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 1309 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6004-6004.1003-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1003	$0$	✓	✓	$0.242$	$0$	$1.00651$	Character $\chi_{6004}(1003, \cdot)$
1-6004-6004.1011-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1011	$0$	✓	✓	$-0.167$	$0$	$0.471774$	Character $\chi_{6004}(1011, \cdot)$
1-6004-6004.1015-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1015	$0$	✓	✓	$-0.224$	$0$	$0.239262$	Character $\chi_{6004}(1015, \cdot)$
1-6004-6004.1023-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1023	$0$	✓	✓	$-0.299$	$0$	$0.572975$	Character $\chi_{6004}(1023, \cdot)$
1-6004-6004.1047-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1047	$0$	✓	✓	$-0.138$	$0$	$0.214692$	Character $\chi_{6004}(1047, \cdot)$
1-6004-6004.1051-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1051	$0$	✓	✓	$0.0846$	$0$	$1.04035$	Character $\chi_{6004}(1051, \cdot)$
1-6004-6004.1059-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1059	$0$	✓	✓	$-0.0487$	$0$	$0.604179$	Character $\chi_{6004}(1059, \cdot)$
1-6004-6004.1063-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1063	$0$	✓	✓	$0.154$	$0$	$0.933560$	Character $\chi_{6004}(1063, \cdot)$
1-6004-6004.1067-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1067	$0$	✓	✓	$0.395$	$0$	$0.0142064$	Character $\chi_{6004}(1067, \cdot)$
1-6004-6004.1075-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1075	$0$	✓	✓	$0.422$	$0$	$1.02309$	Character $\chi_{6004}(1075, \cdot)$
1-6004-6004.1079-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1079	$0$	✓	✓	$0.459$	$0$	$1.37505$	Character $\chi_{6004}(1079, \cdot)$
1-6004-6004.1087-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1087	$0$	✓	✓	$-0.418$	$0$	$0.113028$	Character $\chi_{6004}(1087, \cdot)$
1-6004-6004.1091-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1091	$0$	✓	✓	$0.0222$	$0$	$1.08524$	Character $\chi_{6004}(1091, \cdot)$
1-6004-6004.1115-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1115	$0$	✓	✓	$0.468$	$0$	$1.26371$	Character $\chi_{6004}(1115, \cdot)$
1-6004-6004.1131-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1131	$0$	✓	✓	$-0.490$	$0$	$0.256616$	Character $\chi_{6004}(1131, \cdot)$
1-6004-6004.1147-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1147	$0$	✓	✓	$-0.119$	$0$	$0.695338$	Character $\chi_{6004}(1147, \cdot)$
1-6004-6004.1155-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1155	$0$	✓	✓	$0.175$	$0$	$1.20685$	Character $\chi_{6004}(1155, \cdot)$
1-6004-6004.1163-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1163	$0$	✓	✓	$-0.142$	$0$	$0.510115$	Character $\chi_{6004}(1163, \cdot)$
1-6004-6004.1171-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1171	$0$	✓	✓	$0.0382$	$0$	$0.965097$	Character $\chi_{6004}(1171, \cdot)$
1-6004-6004.1175-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1175	$0$	✓	✓	$-0.261$	$0$	$0.570768$	Character $\chi_{6004}(1175, \cdot)$
1-6004-6004.1183-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1183	$0$	✓	✓	$0.404$	$0$	$0.953992$	Character $\chi_{6004}(1183, \cdot)$
1-6004-6004.1207-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1207	$0$	✓	✓	$0.437$	$0$	$1.19668$	Character $\chi_{6004}(1207, \cdot)$
1-6004-6004.1211-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1211	$0$	✓	✓	$0.00856$	$0$	$0.550755$	Character $\chi_{6004}(1211, \cdot)$
1-6004-6004.1231-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1231	$0$	✓	✓	$-0.0844$	$0$	$0.817923$	Character $\chi_{6004}(1231, \cdot)$
1-6004-6004.1239-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1239	$0$	✓	✓	$0.0174$	$0$	$0.843627$	Character $\chi_{6004}(1239, \cdot)$
1-6004-6004.1247-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1247	$0$	✓	✓	$0.430$	$0$	$1.49168$	Character $\chi_{6004}(1247, \cdot)$
1-6004-6004.1251-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1251	$0$	✓	✓	$-0.00678$	$0$	$0.521975$	Character $\chi_{6004}(1251, \cdot)$
1-6004-6004.1259-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1259	$0$	✓	✓	$0.167$	$0$	$0.426677$	Character $\chi_{6004}(1259, \cdot)$
1-6004-6004.1263-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1263	$0$	✓	✓	$0.113$	$0$	$1.19558$	Character $\chi_{6004}(1263, \cdot)$
1-6004-6004.1271-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1271	$0$	✓	✓	$-0.0467$	$0$	$0.711181$	Character $\chi_{6004}(1271, \cdot)$
1-6004-6004.1275-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1275	$0$	✓	✓	$0.147$	$0$	$1.18507$	Character $\chi_{6004}(1275, \cdot)$
1-6004-6004.1279-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1279	$0$	✓	✓	$0.344$	$0$	$0.862249$	Character $\chi_{6004}(1279, \cdot)$
1-6004-6004.1283-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1283	$0$	✓	✓	$-0.112$	$0$	$0.467197$	Character $\chi_{6004}(1283, \cdot)$
1-6004-6004.1287-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1287	$0$	✓	✓	$-0.242$	$0$	$0.853940$	Character $\chi_{6004}(1287, \cdot)$
1-6004-6004.1295-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1295	$0$	✓	✓	$0.0692$	$0$	$1.09077$	Character $\chi_{6004}(1295, \cdot)$
1-6004-6004.1299-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1299	$0$	✓	✓	$-0.131$	$0$	$0.617967$	Character $\chi_{6004}(1299, \cdot)$
1-6004-6004.1303-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1303	$0$	✓	✓	$0.497$	$0$	$1.09411$	Character $\chi_{6004}(1303, \cdot)$
1-6004-6004.1319-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1319	$0$	✓	✓	$0.0831$	$0$	$0.807664$	Character $\chi_{6004}(1319, \cdot)$
1-6004-6004.1327-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1327	$0$	✓	✓	$0.480$	$0$	$1.68169$	Character $\chi_{6004}(1327, \cdot)$
1-6004-6004.1335-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1335	$0$	✓	✓	$-0.0912$	$0$	$0.479954$	Character $\chi_{6004}(1335, \cdot)$
1-6004-6004.1339-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1339	$0$	✓	✓	$-0.132$	$0$	$0.799091$	Character $\chi_{6004}(1339, \cdot)$
1-6004-6004.1351-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1351	$0$	✓	✓	$-0.380$	$0$	$0.129891$	Character $\chi_{6004}(1351, \cdot)$
1-6004-6004.1355-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1355	$0$	✓	✓	$-0.0758$	$0$	$0.577743$	Character $\chi_{6004}(1355, \cdot)$
1-6004-6004.1359-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1359	$0$	✓	✓	$-0.287$	$0$	$0.704865$	Character $\chi_{6004}(1359, \cdot)$
1-6004-6004.1363-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1363	$0$	✓	✓	$0.134$	$0$	$0.549892$	Character $\chi_{6004}(1363, \cdot)$
1-6004-6004.1383-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1383	$0$	✓	✓	$0.0985$	$0$	$0.390893$	Character $\chi_{6004}(1383, \cdot)$
1-6004-6004.139-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.139	$0$	✓	✓	$0.335$	$0$	$0.975743$	Character $\chi_{6004}(139, \cdot)$
1-6004-6004.1391-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1391	$0$	✓	✓	$-0.478$	$0$	$1.10777$	Character $\chi_{6004}(1391, \cdot)$
1-6004-6004.1395-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1395	$0$	✓	✓	$0.299$	$0$	$1.24094$	Character $\chi_{6004}(1395, \cdot)$
1-6004-6004.1403-r0-0-0	$27.8$	$27.8$	$1$	$2^{2} \cdot 19 \cdot 79$	6004.1403	$0$	✓	✓	$0.228$	$0$	$0.999018$	Character $\chi_{6004}(1403, \cdot)$

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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.