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 98 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-287-287.100-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.100	$0$	✓	✓	$-0.457$	$0$	$2.61672$	Character $\chi_{287}(100, \cdot)$
1-287-287.101-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.101	$0$	✓	✓	$-0.315$	$0$	$0.111207$	Character $\chi_{287}(101, \cdot)$
1-287-287.102-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.102	$0$	✓	✓	$0.231$	$0$	$1.26235$	Character $\chi_{287}(102, \cdot)$
1-287-287.104-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.104	$0$	✓	✓	$-0.0116$	$0$	$1.15341$	Character $\chi_{287}(104, \cdot)$
1-287-287.107-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.107	$0$	✓	✓	$-0.152$	$0$	$0.804381$	Character $\chi_{287}(107, \cdot)$
1-287-287.108-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.108	$0$	✓	✓	$0.126$	$0$	$0.995587$	Character $\chi_{287}(108, \cdot)$
1-287-287.110-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.110	$0$	✓	✓	$-0.175$	$0$	$1.53165$	Character $\chi_{287}(110, \cdot)$
1-287-287.111-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.111	$0$	✓	✓	$0.338$	$0$	$1.85618$	Character $\chi_{287}(111, \cdot)$
1-287-287.114-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.114	$0$	✓	✓	$0.373$	$0$	$2.34523$	Character $\chi_{287}(114, \cdot)$
1-287-287.117-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.117	$0$	✓	✓	$-0.302$	$0$	$0.557322$	Character $\chi_{287}(117, \cdot)$
1-287-287.12-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.12	$0$	✓	✓	$0.227$	$0$	$1.77337$	Character $\chi_{287}(12, \cdot)$
1-287-287.121-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.121	$0$	✓	✓	$-0.231$	$0$	$0.850855$	Character $\chi_{287}(121, \cdot)$
1-287-287.128-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.128	$0$	✓	✓	$-0.259$	$0$	$1.10282$	Character $\chi_{287}(128, \cdot)$
1-287-287.129-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.129	$0$	✓	✓	$0.00919$	$0$	$1.30995$	Character $\chi_{287}(129, \cdot)$
1-287-287.13-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.13	$0$	✓	✓	$0.497$	$0$	$2.51821$	Character $\chi_{287}(13, \cdot)$
1-287-287.136-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.136	$0$	✓	✓	$-0.311$	$0$	$0.830177$	Character $\chi_{287}(136, \cdot)$
1-287-287.138-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.138	$0$	✓	✓	$-0.0682$	$0$	$1.21634$	Character $\chi_{287}(138, \cdot)$
1-287-287.144-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.144	$0$	✓	✓	$-0.0748$	$0$	$1.19145$	Character $\chi_{287}(144, \cdot)$
1-287-287.145-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.145	$0$	✓	✓	$-0.198$	$0$	$0.823840$	Character $\chi_{287}(145, \cdot)$
1-287-287.150-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.150	$0$	✓	✓	$0.00381$	$0$	$1.28150$	Character $\chi_{287}(150, \cdot)$
1-287-287.152-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.152	$0$	✓	✓	$0.151$	$0$	$0.986563$	Character $\chi_{287}(152, \cdot)$
1-287-287.153-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.153	$0$	✓	✓	$0.0598$	$0$	$2.12258$	Character $\chi_{287}(153, \cdot)$
1-287-287.156-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.156	$0$	✓	✓	$0.112$	$0$	$1.04672$	Character $\chi_{287}(156, \cdot)$
1-287-287.157-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.157	$0$	✓	✓	$0.302$	$0$	$1.78024$	Character $\chi_{287}(157, \cdot)$
1-287-287.16-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.16	$0$	✓	✓	$0.311$	$0$	$1.24370$	Character $\chi_{287}(16, \cdot)$
1-287-287.163-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.163	$0$	✓	✓	$0.426$	$0$	$0.557383$	Character $\chi_{287}(163, \cdot)$
1-287-287.167-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.167	$0$	✓	✓	$-0.136$	$0$	$1.29189$	Character $\chi_{287}(167, \cdot)$
1-287-287.17-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.17	$0$	✓	✓	$-0.151$	$0$	$1.33776$	Character $\chi_{287}(17, \cdot)$
1-287-287.171-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.171	$0$	✓	✓	$0.364$	$0$	$0.183052$	Character $\chi_{287}(171, \cdot)$
1-287-287.172-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.172	$0$	✓	✓	$0.0662$	$0$	$2.05431$	Character $\chi_{287}(172, \cdot)$
1-287-287.178-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.178	$0$	✓	✓	$0.323$	$0$	$0.0259051$	Character $\chi_{287}(178, \cdot)$
1-287-287.18-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.18	$0$	✓	✓	$-0.311$	$0$	$0.914846$	Character $\chi_{287}(18, \cdot)$
1-287-287.181-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.181	$0$	✓	✓	$-0.338$	$0$	$0.601742$	Character $\chi_{287}(181, \cdot)$
1-287-287.184-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.184	$0$	✓	✓	$0.0854$	$0$	$1.76617$	Character $\chi_{287}(184, \cdot)$
1-287-287.188-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.188	$0$	✓	✓	$-0.413$	$0$	$0.0493791$	Character $\chi_{287}(188, \cdot)$
1-287-287.19-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.19	$0$	✓	✓	$0.311$	$0$	$1.80097$	Character $\chi_{287}(19, \cdot)$
1-287-287.192-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.192	$0$	✓	✓	$0.198$	$0$	$1.27360$	Character $\chi_{287}(192, \cdot)$
1-287-287.194-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.194	$0$	✓	✓	$-0.126$	$0$	$0.941620$	Character $\chi_{287}(194, \cdot)$
1-287-287.199-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.199	$0$	✓	✓	$0.0714$	$0$	$2.02869$	Character $\chi_{287}(199, \cdot)$
1-287-287.2-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.2	$0$	✓	✓	$0.0748$	$0$	$1.68994$	Character $\chi_{287}(2, \cdot)$
1-287-287.200-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.200	$0$	✓	✓	$0.0802$	$0$	$0.933238$	Character $\chi_{287}(200, \cdot)$
1-287-287.202-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.202	$0$	✓	✓	$0.190$	$0$	$0.120555$	Character $\chi_{287}(202, \cdot)$
1-287-287.207-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.207	$0$	✓	✓	$0.221$	$0$	$0.867389$	Character $\chi_{287}(207, \cdot)$
1-287-287.208-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.208	$0$	✓	✓	$-0.323$	$0$	$1.79253$	Character $\chi_{287}(208, \cdot)$
1-287-287.214-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.214	$0$	✓	✓	$-0.373$	$0$	$1.32022$	Character $\chi_{287}(214, \cdot)$
1-287-287.216-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.216	$0$	✓	✓	$-0.118$	$0$	$1.44403$	Character $\chi_{287}(216, \cdot)$
1-287-287.220-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.220	$0$	✓	✓	$0.305$	$0$	$1.83293$	Character $\chi_{287}(220, \cdot)$
1-287-287.221-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.221	$0$	✓	✓	$0.457$	$0$	$0.420409$	Character $\chi_{287}(221, \cdot)$
1-287-287.222-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.222	$0$	✓	✓	$0.475$	$0$	$2.63882$	Character $\chi_{287}(222, \cdot)$
1-287-287.226-r0-0-0	$1.33$	$1.33$	$1$	$7 \cdot 41$	287.226	$0$	✓	✓	$-0.221$	$0$	$0.807602$	Character $\chi_{287}(226, \cdot)$

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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.