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 82 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-221-221.10-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.10	$1$	✓	✓	$0.355$	$0$	$1.07365$	Character $\chi_{221}(10, \cdot)$
1-221-221.106-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.106	$1$	✓	✓	$0.184$	$0$	$1.27902$	Character $\chi_{221}(106, \cdot)$
1-221-221.107-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.107	$1$	✓	✓	$-0.337$	$0$	$0.545723$	Character $\chi_{221}(107, \cdot)$
1-221-221.108-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.108	$1$	✓	✓	$0.264$	$0$	$0.994517$	Character $\chi_{221}(108, \cdot)$
1-221-221.110-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.110	$1$	✓	✓	$-0.160$	$0$	$0.0267382$	Character $\chi_{221}(110, \cdot)$
1-221-221.111-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.111	$1$	✓	✓	$0.0531$	$0$	$1.29198$	Character $\chi_{221}(111, \cdot)$
1-221-221.113-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.113	$1$	✓	✓	$0.146$	$0$	$1.78374$	Character $\chi_{221}(113, \cdot)$
1-221-221.114-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.114	$1$	✓	✓	$-0.192$	$0$	$2.58163$	Character $\chi_{221}(114, \cdot)$
1-221-221.115-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.115	$1$	✓	✓	$-0.432$	$0$	$1.94573$	Character $\chi_{221}(115, \cdot)$
1-221-221.116-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.116	$1$	✓	✓	$-0.0222$	$0$	$0.334801$	Character $\chi_{221}(116, \cdot)$
1-221-221.12-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.12	$1$	✓	✓	$0.225$	$0$	$0.122322$	Character $\chi_{221}(12, \cdot)$
1-221-221.123-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.123	$1$	✓	✓	$0.432$	$0$	$0.116598$	Character $\chi_{221}(123, \cdot)$
1-221-221.126-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.126	$1$	✓	✓	$0.337$	$0$	$0.751445$	Character $\chi_{221}(126, \cdot)$
1-221-221.128-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.128	$1$	✓	✓	$-0.194$	$0$	$0.501022$	Character $\chi_{221}(128, \cdot)$
1-221-221.129-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.129	$1$	✓	✓	$-0.225$	$0$	$3.12098$	Character $\chi_{221}(129, \cdot)$
1-221-221.132-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.132	$1$	✓	✓	$0.473$	$0$	$0.219398$	Character $\chi_{221}(132, \cdot)$
1-221-221.133-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.133	$1$	✓	✓	$-0.146$	$0$	$0.698102$	Character $\chi_{221}(133, \cdot)$
1-221-221.135-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.135	$1$	✓	✓	$0.296$	$0$	$0.0193974$	Character $\chi_{221}(135, \cdot)$
1-221-221.138-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.138	$1$	✓	✓	$0.320$	$0$	$1.28201$	Character $\chi_{221}(138, \cdot)$
1-221-221.139-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.139	$1$	✓	✓	$0.278$	$0$	$1.46425$	Character $\chi_{221}(139, \cdot)$
1-221-221.142-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.142	$1$	✓	✓	$-0.154$	$0$	$1.06515$	Character $\chi_{221}(142, \cdot)$
1-221-221.145-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.145	$1$	✓	✓	$-0.288$	$0$	$0.328993$	Character $\chi_{221}(145, \cdot)$
1-221-221.146-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.146	$1$	✓	✓	$-0.349$	$0$	$0.705716$	Character $\chi_{221}(146, \cdot)$
1-221-221.147-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.147	$1$	✓	✓	$0.440$	$0$	$1.33600$	Character $\chi_{221}(147, \cdot)$
1-221-221.149-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.149	$1$	✓	✓	$-0.278$	$0$	$1.11148$	Character $\chi_{221}(149, \cdot)$
1-221-221.15-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.15	$1$	✓	✓	$0.0671$	$0$	$0.853413$	Character $\chi_{221}(15, \cdot)$
1-221-221.151-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.151	$1$	✓	✓	$0.441$	$0$	$1.39571$	Character $\chi_{221}(151, \cdot)$
1-221-221.159-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.159	$1$	✓	✓	$-0.278$	$0$	$0.255678$	Character $\chi_{221}(159, \cdot)$
1-221-221.160-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.160	$1$	✓	✓	$-0.367$	$0$	$0.422525$	Character $\chi_{221}(160, \cdot)$
1-221-221.161-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.161	$1$	✓	✓	$-0.441$	$0$	$0.315427$	Character $\chi_{221}(161, \cdot)$
1-221-221.162-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.162	$1$	✓	✓	$-0.0404$	$0$	$0.698989$	Character $\chi_{221}(162, \cdot)$
1-221-221.165-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.165	$1$	✓	✓	$0.349$	$0$	$1.86154$	Character $\chi_{221}(165, \cdot)$
1-221-221.173-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.173	$1$	✓	✓	$-0.426$	$0$	$0.406691$	Character $\chi_{221}(173, \cdot)$
1-221-221.174-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.174	$1$	✓	✓	$0.152$	$0$	$0.595945$	Character $\chi_{221}(174, \cdot)$
1-221-221.181-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.181	$1$	✓	✓	$0.0222$	$0$	$0.602255$	Character $\chi_{221}(181, \cdot)$
1-221-221.189-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.189	$1$	✓	✓	$0.288$	$0$	$0.829874$	Character $\chi_{221}(189, \cdot)$
1-221-221.19-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.19	$1$	✓	✓	$0.194$	$0$	$1.42673$	Character $\chi_{221}(19, \cdot)$
1-221-221.192-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.192	$1$	✓	✓	$0.367$	$0$	$1.26696$	Character $\chi_{221}(192, \cdot)$
1-221-221.194-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.194	$1$	✓	✓	$0.213$	$0$	$1.53252$	Character $\chi_{221}(194, \cdot)$
1-221-221.198-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.198	$1$	✓	✓	$-0.101$	$0$	$0.600819$	Character $\chi_{221}(198, \cdot)$
1-221-221.199-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.199	$1$	✓	✓	$-0.355$	$0$	$0.437492$	Character $\chi_{221}(199, \cdot)$
1-221-221.2-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.2	$1$	✓	✓	$-0.0531$	$0$	$0.247171$	Character $\chi_{221}(2, \cdot)$
1-221-221.200-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.200	$1$	✓	✓	$0.441$	$0$	$1.47481$	Character $\chi_{221}(200, \cdot)$
1-221-221.202-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.202	$1$	✓	✓	$0.408$	$0$	$2.12386$	Character $\chi_{221}(202, \cdot)$
1-221-221.203-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.203	$1$	✓	✓	$-0.296$	$0$	$1.58479$	Character $\chi_{221}(203, \cdot)$
1-221-221.206-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.206	$1$	✓	✓	$0.0404$	$0$	$1.25209$	Character $\chi_{221}(206, \cdot)$
1-221-221.207-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.207	$1$	✓	✓	$0.154$	$0$	$1.20746$	Character $\chi_{221}(207, \cdot)$
1-221-221.21-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.21	$1$	✓	✓	$-0.441$	$0$	$0.847655$	Character $\chi_{221}(21, \cdot)$
1-221-221.211-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.211	$1$	✓	✓	$0.0897$	$0$	$1.75200$	Character $\chi_{221}(211, \cdot)$
1-221-221.213-r1-0-0	$23.7$	$23.7$	$1$	$13 \cdot 17$	221.213	$1$	✓	✓	$-0.320$	$0$	$0.00254782$	Character $\chi_{221}(213, \cdot)$

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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.