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 1450 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3751-3751.100-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.100	$0$	✓	✓	$0.231$	$0$	$0.207821$	Character $\chi_{3751}(100, \cdot)$
1-3751-3751.1002-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1002	$0$	✓	✓	$-0.100$	$0$	$0.606473$	Character $\chi_{3751}(1002, \cdot)$
1-3751-3751.1003-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1003	$0$	✓	✓	$-0.367$	$0$	$0.124869$	Character $\chi_{3751}(1003, \cdot)$
1-3751-3751.1006-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1006	$0$	✓	✓	$0.277$	$0$	$1.20863$	Character $\chi_{3751}(1006, \cdot)$
1-3751-3751.1007-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1007	$0$	✓	✓	$0.236$	$0$	$1.22916$	Character $\chi_{3751}(1007, \cdot)$
1-3751-3751.1009-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1009	$0$	✓	✓	$-0.322$	$0$	$0.691025$	Character $\chi_{3751}(1009, \cdot)$
1-3751-3751.1010-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1010	$0$	✓	✓	$0.319$	$0$	$0.206027$	Character $\chi_{3751}(1010, \cdot)$
1-3751-3751.1014-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1014	$0$	✓	✓	$0.342$	$0$	$0.520165$	Character $\chi_{3751}(1014, \cdot)$
1-3751-3751.1017-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1017	$0$	✓	✓	$-0.280$	$0$	$1.60507$	Character $\chi_{3751}(1017, \cdot)$
1-3751-3751.1018-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1018	$0$	✓	✓	$-0.456$	$0$	$0.832160$	Character $\chi_{3751}(1018, \cdot)$
1-3751-3751.1019-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1019	$0$	✓	✓	$-0.390$	$0$	$0.479687$	Character $\chi_{3751}(1019, \cdot)$
1-3751-3751.102-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.102	$0$	✓	✓	$-0.0345$	$0$	$0.694976$	Character $\chi_{3751}(102, \cdot)$
1-3751-3751.1022-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1022	$0$	✓	✓	$-0.142$	$0$	$0.356400$	Character $\chi_{3751}(1022, \cdot)$
1-3751-3751.1027-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1027	$0$	✓	✓	$-0.163$	$0$	$0.440050$	Character $\chi_{3751}(1027, \cdot)$
1-3751-3751.1028-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1028	$0$	✓	✓	$0.295$	$0$	$1.29515$	Character $\chi_{3751}(1028, \cdot)$
1-3751-3751.1029-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1029	$0$	✓	✓	$0.148$	$0$	$1.70982$	Character $\chi_{3751}(1029, \cdot)$
1-3751-3751.103-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.103	$0$	✓	✓	$0.307$	$0$	$0.902171$	Character $\chi_{3751}(103, \cdot)$
1-3751-3751.1032-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1032	$0$	✓	✓	$-0.234$	$0$	$0.495796$	Character $\chi_{3751}(1032, \cdot)$
1-3751-3751.1036-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1036	$0$	✓	✓	$0.0860$	$0$	$0.347274$	Character $\chi_{3751}(1036, \cdot)$
1-3751-3751.1037-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1037	$0$	✓	✓	$0.282$	$0$	$1.46456$	Character $\chi_{3751}(1037, \cdot)$
1-3751-3751.1039-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1039	$0$	✓	✓	$-0.398$	$0$	$1.16872$	Character $\chi_{3751}(1039, \cdot)$
1-3751-3751.1040-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1040	$0$	✓	✓	$0.292$	$0$	$0.862499$	Character $\chi_{3751}(1040, \cdot)$
1-3751-3751.1043-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1043	$0$	✓	✓	$0.120$	$0$	$0.885424$	Character $\chi_{3751}(1043, \cdot)$
1-3751-3751.1044-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1044	$0$	✓	✓	$-0.338$	$0$	$0.504566$	Character $\chi_{3751}(1044, \cdot)$
1-3751-3751.1047-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1047	$0$	✓	✓	$-0.164$	$0$	$0.354506$	Character $\chi_{3751}(1047, \cdot)$
1-3751-3751.1048-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1048	$0$	✓	✓	$0.104$	$0$	$1.16579$	Character $\chi_{3751}(1048, \cdot)$
1-3751-3751.105-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.105	$0$	✓	✓	$-0.0860$	$0$	$0.721865$	Character $\chi_{3751}(105, \cdot)$
1-3751-3751.1052-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1052	$0$	✓	✓	$-0.436$	$0$	$1.80773$	Character $\chi_{3751}(1052, \cdot)$
1-3751-3751.1053-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1053	$0$	✓	✓	$-0.316$	$0$	$0.370020$	Character $\chi_{3751}(1053, \cdot)$
1-3751-3751.1059-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1059	$0$	✓	✓	$-0.0302$	$0$	$1.02632$	Character $\chi_{3751}(1059, \cdot)$
1-3751-3751.106-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.106	$0$	✓	✓	$0.0662$	$0$	$1.32518$	Character $\chi_{3751}(106, \cdot)$
1-3751-3751.1061-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1061	$0$	✓	✓	$0.100$	$0$	$1.32524$	Character $\chi_{3751}(1061, \cdot)$
1-3751-3751.1066-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1066	$0$	✓	✓	$0.313$	$0$	$0.00376586$	Character $\chi_{3751}(1066, \cdot)$
1-3751-3751.1068-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1068	$0$	✓	✓	$-0.322$	$0$	$0.809395$	Character $\chi_{3751}(1068, \cdot)$
1-3751-3751.1069-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1069	$0$	✓	✓	$0.0962$	$0$	$1.24096$	Character $\chi_{3751}(1069, \cdot)$
1-3751-3751.1070-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1070	$0$	✓	✓	$0.00153$	$0$	$0.882694$	Character $\chi_{3751}(1070, \cdot)$
1-3751-3751.1072-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1072	$0$	✓	✓	$-0.0576$	$0$	$0.903925$	Character $\chi_{3751}(1072, \cdot)$
1-3751-3751.1075-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1075	$0$	✓	✓	$-0.338$	$0$	$0.373566$	Character $\chi_{3751}(1075, \cdot)$
1-3751-3751.1077-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1077	$0$	✓	✓	$-0.475$	$0$	$0.548169$	Character $\chi_{3751}(1077, \cdot)$
1-3751-3751.1079-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1079	$0$	✓	✓	$0.364$	$0$	$0.690663$	Character $\chi_{3751}(1079, \cdot)$
1-3751-3751.1082-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1082	$0$	✓	✓	$0.297$	$0$	$0.797800$	Character $\chi_{3751}(1082, \cdot)$
1-3751-3751.1084-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1084	$0$	✓	✓	$-0.0723$	$0$	$0.522982$	Character $\chi_{3751}(1084, \cdot)$
1-3751-3751.1087-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1087	$0$	✓	✓	$0.205$	$0$	$0.0133173$	Character $\chi_{3751}(1087, \cdot)$
1-3751-3751.1091-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1091	$0$	✓	✓	$0.263$	$0$	$1.20020$	Character $\chi_{3751}(1091, \cdot)$
1-3751-3751.1093-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1093	$0$	✓	✓	$0.0890$	$0$	$0.886174$	Character $\chi_{3751}(1093, \cdot)$
1-3751-3751.1094-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1094	$0$	✓	✓	$-0.256$	$0$	$1.14857$	Character $\chi_{3751}(1094, \cdot)$
1-3751-3751.1096-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1096	$0$	✓	✓	$0.127$	$0$	$0.810052$	Character $\chi_{3751}(1096, \cdot)$
1-3751-3751.1097-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1097	$0$	✓	✓	$-0.0662$	$0$	$0.617611$	Character $\chi_{3751}(1097, \cdot)$
1-3751-3751.1101-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1101	$0$	✓	✓	$0.135$	$0$	$0.524739$	Character $\chi_{3751}(1101, \cdot)$
1-3751-3751.1102-r0-0-0	$17.4$	$17.4$	$1$	$11^{2} \cdot 31$	3751.1102	$0$	✓	✓	$0.302$	$0$	$1.23823$	Character $\chi_{3751}(1102, \cdot)$

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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.