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 60 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-189-189.101-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.101	$0$	✓	✓	$-0.461$	$0$	$0.647805$	Character $\chi_{189}(101, \cdot)$
1-189-189.104-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.104	$0$	✓	✓	$-0.351$	$0$	$0.535793$	Character $\chi_{189}(104, \cdot)$
1-189-189.110-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.110	$0$	✓	✓	$-0.168$	$0$	$1.04690$	Character $\chi_{189}(110, \cdot)$
1-189-189.121-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.121	$0$	✓	✓	$0.158$	$0$	$1.84704$	Character $\chi_{189}(121, \cdot)$
1-189-189.122-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.122	$0$	✓	✓	$0.168$	$0$	$1.12740$	Character $\chi_{189}(122, \cdot)$
1-189-189.130-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.130	$0$	✓	✓	$0.304$	$0$	$2.34936$	Character $\chi_{189}(130, \cdot)$
1-189-189.131-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.131	$0$	✓	✓	$0.461$	$0$	$2.06236$	Character $\chi_{189}(131, \cdot)$
1-189-189.142-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.142	$0$	✓	✓	$0.0286$	$0$	$1.42399$	Character $\chi_{189}(142, \cdot)$
1-189-189.146-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.146	$0$	✓	✓	$0.0185$	$0$	$1.74324$	Character $\chi_{189}(146, \cdot)$
1-189-189.151-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.151	$0$	✓	✓	$-0.158$	$0$	$0.740564$	Character $\chi_{189}(151, \cdot)$
1-189-189.16-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.16	$0$	✓	✓	$-0.304$	$0$	$1.15562$	Character $\chi_{189}(16, \cdot)$
1-189-189.164-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.164	$0$	✓	✓	$0.205$	$0$	$1.50791$	Character $\chi_{189}(164, \cdot)$
1-189-189.167-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.167	$0$	✓	✓	$-0.0185$	$0$	$0.883675$	Character $\chi_{189}(167, \cdot)$
1-189-189.173-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.173	$0$	✓	✓	$-0.168$	$0$	$0.697594$	Character $\chi_{189}(173, \cdot)$
1-189-189.184-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.184	$0$	✓	✓	$0.158$	$0$	$1.22940$	Character $\chi_{189}(184, \cdot)$
1-189-189.185-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.185	$0$	✓	✓	$-0.165$	$0$	$1.50970$	Character $\chi_{189}(185, \cdot)$
1-189-189.20-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.20	$0$	✓	✓	$0.351$	$0$	$1.56459$	Character $\chi_{189}(20, \cdot)$
1-189-189.25-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.25	$0$	✓	✓	$-0.158$	$0$	$1.52687$	Character $\chi_{189}(25, \cdot)$
1-189-189.38-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.38	$0$	✓	✓	$0.205$	$0$	$2.07449$	Character $\chi_{189}(38, \cdot)$
1-189-189.4-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.4	$0$	✓	✓	$-0.0286$	$0$	$1.16703$	Character $\chi_{189}(4, \cdot)$
1-189-189.41-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.41	$0$	✓	✓	$-0.0185$	$0$	$1.85411$	Character $\chi_{189}(41, \cdot)$
1-189-189.47-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.47	$0$	✓	✓	$0.165$	$0$	$2.26919$	Character $\chi_{189}(47, \cdot)$
1-189-189.5-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.5	$0$	✓	✓	$-0.205$	$0$	$1.17245$	Character $\chi_{189}(5, \cdot)$
1-189-189.58-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.58	$0$	✓	✓	$-0.175$	$0$	$1.22636$	Character $\chi_{189}(58, \cdot)$
1-189-189.59-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.59	$0$	✓	✓	$0.168$	$0$	$1.75470$	Character $\chi_{189}(59, \cdot)$
1-189-189.67-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.67	$0$	✓	✓	$0.304$	$0$	$0.0448328$	Character $\chi_{189}(67, \cdot)$
1-189-189.68-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.68	$0$	✓	✓	$-0.205$	$0$	$1.04354$	Character $\chi_{189}(68, \cdot)$
1-189-189.79-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.79	$0$	✓	✓	$-0.304$	$0$	$2.81455$	Character $\chi_{189}(79, \cdot)$
1-189-189.83-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.83	$0$	✓	✓	$0.0185$	$0$	$1.59316$	Character $\chi_{189}(83, \cdot)$
1-189-189.88-r0-0-0	$0.877$	$0.877$	$1$	$3^{3} \cdot 7$	189.88	$0$	✓	✓	$0.175$	$0$	$1.36295$	Character $\chi_{189}(88, \cdot)$
1-189-189.103-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.103	$1$	✓	✓	$-0.455$	$0$	$1.78600$	Character $\chi_{189}(103, \cdot)$
1-189-189.11-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.11	$1$	✓	✓	$0.0917$	$0$	$1.49007$	Character $\chi_{189}(11, \cdot)$
1-189-189.115-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.115	$1$	✓	✓	$-0.211$	$0$	$2.47323$	Character $\chi_{189}(115, \cdot)$
1-189-189.124-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.124	$1$	✓	✓	$0.0816$	$0$	$1.55200$	Character $\chi_{189}(124, \cdot)$
1-189-189.128-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.128	$1$	✓	✓	$0.278$	$0$	$1.66837$	Character $\chi_{189}(128, \cdot)$
1-189-189.13-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.13	$1$	✓	✓	$-0.268$	$0$	$0.508968$	Character $\chi_{189}(13, \cdot)$
1-189-189.137-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.137	$1$	✓	✓	$0.0917$	$0$	$0.695335$	Character $\chi_{189}(137, \cdot)$
1-189-189.139-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.139	$1$	✓	✓	$0.398$	$0$	$2.05918$	Character $\chi_{189}(139, \cdot)$
1-189-189.149-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.149	$1$	✓	✓	$-0.0917$	$0$	$0.609512$	Character $\chi_{189}(149, \cdot)$
1-189-189.157-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.157	$1$	✓	✓	$-0.0816$	$0$	$0.700078$	Character $\chi_{189}(157, \cdot)$
1-189-189.158-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.158	$1$	✓	✓	$-0.278$	$0$	$0.657242$	Character $\chi_{189}(158, \cdot)$
1-189-189.160-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.160	$1$	✓	✓	$0.268$	$0$	$1.37337$	Character $\chi_{189}(160, \cdot)$
1-189-189.166-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.166	$1$	✓	✓	$0.211$	$0$	$0.0328311$	Character $\chi_{189}(166, \cdot)$
1-189-189.178-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.178	$1$	✓	✓	$0.455$	$0$	$0.0427766$	Character $\chi_{189}(178, \cdot)$
1-189-189.187-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.187	$1$	✓	✓	$0.0816$	$0$	$0.841442$	Character $\chi_{189}(187, \cdot)$
1-189-189.2-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.2	$1$	✓	✓	$-0.0547$	$0$	$1.26823$	Character $\chi_{189}(2, \cdot)$
1-189-189.23-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.23	$1$	✓	✓	$-0.425$	$0$	$1.50843$	Character $\chi_{189}(23, \cdot)$
1-189-189.31-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.31	$1$	✓	✓	$-0.415$	$0$	$1.68677$	Character $\chi_{189}(31, \cdot)$
1-189-189.32-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.32	$1$	✓	✓	$0.0547$	$0$	$1.08253$	Character $\chi_{189}(32, \cdot)$
1-189-189.34-r1-0-0	$20.3$	$20.3$	$1$	$3^{3} \cdot 7$	189.34	$1$	✓	✓	$-0.398$	$0$	$0.710318$	Character $\chi_{189}(34, \cdot)$

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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.