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 860 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6369-6369.1022-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1022	$1$	✓	✓	$0.293$	$0$	$0.159599$	Character $\chi_{6369}(1022, \cdot)$
1-6369-6369.1025-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1025	$1$	✓	✓	$0.465$	$0$	$0.123351$	Character $\chi_{6369}(1025, \cdot)$
1-6369-6369.1028-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1028	$1$	✓	✓	$0.0774$	$0$	$0.493370$	Character $\chi_{6369}(1028, \cdot)$
1-6369-6369.1031-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1031	$1$	✓	✓	$-0.195$	$0$	$1.54647$	Character $\chi_{6369}(1031, \cdot)$
1-6369-6369.1037-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1037	$1$	✓	✓	$-0.386$	$0$	$1.41486$	Character $\chi_{6369}(1037, \cdot)$
1-6369-6369.1049-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1049	$1$	✓	✓	$0.202$	$0$	$0.851348$	Character $\chi_{6369}(1049, \cdot)$
1-6369-6369.1052-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1052	$1$	✓	✓	$-0.372$	$0$	$0.235335$	Character $\chi_{6369}(1052, \cdot)$
1-6369-6369.1055-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1055	$1$	✓	✓	$-0.445$	$0$	$0.560027$	Character $\chi_{6369}(1055, \cdot)$
1-6369-6369.1061-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1061	$1$	✓	✓	$-0.212$	$0$	$0.498840$	Character $\chi_{6369}(1061, \cdot)$
1-6369-6369.1064-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1064	$1$	✓	✓	$-0.423$	$0$	$0.218991$	Character $\chi_{6369}(1064, \cdot)$
1-6369-6369.1085-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1085	$1$	✓	✓	$-0.177$	$0$	$1.26206$	Character $\chi_{6369}(1085, \cdot)$
1-6369-6369.1088-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1088	$1$	✓	✓	$-0.457$	$0$	$0.457006$	Character $\chi_{6369}(1088, \cdot)$
1-6369-6369.1094-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1094	$1$	✓	✓	$0.187$	$0$	$0.568269$	Character $\chi_{6369}(1094, \cdot)$
1-6369-6369.1097-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1097	$1$	✓	✓	$0.109$	$0$	$0.179213$	Character $\chi_{6369}(1097, \cdot)$
1-6369-6369.1103-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1103	$1$	✓	✓	$-0.381$	$0$	$0.208613$	Character $\chi_{6369}(1103, \cdot)$
1-6369-6369.1106-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1106	$1$	✓	✓	$-0.369$	$0$	$0.339113$	Character $\chi_{6369}(1106, \cdot)$
1-6369-6369.1109-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1109	$1$	✓	✓	$-0.0774$	$0$	$0.851292$	Character $\chi_{6369}(1109, \cdot)$
1-6369-6369.1115-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1115	$1$	✓	✓	$0.222$	$0$	$0.919518$	Character $\chi_{6369}(1115, \cdot)$
1-6369-6369.1118-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1118	$1$	✓	✓	$-0.462$	$0$	$0.791562$	Character $\chi_{6369}(1118, \cdot)$
1-6369-6369.1121-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1121	$1$	✓	✓	$0.230$	$0$	$0.991099$	Character $\chi_{6369}(1121, \cdot)$
1-6369-6369.1124-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1124	$1$	✓	✓	$-0.0732$	$0$	$0.246034$	Character $\chi_{6369}(1124, \cdot)$
1-6369-6369.1127-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1127	$1$	✓	✓	$-0.306$	$0$	$0.00173889$	Character $\chi_{6369}(1127, \cdot)$
1-6369-6369.1139-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1139	$1$	✓	✓	$-0.395$	$0$	$1.02093$	Character $\chi_{6369}(1139, \cdot)$
1-6369-6369.1142-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1142	$1$	✓	✓	$-0.487$	$0$	$1.01411$	Character $\chi_{6369}(1142, \cdot)$
1-6369-6369.116-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.116	$1$	✓	✓	$-0.237$	$0$	$0.0429212$	Character $\chi_{6369}(116, \cdot)$
1-6369-6369.1160-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1160	$1$	✓	✓	$-0.247$	$0$	$0.251975$	Character $\chi_{6369}(1160, \cdot)$
1-6369-6369.1163-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1163	$1$	✓	✓	$-0.0480$	$0$	$0.674231$	Character $\chi_{6369}(1163, \cdot)$
1-6369-6369.1181-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1181	$1$	✓	✓	$-0.131$	$0$	$0.0283233$	Character $\chi_{6369}(1181, \cdot)$
1-6369-6369.1184-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1184	$1$	✓	✓	$-0.367$	$0$	$0.951265$	Character $\chi_{6369}(1184, \cdot)$
1-6369-6369.1187-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1187	$1$	✓	✓	$-0.310$	$0$	$0.348650$	Character $\chi_{6369}(1187, \cdot)$
1-6369-6369.1196-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1196	$1$	✓	✓	$0.137$	$0$	$0.763526$	Character $\chi_{6369}(1196, \cdot)$
1-6369-6369.1205-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1205	$1$	✓	✓	$0.222$	$0$	$0.671995$	Character $\chi_{6369}(1205, \cdot)$
1-6369-6369.1208-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1208	$1$	✓	✓	$-0.0278$	$0$	$0.635144$	Character $\chi_{6369}(1208, \cdot)$
1-6369-6369.1214-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1214	$1$	✓	✓	$-0.247$	$0$	$0.986719$	Character $\chi_{6369}(1214, \cdot)$
1-6369-6369.1229-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1229	$1$	✓	✓	$0.372$	$0$	$0.650672$	Character $\chi_{6369}(1229, \cdot)$
1-6369-6369.1238-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1238	$1$	✓	✓	$0.497$	$0$	$0.262849$	Character $\chi_{6369}(1238, \cdot)$
1-6369-6369.1241-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1241	$1$	✓	✓	$0.274$	$0$	$0.707012$	Character $\chi_{6369}(1241, \cdot)$
1-6369-6369.1259-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1259	$1$	✓	✓	$-0.0141$	$0$	$0.431450$	Character $\chi_{6369}(1259, \cdot)$
1-6369-6369.1262-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1262	$1$	✓	✓	$-0.0160$	$0$	$0.603324$	Character $\chi_{6369}(1262, \cdot)$
1-6369-6369.1268-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1268	$1$	✓	✓	$0.267$	$0$	$0.241621$	Character $\chi_{6369}(1268, \cdot)$
1-6369-6369.1271-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1271	$1$	✓	✓	$-0.380$	$0$	$0.180995$	Character $\chi_{6369}(1271, \cdot)$
1-6369-6369.1283-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1283	$1$	✓	✓	$0.100$	$0$	$0.556695$	Character $\chi_{6369}(1283, \cdot)$
1-6369-6369.1292-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1292	$1$	✓	✓	$0.139$	$0$	$0.200209$	Character $\chi_{6369}(1292, \cdot)$
1-6369-6369.1301-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1301	$1$	✓	✓	$0.112$	$0$	$0.702961$	Character $\chi_{6369}(1301, \cdot)$
1-6369-6369.1304-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1304	$1$	✓	✓	$0.470$	$0$	$0.262292$	Character $\chi_{6369}(1304, \cdot)$
1-6369-6369.1316-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1316	$1$	✓	✓	$-0.271$	$0$	$0.312760$	Character $\chi_{6369}(1316, \cdot)$
1-6369-6369.1322-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1322	$1$	✓	✓	$-0.401$	$0$	$0.946442$	Character $\chi_{6369}(1322, \cdot)$
1-6369-6369.1358-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1358	$1$	✓	✓	$-0.179$	$0$	$0.326743$	Character $\chi_{6369}(1358, \cdot)$
1-6369-6369.1361-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1361	$1$	✓	✓	$-0.0595$	$0$	$0.958551$	Character $\chi_{6369}(1361, \cdot)$
1-6369-6369.1367-r1-0-0	$684.$	$684.$	$1$	$3 \cdot 11 \cdot 193$	6369.1367	$1$	✓	✓	$0.00891$	$0$	$0.269475$	Character $\chi_{6369}(1367, \cdot)$

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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.