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 417 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-419-419.100-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.100	$0$	✓	✓	$0.495$	$0$	$1.38858$	Character $\chi_{419}(100, \cdot)$
1-419-419.102-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.102	$0$	✓	✓	$-0.402$	$0$	$2.30996$	Character $\chi_{419}(102, \cdot)$
1-419-419.105-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.105	$0$	✓	✓	$-0.333$	$0$	$0.657758$	Character $\chi_{419}(105, \cdot)$
1-419-419.106-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.106	$0$	✓	✓	$-0.249$	$0$	$0.612474$	Character $\chi_{419}(106, \cdot)$
1-419-419.107-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.107	$0$	✓	✓	$-0.131$	$0$	$0.770709$	Character $\chi_{419}(107, \cdot)$
1-419-419.108-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.108	$0$	✓	✓	$0.0344$	$0$	$0.983158$	Character $\chi_{419}(108, \cdot)$
1-419-419.110-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.110	$0$	✓	✓	$0.233$	$0$	$1.35449$	Character $\chi_{419}(110, \cdot)$
1-419-419.111-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.111	$0$	✓	✓	$0.0544$	$0$	$0.993377$	Character $\chi_{419}(111, \cdot)$
1-419-419.112-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.112	$0$	✓	✓	$0.326$	$0$	$1.61557$	Character $\chi_{419}(112, \cdot)$
1-419-419.114-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.114	$0$	✓	✓	$0.438$	$0$	$2.44581$	Character $\chi_{419}(114, \cdot)$
1-419-419.115-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.115	$0$	✓	✓	$0.329$	$0$	$1.70743$	Character $\chi_{419}(115, \cdot)$
1-419-419.116-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.116	$0$	✓	✓	$0.0193$	$0$	$0.734494$	Character $\chi_{419}(116, \cdot)$
1-419-419.117-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.117	$0$	✓	✓	$0.126$	$0$	$1.08340$	Character $\chi_{419}(117, \cdot)$
1-419-419.12-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.12	$0$	✓	✓	$0.292$	$0$	$0.878205$	Character $\chi_{419}(12, \cdot)$
1-419-419.121-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.121	$0$	✓	✓	$0.0270$	$0$	$0.306787$	Character $\chi_{419}(121, \cdot)$
1-419-419.122-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.122	$0$	✓	✓	$-0.308$	$0$	$0.843801$	Character $\chi_{419}(122, \cdot)$
1-419-419.123-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.123	$0$	✓	✓	$-0.300$	$0$	$0.523835$	Character $\chi_{419}(123, \cdot)$
1-419-419.125-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.125	$0$	✓	✓	$0.0322$	$0$	$1.74770$	Character $\chi_{419}(125, \cdot)$
1-419-419.129-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.129	$0$	✓	✓	$-0.445$	$0$	$1.82922$	Character $\chi_{419}(129, \cdot)$
1-419-419.13-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.13	$0$	✓	✓	$0.445$	$0$	$0.737483$	Character $\chi_{419}(13, \cdot)$
1-419-419.131-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.131	$0$	✓	✓	$0.111$	$0$	$1.84876$	Character $\chi_{419}(131, \cdot)$
1-419-419.134-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.134	$0$	✓	✓	$0.188$	$0$	$1.18958$	Character $\chi_{419}(134, \cdot)$
1-419-419.135-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.135	$0$	✓	✓	$0.0605$	$0$	$1.12822$	Character $\chi_{419}(135, \cdot)$
1-419-419.136-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.136	$0$	✓	✓	$-0.438$	$0$	$0.963352$	Character $\chi_{419}(136, \cdot)$
1-419-419.137-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.137	$0$	✓	✓	$-0.205$	$0$	$0.767022$	Character $\chi_{419}(137, \cdot)$
1-419-419.139-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.139	$0$	✓	✓	$0.210$	$0$	$0.601085$	Character $\chi_{419}(139, \cdot)$
1-419-419.140-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.140	$0$	✓	✓	$-0.0651$	$0$	$1.44936$	Character $\chi_{419}(140, \cdot)$
1-419-419.141-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.141	$0$	✓	✓	$0.276$	$0$	$0.0575116$	Character $\chi_{419}(141, \cdot)$
1-419-419.142-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.142	$0$	✓	✓	$0.155$	$0$	$1.52427$	Character $\chi_{419}(142, \cdot)$
1-419-419.144-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.144	$0$	✓	✓	$0.404$	$0$	$0.179302$	Character $\chi_{419}(144, \cdot)$
1-419-419.145-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.145	$0$	✓	✓	$-0.205$	$0$	$1.17436$	Character $\chi_{419}(145, \cdot)$
1-419-419.147-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.147	$0$	✓	✓	$-0.0442$	$0$	$0.960461$	Character $\chi_{419}(147, \cdot)$
1-419-419.148-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.148	$0$	✓	✓	$0.166$	$0$	$1.60364$	Character $\chi_{419}(148, \cdot)$
1-419-419.149-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.149	$0$	✓	✓	$-0.169$	$0$	$1.39730$	Character $\chi_{419}(149, \cdot)$
1-419-419.15-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.15	$0$	✓	✓	$-0.128$	$0$	$1.69889$	Character $\chi_{419}(15, \cdot)$
1-419-419.151-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.151	$0$	✓	✓	$-0.0544$	$0$	$0.875867$	Character $\chi_{419}(151, \cdot)$
1-419-419.152-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.152	$0$	✓	✓	$0.402$	$0$	$0.622383$	Character $\chi_{419}(152, \cdot)$
1-419-419.154-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.154	$0$	✓	✓	$-0.126$	$0$	$1.18984$	Character $\chi_{419}(154, \cdot)$
1-419-419.156-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.156	$0$	✓	✓	$0.0737$	$0$	$1.78878$	Character $\chi_{419}(156, \cdot)$
1-419-419.157-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.157	$0$	✓	✓	$0.0175$	$0$	$0.783210$	Character $\chi_{419}(157, \cdot)$
1-419-419.16-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.16	$0$	✓	✓	$-0.111$	$0$	$1.24519$	Character $\chi_{419}(16, \cdot)$
1-419-419.161-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.161	$0$	✓	✓	$0.430$	$0$	$0.372776$	Character $\chi_{419}(161, \cdot)$
1-419-419.164-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.164	$0$	✓	✓	$-0.104$	$0$	$0.715434$	Character $\chi_{419}(164, \cdot)$
1-419-419.166-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.166	$0$	✓	✓	$0.423$	$0$	$0.619450$	Character $\chi_{419}(166, \cdot)$
1-419-419.169-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.169	$0$	✓	✓	$0.0687$	$0$	$0.844009$	Character $\chi_{419}(169, \cdot)$
1-419-419.170-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.170	$0$	✓	✓	$0.428$	$0$	$1.68868$	Character $\chi_{419}(170, \cdot)$
1-419-419.172-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.172	$0$	✓	✓	$-0.128$	$0$	$1.08685$	Character $\chi_{419}(172, \cdot)$
1-419-419.173-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.173	$0$	✓	✓	$0.180$	$0$	$1.92685$	Character $\chi_{419}(173, \cdot)$
1-419-419.175-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.175	$0$	✓	✓	$-0.428$	$0$	$0.512377$	Character $\chi_{419}(175, \cdot)$
1-419-419.177-r0-0-0	$1.94$	$1.94$	$1$	$419$	419.177	$0$	✓	✓	$-0.0193$	$0$	$1.32843$	Character $\chi_{419}(177, \cdot)$

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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.