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 1111 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1339-1339.100-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.100	$0$	✓	✓	$-0.0596$	$0$	$0.927673$	Character $\chi_{1339}(100, \cdot)$
1-1339-1339.1007-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1007	$0$	✓	✓	$0.352$	$0$	$0.0409977$	Character $\chi_{1339}(1007, \cdot)$
1-1339-1339.1010-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1010	$0$	✓	✓	$-0.453$	$0$	$1.99931$	Character $\chi_{1339}(1010, \cdot)$
1-1339-1339.1012-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1012	$0$	✓	✓	$0.0100$	$0$	$0.444680$	Character $\chi_{1339}(1012, \cdot)$
1-1339-1339.1016-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1016	$0$	✓	✓	$-0.329$	$0$	$0.711899$	Character $\chi_{1339}(1016, \cdot)$
1-1339-1339.1018-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1018	$0$	✓	✓	$0.496$	$0$	$0.401419$	Character $\chi_{1339}(1018, \cdot)$
1-1339-1339.102-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.102	$0$	✓	✓	$0.256$	$0$	$0.117053$	Character $\chi_{1339}(102, \cdot)$
1-1339-1339.1021-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1021	$0$	✓	✓	$0.228$	$0$	$1.23965$	Character $\chi_{1339}(1021, \cdot)$
1-1339-1339.1022-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1022	$0$	✓	✓	$0.210$	$0$	$1.38865$	Character $\chi_{1339}(1022, \cdot)$
1-1339-1339.1024-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1024	$0$	✓	✓	$-0.355$	$0$	$0.500281$	Character $\chi_{1339}(1024, \cdot)$
1-1339-1339.1029-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1029	$0$	✓	✓	$0.162$	$0$	$1.53381$	Character $\chi_{1339}(1029, \cdot)$
1-1339-1339.1033-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1033	$0$	✓	✓	$-0.355$	$0$	$1.63104$	Character $\chi_{1339}(1033, \cdot)$
1-1339-1339.1035-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1035	$0$	✓	✓	$-0.141$	$0$	$0.509474$	Character $\chi_{1339}(1035, \cdot)$
1-1339-1339.1037-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1037	$0$	✓	✓	$-0.373$	$0$	$0.283232$	Character $\chi_{1339}(1037, \cdot)$
1-1339-1339.1039-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1039	$0$	✓	✓	$-0.302$	$0$	$0.0697970$	Character $\chi_{1339}(1039, \cdot)$
1-1339-1339.1042-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1042	$0$	✓	✓	$-0.426$	$0$	$0.946499$	Character $\chi_{1339}(1042, \cdot)$
1-1339-1339.1043-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1043	$0$	✓	✓	$0.00316$	$0$	$0.849161$	Character $\chi_{1339}(1043, \cdot)$
1-1339-1339.1044-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1044	$0$	✓	✓	$-0.297$	$0$	$1.12494$	Character $\chi_{1339}(1044, \cdot)$
1-1339-1339.1049-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1049	$0$	✓	✓	$0.0276$	$0$	$0.280847$	Character $\chi_{1339}(1049, \cdot)$
1-1339-1339.1051-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1051	$0$	✓	✓	$-0.285$	$0$	$0.408213$	Character $\chi_{1339}(1051, \cdot)$
1-1339-1339.1056-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1056	$0$	✓	✓	$0.329$	$0$	$1.15931$	Character $\chi_{1339}(1056, \cdot)$
1-1339-1339.106-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.106	$0$	✓	✓	$0.0632$	$0$	$1.15097$	Character $\chi_{1339}(106, \cdot)$
1-1339-1339.1061-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1061	$0$	✓	✓	$0.414$	$0$	$0.912555$	Character $\chi_{1339}(1061, \cdot)$
1-1339-1339.1062-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1062	$0$	✓	✓	$0.0457$	$0$	$1.28657$	Character $\chi_{1339}(1062, \cdot)$
1-1339-1339.1063-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1063	$0$	✓	✓	$-0.212$	$0$	$0.655566$	Character $\chi_{1339}(1063, \cdot)$
1-1339-1339.107-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.107	$0$	✓	✓	$0.0891$	$0$	$1.20835$	Character $\chi_{1339}(107, \cdot)$
1-1339-1339.1072-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1072	$0$	✓	✓	$-0.292$	$0$	$1.07233$	Character $\chi_{1339}(1072, \cdot)$
1-1339-1339.1073-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1073	$0$	✓	✓	$0.426$	$0$	$1.93357$	Character $\chi_{1339}(1073, \cdot)$
1-1339-1339.1074-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1074	$0$	✓	✓	$-0.445$	$0$	$0.472940$	Character $\chi_{1339}(1074, \cdot)$
1-1339-1339.1076-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1076	$0$	✓	✓	$-0.131$	$0$	$2.09003$	Character $\chi_{1339}(1076, \cdot)$
1-1339-1339.1077-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1077	$0$	✓	✓	$-0.170$	$0$	$0.590673$	Character $\chi_{1339}(1077, \cdot)$
1-1339-1339.1081-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1081	$0$	✓	✓	$0.142$	$0$	$1.37896$	Character $\chi_{1339}(1081, \cdot)$
1-1339-1339.1082-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1082	$0$	✓	✓	$0.310$	$0$	$1.08446$	Character $\chi_{1339}(1082, \cdot)$
1-1339-1339.1084-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1084	$0$	✓	✓	$0.338$	$0$	$0.695275$	Character $\chi_{1339}(1084, \cdot)$
1-1339-1339.1087-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1087	$0$	✓	✓	$-0.370$	$0$	$0.0837585$	Character $\chi_{1339}(1087, \cdot)$
1-1339-1339.1088-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1088	$0$	✓	✓	$-0.343$	$0$	$1.79373$	Character $\chi_{1339}(1088, \cdot)$
1-1339-1339.1089-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1089	$0$	✓	✓	$0.202$	$0$	$1.20924$	Character $\chi_{1339}(1089, \cdot)$
1-1339-1339.109-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.109	$0$	✓	✓	$-0.296$	$0$	$0.596341$	Character $\chi_{1339}(109, \cdot)$
1-1339-1339.1091-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1091	$0$	✓	✓	$-0.228$	$0$	$1.08808$	Character $\chi_{1339}(1091, \cdot)$
1-1339-1339.1096-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1096	$0$	✓	✓	$-0.0108$	$0$	$0.688138$	Character $\chi_{1339}(1096, \cdot)$
1-1339-1339.1097-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1097	$0$	✓	✓	$-0.0735$	$0$	$1.02502$	Character $\chi_{1339}(1097, \cdot)$
1-1339-1339.1099-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1099	$0$	✓	✓	$-0.0632$	$0$	$0.963549$	Character $\chi_{1339}(1099, \cdot)$
1-1339-1339.11-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.11	$0$	✓	✓	$0.381$	$0$	$0.611325$	Character $\chi_{1339}(11, \cdot)$
1-1339-1339.1100-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1100	$0$	✓	✓	$0.343$	$0$	$0.0522503$	Character $\chi_{1339}(1100, \cdot)$
1-1339-1339.1102-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1102	$0$	✓	✓	$0.377$	$0$	$0.818518$	Character $\chi_{1339}(1102, \cdot)$
1-1339-1339.1103-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1103	$0$	✓	✓	$0.395$	$0$	$0.617300$	Character $\chi_{1339}(1103, \cdot)$
1-1339-1339.1107-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1107	$0$	✓	✓	$-0.170$	$0$	$2.71090$	Character $\chi_{1339}(1107, \cdot)$
1-1339-1339.1109-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1109	$0$	✓	✓	$0.466$	$0$	$0.532264$	Character $\chi_{1339}(1109, \cdot)$
1-1339-1339.1110-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1110	$0$	✓	✓	$0.405$	$0$	$1.46996$	Character $\chi_{1339}(1110, \cdot)$
1-1339-1339.1116-r0-0-0	$6.21$	$6.21$	$1$	$13 \cdot 103$	1339.1116	$0$	✓	✓	$0.349$	$0$	$1.39594$	Character $\chi_{1339}(1116, \cdot)$

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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.