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

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1181-1181.100-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.100	$0$	✓	✓	$0.483$	$0$	$1.19886$	Character $\chi_{1181}(100, \cdot)$
1-1181-1181.1001-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1001	$0$	✓	✓	$0.130$	$0$	$0.930127$	Character $\chi_{1181}(1001, \cdot)$
1-1181-1181.1002-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1002	$0$	✓	✓	$-0.380$	$0$	$0.518332$	Character $\chi_{1181}(1002, \cdot)$
1-1181-1181.1003-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1003	$0$	✓	✓	$-0.387$	$0$	$1.82061$	Character $\chi_{1181}(1003, \cdot)$
1-1181-1181.1005-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1005	$0$	✓	✓	$-0.127$	$0$	$0.101752$	Character $\chi_{1181}(1005, \cdot)$
1-1181-1181.101-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.101	$0$	✓	✓	$-0.448$	$0$	$0.449178$	Character $\chi_{1181}(101, \cdot)$
1-1181-1181.1012-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1012	$0$	✓	✓	$0.0829$	$0$	$1.49893$	Character $\chi_{1181}(1012, \cdot)$
1-1181-1181.1014-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1014	$0$	✓	✓	$-0.181$	$0$	$0.553139$	Character $\chi_{1181}(1014, \cdot)$
1-1181-1181.1015-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1015	$0$	✓	✓	$0.0274$	$0$	$0.431210$	Character $\chi_{1181}(1015, \cdot)$
1-1181-1181.1017-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1017	$0$	✓	✓	$-0.241$	$0$	$0.287282$	Character $\chi_{1181}(1017, \cdot)$
1-1181-1181.1018-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1018	$0$	✓	✓	$-0.352$	$0$	$0.580716$	Character $\chi_{1181}(1018, \cdot)$
1-1181-1181.102-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.102	$0$	✓	✓	$-0.169$	$0$	$0.188423$	Character $\chi_{1181}(102, \cdot)$
1-1181-1181.1023-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1023	$0$	✓	✓	$0.423$	$0$	$1.50592$	Character $\chi_{1181}(1023, \cdot)$
1-1181-1181.1024-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1024	$0$	✓	✓	$-0.267$	$0$	$0.678493$	Character $\chi_{1181}(1024, \cdot)$
1-1181-1181.1025-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1025	$0$	✓	✓	$0.0307$	$0$	$1.12705$	Character $\chi_{1181}(1025, \cdot)$
1-1181-1181.1027-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1027	$0$	✓	✓	$0.277$	$0$	$0.997954$	Character $\chi_{1181}(1027, \cdot)$
1-1181-1181.1028-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1028	$0$	✓	✓	$-0.185$	$0$	$0.105302$	Character $\chi_{1181}(1028, \cdot)$
1-1181-1181.1029-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1029	$0$	✓	✓	$0.448$	$0$	$1.45754$	Character $\chi_{1181}(1029, \cdot)$
1-1181-1181.1030-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1030	$0$	✓	✓	$-0.0305$	$0$	$0.982574$	Character $\chi_{1181}(1030, \cdot)$
1-1181-1181.1031-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1031	$0$	✓	✓	$0.0927$	$0$	$0.894527$	Character $\chi_{1181}(1031, \cdot)$
1-1181-1181.1033-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1033	$0$	✓	✓	$0.0114$	$0$	$0.361184$	Character $\chi_{1181}(1033, \cdot)$
1-1181-1181.1035-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1035	$0$	✓	✓	$-0.340$	$0$	$0.436525$	Character $\chi_{1181}(1035, \cdot)$
1-1181-1181.1037-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1037	$0$	✓	✓	$-0.130$	$0$	$0.632820$	Character $\chi_{1181}(1037, \cdot)$
1-1181-1181.104-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.104	$0$	✓	✓	$0.314$	$0$	$1.35786$	Character $\chi_{1181}(104, \cdot)$
1-1181-1181.1042-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1042	$0$	✓	✓	$-0.242$	$0$	$0.347093$	Character $\chi_{1181}(1042, \cdot)$
1-1181-1181.1043-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1043	$0$	✓	✓	$0.245$	$0$	$0.677632$	Character $\chi_{1181}(1043, \cdot)$
1-1181-1181.1047-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1047	$0$	✓	✓	$-0.408$	$0$	$0.566627$	Character $\chi_{1181}(1047, \cdot)$
1-1181-1181.1048-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1048	$0$	✓	✓	$-0.0717$	$0$	$0.775234$	Character $\chi_{1181}(1048, \cdot)$
1-1181-1181.105-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.105	$0$	✓	✓	$0.499$	$0$	$0.842099$	Character $\chi_{1181}(105, \cdot)$
1-1181-1181.1051-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1051	$0$	✓	✓	$0.317$	$0$	$0.448820$	Character $\chi_{1181}(1051, \cdot)$
1-1181-1181.1052-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1052	$0$	✓	✓	$0.120$	$0$	$1.18150$	Character $\chi_{1181}(1052, \cdot)$
1-1181-1181.1054-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1054	$0$	✓	✓	$-0.485$	$0$	$0.709764$	Character $\chi_{1181}(1054, \cdot)$
1-1181-1181.1055-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1055	$0$	✓	✓	$-0.188$	$0$	$0.766895$	Character $\chi_{1181}(1055, \cdot)$
1-1181-1181.1056-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1056	$0$	✓	✓	$0.358$	$0$	$0.730661$	Character $\chi_{1181}(1056, \cdot)$
1-1181-1181.1060-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1060	$0$	✓	✓	$-0.450$	$0$	$0.540084$	Character $\chi_{1181}(1060, \cdot)$
1-1181-1181.1061-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1061	$0$	✓	✓	$-0.246$	$0$	$0.190635$	Character $\chi_{1181}(1061, \cdot)$
1-1181-1181.1066-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1066	$0$	✓	✓	$-0.247$	$0$	$1.02184$	Character $\chi_{1181}(1066, \cdot)$
1-1181-1181.1068-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1068	$0$	✓	✓	$-0.167$	$0$	$1.07134$	Character $\chi_{1181}(1068, \cdot)$
1-1181-1181.107-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.107	$0$	✓	✓	$-0.119$	$0$	$1.07718$	Character $\chi_{1181}(107, \cdot)$
1-1181-1181.1074-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1074	$0$	✓	✓	$0.334$	$0$	$0.00486624$	Character $\chi_{1181}(1074, \cdot)$
1-1181-1181.1076-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1076	$0$	✓	✓	$-0.423$	$0$	$1.28487$	Character $\chi_{1181}(1076, \cdot)$
1-1181-1181.1077-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1077	$0$	✓	✓	$-0.112$	$0$	$0.318270$	Character $\chi_{1181}(1077, \cdot)$
1-1181-1181.1079-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1079	$0$	✓	✓	$-0.274$	$0$	$1.05154$	Character $\chi_{1181}(1079, \cdot)$
1-1181-1181.1080-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1080	$0$	✓	✓	$0.377$	$0$	$0.981057$	Character $\chi_{1181}(1080, \cdot)$
1-1181-1181.1081-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1081	$0$	✓	✓	$-0.265$	$0$	$0.222170$	Character $\chi_{1181}(1081, \cdot)$
1-1181-1181.1082-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1082	$0$	✓	✓	$0.0510$	$0$	$0.723492$	Character $\chi_{1181}(1082, \cdot)$
1-1181-1181.1085-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1085	$0$	✓	✓	$-0.489$	$0$	$2.00367$	Character $\chi_{1181}(1085, \cdot)$
1-1181-1181.1088-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1088	$0$	✓	✓	$0.485$	$0$	$1.66939$	Character $\chi_{1181}(1088, \cdot)$
1-1181-1181.1089-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1089	$0$	✓	✓	$0.0448$	$0$	$1.47872$	Character $\chi_{1181}(1089, \cdot)$
1-1181-1181.1090-r0-0-0	$5.48$	$5.48$	$1$	$1181$	1181.1090	$0$	✓	✓	$-0.0168$	$0$	$0.951910$	Character $\chi_{1181}(1090, \cdot)$

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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.