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
1-5245-5245.1002-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1002	$0$	✓	✓	$0.297$	$0$	$0.315995$	Character $\chi_{5245}(1002, \cdot)$
1-5245-5245.1003-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1003	$0$	✓	✓	$0.0267$	$0$	$0.820072$	Character $\chi_{5245}(1003, \cdot)$
1-5245-5245.1004-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1004	$0$	✓	✓	$-0.323$	$0$	$1.36324$	Character $\chi_{5245}(1004, \cdot)$
1-5245-5245.1008-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1008	$0$	✓	✓	$0.384$	$0$	$1.28516$	Character $\chi_{5245}(1008, \cdot)$
1-5245-5245.1009-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1009	$0$	✓	✓	$0.358$	$0$	$1.42442$	Character $\chi_{5245}(1009, \cdot)$
1-5245-5245.1012-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1012	$0$	✓	✓	$-0.112$	$0$	$0.736698$	Character $\chi_{5245}(1012, \cdot)$
1-5245-5245.1018-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1018	$0$	✓	✓	$0.401$	$0$	$1.18272$	Character $\chi_{5245}(1018, \cdot)$
1-5245-5245.1022-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1022	$0$	✓	✓	$0.0376$	$0$	$0.779539$	Character $\chi_{5245}(1022, \cdot)$
1-5245-5245.1024-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1024	$0$	✓	✓	$-0.386$	$0$	$0.151500$	Character $\chi_{5245}(1024, \cdot)$
1-5245-5245.1029-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1029	$0$	✓	✓	$0.299$	$0$	$0.747791$	Character $\chi_{5245}(1029, \cdot)$
1-5245-5245.1032-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1032	$0$	✓	✓	$-0.300$	$0$	$0.865335$	Character $\chi_{5245}(1032, \cdot)$
1-5245-5245.1037-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1037	$0$	✓	✓	$-0.0888$	$0$	$0.585875$	Character $\chi_{5245}(1037, \cdot)$
1-5245-5245.1039-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1039	$0$	✓	✓	$-0.402$	$0$	$0.00405184$	Character $\chi_{5245}(1039, \cdot)$
1-5245-5245.104-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.104	$0$	✓	✓	$-0.0339$	$0$	$0.824296$	Character $\chi_{5245}(104, \cdot)$
1-5245-5245.1042-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1042	$0$	✓	✓	$0.477$	$0$	$0.848981$	Character $\chi_{5245}(1042, \cdot)$
1-5245-5245.1043-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1043	$0$	✓	✓	$0.333$	$0$	$0.564667$	Character $\chi_{5245}(1043, \cdot)$
1-5245-5245.1044-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1044	$0$	✓	✓	$0.355$	$0$	$0.967441$	Character $\chi_{5245}(1044, \cdot)$
1-5245-5245.1052-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1052	$0$	✓	✓	$0.471$	$0$	$0.526088$	Character $\chi_{5245}(1052, \cdot)$
1-5245-5245.1054-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1054	$0$	✓	✓	$0.188$	$0$	$0.490892$	Character $\chi_{5245}(1054, \cdot)$
1-5245-5245.1059-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1059	$0$	✓	✓	$0.287$	$0$	$0.593823$	Character $\chi_{5245}(1059, \cdot)$
1-5245-5245.1063-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1063	$0$	✓	✓	$-0.206$	$0$	$0.707365$	Character $\chi_{5245}(1063, \cdot)$
1-5245-5245.1069-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1069	$0$	✓	✓	$0.410$	$0$	$1.01520$	Character $\chi_{5245}(1069, \cdot)$
1-5245-5245.1072-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1072	$0$	✓	✓	$0.0627$	$0$	$0.578412$	Character $\chi_{5245}(1072, \cdot)$
1-5245-5245.1073-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1073	$0$	✓	✓	$0.176$	$0$	$0.922050$	Character $\chi_{5245}(1073, \cdot)$
1-5245-5245.1074-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1074	$0$	✓	✓	$0.0103$	$0$	$1.16450$	Character $\chi_{5245}(1074, \cdot)$
1-5245-5245.1077-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1077	$0$	✓	✓	$-0.283$	$0$	$1.65384$	Character $\chi_{5245}(1077, \cdot)$
1-5245-5245.108-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.108	$0$	✓	✓	$0.0685$	$0$	$0.703389$	Character $\chi_{5245}(108, \cdot)$
1-5245-5245.1082-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1082	$0$	✓	✓	$0.450$	$0$	$1.25212$	Character $\chi_{5245}(1082, \cdot)$
1-5245-5245.1083-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1083	$0$	✓	✓	$0.0939$	$0$	$0.677224$	Character $\chi_{5245}(1083, \cdot)$
1-5245-5245.1088-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1088	$0$	✓	✓	$-0.0457$	$0$	$0.818199$	Character $\chi_{5245}(1088, \cdot)$
1-5245-5245.1089-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1089	$0$	✓	✓	$-0.0691$	$0$	$0.0492810$	Character $\chi_{5245}(1089, \cdot)$
1-5245-5245.1094-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1094	$0$	✓	✓	$-0.378$	$0$	$0.279059$	Character $\chi_{5245}(1094, \cdot)$
1-5245-5245.1097-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1097	$0$	✓	✓	$0.370$	$0$	$1.25008$	Character $\chi_{5245}(1097, \cdot)$
1-5245-5245.1099-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1099	$0$	✓	✓	$-0.216$	$0$	$0.442801$	Character $\chi_{5245}(1099, \cdot)$
1-5245-5245.1103-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1103	$0$	✓	✓	$0.439$	$0$	$0.0105875$	Character $\chi_{5245}(1103, \cdot)$
1-5245-5245.1104-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1104	$0$	✓	✓	$-0.0894$	$0$	$1.22842$	Character $\chi_{5245}(1104, \cdot)$
1-5245-5245.1112-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1112	$0$	✓	✓	$0.158$	$0$	$1.05967$	Character $\chi_{5245}(1112, \cdot)$
1-5245-5245.1114-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1114	$0$	✓	✓	$-0.489$	$0$	$0.380418$	Character $\chi_{5245}(1114, \cdot)$
1-5245-5245.1117-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1117	$0$	✓	✓	$-0.0685$	$0$	$0.736637$	Character $\chi_{5245}(1117, \cdot)$
1-5245-5245.112-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.112	$0$	✓	✓	$-0.165$	$0$	$1.98819$	Character $\chi_{5245}(112, \cdot)$
1-5245-5245.1123-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1123	$0$	✓	✓	$-0.255$	$0$	$1.58892$	Character $\chi_{5245}(1123, \cdot)$
1-5245-5245.1127-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1127	$0$	✓	✓	$-0.109$	$0$	$0.159322$	Character $\chi_{5245}(1127, \cdot)$
1-5245-5245.1129-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1129	$0$	✓	✓	$0.0116$	$0$	$1.16407$	Character $\chi_{5245}(1129, \cdot)$
1-5245-5245.1132-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1132	$0$	✓	✓	$0.147$	$0$	$0.912774$	Character $\chi_{5245}(1132, \cdot)$
1-5245-5245.1138-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1138	$0$	✓	✓	$0.290$	$0$	$0.787597$	Character $\chi_{5245}(1138, \cdot)$
1-5245-5245.1139-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1139	$0$	✓	✓	$-0.353$	$0$	$1.15651$	Character $\chi_{5245}(1139, \cdot)$
1-5245-5245.1143-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1143	$0$	✓	✓	$-0.316$	$0$	$0.369915$	Character $\chi_{5245}(1143, \cdot)$
1-5245-5245.1144-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1144	$0$	✓	✓	$0.350$	$0$	$0.166051$	Character $\chi_{5245}(1144, \cdot)$
1-5245-5245.1149-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1149	$0$	✓	✓	$0.243$	$0$	$0.107112$	Character $\chi_{5245}(1149, \cdot)$
1-5245-5245.1154-r0-0-0	$24.3$	$24.3$	$1$	$5 \cdot 1049$	5245.1154	$0$	✓	✓	$-0.287$	$0$	$0.869531$	Character $\chi_{5245}(1154, \cdot)$

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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 $\F_{q}$
Belyi maps

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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.