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 121 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-319-319.102-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.102	$1$	✓	✓	$0.475$	$0$	$1.87193$	Character $\chi_{319}(102, \cdot)$
1-319-319.104-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.104	$1$	✓	✓	$0.162$	$0$	$1.31962$	Character $\chi_{319}(104, \cdot)$
1-319-319.107-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.107	$1$	✓	✓	$-0.196$	$0$	$0.265674$	Character $\chi_{319}(107, \cdot)$
1-319-319.108-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.108	$1$	✓	✓	$0.351$	$0$	$1.17510$	Character $\chi_{319}(108, \cdot)$
1-319-319.109-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.109	$1$	✓	✓	$-0.443$	$0$	$0.137554$	Character $\chi_{319}(109, \cdot)$
1-319-319.112-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.112	$1$	✓	✓	$-0.181$	$0$	$0.747886$	Character $\chi_{319}(112, \cdot)$
1-319-319.113-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.113	$1$	✓	✓	$0.445$	$0$	$0.118148$	Character $\chi_{319}(113, \cdot)$
1-319-319.114-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.114	$1$	✓	✓	$0.354$	$0$	$0.0586839$	Character $\chi_{319}(114, \cdot)$
1-319-319.119-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.119	$1$	✓	✓	$-0.355$	$0$	$0.408557$	Character $\chi_{319}(119, \cdot)$
1-319-319.120-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.120	$1$	✓	✓	$0.443$	$0$	$1.05381$	Character $\chi_{319}(120, \cdot)$
1-319-319.123-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.123	$1$	✓	✓	$-0.325$	$0$	$0.848060$	Character $\chi_{319}(123, \cdot)$
1-319-319.124-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.124	$1$	✓	✓	$-0.463$	$0$	$0.698207$	Character $\chi_{319}(124, \cdot)$
1-319-319.126-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.126	$1$	✓	✓	$0.355$	$0$	$0.723569$	Character $\chi_{319}(126, \cdot)$
1-319-319.129-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.129	$1$	✓	✓	$-0.433$	$0$	$0.478258$	Character $\chi_{319}(129, \cdot)$
1-319-319.13-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.13	$1$	✓	✓	$-0.147$	$0$	$0.776241$	Character $\chi_{319}(13, \cdot)$
1-319-319.130-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.130	$1$	✓	✓	$0.206$	$0$	$1.36340$	Character $\chi_{319}(130, \cdot)$
1-319-319.135-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.135	$1$	✓	✓	$-0.453$	$0$	$2.35050$	Character $\chi_{319}(135, \cdot)$
1-319-319.137-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.137	$1$	✓	✓	$0.236$	$0$	$1.80510$	Character $\chi_{319}(137, \cdot)$
1-319-319.138-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.138	$1$	✓	✓	$0.310$	$0$	$0.258966$	Character $\chi_{319}(138, \cdot)$
1-319-319.139-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.139	$1$	✓	✓	$-0.0106$	$0$	$0.193844$	Character $\chi_{319}(139, \cdot)$
1-319-319.14-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.14	$1$	✓	✓	$-0.354$	$0$	$1.53719$	Character $\chi_{319}(14, \cdot)$
1-319-319.140-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.140	$1$	✓	✓	$0.0106$	$0$	$0.669132$	Character $\chi_{319}(140, \cdot)$
1-319-319.147-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.147	$1$	✓	✓	$-0.475$	$0$	$0.217846$	Character $\chi_{319}(147, \cdot)$
1-319-319.148-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.148	$1$	✓	✓	$-0.469$	$0$	$0.0667316$	Character $\chi_{319}(148, \cdot)$
1-319-319.149-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.149	$1$	✓	✓	$0.196$	$0$	$1.66151$	Character $\chi_{319}(149, \cdot)$
1-319-319.15-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.15	$1$	✓	✓	$0.483$	$0$	$1.44370$	Character $\chi_{319}(15, \cdot)$
1-319-319.150-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.150	$1$	✓	✓	$-0.0100$	$0$	$0.644279$	Character $\chi_{319}(150, \cdot)$
1-319-319.151-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.151	$1$	✓	✓	$0.0100$	$0$	$0.843048$	Character $\chi_{319}(151, \cdot)$
1-319-319.157-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.157	$1$	✓	✓	$0.276$	$0$	$1.31588$	Character $\chi_{319}(157, \cdot)$
1-319-319.159-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.159	$1$	✓	✓	$0.0916$	$0$	$1.12003$	Character $\chi_{319}(159, \cdot)$
1-319-319.161-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.161	$1$	✓	✓	$0.196$	$0$	$1.29137$	Character $\chi_{319}(161, \cdot)$
1-319-319.163-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.163	$1$	✓	✓	$-0.236$	$0$	$1.06064$	Character $\chi_{319}(163, \cdot)$
1-319-319.167-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.167	$1$	✓	✓	$-0.196$	$0$	$0.657780$	Character $\chi_{319}(167, \cdot)$
1-319-319.173-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.173	$1$	✓	✓	$-0.0389$	$0$	$1.50543$	Character $\chi_{319}(173, \cdot)$
1-319-319.178-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.178	$1$	✓	✓	$-0.310$	$0$	$2.27727$	Character $\chi_{319}(178, \cdot)$
1-319-319.183-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.183	$1$	✓	✓	$0.433$	$0$	$1.56213$	Character $\chi_{319}(183, \cdot)$
1-319-319.185-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.185	$1$	✓	✓	$0.0165$	$0$	$0.720584$	Character $\chi_{319}(185, \cdot)$
1-319-319.191-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.191	$1$	✓	✓	$-0.276$	$0$	$0.221876$	Character $\chi_{319}(191, \cdot)$
1-319-319.192-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.192	$1$	✓	✓	$-0.351$	$0$	$0.231571$	Character $\chi_{319}(192, \cdot)$
1-319-319.194-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.194	$1$	✓	✓	$-0.119$	$0$	$0.945600$	Character $\chi_{319}(194, \cdot)$
1-319-319.197-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.197	$1$	✓	✓	$-0.0496$	$0$	$0.445379$	Character $\chi_{319}(197, \cdot)$
1-319-319.201-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.201	$1$	✓	✓	$0.347$	$0$	$1.51563$	Character $\chi_{319}(201, \cdot)$
1-319-319.208-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.208	$1$	✓	✓	$-0.0489$	$0$	$0.611224$	Character $\chi_{319}(208, \cdot)$
1-319-319.213-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.213	$1$	✓	✓	$-0.0835$	$0$	$1.21530$	Character $\chi_{319}(213, \cdot)$
1-319-319.214-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.214	$1$	✓	✓	$-0.0980$	$0$	$0.171816$	Character $\chi_{319}(214, \cdot)$
1-319-319.216-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.216	$1$	✓	✓	$-0.355$	$0$	$0.428921$	Character $\chi_{319}(216, \cdot)$
1-319-319.218-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.218	$1$	✓	✓	$0.0365$	$0$	$0.787141$	Character $\chi_{319}(218, \cdot)$
1-319-319.219-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.219	$1$	✓	✓	$0.158$	$0$	$1.34432$	Character $\chi_{319}(219, \cdot)$
1-319-319.224-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.224	$1$	✓	✓	$-0.202$	$0$	$0.863069$	Character $\chi_{319}(224, \cdot)$
1-319-319.226-r1-0-0	$34.2$	$34.2$	$1$	$11 \cdot 29$	319.226	$1$	✓	✓	$-0.296$	$0$	$0.650174$	Character $\chi_{319}(226, \cdot)$

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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.