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
1-3407-3407.100-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.100	$0$	✓	✓	$-0.382$	$0$	$1.37325$	Character $\chi_{3407}(100, \cdot)$
1-3407-3407.1001-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1001	$0$	✓	✓	$0.361$	$0$	$1.47833$	Character $\chi_{3407}(1001, \cdot)$
1-3407-3407.1002-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1002	$0$	✓	✓	$0.479$	$0$	$1.27162$	Character $\chi_{3407}(1002, \cdot)$
1-3407-3407.1008-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1008	$0$	✓	✓	$-0.0846$	$0$	$0.815357$	Character $\chi_{3407}(1008, \cdot)$
1-3407-3407.1010-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1010	$0$	✓	✓	$0.0838$	$0$	$0.920795$	Character $\chi_{3407}(1010, \cdot)$
1-3407-3407.1011-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1011	$0$	✓	✓	$-0.333$	$0$	$0.167613$	Character $\chi_{3407}(1011, \cdot)$
1-3407-3407.1013-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1013	$0$	✓	✓	$0.449$	$0$	$0.901221$	Character $\chi_{3407}(1013, \cdot)$
1-3407-3407.1014-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1014	$0$	✓	✓	$0.330$	$0$	$0.0468746$	Character $\chi_{3407}(1014, \cdot)$
1-3407-3407.1015-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1015	$0$	✓	✓	$-0.378$	$0$	$0.875474$	Character $\chi_{3407}(1015, \cdot)$
1-3407-3407.1016-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1016	$0$	✓	✓	$0.449$	$0$	$0.426078$	Character $\chi_{3407}(1016, \cdot)$
1-3407-3407.1018-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1018	$0$	✓	✓	$-0.360$	$0$	$0.666406$	Character $\chi_{3407}(1018, \cdot)$
1-3407-3407.1020-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1020	$0$	✓	✓	$-0.159$	$0$	$0.573642$	Character $\chi_{3407}(1020, \cdot)$
1-3407-3407.1021-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1021	$0$	✓	✓	$-0.221$	$0$	$0.496169$	Character $\chi_{3407}(1021, \cdot)$
1-3407-3407.1022-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1022	$0$	✓	✓	$-0.0532$	$0$	$0.923128$	Character $\chi_{3407}(1022, \cdot)$
1-3407-3407.1024-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1024	$0$	✓	✓	$0.122$	$0$	$1.31699$	Character $\chi_{3407}(1024, \cdot)$
1-3407-3407.1025-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1025	$0$	✓	✓	$-0.416$	$0$	$0.717072$	Character $\chi_{3407}(1025, \cdot)$
1-3407-3407.1029-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1029	$0$	✓	✓	$-0.452$	$0$	$1.57119$	Character $\chi_{3407}(1029, \cdot)$
1-3407-3407.1030-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1030	$0$	✓	✓	$-0.323$	$0$	$0.330671$	Character $\chi_{3407}(1030, \cdot)$
1-3407-3407.1034-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1034	$0$	✓	✓	$-0.245$	$0$	$0.897596$	Character $\chi_{3407}(1034, \cdot)$
1-3407-3407.1035-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1035	$0$	✓	✓	$0.0692$	$0$	$1.08323$	Character $\chi_{3407}(1035, \cdot)$
1-3407-3407.1036-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1036	$0$	✓	✓	$-0.207$	$0$	$0.495498$	Character $\chi_{3407}(1036, \cdot)$
1-3407-3407.104-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.104	$0$	✓	✓	$-0.0109$	$0$	$1.03210$	Character $\chi_{3407}(104, \cdot)$
1-3407-3407.1043-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1043	$0$	✓	✓	$-0.438$	$0$	$0.686422$	Character $\chi_{3407}(1043, \cdot)$
1-3407-3407.1045-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1045	$0$	✓	✓	$-0.436$	$0$	$0.0666677$	Character $\chi_{3407}(1045, \cdot)$
1-3407-3407.1046-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1046	$0$	✓	✓	$0.399$	$0$	$1.45054$	Character $\chi_{3407}(1046, \cdot)$
1-3407-3407.1047-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1047	$0$	✓	✓	$-0.357$	$0$	$0.372451$	Character $\chi_{3407}(1047, \cdot)$
1-3407-3407.1049-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1049	$0$	✓	✓	$-0.110$	$0$	$0.382264$	Character $\chi_{3407}(1049, \cdot)$
1-3407-3407.1050-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1050	$0$	✓	✓	$0.0960$	$0$	$0.749161$	Character $\chi_{3407}(1050, \cdot)$
1-3407-3407.1052-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1052	$0$	✓	✓	$-0.0135$	$0$	$0.955578$	Character $\chi_{3407}(1052, \cdot)$
1-3407-3407.1053-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1053	$0$	✓	✓	$0.217$	$0$	$0.792288$	Character $\chi_{3407}(1053, \cdot)$
1-3407-3407.1054-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1054	$0$	✓	✓	$-0.485$	$0$	$0.165262$	Character $\chi_{3407}(1054, \cdot)$
1-3407-3407.1056-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1056	$0$	✓	✓	$-0.324$	$0$	$0.0367559$	Character $\chi_{3407}(1056, \cdot)$
1-3407-3407.1058-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1058	$0$	✓	✓	$-0.299$	$0$	$1.64786$	Character $\chi_{3407}(1058, \cdot)$
1-3407-3407.106-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.106	$0$	✓	✓	$0.262$	$0$	$1.52769$	Character $\chi_{3407}(106, \cdot)$
1-3407-3407.1062-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1062	$0$	✓	✓	$0.0109$	$0$	$0.874362$	Character $\chi_{3407}(1062, \cdot)$
1-3407-3407.1066-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1066	$0$	✓	✓	$0.445$	$0$	$0.942672$	Character $\chi_{3407}(1066, \cdot)$
1-3407-3407.1067-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1067	$0$	✓	✓	$0.417$	$0$	$0.828712$	Character $\chi_{3407}(1067, \cdot)$
1-3407-3407.1068-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1068	$0$	✓	✓	$0.232$	$0$	$1.17938$	Character $\chi_{3407}(1068, \cdot)$
1-3407-3407.1070-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1070	$0$	✓	✓	$0.449$	$0$	$1.41962$	Character $\chi_{3407}(1070, \cdot)$
1-3407-3407.1072-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1072	$0$	✓	✓	$-0.349$	$0$	$0.638183$	Character $\chi_{3407}(1072, \cdot)$
1-3407-3407.1074-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1074	$0$	✓	✓	$-0.157$	$0$	$0.419426$	Character $\chi_{3407}(1074, \cdot)$
1-3407-3407.1078-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1078	$0$	✓	✓	$0.0133$	$0$	$0.867281$	Character $\chi_{3407}(1078, \cdot)$
1-3407-3407.108-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.108	$0$	✓	✓	$-0.282$	$0$	$0.744540$	Character $\chi_{3407}(108, \cdot)$
1-3407-3407.1082-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1082	$0$	✓	✓	$-0.0674$	$0$	$0.884440$	Character $\chi_{3407}(1082, \cdot)$
1-3407-3407.1083-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1083	$0$	✓	✓	$0.443$	$0$	$0.548832$	Character $\chi_{3407}(1083, \cdot)$
1-3407-3407.1085-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1085	$0$	✓	✓	$0.0674$	$0$	$0.181030$	Character $\chi_{3407}(1085, \cdot)$
1-3407-3407.1089-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1089	$0$	✓	✓	$0.120$	$0$	$0.880126$	Character $\chi_{3407}(1089, \cdot)$
1-3407-3407.109-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.109	$0$	✓	✓	$-0.00943$	$0$	$1.04358$	Character $\chi_{3407}(109, \cdot)$
1-3407-3407.1092-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1092	$0$	✓	✓	$-0.204$	$0$	$1.07138$	Character $\chi_{3407}(1092, \cdot)$
1-3407-3407.1094-r0-0-0	$15.8$	$15.8$	$1$	$3407$	3407.1094	$0$	✓	✓	$0.00943$	$0$	$1.29873$	Character $\chi_{3407}(1094, \cdot)$

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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.