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 629 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1259-1259.10-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.10	$1$	✓	✓	$0.439$	$0$	$1.51792$	Character $\chi_{1259}(10, \cdot)$
1-1259-1259.1000-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1000	$1$	✓	✓	$0.102$	$0$	$0.280415$	Character $\chi_{1259}(1000, \cdot)$
1-1259-1259.1002-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1002	$1$	✓	✓	$-0.190$	$0$	$0.265657$	Character $\chi_{1259}(1002, \cdot)$
1-1259-1259.1003-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1003	$1$	✓	✓	$-0.150$	$0$	$0.624537$	Character $\chi_{1259}(1003, \cdot)$
1-1259-1259.1004-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1004	$1$	✓	✓	$-0.424$	$0$	$0.155599$	Character $\chi_{1259}(1004, \cdot)$
1-1259-1259.1007-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1007	$1$	✓	✓	$-0.153$	$0$	$0.398299$	Character $\chi_{1259}(1007, \cdot)$
1-1259-1259.1010-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1010	$1$	✓	✓	$-0.230$	$0$	$1.98264$	Character $\chi_{1259}(1010, \cdot)$
1-1259-1259.1011-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1011	$1$	✓	✓	$-0.328$	$0$	$0.238775$	Character $\chi_{1259}(1011, \cdot)$
1-1259-1259.1012-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1012	$1$	✓	✓	$0.355$	$0$	$1.51862$	Character $\chi_{1259}(1012, \cdot)$
1-1259-1259.1013-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1013	$1$	✓	✓	$-0.350$	$0$	$1.44800$	Character $\chi_{1259}(1013, \cdot)$
1-1259-1259.1014-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1014	$1$	✓	✓	$0.0105$	$0$	$1.30414$	Character $\chi_{1259}(1014, \cdot)$
1-1259-1259.1015-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1015	$1$	✓	✓	$-0.172$	$0$	$1.30664$	Character $\chi_{1259}(1015, \cdot)$
1-1259-1259.1016-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1016	$1$	✓	✓	$0.310$	$0$	$1.07422$	Character $\chi_{1259}(1016, \cdot)$
1-1259-1259.1018-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1018	$1$	✓	✓	$0.211$	$0$	$0.736739$	Character $\chi_{1259}(1018, \cdot)$
1-1259-1259.1019-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1019	$1$	✓	✓	$0.313$	$0$	$1.10241$	Character $\chi_{1259}(1019, \cdot)$
1-1259-1259.102-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.102	$1$	✓	✓	$0.0593$	$0$	$1.28187$	Character $\chi_{1259}(102, \cdot)$
1-1259-1259.1022-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1022	$1$	✓	✓	$0.0700$	$0$	$0.663575$	Character $\chi_{1259}(1022, \cdot)$
1-1259-1259.1025-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1025	$1$	✓	✓	$0.445$	$0$	$0.0234706$	Character $\chi_{1259}(1025, \cdot)$
1-1259-1259.1027-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1027	$1$	✓	✓	$-0.415$	$0$	$1.18733$	Character $\chi_{1259}(1027, \cdot)$
1-1259-1259.103-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.103	$1$	✓	✓	$-0.327$	$0$	$0.368815$	Character $\chi_{1259}(103, \cdot)$
1-1259-1259.1032-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1032	$1$	✓	✓	$-0.325$	$0$	$1.01189$	Character $\chi_{1259}(1032, \cdot)$
1-1259-1259.1034-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1034	$1$	✓	✓	$-0.200$	$0$	$1.35332$	Character $\chi_{1259}(1034, \cdot)$
1-1259-1259.1040-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1040	$1$	✓	✓	$0.171$	$0$	$0.511975$	Character $\chi_{1259}(1040, \cdot)$
1-1259-1259.1044-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1044	$1$	✓	✓	$-0.416$	$0$	$0.218203$	Character $\chi_{1259}(1044, \cdot)$
1-1259-1259.1046-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1046	$1$	✓	✓	$0.416$	$0$	$0.0568889$	Character $\chi_{1259}(1046, \cdot)$
1-1259-1259.1047-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1047	$1$	✓	✓	$0.306$	$0$	$1.08777$	Character $\chi_{1259}(1047, \cdot)$
1-1259-1259.1050-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1050	$1$	✓	✓	$0.454$	$0$	$0.611512$	Character $\chi_{1259}(1050, \cdot)$
1-1259-1259.1052-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1052	$1$	✓	✓	$0.0692$	$0$	$0.241252$	Character $\chi_{1259}(1052, \cdot)$
1-1259-1259.1053-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1053	$1$	✓	✓	$0.0205$	$0$	$1.22023$	Character $\chi_{1259}(1053, \cdot)$
1-1259-1259.1055-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1055	$1$	✓	✓	$0.301$	$0$	$0.789515$	Character $\chi_{1259}(1055, \cdot)$
1-1259-1259.1058-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1058	$1$	✓	✓	$-0.111$	$0$	$0.304842$	Character $\chi_{1259}(1058, \cdot)$
1-1259-1259.106-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.106	$1$	✓	✓	$0.325$	$0$	$0.162503$	Character $\chi_{1259}(106, \cdot)$
1-1259-1259.1061-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1061	$1$	✓	✓	$0.430$	$0$	$1.01893$	Character $\chi_{1259}(1061, \cdot)$
1-1259-1259.1063-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1063	$1$	✓	✓	$0.100$	$0$	$0.760153$	Character $\chi_{1259}(1063, \cdot)$
1-1259-1259.1066-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1066	$1$	✓	✓	$0.248$	$0$	$0.441142$	Character $\chi_{1259}(1066, \cdot)$
1-1259-1259.1067-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1067	$1$	✓	✓	$-0.479$	$0$	$0.939241$	Character $\chi_{1259}(1067, \cdot)$
1-1259-1259.1068-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1068	$1$	✓	✓	$0.0581$	$0$	$0.936588$	Character $\chi_{1259}(1068, \cdot)$
1-1259-1259.1069-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1069	$1$	✓	✓	$0.0839$	$0$	$0.333464$	Character $\chi_{1259}(1069, \cdot)$
1-1259-1259.1070-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1070	$1$	✓	✓	$-0.0625$	$0$	$0.682900$	Character $\chi_{1259}(1070, \cdot)$
1-1259-1259.1073-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1073	$1$	✓	✓	$0.332$	$0$	$0.838623$	Character $\chi_{1259}(1073, \cdot)$
1-1259-1259.1074-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1074	$1$	✓	✓	$-0.0105$	$0$	$0.768445$	Character $\chi_{1259}(1074, \cdot)$
1-1259-1259.1076-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1076	$1$	✓	✓	$-0.125$	$0$	$1.38262$	Character $\chi_{1259}(1076, \cdot)$
1-1259-1259.1077-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1077	$1$	✓	✓	$-0.0821$	$0$	$0.528986$	Character $\chi_{1259}(1077, \cdot)$
1-1259-1259.1079-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1079	$1$	✓	✓	$-0.240$	$0$	$0.147408$	Character $\chi_{1259}(1079, \cdot)$
1-1259-1259.1080-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1080	$1$	✓	✓	$0.0665$	$0$	$0.244659$	Character $\chi_{1259}(1080, \cdot)$
1-1259-1259.1081-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1081	$1$	✓	✓	$-0.188$	$0$	$1.28352$	Character $\chi_{1259}(1081, \cdot)$
1-1259-1259.1084-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1084	$1$	✓	✓	$-0.102$	$0$	$0.959376$	Character $\chi_{1259}(1084, \cdot)$
1-1259-1259.1085-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1085	$1$	✓	✓	$0.344$	$0$	$0.659447$	Character $\chi_{1259}(1085, \cdot)$
1-1259-1259.1087-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1087	$1$	✓	✓	$0.125$	$0$	$0.147208$	Character $\chi_{1259}(1087, \cdot)$
1-1259-1259.1090-r1-0-0	$135.$	$135.$	$1$	$1259$	1259.1090	$1$	✓	✓	$-0.0192$	$0$	$0.630849$	Character $\chi_{1259}(1090, \cdot)$

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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.