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 (33 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
1-520-520.109-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.109	$1$	✓	✓			$-0.203$	$0$	$0.704954$	Character $\chi_{520}(109, \cdot)$
1-520-520.123-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.123	$1$	✓	✓			$-0.344$	$0$	$0.598352$	Character $\chi_{520}(123, \cdot)$
1-520-520.133-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.133	$1$	✓	✓			$-0.378$	$0$	$0.0409787$	Character $\chi_{520}(133, \cdot)$
1-520-520.139-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.139	$1$	✓	✓			$-0.209$	$0$	$0.171565$	Character $\chi_{520}(139, \cdot)$
1-520-520.149-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.149	$1$	✓	✓			$-0.256$	$0$	$0.399078$	Character $\chi_{520}(149, \cdot)$
1-520-520.163-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.163	$1$	✓	✓			$-0.249$	$0$	$0.467062$	Character $\chi_{520}(163, \cdot)$
1-520-520.173-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.173	$1$	✓	✓			$0.497$	$0$	$0.0642512$	Character $\chi_{520}(173, \cdot)$
1-520-520.179-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.179	$1$	✓	✓			$-0.0853$	$0$	$0.938210$	Character $\chi_{520}(179, \cdot)$
1-520-520.187-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.187	$1$	✓	✓			$-0.115$	$0$	$0.833651$	Character $\chi_{520}(187, \cdot)$
1-520-520.189-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.189	$1$	✓	✓			$-0.162$	$0$	$0.609044$	Character $\chi_{520}(189, \cdot)$
1-520-520.203-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.203	$1$	✓	✓			$0.115$	$0$	$0.815234$	Character $\chi_{520}(203, \cdot)$
1-520-520.227-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.227	$1$	✓	✓			$-0.168$	$0$	$0.274160$	Character $\chi_{520}(227, \cdot)$
1-520-520.229-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.229	$1$	✓	✓			$0.203$	$0$	$1.35631$	Character $\chi_{520}(229, \cdot)$
1-520-520.237-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.237	$1$	✓	✓			$-0.202$	$0$	$0.699970$	Character $\chi_{520}(237, \cdot)$
1-520-520.259-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.259	$1$	✓	✓	✓	✓	$0$	$0$	$0.384641$	Character $\chi_{520}(259, \cdot)$
1-520-520.267-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.267	$1$	✓	✓			$-0.0744$	$0$	$0.522621$	Character $\chi_{520}(267, \cdot)$
1-520-520.277-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.277	$1$	✓	✓			$-0.326$	$0$	$0.490993$	Character $\chi_{520}(277, \cdot)$
1-520-520.307-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.307	$1$	✓	✓			$0.291$	$0$	$0.0941588$	Character $\chi_{520}(307, \cdot)$
1-520-520.323-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.323	$1$	✓	✓			$0.168$	$0$	$0.907444$	Character $\chi_{520}(323, \cdot)$
1-520-520.349-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.349	$1$	✓	✓			$0.256$	$0$	$0.881400$	Character $\chi_{520}(349, \cdot)$
1-520-520.373-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.373	$1$	✓	✓			$0.202$	$0$	$0.984030$	Character $\chi_{520}(373, \cdot)$
1-520-520.413-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.413	$1$	✓	✓			$0.326$	$0$	$1.54323$	Character $\chi_{520}(413, \cdot)$
1-520-520.419-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.419	$1$	✓	✓			$0.209$	$0$	$1.15099$	Character $\chi_{520}(419, \cdot)$
1-520-520.427-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.427	$1$	✓	✓			$0.344$	$0$	$1.64421$	Character $\chi_{520}(427, \cdot)$
1-520-520.459-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.459	$1$	✓	✓			$0.0853$	$0$	$0.892873$	Character $\chi_{520}(459, \cdot)$
1-520-520.477-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.477	$1$	✓	✓			$0.378$	$0$	$1.46595$	Character $\chi_{520}(477, \cdot)$
1-520-520.483-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.483	$1$	✓	✓			$0.0744$	$0$	$0.804181$	Character $\chi_{520}(483, \cdot)$
1-520-520.493-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.493	$1$	✓	✓			$0.411$	$0$	$0.0173523$	Character $\chi_{520}(493, \cdot)$
1-520-520.509-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.509	$1$	✓	✓			$0.162$	$0$	$0.681927$	Character $\chi_{520}(509, \cdot)$
1-520-520.517-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.517	$1$	✓	✓			$0.497$	$0$	$1.33880$	Character $\chi_{520}(517, \cdot)$
1-520-520.67-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.67	$1$	✓	✓			$0.249$	$0$	$1.16075$	Character $\chi_{520}(67, \cdot)$
1-520-520.77-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.77	$1$	✓	✓			$-0.411$	$0$	$1.48378$	Character $\chi_{520}(77, \cdot)$
1-520-520.83-r1-0-0	$55.8$	$55.8$	$1$	$2^{3} \cdot 5 \cdot 13$	520.83	$1$	✓	✓			$-0.291$	$0$	$1.81508$	Character $\chi_{520}(83, \cdot)$

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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.