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 256 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4608-4608.1003-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1003	$1$	✓	✓	$0.144$	$0$	$0.966808$	Character $\chi_{4608}(1003, \cdot)$
1-4608-4608.101-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.101	$1$	✓	✓	$-0.374$	$0$	$0.219856$	Character $\chi_{4608}(101, \cdot)$
1-4608-4608.1013-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1013	$1$	✓	✓	$0.394$	$0$	$0.873609$	Character $\chi_{4608}(1013, \cdot)$
1-4608-4608.1037-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1037	$1$	✓	✓	$0.465$	$0$	$0.384580$	Character $\chi_{4608}(1037, \cdot)$
1-4608-4608.1051-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1051	$1$	✓	✓	$-0.374$	$0$	$0.0429296$	Character $\chi_{4608}(1051, \cdot)$
1-4608-4608.1075-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1075	$1$	✓	✓	$-0.312$	$0$	$0.0678344$	Character $\chi_{4608}(1075, \cdot)$
1-4608-4608.1085-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1085	$1$	✓	✓	$-0.422$	$0$	$0.270481$	Character $\chi_{4608}(1085, \cdot)$
1-4608-4608.1109-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1109	$1$	✓	✓	$-0.452$	$0$	$1.09223$	Character $\chi_{4608}(1109, \cdot)$
1-4608-4608.1123-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1123	$1$	✓	✓	$-0.0193$	$0$	$0.643499$	Character $\chi_{4608}(1123, \cdot)$
1-4608-4608.1147-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1147	$1$	✓	✓	$0.0349$	$0$	$0.778252$	Character $\chi_{4608}(1147, \cdot)$
1-4608-4608.115-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.115	$1$	✓	✓	$0.465$	$0$	$1.05608$	Character $\chi_{4608}(115, \cdot)$
1-4608-4608.1157-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1157	$1$	✓	✓	$-0.465$	$0$	$0.132824$	Character $\chi_{4608}(1157, \cdot)$
1-4608-4608.1181-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1181	$1$	✓	✓	$-0.0193$	$0$	$0.166710$	Character $\chi_{4608}(1181, \cdot)$
1-4608-4608.1195-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1195	$1$	✓	✓	$0.0470$	$0$	$0.910082$	Character $\chi_{4608}(1195, \cdot)$
1-4608-4608.1219-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1219	$1$	✓	✓	$0.0779$	$0$	$0.742253$	Character $\chi_{4608}(1219, \cdot)$
1-4608-4608.1229-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1229	$1$	✓	✓	$-0.312$	$0$	$0.235613$	Character $\chi_{4608}(1229, \cdot)$
1-4608-4608.1253-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1253	$1$	✓	✓	$-0.374$	$0$	$1.20518$	Character $\chi_{4608}(1253, \cdot)$
1-4608-4608.1267-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1267	$1$	✓	✓	$-0.0349$	$0$	$0.435471$	Character $\chi_{4608}(1267, \cdot)$
1-4608-4608.1291-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1291	$1$	✓	✓	$0.394$	$0$	$0.100980$	Character $\chi_{4608}(1291, \cdot)$
1-4608-4608.1301-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1301	$1$	✓	✓	$0.144$	$0$	$0.474610$	Character $\chi_{4608}(1301, \cdot)$
1-4608-4608.1325-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1325	$1$	✓	✓	$0.402$	$0$	$0.131682$	Character $\chi_{4608}(1325, \cdot)$
1-4608-4608.1339-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1339	$1$	✓	✓	$-0.187$	$0$	$0.322282$	Character $\chi_{4608}(1339, \cdot)$
1-4608-4608.1363-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1363	$1$	✓	✓	$0.124$	$0$	$0.425933$	Character $\chi_{4608}(1363, \cdot)$
1-4608-4608.1373-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1373	$1$	✓	✓	$-0.172$	$0$	$0.390942$	Character $\chi_{4608}(1373, \cdot)$
1-4608-4608.139-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.139	$1$	✓	✓	$-0.355$	$0$	$0.137900$	Character $\chi_{4608}(139, \cdot)$
1-4608-4608.1397-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1397	$1$	✓	✓	$0.422$	$0$	$0.0909884$	Character $\chi_{4608}(1397, \cdot)$
1-4608-4608.1411-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1411	$1$	✓	✓	$0.480$	$0$	$1.06217$	Character $\chi_{4608}(1411, \cdot)$
1-4608-4608.1435-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1435	$1$	✓	✓	$-0.152$	$0$	$0.266174$	Character $\chi_{4608}(1435, \cdot)$
1-4608-4608.1445-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1445	$1$	✓	✓	$-0.402$	$0$	$1.13245$	Character $\chi_{4608}(1445, \cdot)$
1-4608-4608.1469-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1469	$1$	✓	✓	$0.105$	$0$	$0.505854$	Character $\chi_{4608}(1469, \cdot)$
1-4608-4608.1483-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1483	$1$	✓	✓	$-0.452$	$0$	$1.00556$	Character $\chi_{4608}(1483, \cdot)$
1-4608-4608.149-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.149	$1$	✓	✓	$0.394$	$0$	$0.133193$	Character $\chi_{4608}(149, \cdot)$
1-4608-4608.1507-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1507	$1$	✓	✓	$0.452$	$0$	$0.171091$	Character $\chi_{4608}(1507, \cdot)$
1-4608-4608.1517-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1517	$1$	✓	✓	$0.374$	$0$	$0.653113$	Character $\chi_{4608}(1517, \cdot)$
1-4608-4608.1541-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1541	$1$	✓	✓	$0.312$	$0$	$1.06676$	Character $\chi_{4608}(1541, \cdot)$
1-4608-4608.1555-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1555	$1$	✓	✓	$0.152$	$0$	$0.362371$	Character $\chi_{4608}(1555, \cdot)$
1-4608-4608.1579-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1579	$1$	✓	✓	$0.0193$	$0$	$0.437817$	Character $\chi_{4608}(1579, \cdot)$
1-4608-4608.1589-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1589	$1$	✓	✓	$0.269$	$0$	$0.783105$	Character $\chi_{4608}(1589, \cdot)$
1-4608-4608.1613-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1613	$1$	✓	✓	$0.465$	$0$	$1.05992$	Character $\chi_{4608}(1613, \cdot)$
1-4608-4608.1627-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1627	$1$	✓	✓	$-0.124$	$0$	$0.527823$	Character $\chi_{4608}(1627, \cdot)$
1-4608-4608.1651-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1651	$1$	✓	✓	$-0.312$	$0$	$0.454828$	Character $\chi_{4608}(1651, \cdot)$
1-4608-4608.1661-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1661	$1$	✓	✓	$-0.297$	$0$	$0.0849829$	Character $\chi_{4608}(1661, \cdot)$
1-4608-4608.1685-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1685	$1$	✓	✓	$-0.327$	$0$	$1.29567$	Character $\chi_{4608}(1685, \cdot)$
1-4608-4608.1699-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1699	$1$	✓	✓	$-0.394$	$0$	$1.36833$	Character $\chi_{4608}(1699, \cdot)$
1-4608-4608.1723-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1723	$1$	✓	✓	$-0.465$	$0$	$0.239036$	Character $\chi_{4608}(1723, \cdot)$
1-4608-4608.173-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.173	$1$	✓	✓	$0.402$	$0$	$1.23426$	Character $\chi_{4608}(173, \cdot)$
1-4608-4608.1733-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1733	$1$	✓	✓	$-0.465$	$0$	$1.20310$	Character $\chi_{4608}(1733, \cdot)$
1-4608-4608.1757-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1757	$1$	✓	✓	$-0.144$	$0$	$0.770538$	Character $\chi_{4608}(1757, \cdot)$
1-4608-4608.1771-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1771	$1$	✓	✓	$0.422$	$0$	$0.0271193$	Character $\chi_{4608}(1771, \cdot)$
1-4608-4608.1795-r1-0-0	$495.$	$495.$	$1$	$2^{9} \cdot 3^{2}$	4608.1795	$1$	✓	✓	$0.452$	$0$	$0.791734$	Character $\chi_{4608}(1795, \cdot)$

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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.