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 444 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1017-1017.1003-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.1003	$0$	✓	✓	$0.489$	$0$	$0.0704669$	Character $\chi_{1017}(1003, \cdot)$
1-1017-1017.1006-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.1006	$0$	✓	✓	$-0.382$	$0$	$0.621810$	Character $\chi_{1017}(1006, \cdot)$
1-1017-1017.101-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.101	$0$	✓	✓	$0.319$	$0$	$0.161856$	Character $\chi_{1017}(101, \cdot)$
1-1017-1017.1015-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.1015	$0$	✓	✓	$-0.447$	$0$	$0.498625$	Character $\chi_{1017}(1015, \cdot)$
1-1017-1017.106-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.106	$0$	✓	✓	$-0.242$	$0$	$0.626202$	Character $\chi_{1017}(106, \cdot)$
1-1017-1017.110-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.110	$0$	✓	✓	$-0.0348$	$0$	$0.586947$	Character $\chi_{1017}(110, \cdot)$
1-1017-1017.112-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.112	$0$	✓	✓	$-0.222$	$0$	$1.99797$	Character $\chi_{1017}(112, \cdot)$
1-1017-1017.115-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.115	$0$	✓	✓	$-0.381$	$0$	$0.344653$	Character $\chi_{1017}(115, \cdot)$
1-1017-1017.119-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.119	$0$	✓	✓	$0.444$	$0$	$0.123965$	Character $\chi_{1017}(119, \cdot)$
1-1017-1017.121-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.121	$0$	✓	✓	$0.0662$	$0$	$0.610126$	Character $\chi_{1017}(121, \cdot)$
1-1017-1017.124-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.124	$0$	✓	✓	$0.258$	$0$	$1.45031$	Character $\chi_{1017}(124, \cdot)$
1-1017-1017.13-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.13	$0$	✓	✓	$-0.274$	$0$	$1.00576$	Character $\chi_{1017}(13, \cdot)$
1-1017-1017.137-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.137	$0$	✓	✓	$-0.297$	$0$	$2.37774$	Character $\chi_{1017}(137, \cdot)$
1-1017-1017.139-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.139	$0$	✓	✓	$-0.229$	$0$	$1.02500$	Character $\chi_{1017}(139, \cdot)$
1-1017-1017.140-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.140	$0$	✓	✓	$-0.0365$	$0$	$0.303990$	Character $\chi_{1017}(140, \cdot)$
1-1017-1017.146-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.146	$0$	✓	✓	$0.242$	$0$	$0.900006$	Character $\chi_{1017}(146, \cdot)$
1-1017-1017.155-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.155	$0$	✓	✓	$-0.245$	$0$	$0.0776266$	Character $\chi_{1017}(155, \cdot)$
1-1017-1017.157-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.157	$0$	✓	✓	$0.288$	$0$	$1.66482$	Character $\chi_{1017}(157, \cdot)$
1-1017-1017.158-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.158	$0$	✓	✓	$0.121$	$0$	$1.62825$	Character $\chi_{1017}(158, \cdot)$
1-1017-1017.16-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.16	$0$	✓	✓	$-0.313$	$0$	$0.837070$	Character $\chi_{1017}(16, \cdot)$
1-1017-1017.166-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.166	$0$	✓	✓	$-0.161$	$0$	$1.05047$	Character $\chi_{1017}(166, \cdot)$
1-1017-1017.167-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.167	$0$	✓	✓	$-0.0779$	$0$	$0.361451$	Character $\chi_{1017}(167, \cdot)$
1-1017-1017.169-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.169	$0$	✓	✓	$-0.107$	$0$	$0.884275$	Character $\chi_{1017}(169, \cdot)$
1-1017-1017.175-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.175	$0$	✓	✓	$-0.313$	$0$	$0.689067$	Character $\chi_{1017}(175, \cdot)$
1-1017-1017.191-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.191	$0$	✓	✓	$-0.167$	$0$	$1.16407$	Character $\chi_{1017}(191, \cdot)$
1-1017-1017.196-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.196	$0$	✓	✓	$-0.103$	$0$	$1.22291$	Character $\chi_{1017}(196, \cdot)$
1-1017-1017.20-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.20	$0$	✓	✓	$0.221$	$0$	$1.39403$	Character $\chi_{1017}(20, \cdot)$
1-1017-1017.203-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.203	$0$	✓	✓	$0.133$	$0$	$0.822800$	Character $\chi_{1017}(203, \cdot)$
1-1017-1017.209-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.209	$0$	✓	✓	$0.0314$	$0$	$1.35359$	Character $\chi_{1017}(209, \cdot)$
1-1017-1017.211-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.211	$0$	✓	✓	$0.345$	$0$	$0.960864$	Character $\chi_{1017}(211, \cdot)$
1-1017-1017.22-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.22	$0$	✓	✓	$0.266$	$0$	$1.00578$	Character $\chi_{1017}(22, \cdot)$
1-1017-1017.221-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.221	$0$	✓	✓	$-0.0657$	$0$	$0.951737$	Character $\chi_{1017}(221, \cdot)$
1-1017-1017.23-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.23	$0$	✓	✓	$-0.386$	$0$	$1.42188$	Character $\chi_{1017}(23, \cdot)$
1-1017-1017.236-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.236	$0$	✓	✓	$-0.0165$	$0$	$0.486654$	Character $\chi_{1017}(236, \cdot)$
1-1017-1017.241-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.241	$0$	✓	✓	$-0.345$	$0$	$0.574729$	Character $\chi_{1017}(241, \cdot)$
1-1017-1017.245-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.245	$0$	✓	✓	$0.499$	$0$	$0.365377$	Character $\chi_{1017}(245, \cdot)$
1-1017-1017.25-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.25	$0$	✓	✓	$-0.156$	$0$	$0.238793$	Character $\chi_{1017}(25, \cdot)$
1-1017-1017.256-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.256	$0$	✓	✓	$-0.444$	$0$	$0.361723$	Character $\chi_{1017}(256, \cdot)$
1-1017-1017.263-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.263	$0$	✓	✓	$-0.0616$	$0$	$0.134950$	Character $\chi_{1017}(263, \cdot)$
1-1017-1017.266-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.266	$0$	✓	✓	$-0.138$	$0$	$0.628653$	Character $\chi_{1017}(266, \cdot)$
1-1017-1017.272-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.272	$0$	✓	✓	$-0.151$	$0$	$0.971381$	Character $\chi_{1017}(272, \cdot)$
1-1017-1017.277-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.277	$0$	✓	✓	$0.424$	$0$	$1.28332$	Character $\chi_{1017}(277, \cdot)$
1-1017-1017.281-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.281	$0$	✓	✓	$0.00606$	$0$	$1.38802$	Character $\chi_{1017}(281, \cdot)$
1-1017-1017.283-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.283	$0$	✓	✓	$0.381$	$0$	$1.78384$	Character $\chi_{1017}(283, \cdot)$
1-1017-1017.284-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.284	$0$	✓	✓	$-0.0970$	$0$	$0.826777$	Character $\chi_{1017}(284, \cdot)$
1-1017-1017.286-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.286	$0$	✓	✓	$0.0461$	$0$	$0.347415$	Character $\chi_{1017}(286, \cdot)$
1-1017-1017.29-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.29	$0$	✓	✓	$-0.381$	$0$	$0.727882$	Character $\chi_{1017}(29, \cdot)$
1-1017-1017.293-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.293	$0$	✓	✓	$0.0920$	$0$	$1.36345$	Character $\chi_{1017}(293, \cdot)$
1-1017-1017.295-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.295	$0$	✓	✓	$0.143$	$0$	$0.601811$	Character $\chi_{1017}(295, \cdot)$
1-1017-1017.299-r0-0-0	$4.72$	$4.72$	$1$	$3^{2} \cdot 113$	1017.299	$0$	✓	✓	$-0.372$	$0$	$0.557044$	Character $\chi_{1017}(299, \cdot)$

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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.