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 396 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1053-1053.1019-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.1019	$0$	✓	✓	$-0.428$	$0$	$0.649159$	Character $\chi_{1053}(1019, \cdot)$
1-1053-1053.1022-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.1022	$0$	✓	✓	$0.428$	$0$	$1.55556$	Character $\chi_{1053}(1022, \cdot)$
1-1053-1053.1024-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.1024	$0$	✓	✓	$0.0504$	$0$	$1.42148$	Character $\chi_{1053}(1024, \cdot)$
1-1053-1053.103-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.103	$0$	✓	✓	$0.308$	$0$	$0.160918$	Character $\chi_{1053}(103, \cdot)$
1-1053-1053.1030-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.1030	$0$	✓	✓	$0.184$	$0$	$1.54694$	Character $\chi_{1053}(1030, \cdot)$
1-1053-1053.1039-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.1039	$0$	✓	✓	$0.197$	$0$	$0.767318$	Character $\chi_{1053}(1039, \cdot)$
1-1053-1053.1046-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.1046	$0$	✓	✓	$-0.481$	$0$	$1.63233$	Character $\chi_{1053}(1046, \cdot)$
1-1053-1053.11-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.11	$0$	✓	✓	$0.0308$	$0$	$1.38939$	Character $\chi_{1053}(11, \cdot)$
1-1053-1053.110-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.110	$0$	✓	✓	$-0.0370$	$0$	$0.512611$	Character $\chi_{1053}(110, \cdot)$
1-1053-1053.119-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.119	$0$	✓	✓	$-0.0627$	$0$	$0.918136$	Character $\chi_{1053}(119, \cdot)$
1-1053-1053.121-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.121	$0$	✓	✓	$-0.383$	$0$	$0.304234$	Character $\chi_{1053}(121, \cdot)$
1-1053-1053.122-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.122	$0$	✓	✓	$-0.0890$	$0$	$1.00645$	Character $\chi_{1053}(122, \cdot)$
1-1053-1053.128-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.128	$0$	✓	✓	$0.364$	$0$	$1.47738$	Character $\chi_{1053}(128, \cdot)$
1-1053-1053.133-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.133	$0$	✓	✓	$0.345$	$0$	$1.10023$	Character $\chi_{1053}(133, \cdot)$
1-1053-1053.137-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.137	$0$	✓	✓	$-0.276$	$0$	$0.0263052$	Character $\chi_{1053}(137, \cdot)$
1-1053-1053.139-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.139	$0$	✓	✓	$0.0992$	$0$	$0.711957$	Character $\chi_{1053}(139, \cdot)$
1-1053-1053.142-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.142	$0$	✓	✓	$-0.308$	$0$	$0.518192$	Character $\chi_{1053}(142, \cdot)$
1-1053-1053.149-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.149	$0$	✓	✓	$0.191$	$0$	$1.40874$	Character $\chi_{1053}(149, \cdot)$
1-1053-1053.158-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.158	$0$	✓	✓	$0.0545$	$0$	$0.955999$	Character $\chi_{1053}(158, \cdot)$
1-1053-1053.16-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.16	$0$	✓	✓	$0.234$	$0$	$1.27180$	Character $\chi_{1053}(16, \cdot)$
1-1053-1053.160-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.160	$0$	✓	✓	$-0.112$	$0$	$0.750322$	Character $\chi_{1053}(160, \cdot)$
1-1053-1053.164-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.164	$0$	✓	✓	$0.0890$	$0$	$0.859129$	Character $\chi_{1053}(164, \cdot)$
1-1053-1053.166-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.166	$0$	✓	✓	$-0.443$	$0$	$0.437179$	Character $\chi_{1053}(166, \cdot)$
1-1053-1053.167-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.167	$0$	✓	✓	$0.148$	$0$	$1.65091$	Character $\chi_{1053}(167, \cdot)$
1-1053-1053.176-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.176	$0$	✓	✓	$-0.0483$	$0$	$0.273035$	Character $\chi_{1053}(176, \cdot)$
1-1053-1053.178-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.178	$0$	✓	✓	$0.148$	$0$	$0.0333288$	Character $\chi_{1053}(178, \cdot)$
1-1053-1053.2-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.2	$0$	✓	✓	$0.381$	$0$	$1.71666$	Character $\chi_{1053}(2, \cdot)$
1-1053-1053.20-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.20	$0$	✓	✓	$-0.0545$	$0$	$0.595748$	Character $\chi_{1053}(20, \cdot)$
1-1053-1053.200-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.200	$0$	✓	✓	$0.238$	$0$	$1.22868$	Character $\chi_{1053}(200, \cdot)$
1-1053-1053.203-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.203	$0$	✓	✓	$0.317$	$0$	$0.972548$	Character $\chi_{1053}(203, \cdot)$
1-1053-1053.205-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.205	$0$	✓	✓	$-0.0606$	$0$	$0.622116$	Character $\chi_{1053}(205, \cdot)$
1-1053-1053.211-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.211	$0$	✓	✓	$-0.148$	$0$	$1.13209$	Character $\chi_{1053}(211, \cdot)$
1-1053-1053.22-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.22	$0$	✓	✓	$-0.234$	$0$	$0.967894$	Character $\chi_{1053}(22, \cdot)$
1-1053-1053.220-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.220	$0$	✓	✓	$-0.358$	$0$	$0.129318$	Character $\chi_{1053}(220, \cdot)$
1-1053-1053.227-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.227	$0$	✓	✓	$-0.148$	$0$	$1.04615$	Character $\chi_{1053}(227, \cdot)$
1-1053-1053.236-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.236	$0$	✓	✓	$-0.396$	$0$	$0.659032$	Character $\chi_{1053}(236, \cdot)$
1-1053-1053.238-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.238	$0$	✓	✓	$0.0606$	$0$	$1.01239$	Character $\chi_{1053}(238, \cdot)$
1-1053-1053.239-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.239	$0$	✓	✓	$0.355$	$0$	$1.29585$	Character $\chi_{1053}(239, \cdot)$
1-1053-1053.245-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.245	$0$	✓	✓	$0.475$	$0$	$0.340027$	Character $\chi_{1053}(245, \cdot)$
1-1053-1053.25-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.25	$0$	✓	✓	$0.469$	$0$	$1.57911$	Character $\chi_{1053}(25, \cdot)$
1-1053-1053.250-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.250	$0$	✓	✓	$-0.0992$	$0$	$0.812222$	Character $\chi_{1053}(250, \cdot)$
1-1053-1053.254-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.254	$0$	✓	✓	$-0.0545$	$0$	$0.651341$	Character $\chi_{1053}(254, \cdot)$
1-1053-1053.256-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.256	$0$	✓	✓	$-0.0118$	$0$	$0.908865$	Character $\chi_{1053}(256, \cdot)$
1-1053-1053.259-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.259	$0$	✓	✓	$-0.308$	$0$	$0.308128$	Character $\chi_{1053}(259, \cdot)$
1-1053-1053.266-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.266	$0$	✓	✓	$0.302$	$0$	$1.11391$	Character $\chi_{1053}(266, \cdot)$
1-1053-1053.275-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.275	$0$	✓	✓	$0.0545$	$0$	$0.709659$	Character $\chi_{1053}(275, \cdot)$
1-1053-1053.277-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.277	$0$	✓	✓	$-0.223$	$0$	$1.08121$	Character $\chi_{1053}(277, \cdot)$
1-1053-1053.281-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.281	$0$	✓	✓	$-0.355$	$0$	$2.17316$	Character $\chi_{1053}(281, \cdot)$
1-1053-1053.283-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.283	$0$	✓	✓	$0.112$	$0$	$0.809109$	Character $\chi_{1053}(283, \cdot)$
1-1053-1053.284-r0-0-0	$4.89$	$4.89$	$1$	$3^{4} \cdot 13$	1053.284	$0$	✓	✓	$-0.296$	$0$	$0.605078$	Character $\chi_{1053}(284, \cdot)$

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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.