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 295 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-427-427.10-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.10	$0$	✓	✓	$0.246$	$0$	$1.38857$	Character $\chi_{427}(10, \cdot)$
1-427-427.100-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.100	$0$	✓	✓	$-0.318$	$0$	$0.456751$	Character $\chi_{427}(100, \cdot)$
1-427-427.101-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.101	$0$	✓	✓	$-0.386$	$0$	$0.891933$	Character $\chi_{427}(101, \cdot)$
1-427-427.102-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.102	$0$	✓	✓	$0.362$	$0$	$1.79650$	Character $\chi_{427}(102, \cdot)$
1-427-427.104-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.104	$0$	✓	✓	$-0.234$	$0$	$1.01586$	Character $\chi_{427}(104, \cdot)$
1-427-427.107-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.107	$0$	✓	✓	$-0.146$	$0$	$0.975218$	Character $\chi_{427}(107, \cdot)$
1-427-427.109-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.109	$0$	✓	✓	$-0.246$	$0$	$0.675874$	Character $\chi_{427}(109, \cdot)$
1-427-427.111-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.111	$0$	✓	✓	$-0.180$	$0$	$1.35490$	Character $\chi_{427}(111, \cdot)$
1-427-427.115-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.115	$0$	✓	✓	$-0.0507$	$0$	$1.36089$	Character $\chi_{427}(115, \cdot)$
1-427-427.121-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.121	$0$	✓	✓	$0.0934$	$0$	$0.687405$	Character $\chi_{427}(121, \cdot)$
1-427-427.124-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.124	$0$	✓	✓	$0.445$	$0$	$0.344395$	Character $\chi_{427}(124, \cdot)$
1-427-427.129-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.129	$0$	✓	✓	$0.225$	$0$	$1.62825$	Character $\chi_{427}(129, \cdot)$
1-427-427.132-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.132	$0$	✓	✓	$-0.274$	$0$	$0.704425$	Character $\chi_{427}(132, \cdot)$
1-427-427.135-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.135	$0$	✓	✓	$0.00668$	$0$	$0.286073$	Character $\chi_{427}(135, \cdot)$
1-427-427.137-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.137	$0$	✓	✓	$0.174$	$0$	$1.09792$	Character $\chi_{427}(137, \cdot)$
1-427-427.139-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.139	$0$	✓	✓	$-0.396$	$0$	$0.546303$	Character $\chi_{427}(139, \cdot)$
1-427-427.142-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.142	$0$	✓	✓	$0.151$	$0$	$1.52088$	Character $\chi_{427}(142, \cdot)$
1-427-427.143-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.143	$0$	✓	✓	$0.246$	$0$	$1.30457$	Character $\chi_{427}(143, \cdot)$
1-427-427.144-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.144	$0$	✓	✓	$-0.482$	$0$	$1.95488$	Character $\chi_{427}(144, \cdot)$
1-427-427.145-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.145	$0$	✓	✓	$-0.285$	$0$	$0.535013$	Character $\chi_{427}(145, \cdot)$
1-427-427.146-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.146	$0$	✓	✓	$-0.343$	$0$	$2.07489$	Character $\chi_{427}(146, \cdot)$
1-427-427.149-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.149	$0$	✓	✓	$0.121$	$0$	$1.90263$	Character $\chi_{427}(149, \cdot)$
1-427-427.150-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.150	$0$	✓	✓	$-0.136$	$0$	$0.00305609$	Character $\chi_{427}(150, \cdot)$
1-427-427.152-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.152	$0$	✓	✓	$-0.261$	$0$	$0.510514$	Character $\chi_{427}(152, \cdot)$
1-427-427.153-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.153	$0$	✓	✓	$0.0348$	$0$	$1.29280$	Character $\chi_{427}(153, \cdot)$
1-427-427.156-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.156	$0$	✓	✓	$0.407$	$0$	$1.81615$	Character $\chi_{427}(156, \cdot)$
1-427-427.157-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.157	$0$	✓	✓	$-0.184$	$0$	$0.502157$	Character $\chi_{427}(157, \cdot)$
1-427-427.158-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.158	$0$	✓	✓	$0.318$	$0$	$1.74744$	Character $\chi_{427}(158, \cdot)$
1-427-427.159-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.159	$0$	✓	✓	$0.0508$	$0$	$0.788919$	Character $\chi_{427}(159, \cdot)$
1-427-427.16-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.16	$0$	✓	✓	$0.132$	$0$	$1.72030$	Character $\chi_{427}(16, \cdot)$
1-427-427.160-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.160	$0$	✓	✓	$-0.179$	$0$	$0.183578$	Character $\chi_{427}(160, \cdot)$
1-427-427.163-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.163	$0$	✓	✓	$-0.451$	$0$	$0.445189$	Character $\chi_{427}(163, \cdot)$
1-427-427.166-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.166	$0$	✓	✓	$-0.285$	$0$	$0.631550$	Character $\chi_{427}(166, \cdot)$
1-427-427.17-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.17	$0$	✓	✓	$0.124$	$0$	$1.67390$	Character $\chi_{427}(17, \cdot)$
1-427-427.170-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.170	$0$	✓	✓	$-0.0664$	$0$	$0.928107$	Character $\chi_{427}(170, \cdot)$
1-427-427.173-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.173	$0$	✓	✓	$0.0753$	$0$	$1.04230$	Character $\chi_{427}(173, \cdot)$
1-427-427.179-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.179	$0$	✓	✓	$-0.360$	$0$	$1.09493$	Character $\chi_{427}(179, \cdot)$
1-427-427.181-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.181	$0$	✓	✓	$-0.259$	$0$	$0.781538$	Character $\chi_{427}(181, \cdot)$
1-427-427.185-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.185	$0$	✓	✓	$0.485$	$0$	$1.56690$	Character $\chi_{427}(185, \cdot)$
1-427-427.186-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.186	$0$	✓	✓	$0.451$	$0$	$1.37142$	Character $\chi_{427}(186, \cdot)$
1-427-427.194-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.194	$0$	✓	✓	$-0.339$	$0$	$0.551058$	Character $\chi_{427}(194, \cdot)$
1-427-427.198-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.198	$0$	✓	✓	$0.360$	$0$	$2.12391$	Character $\chi_{427}(198, \cdot)$
1-427-427.201-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.201	$0$	✓	✓	$-0.124$	$0$	$1.41469$	Character $\chi_{427}(201, \cdot)$
1-427-427.205-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.205	$0$	✓	✓	$-0.295$	$0$	$1.00976$	Character $\chi_{427}(205, \cdot)$
1-427-427.206-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.206	$0$	✓	✓	$-0.244$	$0$	$0.594264$	Character $\chi_{427}(206, \cdot)$
1-427-427.209-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.209	$0$	✓	✓	$-0.429$	$0$	$0.438289$	Character $\chi_{427}(209, \cdot)$
1-427-427.213-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.213	$0$	✓	✓	$-0.220$	$0$	$0.998972$	Character $\chi_{427}(213, \cdot)$
1-427-427.215-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.215	$0$	✓	✓	$-0.246$	$0$	$0.680756$	Character $\chi_{427}(215, \cdot)$
1-427-427.216-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.216	$0$	✓	✓	$0.428$	$0$	$1.44567$	Character $\chi_{427}(216, \cdot)$
1-427-427.219-r0-0-0	$1.98$	$1.98$	$1$	$7 \cdot 61$	427.219	$0$	✓	✓	$-0.494$	$0$	$0.877611$	Character $\chi_{427}(219, \cdot)$

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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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Results (1-50 of 295 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.