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 272 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-547-547.10-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.10	$0$	✓	✓	$0.124$	$0$	$0.942791$	Character $\chi_{547}(10, \cdot)$
1-547-547.100-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.100	$0$	✓	✓	$-0.339$	$0$	$0.954593$	Character $\chi_{547}(100, \cdot)$
1-547-547.11-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.11	$0$	✓	✓	$0.219$	$0$	$1.93129$	Character $\chi_{547}(11, \cdot)$
1-547-547.110-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.110	$0$	✓	✓	$0.162$	$0$	$1.24423$	Character $\chi_{547}(110, \cdot)$
1-547-547.111-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.111	$0$	✓	✓	$0.171$	$0$	$1.30870$	Character $\chi_{547}(111, \cdot)$
1-547-547.113-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.113	$0$	✓	✓	$-0.466$	$0$	$1.67286$	Character $\chi_{547}(113, \cdot)$
1-547-547.114-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.114	$0$	✓	✓	$0.129$	$0$	$0.497660$	Character $\chi_{547}(114, \cdot)$
1-547-547.115-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.115	$0$	✓	✓	$0.497$	$0$	$0.857419$	Character $\chi_{547}(115, \cdot)$
1-547-547.116-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.116	$0$	✓	✓	$-0.335$	$0$	$0.349432$	Character $\chi_{547}(116, \cdot)$
1-547-547.117-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.117	$0$	✓	✓	$0.0171$	$0$	$1.43927$	Character $\chi_{547}(117, \cdot)$
1-547-547.118-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.118	$0$	✓	✓	$-0.270$	$0$	$0.674945$	Character $\chi_{547}(118, \cdot)$
1-547-547.119-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.119	$0$	✓	✓	$0.160$	$0$	$1.08580$	Character $\chi_{547}(119, \cdot)$
1-547-547.121-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.121	$0$	✓	✓	$0.156$	$0$	$1.21334$	Character $\chi_{547}(121, \cdot)$
1-547-547.122-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.122	$0$	✓	✓	$-0.0450$	$0$	$0.219221$	Character $\chi_{547}(122, \cdot)$
1-547-547.123-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.123	$0$	✓	✓	$-0.216$	$0$	$0.829146$	Character $\chi_{547}(123, \cdot)$
1-547-547.126-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.126	$0$	✓	✓	$-0.0807$	$0$	$1.14916$	Character $\chi_{547}(126, \cdot)$
1-547-547.127-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.127	$0$	✓	✓	$0.0682$	$0$	$1.55087$	Character $\chi_{547}(127, \cdot)$
1-547-547.129-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.129	$0$	✓	✓	$0.201$	$0$	$2.10456$	Character $\chi_{547}(129, \cdot)$
1-547-547.13-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.13	$0$	✓	✓	$0.470$	$0$	$0.484348$	Character $\chi_{547}(13, \cdot)$
1-547-547.130-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.130	$0$	✓	✓	$-0.255$	$0$	$1.09611$	Character $\chi_{547}(130, \cdot)$
1-547-547.131-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.131	$0$	✓	✓	$0.243$	$0$	$2.21969$	Character $\chi_{547}(131, \cdot)$
1-547-547.135-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.135	$0$	✓	✓	$0.308$	$0$	$0.335240$	Character $\chi_{547}(135, \cdot)$
1-547-547.136-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.136	$0$	✓	✓	$-0.00820$	$0$	$0.707156$	Character $\chi_{547}(136, \cdot)$
1-547-547.137-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.137	$0$	✓	✓	$-0.00578$	$0$	$0.905907$	Character $\chi_{547}(137, \cdot)$
1-547-547.139-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.139	$0$	✓	✓	$0.0450$	$0$	$0.694661$	Character $\chi_{547}(139, \cdot)$
1-547-547.14-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.14	$0$	✓	✓	$-0.247$	$0$	$0.271486$	Character $\chi_{547}(14, \cdot)$
1-547-547.140-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.140	$0$	✓	✓	$-0.488$	$0$	$1.98733$	Character $\chi_{547}(140, \cdot)$
1-547-547.142-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.142	$0$	✓	✓	$-0.191$	$0$	$0.960745$	Character $\chi_{547}(142, \cdot)$
1-547-547.143-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.143	$0$	✓	✓	$0.121$	$0$	$1.28702$	Character $\chi_{547}(143, \cdot)$
1-547-547.144-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.144	$0$	✓	✓	$0.0469$	$0$	$0.580626$	Character $\chi_{547}(144, \cdot)$
1-547-547.149-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.149	$0$	✓	✓	$0.205$	$0$	$0.908855$	Character $\chi_{547}(149, \cdot)$
1-547-547.15-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.15	$0$	✓	✓	$0.316$	$0$	$1.54652$	Character $\chi_{547}(15, \cdot)$
1-547-547.150-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.150	$0$	✓	✓	$0.167$	$0$	$0.969569$	Character $\chi_{547}(150, \cdot)$
1-547-547.154-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.154	$0$	✓	✓	$0.172$	$0$	$1.40045$	Character $\chi_{547}(154, \cdot)$
1-547-547.155-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.155	$0$	✓	✓	$-0.429$	$0$	$0.974391$	Character $\chi_{547}(155, \cdot)$
1-547-547.157-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.157	$0$	✓	✓	$0.00187$	$0$	$0.987502$	Character $\chi_{547}(157, \cdot)$
1-547-547.158-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.158	$0$	✓	✓	$-0.387$	$0$	$0.748041$	Character $\chi_{547}(158, \cdot)$
1-547-547.16-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.16	$0$	✓	✓	$0.222$	$0$	$1.87130$	Character $\chi_{547}(16, \cdot)$
1-547-547.160-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.160	$0$	✓	✓	$0.304$	$0$	$0.868737$	Character $\chi_{547}(160, \cdot)$
1-547-547.161-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.161	$0$	✓	✓	$-0.436$	$0$	$0.482690$	Character $\chi_{547}(161, \cdot)$
1-547-547.165-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.165	$0$	✓	✓	$0.0649$	$0$	$0.871434$	Character $\chi_{547}(165, \cdot)$
1-547-547.166-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.166	$0$	✓	✓	$-0.329$	$0$	$2.74378$	Character $\chi_{547}(166, \cdot)$
1-547-547.167-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.167	$0$	✓	✓	$-0.477$	$0$	$1.42132$	Character $\chi_{547}(167, \cdot)$
1-547-547.169-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.169	$0$	✓	✓	$0.216$	$0$	$1.27722$	Character $\chi_{547}(169, \cdot)$
1-547-547.171-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.171	$0$	✓	✓	$-0.222$	$0$	$1.13471$	Character $\chi_{547}(171, \cdot)$
1-547-547.174-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.174	$0$	✓	✓	$0.0593$	$0$	$1.02824$	Character $\chi_{547}(174, \cdot)$
1-547-547.176-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.176	$0$	✓	✓	$0.497$	$0$	$2.37010$	Character $\chi_{547}(176, \cdot)$
1-547-547.177-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.177	$0$	✓	✓	$0.380$	$0$	$1.79408$	Character $\chi_{547}(177, \cdot)$
1-547-547.178-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.178	$0$	✓	✓	$0.0807$	$0$	$0.590190$	Character $\chi_{547}(178, \cdot)$
1-547-547.179-r0-0-0	$2.54$	$2.54$	$1$	$547$	547.179	$0$	✓	✓	$-0.130$	$0$	$1.23386$	Character $\chi_{547}(179, \cdot)$

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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.