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 708 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-2864-2864.1005-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1005	$0$	✓	✓	$0.483$	$0$	$0.103173$	Character $\chi_{2864}(1005, \cdot)$
1-2864-2864.101-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.101	$0$	✓	✓	$0.412$	$0$	$1.62133$	Character $\chi_{2864}(101, \cdot)$
1-2864-2864.1021-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1021	$0$	✓	✓	$-0.0374$	$0$	$0.598217$	Character $\chi_{2864}(1021, \cdot)$
1-2864-2864.1027-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1027	$0$	✓	✓	$0.427$	$0$	$0.112285$	Character $\chi_{2864}(1027, \cdot)$
1-2864-2864.1035-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1035	$0$	✓	✓	$-0.211$	$0$	$0.718322$	Character $\chi_{2864}(1035, \cdot)$
1-2864-2864.1037-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1037	$0$	✓	✓	$-0.143$	$0$	$0.575218$	Character $\chi_{2864}(1037, \cdot)$
1-2864-2864.1043-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1043	$0$	✓	✓	$-0.0131$	$0$	$0.858854$	Character $\chi_{2864}(1043, \cdot)$
1-2864-2864.1053-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1053	$0$	✓	✓	$-0.0146$	$0$	$0.981054$	Character $\chi_{2864}(1053, \cdot)$
1-2864-2864.1059-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1059	$0$	✓	✓	$0.108$	$0$	$0.953511$	Character $\chi_{2864}(1059, \cdot)$
1-2864-2864.1077-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1077	$0$	✓	✓	$-0.280$	$0$	$0.0450519$	Character $\chi_{2864}(1077, \cdot)$
1-2864-2864.1093-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1093	$0$	✓	✓	$-0.316$	$0$	$0.0433342$	Character $\chi_{2864}(1093, \cdot)$
1-2864-2864.11-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.11	$0$	✓	✓	$-0.267$	$0$	$0.235461$	Character $\chi_{2864}(11, \cdot)$
1-2864-2864.1101-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1101	$0$	✓	✓	$-0.337$	$0$	$0.786917$	Character $\chi_{2864}(1101, \cdot)$
1-2864-2864.1107-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1107	$0$	✓	✓	$0.355$	$0$	$1.12022$	Character $\chi_{2864}(1107, \cdot)$
1-2864-2864.1115-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1115	$0$	✓	✓	$0.329$	$0$	$0.883969$	Character $\chi_{2864}(1115, \cdot)$
1-2864-2864.1117-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1117	$0$	✓	✓	$0.0307$	$0$	$0.717201$	Character $\chi_{2864}(1117, \cdot)$
1-2864-2864.1125-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1125	$0$	✓	✓	$0.324$	$0$	$1.38009$	Character $\chi_{2864}(1125, \cdot)$
1-2864-2864.1133-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1133	$0$	✓	✓	$-0.202$	$0$	$0.311656$	Character $\chi_{2864}(1133, \cdot)$
1-2864-2864.1141-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1141	$0$	✓	✓	$-0.177$	$0$	$0.887253$	Character $\chi_{2864}(1141, \cdot)$
1-2864-2864.1147-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1147	$0$	✓	✓	$-0.309$	$0$	$0.362886$	Character $\chi_{2864}(1147, \cdot)$
1-2864-2864.1149-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1149	$0$	✓	✓	$0.0601$	$0$	$0.437489$	Character $\chi_{2864}(1149, \cdot)$
1-2864-2864.115-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.115	$0$	✓	✓	$-0.224$	$0$	$1.53744$	Character $\chi_{2864}(115, \cdot)$
1-2864-2864.1157-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1157	$0$	✓	✓	$-0.483$	$0$	$1.24527$	Character $\chi_{2864}(1157, \cdot)$
1-2864-2864.117-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.117	$0$	✓	✓	$-0.0497$	$0$	$0.914044$	Character $\chi_{2864}(117, \cdot)$
1-2864-2864.1171-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1171	$0$	✓	✓	$-0.109$	$0$	$0.474326$	Character $\chi_{2864}(1171, \cdot)$
1-2864-2864.1179-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1179	$0$	✓	✓	$-0.303$	$0$	$0.276556$	Character $\chi_{2864}(1179, \cdot)$
1-2864-2864.1181-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1181	$0$	✓	✓	$-0.168$	$0$	$0.182460$	Character $\chi_{2864}(1181, \cdot)$
1-2864-2864.1187-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1187	$0$	✓	✓	$-0.367$	$0$	$0.425514$	Character $\chi_{2864}(1187, \cdot)$
1-2864-2864.1211-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1211	$0$	✓	✓	$0.364$	$0$	$1.15619$	Character $\chi_{2864}(1211, \cdot)$
1-2864-2864.1213-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1213	$0$	✓	✓	$0.0134$	$0$	$0.924398$	Character $\chi_{2864}(1213, \cdot)$
1-2864-2864.1221-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1221	$0$	✓	✓	$-0.188$	$0$	$0.803938$	Character $\chi_{2864}(1221, \cdot)$
1-2864-2864.1229-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1229	$0$	✓	✓	$0.168$	$0$	$0.793201$	Character $\chi_{2864}(1229, \cdot)$
1-2864-2864.123-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.123	$0$	✓	✓	$0.0214$	$0$	$1.11840$	Character $\chi_{2864}(123, \cdot)$
1-2864-2864.1245-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1245	$0$	✓	✓	$0.177$	$0$	$1.36728$	Character $\chi_{2864}(1245, \cdot)$
1-2864-2864.125-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.125	$0$	✓	✓	$-0.165$	$0$	$0.385120$	Character $\chi_{2864}(125, \cdot)$
1-2864-2864.1259-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1259	$0$	✓	✓	$0.364$	$0$	$0.0651885$	Character $\chi_{2864}(1259, \cdot)$
1-2864-2864.1269-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1269	$0$	✓	✓	$-0.0964$	$0$	$0.105066$	Character $\chi_{2864}(1269, \cdot)$
1-2864-2864.1283-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1283	$0$	✓	✓	$-0.364$	$0$	$1.70880$	Character $\chi_{2864}(1283, \cdot)$
1-2864-2864.1291-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1291	$0$	✓	✓	$-0.355$	$0$	$0.497886$	Character $\chi_{2864}(1291, \cdot)$
1-2864-2864.13-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.13	$0$	✓	✓	$0.303$	$0$	$1.11358$	Character $\chi_{2864}(13, \cdot)$
1-2864-2864.1301-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1301	$0$	✓	✓	$-0.133$	$0$	$0.667549$	Character $\chi_{2864}(1301, \cdot)$
1-2864-2864.1307-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1307	$0$	✓	✓	$0.380$	$0$	$1.17874$	Character $\chi_{2864}(1307, \cdot)$
1-2864-2864.1309-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1309	$0$	✓	✓	$0.0964$	$0$	$0.842305$	Character $\chi_{2864}(1309, \cdot)$
1-2864-2864.131-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.131	$0$	✓	✓	$-0.329$	$0$	$0.352695$	Character $\chi_{2864}(131, \cdot)$
1-2864-2864.1315-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1315	$0$	✓	✓	$0.390$	$0$	$0.120428$	Character $\chi_{2864}(1315, \cdot)$
1-2864-2864.1317-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1317	$0$	✓	✓	$-0.420$	$0$	$0.111822$	Character $\chi_{2864}(1317, \cdot)$
1-2864-2864.1331-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1331	$0$	✓	✓	$0.211$	$0$	$1.39580$	Character $\chi_{2864}(1331, \cdot)$
1-2864-2864.1333-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1333	$0$	✓	✓	$-0.110$	$0$	$0.756291$	Character $\chi_{2864}(1333, \cdot)$
1-2864-2864.1339-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1339	$0$	✓	✓	$-0.463$	$0$	$0.0939237$	Character $\chi_{2864}(1339, \cdot)$
1-2864-2864.1341-r0-0-0	$13.3$	$13.3$	$1$	$2^{4} \cdot 179$	2864.1341	$0$	✓	✓	$-0.172$	$0$	$0.520279$	Character $\chi_{2864}(1341, \cdot)$

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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.