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 928 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3968-3968.1003-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1003	$0$	✓	✓	$-0.366$	$0$	$0.502579$	Character $\chi_{3968}(1003, \cdot)$
1-3968-3968.101-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.101	$0$	✓	✓	$0.388$	$0$	$1.05698$	Character $\chi_{3968}(101, \cdot)$
1-3968-3968.1019-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1019	$0$	✓	✓	$0.0911$	$0$	$0.675573$	Character $\chi_{3968}(1019, \cdot)$
1-3968-3968.1035-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1035	$0$	✓	✓	$-0.0515$	$0$	$0.634308$	Character $\chi_{3968}(1035, \cdot)$
1-3968-3968.1037-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1037	$0$	✓	✓	$0.463$	$0$	$1.57398$	Character $\chi_{3968}(1037, \cdot)$
1-3968-3968.1061-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1061	$0$	✓	✓	$-0.0668$	$0$	$0.439513$	Character $\chi_{3968}(1061, \cdot)$
1-3968-3968.1067-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1067	$0$	✓	✓	$-0.307$	$0$	$0.446500$	Character $\chi_{3968}(1067, \cdot)$
1-3968-3968.1075-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1075	$0$	✓	✓	$-0.465$	$0$	$1.17837$	Character $\chi_{3968}(1075, \cdot)$
1-3968-3968.1083-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1083	$0$	✓	✓	$-0.0208$	$0$	$0.425708$	Character $\chi_{3968}(1083, \cdot)$
1-3968-3968.109-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.109	$0$	✓	✓	$0.369$	$0$	$0.00288755$	Character $\chi_{3968}(109, \cdot)$
1-3968-3968.1091-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1091	$0$	✓	✓	$-0.447$	$0$	$1.72803$	Character $\chi_{3968}(1091, \cdot)$
1-3968-3968.1093-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1093	$0$	✓	✓	$-0.361$	$0$	$0.156107$	Character $\chi_{3968}(1093, \cdot)$
1-3968-3968.11-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.11	$0$	✓	✓	$0.133$	$0$	$0.709707$	Character $\chi_{3968}(11, \cdot)$
1-3968-3968.1101-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1101	$0$	✓	✓	$0.119$	$0$	$1.02289$	Character $\chi_{3968}(1101, \cdot)$
1-3968-3968.1107-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1107	$0$	✓	✓	$0.342$	$0$	$0.0957226$	Character $\chi_{3968}(1107, \cdot)$
1-3968-3968.1115-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1115	$0$	✓	✓	$-0.117$	$0$	$0.210221$	Character $\chi_{3968}(1115, \cdot)$
1-3968-3968.1125-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1125	$0$	✓	✓	$0.332$	$0$	$0.125936$	Character $\chi_{3968}(1125, \cdot)$
1-3968-3968.1131-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1131	$0$	✓	✓	$0.473$	$0$	$1.06202$	Character $\chi_{3968}(1131, \cdot)$
1-3968-3968.1139-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1139	$0$	✓	✓	$-0.0911$	$0$	$0.613418$	Character $\chi_{3968}(1139, \cdot)$
1-3968-3968.1141-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1141	$0$	✓	✓	$0.134$	$0$	$0.447909$	Character $\chi_{3968}(1141, \cdot)$
1-3968-3968.1149-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1149	$0$	✓	✓	$0.427$	$0$	$1.62589$	Character $\chi_{3968}(1149, \cdot)$
1-3968-3968.115-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.115	$0$	✓	✓	$0.0926$	$0$	$0.790660$	Character $\chi_{3968}(115, \cdot)$
1-3968-3968.1157-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1157	$0$	✓	✓	$0.116$	$0$	$0.473104$	Character $\chi_{3968}(1157, \cdot)$
1-3968-3968.1165-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1165	$0$	✓	✓	$-0.00795$	$0$	$0.709773$	Character $\chi_{3968}(1165, \cdot)$
1-3968-3968.1171-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1171	$0$	✓	✓	$-0.108$	$0$	$0.403250$	Character $\chi_{3968}(1171, \cdot)$
1-3968-3968.1195-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1195	$0$	✓	✓	$-0.493$	$0$	$1.31988$	Character $\chi_{3968}(1195, \cdot)$
1-3968-3968.1197-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1197	$0$	✓	✓	$0.492$	$0$	$0.557424$	Character $\chi_{3968}(1197, \cdot)$
1-3968-3968.1213-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1213	$0$	✓	✓	$0.173$	$0$	$0.614073$	Character $\chi_{3968}(1213, \cdot)$
1-3968-3968.1229-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1229	$0$	✓	✓	$-0.229$	$0$	$1.89970$	Character $\chi_{3968}(1229, \cdot)$
1-3968-3968.123-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.123	$0$	✓	✓	$0.132$	$0$	$1.13494$	Character $\chi_{3968}(123, \cdot)$
1-3968-3968.1235-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1235	$0$	✓	✓	$0.244$	$0$	$0.748686$	Character $\chi_{3968}(1235, \cdot)$
1-3968-3968.1237-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1237	$0$	✓	✓	$0.337$	$0$	$0.982965$	Character $\chi_{3968}(1237, \cdot)$
1-3968-3968.1243-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1243	$0$	✓	✓	$0.215$	$0$	$1.03410$	Character $\chi_{3968}(1243, \cdot)$
1-3968-3968.1245-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1245	$0$	✓	✓	$-0.134$	$0$	$0.516870$	Character $\chi_{3968}(1245, \cdot)$
1-3968-3968.1251-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1251	$0$	✓	✓	$-0.00682$	$0$	$0.922111$	Character $\chi_{3968}(1251, \cdot)$
1-3968-3968.1267-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1267	$0$	✓	✓	$-0.174$	$0$	$0.585403$	Character $\chi_{3968}(1267, \cdot)$
1-3968-3968.1283-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1283	$0$	✓	✓	$0.307$	$0$	$1.25881$	Character $\chi_{3968}(1283, \cdot)$
1-3968-3968.1285-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1285	$0$	✓	✓	$0.229$	$0$	$0.0959746$	Character $\chi_{3968}(1285, \cdot)$
1-3968-3968.1309-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1309	$0$	✓	✓	$0.230$	$0$	$0.886332$	Character $\chi_{3968}(1309, \cdot)$
1-3968-3968.1315-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1315	$0$	✓	✓	$0.0515$	$0$	$1.11443$	Character $\chi_{3968}(1315, \cdot)$
1-3968-3968.1323-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1323	$0$	✓	✓	$0.487$	$0$	$1.26155$	Character $\chi_{3968}(1323, \cdot)$
1-3968-3968.133-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.133	$0$	✓	✓	$-0.417$	$0$	$1.69623$	Character $\chi_{3968}(133, \cdot)$
1-3968-3968.1331-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1331	$0$	✓	✓	$-0.286$	$0$	$0.764838$	Character $\chi_{3968}(1331, \cdot)$
1-3968-3968.1339-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1339	$0$	✓	✓	$0.00513$	$0$	$0.971774$	Character $\chi_{3968}(1339, \cdot)$
1-3968-3968.1341-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1341	$0$	✓	✓	$-0.314$	$0$	$1.56352$	Character $\chi_{3968}(1341, \cdot)$
1-3968-3968.1349-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1349	$0$	✓	✓	$-0.114$	$0$	$0.971017$	Character $\chi_{3968}(1349, \cdot)$
1-3968-3968.1355-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1355	$0$	✓	✓	$-0.454$	$0$	$0.148328$	Character $\chi_{3968}(1355, \cdot)$
1-3968-3968.1363-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1363	$0$	✓	✓	$0.117$	$0$	$0.680861$	Character $\chi_{3968}(1363, \cdot)$
1-3968-3968.1373-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1373	$0$	✓	✓	$0.129$	$0$	$0.923234$	Character $\chi_{3968}(1373, \cdot)$
1-3968-3968.1379-r0-0-0	$18.4$	$18.4$	$1$	$2^{7} \cdot 31$	3968.1379	$0$	✓	✓	$-0.166$	$0$	$0.545297$	Character $\chi_{3968}(1379, \cdot)$

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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.