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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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6145-6145.1002-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1002	$0$	✓	✓	$-0.209$	$0$	$0.487298$	Character $\chi_{6145}(1002, \cdot)$
1-6145-6145.1003-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1003	$0$	✓	✓	$0.276$	$0$	$0.951742$	Character $\chi_{6145}(1003, \cdot)$
1-6145-6145.1004-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1004	$0$	✓	✓	$0.195$	$0$	$1.07004$	Character $\chi_{6145}(1004, \cdot)$
1-6145-6145.1007-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1007	$0$	✓	✓	$0.154$	$0$	$1.02323$	Character $\chi_{6145}(1007, \cdot)$
1-6145-6145.1014-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1014	$0$	✓	✓	$0.343$	$0$	$0.311902$	Character $\chi_{6145}(1014, \cdot)$
1-6145-6145.1018-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1018	$0$	✓	✓	$-0.0778$	$0$	$0.631551$	Character $\chi_{6145}(1018, \cdot)$
1-6145-6145.1019-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1019	$0$	✓	✓	$-0.488$	$0$	$0.608291$	Character $\chi_{6145}(1019, \cdot)$
1-6145-6145.102-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.102	$0$	✓	✓	$-0.369$	$0$	$0.284681$	Character $\chi_{6145}(102, \cdot)$
1-6145-6145.1022-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1022	$0$	✓	✓	$0.287$	$0$	$1.08002$	Character $\chi_{6145}(1022, \cdot)$
1-6145-6145.1024-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1024	$0$	✓	✓	$0.411$	$0$	$0.903814$	Character $\chi_{6145}(1024, \cdot)$
1-6145-6145.1027-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1027	$0$	✓	✓	$-0.152$	$0$	$0.308302$	Character $\chi_{6145}(1027, \cdot)$
1-6145-6145.1028-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1028	$0$	✓	✓	$0.0671$	$0$	$0.669591$	Character $\chi_{6145}(1028, \cdot)$
1-6145-6145.103-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.103	$0$	✓	✓	$0.382$	$0$	$0.743950$	Character $\chi_{6145}(103, \cdot)$
1-6145-6145.1034-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1034	$0$	✓	✓	$-0.174$	$0$	$0.508896$	Character $\chi_{6145}(1034, \cdot)$
1-6145-6145.1037-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1037	$0$	✓	✓	$0.300$	$0$	$0.655675$	Character $\chi_{6145}(1037, \cdot)$
1-6145-6145.1038-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1038	$0$	✓	✓	$-0.0442$	$0$	$0.394747$	Character $\chi_{6145}(1038, \cdot)$
1-6145-6145.1039-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1039	$0$	✓	✓	$0.288$	$0$	$1.23748$	Character $\chi_{6145}(1039, \cdot)$
1-6145-6145.104-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.104	$0$	✓	✓	$0.0652$	$0$	$0.273427$	Character $\chi_{6145}(104, \cdot)$
1-6145-6145.1049-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1049	$0$	✓	✓	$-0.0374$	$0$	$0.355800$	Character $\chi_{6145}(1049, \cdot)$
1-6145-6145.1052-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1052	$0$	✓	✓	$0.0765$	$0$	$0.784303$	Character $\chi_{6145}(1052, \cdot)$
1-6145-6145.1053-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1053	$0$	✓	✓	$-0.466$	$0$	$0.393288$	Character $\chi_{6145}(1053, \cdot)$
1-6145-6145.1054-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1054	$0$	✓	✓	$-0.292$	$0$	$0.348680$	Character $\chi_{6145}(1054, \cdot)$
1-6145-6145.1058-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1058	$0$	✓	✓	$-0.171$	$0$	$0.421027$	Character $\chi_{6145}(1058, \cdot)$
1-6145-6145.1059-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1059	$0$	✓	✓	$-0.102$	$0$	$0.971174$	Character $\chi_{6145}(1059, \cdot)$
1-6145-6145.1062-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1062	$0$	✓	✓	$-0.366$	$0$	$0.361495$	Character $\chi_{6145}(1062, \cdot)$
1-6145-6145.1064-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1064	$0$	✓	✓	$-0.173$	$0$	$0.748134$	Character $\chi_{6145}(1064, \cdot)$
1-6145-6145.1067-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1067	$0$	✓	✓	$-0.185$	$0$	$0.644464$	Character $\chi_{6145}(1067, \cdot)$
1-6145-6145.1068-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1068	$0$	✓	✓	$-0.445$	$0$	$0.0361137$	Character $\chi_{6145}(1068, \cdot)$
1-6145-6145.1074-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1074	$0$	✓	✓	$-0.106$	$0$	$0.570940$	Character $\chi_{6145}(1074, \cdot)$
1-6145-6145.1079-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1079	$0$	✓	✓	$0.147$	$0$	$0.735397$	Character $\chi_{6145}(1079, \cdot)$
1-6145-6145.108-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.108	$0$	✓	✓	$-0.174$	$0$	$0.367107$	Character $\chi_{6145}(108, \cdot)$
1-6145-6145.1082-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1082	$0$	✓	✓	$-0.382$	$0$	$1.49259$	Character $\chi_{6145}(1082, \cdot)$
1-6145-6145.1083-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1083	$0$	✓	✓	$-0.335$	$0$	$1.84978$	Character $\chi_{6145}(1083, \cdot)$
1-6145-6145.1088-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1088	$0$	✓	✓	$0.135$	$0$	$0.643833$	Character $\chi_{6145}(1088, \cdot)$
1-6145-6145.1089-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1089	$0$	✓	✓	$0.386$	$0$	$0.494497$	Character $\chi_{6145}(1089, \cdot)$
1-6145-6145.1098-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1098	$0$	✓	✓	$0.408$	$0$	$0.965403$	Character $\chi_{6145}(1098, \cdot)$
1-6145-6145.1099-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1099	$0$	✓	✓	$-0.414$	$0$	$1.53196$	Character $\chi_{6145}(1099, \cdot)$
1-6145-6145.1102-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1102	$0$	✓	✓	$-0.376$	$0$	$0.391793$	Character $\chi_{6145}(1102, \cdot)$
1-6145-6145.1103-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1103	$0$	✓	✓	$0.0509$	$0$	$0.553094$	Character $\chi_{6145}(1103, \cdot)$
1-6145-6145.1104-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1104	$0$	✓	✓	$-0.340$	$0$	$0.0368095$	Character $\chi_{6145}(1104, \cdot)$
1-6145-6145.1107-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1107	$0$	✓	✓	$0.484$	$0$	$1.71842$	Character $\chi_{6145}(1107, \cdot)$
1-6145-6145.1109-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1109	$0$	✓	✓	$-0.277$	$0$	$0.555524$	Character $\chi_{6145}(1109, \cdot)$
1-6145-6145.1112-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1112	$0$	✓	✓	$0.395$	$0$	$0.161193$	Character $\chi_{6145}(1112, \cdot)$
1-6145-6145.1113-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1113	$0$	✓	✓	$0.0196$	$0$	$0.607605$	Character $\chi_{6145}(1113, \cdot)$
1-6145-6145.1119-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1119	$0$	✓	✓	$0.446$	$0$	$1.21439$	Character $\chi_{6145}(1119, \cdot)$
1-6145-6145.1123-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1123	$0$	✓	✓	$0.00292$	$0$	$0.823499$	Character $\chi_{6145}(1123, \cdot)$
1-6145-6145.1127-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1127	$0$	✓	✓	$-0.279$	$0$	$0.796432$	Character $\chi_{6145}(1127, \cdot)$
1-6145-6145.1129-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1129	$0$	✓	✓	$-0.0375$	$0$	$0.570671$	Character $\chi_{6145}(1129, \cdot)$
1-6145-6145.1137-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1137	$0$	✓	✓	$0.446$	$0$	$1.17382$	Character $\chi_{6145}(1137, \cdot)$
1-6145-6145.1138-r0-0-0	$28.5$	$28.5$	$1$	$5 \cdot 1229$	6145.1138	$0$	✓	✓	$0.184$	$0$	$0.833669$	Character $\chi_{6145}(1138, \cdot)$

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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.