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

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-5077-5077.10-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.10	$0$	✓	✓	$0.486$	$0$	$1.43348$	Character $\chi_{5077}(10, \cdot)$
1-5077-5077.100-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.100	$0$	✓	✓	$0.354$	$0$	$1.21307$	Character $\chi_{5077}(100, \cdot)$
1-5077-5077.1000-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1000	$0$	✓	✓	$-0.460$	$0$	$0.882397$	Character $\chi_{5077}(1000, \cdot)$
1-5077-5077.1001-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1001	$0$	✓	✓	$0.185$	$0$	$0.446369$	Character $\chi_{5077}(1001, \cdot)$
1-5077-5077.1002-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1002	$0$	✓	✓	$0.380$	$0$	$0.664219$	Character $\chi_{5077}(1002, \cdot)$
1-5077-5077.1005-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1005	$0$	✓	✓	$0.499$	$0$	$0.383750$	Character $\chi_{5077}(1005, \cdot)$
1-5077-5077.1007-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1007	$0$	✓	✓	$0.484$	$0$	$0.151300$	Character $\chi_{5077}(1007, \cdot)$
1-5077-5077.1008-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1008	$0$	✓	✓	$-0.0278$	$0$	$0.990566$	Character $\chi_{5077}(1008, \cdot)$
1-5077-5077.1009-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1009	$0$	✓	✓	$0.0533$	$0$	$0.591989$	Character $\chi_{5077}(1009, \cdot)$
1-5077-5077.1012-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1012	$0$	✓	✓	$-0.242$	$0$	$0.128127$	Character $\chi_{5077}(1012, \cdot)$
1-5077-5077.1015-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1015	$0$	✓	✓	$0.134$	$0$	$0.877383$	Character $\chi_{5077}(1015, \cdot)$
1-5077-5077.1017-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1017	$0$	✓	✓	$0.460$	$0$	$0.374200$	Character $\chi_{5077}(1017, \cdot)$
1-5077-5077.1018-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1018	$0$	✓	✓	$0.464$	$0$	$0.884290$	Character $\chi_{5077}(1018, \cdot)$
1-5077-5077.1019-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1019	$0$	✓	✓	$0.491$	$0$	$1.33686$	Character $\chi_{5077}(1019, \cdot)$
1-5077-5077.102-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.102	$0$	✓	✓	$-0.380$	$0$	$0.0735853$	Character $\chi_{5077}(102, \cdot)$
1-5077-5077.1020-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1020	$0$	✓	✓	$0.321$	$0$	$1.10310$	Character $\chi_{5077}(1020, \cdot)$
1-5077-5077.1022-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1022	$0$	✓	✓	$-0.233$	$0$	$0.535694$	Character $\chi_{5077}(1022, \cdot)$
1-5077-5077.1023-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1023	$0$	✓	✓	$-0.145$	$0$	$1.15554$	Character $\chi_{5077}(1023, \cdot)$
1-5077-5077.1024-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1024	$0$	✓	✓	$-0.266$	$0$	$0.536960$	Character $\chi_{5077}(1024, \cdot)$
1-5077-5077.1029-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1029	$0$	✓	✓	$-0.317$	$0$	$0.565692$	Character $\chi_{5077}(1029, \cdot)$
1-5077-5077.103-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.103	$0$	✓	✓	$-0.247$	$0$	$0.816989$	Character $\chi_{5077}(103, \cdot)$
1-5077-5077.1030-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1030	$0$	✓	✓	$0.271$	$0$	$1.25532$	Character $\chi_{5077}(1030, \cdot)$
1-5077-5077.1032-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1032	$0$	✓	✓	$0.307$	$0$	$0.198989$	Character $\chi_{5077}(1032, \cdot)$
1-5077-5077.1034-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1034	$0$	✓	✓	$-0.376$	$0$	$0.0122545$	Character $\chi_{5077}(1034, \cdot)$
1-5077-5077.1035-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1035	$0$	✓	✓	$-0.00934$	$0$	$0.807703$	Character $\chi_{5077}(1035, \cdot)$
1-5077-5077.1039-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1039	$0$	✓	✓	$-0.0233$	$0$	$0.249395$	Character $\chi_{5077}(1039, \cdot)$
1-5077-5077.104-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.104	$0$	✓	✓	$0.139$	$0$	$0.552464$	Character $\chi_{5077}(104, \cdot)$
1-5077-5077.1040-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1040	$0$	✓	✓	$0.315$	$0$	$0.983022$	Character $\chi_{5077}(1040, \cdot)$
1-5077-5077.1041-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1041	$0$	✓	✓	$0.267$	$0$	$0.0655376$	Character $\chi_{5077}(1041, \cdot)$
1-5077-5077.1045-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1045	$0$	✓	✓	$0.342$	$0$	$1.05206$	Character $\chi_{5077}(1045, \cdot)$
1-5077-5077.1046-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1046	$0$	✓	✓	$-0.400$	$0$	$1.11068$	Character $\chi_{5077}(1046, \cdot)$
1-5077-5077.1047-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1047	$0$	✓	✓	$-0.150$	$0$	$0.536174$	Character $\chi_{5077}(1047, \cdot)$
1-5077-5077.1049-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1049	$0$	✓	✓	$0.290$	$0$	$1.25244$	Character $\chi_{5077}(1049, \cdot)$
1-5077-5077.1051-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1051	$0$	✓	✓	$0.489$	$0$	$0.250418$	Character $\chi_{5077}(1051, \cdot)$
1-5077-5077.1056-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1056	$0$	✓	✓	$-0.0350$	$0$	$1.53701$	Character $\chi_{5077}(1056, \cdot)$
1-5077-5077.1057-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1057	$0$	✓	✓	$0.181$	$0$	$0.692984$	Character $\chi_{5077}(1057, \cdot)$
1-5077-5077.1059-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1059	$0$	✓	✓	$-0.422$	$0$	$0.170023$	Character $\chi_{5077}(1059, \cdot)$
1-5077-5077.1068-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1068	$0$	✓	✓	$-0.101$	$0$	$0.391624$	Character $\chi_{5077}(1068, \cdot)$
1-5077-5077.1069-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1069	$0$	✓	✓	$-0.307$	$0$	$0.771843$	Character $\chi_{5077}(1069, \cdot)$
1-5077-5077.107-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.107	$0$	✓	✓	$0.117$	$0$	$0.664550$	Character $\chi_{5077}(107, \cdot)$
1-5077-5077.1070-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1070	$0$	✓	✓	$-0.186$	$0$	$0.500602$	Character $\chi_{5077}(1070, \cdot)$
1-5077-5077.1073-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1073	$0$	✓	✓	$0.146$	$0$	$1.21223$	Character $\chi_{5077}(1073, \cdot)$
1-5077-5077.1076-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1076	$0$	✓	✓	$-0.417$	$0$	$0.0615546$	Character $\chi_{5077}(1076, \cdot)$
1-5077-5077.1077-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1077	$0$	✓	✓	$-0.222$	$0$	$0.751055$	Character $\chi_{5077}(1077, \cdot)$
1-5077-5077.1078-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1078	$0$	✓	✓	$0.184$	$0$	$1.08590$	Character $\chi_{5077}(1078, \cdot)$
1-5077-5077.1079-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1079	$0$	✓	✓	$0.149$	$0$	$0.695632$	Character $\chi_{5077}(1079, \cdot)$
1-5077-5077.108-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.108	$0$	✓	✓	$0.0320$	$0$	$0.906009$	Character $\chi_{5077}(108, \cdot)$
1-5077-5077.1080-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1080	$0$	✓	✓	$0.324$	$0$	$1.35260$	Character $\chi_{5077}(1080, \cdot)$
1-5077-5077.1082-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1082	$0$	✓	✓	$0.424$	$0$	$1.05261$	Character $\chi_{5077}(1082, \cdot)$
1-5077-5077.1083-r0-0-0	$23.5$	$23.5$	$1$	$5077$	5077.1083	$0$	✓	✓	$0.276$	$0$	$1.38786$	Character $\chi_{5077}(1083, \cdot)$

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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.