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 128 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1800-1800.1003-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1003	$0$	✓	✓	$-0.315$	$0$	$0.391684$	Character $\chi_{1800}(1003, \cdot)$
1-1800-1800.1013-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1013	$0$	✓	✓	$0.124$	$0$	$0.999915$	Character $\chi_{1800}(1013, \cdot)$
1-1800-1800.1019-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1019	$0$	✓	✓	$0.0655$	$0$	$0.895267$	Character $\chi_{1800}(1019, \cdot)$
1-1800-1800.1021-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1021	$0$	✓	✓	$-0.315$	$0$	$0.137982$	Character $\chi_{1800}(1021, \cdot)$
1-1800-1800.1037-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1037	$0$	✓	✓	$-0.264$	$0$	$0.468278$	Character $\chi_{1800}(1037, \cdot)$
1-1800-1800.1069-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1069	$0$	✓	✓	$-0.184$	$0$	$0.499517$	Character $\chi_{1800}(1069, \cdot)$
1-1800-1800.1091-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1091	$0$	✓	✓	$0.485$	$0$	$1.56009$	Character $\chi_{1800}(1091, \cdot)$
1-1800-1800.11-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.11	$0$	✓	✓	$0.125$	$0$	$1.18409$	Character $\chi_{1800}(11, \cdot)$
1-1800-1800.1123-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1123	$0$	✓	✓	$0.125$	$0$	$1.08636$	Character $\chi_{1800}(1123, \cdot)$
1-1800-1800.1139-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1139	$0$	✓	✓	$-0.485$	$0$	$1.42320$	Character $\chi_{1800}(1139, \cdot)$
1-1800-1800.1141-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1141	$0$	✓	✓	$0.235$	$0$	$0.967538$	Character $\chi_{1800}(1141, \cdot)$
1-1800-1800.1147-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1147	$0$	✓	✓	$0.184$	$0$	$1.27606$	Character $\chi_{1800}(1147, \cdot)$
1-1800-1800.1211-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1211	$0$	✓	✓	$-0.485$	$0$	$0.127321$	Character $\chi_{1800}(1211, \cdot)$
1-1800-1800.1253-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1253	$0$	✓	✓	$-0.454$	$0$	$1.51622$	Character $\chi_{1800}(1253, \cdot)$
1-1800-1800.1267-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1267	$0$	✓	✓	$0.315$	$0$	$1.24147$	Character $\chi_{1800}(1267, \cdot)$
1-1800-1800.1309-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1309	$0$	✓	✓	$0.124$	$0$	$1.18965$	Character $\chi_{1800}(1309, \cdot)$
1-1800-1800.131-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.131	$0$	✓	✓	$-0.0455$	$0$	$0.860674$	Character $\chi_{1800}(131, \cdot)$
1-1800-1800.1363-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1363	$0$	✓	✓	$-0.125$	$0$	$0.492166$	Character $\chi_{1800}(1363, \cdot)$
1-1800-1800.1373-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1373	$0$	✓	✓	$0.264$	$0$	$1.29837$	Character $\chi_{1800}(1373, \cdot)$
1-1800-1800.1379-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1379	$0$	✓	✓	$-0.454$	$0$	$0.323654$	Character $\chi_{1800}(1379, \cdot)$
1-1800-1800.1381-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1381	$0$	✓	✓	$0.204$	$0$	$1.04895$	Character $\chi_{1800}(1381, \cdot)$
1-1800-1800.1397-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1397	$0$	✓	✓	$0.0455$	$0$	$1.01765$	Character $\chi_{1800}(1397, \cdot)$
1-1800-1800.1429-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1429	$0$	✓	✓	$0.295$	$0$	$1.27812$	Character $\chi_{1800}(1429, \cdot)$
1-1800-1800.1483-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1483	$0$	✓	✓	$-0.184$	$0$	$0.671819$	Character $\chi_{1800}(1483, \cdot)$
1-1800-1800.1517-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1517	$0$	✓	✓	$0.454$	$0$	$0.0437808$	Character $\chi_{1800}(1517, \cdot)$
1-1800-1800.1571-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1571	$0$	✓	✓	$0.434$	$0$	$1.34279$	Character $\chi_{1800}(1571, \cdot)$
1-1800-1800.1613-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1613	$0$	✓	✓	$-0.264$	$0$	$0.408405$	Character $\chi_{1800}(1613, \cdot)$
1-1800-1800.1627-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1627	$0$	✓	✓	$0.125$	$0$	$0.799544$	Character $\chi_{1800}(1627, \cdot)$
1-1800-1800.1669-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1669	$0$	✓	✓	$-0.295$	$0$	$0.375673$	Character $\chi_{1800}(1669, \cdot)$
1-1800-1800.1723-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1723	$0$	✓	✓	$0.0144$	$0$	$0.789868$	Character $\chi_{1800}(1723, \cdot)$
1-1800-1800.173-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.173	$0$	✓	✓	$-0.124$	$0$	$0.394497$	Character $\chi_{1800}(173, \cdot)$
1-1800-1800.1733-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1733	$0$	✓	✓	$-0.0455$	$0$	$0.817192$	Character $\chi_{1800}(1733, \cdot)$
1-1800-1800.1739-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1739	$0$	✓	✓	$0.125$	$0$	$0.923563$	Character $\chi_{1800}(1739, \cdot)$
1-1800-1800.1741-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1741	$0$	✓	✓	$0.124$	$0$	$1.01733$	Character $\chi_{1800}(1741, \cdot)$
1-1800-1800.1789-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.1789	$0$	✓	✓	$-0.124$	$0$	$0.638535$	Character $\chi_{1800}(1789, \cdot)$
1-1800-1800.187-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.187	$0$	✓	✓	$-0.0144$	$0$	$0.709394$	Character $\chi_{1800}(187, \cdot)$
1-1800-1800.229-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.229	$0$	✓	✓	$0.184$	$0$	$1.15824$	Character $\chi_{1800}(229, \cdot)$
1-1800-1800.283-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.283	$0$	✓	✓	$-0.295$	$0$	$0.461380$	Character $\chi_{1800}(283, \cdot)$
1-1800-1800.317-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.317	$0$	✓	✓	$0.0655$	$0$	$1.22425$	Character $\chi_{1800}(317, \cdot)$
1-1800-1800.371-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.371	$0$	✓	✓	$0.0455$	$0$	$0.900046$	Character $\chi_{1800}(371, \cdot)$
1-1800-1800.403-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.403	$0$	✓	✓	$-0.204$	$0$	$0.468171$	Character $\chi_{1800}(403, \cdot)$
1-1800-1800.419-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.419	$0$	✓	✓	$0.454$	$0$	$1.64189$	Character $\chi_{1800}(419, \cdot)$
1-1800-1800.421-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.421	$0$	✓	✓	$-0.204$	$0$	$0.566609$	Character $\chi_{1800}(421, \cdot)$
1-1800-1800.427-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.427	$0$	✓	✓	$0.0144$	$0$	$0.936268$	Character $\chi_{1800}(427, \cdot)$
1-1800-1800.437-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.437	$0$	✓	✓	$0.124$	$0$	$0.786589$	Character $\chi_{1800}(437, \cdot)$
1-1800-1800.491-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.491	$0$	✓	✓	$-0.125$	$0$	$0.836964$	Character $\chi_{1800}(491, \cdot)$
1-1800-1800.533-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.533	$0$	✓	✓	$-0.434$	$0$	$0.0313676$	Character $\chi_{1800}(533, \cdot)$
1-1800-1800.547-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.547	$0$	✓	✓	$0.295$	$0$	$1.24068$	Character $\chi_{1800}(547, \cdot)$
1-1800-1800.589-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.589	$0$	✓	✓	$-0.235$	$0$	$0.677131$	Character $\chi_{1800}(589, \cdot)$
1-1800-1800.59-r0-0-0	$8.35$	$8.35$	$1$	$2^{3} \cdot 3^{2} \cdot 5^{2}$	1800.59	$0$	✓	✓	$-0.125$	$0$	$0.467753$	Character $\chi_{1800}(59, \cdot)$

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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.