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 1024 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-80e2-6400.1003-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1003	$0$	✓	✓	$-0.0310$	$0$	$0.647369$	Character $\chi_{6400}(1003, \cdot)$
1-80e2-6400.1021-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1021	$0$	✓	✓	$0.461$	$0$	$1.08914$	Character $\chi_{6400}(1021, \cdot)$
1-80e2-6400.1027-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1027	$0$	✓	✓	$-0.00890$	$0$	$0.858250$	Character $\chi_{6400}(1027, \cdot)$
1-80e2-6400.1029-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1029	$0$	✓	✓	$0.000156$	$0$	$0.508769$	Character $\chi_{6400}(1029, \cdot)$
1-80e2-6400.1061-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1061	$0$	✓	✓	$-0.0948$	$0$	$0.338575$	Character $\chi_{6400}(1061, \cdot)$
1-80e2-6400.1067-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1067	$0$	✓	✓	$-0.461$	$0$	$1.28851$	Character $\chi_{6400}(1067, \cdot)$
1-80e2-6400.1069-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1069	$0$	✓	✓	$0.374$	$0$	$0.965446$	Character $\chi_{6400}(1069, \cdot)$
1-80e2-6400.1083-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1083	$0$	✓	✓	$-0.179$	$0$	$0.647557$	Character $\chi_{6400}(1083, \cdot)$
1-80e2-6400.109-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.109	$0$	✓	✓	$0.0948$	$0$	$1.00982$	Character $\chi_{6400}(109, \cdot)$
1-80e2-6400.1109-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1109	$0$	✓	✓	$-0.241$	$0$	$0.744420$	Character $\chi_{6400}(1109, \cdot)$
1-80e2-6400.1123-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1123	$0$	✓	✓	$0.491$	$0$	$1.39250$	Character $\chi_{6400}(1123, \cdot)$
1-80e2-6400.1141-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1141	$0$	✓	✓	$-0.491$	$0$	$0.0173821$	Character $\chi_{6400}(1141, \cdot)$
1-80e2-6400.1147-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1147	$0$	✓	✓	$0.000156$	$0$	$0.623172$	Character $\chi_{6400}(1147, \cdot)$
1-80e2-6400.1163-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1163	$0$	✓	✓	$0.258$	$0$	$0.848897$	Character $\chi_{6400}(1163, \cdot)$
1-80e2-6400.1181-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1181	$0$	✓	✓	$-0.218$	$0$	$0.237066$	Character $\chi_{6400}(1181, \cdot)$
1-80e2-6400.1187-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1187	$0$	✓	✓	$0.498$	$0$	$1.10370$	Character $\chi_{6400}(1187, \cdot)$
1-80e2-6400.1189-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1189	$0$	✓	✓	$0.405$	$0$	$0.683394$	Character $\chi_{6400}(1189, \cdot)$
1-80e2-6400.1203-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1203	$0$	✓	✓	$0.179$	$0$	$1.36511$	Character $\chi_{6400}(1203, \cdot)$
1-80e2-6400.1221-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1221	$0$	✓	✓	$0.000156$	$0$	$0.757663$	Character $\chi_{6400}(1221, \cdot)$
1-80e2-6400.1227-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1227	$0$	✓	✓	$-0.248$	$0$	$0.435994$	Character $\chi_{6400}(1227, \cdot)$
1-80e2-6400.1229-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1229	$0$	✓	✓	$-0.320$	$0$	$1.61021$	Character $\chi_{6400}(1229, \cdot)$
1-80e2-6400.123-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.123	$0$	✓	✓	$-0.469$	$0$	$0.932164$	Character $\chi_{6400}(123, \cdot)$
1-80e2-6400.1261-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1261	$0$	✓	✓	$-0.165$	$0$	$0.165737$	Character $\chi_{6400}(1261, \cdot)$
1-80e2-6400.1267-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1267	$0$	✓	✓	$0.000156$	$0$	$0.973012$	Character $\chi_{6400}(1267, \cdot)$
1-80e2-6400.1269-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1269	$0$	✓	✓	$0.288$	$0$	$0.0671546$	Character $\chi_{6400}(1269, \cdot)$
1-80e2-6400.1283-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1283	$0$	✓	✓	$-0.218$	$0$	$0.478548$	Character $\chi_{6400}(1283, \cdot)$
1-80e2-6400.1309-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1309	$0$	✓	✓	$0.498$	$0$	$0.0449485$	Character $\chi_{6400}(1309, \cdot)$
1-80e2-6400.1323-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1323	$0$	✓	✓	$0.248$	$0$	$0.997269$	Character $\chi_{6400}(1323, \cdot)$
1-80e2-6400.1341-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1341	$0$	✓	✓	$-0.248$	$0$	$0.619726$	Character $\chi_{6400}(1341, \cdot)$
1-80e2-6400.1347-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1347	$0$	✓	✓	$-0.288$	$0$	$0.333290$	Character $\chi_{6400}(1347, \cdot)$
1-80e2-6400.1363-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1363	$0$	✓	✓	$0.344$	$0$	$0.598744$	Character $\chi_{6400}(1363, \cdot)$
1-80e2-6400.1381-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1381	$0$	✓	✓	$0.445$	$0$	$1.28833$	Character $\chi_{6400}(1381, \cdot)$
1-80e2-6400.1387-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1387	$0$	✓	✓	$-0.241$	$0$	$0.636613$	Character $\chi_{6400}(1387, \cdot)$
1-80e2-6400.1389-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1389	$0$	✓	✓	$0.334$	$0$	$1.25966$	Character $\chi_{6400}(1389, \cdot)$
1-80e2-6400.1403-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1403	$0$	✓	✓	$0.000156$	$0$	$0.850959$	Character $\chi_{6400}(1403, \cdot)$
1-80e2-6400.141-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.141	$0$	✓	✓	$-0.280$	$0$	$0.227405$	Character $\chi_{6400}(141, \cdot)$
1-80e2-6400.1421-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1421	$0$	✓	✓	$-0.320$	$0$	$1.16823$	Character $\chi_{6400}(1421, \cdot)$
1-80e2-6400.1427-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1427	$0$	✓	✓	$0.0848$	$0$	$0.817299$	Character $\chi_{6400}(1427, \cdot)$
1-80e2-6400.1429-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1429	$0$	✓	✓	$0.468$	$0$	$0.245980$	Character $\chi_{6400}(1429, \cdot)$
1-80e2-6400.1461-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1461	$0$	✓	✓	$0.498$	$0$	$0.428659$	Character $\chi_{6400}(1461, \cdot)$
1-80e2-6400.1467-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1467	$0$	✓	✓	$-0.179$	$0$	$0.599932$	Character $\chi_{6400}(1467, \cdot)$
1-80e2-6400.1469-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1469	$0$	✓	✓	$-0.468$	$0$	$1.12140$	Character $\chi_{6400}(1469, \cdot)$
1-80e2-6400.147-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.147	$0$	✓	✓	$0.0548$	$0$	$0.534108$	Character $\chi_{6400}(147, \cdot)$
1-80e2-6400.1483-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1483	$0$	✓	✓	$-0.461$	$0$	$1.16010$	Character $\chi_{6400}(1483, \cdot)$
1-80e2-6400.1509-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1509	$0$	✓	✓	$-0.334$	$0$	$0.102914$	Character $\chi_{6400}(1509, \cdot)$
1-80e2-6400.1523-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1523	$0$	✓	✓	$-0.290$	$0$	$0.357939$	Character $\chi_{6400}(1523, \cdot)$
1-80e2-6400.1541-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1541	$0$	✓	✓	$0.0401$	$0$	$0.863612$	Character $\chi_{6400}(1541, \cdot)$
1-80e2-6400.1547-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1547	$0$	✓	✓	$-0.0310$	$0$	$0.918264$	Character $\chi_{6400}(1547, \cdot)$
1-80e2-6400.1563-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1563	$0$	✓	✓	$-0.0848$	$0$	$0.488648$	Character $\chi_{6400}(1563, \cdot)$
1-80e2-6400.1581-r0-0-0	$29.7$	$29.7$	$1$	$2^{8} \cdot 5^{2}$	6400.1581	$0$	✓	✓	$0.374$	$0$	$1.10888$	Character $\chi_{6400}(1581, \cdot)$

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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.