0$	✓	✓	$-0.233$	$0$	$0.615267$	Character $\chi_{373}(111, \cdot)$
1-373-373.112-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.112	$0$	✓	✓	$-0.263$	$0$	$0.396842$	Character $\chi_{373}(112, \cdot)$
1-373-373.114-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.114	$0$	✓	✓	$0.0606$	$0$	$1.42446$	Character $\chi_{373}(114, \cdot)$
1-373-373.115-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.115	$0$	✓	✓	$-0.300$	$0$	$0.387850$	Character $\chi_{373}(115, \cdot)$
1-373-373.116-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.116	$0$	✓	✓	$-0.184$	$0$	$1.50688$	Character $\chi_{373}(116, \cdot)$
1-373-373.117-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.117	$0$	✓	✓	$0.209$	$0$	$1.60622$	Character $\chi_{373}(117, \cdot)$
1-373-373.119-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.119	$0$	✓	✓	$0.397$	$0$	$2.41596$	Character $\chi_{373}(119, \cdot)$
1-373-373.12-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.12	$0$	✓	✓	$-0.0639$	$0$	$1.27812$	Character $\chi_{373}(12, \cdot)$
1-373-373.120-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.120	$0$	✓	✓	$0.497$	$0$	$2.44225$	Character $\chi_{373}(120, \cdot)$
1-373-373.121-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.121	$0$	✓	✓	$-0.398$	$0$	$0.193023$	Character $\chi_{373}(121, \cdot)$
1-373-373.122-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.122	$0$	✓	✓	$-0.120$	$0$	$0.240307$	Character $\chi_{373}(122, \cdot)$
1-373-373.123-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.123	$0$	✓	✓	$-0.0656$	$0$	$1.60036$	Character $\chi_{373}(123, \cdot)$
1-373-373.124-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.124	$0$	✓	✓	$0.203$	$0$	$1.77092$	Character $\chi_{373}(124, \cdot)$
1-373-373.13-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.13	$0$	✓	✓	$-0.0768$	$0$	$0.715943$	Character $\chi_{373}(13, \cdot)$
1-373-373.130-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.130	$0$	✓	✓	$0.244$	$0$	$1.57512$	Character $\chi_{373}(130, \cdot)$
1-373-373.134-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.134	$0$	✓	✓	$0.484$	$0$	$1.92625$	Character $\chi_{373}(134, \cdot)$
1-373-373.137-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.137	$0$	✓	✓	$-0.417$	$0$	$0.247319$	Character $\chi_{373}(137, \cdot)$
1-373-373.138-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.138	$0$	✓	✓	$-0.198$	$0$	$0.733990$	Character $\chi_{373}(138, \cdot)$
1-373-373.144-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.144	$0$	✓	✓	$0.387$	$0$	$1.76307$	Character $\chi_{373}(144, \cdot)$
1-373-373.147-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.147	$0$	✓	✓	$-0.174$	$0$	$0.923494$	Character $\chi_{373}(147, \cdot)$
1-373-373.148-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.148	$0$	✓	✓	$0.455$	$0$	$0.283498$	Character $\chi_{373}(148, \cdot)$
1-373-373.152-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.152	$0$	✓	✓	$0.292$	$0$	$1.85579$	Character $\chi_{373}(152, \cdot)$
1-373-373.153-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.153	$0$	✓	✓	$-0.309$	$0$	$0.224329$	Character $\chi_{373}(153, \cdot)$
1-373-373.154-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.154	$0$	✓	✓	$0.484$	$0$	$2.14899$	Character $\chi_{373}(154, \cdot)$
1-373-373.156-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.156	$0$	✓	✓	$-0.183$	$0$	$1.26132$	Character $\chi_{373}(156, \cdot)$
1-373-373.158-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.158	$0$	✓	✓	$-0.272$	$0$	$0.163737$	Character $\chi_{373}(158, \cdot)$
1-373-373.16-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.16	$0$	✓	✓	$-0.0763$	$0$	$1.31083$	Character $\chi_{373}(16, \cdot)$
1-373-373.160-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.160	$0$	✓	✓	$0.0431$	$0$	$0.782534$	Character $\chi_{373}(160, \cdot)$
1-373-373.163-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.163	$0$	✓	✓	$-0.397$	$0$	$0.225461$	Character $\chi_{373}(163, \cdot)$
1-373-373.164-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.164	$0$	✓	✓	$0.184$	$0$	$1.40054$	Character $\chi_{373}(164, \cdot)$
1-373-373.165-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.165	$0$	✓	✓	$0.113$	$0$	$1.81982$	Character $\chi_{373}(165, \cdot)$
1-373-373.169-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.169	$0$	✓	✓	$-0.142$	$0$	$0.698319$	Character $\chi_{373}(169, \cdot)$
1-373-373.17-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.17	$0$	✓	✓	$0.249$	$0$	$1.23538$	Character $\chi_{373}(17, \cdot)$
1-373-373.170-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.170	$0$	✓	✓	$0.00266$	$0$	$0.869048$	Character $\chi_{373}(170, \cdot)$
1-373-373.175-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.175	$0$	✓	✓	$-0.0845$	$0$	$0.838204$	Character $\chi_{373}(175, \cdot)$
1-373-373.177-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.177	$0$	✓	✓	$-0.272$	$0$	$0.564603$	Character $\chi_{373}(177, \cdot)$
1-373-373.179-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.179	$0$	✓	✓	$-0.236$	$0$	$1.13882$	Character $\chi_{373}(179, \cdot)$
1-373-373.181-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.181	$0$	✓	✓	$0.433$	$0$	$2.18919$	Character $\chi_{373}(181, \cdot)$
1-373-373.184-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.184	$0$	✓	✓	$-0.242$	$0$	$0.882287$	Character $\chi_{373}(184, \cdot)$
1-373-373.189-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.189	$0$	✓	✓	$0.0294$	$0$	$0.523758$	Character $\chi_{373}(189, \cdot)$
1-373-373.192-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.192	$0$	✓	✓	$-0.200$	$0$	$1.07345$	Character $\chi_{373}(192, \cdot)$
1-373-373.194-r0-0-0	$1.73$	$1.73$	$1$	$373$	373.194	$0$	✓	✓	$0.288$	$0$	$1.96297$	Character $\chi_{373}(194, \cdot)$

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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.