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 320 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-5600-5600.1019-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1019	$1$	✓	✓	$0.272$	$0$	$1.01607$	Character $\chi_{5600}(1019, \cdot)$
1-5600-5600.1021-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1021	$1$	✓	✓	$-0.366$	$0$	$0.374076$	Character $\chi_{5600}(1021, \cdot)$
1-5600-5600.1027-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1027	$1$	✓	✓	$0.0435$	$0$	$0.769078$	Character $\chi_{5600}(1027, \cdot)$
1-5600-5600.1059-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1059	$1$	✓	✓	$-0.282$	$0$	$0.521493$	Character $\chi_{5600}(1059, \cdot)$
1-5600-5600.1067-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1067	$1$	✓	✓	$0.386$	$0$	$0.953473$	Character $\chi_{5600}(1067, \cdot)$
1-5600-5600.1069-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1069	$1$	✓	✓	$-0.216$	$0$	$0.491682$	Character $\chi_{5600}(1069, \cdot)$
1-5600-5600.1083-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1083	$1$	✓	✓	$-0.403$	$0$	$0.180912$	Character $\chi_{5600}(1083, \cdot)$
1-5600-5600.11-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.11	$1$	✓	✓	$-0.217$	$0$	$0.210329$	Character $\chi_{5600}(11, \cdot)$
1-5600-5600.1109-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1109	$1$	✓	✓	$-0.293$	$0$	$0.459667$	Character $\chi_{5600}(1109, \cdot)$
1-5600-5600.1117-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1117	$1$	✓	✓	$-0.289$	$0$	$0.299825$	Character $\chi_{5600}(1117, \cdot)$
1-5600-5600.1123-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1123	$1$	✓	✓	$-0.416$	$0$	$0.342977$	Character $\chi_{5600}(1123, \cdot)$
1-5600-5600.1131-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1131	$1$	✓	✓	$0.0228$	$0$	$0.614566$	Character $\chi_{5600}(1131, \cdot)$
1-5600-5600.1147-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1147	$1$	✓	✓	$-0.303$	$0$	$0.208990$	Character $\chi_{5600}(1147, \cdot)$
1-5600-5600.1171-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1171	$1$	✓	✓	$-0.272$	$0$	$0.563614$	Character $\chi_{5600}(1171, \cdot)$
1-5600-5600.1173-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1173	$1$	✓	✓	$0.0328$	$0$	$0.487160$	Character $\chi_{5600}(1173, \cdot)$
1-5600-5600.1181-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1181	$1$	✓	✓	$0.0335$	$0$	$0.557363$	Character $\chi_{5600}(1181, \cdot)$
1-5600-5600.1189-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1189	$1$	✓	✓	$-0.123$	$0$	$0.620339$	Character $\chi_{5600}(1189, \cdot)$
1-5600-5600.1203-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1203	$1$	✓	✓	$-0.116$	$0$	$0.167914$	Character $\chi_{5600}(1203, \cdot)$
1-5600-5600.1213-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1213	$1$	✓	✓	$0.467$	$0$	$0.986576$	Character $\chi_{5600}(1213, \cdot)$
1-5600-5600.1221-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1221	$1$	✓	✓	$0.216$	$0$	$0.179847$	Character $\chi_{5600}(1221, \cdot)$
1-5600-5600.1339-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1339	$1$	✓	✓	$-0.280$	$0$	$0.991354$	Character $\chi_{5600}(1339, \cdot)$
1-5600-5600.1347-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1347	$1$	✓	✓	$-0.346$	$0$	$0.161406$	Character $\chi_{5600}(1347, \cdot)$
1-5600-5600.1363-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1363	$1$	✓	✓	$0.353$	$0$	$0.0972715$	Character $\chi_{5600}(1363, \cdot)$
1-5600-5600.1389-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1389	$1$	✓	✓	$0.0839$	$0$	$0.744143$	Character $\chi_{5600}(1389, \cdot)$
1-5600-5600.1397-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1397	$1$	✓	✓	$0.102$	$0$	$0.317040$	Character $\chi_{5600}(1397, \cdot)$
1-5600-5600.1403-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1403	$1$	✓	✓	$0.216$	$0$	$0.513247$	Character $\chi_{5600}(1403, \cdot)$
1-5600-5600.1411-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1411	$1$	✓	✓	$0.470$	$0$	$0.404183$	Character $\chi_{5600}(1411, \cdot)$
1-5600-5600.1427-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1427	$1$	✓	✓	$0.313$	$0$	$0.835890$	Character $\chi_{5600}(1427, \cdot)$
1-5600-5600.1437-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1437	$1$	✓	✓	$-0.0328$	$0$	$0.487780$	Character $\chi_{5600}(1437, \cdot)$
1-5600-5600.1453-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1453	$1$	✓	✓	$0.0403$	$0$	$0.0486850$	Character $\chi_{5600}(1453, \cdot)$
1-5600-5600.1461-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1461	$1$	✓	✓	$-0.393$	$0$	$1.01073$	Character $\chi_{5600}(1461, \cdot)$
1-5600-5600.1469-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1469	$1$	✓	✓	$-0.446$	$0$	$0.0494667$	Character $\chi_{5600}(1469, \cdot)$
1-5600-5600.1483-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1483	$1$	✓	✓	$-0.133$	$0$	$0.900829$	Character $\chi_{5600}(1483, \cdot)$
1-5600-5600.1579-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1579	$1$	✓	✓	$0.102$	$0$	$0.818452$	Character $\chi_{5600}(1579, \cdot)$
1-5600-5600.1581-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1581	$1$	✓	✓	$0.303$	$0$	$0.964870$	Character $\chi_{5600}(1581, \cdot)$
1-5600-5600.1587-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1587	$1$	✓	✓	$-0.146$	$0$	$0.157083$	Character $\chi_{5600}(1587, \cdot)$
1-5600-5600.1619-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1619	$1$	✓	✓	$-0.352$	$0$	$0.141207$	Character $\chi_{5600}(1619, \cdot)$
1-5600-5600.1627-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1627	$1$	✓	✓	$-0.353$	$0$	$0.978844$	Character $\chi_{5600}(1627, \cdot)$
1-5600-5600.1629-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1629	$1$	✓	✓	$0.113$	$0$	$0.699157$	Character $\chi_{5600}(1629, \cdot)$
1-5600-5600.1669-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1669	$1$	✓	✓	$0.136$	$0$	$0.677677$	Character $\chi_{5600}(1669, \cdot)$
1-5600-5600.1677-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1677	$1$	✓	✓	$0.470$	$0$	$0.0979545$	Character $\chi_{5600}(1677, \cdot)$
1-5600-5600.1683-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1683	$1$	✓	✓	$-0.176$	$0$	$0.256908$	Character $\chi_{5600}(1683, \cdot)$
1-5600-5600.1691-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1691	$1$	✓	✓	$-0.407$	$0$	$0.368298$	Character $\chi_{5600}(1691, \cdot)$
1-5600-5600.1717-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1717	$1$	✓	✓	$-0.290$	$0$	$0.454125$	Character $\chi_{5600}(1717, \cdot)$
1-5600-5600.1731-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1731	$1$	✓	✓	$-0.102$	$0$	$0.683033$	Character $\chi_{5600}(1731, \cdot)$
1-5600-5600.1733-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1733	$1$	✓	✓	$-0.227$	$0$	$0.353118$	Character $\chi_{5600}(1733, \cdot)$
1-5600-5600.1741-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1741	$1$	✓	✓	$0.103$	$0$	$0.945784$	Character $\chi_{5600}(1741, \cdot)$
1-5600-5600.1763-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1763	$1$	✓	✓	$0.123$	$0$	$0.585734$	Character $\chi_{5600}(1763, \cdot)$
1-5600-5600.1773-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1773	$1$	✓	✓	$0.157$	$0$	$0.0588151$	Character $\chi_{5600}(1773, \cdot)$
1-5600-5600.1781-r1-0-0	$601.$	$601.$	$1$	$2^{5} \cdot 5^{2} \cdot 7$	5600.1781	$1$	✓	✓	$-0.113$	$0$	$0.417937$	Character $\chi_{5600}(1781, \cdot)$

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Classical	Maass
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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.