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
1-4017-4017.1004-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1004	$0$	✓	✓	$-0.437$	$0$	$0.322498$	Character $\chi_{4017}(1004, \cdot)$
1-4017-4017.101-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.101	$0$	✓	✓	$0.0918$	$0$	$0.812083$	Character $\chi_{4017}(101, \cdot)$
1-4017-4017.1013-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1013	$0$	✓	✓	$-0.141$	$0$	$1.82943$	Character $\chi_{4017}(1013, \cdot)$
1-4017-4017.1019-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1019	$0$	✓	✓	$-0.240$	$0$	$0.363751$	Character $\chi_{4017}(1019, \cdot)$
1-4017-4017.1025-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1025	$0$	✓	✓	$0.0813$	$0$	$0.400286$	Character $\chi_{4017}(1025, \cdot)$
1-4017-4017.1034-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1034	$0$	✓	✓	$0.0309$	$0$	$0.281424$	Character $\chi_{4017}(1034, \cdot)$
1-4017-4017.1046-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1046	$0$	✓	✓	$-0.160$	$0$	$0.869408$	Character $\chi_{4017}(1046, \cdot)$
1-4017-4017.1052-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1052	$0$	✓	✓	$0.139$	$0$	$0.755717$	Character $\chi_{4017}(1052, \cdot)$
1-4017-4017.1055-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1055	$0$	✓	✓	$0.387$	$0$	$1.11667$	Character $\chi_{4017}(1055, \cdot)$
1-4017-4017.1058-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1058	$0$	✓	✓	$-0.166$	$0$	$0.991591$	Character $\chi_{4017}(1058, \cdot)$
1-4017-4017.1064-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1064	$0$	✓	✓	$0.0279$	$0$	$0.975025$	Character $\chi_{4017}(1064, \cdot)$
1-4017-4017.1070-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1070	$0$	✓	✓	$0.351$	$0$	$1.54939$	Character $\chi_{4017}(1070, \cdot)$
1-4017-4017.1085-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1085	$0$	✓	✓	$0.215$	$0$	$1.21319$	Character $\chi_{4017}(1085, \cdot)$
1-4017-4017.1094-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1094	$0$	✓	✓	$-0.466$	$0$	$0.0431977$	Character $\chi_{4017}(1094, \cdot)$
1-4017-4017.110-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.110	$0$	✓	✓	$-0.347$	$0$	$0.362497$	Character $\chi_{4017}(110, \cdot)$
1-4017-4017.1112-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1112	$0$	✓	✓	$-0.366$	$0$	$0.607575$	Character $\chi_{4017}(1112, \cdot)$
1-4017-4017.1115-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1115	$0$	✓	✓	$-0.351$	$0$	$0.790072$	Character $\chi_{4017}(1115, \cdot)$
1-4017-4017.113-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.113	$0$	✓	✓	$-0.0476$	$0$	$0.919611$	Character $\chi_{4017}(113, \cdot)$
1-4017-4017.1142-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1142	$0$	✓	✓	$0.110$	$0$	$0.807151$	Character $\chi_{4017}(1142, \cdot)$
1-4017-4017.1151-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1151	$0$	✓	✓	$0.0437$	$0$	$1.27872$	Character $\chi_{4017}(1151, \cdot)$
1-4017-4017.1154-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1154	$0$	✓	✓	$-0.352$	$0$	$0.649028$	Character $\chi_{4017}(1154, \cdot)$
1-4017-4017.1160-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1160	$0$	✓	✓	$-0.185$	$0$	$0.145011$	Character $\chi_{4017}(1160, \cdot)$
1-4017-4017.1163-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1163	$0$	✓	✓	$0.146$	$0$	$0.802399$	Character $\chi_{4017}(1163, \cdot)$
1-4017-4017.1187-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1187	$0$	✓	✓	$0.352$	$0$	$1.09337$	Character $\chi_{4017}(1187, \cdot)$
1-4017-4017.119-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.119	$0$	✓	✓	$-0.0754$	$0$	$0.653481$	Character $\chi_{4017}(119, \cdot)$
1-4017-4017.1208-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1208	$0$	✓	✓	$0.0508$	$0$	$0.700663$	Character $\chi_{4017}(1208, \cdot)$
1-4017-4017.1214-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1214	$0$	✓	✓	$-0.173$	$0$	$0.582142$	Character $\chi_{4017}(1214, \cdot)$
1-4017-4017.122-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.122	$0$	✓	✓	$-0.378$	$0$	$0.379991$	Character $\chi_{4017}(122, \cdot)$
1-4017-4017.1232-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1232	$0$	✓	✓	$0.228$	$0$	$0.385818$	Character $\chi_{4017}(1232, \cdot)$
1-4017-4017.1247-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1247	$0$	✓	✓	$-0.0508$	$0$	$0.430774$	Character $\chi_{4017}(1247, \cdot)$
1-4017-4017.1250-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1250	$0$	✓	✓	$0.466$	$0$	$0.0503761$	Character $\chi_{4017}(1250, \cdot)$
1-4017-4017.1253-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1253	$0$	✓	✓	$-0.168$	$0$	$0.563112$	Character $\chi_{4017}(1253, \cdot)$
1-4017-4017.1259-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1259	$0$	✓	✓	$0.0684$	$0$	$0.824412$	Character $\chi_{4017}(1259, \cdot)$
1-4017-4017.1268-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1268	$0$	✓	✓	$-0.123$	$0$	$0.415155$	Character $\chi_{4017}(1268, \cdot)$
1-4017-4017.1271-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1271	$0$	✓	✓	$0.404$	$0$	$1.20356$	Character $\chi_{4017}(1271, \cdot)$
1-4017-4017.128-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.128	$0$	✓	✓	$0.481$	$0$	$0.398176$	Character $\chi_{4017}(128, \cdot)$
1-4017-4017.1283-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1283	$0$	✓	✓	$0.0310$	$0$	$0.979606$	Character $\chi_{4017}(1283, \cdot)$
1-4017-4017.1292-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1292	$0$	✓	✓	$-0.156$	$0$	$0.769335$	Character $\chi_{4017}(1292, \cdot)$
1-4017-4017.1295-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1295	$0$	✓	✓	$-0.0383$	$0$	$0.937101$	Character $\chi_{4017}(1295, \cdot)$
1-4017-4017.1310-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1310	$0$	✓	✓	$0.459$	$0$	$0.934086$	Character $\chi_{4017}(1310, \cdot)$
1-4017-4017.1316-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1316	$0$	✓	✓	$0.328$	$0$	$0.603503$	Character $\chi_{4017}(1316, \cdot)$
1-4017-4017.1319-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1319	$0$	✓	✓	$-0.303$	$0$	$0.0542196$	Character $\chi_{4017}(1319, \cdot)$
1-4017-4017.1322-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1322	$0$	✓	✓	$0.315$	$0$	$0.901691$	Character $\chi_{4017}(1322, \cdot)$
1-4017-4017.1325-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1325	$0$	✓	✓	$-0.139$	$0$	$0.670437$	Character $\chi_{4017}(1325, \cdot)$
1-4017-4017.1328-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1328	$0$	✓	✓	$0.458$	$0$	$1.54037$	Character $\chi_{4017}(1328, \cdot)$
1-4017-4017.1334-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1334	$0$	✓	✓	$-0.304$	$0$	$1.35540$	Character $\chi_{4017}(1334, \cdot)$
1-4017-4017.134-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.134	$0$	✓	✓	$0.256$	$0$	$0.716706$	Character $\chi_{4017}(134, \cdot)$
1-4017-4017.1346-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1346	$0$	✓	✓	$-0.245$	$0$	$0.0277124$	Character $\chi_{4017}(1346, \cdot)$
1-4017-4017.1349-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1349	$0$	✓	✓	$-0.256$	$0$	$0.464510$	Character $\chi_{4017}(1349, \cdot)$
1-4017-4017.1358-r0-0-0	$18.6$	$18.6$	$1$	$3 \cdot 13 \cdot 103$	4017.1358	$0$	✓	✓	$0.235$	$0$	$0.943423$	Character $\chi_{4017}(1358, \cdot)$

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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.