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
1-6017-6017.1005-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1005	$0$	✓	✓	$-0.384$	$0$	$0.413299$	Character $\chi_{6017}(1005, \cdot)$
1-6017-6017.1006-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1006	$0$	✓	✓	$0.208$	$0$	$1.54176$	Character $\chi_{6017}(1006, \cdot)$
1-6017-6017.1008-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1008	$0$	✓	✓	$-0.167$	$0$	$0.610853$	Character $\chi_{6017}(1008, \cdot)$
1-6017-6017.1009-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1009	$0$	✓	✓	$-0.392$	$0$	$1.38340$	Character $\chi_{6017}(1009, \cdot)$
1-6017-6017.101-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.101	$0$	✓	✓	$0.0620$	$0$	$0.419892$	Character $\chi_{6017}(101, \cdot)$
1-6017-6017.1015-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1015	$0$	✓	✓	$0.487$	$0$	$0.842151$	Character $\chi_{6017}(1015, \cdot)$
1-6017-6017.1017-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1017	$0$	✓	✓	$-0.261$	$0$	$0.340018$	Character $\chi_{6017}(1017, \cdot)$
1-6017-6017.1018-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1018	$0$	✓	✓	$0.138$	$0$	$1.13962$	Character $\chi_{6017}(1018, \cdot)$
1-6017-6017.1020-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1020	$0$	✓	✓	$0.495$	$0$	$0.157095$	Character $\chi_{6017}(1020, \cdot)$
1-6017-6017.1025-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1025	$0$	✓	✓	$0.365$	$0$	$0.0798581$	Character $\chi_{6017}(1025, \cdot)$
1-6017-6017.1026-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1026	$0$	✓	✓	$-0.0802$	$0$	$0.880421$	Character $\chi_{6017}(1026, \cdot)$
1-6017-6017.1030-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1030	$0$	✓	✓	$0.305$	$0$	$0.611383$	Character $\chi_{6017}(1030, \cdot)$
1-6017-6017.1037-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1037	$0$	✓	✓	$-0.0772$	$0$	$0.768599$	Character $\chi_{6017}(1037, \cdot)$
1-6017-6017.1039-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1039	$0$	✓	✓	$0.396$	$0$	$0.881163$	Character $\chi_{6017}(1039, \cdot)$
1-6017-6017.1040-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1040	$0$	✓	✓	$0.334$	$0$	$0.306376$	Character $\chi_{6017}(1040, \cdot)$
1-6017-6017.1041-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1041	$0$	✓	✓	$0.495$	$0$	$0.0748108$	Character $\chi_{6017}(1041, \cdot)$
1-6017-6017.1042-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1042	$0$	✓	✓	$0.471$	$0$	$1.16617$	Character $\chi_{6017}(1042, \cdot)$
1-6017-6017.1047-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1047	$0$	✓	✓	$-0.174$	$0$	$1.85145$	Character $\chi_{6017}(1047, \cdot)$
1-6017-6017.1049-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1049	$0$	✓	✓	$0.0400$	$0$	$0.716869$	Character $\chi_{6017}(1049, \cdot)$
1-6017-6017.105-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.105	$0$	✓	✓	$-0.0169$	$0$	$0.435993$	Character $\chi_{6017}(105, \cdot)$
1-6017-6017.1058-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1058	$0$	✓	✓	$-0.138$	$0$	$0.246040$	Character $\chi_{6017}(1058, \cdot)$
1-6017-6017.106-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.106	$0$	✓	✓	$-0.441$	$0$	$1.66892$	Character $\chi_{6017}(106, \cdot)$
1-6017-6017.1061-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1061	$0$	✓	✓	$-0.347$	$0$	$0.561814$	Character $\chi_{6017}(1061, \cdot)$
1-6017-6017.1069-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1069	$0$	✓	✓	$0.456$	$0$	$0.722608$	Character $\chi_{6017}(1069, \cdot)$
1-6017-6017.107-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.107	$0$	✓	✓	$0.169$	$0$	$0.731441$	Character $\chi_{6017}(107, \cdot)$
1-6017-6017.1071-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1071	$0$	✓	✓	$-0.202$	$0$	$1.06851$	Character $\chi_{6017}(1071, \cdot)$
1-6017-6017.1072-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1072	$0$	✓	✓	$0.385$	$0$	$0.913122$	Character $\chi_{6017}(1072, \cdot)$
1-6017-6017.1073-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1073	$0$	✓	✓	$0.129$	$0$	$0.692506$	Character $\chi_{6017}(1073, \cdot)$
1-6017-6017.1075-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1075	$0$	✓	✓	$0.0414$	$0$	$0.691445$	Character $\chi_{6017}(1075, \cdot)$
1-6017-6017.1076-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1076	$0$	✓	✓	$0.114$	$0$	$0.334137$	Character $\chi_{6017}(1076, \cdot)$
1-6017-6017.1080-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1080	$0$	✓	✓	$-0.219$	$0$	$0.956197$	Character $\chi_{6017}(1080, \cdot)$
1-6017-6017.1082-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1082	$0$	✓	✓	$-0.0120$	$0$	$0.667497$	Character $\chi_{6017}(1082, \cdot)$
1-6017-6017.1084-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1084	$0$	✓	✓	$0.106$	$0$	$1.01496$	Character $\chi_{6017}(1084, \cdot)$
1-6017-6017.1085-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1085	$0$	✓	✓	$-0.175$	$0$	$0.366054$	Character $\chi_{6017}(1085, \cdot)$
1-6017-6017.1087-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1087	$0$	✓	✓	$-0.132$	$0$	$1.29727$	Character $\chi_{6017}(1087, \cdot)$
1-6017-6017.1088-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1088	$0$	✓	✓	$-0.137$	$0$	$0.546460$	Character $\chi_{6017}(1088, \cdot)$
1-6017-6017.109-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.109	$0$	✓	✓	$0.481$	$0$	$0.0967418$	Character $\chi_{6017}(109, \cdot)$
1-6017-6017.1092-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1092	$0$	✓	✓	$0.115$	$0$	$0.744681$	Character $\chi_{6017}(1092, \cdot)$
1-6017-6017.1096-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1096	$0$	✓	✓	$-0.321$	$0$	$0.111962$	Character $\chi_{6017}(1096, \cdot)$
1-6017-6017.1097-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1097	$0$	✓	✓	$0.319$	$0$	$1.20794$	Character $\chi_{6017}(1097, \cdot)$
1-6017-6017.1098-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1098	$0$	✓	✓	$-0.0805$	$0$	$0.516054$	Character $\chi_{6017}(1098, \cdot)$
1-6017-6017.1099-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1099	$0$	✓	✓	$0.167$	$0$	$1.16674$	Character $\chi_{6017}(1099, \cdot)$
1-6017-6017.1102-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1102	$0$	✓	✓	$-0.0191$	$0$	$0.0159426$	Character $\chi_{6017}(1102, \cdot)$
1-6017-6017.1103-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1103	$0$	✓	✓	$-0.384$	$0$	$0.846306$	Character $\chi_{6017}(1103, \cdot)$
1-6017-6017.1104-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1104	$0$	✓	✓	$-0.0947$	$0$	$0.511086$	Character $\chi_{6017}(1104, \cdot)$
1-6017-6017.1105-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1105	$0$	✓	✓	$-0.463$	$0$	$1.11761$	Character $\chi_{6017}(1105, \cdot)$
1-6017-6017.1106-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1106	$0$	✓	✓	$-0.149$	$0$	$0.832573$	Character $\chi_{6017}(1106, \cdot)$
1-6017-6017.1109-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1109	$0$	✓	✓	$-0.0777$	$0$	$0.881380$	Character $\chi_{6017}(1109, \cdot)$
1-6017-6017.1115-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1115	$0$	✓	✓	$-0.0126$	$0$	$0.412242$	Character $\chi_{6017}(1115, \cdot)$
1-6017-6017.1117-r0-0-0	$27.9$	$27.9$	$1$	$11 \cdot 547$	6017.1117	$0$	✓	✓	$0.442$	$0$	$0.986966$	Character $\chi_{6017}(1117, \cdot)$

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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.