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 138 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-277-277.101-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.101	$1$	✓	✓	$0.177$	$0$	$0.380807$	Character $\chi_{277}(101, \cdot)$
1-277-277.103-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.103	$1$	✓	✓	$-0.0229$	$0$	$0.740231$	Character $\chi_{277}(103, \cdot)$
1-277-277.104-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.104	$1$	✓	✓	$-0.182$	$0$	$0.273508$	Character $\chi_{277}(104, \cdot)$
1-277-277.105-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.105	$1$	✓	✓	$0.417$	$0$	$0.265282$	Character $\chi_{277}(105, \cdot)$
1-277-277.107-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.107	$1$	✓	✓	$0.275$	$0$	$1.33095$	Character $\chi_{277}(107, \cdot)$
1-277-277.109-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.109	$1$	✓	✓	$-0.300$	$0$	$0.107947$	Character $\chi_{277}(109, \cdot)$
1-277-277.11-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.11	$1$	✓	✓	$0.0466$	$0$	$1.24755$	Character $\chi_{277}(11, \cdot)$
1-277-277.110-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.110	$1$	✓	✓	$0.262$	$0$	$0.819464$	Character $\chi_{277}(110, \cdot)$
1-277-277.111-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.111	$1$	✓	✓	$0.0982$	$0$	$0.919715$	Character $\chi_{277}(111, \cdot)$
1-277-277.114-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.114	$1$	✓	✓	$-0.267$	$0$	$0.995343$	Character $\chi_{277}(114, \cdot)$
1-277-277.115-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.115	$1$	✓	✓	$-0.324$	$0$	$0.0852618$	Character $\chi_{277}(115, \cdot)$
1-277-277.118-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.118	$1$	✓	✓	$-0.426$	$0$	$1.31938$	Character $\chi_{277}(118, \cdot)$
1-277-277.119-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.119	$1$	✓	✓	$0.461$	$0$	$1.65438$	Character $\chi_{277}(119, \cdot)$
1-277-277.124-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.124	$1$	✓	✓	$-0.417$	$0$	$1.97073$	Character $\chi_{277}(124, \cdot)$
1-277-277.125-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.125	$1$	✓	✓	$0.145$	$0$	$1.62604$	Character $\chi_{277}(125, \cdot)$
1-277-277.126-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.126	$1$	✓	✓	$-0.0466$	$0$	$0.206771$	Character $\chi_{277}(126, \cdot)$
1-277-277.127-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.127	$1$	✓	✓	$-0.223$	$0$	$0.968215$	Character $\chi_{277}(127, \cdot)$
1-277-277.128-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.128	$1$	✓	✓	$-0.0666$	$0$	$1.29045$	Character $\chi_{277}(128, \cdot)$
1-277-277.129-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.129	$1$	✓	✓	$0.456$	$0$	$1.23916$	Character $\chi_{277}(129, \cdot)$
1-277-277.132-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.132	$1$	✓	✓	$0.379$	$0$	$1.59977$	Character $\chi_{277}(132, \cdot)$
1-277-277.134-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.134	$1$	✓	✓	$0.411$	$0$	$1.73373$	Character $\chi_{277}(134, \cdot)$
1-277-277.135-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.135	$1$	✓	✓	$-0.267$	$0$	$1.20199$	Character $\chi_{277}(135, \cdot)$
1-277-277.137-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.137	$1$	✓	✓	$-0.341$	$0$	$0.238701$	Character $\chi_{277}(137, \cdot)$
1-277-277.138-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.138	$1$	✓	✓	$-0.0933$	$0$	$0.662286$	Character $\chi_{277}(138, \cdot)$
1-277-277.139-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.139	$1$	✓	✓	$-0.337$	$0$	$0.558138$	Character $\chi_{277}(139, \cdot)$
1-277-277.14-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.14	$1$	✓	✓	$0.276$	$0$	$1.74836$	Character $\chi_{277}(14, \cdot)$
1-277-277.140-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.140	$1$	✓	✓	$-0.134$	$0$	$1.38267$	Character $\chi_{277}(140, \cdot)$
1-277-277.142-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.142	$1$	✓	✓	$-0.461$	$0$	$0.257639$	Character $\chi_{277}(142, \cdot)$
1-277-277.143-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.143	$1$	✓	✓	$-0.119$	$0$	$1.42901$	Character $\chi_{277}(143, \cdot)$
1-277-277.145-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.145	$1$	✓	✓	$0.0666$	$0$	$1.66609$	Character $\chi_{277}(145, \cdot)$
1-277-277.148-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.148	$1$	✓	✓	$-0.121$	$0$	$0.664031$	Character $\chi_{277}(148, \cdot)$
1-277-277.149-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.149	$1$	✓	✓	$-0.379$	$0$	$0.364990$	Character $\chi_{277}(149, \cdot)$
1-277-277.15-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.15	$1$	✓	✓	$0.189$	$0$	$0.101943$	Character $\chi_{277}(15, \cdot)$
1-277-277.150-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.150	$1$	✓	✓	$-0.195$	$0$	$0.439007$	Character $\chi_{277}(150, \cdot)$
1-277-277.151-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.151	$1$	✓	✓	$-0.260$	$0$	$0.173243$	Character $\chi_{277}(151, \cdot)$
1-277-277.152-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.152	$1$	✓	✓	$-0.463$	$0$	$2.44741$	Character $\chi_{277}(152, \cdot)$
1-277-277.153-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.153	$1$	✓	✓	$-0.388$	$0$	$2.07914$	Character $\chi_{277}(153, \cdot)$
1-277-277.158-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.158	$1$	✓	✓	$0.267$	$0$	$1.80666$	Character $\chi_{277}(158, \cdot)$
1-277-277.159-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.159	$1$	✓	✓	$-0.0280$	$0$	$1.29459$	Character $\chi_{277}(159, \cdot)$
1-277-277.162-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.162	$1$	✓	✓	$0.0960$	$0$	$0.946011$	Character $\chi_{277}(162, \cdot)$
1-277-277.163-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.163	$1$	✓	✓	$-0.464$	$0$	$0.0568305$	Character $\chi_{277}(163, \cdot)$
1-277-277.166-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.166	$1$	✓	✓	$0.203$	$0$	$1.31363$	Character $\chi_{277}(166, \cdot)$
1-277-277.167-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.167	$1$	✓	✓	$0.464$	$0$	$2.04703$	Character $\chi_{277}(167, \cdot)$
1-277-277.168-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.168	$1$	✓	✓	$0.0676$	$0$	$0.756942$	Character $\chi_{277}(168, \cdot)$
1-277-277.17-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.17	$1$	✓	✓	$0.464$	$0$	$2.21162$	Character $\chi_{277}(17, \cdot)$
1-277-277.170-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.170	$1$	✓	✓	$-0.230$	$0$	$1.13838$	Character $\chi_{277}(170, \cdot)$
1-277-277.172-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.172	$1$	✓	✓	$0.388$	$0$	$0.414223$	Character $\chi_{277}(172, \cdot)$
1-277-277.173-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.173	$1$	✓	✓	$0.366$	$0$	$0.155688$	Character $\chi_{277}(173, \cdot)$
1-277-277.174-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.174	$1$	✓	✓	$-0.0996$	$0$	$0.657532$	Character $\chi_{277}(174, \cdot)$
1-277-277.176-r1-0-0	$29.7$	$29.7$	$1$	$277$	277.176	$1$	✓	✓	$0.387$	$0$	$1.92216$	Character $\chi_{277}(176, \cdot)$

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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.