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 178 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-511-511.10-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.10	$0$	✓	✓	$-0.0889$	$0$	$0.911128$	Character $\chi_{511}(10, \cdot)$
1-511-511.100-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.100	$0$	✓	✓	$-0.393$	$0$	$0.924804$	Character $\chi_{511}(100, \cdot)$
1-511-511.101-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.101	$0$	✓	✓	$-0.299$	$0$	$0.436062$	Character $\chi_{511}(101, \cdot)$
1-511-511.103-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.103	$0$	✓	✓	$0.357$	$0$	$1.35616$	Character $\chi_{511}(103, \cdot)$
1-511-511.104-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.104	$0$	✓	✓	$0.287$	$0$	$0.799626$	Character $\chi_{511}(104, \cdot)$
1-511-511.109-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.109	$0$	✓	✓	$-0.0692$	$0$	$1.07258$	Character $\chi_{511}(109, \cdot)$
1-511-511.114-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.114	$0$	✓	✓	$0.282$	$0$	$1.52760$	Character $\chi_{511}(114, \cdot)$
1-511-511.115-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.115	$0$	✓	✓	$0.194$	$0$	$1.29333$	Character $\chi_{511}(115, \cdot)$
1-511-511.117-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.117	$0$	✓	✓	$0.419$	$0$	$0.107694$	Character $\chi_{511}(117, \cdot)$
1-511-511.118-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.118	$0$	✓	✓	$0.151$	$0$	$1.12066$	Character $\chi_{511}(118, \cdot)$
1-511-511.121-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.121	$0$	✓	✓	$0.116$	$0$	$1.53503$	Character $\chi_{511}(121, \cdot)$
1-511-511.123-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.123	$0$	✓	✓	$0.406$	$0$	$1.15332$	Character $\chi_{511}(123, \cdot)$
1-511-511.124-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.124	$0$	✓	✓	$-0.142$	$0$	$0.864809$	Character $\chi_{511}(124, \cdot)$
1-511-511.125-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.125	$0$	✓	✓	$-0.0169$	$0$	$0.765400$	Character $\chi_{511}(125, \cdot)$
1-511-511.128-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.128	$0$	✓	✓	$-0.212$	$0$	$1.14606$	Character $\chi_{511}(128, \cdot)$
1-511-511.129-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.129	$0$	✓	✓	$-0.357$	$0$	$0.802292$	Character $\chi_{511}(129, \cdot)$
1-511-511.13-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.13	$0$	✓	✓	$-0.151$	$0$	$0.437423$	Character $\chi_{511}(13, \cdot)$
1-511-511.130-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.130	$0$	✓	✓	$-0.282$	$0$	$0.494429$	Character $\chi_{511}(130, \cdot)$
1-511-511.131-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.131	$0$	✓	✓	$0.0462$	$0$	$0.817461$	Character $\chi_{511}(131, \cdot)$
1-511-511.132-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.132	$0$	✓	✓	$-0.400$	$0$	$0.574200$	Character $\chi_{511}(132, \cdot)$
1-511-511.136-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.136	$0$	✓	✓	$0.142$	$0$	$1.08480$	Character $\chi_{511}(136, \cdot)$
1-511-511.137-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.137	$0$	✓	✓	$-0.199$	$0$	$0.932334$	Character $\chi_{511}(137, \cdot)$
1-511-511.139-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.139	$0$	✓	✓	$0.0169$	$0$	$0.819495$	Character $\chi_{511}(139, \cdot)$
1-511-511.142-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.142	$0$	✓	✓	$-0.241$	$0$	$0.372605$	Character $\chi_{511}(142, \cdot)$
1-511-511.144-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.144	$0$	✓	✓	$-0.450$	$0$	$1.66256$	Character $\chi_{511}(144, \cdot)$
1-511-511.149-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.149	$0$	✓	✓	$-0.204$	$0$	$0.873203$	Character $\chi_{511}(149, \cdot)$
1-511-511.153-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.153	$0$	✓	✓	$0.114$	$0$	$1.34023$	Character $\chi_{511}(153, \cdot)$
1-511-511.157-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.157	$0$	✓	✓	$0.247$	$0$	$1.10778$	Character $\chi_{511}(157, \cdot)$
1-511-511.158-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.158	$0$	✓	✓	$-0.186$	$0$	$0.824659$	Character $\chi_{511}(158, \cdot)$
1-511-511.159-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.159	$0$	✓	✓	$0.00469$	$0$	$0.916258$	Character $\chi_{511}(159, \cdot)$
1-511-511.16-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.16	$0$	✓	✓	$0.286$	$0$	$1.59190$	Character $\chi_{511}(16, \cdot)$
1-511-511.160-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.160	$0$	✓	✓	$-0.0443$	$0$	$1.32801$	Character $\chi_{511}(160, \cdot)$
1-511-511.165-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.165	$0$	✓	✓	$0.0732$	$0$	$1.02316$	Character $\chi_{511}(165, \cdot)$
1-511-511.166-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.166	$0$	✓	✓	$-0.247$	$0$	$0.0932293$	Character $\chi_{511}(166, \cdot)$
1-511-511.167-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.167	$0$	✓	✓	$-0.114$	$0$	$0.794850$	Character $\chi_{511}(167, \cdot)$
1-511-511.17-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.17	$0$	✓	✓	$-0.259$	$0$	$0.975830$	Character $\chi_{511}(17, \cdot)$
1-511-511.170-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.170	$0$	✓	✓	$-0.0825$	$0$	$1.60248$	Character $\chi_{511}(170, \cdot)$
1-511-511.174-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.174	$0$	✓	✓	$-0.153$	$0$	$0.457513$	Character $\chi_{511}(174, \cdot)$
1-511-511.18-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.18	$0$	✓	✓	$0.241$	$0$	$1.00171$	Character $\chi_{511}(18, \cdot)$
1-511-511.180-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.180	$0$	✓	✓	$0.246$	$0$	$1.61499$	Character $\chi_{511}(180, \cdot)$
1-511-511.184-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.184	$0$	✓	✓	$0.0379$	$0$	$0.770654$	Character $\chi_{511}(184, \cdot)$
1-511-511.185-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.185	$0$	✓	✓	$-0.344$	$0$	$0.572327$	Character $\chi_{511}(185, \cdot)$
1-511-511.188-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.188	$0$	✓	✓	$0.341$	$0$	$1.14501$	Character $\chi_{511}(188, \cdot)$
1-511-511.199-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.199	$0$	✓	✓	$-0.386$	$0$	$1.46963$	Character $\chi_{511}(199, \cdot)$
1-511-511.2-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.2	$0$	✓	✓	$-0.354$	$0$	$0.547116$	Character $\chi_{511}(2, \cdot)$
1-511-511.20-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.20	$0$	✓	✓	$-0.394$	$0$	$1.08731$	Character $\chi_{511}(20, \cdot)$
1-511-511.200-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.200	$0$	✓	✓	$-0.373$	$0$	$0.218396$	Character $\chi_{511}(200, \cdot)$
1-511-511.202-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.202	$0$	✓	✓	$-0.210$	$0$	$2.14681$	Character $\chi_{511}(202, \cdot)$
1-511-511.206-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.206	$0$	✓	✓	$0.00666$	$0$	$1.80602$	Character $\chi_{511}(206, \cdot)$
1-511-511.207-r0-0-0	$2.37$	$2.37$	$1$	$7 \cdot 73$	511.207	$0$	✓	✓	$0.0866$	$0$	$1.33769$	Character $\chi_{511}(207, \cdot)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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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.