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
1-5225-5225.1004-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1004	$0$	✓	✓	$0.0275$	$0$	$0.554397$	Character $\chi_{5225}(1004, \cdot)$
1-5225-5225.1009-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1009	$0$	✓	✓	$0.154$	$0$	$1.28069$	Character $\chi_{5225}(1009, \cdot)$
1-5225-5225.1016-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1016	$0$	✓	✓	$-0.113$	$0$	$1.15478$	Character $\chi_{5225}(1016, \cdot)$
1-5225-5225.1017-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1017	$0$	✓	✓	$-0.0602$	$0$	$0.920819$	Character $\chi_{5225}(1017, \cdot)$
1-5225-5225.1019-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1019	$0$	✓	✓	$-0.199$	$0$	$0.367691$	Character $\chi_{5225}(1019, \cdot)$
1-5225-5225.1028-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1028	$0$	✓	✓	$0.145$	$0$	$0.923567$	Character $\chi_{5225}(1028, \cdot)$
1-5225-5225.1029-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1029	$0$	✓	✓	$-0.0397$	$0$	$0.477772$	Character $\chi_{5225}(1029, \cdot)$
1-5225-5225.103-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.103	$0$	✓	✓	$0.0926$	$0$	$0.822539$	Character $\chi_{5225}(103, \cdot)$
1-5225-5225.1033-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1033	$0$	✓	✓	$0.276$	$0$	$1.14384$	Character $\chi_{5225}(1033, \cdot)$
1-5225-5225.1036-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1036	$0$	✓	✓	$0.153$	$0$	$0.00607594$	Character $\chi_{5225}(1036, \cdot)$
1-5225-5225.1038-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1038	$0$	✓	✓	$0.284$	$0$	$1.71205$	Character $\chi_{5225}(1038, \cdot)$
1-5225-5225.104-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.104	$0$	✓	✓	$0.485$	$0$	$0.386710$	Character $\chi_{5225}(104, \cdot)$
1-5225-5225.1041-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1041	$0$	✓	✓	$-0.433$	$0$	$0.285335$	Character $\chi_{5225}(1041, \cdot)$
1-5225-5225.1042-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1042	$0$	✓	✓	$0.362$	$0$	$0.924198$	Character $\chi_{5225}(1042, \cdot)$
1-5225-5225.1044-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1044	$0$	✓	✓	$-0.440$	$0$	$0.717066$	Character $\chi_{5225}(1044, \cdot)$
1-5225-5225.1048-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1048	$0$	✓	✓	$-0.217$	$0$	$0.432636$	Character $\chi_{5225}(1048, \cdot)$
1-5225-5225.1052-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1052	$0$	✓	✓	$-0.274$	$0$	$1.77254$	Character $\chi_{5225}(1052, \cdot)$
1-5225-5225.1054-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1054	$0$	✓	✓	$0.399$	$0$	$0.709497$	Character $\chi_{5225}(1054, \cdot)$
1-5225-5225.1061-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1061	$0$	✓	✓	$0.354$	$0$	$1.15291$	Character $\chi_{5225}(1061, \cdot)$
1-5225-5225.1062-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1062	$0$	✓	✓	$0.430$	$0$	$0.279640$	Character $\chi_{5225}(1062, \cdot)$
1-5225-5225.1066-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1066	$0$	✓	✓	$0.492$	$0$	$0.186610$	Character $\chi_{5225}(1066, \cdot)$
1-5225-5225.1071-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1071	$0$	✓	✓	$-0.290$	$0$	$1.63188$	Character $\chi_{5225}(1071, \cdot)$
1-5225-5225.1072-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1072	$0$	✓	✓	$0.331$	$0$	$0.705670$	Character $\chi_{5225}(1072, \cdot)$
1-5225-5225.1073-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1073	$0$	✓	✓	$0.276$	$0$	$0.449164$	Character $\chi_{5225}(1073, \cdot)$
1-5225-5225.108-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.108	$0$	✓	✓	$0.100$	$0$	$0.859233$	Character $\chi_{5225}(108, \cdot)$
1-5225-5225.1081-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1081	$0$	✓	✓	$-0.246$	$0$	$0.551234$	Character $\chi_{5225}(1081, \cdot)$
1-5225-5225.1086-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1086	$0$	✓	✓	$0.247$	$0$	$0.985288$	Character $\chi_{5225}(1086, \cdot)$
1-5225-5225.1088-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1088	$0$	✓	✓	$0.0584$	$0$	$0.356271$	Character $\chi_{5225}(1088, \cdot)$
1-5225-5225.109-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.109	$0$	✓	✓	$-0.0675$	$0$	$0.637998$	Character $\chi_{5225}(109, \cdot)$
1-5225-5225.1091-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1091	$0$	✓	✓	$0.325$	$0$	$0.720258$	Character $\chi_{5225}(1091, \cdot)$
1-5225-5225.1094-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1094	$0$	✓	✓	$0.136$	$0$	$1.04672$	Character $\chi_{5225}(1094, \cdot)$
1-5225-5225.1096-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1096	$0$	✓	✓	$0.112$	$0$	$0.639997$	Character $\chi_{5225}(1096, \cdot)$
1-5225-5225.1098-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1098	$0$	✓	✓	$0.0247$	$0$	$0.818205$	Character $\chi_{5225}(1098, \cdot)$
1-5225-5225.1108-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1108	$0$	✓	✓	$-0.420$	$0$	$0.897577$	Character $\chi_{5225}(1108, \cdot)$
1-5225-5225.1109-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1109	$0$	✓	✓	$0.00340$	$0$	$0.857526$	Character $\chi_{5225}(1109, \cdot)$
1-5225-5225.1113-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1113	$0$	✓	✓	$-0.239$	$0$	$0.357440$	Character $\chi_{5225}(1113, \cdot)$
1-5225-5225.112-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.112	$0$	✓	✓	$-0.276$	$0$	$1.81540$	Character $\chi_{5225}(112, \cdot)$
1-5225-5225.1128-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1128	$0$	✓	✓	$0.00962$	$0$	$1.01433$	Character $\chi_{5225}(1128, \cdot)$
1-5225-5225.1129-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1129	$0$	✓	✓	$-0.122$	$0$	$0.452789$	Character $\chi_{5225}(1129, \cdot)$
1-5225-5225.113-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.113	$0$	✓	✓	$0.276$	$0$	$0.476467$	Character $\chi_{5225}(113, \cdot)$
1-5225-5225.1139-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1139	$0$	✓	✓	$-0.226$	$0$	$0.875223$	Character $\chi_{5225}(1139, \cdot)$
1-5225-5225.1142-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1142	$0$	✓	✓	$-0.319$	$0$	$1.50058$	Character $\chi_{5225}(1142, \cdot)$
1-5225-5225.1148-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1148	$0$	✓	✓	$-0.177$	$0$	$0.696705$	Character $\chi_{5225}(1148, \cdot)$
1-5225-5225.1153-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1153	$0$	✓	✓	$0.480$	$0$	$0.125942$	Character $\chi_{5225}(1153, \cdot)$
1-5225-5225.1154-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1154	$0$	✓	✓	$-0.207$	$0$	$0.623010$	Character $\chi_{5225}(1154, \cdot)$
1-5225-5225.1158-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1158	$0$	✓	✓	$-0.493$	$0$	$1.46754$	Character $\chi_{5225}(1158, \cdot)$
1-5225-5225.116-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.116	$0$	✓	✓	$-0.153$	$0$	$1.29501$	Character $\chi_{5225}(116, \cdot)$
1-5225-5225.1161-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1161	$0$	✓	✓	$-0.313$	$0$	$0.434517$	Character $\chi_{5225}(1161, \cdot)$
1-5225-5225.1163-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1163	$0$	✓	✓	$0.262$	$0$	$0.751212$	Character $\chi_{5225}(1163, \cdot)$
1-5225-5225.1164-r0-0-0	$24.2$	$24.2$	$1$	$5^{2} \cdot 11 \cdot 19$	5225.1164	$0$	✓	✓	$-0.144$	$0$	$0.758895$	Character $\chi_{5225}(1164, \cdot)$

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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.