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

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Results (1-50 of 84 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-368-368.101-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.101	$0$	✓	✓	$0.0474$	$0$	$1.56675$	Character $\chi_{368}(101, \cdot)$
1-368-368.107-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.107	$0$	✓	✓	$-0.382$	$0$	$0.487004$	Character $\chi_{368}(107, \cdot)$
1-368-368.11-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.11	$0$	✓	✓	$0.470$	$0$	$0.404549$	Character $\chi_{368}(11, \cdot)$
1-368-368.117-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.117	$0$	✓	✓	$0.398$	$0$	$2.03328$	Character $\chi_{368}(117, \cdot)$
1-368-368.13-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.13	$0$	✓	✓	$-0.0947$	$0$	$0.452141$	Character $\chi_{368}(13, \cdot)$
1-368-368.133-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.133	$0$	✓	✓	$-0.172$	$0$	$0.834156$	Character $\chi_{368}(133, \cdot)$
1-368-368.141-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.141	$0$	✓	✓	$0.193$	$0$	$1.63795$	Character $\chi_{368}(141, \cdot)$
1-368-368.155-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.155	$0$	✓	✓	$0.299$	$0$	$1.36858$	Character $\chi_{368}(155, \cdot)$
1-368-368.165-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.165	$0$	✓	✓	$-0.0210$	$0$	$1.06811$	Character $\chi_{368}(165, \cdot)$
1-368-368.171-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.171	$0$	✓	✓	$0.168$	$0$	$0.975087$	Character $\chi_{368}(171, \cdot)$
1-368-368.173-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.173	$0$	✓	✓	$-0.398$	$0$	$0.779101$	Character $\chi_{368}(173, \cdot)$
1-368-368.19-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.19	$0$	✓	✓	$-0.299$	$0$	$0.544907$	Character $\chi_{368}(19, \cdot)$
1-368-368.195-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.195	$0$	✓	✓	$0.0956$	$0$	$1.14307$	Character $\chi_{368}(195, \cdot)$
1-368-368.197-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.197	$0$	✓	✓	$-0.219$	$0$	$1.03915$	Character $\chi_{368}(197, \cdot)$
1-368-368.203-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.203	$0$	✓	✓	$0.0759$	$0$	$1.50580$	Character $\chi_{368}(203, \cdot)$
1-368-368.213-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.213	$0$	✓	✓	$-0.103$	$0$	$1.35452$	Character $\chi_{368}(213, \cdot)$
1-368-368.227-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.227	$0$	✓	✓	$0.382$	$0$	$1.78384$	Character $\chi_{368}(227, \cdot)$
1-368-368.235-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.235	$0$	✓	✓	$0.0766$	$0$	$1.60170$	Character $\chi_{368}(235, \cdot)$
1-368-368.251-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.251	$0$	✓	✓	$-0.0956$	$0$	$1.33088$	Character $\chi_{368}(251, \cdot)$
1-368-368.261-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.261	$0$	✓	✓	$-0.193$	$0$	$0.573795$	Character $\chi_{368}(261, \cdot)$
1-368-368.267-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.267	$0$	✓	✓	$0.298$	$0$	$1.67582$	Character $\chi_{368}(267, \cdot)$
1-368-368.269-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.269	$0$	✓	✓	$0.219$	$0$	$1.99456$	Character $\chi_{368}(269, \cdot)$
1-368-368.275-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.275	$0$	✓	✓	$0.312$	$0$	$1.72456$	Character $\chi_{368}(275, \cdot)$
1-368-368.283-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.283	$0$	✓	✓	$0.206$	$0$	$1.84356$	Character $\chi_{368}(283, \cdot)$
1-368-368.285-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.285	$0$	✓	✓	$0.172$	$0$	$1.35710$	Character $\chi_{368}(285, \cdot)$
1-368-368.29-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.29	$0$	✓	✓	$0.0210$	$0$	$0.848951$	Character $\chi_{368}(29, \cdot)$
1-368-368.291-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.291	$0$	✓	✓	$0.242$	$0$	$1.57314$	Character $\chi_{368}(291, \cdot)$
1-368-368.301-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.301	$0$	✓	✓	$-0.476$	$0$	$0.355859$	Character $\chi_{368}(301, \cdot)$
1-368-368.317-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.317	$0$	✓	✓	$-0.0474$	$0$	$1.21791$	Character $\chi_{368}(317, \cdot)$
1-368-368.325-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.325	$0$	✓	✓	$0.0680$	$0$	$1.08614$	Character $\chi_{368}(325, \cdot)$
1-368-368.339-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.339	$0$	✓	✓	$-0.0759$	$0$	$1.51252$	Character $\chi_{368}(339, \cdot)$
1-368-368.349-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.349	$0$	✓	✓	$0.103$	$0$	$1.55462$	Character $\chi_{368}(349, \cdot)$
1-368-368.355-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.355	$0$	✓	✓	$-0.206$	$0$	$1.03525$	Character $\chi_{368}(355, \cdot)$
1-368-368.357-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.357	$0$	✓	✓	$0.476$	$0$	$2.02222$	Character $\chi_{368}(357, \cdot)$
1-368-368.43-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.43	$0$	✓	✓	$-0.242$	$0$	$0.716496$	Character $\chi_{368}(43, \cdot)$
1-368-368.51-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.51	$0$	✓	✓	$-0.298$	$0$	$0.632058$	Character $\chi_{368}(51, \cdot)$
1-368-368.67-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.67	$0$	✓	✓	$-0.470$	$0$	$2.51028$	Character $\chi_{368}(67, \cdot)$
1-368-368.77-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.77	$0$	✓	✓	$-0.0680$	$0$	$1.14536$	Character $\chi_{368}(77, \cdot)$
1-368-368.83-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.83	$0$	✓	✓	$-0.0766$	$0$	$1.20444$	Character $\chi_{368}(83, \cdot)$
1-368-368.85-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.85	$0$	✓	✓	$0.0947$	$0$	$0.935766$	Character $\chi_{368}(85, \cdot)$
1-368-368.91-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.91	$0$	✓	✓	$-0.312$	$0$	$0.231803$	Character $\chi_{368}(91, \cdot)$
1-368-368.99-r0-0-0	$1.70$	$1.70$	$1$	$2^{4} \cdot 23$	368.99	$0$	✓	✓	$-0.168$	$0$	$0.627586$	Character $\chi_{368}(99, \cdot)$
1-368-368.109-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.109	$1$	✓	✓	$0.174$	$0$	$0.815079$	Character $\chi_{368}(109, \cdot)$
1-368-368.123-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.123	$1$	✓	✓	$-0.443$	$0$	$0.0493634$	Character $\chi_{368}(123, \cdot)$
1-368-368.125-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.125	$1$	✓	✓	$0.0437$	$0$	$1.00688$	Character $\chi_{368}(125, \cdot)$
1-368-368.131-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.131	$1$	✓	✓	$0.469$	$0$	$1.56727$	Character $\chi_{368}(131, \cdot)$
1-368-368.147-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.147	$1$	✓	✓	$0.422$	$0$	$1.78882$	Character $\chi_{368}(147, \cdot)$
1-368-368.149-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.149	$1$	✓	✓	$0.220$	$0$	$0.869521$	Character $\chi_{368}(149, \cdot)$
1-368-368.157-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.157	$1$	✓	✓	$-0.0490$	$0$	$0.430180$	Character $\chi_{368}(157, \cdot)$
1-368-368.163-r1-0-0	$39.5$	$39.5$	$1$	$2^{4} \cdot 23$	368.163	$1$	✓	✓	$-0.226$	$0$	$0.431977$	Character $\chi_{368}(163, \cdot)$

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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.