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 347 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-349-349.100-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.100	$0$	✓	✓	$0.0529$	$0$	$1.65682$	Character $\chi_{349}(100, \cdot)$
1-349-349.104-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.104	$0$	✓	✓	$-0.148$	$0$	$0.878533$	Character $\chi_{349}(104, \cdot)$
1-349-349.106-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.106	$0$	✓	✓	$0.276$	$0$	$0.0554365$	Character $\chi_{349}(106, \cdot)$
1-349-349.108-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.108	$0$	✓	✓	$0.385$	$0$	$1.96438$	Character $\chi_{349}(108, \cdot)$
1-349-349.109-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.109	$0$	✓	✓	$-0.0942$	$0$	$0.770364$	Character $\chi_{349}(109, \cdot)$
1-349-349.110-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.110	$0$	✓	✓	$0.0635$	$0$	$1.96173$	Character $\chi_{349}(110, \cdot)$
1-349-349.111-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.111	$0$	✓	✓	$-0.491$	$0$	$1.80831$	Character $\chi_{349}(111, \cdot)$
1-349-349.115-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.115	$0$	✓	✓	$0.320$	$0$	$1.39859$	Character $\chi_{349}(115, \cdot)$
1-349-349.116-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.116	$0$	✓	✓	$0.198$	$0$	$1.22737$	Character $\chi_{349}(116, \cdot)$
1-349-349.118-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.118	$0$	✓	✓	$0.183$	$0$	$1.56917$	Character $\chi_{349}(118, \cdot)$
1-349-349.12-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.12	$0$	✓	✓	$0.350$	$0$	$2.71128$	Character $\chi_{349}(12, \cdot)$
1-349-349.121-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.121	$0$	✓	✓	$0.296$	$0$	$2.12475$	Character $\chi_{349}(121, \cdot)$
1-349-349.122-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.122	$0$	✓	✓	$-0.00740$	$0$	$0.821368$	Character $\chi_{349}(122, \cdot)$
1-349-349.123-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.123	$0$	✓	✓	$0.318$	$0$	$0.541473$	Character $\chi_{349}(123, \cdot)$
1-349-349.124-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.124	$0$	✓	✓	$0.194$	$0$	$1.19613$	Character $\chi_{349}(124, \cdot)$
1-349-349.125-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.125	$0$	✓	✓	$-0.0553$	$0$	$0.996015$	Character $\chi_{349}(125, \cdot)$
1-349-349.126-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.126	$0$	✓	✓	$0.284$	$0$	$1.71044$	Character $\chi_{349}(126, \cdot)$
1-349-349.130-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.130	$0$	✓	✓	$0.311$	$0$	$0.366301$	Character $\chi_{349}(130, \cdot)$
1-349-349.135-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.135	$0$	✓	✓	$-0.276$	$0$	$2.77839$	Character $\chi_{349}(135, \cdot)$
1-349-349.139-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.139	$0$	✓	✓	$0.123$	$0$	$1.55662$	Character $\chi_{349}(139, \cdot)$
1-349-349.14-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.14	$0$	✓	✓	$0.440$	$0$	$2.16018$	Character $\chi_{349}(14, \cdot)$
1-349-349.142-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.142	$0$	✓	✓	$0.0235$	$0$	$1.04561$	Character $\chi_{349}(142, \cdot)$
1-349-349.143-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.143	$0$	✓	✓	$0.320$	$0$	$0.225344$	Character $\chi_{349}(143, \cdot)$
1-349-349.144-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.144	$0$	✓	✓	$-0.320$	$0$	$2.69103$	Character $\chi_{349}(144, \cdot)$
1-349-349.145-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.145	$0$	✓	✓	$0.351$	$0$	$1.17792$	Character $\chi_{349}(145, \cdot)$
1-349-349.147-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.147	$0$	✓	✓	$-0.269$	$0$	$0.520840$	Character $\chi_{349}(147, \cdot)$
1-349-349.148-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.148	$0$	✓	✓	$0.478$	$0$	$0.0843497$	Character $\chi_{349}(148, \cdot)$
1-349-349.15-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.15	$0$	✓	✓	$-0.223$	$0$	$0.726497$	Character $\chi_{349}(15, \cdot)$
1-349-349.151-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.151	$0$	✓	✓	$-0.375$	$0$	$0.968625$	Character $\chi_{349}(151, \cdot)$
1-349-349.153-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.153	$0$	✓	✓	$-0.322$	$0$	$0.794511$	Character $\chi_{349}(153, \cdot)$
1-349-349.155-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.155	$0$	✓	✓	$0.422$	$0$	$1.85591$	Character $\chi_{349}(155, \cdot)$
1-349-349.157-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.157	$0$	✓	✓	$0.392$	$0$	$1.44418$	Character $\chi_{349}(157, \cdot)$
1-349-349.158-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.158	$0$	✓	✓	$-0.478$	$0$	$1.72815$	Character $\chi_{349}(158, \cdot)$
1-349-349.16-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.16	$0$	✓	✓	$0.106$	$0$	$1.38125$	Character $\chi_{349}(16, \cdot)$
1-349-349.164-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.164	$0$	✓	✓	$-0.232$	$0$	$1.56453$	Character $\chi_{349}(164, \cdot)$
1-349-349.168-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.168	$0$	✓	✓	$0.0491$	$0$	$0.580713$	Character $\chi_{349}(168, \cdot)$
1-349-349.169-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.169	$0$	✓	✓	$-0.0249$	$0$	$0.915860$	Character $\chi_{349}(169, \cdot)$
1-349-349.17-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.17	$0$	✓	✓	$0.417$	$0$	$0.165159$	Character $\chi_{349}(17, \cdot)$
1-349-349.171-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.171	$0$	✓	✓	$-0.333$	$0$	$0.796251$	Character $\chi_{349}(171, \cdot)$
1-349-349.178-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.178	$0$	✓	✓	$-0.0529$	$0$	$0.811918$	Character $\chi_{349}(178, \cdot)$
1-349-349.180-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.180	$0$	✓	✓	$0.114$	$0$	$1.49545$	Character $\chi_{349}(180, \cdot)$
1-349-349.181-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.181	$0$	✓	✓	$0.0114$	$0$	$1.42750$	Character $\chi_{349}(181, \cdot)$
1-349-349.185-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.185	$0$	✓	✓	$-0.130$	$0$	$0.773278$	Character $\chi_{349}(185, \cdot)$
1-349-349.19-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.19	$0$	✓	✓	$0.269$	$0$	$1.82908$	Character $\chi_{349}(19, \cdot)$
1-349-349.191-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.191	$0$	✓	✓	$0.0842$	$0$	$0.795182$	Character $\chi_{349}(191, \cdot)$
1-349-349.192-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.192	$0$	✓	✓	$0.222$	$0$	$1.54693$	Character $\chi_{349}(192, \cdot)$
1-349-349.194-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.194	$0$	✓	✓	$-0.0873$	$0$	$1.67544$	Character $\chi_{349}(194, \cdot)$
1-349-349.196-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.196	$0$	✓	✓	$0.268$	$0$	$1.38426$	Character $\chi_{349}(196, \cdot)$
1-349-349.198-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.198	$0$	✓	✓	$0.148$	$0$	$0.878162$	Character $\chi_{349}(198, \cdot)$
1-349-349.20-r0-0-0	$1.62$	$1.62$	$1$	$349$	349.20	$0$	✓	✓	$-0.222$	$0$	$1.33893$	Character $\chi_{349}(20, \cdot)$

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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.