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 98 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1148-1148.1011-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1011	$1$	✓	✓	$-0.337$	$0$	$1.23802$	Character $\chi_{1148}(1011, \cdot)$
1-1148-1148.1039-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1039	$1$	✓	✓	$-0.00953$	$0$	$0.815711$	Character $\chi_{1148}(1039, \cdot)$
1-1148-1148.1055-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1055	$1$	✓	✓	$-0.393$	$0$	$0.435439$	Character $\chi_{1148}(1055, \cdot)$
1-1148-1148.1063-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1063	$1$	✓	✓	$0.190$	$0$	$0.968783$	Character $\chi_{1148}(1063, \cdot)$
1-1148-1148.107-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.107	$1$	✓	✓	$-0.119$	$0$	$0.481014$	Character $\chi_{1148}(107, \cdot)$
1-1148-1148.1075-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1075	$1$	✓	✓	$-0.206$	$0$	$0.253774$	Character $\chi_{1148}(1075, \cdot)$
1-1148-1148.1083-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1083	$1$	✓	✓	$0.208$	$0$	$0.959216$	Character $\chi_{1148}(1083, \cdot)$
1-1148-1148.1087-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1087	$1$	✓	✓	$-0.187$	$0$	$0.321130$	Character $\chi_{1148}(1087, \cdot)$
1-1148-1148.1095-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1095	$1$	✓	✓	$-0.208$	$0$	$0.416010$	Character $\chi_{1148}(1095, \cdot)$
1-1148-1148.1103-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1103	$1$	✓	✓	$-0.165$	$0$	$0.414173$	Character $\chi_{1148}(1103, \cdot)$
1-1148-1148.111-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.111	$1$	✓	✓	$-0.0619$	$0$	$0.536812$	Character $\chi_{1148}(111, \cdot)$
1-1148-1148.1115-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1115	$1$	✓	✓	$0.153$	$0$	$0.693811$	Character $\chi_{1148}(1115, \cdot)$
1-1148-1148.1119-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1119	$1$	✓	✓	$0.0139$	$0$	$0.395801$	Character $\chi_{1148}(1119, \cdot)$
1-1148-1148.1143-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.1143	$1$	✓	✓	$0.367$	$0$	$0.0871400$	Character $\chi_{1148}(1143, \cdot)$
1-1148-1148.163-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.163	$1$	✓	✓	$0.260$	$0$	$0.568977$	Character $\chi_{1148}(163, \cdot)$
1-1148-1148.167-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.167	$1$	✓	✓	$-0.136$	$0$	$0.634104$	Character $\chi_{1148}(167, \cdot)$
1-1148-1148.171-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.171	$1$	✓	✓	$0.231$	$0$	$0.686637$	Character $\chi_{1148}(171, \cdot)$
1-1148-1148.19-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.19	$1$	✓	✓	$-0.155$	$0$	$0.402613$	Character $\chi_{1148}(19, \cdot)$
1-1148-1148.199-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.199	$1$	✓	✓	$-0.461$	$0$	$0.145866$	Character $\chi_{1148}(199, \cdot)$
1-1148-1148.207-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.207	$1$	✓	✓	$0.187$	$0$	$1.25222$	Character $\chi_{1148}(207, \cdot)$
1-1148-1148.227-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.227	$1$	✓	✓	$0.0418$	$0$	$0.896557$	Character $\chi_{1148}(227, \cdot)$
1-1148-1148.23-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.23	$1$	✓	✓	$-0.360$	$0$	$1.07722$	Character $\chi_{1148}(23, \cdot)$
1-1148-1148.243-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.243	$1$	✓	✓	$0.337$	$0$	$0.00622225$	Character $\chi_{1148}(243, \cdot)$
1-1148-1148.27-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.27	$1$	✓	✓	$-0.190$	$0$	$0.537864$	Character $\chi_{1148}(27, \cdot)$
1-1148-1148.291-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.291	$1$	✓	✓	$0.129$	$0$	$0.943519$	Character $\chi_{1148}(291, \cdot)$
1-1148-1148.299-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.299	$1$	✓	✓	$0.160$	$0$	$0.839675$	Character $\chi_{1148}(299, \cdot)$
1-1148-1148.3-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.3	$1$	✓	✓	$-0.283$	$0$	$1.66327$	Character $\chi_{1148}(3, \cdot)$
1-1148-1148.303-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.303	$1$	✓	✓	$0.344$	$0$	$0.216566$	Character $\chi_{1148}(303, \cdot)$
1-1148-1148.311-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.311	$1$	✓	✓	$-0.160$	$0$	$0.493554$	Character $\chi_{1148}(311, \cdot)$
1-1148-1148.319-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.319	$1$	✓	✓	$-0.313$	$0$	$0.847507$	Character $\chi_{1148}(319, \cdot)$
1-1148-1148.335-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.335	$1$	✓	✓	$0.377$	$0$	$0.122908$	Character $\chi_{1148}(335, \cdot)$
1-1148-1148.339-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.339	$1$	✓	✓	$0.134$	$0$	$0.666606$	Character $\chi_{1148}(339, \cdot)$
1-1148-1148.355-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.355	$1$	✓	✓	$-0.0441$	$0$	$0.518003$	Character $\chi_{1148}(355, \cdot)$
1-1148-1148.359-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.359	$1$	✓	✓	$-0.129$	$0$	$0.305547$	Character $\chi_{1148}(359, \cdot)$
1-1148-1148.363-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.363	$1$	✓	✓	$-0.315$	$0$	$0.565744$	Character $\chi_{1148}(363, \cdot)$
1-1148-1148.383-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.383	$1$	✓	✓	$0.283$	$0$	$0.0643761$	Character $\chi_{1148}(383, \cdot)$
1-1148-1148.387-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.387	$1$	✓	✓	$0.175$	$0$	$0.822573$	Character $\chi_{1148}(387, \cdot)$
1-1148-1148.39-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.39	$1$	✓	✓	$-0.118$	$0$	$0.337991$	Character $\chi_{1148}(39, \cdot)$
1-1148-1148.391-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.391	$1$	✓	✓	$0.188$	$0$	$0.858384$	Character $\chi_{1148}(391, \cdot)$
1-1148-1148.395-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.395	$1$	✓	✓	$0.393$	$0$	$1.41907$	Character $\chi_{1148}(395, \cdot)$
1-1148-1148.415-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.415	$1$	✓	✓	$0.173$	$0$	$1.02330$	Character $\chi_{1148}(415, \cdot)$
1-1148-1148.423-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.423	$1$	✓	✓	$0.155$	$0$	$0.601485$	Character $\chi_{1148}(423, \cdot)$
1-1148-1148.431-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.431	$1$	✓	✓	$0.291$	$0$	$1.03698$	Character $\chi_{1148}(431, \cdot)$
1-1148-1148.439-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.439	$1$	✓	✓	$0.0845$	$0$	$1.12689$	Character $\chi_{1148}(439, \cdot)$
1-1148-1148.443-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.443	$1$	✓	✓	$0.346$	$0$	$1.12925$	Character $\chi_{1148}(443, \cdot)$
1-1148-1148.459-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.459	$1$	✓	✓	$-0.367$	$0$	$1.29253$	Character $\chi_{1148}(459, \cdot)$
1-1148-1148.47-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.47	$1$	✓	✓	$-0.231$	$0$	$0.693312$	Character $\chi_{1148}(47, \cdot)$
1-1148-1148.471-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.471	$1$	✓	✓	$0.118$	$0$	$0.487518$	Character $\chi_{1148}(471, \cdot)$
1-1148-1148.475-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.475	$1$	✓	✓	$-0.0139$	$0$	$0.773179$	Character $\chi_{1148}(475, \cdot)$
1-1148-1148.479-r1-0-0	$123.$	$123.$	$1$	$2^{2} \cdot 7 \cdot 41$	1148.479	$1$	✓	✓	$-0.334$	$0$	$0.676958$	Character $\chi_{1148}(479, \cdot)$

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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.