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
1-6145-6145.1008-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1008	$1$	✓	✓	$-0.370$	$0$	$0.401798$	Character $\chi_{6145}(1008, \cdot)$
1-6145-6145.1009-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1009	$1$	✓	✓	$0.127$	$0$	$0.737694$	Character $\chi_{6145}(1009, \cdot)$
1-6145-6145.1012-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1012	$1$	✓	✓	$-0.295$	$0$	$0.210013$	Character $\chi_{6145}(1012, \cdot)$
1-6145-6145.1013-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1013	$1$	✓	✓	$0.197$	$0$	$0.120854$	Character $\chi_{6145}(1013, \cdot)$
1-6145-6145.1017-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1017	$1$	✓	✓	$-0.0549$	$0$	$0.668361$	Character $\chi_{6145}(1017, \cdot)$
1-6145-6145.1023-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1023	$1$	✓	✓	$-0.209$	$0$	$0.696978$	Character $\chi_{6145}(1023, \cdot)$
1-6145-6145.1029-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1029	$1$	✓	✓	$-0.0361$	$0$	$1.28921$	Character $\chi_{6145}(1029, \cdot)$
1-6145-6145.1032-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1032	$1$	✓	✓	$0.230$	$0$	$0.128993$	Character $\chi_{6145}(1032, \cdot)$
1-6145-6145.1033-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1033	$1$	✓	✓	$0.299$	$0$	$0.469706$	Character $\chi_{6145}(1033, \cdot)$
1-6145-6145.1042-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1042	$1$	✓	✓	$0.305$	$0$	$0.0754787$	Character $\chi_{6145}(1042, \cdot)$
1-6145-6145.1043-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1043	$1$	✓	✓	$0.208$	$0$	$1.21429$	Character $\chi_{6145}(1043, \cdot)$
1-6145-6145.1044-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1044	$1$	✓	✓	$-0.123$	$0$	$0.911183$	Character $\chi_{6145}(1044, \cdot)$
1-6145-6145.1047-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1047	$1$	✓	✓	$-0.288$	$0$	$0.577832$	Character $\chi_{6145}(1047, \cdot)$
1-6145-6145.1048-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1048	$1$	✓	✓	$-0.114$	$0$	$0.174591$	Character $\chi_{6145}(1048, \cdot)$
1-6145-6145.1057-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1057	$1$	✓	✓	$-0.00719$	$0$	$0.435326$	Character $\chi_{6145}(1057, \cdot)$
1-6145-6145.1063-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1063	$1$	✓	✓	$-0.405$	$0$	$0.389357$	Character $\chi_{6145}(1063, \cdot)$
1-6145-6145.1069-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1069	$1$	✓	✓	$-0.0237$	$0$	$0.585247$	Character $\chi_{6145}(1069, \cdot)$
1-6145-6145.107-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.107	$1$	✓	✓	$0.359$	$0$	$0.297318$	Character $\chi_{6145}(107, \cdot)$
1-6145-6145.1072-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1072	$1$	✓	✓	$0.231$	$0$	$0.302012$	Character $\chi_{6145}(1072, \cdot)$
1-6145-6145.1073-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1073	$1$	✓	✓	$-0.130$	$0$	$0.364338$	Character $\chi_{6145}(1073, \cdot)$
1-6145-6145.1077-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1077	$1$	✓	✓	$0.00588$	$0$	$0.112688$	Character $\chi_{6145}(1077, \cdot)$
1-6145-6145.1078-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1078	$1$	✓	✓	$-0.213$	$0$	$0.0330815$	Character $\chi_{6145}(1078, \cdot)$
1-6145-6145.1084-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1084	$1$	✓	✓	$0.0648$	$0$	$0.498361$	Character $\chi_{6145}(1084, \cdot)$
1-6145-6145.1087-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1087	$1$	✓	✓	$0.147$	$0$	$0.836775$	Character $\chi_{6145}(1087, \cdot)$
1-6145-6145.109-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.109	$1$	✓	✓	$0.0392$	$0$	$0.450093$	Character $\chi_{6145}(109, \cdot)$
1-6145-6145.1092-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1092	$1$	✓	✓	$0.329$	$0$	$0.190042$	Character $\chi_{6145}(1092, \cdot)$
1-6145-6145.1093-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1093	$1$	✓	✓	$0.396$	$0$	$0.247501$	Character $\chi_{6145}(1093, \cdot)$
1-6145-6145.1094-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1094	$1$	✓	✓	$-0.165$	$0$	$0.213886$	Character $\chi_{6145}(1094, \cdot)$
1-6145-6145.1097-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1097	$1$	✓	✓	$-0.0637$	$0$	$0.724278$	Character $\chi_{6145}(1097, \cdot)$
1-6145-6145.1108-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1108	$1$	✓	✓	$-0.0491$	$0$	$0.564224$	Character $\chi_{6145}(1108, \cdot)$
1-6145-6145.1114-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1114	$1$	✓	✓	$0.0835$	$0$	$0.830038$	Character $\chi_{6145}(1114, \cdot)$
1-6145-6145.1117-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1117	$1$	✓	✓	$-0.0311$	$0$	$0.492432$	Character $\chi_{6145}(1117, \cdot)$
1-6145-6145.1118-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1118	$1$	✓	✓	$-0.449$	$0$	$0.155541$	Character $\chi_{6145}(1118, \cdot)$
1-6145-6145.112-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.112	$1$	✓	✓	$0.272$	$0$	$0.551189$	Character $\chi_{6145}(112, \cdot)$
1-6145-6145.1122-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1122	$1$	✓	✓	$-0.0673$	$0$	$0.589640$	Character $\chi_{6145}(1122, \cdot)$
1-6145-6145.1124-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1124	$1$	✓	✓	$0.195$	$0$	$0.592927$	Character $\chi_{6145}(1124, \cdot)$
1-6145-6145.1128-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1128	$1$	✓	✓	$0.0716$	$0$	$0.566408$	Character $\chi_{6145}(1128, \cdot)$
1-6145-6145.113-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.113	$1$	✓	✓	$0.225$	$0$	$0.356903$	Character $\chi_{6145}(113, \cdot)$
1-6145-6145.1132-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1132	$1$	✓	✓	$0.161$	$0$	$0.668686$	Character $\chi_{6145}(1132, \cdot)$
1-6145-6145.1133-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1133	$1$	✓	✓	$-0.303$	$0$	$0.442586$	Character $\chi_{6145}(1133, \cdot)$
1-6145-6145.1134-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1134	$1$	✓	✓	$-0.199$	$0$	$0.259387$	Character $\chi_{6145}(1134, \cdot)$
1-6145-6145.1139-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1139	$1$	✓	✓	$0.260$	$0$	$0.709494$	Character $\chi_{6145}(1139, \cdot)$
1-6145-6145.114-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.114	$1$	✓	✓	$0.270$	$0$	$0.780548$	Character $\chi_{6145}(114, \cdot)$
1-6145-6145.1142-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1142	$1$	✓	✓	$-0.225$	$0$	$0.347955$	Character $\chi_{6145}(1142, \cdot)$
1-6145-6145.1144-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1144	$1$	✓	✓	$-0.485$	$0$	$0.463471$	Character $\chi_{6145}(1144, \cdot)$
1-6145-6145.1148-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1148	$1$	✓	✓	$0.290$	$0$	$0.392359$	Character $\chi_{6145}(1148, \cdot)$
1-6145-6145.1154-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1154	$1$	✓	✓	$0.115$	$0$	$0.321936$	Character $\chi_{6145}(1154, \cdot)$
1-6145-6145.1159-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1159	$1$	✓	✓	$-0.227$	$0$	$1.12299$	Character $\chi_{6145}(1159, \cdot)$
1-6145-6145.1162-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1162	$1$	✓	✓	$0.454$	$0$	$1.24388$	Character $\chi_{6145}(1162, \cdot)$
1-6145-6145.1164-r1-0-0	$660.$	$660.$	$1$	$5 \cdot 1229$	6145.1164	$1$	✓	✓	$0.136$	$0$	$0.755707$	Character $\chi_{6145}(1164, \cdot)$

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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.