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 360 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1183-1183.100-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.100	$0$	✓	✓	$-0.215$	$0$	$0.721326$	Character $\chi_{1183}(100, \cdot)$
1-1183-1183.1005-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1005	$0$	✓	✓	$-0.121$	$0$	$0.774608$	Character $\chi_{1183}(1005, \cdot)$
1-1183-1183.1006-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1006	$0$	✓	✓	$0.114$	$0$	$0.661459$	Character $\chi_{1183}(1006, \cdot)$
1-1183-1183.1007-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1007	$0$	✓	✓	$-0.364$	$0$	$1.59732$	Character $\chi_{1183}(1007, \cdot)$
1-1183-1183.1010-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1010	$0$	✓	✓	$0.384$	$0$	$1.53917$	Character $\chi_{1183}(1010, \cdot)$
1-1183-1183.1017-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1017	$0$	✓	✓	$-0.215$	$0$	$0.749006$	Character $\chi_{1183}(1017, \cdot)$
1-1183-1183.1020-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1020	$0$	✓	✓	$0.00390$	$0$	$0.464922$	Character $\chi_{1183}(1020, \cdot)$
1-1183-1183.1021-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1021	$0$	✓	✓	$0.135$	$0$	$0.935622$	Character $\chi_{1183}(1021, \cdot)$
1-1183-1183.1024-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1024	$0$	✓	✓	$-0.208$	$0$	$0.453028$	Character $\chi_{1183}(1024, \cdot)$
1-1183-1183.1025-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1025	$0$	✓	✓	$-0.118$	$0$	$1.14476$	Character $\chi_{1183}(1025, \cdot)$
1-1183-1183.1026-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1026	$0$	✓	✓	$-0.367$	$0$	$0.235205$	Character $\chi_{1183}(1026, \cdot)$
1-1183-1183.1031-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1031	$0$	✓	✓	$0.0618$	$0$	$0.836922$	Character $\chi_{1183}(1031, \cdot)$
1-1183-1183.1032-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1032	$0$	✓	✓	$0.0610$	$0$	$1.58606$	Character $\chi_{1183}(1032, \cdot)$
1-1183-1183.1034-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1034	$0$	✓	✓	$0.272$	$0$	$0.225513$	Character $\chi_{1183}(1034, \cdot)$
1-1183-1183.1035-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1035	$0$	✓	✓	$-0.301$	$0$	$0.283073$	Character $\chi_{1183}(1035, \cdot)$
1-1183-1183.1042-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1042	$0$	✓	✓	$-0.182$	$0$	$0.831737$	Character $\chi_{1183}(1042, \cdot)$
1-1183-1183.1046-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1046	$0$	✓	✓	$0.337$	$0$	$1.25277$	Character $\chi_{1183}(1046, \cdot)$
1-1183-1183.1048-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1048	$0$	✓	✓	$-0.246$	$0$	$0.509710$	Character $\chi_{1183}(1048, \cdot)$
1-1183-1183.1052-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1052	$0$	✓	✓	$0.0658$	$0$	$1.03652$	Character $\chi_{1183}(1052, \cdot)$
1-1183-1183.1054-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1054	$0$	✓	✓	$0.434$	$0$	$1.33205$	Character $\chi_{1183}(1054, \cdot)$
1-1183-1183.1055-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1055	$0$	✓	✓	$-0.0788$	$0$	$0.108030$	Character $\chi_{1183}(1055, \cdot)$
1-1183-1183.1060-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1060	$0$	✓	✓	$-0.00744$	$0$	$0.0738683$	Character $\chi_{1183}(1060, \cdot)$
1-1183-1183.107-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.107	$0$	✓	✓	$-0.0140$	$0$	$0.587618$	Character $\chi_{1183}(107, \cdot)$
1-1183-1183.1074-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1074	$0$	✓	✓	$-0.329$	$0$	$0.0605222$	Character $\chi_{1183}(1074, \cdot)$
1-1183-1183.1075-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1075	$0$	✓	✓	$0.104$	$0$	$0.771249$	Character $\chi_{1183}(1075, \cdot)$
1-1183-1183.1077-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1077	$0$	✓	✓	$-0.0591$	$0$	$0.606075$	Character $\chi_{1183}(1077, \cdot)$
1-1183-1183.1080-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1080	$0$	✓	✓	$-0.215$	$0$	$0.409705$	Character $\chi_{1183}(1080, \cdot)$
1-1183-1183.1081-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1081	$0$	✓	✓	$-0.0207$	$0$	$1.06551$	Character $\chi_{1183}(1081, \cdot)$
1-1183-1183.1082-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1082	$0$	✓	✓	$0.140$	$0$	$0.609429$	Character $\chi_{1183}(1082, \cdot)$
1-1183-1183.1089-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1089	$0$	✓	✓	$0.267$	$0$	$0.540037$	Character $\chi_{1183}(1089, \cdot)$
1-1183-1183.1090-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1090	$0$	✓	✓	$0.354$	$0$	$1.89006$	Character $\chi_{1183}(1090, \cdot)$
1-1183-1183.1096-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1096	$0$	✓	✓	$0.00618$	$0$	$1.39122$	Character $\chi_{1183}(1096, \cdot)$
1-1183-1183.1097-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1097	$0$	✓	✓	$-0.294$	$0$	$1.02422$	Character $\chi_{1183}(1097, \cdot)$
1-1183-1183.1098-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1098	$0$	✓	✓	$-0.472$	$0$	$0.376327$	Character $\chi_{1183}(1098, \cdot)$
1-1183-1183.110-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.110	$0$	✓	✓	$-0.127$	$0$	$0.733340$	Character $\chi_{1183}(110, \cdot)$
1-1183-1183.1101-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1101	$0$	✓	✓	$-0.140$	$0$	$0.944129$	Character $\chi_{1183}(1101, \cdot)$
1-1183-1183.1108-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1108	$0$	✓	✓	$-0.378$	$0$	$2.20156$	Character $\chi_{1183}(1108, \cdot)$
1-1183-1183.111-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.111	$0$	✓	✓	$0.207$	$0$	$1.38722$	Character $\chi_{1183}(111, \cdot)$
1-1183-1183.1111-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1111	$0$	✓	✓	$0.246$	$0$	$1.22899$	Character $\chi_{1183}(1111, \cdot)$
1-1183-1183.1112-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1112	$0$	✓	✓	$0.107$	$0$	$0.873874$	Character $\chi_{1183}(1112, \cdot)$
1-1183-1183.1115-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1115	$0$	✓	✓	$-0.00618$	$0$	$0.907150$	Character $\chi_{1183}(1115, \cdot)$
1-1183-1183.1116-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1116	$0$	✓	✓	$-0.0207$	$0$	$0.602874$	Character $\chi_{1183}(1116, \cdot)$
1-1183-1183.1117-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1117	$0$	✓	✓	$-0.0687$	$0$	$0.837585$	Character $\chi_{1183}(1117, \cdot)$
1-1183-1183.1122-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1122	$0$	✓	✓	$0.458$	$0$	$1.95405$	Character $\chi_{1183}(1122, \cdot)$
1-1183-1183.1123-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1123	$0$	✓	✓	$-0.329$	$0$	$0.316756$	Character $\chi_{1183}(1123, \cdot)$
1-1183-1183.1125-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1125	$0$	✓	✓	$0.0207$	$0$	$0.725985$	Character $\chi_{1183}(1125, \cdot)$
1-1183-1183.1126-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1126	$0$	✓	✓	$0.107$	$0$	$1.35913$	Character $\chi_{1183}(1126, \cdot)$
1-1183-1183.1133-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1133	$0$	✓	✓	$-0.107$	$0$	$0.889690$	Character $\chi_{1183}(1133, \cdot)$
1-1183-1183.1137-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1137	$0$	✓	✓	$0.492$	$0$	$0.176888$	Character $\chi_{1183}(1137, \cdot)$
1-1183-1183.1139-r0-0-0	$5.49$	$5.49$	$1$	$7 \cdot 13^{2}$	1183.1139	$0$	✓	✓	$-0.0477$	$0$	$0.961259$	Character $\chi_{1183}(1139, \cdot)$

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Classical	Maass
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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.