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 5265 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6001-6001.10-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.10	$0$	✓	✓	$-0.0308$	$0$	$0.796093$	Character $\chi_{6001}(10, \cdot)$
1-6001-6001.100-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.100	$0$	✓	✓	$0.289$	$0$	$1.53395$	Character $\chi_{6001}(100, \cdot)$
1-6001-6001.1000-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1000	$0$	✓	✓	$-0.119$	$0$	$0.623392$	Character $\chi_{6001}(1000, \cdot)$
1-6001-6001.1001-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1001	$0$	✓	✓	$-0.262$	$0$	$0.147005$	Character $\chi_{6001}(1001, \cdot)$
1-6001-6001.1006-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1006	$0$	✓	✓	$-0.0288$	$0$	$0.875765$	Character $\chi_{6001}(1006, \cdot)$
1-6001-6001.1008-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1008	$0$	✓	✓	$-0.466$	$0$	$1.39835$	Character $\chi_{6001}(1008, \cdot)$
1-6001-6001.1012-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1012	$0$	✓	✓	$-0.387$	$0$	$0.901487$	Character $\chi_{6001}(1012, \cdot)$
1-6001-6001.1014-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1014	$0$	✓	✓	$-0.353$	$0$	$0.715742$	Character $\chi_{6001}(1014, \cdot)$
1-6001-6001.1016-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1016	$0$	✓	✓	$0.219$	$0$	$1.10768$	Character $\chi_{6001}(1016, \cdot)$
1-6001-6001.1018-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1018	$0$	✓	✓	$0.302$	$0$	$0.0701938$	Character $\chi_{6001}(1018, \cdot)$
1-6001-6001.1024-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1024	$0$	✓	✓	$0.355$	$0$	$0.662260$	Character $\chi_{6001}(1024, \cdot)$
1-6001-6001.1026-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1026	$0$	✓	✓	$-0.242$	$0$	$0.613027$	Character $\chi_{6001}(1026, \cdot)$
1-6001-6001.1029-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1029	$0$	✓	✓	$-0.140$	$0$	$0.645097$	Character $\chi_{6001}(1029, \cdot)$
1-6001-6001.1031-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1031	$0$	✓	✓	$0.345$	$0$	$0.986463$	Character $\chi_{6001}(1031, \cdot)$
1-6001-6001.1032-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1032	$0$	✓	✓	$0.436$	$0$	$1.17567$	Character $\chi_{6001}(1032, \cdot)$
1-6001-6001.1036-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1036	$0$	✓	✓	$-0.306$	$0$	$0.412128$	Character $\chi_{6001}(1036, \cdot)$
1-6001-6001.1041-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1041	$0$	✓	✓	$-0.278$	$0$	$0.560579$	Character $\chi_{6001}(1041, \cdot)$
1-6001-6001.1047-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1047	$0$	✓	✓	$0.226$	$0$	$1.31692$	Character $\chi_{6001}(1047, \cdot)$
1-6001-6001.1049-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1049	$0$	✓	✓	$0.332$	$0$	$0.162454$	Character $\chi_{6001}(1049, \cdot)$
1-6001-6001.105-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.105	$0$	✓	✓	$-0.244$	$0$	$0.0199387$	Character $\chi_{6001}(105, \cdot)$
1-6001-6001.1050-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1050	$0$	✓	✓	$-0.462$	$0$	$0.197135$	Character $\chi_{6001}(1050, \cdot)$
1-6001-6001.1058-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1058	$0$	✓	✓	$-0.144$	$0$	$1.45299$	Character $\chi_{6001}(1058, \cdot)$
1-6001-6001.1063-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1063	$0$	✓	✓	$-0.447$	$0$	$0.278207$	Character $\chi_{6001}(1063, \cdot)$
1-6001-6001.1064-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1064	$0$	✓	✓	$0.204$	$0$	$1.30182$	Character $\chi_{6001}(1064, \cdot)$
1-6001-6001.1065-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1065	$0$	✓	✓	$-0.0372$	$0$	$1.16755$	Character $\chi_{6001}(1065, \cdot)$
1-6001-6001.1066-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1066	$0$	✓	✓	$-0.0450$	$0$	$0.742211$	Character $\chi_{6001}(1066, \cdot)$
1-6001-6001.1067-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1067	$0$	✓	✓	$0.00379$	$0$	$0.920557$	Character $\chi_{6001}(1067, \cdot)$
1-6001-6001.107-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.107	$0$	✓	✓	$0.0268$	$0$	$1.03303$	Character $\chi_{6001}(107, \cdot)$
1-6001-6001.1070-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1070	$0$	✓	✓	$-0.194$	$0$	$0.579542$	Character $\chi_{6001}(1070, \cdot)$
1-6001-6001.1075-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1075	$0$	✓	✓	$0.343$	$0$	$1.03621$	Character $\chi_{6001}(1075, \cdot)$
1-6001-6001.108-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.108	$0$	✓	✓	$-0.345$	$0$	$0.140234$	Character $\chi_{6001}(108, \cdot)$
1-6001-6001.1080-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1080	$0$	✓	✓	$0.0555$	$0$	$0.229862$	Character $\chi_{6001}(1080, \cdot)$
1-6001-6001.1083-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1083	$0$	✓	✓	$-0.120$	$0$	$0.279352$	Character $\chi_{6001}(1083, \cdot)$
1-6001-6001.1084-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1084	$0$	✓	✓	$-0.0344$	$0$	$0.673648$	Character $\chi_{6001}(1084, \cdot)$
1-6001-6001.1085-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1085	$0$	✓	✓	$0.336$	$0$	$1.05156$	Character $\chi_{6001}(1085, \cdot)$
1-6001-6001.1097-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1097	$0$	✓	✓	$-0.187$	$0$	$0.857681$	Character $\chi_{6001}(1097, \cdot)$
1-6001-6001.1099-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1099	$0$	✓	✓	$0.257$	$0$	$0.568798$	Character $\chi_{6001}(1099, \cdot)$
1-6001-6001.1101-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1101	$0$	✓	✓	$-0.0705$	$0$	$0.985718$	Character $\chi_{6001}(1101, \cdot)$
1-6001-6001.1103-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1103	$0$	✓	✓	$0.0937$	$0$	$0.691079$	Character $\chi_{6001}(1103, \cdot)$
1-6001-6001.1109-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1109	$0$	✓	✓	$0.141$	$0$	$1.24497$	Character $\chi_{6001}(1109, \cdot)$
1-6001-6001.111-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.111	$0$	✓	✓	$0.211$	$0$	$0.657502$	Character $\chi_{6001}(111, \cdot)$
1-6001-6001.1110-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1110	$0$	✓	✓	$0.00484$	$0$	$0.824843$	Character $\chi_{6001}(1110, \cdot)$
1-6001-6001.1111-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1111	$0$	✓	✓	$0.459$	$0$	$0.199786$	Character $\chi_{6001}(1111, \cdot)$
1-6001-6001.1112-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1112	$0$	✓	✓	$-0.199$	$0$	$0.722550$	Character $\chi_{6001}(1112, \cdot)$
1-6001-6001.1115-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1115	$0$	✓	✓	$-0.293$	$0$	$0.788653$	Character $\chi_{6001}(1115, \cdot)$
1-6001-6001.1116-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1116	$0$	✓	✓	$-0.0340$	$0$	$0.481336$	Character $\chi_{6001}(1116, \cdot)$
1-6001-6001.112-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.112	$0$	✓	✓	$-0.136$	$0$	$0.319681$	Character $\chi_{6001}(112, \cdot)$
1-6001-6001.1120-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1120	$0$	✓	✓	$-0.364$	$0$	$0.380523$	Character $\chi_{6001}(1120, \cdot)$
1-6001-6001.1124-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1124	$0$	✓	✓	$-0.121$	$0$	$0.160219$	Character $\chi_{6001}(1124, \cdot)$
1-6001-6001.1125-r0-0-0	$27.8$	$27.8$	$1$	$17 \cdot 353$	6001.1125	$0$	✓	✓	$0.162$	$0$	$0.308076$	Character $\chi_{6001}(1125, \cdot)$

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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.