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 3219 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3503-3503.100-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.100	$0$	✓	✓	$-0.0970$	$0$	$0.730788$	Character $\chi_{3503}(100, \cdot)$
1-3503-3503.1001-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1001	$0$	✓	✓	$0.131$	$0$	$1.23868$	Character $\chi_{3503}(1001, \cdot)$
1-3503-3503.1002-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1002	$0$	✓	✓	$-0.365$	$0$	$1.49201$	Character $\chi_{3503}(1002, \cdot)$
1-3503-3503.1005-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1005	$0$	✓	✓	$0.267$	$0$	$1.10684$	Character $\chi_{3503}(1005, \cdot)$
1-3503-3503.1006-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1006	$0$	✓	✓	$-0.377$	$0$	$0.723081$	Character $\chi_{3503}(1006, \cdot)$
1-3503-3503.1007-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1007	$0$	✓	✓	$0.00696$	$0$	$1.22327$	Character $\chi_{3503}(1007, \cdot)$
1-3503-3503.1008-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1008	$0$	✓	✓	$-0.261$	$0$	$0.934776$	Character $\chi_{3503}(1008, \cdot)$
1-3503-3503.1010-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1010	$0$	✓	✓	$-0.327$	$0$	$0.602414$	Character $\chi_{3503}(1010, \cdot)$
1-3503-3503.1014-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1014	$0$	✓	✓	$-0.0196$	$0$	$0.817084$	Character $\chi_{3503}(1014, \cdot)$
1-3503-3503.102-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.102	$0$	✓	✓	$-0.357$	$0$	$1.49560$	Character $\chi_{3503}(102, \cdot)$
1-3503-3503.1022-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1022	$0$	✓	✓	$0.000395$	$0$	$0.792814$	Character $\chi_{3503}(1022, \cdot)$
1-3503-3503.1025-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1025	$0$	✓	✓	$0.214$	$0$	$1.33751$	Character $\chi_{3503}(1025, \cdot)$
1-3503-3503.1028-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1028	$0$	✓	✓	$0.0202$	$0$	$1.03307$	Character $\chi_{3503}(1028, \cdot)$
1-3503-3503.1029-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1029	$0$	✓	✓	$0.140$	$0$	$1.21471$	Character $\chi_{3503}(1029, \cdot)$
1-3503-3503.1030-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1030	$0$	✓	✓	$-0.156$	$0$	$0.801857$	Character $\chi_{3503}(1030, \cdot)$
1-3503-3503.1031-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1031	$0$	✓	✓	$0.495$	$0$	$0.326293$	Character $\chi_{3503}(1031, \cdot)$
1-3503-3503.1032-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1032	$0$	✓	✓	$-0.0348$	$0$	$0.913309$	Character $\chi_{3503}(1032, \cdot)$
1-3503-3503.1033-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1033	$0$	✓	✓	$0.102$	$0$	$0.742749$	Character $\chi_{3503}(1033, \cdot)$
1-3503-3503.1034-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1034	$0$	✓	✓	$-0.459$	$0$	$0.710816$	Character $\chi_{3503}(1034, \cdot)$
1-3503-3503.1036-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1036	$0$	✓	✓	$0.161$	$0$	$0.574546$	Character $\chi_{3503}(1036, \cdot)$
1-3503-3503.1038-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1038	$0$	✓	✓	$-0.472$	$0$	$0.429393$	Character $\chi_{3503}(1038, \cdot)$
1-3503-3503.1039-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1039	$0$	✓	✓	$-0.152$	$0$	$1.03506$	Character $\chi_{3503}(1039, \cdot)$
1-3503-3503.1040-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1040	$0$	✓	✓	$-0.489$	$0$	$0.0585850$	Character $\chi_{3503}(1040, \cdot)$
1-3503-3503.1042-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1042	$0$	✓	✓	$0.0558$	$0$	$1.12389$	Character $\chi_{3503}(1042, \cdot)$
1-3503-3503.1043-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1043	$0$	✓	✓	$0.0506$	$0$	$0.738529$	Character $\chi_{3503}(1043, \cdot)$
1-3503-3503.1044-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1044	$0$	✓	✓	$0.221$	$0$	$1.07963$	Character $\chi_{3503}(1044, \cdot)$
1-3503-3503.1046-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1046	$0$	✓	✓	$-0.169$	$0$	$0.288362$	Character $\chi_{3503}(1046, \cdot)$
1-3503-3503.1048-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1048	$0$	✓	✓	$0.249$	$0$	$0.0571493$	Character $\chi_{3503}(1048, \cdot)$
1-3503-3503.1050-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1050	$0$	✓	✓	$0.371$	$0$	$0.0153968$	Character $\chi_{3503}(1050, \cdot)$
1-3503-3503.1052-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1052	$0$	✓	✓	$0.0644$	$0$	$1.20486$	Character $\chi_{3503}(1052, \cdot)$
1-3503-3503.1057-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1057	$0$	✓	✓	$-0.166$	$0$	$0.389791$	Character $\chi_{3503}(1057, \cdot)$
1-3503-3503.1058-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1058	$0$	✓	✓	$-0.365$	$0$	$0.155963$	Character $\chi_{3503}(1058, \cdot)$
1-3503-3503.1060-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1060	$0$	✓	✓	$0.232$	$0$	$0.829201$	Character $\chi_{3503}(1060, \cdot)$
1-3503-3503.1061-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1061	$0$	✓	✓	$-0.0222$	$0$	$1.14760$	Character $\chi_{3503}(1061, \cdot)$
1-3503-3503.1065-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1065	$0$	✓	✓	$-0.00888$	$0$	$0.763921$	Character $\chi_{3503}(1065, \cdot)$
1-3503-3503.1068-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1068	$0$	✓	✓	$0.287$	$0$	$1.23701$	Character $\chi_{3503}(1068, \cdot)$
1-3503-3503.1070-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1070	$0$	✓	✓	$-0.151$	$0$	$0.277742$	Character $\chi_{3503}(1070, \cdot)$
1-3503-3503.1071-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1071	$0$	✓	✓	$-0.323$	$0$	$0.968425$	Character $\chi_{3503}(1071, \cdot)$
1-3503-3503.1073-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1073	$0$	✓	✓	$-0.181$	$0$	$0.756044$	Character $\chi_{3503}(1073, \cdot)$
1-3503-3503.1074-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1074	$0$	✓	✓	$-0.0529$	$0$	$0.0261402$	Character $\chi_{3503}(1074, \cdot)$
1-3503-3503.1075-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1075	$0$	✓	✓	$0.161$	$0$	$1.55889$	Character $\chi_{3503}(1075, \cdot)$
1-3503-3503.1076-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1076	$0$	✓	✓	$0.401$	$0$	$1.19865$	Character $\chi_{3503}(1076, \cdot)$
1-3503-3503.1079-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1079	$0$	✓	✓	$0.210$	$0$	$0.176559$	Character $\chi_{3503}(1079, \cdot)$
1-3503-3503.108-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.108	$0$	✓	✓	$-0.368$	$0$	$0.725240$	Character $\chi_{3503}(108, \cdot)$
1-3503-3503.1083-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1083	$0$	✓	✓	$0.245$	$0$	$0.842802$	Character $\chi_{3503}(1083, \cdot)$
1-3503-3503.1084-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1084	$0$	✓	✓	$-0.221$	$0$	$0.581780$	Character $\chi_{3503}(1084, \cdot)$
1-3503-3503.1088-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1088	$0$	✓	✓	$0.139$	$0$	$0.910415$	Character $\chi_{3503}(1088, \cdot)$
1-3503-3503.1089-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1089	$0$	✓	✓	$-0.00675$	$0$	$0.905474$	Character $\chi_{3503}(1089, \cdot)$
1-3503-3503.109-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.109	$0$	✓	✓	$-0.188$	$0$	$0.232069$	Character $\chi_{3503}(109, \cdot)$
1-3503-3503.1091-r0-0-0	$16.2$	$16.2$	$1$	$31 \cdot 113$	3503.1091	$0$	✓	✓	$0.460$	$0$	$1.15159$	Character $\chi_{3503}(1091, \cdot)$

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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.