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 128 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-800-800.109-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.109	$0$	✓	✓	$-0.126$	$0$	$0.495339$	Character $\chi_{800}(109, \cdot)$
1-800-800.123-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.123	$0$	✓	✓	$0.126$	$0$	$1.14039$	Character $\chi_{800}(123, \cdot)$
1-800-800.141-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.141	$0$	✓	✓	$-0.126$	$0$	$0.894945$	Character $\chi_{800}(141, \cdot)$
1-800-800.147-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.147	$0$	✓	✓	$0.383$	$0$	$1.73120$	Character $\chi_{800}(147, \cdot)$
1-800-800.163-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.163	$0$	✓	✓	$0.123$	$0$	$0.957409$	Character $\chi_{800}(163, \cdot)$
1-800-800.181-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.181	$0$	✓	✓	$0.116$	$0$	$1.10261$	Character $\chi_{800}(181, \cdot)$
1-800-800.187-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.187	$0$	✓	✓	$0.186$	$0$	$1.72805$	Character $\chi_{800}(187, \cdot)$
1-800-800.189-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.189	$0$	✓	✓	$-0.436$	$0$	$1.96477$	Character $\chi_{800}(189, \cdot)$
1-800-800.203-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.203	$0$	✓	✓	$-0.0537$	$0$	$1.07331$	Character $\chi_{800}(203, \cdot)$
1-800-800.21-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.21	$0$	✓	✓	$0.196$	$0$	$1.43948$	Character $\chi_{800}(21, \cdot)$
1-800-800.221-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.221	$0$	✓	✓	$-0.116$	$0$	$0.489305$	Character $\chi_{800}(221, \cdot)$
1-800-800.227-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.227	$0$	✓	✓	$0.0637$	$0$	$1.23943$	Character $\chi_{800}(227, \cdot)$
1-800-800.229-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.229	$0$	✓	✓	$-0.0537$	$0$	$0.936458$	Character $\chi_{800}(229, \cdot)$
1-800-800.261-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.261	$0$	✓	✓	$0.126$	$0$	$1.46851$	Character $\chi_{800}(261, \cdot)$
1-800-800.267-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.267	$0$	✓	✓	$-0.133$	$0$	$1.11682$	Character $\chi_{800}(267, \cdot)$
1-800-800.269-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.269	$0$	✓	✓	$0.0537$	$0$	$1.37326$	Character $\chi_{800}(269, \cdot)$
1-800-800.27-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.27	$0$	✓	✓	$0.126$	$0$	$1.12743$	Character $\chi_{800}(27, \cdot)$
1-800-800.283-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.283	$0$	✓	✓	$-0.383$	$0$	$0.392302$	Character $\chi_{800}(283, \cdot)$
1-800-800.29-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.29	$0$	✓	✓	$0.383$	$0$	$1.73494$	Character $\chi_{800}(29, \cdot)$
1-800-800.3-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.3	$0$	✓	✓	$0.133$	$0$	$1.53636$	Character $\chi_{800}(3, \cdot)$
1-800-800.309-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.309	$0$	✓	✓	$0.436$	$0$	$0.241969$	Character $\chi_{800}(309, \cdot)$
1-800-800.323-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.323	$0$	✓	✓	$0.0637$	$0$	$1.05430$	Character $\chi_{800}(323, \cdot)$
1-800-800.341-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.341	$0$	✓	✓	$0.436$	$0$	$1.63139$	Character $\chi_{800}(341, \cdot)$
1-800-800.347-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.347	$0$	✓	✓	$-0.303$	$0$	$0.749492$	Character $\chi_{800}(347, \cdot)$
1-800-800.363-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.363	$0$	✓	✓	$-0.0637$	$0$	$0.898383$	Character $\chi_{800}(363, \cdot)$
1-800-800.381-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.381	$0$	✓	✓	$-0.196$	$0$	$0.869579$	Character $\chi_{800}(381, \cdot)$
1-800-800.387-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.387	$0$	✓	✓	$0.123$	$0$	$1.15343$	Character $\chi_{800}(387, \cdot)$
1-800-800.389-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.389	$0$	✓	✓	$0.126$	$0$	$0.884879$	Character $\chi_{800}(389, \cdot)$
1-800-800.403-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.403	$0$	✓	✓	$-0.116$	$0$	$0.793480$	Character $\chi_{800}(403, \cdot)$
1-800-800.421-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.421	$0$	✓	✓	$0.446$	$0$	$1.75805$	Character $\chi_{800}(421, \cdot)$
1-800-800.427-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.427	$0$	✓	✓	$-0.123$	$0$	$0.906633$	Character $\chi_{800}(427, \cdot)$
1-800-800.429-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.429	$0$	✓	✓	$0.133$	$0$	$0.960408$	Character $\chi_{800}(429, \cdot)$
1-800-800.461-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.461	$0$	✓	✓	$0.313$	$0$	$1.37436$	Character $\chi_{800}(461, \cdot)$
1-800-800.467-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.467	$0$	✓	✓	$-0.196$	$0$	$0.559143$	Character $\chi_{800}(467, \cdot)$
1-800-800.469-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.469	$0$	✓	✓	$-0.383$	$0$	$0.0455530$	Character $\chi_{800}(469, \cdot)$
1-800-800.483-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.483	$0$	✓	✓	$-0.446$	$0$	$0.337388$	Character $\chi_{800}(483, \cdot)$
1-800-800.509-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.509	$0$	✓	✓	$0.123$	$0$	$1.46072$	Character $\chi_{800}(509, \cdot)$
1-800-800.523-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.523	$0$	✓	✓	$-0.123$	$0$	$0.387297$	Character $\chi_{800}(523, \cdot)$
1-800-800.541-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.541	$0$	✓	✓	$0.123$	$0$	$1.08244$	Character $\chi_{800}(541, \cdot)$
1-800-800.547-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.547	$0$	✓	✓	$-0.366$	$0$	$0.320521$	Character $\chi_{800}(547, \cdot)$
1-800-800.563-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.563	$0$	✓	✓	$-0.126$	$0$	$1.12487$	Character $\chi_{800}(563, \cdot)$
1-800-800.581-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.581	$0$	✓	✓	$0.366$	$0$	$1.65919$	Character $\chi_{800}(581, \cdot)$
1-800-800.587-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.587	$0$	✓	✓	$-0.0637$	$0$	$0.937216$	Character $\chi_{800}(587, \cdot)$
1-800-800.589-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.589	$0$	✓	✓	$0.313$	$0$	$1.61603$	Character $\chi_{800}(589, \cdot)$
1-800-800.603-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.603	$0$	✓	✓	$0.196$	$0$	$0.863339$	Character $\chi_{800}(603, \cdot)$
1-800-800.61-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.61	$0$	✓	✓	$-0.436$	$0$	$0.580363$	Character $\chi_{800}(61, \cdot)$
1-800-800.621-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.621	$0$	✓	✓	$-0.366$	$0$	$0.655546$	Character $\chi_{800}(621, \cdot)$
1-800-800.627-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.627	$0$	✓	✓	$-0.186$	$0$	$0.422702$	Character $\chi_{800}(627, \cdot)$
1-800-800.629-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.629	$0$	✓	✓	$-0.303$	$0$	$0.547735$	Character $\chi_{800}(629, \cdot)$
1-800-800.661-r0-0-0	$3.71$	$3.71$	$1$	$2^{5} \cdot 5^{2}$	800.661	$0$	✓	✓	$-0.123$	$0$	$0.557411$	Character $\chi_{800}(661, \cdot)$

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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.