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 675 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1309-1309.1005-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1005	$0$	✓	✓	$-0.422$	$0$	$0.251088$	Character $\chi_{1309}(1005, \cdot)$
1-1309-1309.1006-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1006	$0$	✓	✓	$0.0521$	$0$	$1.69263$	Character $\chi_{1309}(1006, \cdot)$
1-1309-1309.1007-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1007	$0$	✓	✓	$-0.290$	$0$	$0.239621$	Character $\chi_{1309}(1007, \cdot)$
1-1309-1309.101-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.101	$0$	✓	✓	$0.166$	$0$	$0.845085$	Character $\chi_{1309}(101, \cdot)$
1-1309-1309.1011-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1011	$0$	✓	✓	$-0.467$	$0$	$0.490070$	Character $\chi_{1309}(1011, \cdot)$
1-1309-1309.1018-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1018	$0$	✓	✓	$-0.138$	$0$	$0.639408$	Character $\chi_{1309}(1018, \cdot)$
1-1309-1309.1027-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1027	$0$	✓	✓	$-0.377$	$0$	$1.68280$	Character $\chi_{1309}(1027, \cdot)$
1-1309-1309.1031-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1031	$0$	✓	✓	$0.401$	$0$	$1.83517$	Character $\chi_{1309}(1031, \cdot)$
1-1309-1309.1032-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1032	$0$	✓	✓	$-0.421$	$0$	$1.42427$	Character $\chi_{1309}(1032, \cdot)$
1-1309-1309.1040-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1040	$0$	✓	✓	$0.289$	$0$	$1.63246$	Character $\chi_{1309}(1040, \cdot)$
1-1309-1309.1041-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1041	$0$	✓	✓	$-0.325$	$0$	$0.588551$	Character $\chi_{1309}(1041, \cdot)$
1-1309-1309.1047-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1047	$0$	✓	✓	$-0.0476$	$0$	$0.929084$	Character $\chi_{1309}(1047, \cdot)$
1-1309-1309.1048-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1048	$0$	✓	✓	$0.323$	$0$	$0.0667222$	Character $\chi_{1309}(1048, \cdot)$
1-1309-1309.1049-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1049	$0$	✓	✓	$-0.0954$	$0$	$0.855368$	Character $\chi_{1309}(1049, \cdot)$
1-1309-1309.1053-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1053	$0$	✓	✓	$-0.318$	$0$	$0.433342$	Character $\chi_{1309}(1053, \cdot)$
1-1309-1309.1060-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1060	$0$	✓	✓	$-0.205$	$0$	$0.499556$	Character $\chi_{1309}(1060, \cdot)$
1-1309-1309.1062-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1062	$0$	✓	✓	$-0.154$	$0$	$0.659124$	Character $\chi_{1309}(1062, \cdot)$
1-1309-1309.1063-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1063	$0$	✓	✓	$-0.0286$	$0$	$0.569125$	Character $\chi_{1309}(1063, \cdot)$
1-1309-1309.1066-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1066	$0$	✓	✓	$-0.305$	$0$	$0.336135$	Character $\chi_{1309}(1066, \cdot)$
1-1309-1309.1069-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1069	$0$	✓	✓	$0.114$	$0$	$1.42016$	Character $\chi_{1309}(1069, \cdot)$
1-1309-1309.107-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.107	$0$	✓	✓	$0.415$	$0$	$1.19343$	Character $\chi_{1309}(107, \cdot)$
1-1309-1309.1076-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1076	$0$	✓	✓	$0.0984$	$0$	$1.52218$	Character $\chi_{1309}(1076, \cdot)$
1-1309-1309.108-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.108	$0$	✓	✓	$-0.0521$	$0$	$1.27371$	Character $\chi_{1309}(108, \cdot)$
1-1309-1309.1081-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1081	$0$	✓	✓	$-0.384$	$0$	$0.931034$	Character $\chi_{1309}(1081, \cdot)$
1-1309-1309.1083-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1083	$0$	✓	✓	$-0.376$	$0$	$0.514081$	Character $\chi_{1309}(1083, \cdot)$
1-1309-1309.1084-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1084	$0$	✓	✓	$0.00200$	$0$	$0.667933$	Character $\chi_{1309}(1084, \cdot)$
1-1309-1309.1087-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1087	$0$	✓	✓	$0.0507$	$0$	$0.490427$	Character $\chi_{1309}(1087, \cdot)$
1-1309-1309.109-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.109	$0$	✓	✓	$-0.245$	$0$	$0.244452$	Character $\chi_{1309}(109, \cdot)$
1-1309-1309.1097-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1097	$0$	✓	✓	$-0.226$	$0$	$0.549270$	Character $\chi_{1309}(1097, \cdot)$
1-1309-1309.1098-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1098	$0$	✓	✓	$-0.143$	$0$	$0.430596$	Character $\chi_{1309}(1098, \cdot)$
1-1309-1309.1103-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1103	$0$	✓	✓	$0.0907$	$0$	$0.470723$	Character $\chi_{1309}(1103, \cdot)$
1-1309-1309.1108-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1108	$0$	✓	✓	$0.284$	$0$	$0.145186$	Character $\chi_{1309}(1108, \cdot)$
1-1309-1309.1110-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1110	$0$	✓	✓	$0.0678$	$0$	$0.960208$	Character $\chi_{1309}(1110, \cdot)$
1-1309-1309.1116-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1116	$0$	✓	✓	$0.210$	$0$	$0.274207$	Character $\chi_{1309}(1116, \cdot)$
1-1309-1309.1117-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1117	$0$	✓	✓	$-0.139$	$0$	$0.872117$	Character $\chi_{1309}(1117, \cdot)$
1-1309-1309.1118-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1118	$0$	✓	✓	$-0.0367$	$0$	$1.18398$	Character $\chi_{1309}(1118, \cdot)$
1-1309-1309.1125-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1125	$0$	✓	✓	$0.205$	$0$	$0.557873$	Character $\chi_{1309}(1125, \cdot)$
1-1309-1309.1129-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1129	$0$	✓	✓	$-0.228$	$0$	$0.848413$	Character $\chi_{1309}(1129, \cdot)$
1-1309-1309.1130-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1130	$0$	✓	✓	$-0.306$	$0$	$1.83923$	Character $\chi_{1309}(1130, \cdot)$
1-1309-1309.1131-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1131	$0$	✓	✓	$0.00373$	$0$	$0.858388$	Character $\chi_{1309}(1131, \cdot)$
1-1309-1309.1138-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1138	$0$	✓	✓	$-0.0507$	$0$	$0.496242$	Character $\chi_{1309}(1138, \cdot)$
1-1309-1309.1150-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1150	$0$	✓	✓	$-0.405$	$0$	$0.430752$	Character $\chi_{1309}(1150, \cdot)$
1-1309-1309.1153-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1153	$0$	✓	✓	$-0.210$	$0$	$2.30129$	Character $\chi_{1309}(1153, \cdot)$
1-1309-1309.1154-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1154	$0$	✓	✓	$-0.0120$	$0$	$1.05943$	Character $\chi_{1309}(1154, \cdot)$
1-1309-1309.116-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.116	$0$	✓	✓	$0.112$	$0$	$0.774638$	Character $\chi_{1309}(116, \cdot)$
1-1309-1309.1164-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1164	$0$	✓	✓	$0.0627$	$0$	$1.49588$	Character $\chi_{1309}(1164, \cdot)$
1-1309-1309.1165-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1165	$0$	✓	✓	$-0.347$	$0$	$1.44842$	Character $\chi_{1309}(1165, \cdot)$
1-1309-1309.117-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.117	$0$	✓	✓	$0.306$	$0$	$0.251554$	Character $\chi_{1309}(117, \cdot)$
1-1309-1309.1171-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1171	$0$	✓	✓	$0.124$	$0$	$1.07905$	Character $\chi_{1309}(1171, \cdot)$
1-1309-1309.1172-r0-0-0	$6.07$	$6.07$	$1$	$7 \cdot 11 \cdot 17$	1309.1172	$0$	✓	✓	$-0.126$	$0$	$0.620681$	Character $\chi_{1309}(1172, \cdot)$

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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.