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 176 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-3744-3744.101-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.101	$1$	✓	✓	$-0.165$	$0$	$0.419771$	Character $\chi_{3744}(101, \cdot)$
1-3744-3744.1013-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1013	$1$	✓	✓	$0.225$	$0$	$0.734340$	Character $\chi_{3744}(1013, \cdot)$
1-3744-3744.1019-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1019	$1$	✓	✓	$-0.116$	$0$	$0.281709$	Character $\chi_{3744}(1019, \cdot)$
1-3744-3744.1021-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1021	$1$	✓	✓	$0.167$	$0$	$0.608070$	Character $\chi_{3744}(1021, \cdot)$
1-3744-3744.1037-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1037	$1$	✓	✓	$0.272$	$0$	$0.608327$	Character $\chi_{3744}(1037, \cdot)$
1-3744-3744.1075-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1075	$1$	✓	✓	$0.370$	$0$	$1.00441$	Character $\chi_{3744}(1075, \cdot)$
1-3744-3744.11-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.11	$1$	✓	✓	$0.426$	$0$	$0.158805$	Character $\chi_{3744}(11, \cdot)$
1-3744-3744.1109-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1109	$1$	✓	✓	$-0.411$	$0$	$0.170550$	Character $\chi_{3744}(1109, \cdot)$
1-3744-3744.1139-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1139	$1$	✓	✓	$0.116$	$0$	$0.229022$	Character $\chi_{3744}(1139, \cdot)$
1-3744-3744.1147-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1147	$1$	✓	✓	$-0.481$	$0$	$0.235517$	Character $\chi_{3744}(1147, \cdot)$
1-3744-3744.1163-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1163	$1$	✓	✓	$-0.247$	$0$	$0.283101$	Character $\chi_{3744}(1163, \cdot)$
1-3744-3744.1165-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1165	$1$	✓	✓	$0.116$	$0$	$0.756527$	Character $\chi_{3744}(1165, \cdot)$
1-3744-3744.1195-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1195	$1$	✓	✓	$-0.163$	$0$	$0.298464$	Character $\chi_{3744}(1195, \cdot)$
1-3744-3744.1211-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1211	$1$	✓	✓	$-0.0284$	$0$	$0.620561$	Character $\chi_{3744}(1211, \cdot)$
1-3744-3744.1219-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1219	$1$	✓	✓	$0.411$	$0$	$0.104828$	Character $\chi_{3744}(1219, \cdot)$
1-3744-3744.1237-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1237	$1$	✓	✓	$-0.278$	$0$	$0.220374$	Character $\chi_{3744}(1237, \cdot)$
1-3744-3744.1285-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1285	$1$	✓	✓	$0.176$	$0$	$0.505687$	Character $\chi_{3744}(1285, \cdot)$
1-3744-3744.1291-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1291	$1$	✓	✓	$0.477$	$0$	$0.249622$	Character $\chi_{3744}(1291, \cdot)$
1-3744-3744.1307-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1307	$1$	✓	✓	$0.0909$	$0$	$0.516074$	Character $\chi_{3744}(1307, \cdot)$
1-3744-3744.1325-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1325	$1$	✓	✓	$0.0243$	$0$	$0.684057$	Character $\chi_{3744}(1325, \cdot)$
1-3744-3744.1357-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1357	$1$	✓	✓	$0.321$	$0$	$1.15923$	Character $\chi_{3744}(1357, \cdot)$
1-3744-3744.139-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.139	$1$	✓	✓	$-0.316$	$0$	$1.08388$	Character $\chi_{3744}(139, \cdot)$
1-3744-3744.1451-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1451	$1$	✓	✓	$0.0400$	$0$	$0.505625$	Character $\chi_{3744}(1451, \cdot)$
1-3744-3744.1501-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1501	$1$	✓	✓	$-0.315$	$0$	$0.0926140$	Character $\chi_{3744}(1501, \cdot)$
1-3744-3744.1507-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1507	$1$	✓	✓	$0.163$	$0$	$0.533812$	Character $\chi_{3744}(1507, \cdot)$
1-3744-3744.1517-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1517	$1$	✓	✓	$0.370$	$0$	$0.991578$	Character $\chi_{3744}(1517, \cdot)$
1-3744-3744.1523-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1523	$1$	✓	✓	$-0.479$	$0$	$0.0620849$	Character $\chi_{3744}(1523, \cdot)$
1-3744-3744.1571-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1571	$1$	✓	✓	$0.247$	$0$	$1.03228$	Character $\chi_{3744}(1571, \cdot)$
1-3744-3744.1589-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1589	$1$	✓	✓	$0.268$	$0$	$0.871197$	Character $\chi_{3744}(1589, \cdot)$
1-3744-3744.1597-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1597	$1$	✓	✓	$0.247$	$0$	$0.428701$	Character $\chi_{3744}(1597, \cdot)$
1-3744-3744.1643-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1643	$1$	✓	✓	$-0.477$	$0$	$0.178050$	Character $\chi_{3744}(1643, \cdot)$
1-3744-3744.1645-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1645	$1$	✓	✓	$-0.471$	$0$	$0.0113116$	Character $\chi_{3744}(1645, \cdot)$
1-3744-3744.1661-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1661	$1$	✓	✓	$0.411$	$0$	$0.965360$	Character $\chi_{3744}(1661, \cdot)$
1-3744-3744.1669-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1669	$1$	✓	✓	$-0.227$	$0$	$0.378577$	Character $\chi_{3744}(1669, \cdot)$
1-3744-3744.1699-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1699	$1$	✓	✓	$0.231$	$0$	$0.642593$	Character $\chi_{3744}(1699, \cdot)$
1-3744-3744.173-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.173	$1$	✓	✓	$-0.223$	$0$	$0.119293$	Character $\chi_{3744}(173, \cdot)$
1-3744-3744.1733-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1733	$1$	✓	✓	$-0.272$	$0$	$0.283891$	Character $\chi_{3744}(1733, \cdot)$
1-3744-3744.1771-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1771	$1$	✓	✓	$-0.120$	$0$	$0.577448$	Character $\chi_{3744}(1771, \cdot)$
1-3744-3744.1787-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1787	$1$	✓	✓	$-0.113$	$0$	$0.625771$	Character $\chi_{3744}(1787, \cdot)$
1-3744-3744.1789-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1789	$1$	✓	✓	$-0.0224$	$0$	$0.670732$	Character $\chi_{3744}(1789, \cdot)$
1-3744-3744.1813-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1813	$1$	✓	✓	$-0.363$	$0$	$1.43872$	Character $\chi_{3744}(1813, \cdot)$
1-3744-3744.1829-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1829	$1$	✓	✓	$-0.455$	$0$	$1.35811$	Character $\chi_{3744}(1829, \cdot)$
1-3744-3744.1843-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1843	$1$	✓	✓	$-0.227$	$0$	$0.254079$	Character $\chi_{3744}(1843, \cdot)$
1-3744-3744.1861-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1861	$1$	✓	✓	$-0.417$	$0$	$0.100467$	Character $\chi_{3744}(1861, \cdot)$
1-3744-3744.1883-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1883	$1$	✓	✓	$0.176$	$0$	$0.772610$	Character $\chi_{3744}(1883, \cdot)$
1-3744-3744.1901-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1901	$1$	✓	✓	$0.0669$	$0$	$0.743927$	Character $\chi_{3744}(1901, \cdot)$
1-3744-3744.1915-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1915	$1$	✓	✓	$0.338$	$0$	$1.19926$	Character $\chi_{3744}(1915, \cdot)$
1-3744-3744.1931-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1931	$1$	✓	✓	$-0.270$	$0$	$0.247191$	Character $\chi_{3744}(1931, \cdot)$
1-3744-3744.1949-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1949	$1$	✓	✓	$0.163$	$0$	$0.851554$	Character $\chi_{3744}(1949, \cdot)$
1-3744-3744.1955-r1-0-0	$402.$	$402.$	$1$	$2^{5} \cdot 3^{2} \cdot 13$	3744.1955	$1$	✓	✓	$-0.428$	$0$	$0.124740$	Character $\chi_{3744}(1955, \cdot)$

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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.