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 478 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1157-1157.1005-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1005	$1$	✓	✓	$-0.278$	$0$	$1.19609$	Character $\chi_{1157}(1005, \cdot)$
1-1157-1157.101-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.101	$1$	✓	✓	$-0.235$	$0$	$0.611425$	Character $\chi_{1157}(101, \cdot)$
1-1157-1157.1010-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1010	$1$	✓	✓	$-0.409$	$0$	$0.0374893$	Character $\chi_{1157}(1010, \cdot)$
1-1157-1157.1017-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1017	$1$	✓	✓	$0.173$	$0$	$1.00792$	Character $\chi_{1157}(1017, \cdot)$
1-1157-1157.1019-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1019	$1$	✓	✓	$-0.209$	$0$	$0.211681$	Character $\chi_{1157}(1019, \cdot)$
1-1157-1157.1021-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1021	$1$	✓	✓	$-0.242$	$0$	$0.500692$	Character $\chi_{1157}(1021, \cdot)$
1-1157-1157.1029-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1029	$1$	✓	✓	$0.424$	$0$	$0.969463$	Character $\chi_{1157}(1029, \cdot)$
1-1157-1157.103-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.103	$1$	✓	✓	$0.131$	$0$	$0.696660$	Character $\chi_{1157}(103, \cdot)$
1-1157-1157.1030-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1030	$1$	✓	✓	$0.164$	$0$	$0.830897$	Character $\chi_{1157}(1030, \cdot)$
1-1157-1157.1031-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1031	$1$	✓	✓	$0.235$	$0$	$0.225224$	Character $\chi_{1157}(1031, \cdot)$
1-1157-1157.1032-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1032	$1$	✓	✓	$-0.456$	$0$	$0.910308$	Character $\chi_{1157}(1032, \cdot)$
1-1157-1157.1034-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1034	$1$	✓	✓	$0.334$	$0$	$0.196288$	Character $\chi_{1157}(1034, \cdot)$
1-1157-1157.1037-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1037	$1$	✓	✓	$-0.194$	$0$	$1.74777$	Character $\chi_{1157}(1037, \cdot)$
1-1157-1157.1039-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1039	$1$	✓	✓	$0.303$	$0$	$0.451359$	Character $\chi_{1157}(1039, \cdot)$
1-1157-1157.1044-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1044	$1$	✓	✓	$0.406$	$0$	$1.05795$	Character $\chi_{1157}(1044, \cdot)$
1-1157-1157.1046-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1046	$1$	✓	✓	$-0.0864$	$0$	$0.0722583$	Character $\chi_{1157}(1046, \cdot)$
1-1157-1157.1047-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1047	$1$	✓	✓	$0.147$	$0$	$1.01692$	Character $\chi_{1157}(1047, \cdot)$
1-1157-1157.1048-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1048	$1$	✓	✓	$0.209$	$0$	$1.12065$	Character $\chi_{1157}(1048, \cdot)$
1-1157-1157.1049-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1049	$1$	✓	✓	$-0.174$	$0$	$0.703919$	Character $\chi_{1157}(1049, \cdot)$
1-1157-1157.1051-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1051	$1$	✓	✓	$0.446$	$0$	$0.333995$	Character $\chi_{1157}(1051, \cdot)$
1-1157-1157.1056-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1056	$1$	✓	✓	$-0.392$	$0$	$0.983023$	Character $\chi_{1157}(1056, \cdot)$
1-1157-1157.1058-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1058	$1$	✓	✓	$-0.111$	$0$	$0.145252$	Character $\chi_{1157}(1058, \cdot)$
1-1157-1157.1059-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1059	$1$	✓	✓	$-0.180$	$0$	$0.487511$	Character $\chi_{1157}(1059, \cdot)$
1-1157-1157.106-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.106	$1$	✓	✓	$0.449$	$0$	$0.435496$	Character $\chi_{1157}(106, \cdot)$
1-1157-1157.1060-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1060	$1$	✓	✓	$0.187$	$0$	$0.918339$	Character $\chi_{1157}(1060, \cdot)$
1-1157-1157.1062-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1062	$1$	✓	✓	$-0.340$	$0$	$0.0803371$	Character $\chi_{1157}(1062, \cdot)$
1-1157-1157.1064-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1064	$1$	✓	✓	$-0.152$	$0$	$0.0314093$	Character $\chi_{1157}(1064, \cdot)$
1-1157-1157.1065-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1065	$1$	✓	✓	$0.279$	$0$	$1.02067$	Character $\chi_{1157}(1065, \cdot)$
1-1157-1157.1072-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1072	$1$	✓	✓	$0.407$	$0$	$1.13507$	Character $\chi_{1157}(1072, \cdot)$
1-1157-1157.1073-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1073	$1$	✓	✓	$0.0240$	$0$	$0.543932$	Character $\chi_{1157}(1073, \cdot)$
1-1157-1157.1075-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1075	$1$	✓	✓	$-0.164$	$0$	$0.480823$	Character $\chi_{1157}(1075, \cdot)$
1-1157-1157.1077-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1077	$1$	✓	✓	$-0.112$	$0$	$0.720490$	Character $\chi_{1157}(1077, \cdot)$
1-1157-1157.108-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.108	$1$	✓	✓	$-0.0738$	$0$	$0.437218$	Character $\chi_{1157}(108, \cdot)$
1-1157-1157.1082-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1082	$1$	✓	✓	$0.174$	$0$	$1.28950$	Character $\chi_{1157}(1082, \cdot)$
1-1157-1157.1083-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1083	$1$	✓	✓	$0.317$	$0$	$1.23953$	Character $\chi_{1157}(1083, \cdot)$
1-1157-1157.1084-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1084	$1$	✓	✓	$0.438$	$0$	$1.09716$	Character $\chi_{1157}(1084, \cdot)$
1-1157-1157.1085-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1085	$1$	✓	✓	$0.363$	$0$	$0.0463280$	Character $\chi_{1157}(1085, \cdot)$
1-1157-1157.1086-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1086	$1$	✓	✓	$0.484$	$0$	$0.203381$	Character $\chi_{1157}(1086, \cdot)$
1-1157-1157.109-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.109	$1$	✓	✓	$-0.155$	$0$	$0.0569408$	Character $\chi_{1157}(109, \cdot)$
1-1157-1157.1090-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1090	$1$	✓	✓	$-0.168$	$0$	$0.396879$	Character $\chi_{1157}(1090, \cdot)$
1-1157-1157.1091-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1091	$1$	✓	✓	$0.366$	$0$	$0.523476$	Character $\chi_{1157}(1091, \cdot)$
1-1157-1157.1095-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1095	$1$	✓	✓	$0.282$	$0$	$0.868565$	Character $\chi_{1157}(1095, \cdot)$
1-1157-1157.1096-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1096	$1$	✓	✓	$-0.281$	$0$	$0.724980$	Character $\chi_{1157}(1096, \cdot)$
1-1157-1157.11-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.11	$1$	✓	✓	$0.405$	$0$	$1.34577$	Character $\chi_{1157}(11, \cdot)$
1-1157-1157.110-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.110	$1$	✓	✓	$-0.0428$	$0$	$0.462628$	Character $\chi_{1157}(110, \cdot)$
1-1157-1157.1100-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1100	$1$	✓	✓	$-0.449$	$0$	$0.608152$	Character $\chi_{1157}(1100, \cdot)$
1-1157-1157.1101-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1101	$1$	✓	✓	$-0.282$	$0$	$0.222502$	Character $\chi_{1157}(1101, \cdot)$
1-1157-1157.1107-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1107	$1$	✓	✓	$0.354$	$0$	$1.03610$	Character $\chi_{1157}(1107, \cdot)$
1-1157-1157.1109-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.1109	$1$	✓	✓	$0.0734$	$0$	$1.39771$	Character $\chi_{1157}(1109, \cdot)$
1-1157-1157.111-r1-0-0	$124.$	$124.$	$1$	$13 \cdot 89$	1157.111	$1$	✓	✓	$-0.246$	$0$	$0.486180$	Character $\chi_{1157}(111, \cdot)$

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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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Results (1-50 of 478 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.