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 94 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1012-1012.1007-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.1007	$0$	✓	✓	$0.370$	$0$	$1.39505$	Character $\chi_{1012}(1007, \cdot)$
1-1012-1012.103-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.103	$0$	✓	✓	$-0.167$	$0$	$0.645464$	Character $\chi_{1012}(103, \cdot)$
1-1012-1012.123-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.123	$0$	✓	✓	$0.479$	$0$	$0.280712$	Character $\chi_{1012}(123, \cdot)$
1-1012-1012.127-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.127	$0$	✓	✓	$-0.162$	$0$	$0.292712$	Character $\chi_{1012}(127, \cdot)$
1-1012-1012.131-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.131	$0$	✓	✓	$-0.0246$	$0$	$0.516190$	Character $\chi_{1012}(131, \cdot)$
1-1012-1012.135-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.135	$0$	✓	✓	$0.202$	$0$	$0.850916$	Character $\chi_{1012}(135, \cdot)$
1-1012-1012.15-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.15	$0$	✓	✓	$-0.202$	$0$	$0.414619$	Character $\chi_{1012}(15, \cdot)$
1-1012-1012.151-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.151	$0$	✓	✓	$-0.0143$	$0$	$1.11914$	Character $\chi_{1012}(151, \cdot)$
1-1012-1012.159-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.159	$0$	✓	✓	$-0.385$	$0$	$2.05560$	Character $\chi_{1012}(159, \cdot)$
1-1012-1012.167-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.167	$0$	✓	✓	$0.295$	$0$	$1.04705$	Character $\chi_{1012}(167, \cdot)$
1-1012-1012.191-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.191	$0$	✓	✓	$-0.159$	$0$	$0.840340$	Character $\chi_{1012}(191, \cdot)$
1-1012-1012.203-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.203	$0$	✓	✓	$0.240$	$0$	$1.20142$	Character $\chi_{1012}(203, \cdot)$
1-1012-1012.211-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.211	$0$	✓	✓	$0.197$	$0$	$0.880533$	Character $\chi_{1012}(211, \cdot)$
1-1012-1012.215-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.215	$0$	✓	✓	$-0.0133$	$0$	$1.27895$	Character $\chi_{1012}(215, \cdot)$
1-1012-1012.219-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.219	$0$	✓	✓	$0.0844$	$0$	$1.35572$	Character $\chi_{1012}(219, \cdot)$
1-1012-1012.235-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.235	$0$	✓	✓	$-0.379$	$0$	$0.876323$	Character $\chi_{1012}(235, \cdot)$
1-1012-1012.239-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.239	$0$	✓	✓	$0.343$	$0$	$1.36894$	Character $\chi_{1012}(239, \cdot)$
1-1012-1012.247-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.247	$0$	✓	✓	$-0.354$	$0$	$0.591550$	Character $\chi_{1012}(247, \cdot)$
1-1012-1012.251-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.251	$0$	✓	✓	$-0.271$	$0$	$0.870210$	Character $\chi_{1012}(251, \cdot)$
1-1012-1012.255-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.255	$0$	✓	✓	$0.162$	$0$	$1.18255$	Character $\chi_{1012}(255, \cdot)$
1-1012-1012.259-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.259	$0$	✓	✓	$-0.197$	$0$	$0.503484$	Character $\chi_{1012}(259, \cdot)$
1-1012-1012.267-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.267	$0$	✓	✓	$0.379$	$0$	$1.77419$	Character $\chi_{1012}(267, \cdot)$
1-1012-1012.271-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.271	$0$	✓	✓	$-0.343$	$0$	$0.479609$	Character $\chi_{1012}(271, \cdot)$
1-1012-1012.291-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.291	$0$	✓	✓	$0.235$	$0$	$1.51234$	Character $\chi_{1012}(291, \cdot)$
1-1012-1012.295-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.295	$0$	✓	✓	$0.354$	$0$	$1.51350$	Character $\chi_{1012}(295, \cdot)$
1-1012-1012.303-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.303	$0$	✓	✓	$-0.295$	$0$	$0.448522$	Character $\chi_{1012}(303, \cdot)$
1-1012-1012.307-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.307	$0$	✓	✓	$0.233$	$0$	$1.61165$	Character $\chi_{1012}(307, \cdot)$
1-1012-1012.315-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.315	$0$	✓	✓	$0.0143$	$0$	$1.16205$	Character $\chi_{1012}(315, \cdot)$
1-1012-1012.339-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.339	$0$	✓	✓	$-0.240$	$0$	$0.562806$	Character $\chi_{1012}(339, \cdot)$
1-1012-1012.347-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.347	$0$	✓	✓	$-0.330$	$0$	$0.188499$	Character $\chi_{1012}(347, \cdot)$
1-1012-1012.35-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.35	$0$	✓	✓	$0.330$	$0$	$1.44502$	Character $\chi_{1012}(35, \cdot)$
1-1012-1012.351-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.351	$0$	✓	✓	$0.0494$	$0$	$1.05589$	Character $\chi_{1012}(351, \cdot)$
1-1012-1012.355-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.355	$0$	✓	✓	$0.159$	$0$	$1.12695$	Character $\chi_{1012}(355, \cdot)$
1-1012-1012.367-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.367	$0$	✓	✓	$0.496$	$0$	$2.03490$	Character $\chi_{1012}(367, \cdot)$
1-1012-1012.371-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.371	$0$	✓	✓	$-0.272$	$0$	$0.403101$	Character $\chi_{1012}(371, \cdot)$
1-1012-1012.379-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.379	$0$	✓	✓	$0.271$	$0$	$1.47362$	Character $\chi_{1012}(379, \cdot)$
1-1012-1012.383-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.383	$0$	✓	✓	$0.350$	$0$	$1.40991$	Character $\chi_{1012}(383, \cdot)$
1-1012-1012.39-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.39	$0$	✓	✓	$-0.271$	$0$	$0.613030$	Character $\chi_{1012}(39, \cdot)$
1-1012-1012.395-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.395	$0$	✓	✓	$-0.0494$	$0$	$0.492585$	Character $\chi_{1012}(395, \cdot)$
1-1012-1012.403-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.403	$0$	✓	✓	$0.123$	$0$	$0.983894$	Character $\chi_{1012}(403, \cdot)$
1-1012-1012.411-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.411	$0$	✓	✓	$0.210$	$0$	$1.55814$	Character $\chi_{1012}(411, \cdot)$
1-1012-1012.439-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.439	$0$	✓	✓	$-0.0844$	$0$	$1.12242$	Character $\chi_{1012}(439, \cdot)$
1-1012-1012.467-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.467	$0$	✓	✓	$0.279$	$0$	$0.842400$	Character $\chi_{1012}(467, \cdot)$
1-1012-1012.471-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.471	$0$	✓	✓	$0.385$	$0$	$0.108313$	Character $\chi_{1012}(471, \cdot)$
1-1012-1012.491-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.491	$0$	✓	✓	$0.272$	$0$	$1.10334$	Character $\chi_{1012}(491, \cdot)$
1-1012-1012.511-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.511	$0$	✓	✓	$0.0591$	$0$	$0.832947$	Character $\chi_{1012}(511, \cdot)$
1-1012-1012.519-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.519	$0$	✓	✓	$0.271$	$0$	$1.33745$	Character $\chi_{1012}(519, \cdot)$
1-1012-1012.535-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.535	$0$	✓	✓	$0.0883$	$0$	$0.987011$	Character $\chi_{1012}(535, \cdot)$
1-1012-1012.543-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.543	$0$	✓	✓	$0.387$	$0$	$1.28283$	Character $\chi_{1012}(543, \cdot)$
1-1012-1012.547-r0-0-0	$4.69$	$4.69$	$1$	$2^{2} \cdot 11 \cdot 23$	1012.547	$0$	✓	✓	$-0.421$	$0$	$0.500462$	Character $\chi_{1012}(547, \cdot)$

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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.