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 (43 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1860-1860.1019-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1019	$1$	✓	✓			$-0.441$	$0$	$0.180071$	Character $\chi_{1860}(1019, \cdot)$
1-1860-1860.1043-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1043	$1$	✓	✓			$0.415$	$0$	$1.28284$	Character $\chi_{1860}(1043, \cdot)$
1-1860-1860.107-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.107	$1$	✓	✓			$-0.415$	$0$	$0.175995$	Character $\chi_{1860}(107, \cdot)$
1-1860-1860.1103-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1103	$1$	✓	✓			$0.236$	$0$	$0.723486$	Character $\chi_{1860}(1103, \cdot)$
1-1860-1860.1139-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1139	$1$	✓	✓			$0.441$	$0$	$1.10922$	Character $\chi_{1860}(1139, \cdot)$
1-1860-1860.1163-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1163	$1$	✓	✓			$0.364$	$0$	$0.0938712$	Character $\chi_{1860}(1163, \cdot)$
1-1860-1860.1187-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1187	$1$	✓	✓			$-0.0622$	$0$	$0.276362$	Character $\chi_{1860}(1187, \cdot)$
1-1860-1860.119-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.119	$1$	✓	✓			$0.127$	$0$	$0.810608$	Character $\chi_{1860}(119, \cdot)$
1-1860-1860.1199-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1199	$1$	✓	✓			$0.467$	$0$	$1.36194$	Character $\chi_{1860}(1199, \cdot)$
1-1860-1860.1223-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1223	$1$	✓	✓			$-0.0913$	$0$	$0.620153$	Character $\chi_{1860}(1223, \cdot)$
1-1860-1860.1247-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1247	$1$	✓	✓			$-0.261$	$0$	$0.359648$	Character $\chi_{1860}(1247, \cdot)$
1-1860-1860.1307-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1307	$1$	✓	✓			$0.274$	$0$	$0.781958$	Character $\chi_{1860}(1307, \cdot)$
1-1860-1860.1319-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1319	$1$	✓	✓			$0.0865$	$0$	$0.493448$	Character $\chi_{1860}(1319, \cdot)$
1-1860-1860.1343-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1343	$1$	✓	✓			$0.195$	$0$	$0.664369$	Character $\chi_{1860}(1343, \cdot)$
1-1860-1860.1379-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1379	$1$	✓	✓			$0.353$	$0$	$1.03771$	Character $\chi_{1860}(1379, \cdot)$
1-1860-1860.1403-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1403	$1$	✓	✓			$0.317$	$0$	$0.840369$	Character $\chi_{1860}(1403, \cdot)$
1-1860-1860.143-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.143	$1$	✓	✓			$0.0870$	$0$	$0.870532$	Character $\chi_{1860}(143, \cdot)$
1-1860-1860.1439-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1439	$1$	✓	✓			$0.0718$	$0$	$0.448762$	Character $\chi_{1860}(1439, \cdot)$
1-1860-1860.1499-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1499	$1$	✓	✓			$-0.0865$	$0$	$0.335578$	Character $\chi_{1860}(1499, \cdot)$
1-1860-1860.1523-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1523	$1$	✓	✓			$0.00589$	$0$	$0.662164$	Character $\chi_{1860}(1523, \cdot)$
1-1860-1860.1547-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1547	$1$	✓	✓			$-0.195$	$0$	$0.317071$	Character $\chi_{1860}(1547, \cdot)$
1-1860-1860.1583-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1583	$1$	✓	✓			$-0.0404$	$0$	$0.568349$	Character $\chi_{1860}(1583, \cdot)$
1-1860-1860.1739-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1739	$1$	✓	✓			$-0.467$	$0$	$0.187846$	Character $\chi_{1860}(1739, \cdot)$
1-1860-1860.1787-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1787	$1$	✓	✓			$0.0913$	$0$	$0.705087$	Character $\chi_{1860}(1787, \cdot)$
1-1860-1860.179-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.179	$1$	✓	✓			$0.374$	$0$	$1.39132$	Character $\chi_{1860}(179, \cdot)$
1-1860-1860.1823-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1823	$1$	✓	✓			$-0.274$	$0$	$0.330135$	Character $\chi_{1860}(1823, \cdot)$
1-1860-1860.1847-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1847	$1$	✓	✓			$-0.0870$	$0$	$0.601784$	Character $\chi_{1860}(1847, \cdot)$
1-1860-1860.1859-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.1859	$1$	✓	✓	✓	✓	$0$	$0$	$0.626181$	Character $\chi_{1860}(1859, \cdot)$
1-1860-1860.227-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.227	$1$	✓	✓			$-0.128$	$0$	$0.817278$	Character $\chi_{1860}(227, \cdot)$
1-1860-1860.239-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.239	$1$	✓	✓			$-0.374$	$0$	$0.401871$	Character $\chi_{1860}(239, \cdot)$
1-1860-1860.287-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.287	$1$	✓	✓			$-0.00589$	$0$	$0.611572$	Character $\chi_{1860}(287, \cdot)$
1-1860-1860.407-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.407	$1$	✓	✓			$-0.317$	$0$	$0.229267$	Character $\chi_{1860}(407, \cdot)$
1-1860-1860.443-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.443	$1$	✓	✓			$0.261$	$0$	$0.943402$	Character $\chi_{1860}(443, \cdot)$
1-1860-1860.467-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.467	$1$	✓	✓			$-0.364$	$0$	$1.51765$	Character $\chi_{1860}(467, \cdot)$
1-1860-1860.47-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.47	$1$	✓	✓			$0.0404$	$0$	$0.591085$	Character $\chi_{1860}(47, \cdot)$
1-1860-1860.503-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.503	$1$	✓	✓			$0.0622$	$0$	$0.346776$	Character $\chi_{1860}(503, \cdot)$
1-1860-1860.539-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.539	$1$	✓	✓			$-0.0718$	$0$	$0.413647$	Character $\chi_{1860}(539, \cdot)$
1-1860-1860.563-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.563	$1$	✓	✓			$-0.401$	$0$	$0.169946$	Character $\chi_{1860}(563, \cdot)$
1-1860-1860.707-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.707	$1$	✓	✓			$0.401$	$0$	$1.09611$	Character $\chi_{1860}(707, \cdot)$
1-1860-1860.719-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.719	$1$	✓	✓			$-0.127$	$0$	$0.413256$	Character $\chi_{1860}(719, \cdot)$
1-1860-1860.803-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.803	$1$	✓	✓			$0.128$	$0$	$0.829445$	Character $\chi_{1860}(803, \cdot)$
1-1860-1860.887-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.887	$1$	✓	✓			$-0.236$	$0$	$0.176210$	Character $\chi_{1860}(887, \cdot)$
1-1860-1860.959-r1-0-0	$199.$	$199.$	$1$	$2^{2} \cdot 3 \cdot 5 \cdot 31$	1860.959	$1$	✓	✓			$-0.353$	$0$	$0.227060$	Character $\chi_{1860}(959, \cdot)$

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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.