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 472 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1081-1081.1002-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1002	$1$	✓	✓	$0.0673$	$0$	$0.649675$	Character $\chi_{1081}(1002, \cdot)$
1-1081-1081.1003-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1003	$1$	✓	✓	$0.162$	$0$	$0.529309$	Character $\chi_{1081}(1003, \cdot)$
1-1081-1081.1004-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1004	$1$	✓	✓	$-0.295$	$0$	$0.351016$	Character $\chi_{1081}(1004, \cdot)$
1-1081-1081.1007-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1007	$1$	✓	✓	$-0.0487$	$0$	$0.504441$	Character $\chi_{1081}(1007, \cdot)$
1-1081-1081.1008-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1008	$1$	✓	✓	$-0.247$	$0$	$0.786780$	Character $\chi_{1081}(1008, \cdot)$
1-1081-1081.1011-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1011	$1$	✓	✓	$0.0506$	$0$	$1.11722$	Character $\chi_{1081}(1011, \cdot)$
1-1081-1081.1016-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1016	$1$	✓	✓	$0.141$	$0$	$1.19959$	Character $\chi_{1081}(1016, \cdot)$
1-1081-1081.1018-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1018	$1$	✓	✓	$-0.309$	$0$	$0.742111$	Character $\chi_{1081}(1018, \cdot)$
1-1081-1081.1019-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1019	$1$	✓	✓	$-0.353$	$0$	$0.812455$	Character $\chi_{1081}(1019, \cdot)$
1-1081-1081.102-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.102	$1$	✓	✓	$-0.455$	$0$	$1.03109$	Character $\chi_{1081}(102, \cdot)$
1-1081-1081.1020-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1020	$1$	✓	✓	$0.499$	$0$	$1.74601$	Character $\chi_{1081}(1020, \cdot)$
1-1081-1081.1023-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1023	$1$	✓	✓	$-0.445$	$0$	$0.0980761$	Character $\chi_{1081}(1023, \cdot)$
1-1081-1081.1025-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1025	$1$	✓	✓	$-0.155$	$0$	$1.02128$	Character $\chi_{1081}(1025, \cdot)$
1-1081-1081.1028-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1028	$1$	✓	✓	$-0.292$	$0$	$0.190882$	Character $\chi_{1081}(1028, \cdot)$
1-1081-1081.1029-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1029	$1$	✓	✓	$0.428$	$0$	$0.00579907$	Character $\chi_{1081}(1029, \cdot)$
1-1081-1081.103-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.103	$1$	✓	✓	$-0.303$	$0$	$0.277191$	Character $\chi_{1081}(103, \cdot)$
1-1081-1081.1030-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1030	$1$	✓	✓	$-0.373$	$0$	$0.958332$	Character $\chi_{1081}(1030, \cdot)$
1-1081-1081.1039-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1039	$1$	✓	✓	$0.404$	$0$	$1.09564$	Character $\chi_{1081}(1039, \cdot)$
1-1081-1081.104-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.104	$1$	✓	✓	$0.454$	$0$	$0.963230$	Character $\chi_{1081}(104, \cdot)$
1-1081-1081.1040-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1040	$1$	✓	✓	$-0.128$	$0$	$0.591339$	Character $\chi_{1081}(1040, \cdot)$
1-1081-1081.1042-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1042	$1$	✓	✓	$-0.235$	$0$	$0.695086$	Character $\chi_{1081}(1042, \cdot)$
1-1081-1081.1044-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1044	$1$	✓	✓	$-0.337$	$0$	$0.392958$	Character $\chi_{1081}(1044, \cdot)$
1-1081-1081.1046-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1046	$1$	✓	✓	$-0.404$	$0$	$0.698841$	Character $\chi_{1081}(1046, \cdot)$
1-1081-1081.1047-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1047	$1$	✓	✓	$-0.288$	$0$	$1.63753$	Character $\chi_{1081}(1047, \cdot)$
1-1081-1081.105-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.105	$1$	✓	✓	$-0.100$	$0$	$0.674925$	Character $\chi_{1081}(105, \cdot)$
1-1081-1081.1050-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1050	$1$	✓	✓	$-0.0638$	$0$	$0.799993$	Character $\chi_{1081}(1050, \cdot)$
1-1081-1081.1052-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1052	$1$	✓	✓	$0.482$	$0$	$0.428361$	Character $\chi_{1081}(1052, \cdot)$
1-1081-1081.1053-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1053	$1$	✓	✓	$-0.290$	$0$	$0.112977$	Character $\chi_{1081}(1053, \cdot)$
1-1081-1081.1055-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1055	$1$	✓	✓	$0.0657$	$0$	$0.474634$	Character $\chi_{1081}(1055, \cdot)$
1-1081-1081.106-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.106	$1$	✓	✓	$0.0597$	$0$	$1.19481$	Character $\chi_{1081}(106, \cdot)$
1-1081-1081.1060-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1060	$1$	✓	✓	$-0.358$	$0$	$0.287811$	Character $\chi_{1081}(1060, \cdot)$
1-1081-1081.1064-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1064	$1$	✓	✓	$0.265$	$0$	$0.0176665$	Character $\chi_{1081}(1064, \cdot)$
1-1081-1081.1067-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1067	$1$	✓	✓	$0.285$	$0$	$1.15975$	Character $\chi_{1081}(1067, \cdot)$
1-1081-1081.1068-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1068	$1$	✓	✓	$-0.0262$	$0$	$0.945717$	Character $\chi_{1081}(1068, \cdot)$
1-1081-1081.1074-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.1074	$1$	✓	✓	$-0.176$	$0$	$0.176538$	Character $\chi_{1081}(1074, \cdot)$
1-1081-1081.111-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.111	$1$	✓	✓	$-0.109$	$0$	$0.874997$	Character $\chi_{1081}(111, \cdot)$
1-1081-1081.112-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.112	$1$	✓	✓	$-0.331$	$0$	$0.239633$	Character $\chi_{1081}(112, \cdot)$
1-1081-1081.117-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.117	$1$	✓	✓	$-0.144$	$0$	$2.08120$	Character $\chi_{1081}(117, \cdot)$
1-1081-1081.122-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.122	$1$	✓	✓	$0.246$	$0$	$0.317846$	Character $\chi_{1081}(122, \cdot)$
1-1081-1081.123-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.123	$1$	✓	✓	$0.242$	$0$	$0.689176$	Character $\chi_{1081}(123, \cdot)$
1-1081-1081.124-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.124	$1$	✓	✓	$0.326$	$0$	$0.617625$	Character $\chi_{1081}(124, \cdot)$
1-1081-1081.126-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.126	$1$	✓	✓	$-0.452$	$0$	$1.66102$	Character $\chi_{1081}(126, \cdot)$
1-1081-1081.127-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.127	$1$	✓	✓	$0.0777$	$0$	$0.321572$	Character $\chi_{1081}(127, \cdot)$
1-1081-1081.13-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.13	$1$	✓	✓	$0.196$	$0$	$1.15322$	Character $\chi_{1081}(13, \cdot)$
1-1081-1081.130-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.130	$1$	✓	✓	$-0.208$	$0$	$0.148047$	Character $\chi_{1081}(130, \cdot)$
1-1081-1081.133-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.133	$1$	✓	✓	$0.0674$	$0$	$0.186620$	Character $\chi_{1081}(133, \cdot)$
1-1081-1081.136-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.136	$1$	✓	✓	$-0.147$	$0$	$0.928915$	Character $\chi_{1081}(136, \cdot)$
1-1081-1081.14-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.14	$1$	✓	✓	$0.186$	$0$	$1.38167$	Character $\chi_{1081}(14, \cdot)$
1-1081-1081.140-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.140	$1$	✓	✓	$-0.266$	$0$	$0.202884$	Character $\chi_{1081}(140, \cdot)$
1-1081-1081.143-r1-0-0	$116.$	$116.$	$1$	$23 \cdot 47$	1081.143	$1$	✓	✓	$-0.0251$	$0$	$0.0350404$	Character $\chi_{1081}(143, \cdot)$

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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.