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 1600 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-41e2-1681.10-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.10	$0$	✓	✓	$0.110$	$0$	$1.34622$	Character $\chi_{1681}(10, \cdot)$
1-41e2-1681.100-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.100	$0$	✓	✓	$0.230$	$0$	$1.49700$	Character $\chi_{1681}(100, \cdot)$
1-41e2-1681.1000-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1000	$0$	✓	✓	$0.0138$	$0$	$1.12286$	Character $\chi_{1681}(1000, \cdot)$
1-41e2-1681.1002-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1002	$0$	✓	✓	$0.000594$	$0$	$0.796922$	Character $\chi_{1681}(1002, \cdot)$
1-41e2-1681.1004-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1004	$0$	✓	✓	$0.333$	$0$	$0.960752$	Character $\chi_{1681}(1004, \cdot)$
1-41e2-1681.1005-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1005	$0$	✓	✓	$-0.231$	$0$	$0.0714787$	Character $\chi_{1681}(1005, \cdot)$
1-41e2-1681.1007-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1007	$0$	✓	✓	$0.0383$	$0$	$1.20180$	Character $\chi_{1681}(1007, \cdot)$
1-41e2-1681.1009-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1009	$0$	✓	✓	$0.000594$	$0$	$1.40099$	Character $\chi_{1681}(1009, \cdot)$
1-41e2-1681.1015-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1015	$0$	✓	✓	$-0.378$	$0$	$1.85295$	Character $\chi_{1681}(1015, \cdot)$
1-41e2-1681.1016-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1016	$0$	✓	✓	$0.428$	$0$	$1.45182$	Character $\chi_{1681}(1016, \cdot)$
1-41e2-1681.1017-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1017	$0$	✓	✓	$-0.466$	$0$	$0.625100$	Character $\chi_{1681}(1017, \cdot)$
1-41e2-1681.102-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.102	$0$	✓	✓	$0.223$	$0$	$0.830149$	Character $\chi_{1681}(102, \cdot)$
1-41e2-1681.1020-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1020	$0$	✓	✓	$0.271$	$0$	$0.331027$	Character $\chi_{1681}(1020, \cdot)$
1-41e2-1681.1021-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1021	$0$	✓	✓	$0.224$	$0$	$0.279331$	Character $\chi_{1681}(1021, \cdot)$
1-41e2-1681.1023-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1023	$0$	✓	✓	$-0.333$	$0$	$0.276510$	Character $\chi_{1681}(1023, \cdot)$
1-41e2-1681.1024-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1024	$0$	✓	✓	$0.280$	$0$	$0.859686$	Character $\chi_{1681}(1024, \cdot)$
1-41e2-1681.1026-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1026	$0$	✓	✓	$-0.280$	$0$	$0.971974$	Character $\chi_{1681}(1026, \cdot)$
1-41e2-1681.1027-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1027	$0$	✓	✓	$0.231$	$0$	$0.642535$	Character $\chi_{1681}(1027, \cdot)$
1-41e2-1681.1029-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1029	$0$	✓	✓	$0.000594$	$0$	$0.602811$	Character $\chi_{1681}(1029, \cdot)$
1-41e2-1681.103-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.103	$0$	✓	✓	$-0.0925$	$0$	$0.625742$	Character $\chi_{1681}(103, \cdot)$
1-41e2-1681.1030-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1030	$0$	✓	✓	$0.000594$	$0$	$0.278927$	Character $\chi_{1681}(1030, \cdot)$
1-41e2-1681.1033-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1033	$0$	✓	✓	$0.0472$	$0$	$0.662801$	Character $\chi_{1681}(1033, \cdot)$
1-41e2-1681.1034-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1034	$0$	✓	✓	$0.0880$	$0$	$1.20437$	Character $\chi_{1681}(1034, \cdot)$
1-41e2-1681.1035-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1035	$0$	✓	✓	$-0.461$	$0$	$0.454540$	Character $\chi_{1681}(1035, \cdot)$
1-41e2-1681.1041-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1041	$0$	✓	✓	$0.102$	$0$	$1.02396$	Character $\chi_{1681}(1041, \cdot)$
1-41e2-1681.1043-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1043	$0$	✓	✓	$0.172$	$0$	$1.33335$	Character $\chi_{1681}(1043, \cdot)$
1-41e2-1681.1045-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1045	$0$	✓	✓	$0.292$	$0$	$0.163506$	Character $\chi_{1681}(1045, \cdot)$
1-41e2-1681.1046-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1046	$0$	✓	✓	$-0.230$	$0$	$0.0724843$	Character $\chi_{1681}(1046, \cdot)$
1-41e2-1681.1048-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1048	$0$	✓	✓	$0.397$	$0$	$0.595787$	Character $\chi_{1681}(1048, \cdot)$
1-41e2-1681.105-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.105	$0$	✓	✓	$-0.268$	$0$	$0.616006$	Character $\chi_{1681}(105, \cdot)$
1-41e2-1681.1050-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1050	$0$	✓	✓	$-0.0383$	$0$	$1.51465$	Character $\chi_{1681}(1050, \cdot)$
1-41e2-1681.1056-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1056	$0$	✓	✓	$-0.483$	$0$	$0.428893$	Character $\chi_{1681}(1056, \cdot)$
1-41e2-1681.1057-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1057	$0$	✓	✓	$-0.192$	$0$	$2.04399$	Character $\chi_{1681}(1057, \cdot)$
1-41e2-1681.1058-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1058	$0$	✓	✓	$-0.111$	$0$	$0.663046$	Character $\chi_{1681}(1058, \cdot)$
1-41e2-1681.1061-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1061	$0$	✓	✓	$-0.0472$	$0$	$1.17613$	Character $\chi_{1681}(1061, \cdot)$
1-41e2-1681.1062-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1062	$0$	✓	✓	$0.000594$	$0$	$0.569697$	Character $\chi_{1681}(1062, \cdot)$
1-41e2-1681.1064-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1064	$0$	✓	✓	$0.309$	$0$	$1.53220$	Character $\chi_{1681}(1064, \cdot)$
1-41e2-1681.1065-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1065	$0$	✓	✓	$-0.116$	$0$	$0.448675$	Character $\chi_{1681}(1065, \cdot)$
1-41e2-1681.1067-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1067	$0$	✓	✓	$-0.383$	$0$	$0.379519$	Character $\chi_{1681}(1067, \cdot)$
1-41e2-1681.1068-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1068	$0$	✓	✓	$0.168$	$0$	$1.03630$	Character $\chi_{1681}(1068, \cdot)$
1-41e2-1681.107-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.107	$0$	✓	✓	$-0.276$	$0$	$0.574944$	Character $\chi_{1681}(107, \cdot)$
1-41e2-1681.1070-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1070	$0$	✓	✓	$0.0212$	$0$	$1.42726$	Character $\chi_{1681}(1070, \cdot)$
1-41e2-1681.1071-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1071	$0$	✓	✓	$0.106$	$0$	$0.589700$	Character $\chi_{1681}(1071, \cdot)$
1-41e2-1681.1074-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1074	$0$	✓	✓	$0.149$	$0$	$0.670756$	Character $\chi_{1681}(1074, \cdot)$
1-41e2-1681.1075-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1075	$0$	✓	✓	$0.447$	$0$	$0.313687$	Character $\chi_{1681}(1075, \cdot)$
1-41e2-1681.1076-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1076	$0$	✓	✓	$0.0768$	$0$	$1.32959$	Character $\chi_{1681}(1076, \cdot)$
1-41e2-1681.1082-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1082	$0$	✓	✓	$-0.0277$	$0$	$0.681749$	Character $\chi_{1681}(1082, \cdot)$
1-41e2-1681.1084-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1084	$0$	✓	✓	$0.276$	$0$	$1.42345$	Character $\chi_{1681}(1084, \cdot)$
1-41e2-1681.1086-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1086	$0$	✓	✓	$-0.247$	$0$	$0.894403$	Character $\chi_{1681}(1086, \cdot)$
1-41e2-1681.1087-r0-0-0	$7.80$	$7.80$	$1$	$41^{2}$	1681.1087	$0$	✓	✓	$0.150$	$0$	$1.05938$	Character $\chi_{1681}(1087, \cdot)$

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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.