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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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4027-4027.10-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.10	$0$	✓	✓	$0.200$	$0$	$1.02968$	Character $\chi_{4027}(10, \cdot)$
1-4027-4027.100-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.100	$0$	✓	✓	$-0.416$	$0$	$0.279327$	Character $\chi_{4027}(100, \cdot)$
1-4027-4027.1000-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1000	$0$	✓	✓	$0.394$	$0$	$0.280252$	Character $\chi_{4027}(1000, \cdot)$
1-4027-4027.1001-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1001	$0$	✓	✓	$0.0180$	$0$	$0.560196$	Character $\chi_{4027}(1001, \cdot)$
1-4027-4027.1004-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1004	$0$	✓	✓	$-0.452$	$0$	$1.40538$	Character $\chi_{4027}(1004, \cdot)$
1-4027-4027.1005-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1005	$0$	✓	✓	$-0.121$	$0$	$0.471247$	Character $\chi_{4027}(1005, \cdot)$
1-4027-4027.1006-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1006	$0$	✓	✓	$0.0280$	$0$	$0.649045$	Character $\chi_{4027}(1006, \cdot)$
1-4027-4027.1007-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1007	$0$	✓	✓	$-0.0469$	$0$	$0.597998$	Character $\chi_{4027}(1007, \cdot)$
1-4027-4027.1009-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1009	$0$	✓	✓	$-0.215$	$0$	$0.357285$	Character $\chi_{4027}(1009, \cdot)$
1-4027-4027.101-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.101	$0$	✓	✓	$-0.223$	$0$	$0.900316$	Character $\chi_{4027}(101, \cdot)$
1-4027-4027.1010-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1010	$0$	✓	✓	$-0.423$	$0$	$0.331489$	Character $\chi_{4027}(1010, \cdot)$
1-4027-4027.1011-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1011	$0$	✓	✓	$0.385$	$0$	$1.54041$	Character $\chi_{4027}(1011, \cdot)$
1-4027-4027.1012-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1012	$0$	✓	✓	$-0.440$	$0$	$0.412705$	Character $\chi_{4027}(1012, \cdot)$
1-4027-4027.1013-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1013	$0$	✓	✓	$0.312$	$0$	$0.0852771$	Character $\chi_{4027}(1013, \cdot)$
1-4027-4027.1014-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1014	$0$	✓	✓	$-0.0671$	$0$	$0.426700$	Character $\chi_{4027}(1014, \cdot)$
1-4027-4027.1015-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1015	$0$	✓	✓	$-0.217$	$0$	$0.407993$	Character $\chi_{4027}(1015, \cdot)$
1-4027-4027.1017-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1017	$0$	✓	✓	$0.366$	$0$	$1.15053$	Character $\chi_{4027}(1017, \cdot)$
1-4027-4027.1019-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1019	$0$	✓	✓	$-0.319$	$0$	$0.349541$	Character $\chi_{4027}(1019, \cdot)$
1-4027-4027.102-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.102	$0$	✓	✓	$0.219$	$0$	$0.473527$	Character $\chi_{4027}(102, \cdot)$
1-4027-4027.1020-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1020	$0$	✓	✓	$0.358$	$0$	$1.10216$	Character $\chi_{4027}(1020, \cdot)$
1-4027-4027.1022-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1022	$0$	✓	✓	$0.129$	$0$	$0.821613$	Character $\chi_{4027}(1022, \cdot)$
1-4027-4027.1024-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1024	$0$	✓	✓	$-0.363$	$0$	$0.147857$	Character $\chi_{4027}(1024, \cdot)$
1-4027-4027.1025-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1025	$0$	✓	✓	$-0.243$	$0$	$0.500000$	Character $\chi_{4027}(1025, \cdot)$
1-4027-4027.1026-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1026	$0$	✓	✓	$-0.376$	$0$	$0.233548$	Character $\chi_{4027}(1026, \cdot)$
1-4027-4027.1027-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1027	$0$	✓	✓	$0.342$	$0$	$0.995421$	Character $\chi_{4027}(1027, \cdot)$
1-4027-4027.1029-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1029	$0$	✓	✓	$-0.461$	$0$	$0.247546$	Character $\chi_{4027}(1029, \cdot)$
1-4027-4027.103-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.103	$0$	✓	✓	$0.449$	$0$	$0.170645$	Character $\chi_{4027}(103, \cdot)$
1-4027-4027.1030-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1030	$0$	✓	✓	$0.163$	$0$	$0.270413$	Character $\chi_{4027}(1030, \cdot)$
1-4027-4027.1031-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1031	$0$	✓	✓	$0.495$	$0$	$0.711575$	Character $\chi_{4027}(1031, \cdot)$
1-4027-4027.1032-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1032	$0$	✓	✓	$0.242$	$0$	$0.460305$	Character $\chi_{4027}(1032, \cdot)$
1-4027-4027.1035-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1035	$0$	✓	✓	$0.409$	$0$	$1.53845$	Character $\chi_{4027}(1035, \cdot)$
1-4027-4027.1036-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1036	$0$	✓	✓	$-0.161$	$0$	$0.751463$	Character $\chi_{4027}(1036, \cdot)$
1-4027-4027.1037-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1037	$0$	✓	✓	$0.0981$	$0$	$1.25841$	Character $\chi_{4027}(1037, \cdot)$
1-4027-4027.1042-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1042	$0$	✓	✓	$-0.266$	$0$	$1.41869$	Character $\chi_{4027}(1042, \cdot)$
1-4027-4027.1044-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1044	$0$	✓	✓	$0.0468$	$0$	$0.355364$	Character $\chi_{4027}(1044, \cdot)$
1-4027-4027.1045-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1045	$0$	✓	✓	$0.114$	$0$	$1.34871$	Character $\chi_{4027}(1045, \cdot)$
1-4027-4027.1047-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1047	$0$	✓	✓	$0.292$	$0$	$1.24783$	Character $\chi_{4027}(1047, \cdot)$
1-4027-4027.1049-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1049	$0$	✓	✓	$-0.462$	$0$	$0.365481$	Character $\chi_{4027}(1049, \cdot)$
1-4027-4027.1051-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1051	$0$	✓	✓	$0.198$	$0$	$0.340847$	Character $\chi_{4027}(1051, \cdot)$
1-4027-4027.1052-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1052	$0$	✓	✓	$0.169$	$0$	$0.547979$	Character $\chi_{4027}(1052, \cdot)$
1-4027-4027.1053-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1053	$0$	✓	✓	$0.0422$	$0$	$0.885092$	Character $\chi_{4027}(1053, \cdot)$
1-4027-4027.1054-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1054	$0$	✓	✓	$0.366$	$0$	$0.947613$	Character $\chi_{4027}(1054, \cdot)$
1-4027-4027.1061-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1061	$0$	✓	✓	$-0.473$	$0$	$1.35050$	Character $\chi_{4027}(1061, \cdot)$
1-4027-4027.1062-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1062	$0$	✓	✓	$-0.0147$	$0$	$1.15336$	Character $\chi_{4027}(1062, \cdot)$
1-4027-4027.1063-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1063	$0$	✓	✓	$-0.485$	$0$	$1.67900$	Character $\chi_{4027}(1063, \cdot)$
1-4027-4027.1064-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1064	$0$	✓	✓	$0.233$	$0$	$0.305738$	Character $\chi_{4027}(1064, \cdot)$
1-4027-4027.1065-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1065	$0$	✓	✓	$0.349$	$0$	$0.884962$	Character $\chi_{4027}(1065, \cdot)$
1-4027-4027.107-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.107	$0$	✓	✓	$0.236$	$0$	$0.190902$	Character $\chi_{4027}(107, \cdot)$
1-4027-4027.1070-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1070	$0$	✓	✓	$0.113$	$0$	$0.981309$	Character $\chi_{4027}(1070, \cdot)$
1-4027-4027.1072-r0-0-0	$18.7$	$18.7$	$1$	$4027$	4027.1072	$0$	✓	✓	$0.232$	$0$	$1.08140$	Character $\chi_{4027}(1072, \cdot)$

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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.