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 68 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-235-235.107-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.107	$0$	✓	✓	$-0.173$	$0$	$0.811417$	Character $\chi_{235}(107, \cdot)$
1-235-235.113-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.113	$0$	✓	✓	$-0.0684$	$0$	$1.09135$	Character $\chi_{235}(113, \cdot)$
1-235-235.117-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.117	$0$	✓	✓	$0.0248$	$0$	$1.16373$	Character $\chi_{235}(117, \cdot)$
1-235-235.119-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.119	$0$	✓	✓	$0.288$	$0$	$1.19307$	Character $\chi_{235}(119, \cdot)$
1-235-235.123-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.123	$0$	✓	✓	$0.173$	$0$	$1.14789$	Character $\chi_{235}(123, \cdot)$
1-235-235.127-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.127	$0$	✓	✓	$-0.198$	$0$	$1.12025$	Character $\chi_{235}(127, \cdot)$
1-235-235.13-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.13	$0$	✓	✓	$0.150$	$0$	$2.21794$	Character $\chi_{235}(13, \cdot)$
1-235-235.132-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.132	$0$	✓	✓	$-0.0474$	$0$	$1.74031$	Character $\chi_{235}(132, \cdot)$
1-235-235.133-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.133	$0$	✓	✓	$-0.492$	$0$	$0.694236$	Character $\chi_{235}(133, \cdot)$
1-235-235.137-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.137	$0$	✓	✓	$0.307$	$0$	$1.19561$	Character $\chi_{235}(137, \cdot)$
1-235-235.138-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.138	$0$	✓	✓	$-0.354$	$0$	$0.663948$	Character $\chi_{235}(138, \cdot)$
1-235-235.14-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.14	$0$	✓	✓	$0.364$	$0$	$2.69449$	Character $\chi_{235}(14, \cdot)$
1-235-235.144-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.144	$0$	✓	✓	$-0.427$	$0$	$2.16203$	Character $\chi_{235}(144, \cdot)$
1-235-235.149-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.149	$0$	✓	✓	$-0.0412$	$0$	$1.69820$	Character $\chi_{235}(149, \cdot)$
1-235-235.152-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.152	$0$	✓	✓	$-0.123$	$0$	$1.74220$	Character $\chi_{235}(152, \cdot)$
1-235-235.159-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.159	$0$	✓	✓	$-0.126$	$0$	$0.739639$	Character $\chi_{235}(159, \cdot)$
1-235-235.163-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.163	$0$	✓	✓	$0.172$	$0$	$1.70012$	Character $\chi_{235}(163, \cdot)$
1-235-235.167-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.167	$0$	✓	✓	$-0.276$	$0$	$0.300034$	Character $\chi_{235}(167, \cdot)$
1-235-235.169-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.169	$0$	✓	✓	$0.224$	$0$	$2.13216$	Character $\chi_{235}(169, \cdot)$
1-235-235.172-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.172	$0$	✓	✓	$0.354$	$0$	$2.00946$	Character $\chi_{235}(172, \cdot)$
1-235-235.182-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.182	$0$	✓	✓	$0.492$	$0$	$2.55010$	Character $\chi_{235}(182, \cdot)$
1-235-235.187-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.187	$0$	✓	✓	$0.338$	$0$	$1.67299$	Character $\chi_{235}(187, \cdot)$
1-235-235.193-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.193	$0$	✓	✓	$0.392$	$0$	$2.05501$	Character $\chi_{235}(193, \cdot)$
1-235-235.194-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.194	$0$	✓	✓	$0.0412$	$0$	$1.21553$	Character $\chi_{235}(194, \cdot)$
1-235-235.198-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.198	$0$	✓	✓	$0.198$	$0$	$1.21521$	Character $\chi_{235}(198, \cdot)$
1-235-235.203-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.203	$0$	✓	✓	$0.151$	$0$	$1.80408$	Character $\chi_{235}(203, \cdot)$
1-235-235.204-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.204	$0$	✓	✓	$0.427$	$0$	$0.481334$	Character $\chi_{235}(204, \cdot)$
1-235-235.207-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.207	$0$	✓	✓	$-0.392$	$0$	$0.478883$	Character $\chi_{235}(207, \cdot)$
1-235-235.208-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.208	$0$	✓	✓	$-0.130$	$0$	$0.129273$	Character $\chi_{235}(208, \cdot)$
1-235-235.209-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.209	$0$	✓	✓	$-0.208$	$0$	$1.24311$	Character $\chi_{235}(209, \cdot)$
1-235-235.217-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.217	$0$	✓	✓	$-0.150$	$0$	$1.61701$	Character $\chi_{235}(217, \cdot)$
1-235-235.218-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.218	$0$	✓	✓	$0.123$	$0$	$1.93989$	Character $\chi_{235}(218, \cdot)$
1-235-235.22-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.22	$0$	✓	✓	$-0.151$	$0$	$1.04134$	Character $\chi_{235}(22, \cdot)$
1-235-235.223-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.223	$0$	✓	✓	$-0.307$	$0$	$0.830816$	Character $\chi_{235}(223, \cdot)$
1-235-235.224-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.224	$0$	✓	✓	$-0.0650$	$0$	$0.438411$	Character $\chi_{235}(224, \cdot)$
1-235-235.227-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.227	$0$	✓	✓	$0.183$	$0$	$1.14226$	Character $\chi_{235}(227, \cdot)$
1-235-235.228-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.228	$0$	✓	✓	$0.454$	$0$	$2.02634$	Character $\chi_{235}(228, \cdot)$
1-235-235.23-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.23	$0$	✓	✓	$0.348$	$0$	$1.80088$	Character $\chi_{235}(23, \cdot)$
1-235-235.232-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.232	$0$	✓	✓	$0.321$	$0$	$2.00385$	Character $\chi_{235}(232, \cdot)$
1-235-235.233-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.233	$0$	✓	✓	$-0.0248$	$0$	$1.81934$	Character $\chi_{235}(233, \cdot)$
1-235-235.24-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.24	$0$	✓	✓	$0.115$	$0$	$1.48232$	Character $\chi_{235}(24, \cdot)$
1-235-235.33-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.33	$0$	✓	✓	$0.125$	$0$	$1.27274$	Character $\chi_{235}(33, \cdot)$
1-235-235.34-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.34	$0$	✓	✓	$0.126$	$0$	$1.76691$	Character $\chi_{235}(34, \cdot)$
1-235-235.38-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.38	$0$	✓	✓	$0.276$	$0$	$1.24798$	Character $\chi_{235}(38, \cdot)$
1-235-235.4-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.4	$0$	✓	✓	$0.284$	$0$	$1.82294$	Character $\chi_{235}(4, \cdot)$
1-235-235.43-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.43	$0$	✓	✓	$-0.368$	$0$	$1.23506$	Character $\chi_{235}(43, \cdot)$
1-235-235.49-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.49	$0$	✓	✓	$-0.115$	$0$	$0.708663$	Character $\chi_{235}(49, \cdot)$
1-235-235.52-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.52	$0$	✓	✓	$0.0684$	$0$	$1.52143$	Character $\chi_{235}(52, \cdot)$
1-235-235.54-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.54	$0$	✓	✓	$0.0481$	$0$	$1.37554$	Character $\chi_{235}(54, \cdot)$
1-235-235.57-r0-0-0	$1.09$	$1.09$	$1$	$5 \cdot 47$	235.57	$0$	✓	✓	$-0.125$	$0$	$1.30421$	Character $\chi_{235}(57, \cdot)$

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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.