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 704 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3328-3328.1003-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1003	$0$	✓	✓	$-0.151$	$0$	$0.376877$	Character $\chi_{3328}(1003, \cdot)$
1-3328-3328.1005-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1005	$0$	✓	✓	$0.305$	$0$	$0.913637$	Character $\chi_{3328}(1005, \cdot)$
1-3328-3328.101-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.101	$0$	✓	✓	$0.194$	$0$	$0.542281$	Character $\chi_{3328}(101, \cdot)$
1-3328-3328.1013-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1013	$0$	✓	✓	$-0.105$	$0$	$0.685143$	Character $\chi_{3328}(1013, \cdot)$
1-3328-3328.1019-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1019	$0$	✓	✓	$-0.0899$	$0$	$0.973372$	Character $\chi_{3328}(1019, \cdot)$
1-3328-3328.1035-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1035	$0$	✓	✓	$0.347$	$0$	$1.18393$	Character $\chi_{3328}(1035, \cdot)$
1-3328-3328.1037-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1037	$0$	✓	✓	$0.468$	$0$	$1.58711$	Character $\chi_{3328}(1037, \cdot)$
1-3328-3328.1051-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1051	$0$	✓	✓	$0.286$	$0$	$1.12647$	Character $\chi_{3328}(1051, \cdot)$
1-3328-3328.1059-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1059	$0$	✓	✓	$-0.0673$	$0$	$0.704349$	Character $\chi_{3328}(1059, \cdot)$
1-3328-3328.1069-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1069	$0$	✓	✓	$0.0127$	$0$	$0.685842$	Character $\chi_{3328}(1069, \cdot)$
1-3328-3328.1099-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1099	$0$	✓	✓	$-0.184$	$0$	$0.394183$	Character $\chi_{3328}(1099, \cdot)$
1-3328-3328.11-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.11	$0$	✓	✓	$0.0673$	$0$	$0.441320$	Character $\chi_{3328}(11, \cdot)$
1-3328-3328.1101-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1101	$0$	✓	✓	$-0.239$	$0$	$0.377279$	Character $\chi_{3328}(1101, \cdot)$
1-3328-3328.1107-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1107	$0$	✓	✓	$0.215$	$0$	$0.768157$	Character $\chi_{3328}(1107, \cdot)$
1-3328-3328.1109-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1109	$0$	✓	✓	$0.188$	$0$	$0.997070$	Character $\chi_{3328}(1109, \cdot)$
1-3328-3328.1117-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1117	$0$	✓	✓	$0.105$	$0$	$0.705516$	Character $\chi_{3328}(1117, \cdot)$
1-3328-3328.1123-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1123	$0$	✓	✓	$0.152$	$0$	$0.761108$	Character $\chi_{3328}(1123, \cdot)$
1-3328-3328.1139-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1139	$0$	✓	✓	$0.339$	$0$	$1.05061$	Character $\chi_{3328}(1139, \cdot)$
1-3328-3328.1141-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1141	$0$	✓	✓	$0.475$	$0$	$1.00799$	Character $\chi_{3328}(1141, \cdot)$
1-3328-3328.115-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.115	$0$	✓	✓	$0.0595$	$0$	$0.680897$	Character $\chi_{3328}(115, \cdot)$
1-3328-3328.1155-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1155	$0$	✓	✓	$-0.0967$	$0$	$0.124169$	Character $\chi_{3328}(1155, \cdot)$
1-3328-3328.1163-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1163	$0$	✓	✓	$0.221$	$0$	$0.797317$	Character $\chi_{3328}(1163, \cdot)$
1-3328-3328.1173-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1173	$0$	✓	✓	$-0.354$	$0$	$0.0139089$	Character $\chi_{3328}(1173, \cdot)$
1-3328-3328.1203-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1203	$0$	✓	✓	$-0.442$	$0$	$1.62034$	Character $\chi_{3328}(1203, \cdot)$
1-3328-3328.1205-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1205	$0$	✓	✓	$-0.481$	$0$	$0.310673$	Character $\chi_{3328}(1205, \cdot)$
1-3328-3328.1211-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1211	$0$	✓	✓	$-0.307$	$0$	$0.247362$	Character $\chi_{3328}(1211, \cdot)$
1-3328-3328.1213-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1213	$0$	✓	✓	$-0.350$	$0$	$0.324357$	Character $\chi_{3328}(1213, \cdot)$
1-3328-3328.1221-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1221	$0$	✓	✓	$0.113$	$0$	$0.721088$	Character $\chi_{3328}(1221, \cdot)$
1-3328-3328.1227-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1227	$0$	✓	✓	$0.441$	$0$	$1.06049$	Character $\chi_{3328}(1227, \cdot)$
1-3328-3328.123-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.123	$0$	✓	✓	$-0.309$	$0$	$1.84683$	Character $\chi_{3328}(123, \cdot)$
1-3328-3328.1243-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1243	$0$	✓	✓	$-0.183$	$0$	$0.197272$	Character $\chi_{3328}(1243, \cdot)$
1-3328-3328.1245-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1245	$0$	✓	✓	$-0.313$	$0$	$0.254531$	Character $\chi_{3328}(1245, \cdot)$
1-3328-3328.1259-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1259	$0$	✓	✓	$-0.0576$	$0$	$0.691945$	Character $\chi_{3328}(1259, \cdot)$
1-3328-3328.1267-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1267	$0$	✓	✓	$-0.286$	$0$	$0.429947$	Character $\chi_{3328}(1267, \cdot)$
1-3328-3328.1277-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1277	$0$	✓	✓	$0.106$	$0$	$0.834429$	Character $\chi_{3328}(1277, \cdot)$
1-3328-3328.1307-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1307	$0$	✓	✓	$-0.465$	$0$	$0.275697$	Character $\chi_{3328}(1307, \cdot)$
1-3328-3328.1309-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1309	$0$	✓	✓	$-0.270$	$0$	$0.645193$	Character $\chi_{3328}(1309, \cdot)$
1-3328-3328.1315-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1315	$0$	✓	✓	$-0.315$	$0$	$0.716127$	Character $\chi_{3328}(1315, \cdot)$
1-3328-3328.1317-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1317	$0$	✓	✓	$-0.218$	$0$	$0.393611$	Character $\chi_{3328}(1317, \cdot)$
1-3328-3328.1325-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1325	$0$	✓	✓	$0.136$	$0$	$0.993644$	Character $\chi_{3328}(1325, \cdot)$
1-3328-3328.133-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.133	$0$	✓	✓	$0.239$	$0$	$0.803896$	Character $\chi_{3328}(133, \cdot)$
1-3328-3328.1331-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1331	$0$	✓	✓	$-0.316$	$0$	$0.617060$	Character $\chi_{3328}(1331, \cdot)$
1-3328-3328.1347-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1347	$0$	✓	✓	$0.183$	$0$	$0.988610$	Character $\chi_{3328}(1347, \cdot)$
1-3328-3328.1349-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1349	$0$	✓	✓	$0.194$	$0$	$1.02234$	Character $\chi_{3328}(1349, \cdot)$
1-3328-3328.1363-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1363	$0$	✓	✓	$0.309$	$0$	$1.33647$	Character $\chi_{3328}(1363, \cdot)$
1-3328-3328.1371-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1371	$0$	✓	✓	$0.190$	$0$	$0.964118$	Character $\chi_{3328}(1371, \cdot)$
1-3328-3328.1381-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1381	$0$	✓	✓	$0.489$	$0$	$1.41225$	Character $\chi_{3328}(1381, \cdot)$
1-3328-3328.1411-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1411	$0$	✓	✓	$0.151$	$0$	$1.27473$	Character $\chi_{3328}(1411, \cdot)$
1-3328-3328.1413-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1413	$0$	✓	✓	$0.487$	$0$	$0.184377$	Character $\chi_{3328}(1413, \cdot)$
1-3328-3328.1419-r0-0-0	$15.4$	$15.4$	$1$	$2^{8} \cdot 13$	3328.1419	$0$	✓	✓	$-0.0262$	$0$	$0.818030$	Character $\chi_{3328}(1419, \cdot)$

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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.