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 958 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4015-4015.1003-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1003	$0$	✓	✓	$0.000878$	$0$	$0.588190$	Character $\chi_{4015}(1003, \cdot)$
1-4015-4015.1004-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1004	$0$	✓	✓	$-0.387$	$0$	$0.245505$	Character $\chi_{4015}(1004, \cdot)$
1-4015-4015.1009-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1009	$0$	✓	✓	$0.161$	$0$	$0.921190$	Character $\chi_{4015}(1009, \cdot)$
1-4015-4015.1017-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1017	$0$	✓	✓	$-0.0272$	$0$	$1.01659$	Character $\chi_{4015}(1017, \cdot)$
1-4015-4015.1018-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1018	$0$	✓	✓	$-0.375$	$0$	$0.462438$	Character $\chi_{4015}(1018, \cdot)$
1-4015-4015.102-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.102	$0$	✓	✓	$-0.0575$	$0$	$1.25033$	Character $\chi_{4015}(102, \cdot)$
1-4015-4015.1027-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1027	$0$	✓	✓	$-0.311$	$0$	$0.149245$	Character $\chi_{4015}(1027, \cdot)$
1-4015-4015.1029-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1029	$0$	✓	✓	$-0.490$	$0$	$1.43254$	Character $\chi_{4015}(1029, \cdot)$
1-4015-4015.103-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.103	$0$	✓	✓	$-0.0320$	$0$	$0.854388$	Character $\chi_{4015}(103, \cdot)$
1-4015-4015.1032-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1032	$0$	✓	✓	$-0.272$	$0$	$0.415387$	Character $\chi_{4015}(1032, \cdot)$
1-4015-4015.1037-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1037	$0$	✓	✓	$0.468$	$0$	$0.410458$	Character $\chi_{4015}(1037, \cdot)$
1-4015-4015.1043-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1043	$0$	✓	✓	$0.463$	$0$	$0.171074$	Character $\chi_{4015}(1043, \cdot)$
1-4015-4015.1044-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1044	$0$	✓	✓	$-0.432$	$0$	$0.492607$	Character $\chi_{4015}(1044, \cdot)$
1-4015-4015.1047-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1047	$0$	✓	✓	$0.345$	$0$	$0.189225$	Character $\chi_{4015}(1047, \cdot)$
1-4015-4015.1048-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1048	$0$	✓	✓	$0.160$	$0$	$1.07766$	Character $\chi_{4015}(1048, \cdot)$
1-4015-4015.1049-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1049	$0$	✓	✓	$-0.0997$	$0$	$0.711983$	Character $\chi_{4015}(1049, \cdot)$
1-4015-4015.1054-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1054	$0$	✓	✓	$-0.290$	$0$	$0.465714$	Character $\chi_{4015}(1054, \cdot)$
1-4015-4015.1058-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1058	$0$	✓	✓	$-0.0563$	$0$	$0.657849$	Character $\chi_{4015}(1058, \cdot)$
1-4015-4015.1059-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1059	$0$	✓	✓	$0.255$	$0$	$0.456229$	Character $\chi_{4015}(1059, \cdot)$
1-4015-4015.1063-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1063	$0$	✓	✓	$0.301$	$0$	$1.28315$	Character $\chi_{4015}(1063, \cdot)$
1-4015-4015.1064-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1064	$0$	✓	✓	$0.0162$	$0$	$1.12820$	Character $\chi_{4015}(1064, \cdot)$
1-4015-4015.1069-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1069	$0$	✓	✓	$0.0936$	$0$	$1.12675$	Character $\chi_{4015}(1069, \cdot)$
1-4015-4015.1074-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1074	$0$	✓	✓	$0.280$	$0$	$0.634097$	Character $\chi_{4015}(1074, \cdot)$
1-4015-4015.1077-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1077	$0$	✓	✓	$0.245$	$0$	$1.12699$	Character $\chi_{4015}(1077, \cdot)$
1-4015-4015.1082-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1082	$0$	✓	✓	$0.142$	$0$	$0.903651$	Character $\chi_{4015}(1082, \cdot)$
1-4015-4015.1084-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1084	$0$	✓	✓	$0.162$	$0$	$0.607891$	Character $\chi_{4015}(1084, \cdot)$
1-4015-4015.1094-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1094	$0$	✓	✓	$0.0427$	$0$	$1.10242$	Character $\chi_{4015}(1094, \cdot)$
1-4015-4015.1097-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1097	$0$	✓	✓	$-0.0598$	$0$	$0.747178$	Character $\chi_{4015}(1097, \cdot)$
1-4015-4015.1104-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1104	$0$	✓	✓	$0.348$	$0$	$1.39942$	Character $\chi_{4015}(1104, \cdot)$
1-4015-4015.1107-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1107	$0$	✓	✓	$-0.221$	$0$	$1.45579$	Character $\chi_{4015}(1107, \cdot)$
1-4015-4015.1113-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1113	$0$	✓	✓	$-0.300$	$0$	$0.368589$	Character $\chi_{4015}(1113, \cdot)$
1-4015-4015.1114-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1114	$0$	✓	✓	$0.335$	$0$	$0.887757$	Character $\chi_{4015}(1114, \cdot)$
1-4015-4015.1118-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1118	$0$	✓	✓	$-0.191$	$0$	$0.554672$	Character $\chi_{4015}(1118, \cdot)$
1-4015-4015.1124-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1124	$0$	✓	✓	$0.0546$	$0$	$0.380255$	Character $\chi_{4015}(1124, \cdot)$
1-4015-4015.1129-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1129	$0$	✓	✓	$-0.296$	$0$	$0.275515$	Character $\chi_{4015}(1129, \cdot)$
1-4015-4015.113-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.113	$0$	✓	✓	$0.00292$	$0$	$0.566945$	Character $\chi_{4015}(113, \cdot)$
1-4015-4015.1132-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1132	$0$	✓	✓	$-0.102$	$0$	$0.939343$	Character $\chi_{4015}(1132, \cdot)$
1-4015-4015.1137-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1137	$0$	✓	✓	$0.00292$	$0$	$0.477404$	Character $\chi_{4015}(1137, \cdot)$
1-4015-4015.1138-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1138	$0$	✓	✓	$-0.390$	$0$	$0.659842$	Character $\chi_{4015}(1138, \cdot)$
1-4015-4015.1139-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1139	$0$	✓	✓	$-0.193$	$0$	$0.154571$	Character $\chi_{4015}(1139, \cdot)$
1-4015-4015.114-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.114	$0$	✓	✓	$0.104$	$0$	$0.520293$	Character $\chi_{4015}(114, \cdot)$
1-4015-4015.1142-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1142	$0$	✓	✓	$-0.257$	$0$	$0.0876894$	Character $\chi_{4015}(1142, \cdot)$
1-4015-4015.1143-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1143	$0$	✓	✓	$0.156$	$0$	$0.593752$	Character $\chi_{4015}(1143, \cdot)$
1-4015-4015.1147-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1147	$0$	✓	✓	$-0.0243$	$0$	$0.221856$	Character $\chi_{4015}(1147, \cdot)$
1-4015-4015.1148-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1148	$0$	✓	✓	$-0.343$	$0$	$0.306189$	Character $\chi_{4015}(1148, \cdot)$
1-4015-4015.1149-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1149	$0$	✓	✓	$0.235$	$0$	$0.0151565$	Character $\chi_{4015}(1149, \cdot)$
1-4015-4015.1152-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1152	$0$	✓	✓	$-0.301$	$0$	$0.296473$	Character $\chi_{4015}(1152, \cdot)$
1-4015-4015.1153-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1153	$0$	✓	✓	$-0.244$	$0$	$0.210538$	Character $\chi_{4015}(1153, \cdot)$
1-4015-4015.1154-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1154	$0$	✓	✓	$-0.302$	$0$	$0.448271$	Character $\chi_{4015}(1154, \cdot)$
1-4015-4015.1158-r0-0-0	$18.6$	$18.6$	$1$	$5 \cdot 11 \cdot 73$	4015.1158	$0$	✓	✓	$0.0220$	$0$	$0.831667$	Character $\chi_{4015}(1158, \cdot)$

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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.