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 972 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2349-2349.1001-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1001	$0$	✓	✓	$-0.419$	$0$	$0.478797$	Character $\chi_{2349}(1001, \cdot)$
1-2349-2349.1004-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1004	$0$	✓	✓	$-0.0144$	$0$	$0.899737$	Character $\chi_{2349}(1004, \cdot)$
1-2349-2349.1006-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1006	$0$	✓	✓	$0.340$	$0$	$0.824832$	Character $\chi_{2349}(1006, \cdot)$
1-2349-2349.101-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.101	$0$	✓	✓	$-0.305$	$0$	$0.902819$	Character $\chi_{2349}(101, \cdot)$
1-2349-2349.1013-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1013	$0$	✓	✓	$-0.249$	$0$	$0.171693$	Character $\chi_{2349}(1013, \cdot)$
1-2349-2349.1021-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1021	$0$	✓	✓	$-0.0286$	$0$	$0.958874$	Character $\chi_{2349}(1021, \cdot)$
1-2349-2349.1024-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1024	$0$	✓	✓	$0.281$	$0$	$1.22652$	Character $\chi_{2349}(1024, \cdot)$
1-2349-2349.103-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.103	$0$	✓	✓	$-0.229$	$0$	$0.386989$	Character $\chi_{2349}(103, \cdot)$
1-2349-2349.1039-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1039	$0$	✓	✓	$-0.0517$	$0$	$0.522446$	Character $\chi_{2349}(1039, \cdot)$
1-2349-2349.104-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.104	$0$	✓	✓	$0.269$	$0$	$1.64345$	Character $\chi_{2349}(104, \cdot)$
1-2349-2349.1046-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1046	$0$	✓	✓	$0.0427$	$0$	$1.32916$	Character $\chi_{2349}(1046, \cdot)$
1-2349-2349.1048-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1048	$0$	✓	✓	$-0.246$	$0$	$0.845871$	Character $\chi_{2349}(1048, \cdot)$
1-2349-2349.1051-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1051	$0$	✓	✓	$-0.0420$	$0$	$0.771153$	Character $\chi_{2349}(1051, \cdot)$
1-2349-2349.1055-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1055	$0$	✓	✓	$-0.0821$	$0$	$1.20230$	Character $\chi_{2349}(1055, \cdot)$
1-2349-2349.1057-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1057	$0$	✓	✓	$0.274$	$0$	$1.24423$	Character $\chi_{2349}(1057, \cdot)$
1-2349-2349.1058-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1058	$0$	✓	✓	$-0.261$	$0$	$0.777982$	Character $\chi_{2349}(1058, \cdot)$
1-2349-2349.1060-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1060	$0$	✓	✓	$-0.105$	$0$	$0.510457$	Character $\chi_{2349}(1060, \cdot)$
1-2349-2349.1066-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1066	$0$	✓	✓	$0.241$	$0$	$1.23062$	Character $\chi_{2349}(1066, \cdot)$
1-2349-2349.1069-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1069	$0$	✓	✓	$0.0544$	$0$	$0.909884$	Character $\chi_{2349}(1069, \cdot)$
1-2349-2349.1076-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1076	$0$	✓	✓	$0.493$	$0$	$1.04081$	Character $\chi_{2349}(1076, \cdot)$
1-2349-2349.1078-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1078	$0$	✓	✓	$-0.304$	$0$	$0.765318$	Character $\chi_{2349}(1078, \cdot)$
1-2349-2349.1085-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1085	$0$	✓	✓	$-0.225$	$0$	$0.102702$	Character $\chi_{2349}(1085, \cdot)$
1-2349-2349.1091-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1091	$0$	✓	✓	$0.497$	$0$	$0.993149$	Character $\chi_{2349}(1091, \cdot)$
1-2349-2349.1093-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1093	$0$	✓	✓	$-0.116$	$0$	$0.564311$	Character $\chi_{2349}(1093, \cdot)$
1-2349-2349.1094-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1094	$0$	✓	✓	$-0.164$	$0$	$0.990097$	Character $\chi_{2349}(1094, \cdot)$
1-2349-2349.1096-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1096	$0$	✓	✓	$0.385$	$0$	$1.60195$	Character $\chi_{2349}(1096, \cdot)$
1-2349-2349.11-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.11	$0$	✓	✓	$-0.0821$	$0$	$0.216060$	Character $\chi_{2349}(11, \cdot)$
1-2349-2349.1100-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1100	$0$	✓	✓	$-0.293$	$0$	$0.595740$	Character $\chi_{2349}(1100, \cdot)$
1-2349-2349.1111-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1111	$0$	✓	✓	$0.157$	$0$	$1.19810$	Character $\chi_{2349}(1111, \cdot)$
1-2349-2349.1112-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1112	$0$	✓	✓	$-0.117$	$0$	$0.641234$	Character $\chi_{2349}(1112, \cdot)$
1-2349-2349.112-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.112	$0$	✓	✓	$-0.0690$	$0$	$1.26769$	Character $\chi_{2349}(112, \cdot)$
1-2349-2349.1121-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1121	$0$	✓	✓	$0.0203$	$0$	$1.33199$	Character $\chi_{2349}(1121, \cdot)$
1-2349-2349.113-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.113	$0$	✓	✓	$-0.199$	$0$	$0.754842$	Character $\chi_{2349}(113, \cdot)$
1-2349-2349.1138-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1138	$0$	✓	✓	$0.167$	$0$	$0.882312$	Character $\chi_{2349}(1138, \cdot)$
1-2349-2349.1139-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1139	$0$	✓	✓	$0.415$	$0$	$1.59298$	Character $\chi_{2349}(1139, \cdot)$
1-2349-2349.1145-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1145	$0$	✓	✓	$0.249$	$0$	$0.0837941$	Character $\chi_{2349}(1145, \cdot)$
1-2349-2349.1147-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1147	$0$	✓	✓	$-0.229$	$0$	$0.169321$	Character $\chi_{2349}(1147, \cdot)$
1-2349-2349.1148-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1148	$0$	✓	✓	$0.0468$	$0$	$1.14549$	Character $\chi_{2349}(1148, \cdot)$
1-2349-2349.115-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.115	$0$	✓	✓	$0.283$	$0$	$0.952399$	Character $\chi_{2349}(115, \cdot)$
1-2349-2349.1156-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1156	$0$	✓	✓	$0.0420$	$0$	$0.904460$	Character $\chi_{2349}(1156, \cdot)$
1-2349-2349.1157-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1157	$0$	✓	✓	$0.356$	$0$	$0.300935$	Character $\chi_{2349}(1157, \cdot)$
1-2349-2349.1159-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1159	$0$	✓	✓	$0.172$	$0$	$0.512864$	Character $\chi_{2349}(1159, \cdot)$
1-2349-2349.1163-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1163	$0$	✓	✓	$0.117$	$0$	$1.19995$	Character $\chi_{2349}(1163, \cdot)$
1-2349-2349.1165-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1165	$0$	✓	✓	$0.238$	$0$	$0.838101$	Character $\chi_{2349}(1165, \cdot)$
1-2349-2349.1172-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1172	$0$	✓	✓	$0.286$	$0$	$0.748108$	Character $\chi_{2349}(1172, \cdot)$
1-2349-2349.1175-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1175	$0$	✓	✓	$-0.264$	$0$	$0.786654$	Character $\chi_{2349}(1175, \cdot)$
1-2349-2349.1181-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1181	$0$	✓	✓	$-0.207$	$0$	$0.532408$	Character $\chi_{2349}(1181, \cdot)$
1-2349-2349.1183-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1183	$0$	✓	✓	$0.372$	$0$	$0.794934$	Character $\chi_{2349}(1183, \cdot)$
1-2349-2349.119-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.119	$0$	✓	✓	$0.450$	$0$	$1.44308$	Character $\chi_{2349}(119, \cdot)$
1-2349-2349.1195-r0-0-0	$10.9$	$10.9$	$1$	$3^{4} \cdot 29$	2349.1195	$0$	✓	✓	$0.0948$	$0$	$0.850543$	Character $\chi_{2349}(1195, \cdot)$

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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
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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.