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

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-4031-4031.10-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.10	$0$	✓	✓	$0.291$	$0$	$0.936955$	Character $\chi_{4031}(10, \cdot)$
1-4031-4031.100-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.100	$0$	✓	✓	$0.383$	$0$	$0.496042$	Character $\chi_{4031}(100, \cdot)$
1-4031-4031.1000-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1000	$0$	✓	✓	$0.395$	$0$	$1.28983$	Character $\chi_{4031}(1000, \cdot)$
1-4031-4031.1002-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1002	$0$	✓	✓	$-0.362$	$0$	$0.768656$	Character $\chi_{4031}(1002, \cdot)$
1-4031-4031.1005-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1005	$0$	✓	✓	$0.459$	$0$	$1.15709$	Character $\chi_{4031}(1005, \cdot)$
1-4031-4031.1008-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1008	$0$	✓	✓	$0.0484$	$0$	$1.21063$	Character $\chi_{4031}(1008, \cdot)$
1-4031-4031.1009-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1009	$0$	✓	✓	$0.147$	$0$	$0.800754$	Character $\chi_{4031}(1009, \cdot)$
1-4031-4031.101-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.101	$0$	✓	✓	$0.229$	$0$	$0.938701$	Character $\chi_{4031}(101, \cdot)$
1-4031-4031.1010-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1010	$0$	✓	✓	$0.347$	$0$	$1.52013$	Character $\chi_{4031}(1010, \cdot)$
1-4031-4031.1011-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1011	$0$	✓	✓	$-0.357$	$0$	$1.87744$	Character $\chi_{4031}(1011, \cdot)$
1-4031-4031.1012-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1012	$0$	✓	✓	$0.0451$	$0$	$0.562749$	Character $\chi_{4031}(1012, \cdot)$
1-4031-4031.1013-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1013	$0$	✓	✓	$-0.255$	$0$	$1.58601$	Character $\chi_{4031}(1013, \cdot)$
1-4031-4031.1014-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1014	$0$	✓	✓	$-0.221$	$0$	$0.899946$	Character $\chi_{4031}(1014, \cdot)$
1-4031-4031.1019-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1019	$0$	✓	✓	$0.284$	$0$	$1.24236$	Character $\chi_{4031}(1019, \cdot)$
1-4031-4031.102-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.102	$0$	✓	✓	$0.415$	$0$	$1.79474$	Character $\chi_{4031}(102, \cdot)$
1-4031-4031.1020-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1020	$0$	✓	✓	$0.291$	$0$	$0.938221$	Character $\chi_{4031}(1020, \cdot)$
1-4031-4031.1022-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1022	$0$	✓	✓	$-0.0558$	$0$	$0.636678$	Character $\chi_{4031}(1022, \cdot)$
1-4031-4031.1023-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1023	$0$	✓	✓	$0.185$	$0$	$1.13590$	Character $\chi_{4031}(1023, \cdot)$
1-4031-4031.1024-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1024	$0$	✓	✓	$0.0550$	$0$	$0.909193$	Character $\chi_{4031}(1024, \cdot)$
1-4031-4031.1026-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1026	$0$	✓	✓	$0.151$	$0$	$0.844365$	Character $\chi_{4031}(1026, \cdot)$
1-4031-4031.1028-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1028	$0$	✓	✓	$-0.466$	$0$	$1.43896$	Character $\chi_{4031}(1028, \cdot)$
1-4031-4031.1029-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1029	$0$	✓	✓	$-0.331$	$0$	$0.628048$	Character $\chi_{4031}(1029, \cdot)$
1-4031-4031.1032-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1032	$0$	✓	✓	$-0.0801$	$0$	$1.15515$	Character $\chi_{4031}(1032, \cdot)$
1-4031-4031.1033-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1033	$0$	✓	✓	$0.00293$	$0$	$0.321757$	Character $\chi_{4031}(1033, \cdot)$
1-4031-4031.1034-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1034	$0$	✓	✓	$-0.456$	$0$	$1.44101$	Character $\chi_{4031}(1034, \cdot)$
1-4031-4031.1037-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1037	$0$	✓	✓	$0.414$	$0$	$1.32663$	Character $\chi_{4031}(1037, \cdot)$
1-4031-4031.1038-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1038	$0$	✓	✓	$0.477$	$0$	$1.73307$	Character $\chi_{4031}(1038, \cdot)$
1-4031-4031.1039-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1039	$0$	✓	✓	$0.248$	$0$	$0.841464$	Character $\chi_{4031}(1039, \cdot)$
1-4031-4031.104-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.104	$0$	✓	✓	$0.390$	$0$	$0.686307$	Character $\chi_{4031}(104, \cdot)$
1-4031-4031.1040-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1040	$0$	✓	✓	$0.103$	$0$	$0.763399$	Character $\chi_{4031}(1040, \cdot)$
1-4031-4031.1041-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1041	$0$	✓	✓	$0.472$	$0$	$0.504263$	Character $\chi_{4031}(1041, \cdot)$
1-4031-4031.1046-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1046	$0$	✓	✓	$0.270$	$0$	$0.871358$	Character $\chi_{4031}(1046, \cdot)$
1-4031-4031.1047-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1047	$0$	✓	✓	$0.0640$	$0$	$0.911842$	Character $\chi_{4031}(1047, \cdot)$
1-4031-4031.105-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.105	$0$	✓	✓	$0.469$	$0$	$0.256367$	Character $\chi_{4031}(105, \cdot)$
1-4031-4031.1050-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1050	$0$	✓	✓	$-0.120$	$0$	$1.80171$	Character $\chi_{4031}(1050, \cdot)$
1-4031-4031.1051-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1051	$0$	✓	✓	$0.00635$	$0$	$0.362838$	Character $\chi_{4031}(1051, \cdot)$
1-4031-4031.1053-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1053	$0$	✓	✓	$-0.0498$	$0$	$0.973812$	Character $\chi_{4031}(1053, \cdot)$
1-4031-4031.1055-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1055	$0$	✓	✓	$0.00666$	$0$	$2.16113$	Character $\chi_{4031}(1055, \cdot)$
1-4031-4031.1058-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1058	$0$	✓	✓	$-0.396$	$0$	$0.553005$	Character $\chi_{4031}(1058, \cdot)$
1-4031-4031.1061-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1061	$0$	✓	✓	$-0.247$	$0$	$0.0486556$	Character $\chi_{4031}(1061, \cdot)$
1-4031-4031.1063-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1063	$0$	✓	✓	$-0.237$	$0$	$0.490013$	Character $\chi_{4031}(1063, \cdot)$
1-4031-4031.1064-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1064	$0$	✓	✓	$0.414$	$0$	$1.51739$	Character $\chi_{4031}(1064, \cdot)$
1-4031-4031.1065-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1065	$0$	✓	✓	$0.343$	$0$	$0.0929494$	Character $\chi_{4031}(1065, \cdot)$
1-4031-4031.1069-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1069	$0$	✓	✓	$0.0364$	$0$	$0.585134$	Character $\chi_{4031}(1069, \cdot)$
1-4031-4031.107-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.107	$0$	✓	✓	$0.414$	$0$	$1.01364$	Character $\chi_{4031}(107, \cdot)$
1-4031-4031.1070-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1070	$0$	✓	✓	$0.366$	$0$	$1.15441$	Character $\chi_{4031}(1070, \cdot)$
1-4031-4031.1071-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1071	$0$	✓	✓	$0.0721$	$0$	$0.636642$	Character $\chi_{4031}(1071, \cdot)$
1-4031-4031.1072-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1072	$0$	✓	✓	$-0.130$	$0$	$0.302364$	Character $\chi_{4031}(1072, \cdot)$
1-4031-4031.1075-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1075	$0$	✓	✓	$0.0997$	$0$	$0.455610$	Character $\chi_{4031}(1075, \cdot)$
1-4031-4031.1076-r0-0-0	$18.7$	$18.7$	$1$	$29 \cdot 139$	4031.1076	$0$	✓	✓	$0.126$	$0$	$0.157276$	Character $\chi_{4031}(1076, \cdot)$

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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.