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 52 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-483-483.101-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.101	$0$	✓	✓	$-0.430$	$0$	$0.660348$	Character $\chi_{483}(101, \cdot)$
1-483-483.104-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.104	$0$	✓	✓	$0.0844$	$0$	$0.980810$	Character $\chi_{483}(104, \cdot)$
1-483-483.107-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.107	$0$	✓	✓	$-0.279$	$0$	$0.936771$	Character $\chi_{483}(107, \cdot)$
1-483-483.11-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.11	$0$	✓	✓	$-0.0981$	$0$	$0.919629$	Character $\chi_{483}(11, \cdot)$
1-483-483.110-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.110	$0$	✓	✓	$0.430$	$0$	$1.50701$	Character $\chi_{483}(110, \cdot)$
1-483-483.131-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.131	$0$	✓	✓	$-0.211$	$0$	$1.18608$	Character $\chi_{483}(131, \cdot)$
1-483-483.137-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.137	$0$	✓	✓	$-0.426$	$0$	$0.486792$	Character $\chi_{483}(137, \cdot)$
1-483-483.146-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.146	$0$	✓	✓	$0.233$	$0$	$1.82882$	Character $\chi_{483}(146, \cdot)$
1-483-483.149-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.149	$0$	✓	✓	$-0.244$	$0$	$0.746366$	Character $\chi_{483}(149, \cdot)$
1-483-483.158-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.158	$0$	✓	✓	$0.279$	$0$	$1.32269$	Character $\chi_{483}(158, \cdot)$
1-483-483.164-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.164	$0$	✓	✓	$-0.0462$	$0$	$0.617148$	Character $\chi_{483}(164, \cdot)$
1-483-483.167-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.167	$0$	✓	✓	$0.0494$	$0$	$1.04341$	Character $\chi_{483}(167, \cdot)$
1-483-483.173-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.173	$0$	✓	✓	$-0.102$	$0$	$1.12337$	Character $\chi_{483}(173, \cdot)$
1-483-483.188-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.188	$0$	✓	✓	$-0.0494$	$0$	$1.50030$	Character $\chi_{483}(188, \cdot)$
1-483-483.191-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.191	$0$	✓	✓	$-0.236$	$0$	$1.11072$	Character $\chi_{483}(191, \cdot)$
1-483-483.209-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.209	$0$	✓	✓	$-0.0844$	$0$	$1.08949$	Character $\chi_{483}(209, \cdot)$
1-483-483.212-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.212	$0$	✓	✓	$-0.456$	$0$	$1.78123$	Character $\chi_{483}(212, \cdot)$
1-483-483.215-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.215	$0$	✓	✓	$0.0462$	$0$	$1.62282$	Character $\chi_{483}(215, \cdot)$
1-483-483.221-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.221	$0$	✓	✓	$0.456$	$0$	$0.460459$	Character $\chi_{483}(221, \cdot)$
1-483-483.236-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.236	$0$	✓	✓	$-0.137$	$0$	$1.01263$	Character $\chi_{483}(236, \cdot)$
1-483-483.248-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.248	$0$	✓	✓	$-0.195$	$0$	$1.35074$	Character $\chi_{483}(248, \cdot)$
1-483-483.257-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.257	$0$	✓	✓	$-0.236$	$0$	$0.685804$	Character $\chi_{483}(257, \cdot)$
1-483-483.26-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.26	$0$	✓	✓	$-0.419$	$0$	$0.167448$	Character $\chi_{483}(26, \cdot)$
1-483-483.263-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.263	$0$	✓	✓	$0.236$	$0$	$1.70591$	Character $\chi_{483}(263, \cdot)$
1-483-483.269-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.269	$0$	✓	✓	$0.162$	$0$	$1.18701$	Character $\chi_{483}(269, \cdot)$
1-483-483.275-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.275	$0$	✓	✓	$0.426$	$0$	$1.60248$	Character $\chi_{483}(275, \cdot)$
1-483-483.278-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.278	$0$	✓	✓	$-0.271$	$0$	$0.415692$	Character $\chi_{483}(278, \cdot)$
1-483-483.296-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.296	$0$	✓	✓	$0.133$	$0$	$1.21314$	Character $\chi_{483}(296, \cdot)$
1-483-483.311-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.311	$0$	✓	✓	$0.271$	$0$	$1.69533$	Character $\chi_{483}(311, \cdot)$
1-483-483.335-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.335	$0$	✓	✓	$0.0246$	$0$	$1.26568$	Character $\chi_{483}(335, \cdot)$
1-483-483.353-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.353	$0$	✓	✓	$0.419$	$0$	$1.24110$	Character $\chi_{483}(353, \cdot)$
1-483-483.359-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.359	$0$	✓	✓	$0.310$	$0$	$2.13176$	Character $\chi_{483}(359, \cdot)$
1-483-483.374-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.374	$0$	✓	✓	$0.236$	$0$	$1.35040$	Character $\chi_{483}(374, \cdot)$
1-483-483.377-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.377	$0$	✓	✓	$0.382$	$0$	$1.23585$	Character $\chi_{483}(377, \cdot)$
1-483-483.389-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.389	$0$	✓	✓	$0.244$	$0$	$1.80638$	Character $\chi_{483}(389, \cdot)$
1-483-483.395-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.395	$0$	✓	✓	$0.137$	$0$	$0.831156$	Character $\chi_{483}(395, \cdot)$
1-483-483.401-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.401	$0$	✓	✓	$0.0898$	$0$	$0.939169$	Character $\chi_{483}(401, \cdot)$
1-483-483.404-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.404	$0$	✓	✓	$-0.162$	$0$	$0.361331$	Character $\chi_{483}(404, \cdot)$
1-483-483.41-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.41	$0$	✓	✓	$-0.382$	$0$	$0.313725$	Character $\chi_{483}(41, \cdot)$
1-483-483.410-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.410	$0$	✓	✓	$-0.129$	$0$	$0.248814$	Character $\chi_{483}(410, \cdot)$
1-483-483.416-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.416	$0$	✓	✓	$0.102$	$0$	$1.45195$	Character $\chi_{483}(416, \cdot)$
1-483-483.431-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.431	$0$	✓	✓	$0.275$	$0$	$1.50283$	Character $\chi_{483}(431, \cdot)$
1-483-483.44-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.44	$0$	✓	✓	$0.0981$	$0$	$1.01174$	Character $\chi_{483}(44, \cdot)$
1-483-483.440-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.440	$0$	✓	✓	$-0.233$	$0$	$1.06404$	Character $\chi_{483}(440, \cdot)$
1-483-483.446-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.446	$0$	✓	✓	$0.195$	$0$	$1.69949$	Character $\chi_{483}(446, \cdot)$
1-483-483.452-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.452	$0$	✓	✓	$-0.133$	$0$	$0.556484$	Character $\chi_{483}(452, \cdot)$
1-483-483.53-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.53	$0$	✓	✓	$-0.0898$	$0$	$1.01151$	Character $\chi_{483}(53, \cdot)$
1-483-483.59-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.59	$0$	✓	✓	$0.211$	$0$	$1.64382$	Character $\chi_{483}(59, \cdot)$
1-483-483.62-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.62	$0$	✓	✓	$-0.0246$	$0$	$0.425983$	Character $\chi_{483}(62, \cdot)$
1-483-483.65-r0-0-0	$2.24$	$2.24$	$1$	$3 \cdot 7 \cdot 23$	483.65	$0$	✓	✓	$-0.275$	$0$	$0.654483$	Character $\chi_{483}(65, \cdot)$

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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.