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 945 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4011-4011.1004-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1004	$0$	✓	✓	$0.276$	$0$	$1.26940$	Character $\chi_{4011}(1004, \cdot)$
1-4011-4011.1007-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1007	$0$	✓	✓	$-0.178$	$0$	$0.666059$	Character $\chi_{4011}(1007, \cdot)$
1-4011-4011.1010-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1010	$0$	✓	✓	$0.0647$	$0$	$0.488843$	Character $\chi_{4011}(1010, \cdot)$
1-4011-4011.1031-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1031	$0$	✓	✓	$0.333$	$0$	$0.238552$	Character $\chi_{4011}(1031, \cdot)$
1-4011-4011.1034-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1034	$0$	✓	✓	$-0.181$	$0$	$0.498161$	Character $\chi_{4011}(1034, \cdot)$
1-4011-4011.104-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.104	$0$	✓	✓	$0.0965$	$0$	$0.963243$	Character $\chi_{4011}(104, \cdot)$
1-4011-4011.1055-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1055	$0$	✓	✓	$0.142$	$0$	$1.17669$	Character $\chi_{4011}(1055, \cdot)$
1-4011-4011.1061-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1061	$0$	✓	✓	$-0.441$	$0$	$1.46344$	Character $\chi_{4011}(1061, \cdot)$
1-4011-4011.1070-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1070	$0$	✓	✓	$0.199$	$0$	$0.732812$	Character $\chi_{4011}(1070, \cdot)$
1-4011-4011.1076-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1076	$0$	✓	✓	$-0.0646$	$0$	$0.669784$	Character $\chi_{4011}(1076, \cdot)$
1-4011-4011.1082-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1082	$0$	✓	✓	$0.0189$	$0$	$0.881568$	Character $\chi_{4011}(1082, \cdot)$
1-4011-4011.1088-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1088	$0$	✓	✓	$0.309$	$0$	$1.15427$	Character $\chi_{4011}(1088, \cdot)$
1-4011-4011.1091-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1091	$0$	✓	✓	$0.0501$	$0$	$0.713075$	Character $\chi_{4011}(1091, \cdot)$
1-4011-4011.1094-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1094	$0$	✓	✓	$-0.148$	$0$	$0.823970$	Character $\chi_{4011}(1094, \cdot)$
1-4011-4011.11-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.11	$0$	✓	✓	$0.148$	$0$	$0.905757$	Character $\chi_{4011}(11, \cdot)$
1-4011-4011.1103-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1103	$0$	✓	✓	$0.238$	$0$	$1.23046$	Character $\chi_{4011}(1103, \cdot)$
1-4011-4011.1109-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1109	$0$	✓	✓	$-0.0275$	$0$	$1.87498$	Character $\chi_{4011}(1109, \cdot)$
1-4011-4011.1118-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1118	$0$	✓	✓	$0.137$	$0$	$0.829843$	Character $\chi_{4011}(1118, \cdot)$
1-4011-4011.1136-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1136	$0$	✓	✓	$0.409$	$0$	$0.103033$	Character $\chi_{4011}(1136, \cdot)$
1-4011-4011.1139-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1139	$0$	✓	✓	$0.187$	$0$	$0.101923$	Character $\chi_{4011}(1139, \cdot)$
1-4011-4011.1145-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1145	$0$	✓	✓	$-0.426$	$0$	$0.792473$	Character $\chi_{4011}(1145, \cdot)$
1-4011-4011.1151-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1151	$0$	✓	✓	$0.365$	$0$	$0.894311$	Character $\chi_{4011}(1151, \cdot)$
1-4011-4011.1154-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1154	$0$	✓	✓	$-0.487$	$0$	$1.53416$	Character $\chi_{4011}(1154, \cdot)$
1-4011-4011.1157-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1157	$0$	✓	✓	$0.00219$	$0$	$1.02651$	Character $\chi_{4011}(1157, \cdot)$
1-4011-4011.116-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.116	$0$	✓	✓	$-0.291$	$0$	$0.570365$	Character $\chi_{4011}(116, \cdot)$
1-4011-4011.1172-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1172	$0$	✓	✓	$-0.264$	$0$	$0.467878$	Character $\chi_{4011}(1172, \cdot)$
1-4011-4011.1187-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1187	$0$	✓	✓	$0.383$	$0$	$1.60377$	Character $\chi_{4011}(1187, \cdot)$
1-4011-4011.1196-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1196	$0$	✓	✓	$-0.0945$	$0$	$1.13102$	Character $\chi_{4011}(1196, \cdot)$
1-4011-4011.1199-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1199	$0$	✓	✓	$0.0109$	$0$	$0.334342$	Character $\chi_{4011}(1199, \cdot)$
1-4011-4011.1208-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1208	$0$	✓	✓	$-0.375$	$0$	$0.0253406$	Character $\chi_{4011}(1208, \cdot)$
1-4011-4011.1214-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1214	$0$	✓	✓	$-0.199$	$0$	$0.578074$	Character $\chi_{4011}(1214, \cdot)$
1-4011-4011.1220-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1220	$0$	✓	✓	$0.267$	$0$	$0.131536$	Character $\chi_{4011}(1220, \cdot)$
1-4011-4011.1223-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1223	$0$	✓	✓	$-0.190$	$0$	$0.234457$	Character $\chi_{4011}(1223, \cdot)$
1-4011-4011.1229-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1229	$0$	✓	✓	$0.0646$	$0$	$1.03075$	Character $\chi_{4011}(1229, \cdot)$
1-4011-4011.1238-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1238	$0$	✓	✓	$0.442$	$0$	$0.173961$	Character $\chi_{4011}(1238, \cdot)$
1-4011-4011.1241-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1241	$0$	✓	✓	$-0.0641$	$0$	$0.948382$	Character $\chi_{4011}(1241, \cdot)$
1-4011-4011.1244-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1244	$0$	✓	✓	$-0.386$	$0$	$1.51377$	Character $\chi_{4011}(1244, \cdot)$
1-4011-4011.125-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.125	$0$	✓	✓	$-0.0501$	$0$	$0.197008$	Character $\chi_{4011}(125, \cdot)$
1-4011-4011.1262-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1262	$0$	✓	✓	$-0.438$	$0$	$1.42683$	Character $\chi_{4011}(1262, \cdot)$
1-4011-4011.1280-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1280	$0$	✓	✓	$-0.203$	$0$	$0.445170$	Character $\chi_{4011}(1280, \cdot)$
1-4011-4011.1283-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1283	$0$	✓	✓	$-0.0727$	$0$	$0.841718$	Character $\chi_{4011}(1283, \cdot)$
1-4011-4011.1292-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1292	$0$	✓	✓	$0.257$	$0$	$0.945336$	Character $\chi_{4011}(1292, \cdot)$
1-4011-4011.1313-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1313	$0$	✓	✓	$0.437$	$0$	$1.07745$	Character $\chi_{4011}(1313, \cdot)$
1-4011-4011.1325-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1325	$0$	✓	✓	$0.198$	$0$	$0.927095$	Character $\chi_{4011}(1325, \cdot)$
1-4011-4011.1334-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1334	$0$	✓	✓	$0.127$	$0$	$0.738562$	Character $\chi_{4011}(1334, \cdot)$
1-4011-4011.1340-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1340	$0$	✓	✓	$0.401$	$0$	$0.238415$	Character $\chi_{4011}(1340, \cdot)$
1-4011-4011.1343-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1343	$0$	✓	✓	$0.224$	$0$	$1.05400$	Character $\chi_{4011}(1343, \cdot)$
1-4011-4011.1349-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1349	$0$	✓	✓	$-0.260$	$0$	$0.133449$	Character $\chi_{4011}(1349, \cdot)$
1-4011-4011.1361-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1361	$0$	✓	✓	$-0.325$	$0$	$0.114996$	Character $\chi_{4011}(1361, \cdot)$
1-4011-4011.1364-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 7 \cdot 191$	4011.1364	$0$	✓	✓	$-0.442$	$0$	$1.34834$	Character $\chi_{4011}(1364, \cdot)$

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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.