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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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4029-4029.1001-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1001	$0$	✓	✓	$-0.0531$	$0$	$0.660986$	Character $\chi_{4029}(1001, \cdot)$
1-4029-4029.1007-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1007	$0$	✓	✓	$-0.0520$	$0$	$0.722061$	Character $\chi_{4029}(1007, \cdot)$
1-4029-4029.1010-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1010	$0$	✓	✓	$-0.186$	$0$	$0.148533$	Character $\chi_{4029}(1010, \cdot)$
1-4029-4029.1013-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1013	$0$	✓	✓	$-0.325$	$0$	$0.153145$	Character $\chi_{4029}(1013, \cdot)$
1-4029-4029.1016-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1016	$0$	✓	✓	$0.255$	$0$	$0.721686$	Character $\chi_{4029}(1016, \cdot)$
1-4029-4029.1019-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1019	$0$	✓	✓	$0.438$	$0$	$1.13699$	Character $\chi_{4029}(1019, \cdot)$
1-4029-4029.1022-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1022	$0$	✓	✓	$0.276$	$0$	$1.38703$	Character $\chi_{4029}(1022, \cdot)$
1-4029-4029.1031-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1031	$0$	✓	✓	$0.366$	$0$	$1.59399$	Character $\chi_{4029}(1031, \cdot)$
1-4029-4029.1040-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1040	$0$	✓	✓	$-0.129$	$0$	$0.543015$	Character $\chi_{4029}(1040, \cdot)$
1-4029-4029.1043-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1043	$0$	✓	✓	$-0.0822$	$0$	$0.736940$	Character $\chi_{4029}(1043, \cdot)$
1-4029-4029.1049-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1049	$0$	✓	✓	$-0.400$	$0$	$0.602111$	Character $\chi_{4029}(1049, \cdot)$
1-4029-4029.1070-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1070	$0$	✓	✓	$-0.110$	$0$	$0.907230$	Character $\chi_{4029}(1070, \cdot)$
1-4029-4029.1076-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1076	$0$	✓	✓	$0.324$	$0$	$0.608012$	Character $\chi_{4029}(1076, \cdot)$
1-4029-4029.1082-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1082	$0$	✓	✓	$-0.410$	$0$	$1.47297$	Character $\chi_{4029}(1082, \cdot)$
1-4029-4029.1091-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1091	$0$	✓	✓	$-0.377$	$0$	$0.622249$	Character $\chi_{4029}(1091, \cdot)$
1-4029-4029.1094-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1094	$0$	✓	✓	$0.0281$	$0$	$0.612346$	Character $\chi_{4029}(1094, \cdot)$
1-4029-4029.1097-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1097	$0$	✓	✓	$0.351$	$0$	$0.946447$	Character $\chi_{4029}(1097, \cdot)$
1-4029-4029.11-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.11	$0$	✓	✓	$-0.0742$	$0$	$0.567673$	Character $\chi_{4029}(11, \cdot)$
1-4029-4029.1100-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1100	$0$	✓	✓	$0.00964$	$0$	$0.341623$	Character $\chi_{4029}(1100, \cdot)$
1-4029-4029.1109-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1109	$0$	✓	✓	$0.146$	$0$	$1.15997$	Character $\chi_{4029}(1109, \cdot)$
1-4029-4029.1115-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1115	$0$	✓	✓	$0.246$	$0$	$0.613975$	Character $\chi_{4029}(1115, \cdot)$
1-4029-4029.1118-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1118	$0$	✓	✓	$-0.0614$	$0$	$0.901172$	Character $\chi_{4029}(1118, \cdot)$
1-4029-4029.1121-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1121	$0$	✓	✓	$-0.246$	$0$	$0.558638$	Character $\chi_{4029}(1121, \cdot)$
1-4029-4029.1127-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1127	$0$	✓	✓	$-0.181$	$0$	$0.709677$	Character $\chi_{4029}(1127, \cdot)$
1-4029-4029.1130-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1130	$0$	✓	✓	$-0.206$	$0$	$0.972714$	Character $\chi_{4029}(1130, \cdot)$
1-4029-4029.1142-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1142	$0$	✓	✓	$0.248$	$0$	$0.277655$	Character $\chi_{4029}(1142, \cdot)$
1-4029-4029.1151-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1151	$0$	✓	✓	$0.459$	$0$	$0.932404$	Character $\chi_{4029}(1151, \cdot)$
1-4029-4029.1154-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1154	$0$	✓	✓	$-0.463$	$0$	$0.491595$	Character $\chi_{4029}(1154, \cdot)$
1-4029-4029.1160-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1160	$0$	✓	✓	$-0.0418$	$0$	$0.735601$	Character $\chi_{4029}(1160, \cdot)$
1-4029-4029.1169-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1169	$0$	✓	✓	$-0.0145$	$0$	$0.906646$	Character $\chi_{4029}(1169, \cdot)$
1-4029-4029.1172-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1172	$0$	✓	✓	$0.200$	$0$	$0.831354$	Character $\chi_{4029}(1172, \cdot)$
1-4029-4029.1175-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1175	$0$	✓	✓	$-0.321$	$0$	$1.68513$	Character $\chi_{4029}(1175, \cdot)$
1-4029-4029.1178-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1178	$0$	✓	✓	$0.0525$	$0$	$0.893739$	Character $\chi_{4029}(1178, \cdot)$
1-4029-4029.1181-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1181	$0$	✓	✓	$-0.330$	$0$	$0.680974$	Character $\chi_{4029}(1181, \cdot)$
1-4029-4029.1187-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1187	$0$	✓	✓	$-0.368$	$0$	$0.339841$	Character $\chi_{4029}(1187, \cdot)$
1-4029-4029.1193-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1193	$0$	✓	✓	$-0.0468$	$0$	$0.709163$	Character $\chi_{4029}(1193, \cdot)$
1-4029-4029.1196-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1196	$0$	✓	✓	$-0.248$	$0$	$1.80604$	Character $\chi_{4029}(1196, \cdot)$
1-4029-4029.1199-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1199	$0$	✓	✓	$-0.455$	$0$	$1.21586$	Character $\chi_{4029}(1199, \cdot)$
1-4029-4029.1217-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1217	$0$	✓	✓	$0.285$	$0$	$0.641949$	Character $\chi_{4029}(1217, \cdot)$
1-4029-4029.1220-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1220	$0$	✓	✓	$-0.325$	$0$	$0.572104$	Character $\chi_{4029}(1220, \cdot)$
1-4029-4029.1226-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1226	$0$	✓	✓	$-0.109$	$0$	$0.552073$	Character $\chi_{4029}(1226, \cdot)$
1-4029-4029.1229-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1229	$0$	✓	✓	$0.307$	$0$	$1.20274$	Character $\chi_{4029}(1229, \cdot)$
1-4029-4029.1232-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1232	$0$	✓	✓	$0.285$	$0$	$0.806378$	Character $\chi_{4029}(1232, \cdot)$
1-4029-4029.1235-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1235	$0$	✓	✓	$0.484$	$0$	$0.846178$	Character $\chi_{4029}(1235, \cdot)$
1-4029-4029.1247-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1247	$0$	✓	✓	$0.445$	$0$	$0.227628$	Character $\chi_{4029}(1247, \cdot)$
1-4029-4029.125-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.125	$0$	✓	✓	$0.162$	$0$	$0.734962$	Character $\chi_{4029}(125, \cdot)$
1-4029-4029.1256-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1256	$0$	✓	✓	$-0.323$	$0$	$0.368616$	Character $\chi_{4029}(1256, \cdot)$
1-4029-4029.1262-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1262	$0$	✓	✓	$-0.364$	$0$	$1.03159$	Character $\chi_{4029}(1262, \cdot)$
1-4029-4029.1268-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1268	$0$	✓	✓	$0.118$	$0$	$0.962614$	Character $\chi_{4029}(1268, \cdot)$
1-4029-4029.1271-r0-0-0	$18.7$	$18.7$	$1$	$3 \cdot 17 \cdot 79$	4029.1271	$0$	✓	✓	$-0.0193$	$0$	$1.13777$	Character $\chi_{4029}(1271, \cdot)$

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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.