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 479 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1157-1157.10-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.10	$0$	✓	✓	$0.200$	$0$	$0.897828$	Character $\chi_{1157}(10, \cdot)$
1-1157-1157.100-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.100	$0$	✓	✓	$-0.476$	$0$	$0.835328$	Character $\chi_{1157}(100, \cdot)$
1-1157-1157.1000-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1000	$0$	✓	✓	$-0.203$	$0$	$0.866959$	Character $\chi_{1157}(1000, \cdot)$
1-1157-1157.1003-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1003	$0$	✓	✓	$-0.223$	$0$	$1.14172$	Character $\chi_{1157}(1003, \cdot)$
1-1157-1157.1004-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1004	$0$	✓	✓	$-0.195$	$0$	$0.917343$	Character $\chi_{1157}(1004, \cdot)$
1-1157-1157.1006-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1006	$0$	✓	✓	$0.286$	$0$	$1.40504$	Character $\chi_{1157}(1006, \cdot)$
1-1157-1157.1007-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1007	$0$	✓	✓	$-0.372$	$0$	$0.766515$	Character $\chi_{1157}(1007, \cdot)$
1-1157-1157.1008-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1008	$0$	✓	✓	$0.239$	$0$	$1.00233$	Character $\chi_{1157}(1008, \cdot)$
1-1157-1157.1009-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1009	$0$	✓	✓	$0.0484$	$0$	$1.12624$	Character $\chi_{1157}(1009, \cdot)$
1-1157-1157.1011-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1011	$0$	✓	✓	$0.345$	$0$	$1.14139$	Character $\chi_{1157}(1011, \cdot)$
1-1157-1157.1012-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1012	$0$	✓	✓	$0.0999$	$0$	$1.05883$	Character $\chi_{1157}(1012, \cdot)$
1-1157-1157.1013-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1013	$0$	✓	✓	$0.419$	$0$	$1.30871$	Character $\chi_{1157}(1013, \cdot)$
1-1157-1157.1016-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1016	$0$	✓	✓	$0.181$	$0$	$0.959828$	Character $\chi_{1157}(1016, \cdot)$
1-1157-1157.1018-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1018	$0$	✓	✓	$-0.139$	$0$	$1.07112$	Character $\chi_{1157}(1018, \cdot)$
1-1157-1157.102-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.102	$0$	✓	✓	$0.455$	$0$	$0.444167$	Character $\chi_{1157}(102, \cdot)$
1-1157-1157.1020-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1020	$0$	✓	✓	$-0.0181$	$0$	$0.715027$	Character $\chi_{1157}(1020, \cdot)$
1-1157-1157.1022-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1022	$0$	✓	✓	$-0.0326$	$0$	$0.141574$	Character $\chi_{1157}(1022, \cdot)$
1-1157-1157.1023-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1023	$0$	✓	✓	$0.101$	$0$	$1.57426$	Character $\chi_{1157}(1023, \cdot)$
1-1157-1157.1024-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1024	$0$	✓	✓	$-0.325$	$0$	$0.534153$	Character $\chi_{1157}(1024, \cdot)$
1-1157-1157.1025-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1025	$0$	✓	✓	$0.0357$	$0$	$1.05842$	Character $\chi_{1157}(1025, \cdot)$
1-1157-1157.1026-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1026	$0$	✓	✓	$0.182$	$0$	$0.770525$	Character $\chi_{1157}(1026, \cdot)$
1-1157-1157.1033-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1033	$0$	✓	✓	$-0.388$	$0$	$1.13646$	Character $\chi_{1157}(1033, \cdot)$
1-1157-1157.1035-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1035	$0$	✓	✓	$-0.419$	$0$	$0.444353$	Character $\chi_{1157}(1035, \cdot)$
1-1157-1157.1036-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1036	$0$	✓	✓	$0.195$	$0$	$0.814236$	Character $\chi_{1157}(1036, \cdot)$
1-1157-1157.1038-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1038	$0$	✓	✓	$0.0601$	$0$	$1.04301$	Character $\chi_{1157}(1038, \cdot)$
1-1157-1157.1042-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1042	$0$	✓	✓	$0.0914$	$0$	$0.482241$	Character $\chi_{1157}(1042, \cdot)$
1-1157-1157.1043-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1043	$0$	✓	✓	$-0.0548$	$0$	$0.849858$	Character $\chi_{1157}(1043, \cdot)$
1-1157-1157.1045-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1045	$0$	✓	✓	$0.489$	$0$	$2.16184$	Character $\chi_{1157}(1045, \cdot)$
1-1157-1157.1050-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1050	$0$	✓	✓	$0.210$	$0$	$1.55456$	Character $\chi_{1157}(1050, \cdot)$
1-1157-1157.1052-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1052	$0$	✓	✓	$-0.178$	$0$	$2.31717$	Character $\chi_{1157}(1052, \cdot)$
1-1157-1157.1055-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1055	$0$	✓	✓	$0.424$	$0$	$1.32006$	Character $\chi_{1157}(1055, \cdot)$
1-1157-1157.1057-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1057	$0$	✓	✓	$-0.262$	$0$	$0.00750768$	Character $\chi_{1157}(1057, \cdot)$
1-1157-1157.1061-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1061	$0$	✓	✓	$-0.177$	$0$	$0.910555$	Character $\chi_{1157}(1061, \cdot)$
1-1157-1157.1063-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1063	$0$	✓	✓	$0.285$	$0$	$1.27582$	Character $\chi_{1157}(1063, \cdot)$
1-1157-1157.107-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.107	$0$	✓	✓	$-0.227$	$0$	$0.312977$	Character $\chi_{1157}(107, \cdot)$
1-1157-1157.1070-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1070	$0$	✓	✓	$0.325$	$0$	$1.71684$	Character $\chi_{1157}(1070, \cdot)$
1-1157-1157.1071-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1071	$0$	✓	✓	$-0.0484$	$0$	$1.36147$	Character $\chi_{1157}(1071, \cdot)$
1-1157-1157.1074-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1074	$0$	✓	✓	$0.387$	$0$	$1.06886$	Character $\chi_{1157}(1074, \cdot)$
1-1157-1157.1076-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1076	$0$	✓	✓	$0.262$	$0$	$1.25397$	Character $\chi_{1157}(1076, \cdot)$
1-1157-1157.1078-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1078	$0$	✓	✓	$-0.0476$	$0$	$0.826339$	Character $\chi_{1157}(1078, \cdot)$
1-1157-1157.1081-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1081	$0$	✓	✓	$-0.137$	$0$	$0.370217$	Character $\chi_{1157}(1081, \cdot)$
1-1157-1157.1087-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1087	$0$	✓	✓	$0.127$	$0$	$1.19910$	Character $\chi_{1157}(1087, \cdot)$
1-1157-1157.1088-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1088	$0$	✓	✓	$0.245$	$0$	$1.28172$	Character $\chi_{1157}(1088, \cdot)$
1-1157-1157.1089-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1089	$0$	✓	✓	$0.0446$	$0$	$0.923024$	Character $\chi_{1157}(1089, \cdot)$
1-1157-1157.1094-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1094	$0$	✓	✓	$-0.284$	$0$	$0.594459$	Character $\chi_{1157}(1094, \cdot)$
1-1157-1157.1097-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1097	$0$	✓	✓	$0.0326$	$0$	$0.588273$	Character $\chi_{1157}(1097, \cdot)$
1-1157-1157.1098-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1098	$0$	✓	✓	$-0.244$	$0$	$0.462068$	Character $\chi_{1157}(1098, \cdot)$
1-1157-1157.1099-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1099	$0$	✓	✓	$-0.112$	$0$	$1.11550$	Character $\chi_{1157}(1099, \cdot)$
1-1157-1157.1102-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1102	$0$	✓	✓	$-0.332$	$0$	$0.757767$	Character $\chi_{1157}(1102, \cdot)$
1-1157-1157.1103-r0-0-0	$5.37$	$5.37$	$1$	$13 \cdot 89$	1157.1103	$0$	✓	✓	$0.372$	$0$	$2.10705$	Character $\chi_{1157}(1103, \cdot)$

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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.