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 624 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2624-2624.1003-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1003	$0$	✓	✓	$0.463$	$0$	$1.24669$	Character $\chi_{2624}(1003, \cdot)$
1-2624-2624.1005-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1005	$0$	✓	✓	$0.286$	$0$	$1.26938$	Character $\chi_{2624}(1005, \cdot)$
1-2624-2624.1011-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1011	$0$	✓	✓	$0.168$	$0$	$0.884379$	Character $\chi_{2624}(1011, \cdot)$
1-2624-2624.1019-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1019	$0$	✓	✓	$-0.424$	$0$	$0.122695$	Character $\chi_{2624}(1019, \cdot)$
1-2624-2624.1021-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1021	$0$	✓	✓	$0.204$	$0$	$0.932589$	Character $\chi_{2624}(1021, \cdot)$
1-2624-2624.1029-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1029	$0$	✓	✓	$0.404$	$0$	$1.22804$	Character $\chi_{2624}(1029, \cdot)$
1-2624-2624.1045-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1045	$0$	✓	✓	$0.000669$	$0$	$0.340625$	Character $\chi_{2624}(1045, \cdot)$
1-2624-2624.1051-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1051	$0$	✓	✓	$0.430$	$0$	$0.281157$	Character $\chi_{2624}(1051, \cdot)$
1-2624-2624.1059-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1059	$0$	✓	✓	$0.0497$	$0$	$1.06375$	Character $\chi_{2624}(1059, \cdot)$
1-2624-2624.1061-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1061	$0$	✓	✓	$0.372$	$0$	$0.898098$	Character $\chi_{2624}(1061, \cdot)$
1-2624-2624.1083-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1083	$0$	✓	✓	$0.452$	$0$	$1.72169$	Character $\chi_{2624}(1083, \cdot)$
1-2624-2624.11-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.11	$0$	✓	✓	$0.297$	$0$	$1.23570$	Character $\chi_{2624}(11, \cdot)$
1-2624-2624.1109-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1109	$0$	✓	✓	$-0.411$	$0$	$1.72427$	Character $\chi_{2624}(1109, \cdot)$
1-2624-2624.1117-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1117	$0$	✓	✓	$0.0144$	$0$	$0.918831$	Character $\chi_{2624}(1117, \cdot)$
1-2624-2624.1125-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1125	$0$	✓	✓	$-0.0686$	$0$	$0.654906$	Character $\chi_{2624}(1125, \cdot)$
1-2624-2624.1131-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1131	$0$	✓	✓	$0.248$	$0$	$1.33348$	Character $\chi_{2624}(1131, \cdot)$
1-2624-2624.1155-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1155	$0$	✓	✓	$-0.387$	$0$	$0.180452$	Character $\chi_{2624}(1155, \cdot)$
1-2624-2624.1157-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1157	$0$	✓	✓	$0.319$	$0$	$0.894187$	Character $\chi_{2624}(1157, \cdot)$
1-2624-2624.1163-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1163	$0$	✓	✓	$-0.0158$	$0$	$0.610813$	Character $\chi_{2624}(1163, \cdot)$
1-2624-2624.1173-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1173	$0$	✓	✓	$0.0113$	$0$	$1.21936$	Character $\chi_{2624}(1173, \cdot)$
1-2624-2624.1181-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1181	$0$	✓	✓	$0.445$	$0$	$0.242219$	Character $\chi_{2624}(1181, \cdot)$
1-2624-2624.1195-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1195	$0$	✓	✓	$0.387$	$0$	$0.732761$	Character $\chi_{2624}(1195, \cdot)$
1-2624-2624.1197-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1197	$0$	✓	✓	$-0.372$	$0$	$0.00583294$	Character $\chi_{2624}(1197, \cdot)$
1-2624-2624.1203-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1203	$0$	✓	✓	$0.00366$	$0$	$0.791778$	Character $\chi_{2624}(1203, \cdot)$
1-2624-2624.1205-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1205	$0$	✓	✓	$-0.0250$	$0$	$0.624136$	Character $\chi_{2624}(1205, \cdot)$
1-2624-2624.1211-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1211	$0$	✓	✓	$0.0789$	$0$	$0.767045$	Character $\chi_{2624}(1211, \cdot)$
1-2624-2624.1219-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1219	$0$	✓	✓	$-0.305$	$0$	$0.773330$	Character $\chi_{2624}(1219, \cdot)$
1-2624-2624.1221-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1221	$0$	✓	✓	$-0.288$	$0$	$0.474959$	Character $\chi_{2624}(1221, \cdot)$
1-2624-2624.1227-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1227	$0$	✓	✓	$0.206$	$0$	$0.0868026$	Character $\chi_{2624}(1227, \cdot)$
1-2624-2624.1229-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1229	$0$	✓	✓	$-0.0156$	$0$	$0.734089$	Character $\chi_{2624}(1229, \cdot)$
1-2624-2624.1243-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1243	$0$	✓	✓	$-0.0573$	$0$	$0.560952$	Character $\chi_{2624}(1243, \cdot)$
1-2624-2624.125-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.125	$0$	✓	✓	$-0.192$	$0$	$0.221696$	Character $\chi_{2624}(125, \cdot)$
1-2624-2624.1253-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1253	$0$	✓	✓	$-0.105$	$0$	$0.192064$	Character $\chi_{2624}(1253, \cdot)$
1-2624-2624.1259-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1259	$0$	✓	✓	$0.453$	$0$	$0.111606$	Character $\chi_{2624}(1259, \cdot)$
1-2624-2624.1261-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1261	$0$	✓	✓	$0.0950$	$0$	$1.13015$	Character $\chi_{2624}(1261, \cdot)$
1-2624-2624.1269-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1269	$0$	✓	✓	$-0.218$	$0$	$0.307924$	Character $\chi_{2624}(1269, \cdot)$
1-2624-2624.1283-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1283	$0$	✓	✓	$-0.248$	$0$	$0.241315$	Character $\chi_{2624}(1283, \cdot)$
1-2624-2624.1299-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1299	$0$	✓	✓	$0.421$	$0$	$0.0335531$	Character $\chi_{2624}(1299, \cdot)$
1-2624-2624.1315-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1315	$0$	✓	✓	$0.0974$	$0$	$1.04586$	Character $\chi_{2624}(1315, \cdot)$
1-2624-2624.1317-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1317	$0$	✓	✓	$-0.320$	$0$	$0.540877$	Character $\chi_{2624}(1317, \cdot)$
1-2624-2624.1323-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1323	$0$	✓	✓	$0.297$	$0$	$0.990658$	Character $\chi_{2624}(1323, \cdot)$
1-2624-2624.133-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.133	$0$	✓	✓	$0.420$	$0$	$1.14621$	Character $\chi_{2624}(133, \cdot)$
1-2624-2624.1331-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1331	$0$	✓	✓	$-0.442$	$0$	$0.609248$	Character $\chi_{2624}(1331, \cdot)$
1-2624-2624.1333-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1333	$0$	✓	✓	$0.192$	$0$	$0.992685$	Character $\chi_{2624}(1333, \cdot)$
1-2624-2624.1339-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1339	$0$	✓	✓	$-0.300$	$0$	$0.580574$	Character $\chi_{2624}(1339, \cdot)$
1-2624-2624.1347-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1347	$0$	✓	✓	$-0.330$	$0$	$0.723852$	Character $\chi_{2624}(1347, \cdot)$
1-2624-2624.1349-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1349	$0$	✓	✓	$-0.389$	$0$	$0.251056$	Character $\chi_{2624}(1349, \cdot)$
1-2624-2624.1357-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1357	$0$	✓	✓	$0.373$	$0$	$0.961716$	Character $\chi_{2624}(1357, \cdot)$
1-2624-2624.1373-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1373	$0$	✓	✓	$0.218$	$0$	$1.22226$	Character $\chi_{2624}(1373, \cdot)$
1-2624-2624.1379-r0-0-0	$12.1$	$12.1$	$1$	$2^{6} \cdot 41$	2624.1379	$0$	✓	✓	$0.0245$	$0$	$1.26001$	Character $\chi_{2624}(1379, \cdot)$

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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.