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 512 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4608-4608.1019-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1019	$0$	✓	✓	$-0.437$	$0$	$0.274345$	Character $\chi_{4608}(1019, \cdot)$
1-4608-4608.1021-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1021	$0$	✓	✓	$-0.297$	$0$	$0.417916$	Character $\chi_{4608}(1021, \cdot)$
1-4608-4608.1067-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1067	$0$	✓	✓	$-0.230$	$0$	$0.473421$	Character $\chi_{4608}(1067, \cdot)$
1-4608-4608.1069-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1069	$0$	✓	✓	$-0.347$	$0$	$0.684155$	Character $\chi_{4608}(1069, \cdot)$
1-4608-4608.1091-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1091	$0$	✓	✓	$-0.144$	$0$	$0.816467$	Character $\chi_{4608}(1091, \cdot)$
1-4608-4608.1093-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1093	$0$	✓	✓	$-0.215$	$0$	$0.579294$	Character $\chi_{4608}(1093, \cdot)$
1-4608-4608.11-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.11	$0$	✓	✓	$-0.0779$	$0$	$0.489747$	Character $\chi_{4608}(11, \cdot)$
1-4608-4608.1139-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1139	$0$	✓	✓	$0.437$	$0$	$1.04629$	Character $\chi_{4608}(1139, \cdot)$
1-4608-4608.1141-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1141	$0$	✓	✓	$0.172$	$0$	$0.820544$	Character $\chi_{4608}(1141, \cdot)$
1-4608-4608.1163-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1163	$0$	✓	✓	$-0.327$	$0$	$0.480189$	Character $\chi_{4608}(1163, \cdot)$
1-4608-4608.1165-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1165	$0$	✓	✓	$0.437$	$0$	$1.50932$	Character $\chi_{4608}(1165, \cdot)$
1-4608-4608.1211-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1211	$0$	✓	✓	$0.284$	$0$	$1.20442$	Character $\chi_{4608}(1211, \cdot)$
1-4608-4608.1213-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1213	$0$	✓	✓	$-0.144$	$0$	$0.509238$	Character $\chi_{4608}(1213, \cdot)$
1-4608-4608.1235-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1235	$0$	✓	✓	$0.152$	$0$	$0.988617$	Character $\chi_{4608}(1235, \cdot)$
1-4608-4608.1237-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1237	$0$	✓	✓	$-0.230$	$0$	$0.229948$	Character $\chi_{4608}(1237, \cdot)$
1-4608-4608.1283-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1283	$0$	✓	✓	$0.202$	$0$	$1.29640$	Character $\chi_{4608}(1283, \cdot)$
1-4608-4608.1285-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1285	$0$	✓	✓	$-0.437$	$0$	$0.192748$	Character $\chi_{4608}(1285, \cdot)$
1-4608-4608.13-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.13	$0$	✓	✓	$-0.0627$	$0$	$0.610769$	Character $\chi_{4608}(13, \cdot)$
1-4608-4608.1307-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1307	$0$	✓	✓	$-0.124$	$0$	$0.685236$	Character $\chi_{4608}(1307, \cdot)$
1-4608-4608.1309-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1309	$0$	✓	✓	$-0.297$	$0$	$0.181651$	Character $\chi_{4608}(1309, \cdot)$
1-4608-4608.131-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.131	$0$	✓	✓	$-0.0470$	$0$	$0.792098$	Character $\chi_{4608}(131, \cdot)$
1-4608-4608.133-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.133	$0$	✓	✓	$0.0627$	$0$	$0.857812$	Character $\chi_{4608}(133, \cdot)$
1-4608-4608.1355-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1355	$0$	✓	✓	$-0.230$	$0$	$0.313794$	Character $\chi_{4608}(1355, \cdot)$
1-4608-4608.1357-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1357	$0$	✓	✓	$-0.284$	$0$	$0.460648$	Character $\chi_{4608}(1357, \cdot)$
1-4608-4608.1379-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1379	$0$	✓	✓	$-0.269$	$0$	$0.322041$	Character $\chi_{4608}(1379, \cdot)$
1-4608-4608.1381-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1381	$0$	✓	✓	$0.0974$	$0$	$0.638591$	Character $\chi_{4608}(1381, \cdot)$
1-4608-4608.1427-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1427	$0$	✓	✓	$0.124$	$0$	$0.814677$	Character $\chi_{4608}(1427, \cdot)$
1-4608-4608.1429-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1429	$0$	✓	✓	$0.422$	$0$	$1.06203$	Character $\chi_{4608}(1429, \cdot)$
1-4608-4608.1451-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1451	$0$	✓	✓	$-0.202$	$0$	$0.566790$	Character $\chi_{4608}(1451, \cdot)$
1-4608-4608.1453-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1453	$0$	✓	✓	$-0.125$	$0$	$0.613140$	Character $\chi_{4608}(1453, \cdot)$
1-4608-4608.1499-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1499	$0$	✓	✓	$-0.152$	$0$	$0.315930$	Character $\chi_{4608}(1499, \cdot)$
1-4608-4608.1501-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1501	$0$	✓	✓	$-0.394$	$0$	$0.152643$	Character $\chi_{4608}(1501, \cdot)$
1-4608-4608.1523-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1523	$0$	✓	✓	$0.215$	$0$	$0.673561$	Character $\chi_{4608}(1523, \cdot)$
1-4608-4608.1525-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1525	$0$	✓	✓	$0.144$	$0$	$0.582024$	Character $\chi_{4608}(1525, \cdot)$
1-4608-4608.155-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.155	$0$	✓	✓	$-0.124$	$0$	$0.505259$	Character $\chi_{4608}(155, \cdot)$
1-4608-4608.157-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.157	$0$	✓	✓	$0.452$	$0$	$0.00886274$	Character $\chi_{4608}(157, \cdot)$
1-4608-4608.1571-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1571	$0$	✓	✓	$-0.172$	$0$	$0.659237$	Character $\chi_{4608}(1571, \cdot)$
1-4608-4608.1573-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1573	$0$	✓	✓	$0.125$	$0$	$0.774080$	Character $\chi_{4608}(1573, \cdot)$
1-4608-4608.1595-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1595	$0$	✓	✓	$0.0627$	$0$	$0.671234$	Character $\chi_{4608}(1595, \cdot)$
1-4608-4608.1597-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1597	$0$	✓	✓	$0.327$	$0$	$0.876119$	Character $\chi_{4608}(1597, \cdot)$
1-4608-4608.1643-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1643	$0$	✓	✓	$0.144$	$0$	$0.805483$	Character $\chi_{4608}(1643, \cdot)$
1-4608-4608.1645-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1645	$0$	✓	✓	$-0.0974$	$0$	$0.272123$	Character $\chi_{4608}(1645, \cdot)$
1-4608-4608.1667-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1667	$0$	✓	✓	$0.230$	$0$	$0.897637$	Character $\chi_{4608}(1667, \cdot)$
1-4608-4608.1669-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1669	$0$	✓	✓	$0.284$	$0$	$0.734115$	Character $\chi_{4608}(1669, \cdot)$
1-4608-4608.1715-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1715	$0$	✓	✓	$-0.0627$	$0$	$0.796968$	Character $\chi_{4608}(1715, \cdot)$
1-4608-4608.1717-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1717	$0$	✓	✓	$0.0470$	$0$	$0.909381$	Character $\chi_{4608}(1717, \cdot)$
1-4608-4608.1739-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1739	$0$	✓	✓	$0.297$	$0$	$0.955496$	Character $\chi_{4608}(1739, \cdot)$
1-4608-4608.1741-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1741	$0$	✓	✓	$0.437$	$0$	$0.518065$	Character $\chi_{4608}(1741, \cdot)$
1-4608-4608.1787-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1787	$0$	✓	✓	$0.284$	$0$	$0.866096$	Character $\chi_{4608}(1787, \cdot)$
1-4608-4608.1789-r0-0-0	$21.3$	$21.3$	$1$	$2^{9} \cdot 3^{2}$	4608.1789	$0$	✓	✓	$-0.0193$	$0$	$0.710736$	Character $\chi_{4608}(1789, \cdot)$

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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.