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
1-4003-4003.10-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.10	$0$	✓	✓	$0.236$	$0$	$1.27712$	Character $\chi_{4003}(10, \cdot)$
1-4003-4003.100-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.100	$0$	✓	✓	$-0.0670$	$0$	$1.04959$	Character $\chi_{4003}(100, \cdot)$
1-4003-4003.1000-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1000	$0$	✓	✓	$-0.385$	$0$	$1.96360$	Character $\chi_{4003}(1000, \cdot)$
1-4003-4003.1001-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1001	$0$	✓	✓	$-0.0993$	$0$	$1.08942$	Character $\chi_{4003}(1001, \cdot)$
1-4003-4003.1003-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1003	$0$	✓	✓	$-0.289$	$0$	$1.21267$	Character $\chi_{4003}(1003, \cdot)$
1-4003-4003.1004-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1004	$0$	✓	✓	$0.143$	$0$	$1.04772$	Character $\chi_{4003}(1004, \cdot)$
1-4003-4003.1005-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1005	$0$	✓	✓	$-0.335$	$0$	$0.382643$	Character $\chi_{4003}(1005, \cdot)$
1-4003-4003.1007-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1007	$0$	✓	✓	$-0.482$	$0$	$0.241401$	Character $\chi_{4003}(1007, \cdot)$
1-4003-4003.1008-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1008	$0$	✓	✓	$-0.279$	$0$	$0.666768$	Character $\chi_{4003}(1008, \cdot)$
1-4003-4003.101-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.101	$0$	✓	✓	$-0.249$	$0$	$0.403460$	Character $\chi_{4003}(101, \cdot)$
1-4003-4003.1010-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1010	$0$	✓	✓	$0.317$	$0$	$0.745996$	Character $\chi_{4003}(1010, \cdot)$
1-4003-4003.1013-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1013	$0$	✓	✓	$0.349$	$0$	$1.30116$	Character $\chi_{4003}(1013, \cdot)$
1-4003-4003.1014-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1014	$0$	✓	✓	$-0.0952$	$0$	$0.851689$	Character $\chi_{4003}(1014, \cdot)$
1-4003-4003.1018-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1018	$0$	✓	✓	$0.0995$	$0$	$0.0687748$	Character $\chi_{4003}(1018, \cdot)$
1-4003-4003.1019-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1019	$0$	✓	✓	$0.286$	$0$	$1.53009$	Character $\chi_{4003}(1019, \cdot)$
1-4003-4003.102-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.102	$0$	✓	✓	$0.419$	$0$	$0.0642335$	Character $\chi_{4003}(102, \cdot)$
1-4003-4003.1020-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1020	$0$	✓	✓	$0.480$	$0$	$0.352501$	Character $\chi_{4003}(1020, \cdot)$
1-4003-4003.1021-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1021	$0$	✓	✓	$0.114$	$0$	$0.948431$	Character $\chi_{4003}(1021, \cdot)$
1-4003-4003.1023-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1023	$0$	✓	✓	$0.0781$	$0$	$0.378106$	Character $\chi_{4003}(1023, \cdot)$
1-4003-4003.1024-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1024	$0$	✓	✓	$0.217$	$0$	$1.37051$	Character $\chi_{4003}(1024, \cdot)$
1-4003-4003.1026-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1026	$0$	✓	✓	$-0.259$	$0$	$0.0611993$	Character $\chi_{4003}(1026, \cdot)$
1-4003-4003.1027-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1027	$0$	✓	✓	$-0.453$	$0$	$0.502421$	Character $\chi_{4003}(1027, \cdot)$
1-4003-4003.103-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.103	$0$	✓	✓	$-0.0194$	$0$	$1.11859$	Character $\chi_{4003}(103, \cdot)$
1-4003-4003.1030-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1030	$0$	✓	✓	$0.167$	$0$	$0.536228$	Character $\chi_{4003}(1030, \cdot)$
1-4003-4003.1031-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1031	$0$	✓	✓	$0.221$	$0$	$0.0101034$	Character $\chi_{4003}(1031, \cdot)$
1-4003-4003.1033-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1033	$0$	✓	✓	$0.418$	$0$	$1.33258$	Character $\chi_{4003}(1033, \cdot)$
1-4003-4003.1034-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1034	$0$	✓	✓	$0.312$	$0$	$0.748869$	Character $\chi_{4003}(1034, \cdot)$
1-4003-4003.1035-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1035	$0$	✓	✓	$0.364$	$0$	$0.0576454$	Character $\chi_{4003}(1035, \cdot)$
1-4003-4003.1036-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1036	$0$	✓	✓	$-0.419$	$0$	$0.496352$	Character $\chi_{4003}(1036, \cdot)$
1-4003-4003.1038-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1038	$0$	✓	✓	$0.0919$	$0$	$0.802394$	Character $\chi_{4003}(1038, \cdot)$
1-4003-4003.1039-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1039	$0$	✓	✓	$-0.388$	$0$	$1.40577$	Character $\chi_{4003}(1039, \cdot)$
1-4003-4003.1042-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1042	$0$	✓	✓	$-0.0606$	$0$	$0.155770$	Character $\chi_{4003}(1042, \cdot)$
1-4003-4003.1043-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1043	$0$	✓	✓	$0.198$	$0$	$0.789299$	Character $\chi_{4003}(1043, \cdot)$
1-4003-4003.1044-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1044	$0$	✓	✓	$-0.350$	$0$	$0.499389$	Character $\chi_{4003}(1044, \cdot)$
1-4003-4003.1049-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1049	$0$	✓	✓	$-0.111$	$0$	$0.371986$	Character $\chi_{4003}(1049, \cdot)$
1-4003-4003.105-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.105	$0$	✓	✓	$-0.0194$	$0$	$0.842338$	Character $\chi_{4003}(105, \cdot)$
1-4003-4003.1050-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1050	$0$	✓	✓	$-0.154$	$0$	$1.10249$	Character $\chi_{4003}(1050, \cdot)$
1-4003-4003.1052-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1052	$0$	✓	✓	$-0.479$	$0$	$1.39160$	Character $\chi_{4003}(1052, \cdot)$
1-4003-4003.1053-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1053	$0$	✓	✓	$0.371$	$0$	$0.118243$	Character $\chi_{4003}(1053, \cdot)$
1-4003-4003.1054-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1054	$0$	✓	✓	$-0.347$	$0$	$0.603355$	Character $\chi_{4003}(1054, \cdot)$
1-4003-4003.1056-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1056	$0$	✓	✓	$0.0279$	$0$	$1.13759$	Character $\chi_{4003}(1056, \cdot)$
1-4003-4003.1057-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1057	$0$	✓	✓	$0.130$	$0$	$1.09625$	Character $\chi_{4003}(1057, \cdot)$
1-4003-4003.1061-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1061	$0$	✓	✓	$0.451$	$0$	$0.553131$	Character $\chi_{4003}(1061, \cdot)$
1-4003-4003.1066-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1066	$0$	✓	✓	$0.0278$	$0$	$0.684866$	Character $\chi_{4003}(1066, \cdot)$
1-4003-4003.1071-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1071	$0$	✓	✓	$-0.125$	$0$	$1.05392$	Character $\chi_{4003}(1071, \cdot)$
1-4003-4003.1072-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1072	$0$	✓	✓	$-0.131$	$0$	$0.491639$	Character $\chi_{4003}(1072, \cdot)$
1-4003-4003.1073-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1073	$0$	✓	✓	$-0.487$	$0$	$0.204929$	Character $\chi_{4003}(1073, \cdot)$
1-4003-4003.1077-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1077	$0$	✓	✓	$0.0167$	$0$	$1.16481$	Character $\chi_{4003}(1077, \cdot)$
1-4003-4003.1079-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1079	$0$	✓	✓	$-0.264$	$0$	$0.429067$	Character $\chi_{4003}(1079, \cdot)$
1-4003-4003.1081-r0-0-0	$18.5$	$18.5$	$1$	$4003$	4003.1081	$0$	✓	✓	$0.222$	$0$	$0.761741$	Character $\chi_{4003}(1081, \cdot)$

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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.