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 965 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-967-967.100-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.100	$0$	✓	✓	$-0.198$	$0$	$0.543144$	Character $\chi_{967}(100, \cdot)$
1-967-967.101-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.101	$0$	✓	✓	$-0.189$	$0$	$0.887202$	Character $\chi_{967}(101, \cdot)$
1-967-967.103-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.103	$0$	✓	✓	$0.325$	$0$	$0.965840$	Character $\chi_{967}(103, \cdot)$
1-967-967.106-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.106	$0$	✓	✓	$-0.171$	$0$	$0.950676$	Character $\chi_{967}(106, \cdot)$
1-967-967.11-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.11	$0$	✓	✓	$0.377$	$0$	$0.553756$	Character $\chi_{967}(11, \cdot)$
1-967-967.111-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.111	$0$	✓	✓	$0.239$	$0$	$0.940644$	Character $\chi_{967}(111, \cdot)$
1-967-967.113-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.113	$0$	✓	✓	$0.0658$	$0$	$1.66576$	Character $\chi_{967}(113, \cdot)$
1-967-967.114-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.114	$0$	✓	✓	$-0.166$	$0$	$0.455409$	Character $\chi_{967}(114, \cdot)$
1-967-967.115-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.115	$0$	✓	✓	$0.386$	$0$	$0.295206$	Character $\chi_{967}(115, \cdot)$
1-967-967.118-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.118	$0$	✓	✓	$-0.417$	$0$	$2.02291$	Character $\chi_{967}(118, \cdot)$
1-967-967.120-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.120	$0$	✓	✓	$0.289$	$0$	$1.21281$	Character $\chi_{967}(120, \cdot)$
1-967-967.121-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.121	$0$	✓	✓	$0.115$	$0$	$1.17080$	Character $\chi_{967}(121, \cdot)$
1-967-967.122-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.122	$0$	✓	✓	$0.377$	$0$	$1.89071$	Character $\chi_{967}(122, \cdot)$
1-967-967.123-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.123	$0$	✓	✓	$0.437$	$0$	$1.37500$	Character $\chi_{967}(123, \cdot)$
1-967-967.124-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.124	$0$	✓	✓	$-0.237$	$0$	$1.90355$	Character $\chi_{967}(124, \cdot)$
1-967-967.127-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.127	$0$	✓	✓	$-0.370$	$0$	$0.376946$	Character $\chi_{967}(127, \cdot)$
1-967-967.128-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.128	$0$	✓	✓	$0.243$	$0$	$0.799868$	Character $\chi_{967}(128, \cdot)$
1-967-967.129-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.129	$0$	✓	✓	$-0.0464$	$0$	$1.07148$	Character $\chi_{967}(129, \cdot)$
1-967-967.130-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.130	$0$	✓	✓	$0.383$	$0$	$1.75826$	Character $\chi_{967}(130, \cdot)$
1-967-967.131-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.131	$0$	✓	✓	$-0.0470$	$0$	$1.08685$	Character $\chi_{967}(131, \cdot)$
1-967-967.133-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.133	$0$	✓	✓	$-0.424$	$0$	$0.158695$	Character $\chi_{967}(133, \cdot)$
1-967-967.135-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.135	$0$	✓	✓	$-0.283$	$0$	$0.709397$	Character $\chi_{967}(135, \cdot)$
1-967-967.136-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.136	$0$	✓	✓	$-0.381$	$0$	$1.26325$	Character $\chi_{967}(136, \cdot)$
1-967-967.137-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.137	$0$	✓	✓	$-0.289$	$0$	$0.388611$	Character $\chi_{967}(137, \cdot)$
1-967-967.138-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.138	$0$	✓	✓	$0.329$	$0$	$1.87163$	Character $\chi_{967}(138, \cdot)$
1-967-967.139-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.139	$0$	✓	✓	$0.125$	$0$	$0.877700$	Character $\chi_{967}(139, \cdot)$
1-967-967.140-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.140	$0$	✓	✓	$-0.170$	$0$	$0.958261$	Character $\chi_{967}(140, \cdot)$
1-967-967.141-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.141	$0$	✓	✓	$0.416$	$0$	$1.60870$	Character $\chi_{967}(141, \cdot)$
1-967-967.142-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.142	$0$	✓	✓	$-0.121$	$0$	$0.720352$	Character $\chi_{967}(142, \cdot)$
1-967-967.144-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.144	$0$	✓	✓	$-0.469$	$0$	$0.244695$	Character $\chi_{967}(144, \cdot)$
1-967-967.145-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.145	$0$	✓	✓	$-0.482$	$0$	$0.435332$	Character $\chi_{967}(145, \cdot)$
1-967-967.146-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.146	$0$	✓	✓	$-0.232$	$0$	$0.492780$	Character $\chi_{967}(146, \cdot)$
1-967-967.149-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.149	$0$	✓	✓	$0.312$	$0$	$1.62340$	Character $\chi_{967}(149, \cdot)$
1-967-967.15-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.15	$0$	✓	✓	$0.0464$	$0$	$0.300436$	Character $\chi_{967}(15, \cdot)$
1-967-967.151-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.151	$0$	✓	✓	$-0.484$	$0$	$0.857692$	Character $\chi_{967}(151, \cdot)$
1-967-967.153-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.153	$0$	✓	✓	$-0.0815$	$0$	$0.291582$	Character $\chi_{967}(153, \cdot)$
1-967-967.156-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.156	$0$	✓	✓	$0.238$	$0$	$0.759029$	Character $\chi_{967}(156, \cdot)$
1-967-967.157-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.157	$0$	✓	✓	$0.342$	$0$	$1.44160$	Character $\chi_{967}(157, \cdot)$
1-967-967.16-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.16	$0$	✓	✓	$0.331$	$0$	$1.23247$	Character $\chi_{967}(16, \cdot)$
1-967-967.161-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.161	$0$	✓	✓	$-0.00984$	$0$	$0.973580$	Character $\chi_{967}(161, \cdot)$
1-967-967.162-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.162	$0$	✓	✓	$-0.159$	$0$	$0.508982$	Character $\chi_{967}(162, \cdot)$
1-967-967.165-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.165	$0$	✓	✓	$0.212$	$0$	$1.86236$	Character $\chi_{967}(165, \cdot)$
1-967-967.166-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.166	$0$	✓	✓	$0.247$	$0$	$1.71587$	Character $\chi_{967}(166, \cdot)$
1-967-967.168-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.168	$0$	✓	✓	$0.00357$	$0$	$1.05154$	Character $\chi_{967}(168, \cdot)$
1-967-967.169-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.169	$0$	✓	✓	$-0.325$	$0$	$0.317447$	Character $\chi_{967}(169, \cdot)$
1-967-967.17-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.17	$0$	✓	✓	$0.0221$	$0$	$0.890763$	Character $\chi_{967}(17, \cdot)$
1-967-967.174-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.174	$0$	✓	✓	$-0.0388$	$0$	$0.105908$	Character $\chi_{967}(174, \cdot)$
1-967-967.176-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.176	$0$	✓	✓	$-0.00947$	$0$	$1.25005$	Character $\chi_{967}(176, \cdot)$
1-967-967.179-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.179	$0$	✓	✓	$0.255$	$0$	$1.73209$	Character $\chi_{967}(179, \cdot)$
1-967-967.18-r0-0-0	$4.49$	$4.49$	$1$	$967$	967.18	$0$	✓	✓	$0.107$	$0$	$1.12925$	Character $\chi_{967}(18, \cdot)$

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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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Results (1-50 of 965 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.