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 189 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-764-764.11-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.11	$0$	✓	✓	$0.0491$	$0$	$0.721923$	Character $\chi_{764}(11, \cdot)$
1-764-764.111-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.111	$0$	✓	✓	$0.453$	$0$	$1.32854$	Character $\chi_{764}(111, \cdot)$
1-764-764.119-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.119	$0$	✓	✓	$0.428$	$0$	$0.433285$	Character $\chi_{764}(119, \cdot)$
1-764-764.123-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.123	$0$	✓	✓	$0.0968$	$0$	$1.36637$	Character $\chi_{764}(123, \cdot)$
1-764-764.127-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.127	$0$	✓	✓	$-0.0595$	$0$	$0.707064$	Character $\chi_{764}(127, \cdot)$
1-764-764.131-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.131	$0$	✓	✓	$0.445$	$0$	$0.276000$	Character $\chi_{764}(131, \cdot)$
1-764-764.139-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.139	$0$	✓	✓	$-0.0491$	$0$	$0.967010$	Character $\chi_{764}(139, \cdot)$
1-764-764.143-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.143	$0$	✓	✓	$-0.490$	$0$	$0.540990$	Character $\chi_{764}(143, \cdot)$
1-764-764.151-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.151	$0$	✓	✓	$-0.286$	$0$	$0.719604$	Character $\chi_{764}(151, \cdot)$
1-764-764.155-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.155	$0$	✓	✓	$-0.0327$	$0$	$1.24646$	Character $\chi_{764}(155, \cdot)$
1-764-764.159-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.159	$0$	✓	✓	$-0.345$	$0$	$0.711353$	Character $\chi_{764}(159, \cdot)$
1-764-764.167-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.167	$0$	✓	✓	$0.117$	$0$	$1.54299$	Character $\chi_{764}(167, \cdot)$
1-764-764.171-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.171	$0$	✓	✓	$0.276$	$0$	$1.46312$	Character $\chi_{764}(171, \cdot)$
1-764-764.175-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.175	$0$	✓	✓	$-0.108$	$0$	$0.778019$	Character $\chi_{764}(175, \cdot)$
1-764-764.179-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.179	$0$	✓	✓	$0.108$	$0$	$1.27669$	Character $\chi_{764}(179, \cdot)$
1-764-764.183-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.183	$0$	✓	✓	$-0.117$	$0$	$0.965101$	Character $\chi_{764}(183, \cdot)$
1-764-764.187-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.187	$0$	✓	✓	$0.490$	$0$	$2.10733$	Character $\chi_{764}(187, \cdot)$
1-764-764.19-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.19	$0$	✓	✓	$0.469$	$0$	$2.00964$	Character $\chi_{764}(19, \cdot)$
1-764-764.219-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.219	$0$	✓	✓	$0.0964$	$0$	$0.974174$	Character $\chi_{764}(219, \cdot)$
1-764-764.235-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.235	$0$	✓	✓	$0.276$	$0$	$1.46962$	Character $\chi_{764}(235, \cdot)$
1-764-764.247-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.247	$0$	✓	✓	$0.130$	$0$	$1.10997$	Character $\chi_{764}(247, \cdot)$
1-764-764.267-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.267	$0$	✓	✓	$0.190$	$0$	$1.19464$	Character $\chi_{764}(267, \cdot)$
1-764-764.275-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.275	$0$	✓	✓	$0.104$	$0$	$1.05717$	Character $\chi_{764}(275, \cdot)$
1-764-764.279-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.279	$0$	✓	✓	$-0.0978$	$0$	$1.08130$	Character $\chi_{764}(279, \cdot)$
1-764-764.303-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.303	$0$	✓	✓	$0.345$	$0$	$1.15334$	Character $\chi_{764}(303, \cdot)$
1-764-764.307-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.307	$0$	✓	✓	$-0.0964$	$0$	$0.534543$	Character $\chi_{764}(307, \cdot)$
1-764-764.31-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.31	$0$	✓	✓	$0.168$	$0$	$1.22915$	Character $\chi_{764}(31, \cdot)$
1-764-764.315-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.315	$0$	✓	✓	$0.241$	$0$	$1.76460$	Character $\chi_{764}(315, \cdot)$
1-764-764.323-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.323	$0$	✓	✓	$-0.0968$	$0$	$1.11016$	Character $\chi_{764}(323, \cdot)$
1-764-764.331-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.331	$0$	✓	✓	$-0.481$	$0$	$1.85635$	Character $\chi_{764}(331, \cdot)$
1-764-764.339-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.339	$0$	✓	✓	$0.286$	$0$	$1.28710$	Character $\chi_{764}(339, \cdot)$
1-764-764.343-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.343	$0$	✓	✓	$0.0639$	$0$	$1.40486$	Character $\chi_{764}(343, \cdot)$
1-764-764.35-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.35	$0$	✓	✓	$-0.445$	$0$	$1.76780$	Character $\chi_{764}(35, \cdot)$
1-764-764.355-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.355	$0$	✓	✓	$-0.0964$	$0$	$0.930767$	Character $\chi_{764}(355, \cdot)$
1-764-764.359-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.359	$0$	✓	✓	$0.161$	$0$	$0.905418$	Character $\chi_{764}(359, \cdot)$
1-764-764.367-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.367	$0$	✓	✓	$0.481$	$0$	$0.292220$	Character $\chi_{764}(367, \cdot)$
1-764-764.379-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.379	$0$	✓	✓	$0.0595$	$0$	$0.565948$	Character $\chi_{764}(379, \cdot)$
1-764-764.403-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.403	$0$	✓	✓	$-0.306$	$0$	$0.760987$	Character $\chi_{764}(403, \cdot)$
1-764-764.411-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.411	$0$	✓	✓	$-0.345$	$0$	$0.406935$	Character $\chi_{764}(411, \cdot)$
1-764-764.415-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.415	$0$	✓	✓	$-0.356$	$0$	$0.0263794$	Character $\chi_{764}(415, \cdot)$
1-764-764.419-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.419	$0$	✓	✓	$-0.168$	$0$	$1.00202$	Character $\chi_{764}(419, \cdot)$
1-764-764.423-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.423	$0$	✓	✓	$0.494$	$0$	$1.76569$	Character $\chi_{764}(423, \cdot)$
1-764-764.435-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.435	$0$	✓	✓	$-0.342$	$0$	$0.246036$	Character $\chi_{764}(435, \cdot)$
1-764-764.439-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.439	$0$	✓	✓	$-0.241$	$0$	$1.22125$	Character $\chi_{764}(439, \cdot)$
1-764-764.443-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.443	$0$	✓	✓	$-0.428$	$0$	$2.01825$	Character $\chi_{764}(443, \cdot)$
1-764-764.455-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.455	$0$	✓	✓	$0.183$	$0$	$1.35242$	Character $\chi_{764}(455, \cdot)$
1-764-764.47-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.47	$0$	✓	✓	$-0.356$	$0$	$0.0521575$	Character $\chi_{764}(47, \cdot)$
1-764-764.471-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.471	$0$	✓	✓	$0.0978$	$0$	$1.71271$	Character $\chi_{764}(471, \cdot)$
1-764-764.475-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.475	$0$	✓	✓	$-0.190$	$0$	$0.312188$	Character $\chi_{764}(475, \cdot)$
1-764-764.483-r0-0-0	$3.54$	$3.54$	$1$	$2^{2} \cdot 191$	764.483	$0$	✓	✓	$-0.00832$	$0$	$0.911536$	Character $\chi_{764}(483, \cdot)$

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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.