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
1-2557-2557.10-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.10	$0$	✓	✓	$-0.386$	$0$	$0.522480$	Character $\chi_{2557}(10, \cdot)$
1-2557-2557.100-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.100	$0$	✓	✓	$-0.244$	$0$	$0.760406$	Character $\chi_{2557}(100, \cdot)$
1-2557-2557.1000-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1000	$0$	✓	✓	$-0.111$	$0$	$1.40511$	Character $\chi_{2557}(1000, \cdot)$
1-2557-2557.1001-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1001	$0$	✓	✓	$0.208$	$0$	$1.07545$	Character $\chi_{2557}(1001, \cdot)$
1-2557-2557.1002-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1002	$0$	✓	✓	$-0.146$	$0$	$0.179544$	Character $\chi_{2557}(1002, \cdot)$
1-2557-2557.1005-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1005	$0$	✓	✓	$0.462$	$0$	$0.100613$	Character $\chi_{2557}(1005, \cdot)$
1-2557-2557.1007-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1007	$0$	✓	✓	$-0.424$	$0$	$0.396457$	Character $\chi_{2557}(1007, \cdot)$
1-2557-2557.1008-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1008	$0$	✓	✓	$0.146$	$0$	$0.351581$	Character $\chi_{2557}(1008, \cdot)$
1-2557-2557.1012-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1012	$0$	✓	✓	$0.372$	$0$	$1.12745$	Character $\chi_{2557}(1012, \cdot)$
1-2557-2557.1018-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1018	$0$	✓	✓	$0.170$	$0$	$0.580157$	Character $\chi_{2557}(1018, \cdot)$
1-2557-2557.102-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.102	$0$	✓	✓	$-0.213$	$0$	$0.819057$	Character $\chi_{2557}(102, \cdot)$
1-2557-2557.1020-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1020	$0$	✓	✓	$0.219$	$0$	$0.643793$	Character $\chi_{2557}(1020, \cdot)$
1-2557-2557.1024-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1024	$0$	✓	✓	$0.137$	$0$	$0.963988$	Character $\chi_{2557}(1024, \cdot)$
1-2557-2557.1028-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1028	$0$	✓	✓	$-0.484$	$0$	$0.614283$	Character $\chi_{2557}(1028, \cdot)$
1-2557-2557.1029-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1029	$0$	✓	✓	$-0.279$	$0$	$1.11770$	Character $\chi_{2557}(1029, \cdot)$
1-2557-2557.1031-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1031	$0$	✓	✓	$-0.471$	$0$	$1.22643$	Character $\chi_{2557}(1031, \cdot)$
1-2557-2557.1032-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1032	$0$	✓	✓	$0.186$	$0$	$1.22572$	Character $\chi_{2557}(1032, \cdot)$
1-2557-2557.1033-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1033	$0$	✓	✓	$-0.202$	$0$	$0.229544$	Character $\chi_{2557}(1033, \cdot)$
1-2557-2557.1034-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1034	$0$	✓	✓	$0.225$	$0$	$0.0375054$	Character $\chi_{2557}(1034, \cdot)$
1-2557-2557.1036-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1036	$0$	✓	✓	$0.362$	$0$	$0.121587$	Character $\chi_{2557}(1036, \cdot)$
1-2557-2557.1042-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1042	$0$	✓	✓	$0.101$	$0$	$1.57381$	Character $\chi_{2557}(1042, \cdot)$
1-2557-2557.1043-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1043	$0$	✓	✓	$-0.452$	$0$	$0.255483$	Character $\chi_{2557}(1043, \cdot)$
1-2557-2557.1044-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1044	$0$	✓	✓	$0.192$	$0$	$0.932030$	Character $\chi_{2557}(1044, \cdot)$
1-2557-2557.1048-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1048	$0$	✓	✓	$0.218$	$0$	$0.198633$	Character $\chi_{2557}(1048, \cdot)$
1-2557-2557.1049-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1049	$0$	✓	✓	$-0.115$	$0$	$0.778267$	Character $\chi_{2557}(1049, \cdot)$
1-2557-2557.1051-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1051	$0$	✓	✓	$-0.239$	$0$	$0.992712$	Character $\chi_{2557}(1051, \cdot)$
1-2557-2557.1052-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1052	$0$	✓	✓	$-0.377$	$0$	$0.684330$	Character $\chi_{2557}(1052, \cdot)$
1-2557-2557.1053-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1053	$0$	✓	✓	$0.0913$	$0$	$0.928277$	Character $\chi_{2557}(1053, \cdot)$
1-2557-2557.1059-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1059	$0$	✓	✓	$0.465$	$0$	$1.04299$	Character $\chi_{2557}(1059, \cdot)$
1-2557-2557.1061-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1061	$0$	✓	✓	$0.289$	$0$	$0.483794$	Character $\chi_{2557}(1061, \cdot)$
1-2557-2557.1063-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1063	$0$	✓	✓	$0.189$	$0$	$1.48858$	Character $\chi_{2557}(1063, \cdot)$
1-2557-2557.1066-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1066	$0$	✓	✓	$-0.303$	$0$	$0.517524$	Character $\chi_{2557}(1066, \cdot)$
1-2557-2557.1067-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1067	$0$	✓	✓	$-0.479$	$0$	$0.0988556$	Character $\chi_{2557}(1067, \cdot)$
1-2557-2557.1073-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1073	$0$	✓	✓	$-0.249$	$0$	$0.610210$	Character $\chi_{2557}(1073, \cdot)$
1-2557-2557.1076-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1076	$0$	✓	✓	$0.135$	$0$	$0.625213$	Character $\chi_{2557}(1076, \cdot)$
1-2557-2557.1077-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1077	$0$	✓	✓	$0.217$	$0$	$0.993986$	Character $\chi_{2557}(1077, \cdot)$
1-2557-2557.108-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.108	$0$	✓	✓	$-0.279$	$0$	$0.473659$	Character $\chi_{2557}(108, \cdot)$
1-2557-2557.1080-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1080	$0$	✓	✓	$-0.412$	$0$	$0.578105$	Character $\chi_{2557}(1080, \cdot)$
1-2557-2557.1082-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1082	$0$	✓	✓	$0.484$	$0$	$1.29003$	Character $\chi_{2557}(1082, \cdot)$
1-2557-2557.1083-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1083	$0$	✓	✓	$0.247$	$0$	$0.845314$	Character $\chi_{2557}(1083, \cdot)$
1-2557-2557.1085-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1085	$0$	✓	✓	$0.377$	$0$	$1.70614$	Character $\chi_{2557}(1085, \cdot)$
1-2557-2557.1086-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1086	$0$	✓	✓	$-0.0689$	$0$	$2.29258$	Character $\chi_{2557}(1086, \cdot)$
1-2557-2557.1087-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1087	$0$	✓	✓	$-0.183$	$0$	$0.935668$	Character $\chi_{2557}(1087, \cdot)$
1-2557-2557.1089-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1089	$0$	✓	✓	$-0.372$	$0$	$0.406584$	Character $\chi_{2557}(1089, \cdot)$
1-2557-2557.1091-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1091	$0$	✓	✓	$-0.300$	$0$	$1.00520$	Character $\chi_{2557}(1091, \cdot)$
1-2557-2557.1092-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1092	$0$	✓	✓	$-0.0671$	$0$	$0.719804$	Character $\chi_{2557}(1092, \cdot)$
1-2557-2557.1094-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1094	$0$	✓	✓	$0.485$	$0$	$1.49843$	Character $\chi_{2557}(1094, \cdot)$
1-2557-2557.1096-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.1096	$0$	✓	✓	$-0.0688$	$0$	$0.429618$	Character $\chi_{2557}(1096, \cdot)$
1-2557-2557.11-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.11	$0$	✓	✓	$0.0310$	$0$	$1.26762$	Character $\chi_{2557}(11, \cdot)$
1-2557-2557.110-r0-0-0	$11.8$	$11.8$	$1$	$2557$	2557.110	$0$	✓	✓	$-0.162$	$0$	$0.611348$	Character $\chi_{2557}(110, \cdot)$

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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.