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 80 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-448-448.109-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.109	$0$	✓	✓	$-0.192$	$0$	$1.00805$	Character $\chi_{448}(109, \cdot)$
1-448-448.115-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.115	$0$	✓	✓	$-0.328$	$0$	$0.480598$	Character $\chi_{448}(115, \cdot)$
1-448-448.131-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.131	$0$	✓	✓	$-0.0774$	$0$	$1.06200$	Character $\chi_{448}(131, \cdot)$
1-448-448.139-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.139	$0$	✓	✓	$-0.109$	$0$	$1.39326$	Character $\chi_{448}(139, \cdot)$
1-448-448.149-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.149	$0$	✓	✓	$0.0673$	$0$	$1.20004$	Character $\chi_{448}(149, \cdot)$
1-448-448.165-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.165	$0$	✓	✓	$0.338$	$0$	$1.52153$	Character $\chi_{448}(165, \cdot)$
1-448-448.171-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.171	$0$	✓	✓	$0.0774$	$0$	$1.24576$	Character $\chi_{448}(171, \cdot)$
1-448-448.187-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.187	$0$	✓	✓	$0.328$	$0$	$1.53575$	Character $\chi_{448}(187, \cdot)$
1-448-448.19-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.19	$0$	✓	✓	$-0.202$	$0$	$0.805549$	Character $\chi_{448}(19, \cdot)$
1-448-448.195-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.195	$0$	✓	✓	$0.109$	$0$	$1.07706$	Character $\chi_{448}(195, \cdot)$
1-448-448.205-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.205	$0$	✓	✓	$0.161$	$0$	$1.33913$	Character $\chi_{448}(205, \cdot)$
1-448-448.221-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.221	$0$	✓	✓	$-0.0673$	$0$	$1.30712$	Character $\chi_{448}(221, \cdot)$
1-448-448.227-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.227	$0$	✓	✓	$0.296$	$0$	$1.37072$	Character $\chi_{448}(227, \cdot)$
1-448-448.243-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.243	$0$	✓	✓	$0.297$	$0$	$1.90542$	Character $\chi_{448}(243, \cdot)$
1-448-448.251-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.251	$0$	✓	✓	$-0.484$	$0$	$1.94239$	Character $\chi_{448}(251, \cdot)$
1-448-448.261-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.261	$0$	✓	✓	$-0.307$	$0$	$0.567839$	Character $\chi_{448}(261, \cdot)$
1-448-448.27-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.27	$0$	✓	✓	$0.0156$	$0$	$1.34869$	Character $\chi_{448}(27, \cdot)$
1-448-448.277-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.277	$0$	✓	✓	$0.213$	$0$	$1.75845$	Character $\chi_{448}(277, \cdot)$
1-448-448.283-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.283	$0$	✓	✓	$0.202$	$0$	$1.08584$	Character $\chi_{448}(283, \cdot)$
1-448-448.299-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.299	$0$	✓	✓	$-0.296$	$0$	$0.834181$	Character $\chi_{448}(299, \cdot)$
1-448-448.3-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.3	$0$	✓	✓	$0.296$	$0$	$1.78719$	Character $\chi_{448}(3, \cdot)$
1-448-448.307-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.307	$0$	✓	✓	$0.484$	$0$	$0.169662$	Character $\chi_{448}(307, \cdot)$
1-448-448.317-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.317	$0$	✓	✓	$-0.213$	$0$	$1.07219$	Character $\chi_{448}(317, \cdot)$
1-448-448.333-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.333	$0$	✓	✓	$0.307$	$0$	$1.40092$	Character $\chi_{448}(333, \cdot)$
1-448-448.339-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.339	$0$	✓	✓	$0.171$	$0$	$1.73856$	Character $\chi_{448}(339, \cdot)$
1-448-448.355-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.355	$0$	✓	✓	$-0.0774$	$0$	$0.800713$	Character $\chi_{448}(355, \cdot)$
1-448-448.363-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.363	$0$	✓	✓	$-0.109$	$0$	$0.467372$	Character $\chi_{448}(363, \cdot)$
1-448-448.37-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.37	$0$	✓	✓	$0.192$	$0$	$1.83443$	Character $\chi_{448}(37, \cdot)$
1-448-448.373-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.373	$0$	✓	✓	$0.0673$	$0$	$1.11512$	Character $\chi_{448}(373, \cdot)$
1-448-448.389-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.389	$0$	✓	✓	$-0.161$	$0$	$0.915912$	Character $\chi_{448}(389, \cdot)$
1-448-448.395-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.395	$0$	✓	✓	$0.0774$	$0$	$1.22246$	Character $\chi_{448}(395, \cdot)$
1-448-448.411-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.411	$0$	✓	✓	$-0.171$	$0$	$0.933785$	Character $\chi_{448}(411, \cdot)$
1-448-448.419-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.419	$0$	✓	✓	$0.109$	$0$	$1.50505$	Character $\chi_{448}(419, \cdot)$
1-448-448.429-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.429	$0$	✓	✓	$-0.338$	$0$	$0.429717$	Character $\chi_{448}(429, \cdot)$
1-448-448.445-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.445	$0$	✓	✓	$-0.0673$	$0$	$0.596919$	Character $\chi_{448}(445, \cdot)$
1-448-448.53-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.53	$0$	✓	✓	$0.213$	$0$	$1.22718$	Character $\chi_{448}(53, \cdot)$
1-448-448.59-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.59	$0$	✓	✓	$-0.297$	$0$	$0.828325$	Character $\chi_{448}(59, \cdot)$
1-448-448.75-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.75	$0$	✓	✓	$-0.296$	$0$	$0.0470954$	Character $\chi_{448}(75, \cdot)$
1-448-448.83-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.83	$0$	✓	✓	$-0.0156$	$0$	$0.903195$	Character $\chi_{448}(83, \cdot)$
1-448-448.93-r0-0-0	$2.08$	$2.08$	$1$	$2^{6} \cdot 7$	448.93	$0$	✓	✓	$-0.213$	$0$	$0.242920$	Character $\chi_{448}(93, \cdot)$
1-448-448.101-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.101	$1$	✓	✓	$0.452$	$0$	$0.0899990$	Character $\chi_{448}(101, \cdot)$
1-448-448.107-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.107	$1$	✓	✓	$0.317$	$0$	$0.979014$	Character $\chi_{448}(107, \cdot)$
1-448-448.11-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.11	$1$	✓	✓	$0.463$	$0$	$1.45223$	Character $\chi_{448}(11, \cdot)$
1-448-448.117-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.117	$1$	✓	✓	$-0.0462$	$0$	$0.763926$	Character $\chi_{448}(117, \cdot)$
1-448-448.123-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.123	$1$	✓	✓	$0.0888$	$0$	$0.456090$	Character $\chi_{448}(123, \cdot)$
1-448-448.125-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.125	$1$	✓	✓	$-0.140$	$0$	$0.697880$	Character $\chi_{448}(125, \cdot)$
1-448-448.13-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.13	$1$	✓	✓	$0.234$	$0$	$0.676171$	Character $\chi_{448}(13, \cdot)$
1-448-448.157-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.157	$1$	✓	✓	$0.0462$	$0$	$0.553351$	Character $\chi_{448}(157, \cdot)$
1-448-448.163-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.163	$1$	✓	✓	$-0.463$	$0$	$0.0687856$	Character $\chi_{448}(163, \cdot)$
1-448-448.173-r1-0-0	$48.1$	$48.1$	$1$	$2^{6} \cdot 7$	448.173	$1$	✓	✓	$-0.452$	$0$	$1.59431$	Character $\chi_{448}(173, \cdot)$

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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.