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 272 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3800-3800.1003-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1003	$1$	✓	✓	$-0.212$	$0$	$0.270773$	Character $\chi_{3800}(1003, \cdot)$
1-3800-3800.1011-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1011	$1$	✓	✓	$-0.458$	$0$	$1.45347$	Character $\chi_{3800}(1011, \cdot)$
1-3800-3800.1013-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1013	$1$	✓	✓	$0.338$	$0$	$0.674291$	Character $\chi_{3800}(1013, \cdot)$
1-3800-3800.1021-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1021	$1$	✓	✓	$-0.00750$	$0$	$0.507001$	Character $\chi_{3800}(1021, \cdot)$
1-3800-3800.1029-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1029	$1$	✓	✓	$0.306$	$0$	$0.0902226$	Character $\chi_{3800}(1029, \cdot)$
1-3800-3800.1037-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1037	$1$	✓	✓	$0.263$	$0$	$0.395457$	Character $\chi_{3800}(1037, \cdot)$
1-3800-3800.1067-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1067	$1$	✓	✓	$0.0267$	$0$	$0.835802$	Character $\chi_{3800}(1067, \cdot)$
1-3800-3800.109-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.109	$1$	✓	✓	$-0.167$	$0$	$0.320667$	Character $\chi_{3800}(109, \cdot)$
1-3800-3800.11-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.11	$1$	✓	✓	$-0.446$	$0$	$0.0170526$	Character $\chi_{3800}(11, \cdot)$
1-3800-3800.1123-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1123	$1$	✓	✓	$-0.317$	$0$	$0.194847$	Character $\chi_{3800}(1123, \cdot)$
1-3800-3800.1181-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1181	$1$	✓	✓	$-0.473$	$0$	$0.147202$	Character $\chi_{3800}(1181, \cdot)$
1-3800-3800.1213-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1213	$1$	✓	✓	$0.121$	$0$	$0.755612$	Character $\chi_{3800}(1213, \cdot)$
1-3800-3800.1229-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1229	$1$	✓	✓	$-0.0267$	$0$	$0.645056$	Character $\chi_{3800}(1229, \cdot)$
1-3800-3800.1259-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1259	$1$	✓	✓	$0.458$	$0$	$0.907849$	Character $\chi_{3800}(1259, \cdot)$
1-3800-3800.1267-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1267	$1$	✓	✓	$-0.306$	$0$	$1.27041$	Character $\chi_{3800}(1267, \cdot)$
1-3800-3800.1269-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1269	$1$	✓	✓	$-0.492$	$0$	$0.0882620$	Character $\chi_{3800}(1269, \cdot)$
1-3800-3800.1277-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1277	$1$	✓	✓	$-0.208$	$0$	$0.375983$	Character $\chi_{3800}(1277, \cdot)$
1-3800-3800.1283-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1283	$1$	✓	✓	$-0.0529$	$0$	$0.500889$	Character $\chi_{3800}(1283, \cdot)$
1-3800-3800.131-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.131	$1$	✓	✓	$-0.142$	$0$	$0.759130$	Character $\chi_{3800}(131, \cdot)$
1-3800-3800.1317-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1317	$1$	✓	✓	$0.468$	$0$	$1.08482$	Character $\chi_{3800}(1317, \cdot)$
1-3800-3800.1323-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1323	$1$	✓	✓	$-0.328$	$0$	$0.183166$	Character $\chi_{3800}(1323, \cdot)$
1-3800-3800.1339-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1339	$1$	✓	✓	$0.0225$	$0$	$0.619175$	Character $\chi_{3800}(1339, \cdot)$
1-3800-3800.1363-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1363	$1$	✓	✓	$0.0824$	$0$	$0.557578$	Character $\chi_{3800}(1363, \cdot)$
1-3800-3800.1373-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1373	$1$	✓	✓	$-0.248$	$0$	$0.514594$	Character $\chi_{3800}(1373, \cdot)$
1-3800-3800.1379-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1379	$1$	✓	✓	$0.173$	$0$	$0.698277$	Character $\chi_{3800}(1379, \cdot)$
1-3800-3800.1381-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1381	$1$	✓	✓	$0.193$	$0$	$0.930640$	Character $\chi_{3800}(1381, \cdot)$
1-3800-3800.1389-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1389	$1$	✓	✓	$-0.0670$	$0$	$0.338744$	Character $\chi_{3800}(1389, \cdot)$
1-3800-3800.139-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.139	$1$	✓	✓	$-0.371$	$0$	$1.13109$	Character $\chi_{3800}(139, \cdot)$
1-3800-3800.141-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.141	$1$	✓	✓	$0.0789$	$0$	$0.759872$	Character $\chi_{3800}(141, \cdot)$
1-3800-3800.1411-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1411	$1$	✓	✓	$0.498$	$0$	$1.16208$	Character $\chi_{3800}(1411, \cdot)$
1-3800-3800.1413-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1413	$1$	✓	✓	$0.196$	$0$	$0.748178$	Character $\chi_{3800}(1413, \cdot)$
1-3800-3800.1421-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1421	$1$	✓	✓	$0.287$	$0$	$0.874038$	Character $\chi_{3800}(1421, \cdot)$
1-3800-3800.1427-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1427	$1$	✓	✓	$-0.317$	$0$	$0.0674903$	Character $\chi_{3800}(1427, \cdot)$
1-3800-3800.1453-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1453	$1$	✓	✓	$0.142$	$0$	$0.482195$	Character $\chi_{3800}(1453, \cdot)$
1-3800-3800.147-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.147	$1$	✓	✓	$-0.00750$	$0$	$0.662890$	Character $\chi_{3800}(147, \cdot)$
1-3800-3800.1491-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1491	$1$	✓	✓	$-0.0174$	$0$	$0.199306$	Character $\chi_{3800}(1491, \cdot)$
1-3800-3800.1509-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1509	$1$	✓	✓	$0.0789$	$0$	$0.508073$	Character $\chi_{3800}(1509, \cdot)$
1-3800-3800.1517-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1517	$1$	✓	✓	$0.248$	$0$	$0.0282171$	Character $\chi_{3800}(1517, \cdot)$
1-3800-3800.1523-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1523	$1$	✓	✓	$0.436$	$0$	$0.557050$	Character $\chi_{3800}(1523, \cdot)$
1-3800-3800.1531-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1531	$1$	✓	✓	$0.393$	$0$	$0.587405$	Character $\chi_{3800}(1531, \cdot)$
1-3800-3800.1541-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1541	$1$	✓	✓	$-0.107$	$0$	$0.151487$	Character $\chi_{3800}(1541, \cdot)$
1-3800-3800.1547-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1547	$1$	✓	✓	$0.238$	$0$	$0.664047$	Character $\chi_{3800}(1547, \cdot)$
1-3800-3800.1587-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1587	$1$	✓	✓	$0.317$	$0$	$0.526818$	Character $\chi_{3800}(1587, \cdot)$
1-3800-3800.1589-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1589	$1$	✓	✓	$-0.0789$	$0$	$0.161926$	Character $\chi_{3800}(1589, \cdot)$
1-3800-3800.1613-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1613	$1$	✓	✓	$-0.272$	$0$	$0.0458790$	Character $\chi_{3800}(1613, \cdot)$
1-3800-3800.1619-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1619	$1$	✓	✓	$-0.118$	$0$	$0.593015$	Character $\chi_{3800}(1619, \cdot)$
1-3800-3800.1627-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1627	$1$	✓	✓	$-0.328$	$0$	$0.244417$	Character $\chi_{3800}(1627, \cdot)$
1-3800-3800.1629-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1629	$1$	✓	✓	$0.492$	$0$	$0.897514$	Character $\chi_{3800}(1629, \cdot)$
1-3800-3800.1659-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1659	$1$	✓	✓	$-0.411$	$0$	$0.355715$	Character $\chi_{3800}(1659, \cdot)$
1-3800-3800.1661-r1-0-0	$408.$	$408.$	$1$	$2^{3} \cdot 5^{2} \cdot 19$	3800.1661	$1$	✓	✓	$0.118$	$0$	$0.534863$	Character $\chi_{3800}(1661, \cdot)$

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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.