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 648 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1859-1859.1003-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1003	$0$	✓	✓	$-0.200$	$0$	$0.627039$	Character $\chi_{1859}(1003, \cdot)$
1-1859-1859.1004-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1004	$0$	✓	✓	$-0.395$	$0$	$1.18115$	Character $\chi_{1859}(1004, \cdot)$
1-1859-1859.1005-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1005	$0$	✓	✓	$-0.0494$	$0$	$0.727518$	Character $\chi_{1859}(1005, \cdot)$
1-1859-1859.1007-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1007	$0$	✓	✓	$-0.354$	$0$	$2.08096$	Character $\chi_{1859}(1007, \cdot)$
1-1859-1859.1008-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1008	$0$	✓	✓	$0.0167$	$0$	$1.27599$	Character $\chi_{1859}(1008, \cdot)$
1-1859-1859.1009-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1009	$0$	✓	✓	$0.289$	$0$	$1.44339$	Character $\chi_{1859}(1009, \cdot)$
1-1859-1859.1010-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1010	$0$	✓	✓	$0.463$	$0$	$1.49795$	Character $\chi_{1859}(1010, \cdot)$
1-1859-1859.1017-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1017	$0$	✓	✓	$-0.378$	$0$	$0.370755$	Character $\chi_{1859}(1017, \cdot)$
1-1859-1859.1019-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1019	$0$	✓	✓	$-0.132$	$0$	$0.887441$	Character $\chi_{1859}(1019, \cdot)$
1-1859-1859.1020-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1020	$0$	✓	✓	$-0.0611$	$0$	$0.673876$	Character $\chi_{1859}(1020, \cdot)$
1-1859-1859.1022-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1022	$0$	✓	✓	$-0.275$	$0$	$0.0459435$	Character $\chi_{1859}(1022, \cdot)$
1-1859-1859.1025-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1025	$0$	✓	✓	$0.299$	$0$	$1.28751$	Character $\chi_{1859}(1025, \cdot)$
1-1859-1859.1026-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1026	$0$	✓	✓	$-0.175$	$0$	$0.642908$	Character $\chi_{1859}(1026, \cdot)$
1-1859-1859.1028-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1028	$0$	✓	✓	$0.114$	$0$	$1.29784$	Character $\chi_{1859}(1028, \cdot)$
1-1859-1859.1029-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1029	$0$	✓	✓	$0.311$	$0$	$0.0319803$	Character $\chi_{1859}(1029, \cdot)$
1-1859-1859.103-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.103	$0$	✓	✓	$-0.484$	$0$	$1.42738$	Character $\chi_{1859}(103, \cdot)$
1-1859-1859.1039-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1039	$0$	✓	✓	$0.214$	$0$	$0.886923$	Character $\chi_{1859}(1039, \cdot)$
1-1859-1859.1042-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1042	$0$	✓	✓	$-0.0167$	$0$	$1.11726$	Character $\chi_{1859}(1042, \cdot)$
1-1859-1859.1043-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1043	$0$	✓	✓	$0.00402$	$0$	$0.942064$	Character $\chi_{1859}(1043, \cdot)$
1-1859-1859.1047-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1047	$0$	✓	✓	$0.317$	$0$	$0.837907$	Character $\chi_{1859}(1047, \cdot)$
1-1859-1859.1049-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1049	$0$	✓	✓	$-0.442$	$0$	$0.646857$	Character $\chi_{1859}(1049, \cdot)$
1-1859-1859.1050-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1050	$0$	✓	✓	$0.000902$	$0$	$1.47560$	Character $\chi_{1859}(1050, \cdot)$
1-1859-1859.1051-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1051	$0$	✓	✓	$-0.268$	$0$	$0.438850$	Character $\chi_{1859}(1051, \cdot)$
1-1859-1859.1054-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1054	$0$	✓	✓	$0.110$	$0$	$0.793302$	Character $\chi_{1859}(1054, \cdot)$
1-1859-1859.1055-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1055	$0$	✓	✓	$-0.0714$	$0$	$1.03752$	Character $\chi_{1859}(1055, \cdot)$
1-1859-1859.1058-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1058	$0$	✓	✓	$0.193$	$0$	$0.888100$	Character $\chi_{1859}(1058, \cdot)$
1-1859-1859.106-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.106	$0$	✓	✓	$0.377$	$0$	$0.270412$	Character $\chi_{1859}(106, \cdot)$
1-1859-1859.1064-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1064	$0$	✓	✓	$0.365$	$0$	$0.934291$	Character $\chi_{1859}(1064, \cdot)$
1-1859-1859.1065-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1065	$0$	✓	✓	$0.332$	$0$	$0.894475$	Character $\chi_{1859}(1065, \cdot)$
1-1859-1859.1070-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1070	$0$	✓	✓	$-0.182$	$0$	$0.710025$	Character $\chi_{1859}(1070, \cdot)$
1-1859-1859.1073-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1073	$0$	✓	✓	$0.415$	$0$	$1.49734$	Character $\chi_{1859}(1073, \cdot)$
1-1859-1859.1074-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1074	$0$	✓	✓	$0.0611$	$0$	$0.828083$	Character $\chi_{1859}(1074, \cdot)$
1-1859-1859.1076-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1076	$0$	✓	✓	$0.0523$	$0$	$0.786726$	Character $\chi_{1859}(1076, \cdot)$
1-1859-1859.1077-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1077	$0$	✓	✓	$-0.161$	$0$	$0.594311$	Character $\chi_{1859}(1077, \cdot)$
1-1859-1859.108-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.108	$0$	✓	✓	$0.000902$	$0$	$1.28455$	Character $\chi_{1859}(108, \cdot)$
1-1859-1859.1082-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1082	$0$	✓	✓	$-0.224$	$0$	$1.91854$	Character $\chi_{1859}(1082, \cdot)$
1-1859-1859.1083-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1083	$0$	✓	✓	$0.287$	$0$	$1.90517$	Character $\chi_{1859}(1083, \cdot)$
1-1859-1859.1085-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1085	$0$	✓	✓	$-0.365$	$0$	$0.452623$	Character $\chi_{1859}(1085, \cdot)$
1-1859-1859.1086-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1086	$0$	✓	✓	$0.465$	$0$	$0.470808$	Character $\chi_{1859}(1086, \cdot)$
1-1859-1859.109-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.109	$0$	✓	✓	$0.0221$	$0$	$0.726884$	Character $\chi_{1859}(109, \cdot)$
1-1859-1859.1093-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1093	$0$	✓	✓	$-0.235$	$0$	$0.309247$	Character $\chi_{1859}(1093, \cdot)$
1-1859-1859.1097-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1097	$0$	✓	✓	$-0.300$	$0$	$0.425384$	Character $\chi_{1859}(1097, \cdot)$
1-1859-1859.1099-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1099	$0$	✓	✓	$0.0532$	$0$	$0.843569$	Character $\chi_{1859}(1099, \cdot)$
1-1859-1859.1104-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1104	$0$	✓	✓	$-0.235$	$0$	$0.817697$	Character $\chi_{1859}(1104, \cdot)$
1-1859-1859.1107-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1107	$0$	✓	✓	$-0.138$	$0$	$0.798642$	Character $\chi_{1859}(1107, \cdot)$
1-1859-1859.1109-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1109	$0$	✓	✓	$-0.280$	$0$	$0.431820$	Character $\chi_{1859}(1109, \cdot)$
1-1859-1859.1110-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1110	$0$	✓	✓	$-0.446$	$0$	$1.14466$	Character $\chi_{1859}(1110, \cdot)$
1-1859-1859.1114-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1114	$0$	✓	✓	$-0.158$	$0$	$0.423503$	Character $\chi_{1859}(1114, \cdot)$
1-1859-1859.1115-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.1115	$0$	✓	✓	$-0.224$	$0$	$0.353286$	Character $\chi_{1859}(1115, \cdot)$
1-1859-1859.112-r0-0-0	$8.63$	$8.63$	$1$	$11 \cdot 13^{2}$	1859.112	$0$	✓	✓	$-0.491$	$0$	$0.633299$	Character $\chi_{1859}(112, \cdot)$

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Classical	Maass
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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.