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 64 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-20e2-400.109-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.109	$0$	✓	✓	$0.142$	$0$	$1.49851$	Character $\chi_{400}(109, \cdot)$
1-20e2-400.123-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.123	$0$	✓	✓	$0.107$	$0$	$1.41139$	Character $\chi_{400}(123, \cdot)$
1-20e2-400.141-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.141	$0$	✓	✓	$-0.357$	$0$	$0.473144$	Character $\chi_{400}(141, \cdot)$
1-20e2-400.147-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.147	$0$	✓	✓	$0.00250$	$0$	$1.19870$	Character $\chi_{400}(147, \cdot)$
1-20e2-400.163-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.163	$0$	✓	✓	$0.392$	$0$	$1.48490$	Character $\chi_{400}(163, \cdot)$
1-20e2-400.181-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.181	$0$	✓	✓	$0.00250$	$0$	$0.845358$	Character $\chi_{400}(181, \cdot)$
1-20e2-400.187-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.187	$0$	✓	✓	$0.267$	$0$	$1.37596$	Character $\chi_{400}(187, \cdot)$
1-20e2-400.189-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.189	$0$	✓	✓	$-0.0175$	$0$	$0.837652$	Character $\chi_{400}(189, \cdot)$
1-20e2-400.203-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.203	$0$	✓	✓	$0.377$	$0$	$0.0521393$	Character $\chi_{400}(203, \cdot)$
1-20e2-400.21-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.21	$0$	✓	✓	$-0.122$	$0$	$1.04595$	Character $\chi_{400}(21, \cdot)$
1-20e2-400.221-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.221	$0$	✓	✓	$0.00250$	$0$	$0.743595$	Character $\chi_{400}(221, \cdot)$
1-20e2-400.227-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.227	$0$	✓	✓	$0.232$	$0$	$1.85847$	Character $\chi_{400}(227, \cdot)$
1-20e2-400.229-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.229	$0$	✓	✓	$-0.122$	$0$	$0.726473$	Character $\chi_{400}(229, \cdot)$
1-20e2-400.261-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.261	$0$	✓	✓	$0.357$	$0$	$1.47375$	Character $\chi_{400}(261, \cdot)$
1-20e2-400.267-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.267	$0$	✓	✓	$0.00250$	$0$	$1.38292$	Character $\chi_{400}(267, \cdot)$
1-20e2-400.269-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.269	$0$	✓	✓	$0.122$	$0$	$1.32480$	Character $\chi_{400}(269, \cdot)$
1-20e2-400.27-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.27	$0$	✓	✓	$-0.392$	$0$	$0.264988$	Character $\chi_{400}(27, \cdot)$
1-20e2-400.283-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.283	$0$	✓	✓	$0.00250$	$0$	$0.840090$	Character $\chi_{400}(283, \cdot)$
1-20e2-400.29-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.29	$0$	✓	✓	$0.00250$	$0$	$1.57003$	Character $\chi_{400}(29, \cdot)$
1-20e2-400.3-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.3	$0$	✓	✓	$0.00250$	$0$	$0.982415$	Character $\chi_{400}(3, \cdot)$
1-20e2-400.309-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.309	$0$	✓	✓	$0.0175$	$0$	$1.28321$	Character $\chi_{400}(309, \cdot)$
1-20e2-400.323-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.323	$0$	✓	✓	$-0.267$	$0$	$0.687313$	Character $\chi_{400}(323, \cdot)$
1-20e2-400.341-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.341	$0$	✓	✓	$-0.482$	$0$	$2.33060$	Character $\chi_{400}(341, \cdot)$
1-20e2-400.347-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.347	$0$	✓	✓	$0.377$	$0$	$1.95493$	Character $\chi_{400}(347, \cdot)$
1-20e2-400.363-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.363	$0$	✓	✓	$-0.232$	$0$	$0.975396$	Character $\chi_{400}(363, \cdot)$
1-20e2-400.381-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.381	$0$	✓	✓	$0.122$	$0$	$1.50350$	Character $\chi_{400}(381, \cdot)$
1-20e2-400.387-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.387	$0$	✓	✓	$-0.107$	$0$	$1.10089$	Character $\chi_{400}(387, \cdot)$
1-20e2-400.389-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.389	$0$	✓	✓	$-0.142$	$0$	$1.21831$	Character $\chi_{400}(389, \cdot)$
1-20e2-400.61-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.61	$0$	✓	✓	$0.482$	$0$	$0.199559$	Character $\chi_{400}(61, \cdot)$
1-20e2-400.67-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.67	$0$	✓	✓	$-0.377$	$0$	$2.26473$	Character $\chi_{400}(67, \cdot)$
1-20e2-400.69-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.69	$0$	✓	✓	$0.00250$	$0$	$1.31207$	Character $\chi_{400}(69, \cdot)$
1-20e2-400.83-r0-0-0	$1.85$	$1.85$	$1$	$2^{4} \cdot 5^{2}$	400.83	$0$	✓	✓	$-0.377$	$0$	$0.658228$	Character $\chi_{400}(83, \cdot)$
1-20e2-400.11-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.11	$1$	✓	✓	$-0.392$	$0$	$0.473132$	Character $\chi_{400}(11, \cdot)$
1-20e2-400.117-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.117	$1$	✓	✓	$0.247$	$0$	$0.902249$	Character $\chi_{400}(117, \cdot)$
1-20e2-400.13-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.13	$1$	✓	✓	$0.142$	$0$	$1.36851$	Character $\chi_{400}(13, \cdot)$
1-20e2-400.131-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.131	$1$	✓	✓	$-0.127$	$0$	$0.689140$	Character $\chi_{400}(131, \cdot)$
1-20e2-400.133-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.133	$1$	✓	✓	$0.247$	$0$	$1.24480$	Character $\chi_{400}(133, \cdot)$
1-20e2-400.139-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.139	$1$	✓	✓	$0.107$	$0$	$0.504943$	Character $\chi_{400}(139, \cdot)$
1-20e2-400.171-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.171	$1$	✓	✓	$0.127$	$0$	$0.910120$	Character $\chi_{400}(171, \cdot)$
1-20e2-400.173-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.173	$1$	✓	✓	$0.482$	$0$	$1.82502$	Character $\chi_{400}(173, \cdot)$
1-20e2-400.179-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.179	$1$	✓	✓	$-0.247$	$0$	$0.234131$	Character $\chi_{400}(179, \cdot)$
1-20e2-400.19-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.19	$1$	✓	✓	$-0.127$	$0$	$0.576708$	Character $\chi_{400}(19, \cdot)$
1-20e2-400.197-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.197	$1$	✓	✓	$-0.372$	$0$	$0.658355$	Character $\chi_{400}(197, \cdot)$
1-20e2-400.211-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.211	$1$	✓	✓	$0.232$	$0$	$1.02818$	Character $\chi_{400}(211, \cdot)$
1-20e2-400.213-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.213	$1$	✓	✓	$0.0175$	$0$	$0.518494$	Character $\chi_{400}(213, \cdot)$
1-20e2-400.219-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.219	$1$	✓	✓	$0.247$	$0$	$0.930355$	Character $\chi_{400}(219, \cdot)$
1-20e2-400.237-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.237	$1$	✓	✓	$-0.357$	$0$	$0.274309$	Character $\chi_{400}(237, \cdot)$
1-20e2-400.253-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.253	$1$	✓	✓	$-0.247$	$0$	$0.426350$	Character $\chi_{400}(253, \cdot)$
1-20e2-400.259-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.259	$1$	✓	✓	$-0.107$	$0$	$0.462595$	Character $\chi_{400}(259, \cdot)$
1-20e2-400.277-r1-0-0	$42.9$	$42.9$	$1$	$2^{4} \cdot 5^{2}$	400.277	$1$	✓	✓	$-0.142$	$0$	$0.621293$	Character $\chi_{400}(277, \cdot)$

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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.