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

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Results (50 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-363-363.101-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.101	$0$	✓	✓	$-0.275$	$0$	$0.665059$	Character $\chi_{363}(101, \cdot)$
1-363-363.107-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.107	$0$	✓	✓	$0.0731$	$0$	$1.59302$	Character $\chi_{363}(107, \cdot)$
1-363-363.116-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.116	$0$	✓	✓	$0.273$	$0$	$1.83930$	Character $\chi_{363}(116, \cdot)$
1-363-363.128-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.128	$0$	✓	✓	$0.474$	$0$	$2.01293$	Character $\chi_{363}(128, \cdot)$
1-363-363.131-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.131	$0$	✓	✓	$0.0805$	$0$	$1.08808$	Character $\chi_{363}(131, \cdot)$
1-363-363.134-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.134	$0$	✓	✓	$-0.0805$	$0$	$0.467830$	Character $\chi_{363}(134, \cdot)$
1-363-363.140-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.140	$0$	✓	✓	$-0.341$	$0$	$2.18722$	Character $\chi_{363}(140, \cdot)$
1-363-363.149-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.149	$0$	✓	✓	$0.0805$	$0$	$0.992908$	Character $\chi_{363}(149, \cdot)$
1-363-363.164-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.164	$0$	✓	✓	$-0.473$	$0$	$0.298799$	Character $\chi_{363}(164, \cdot)$
1-363-363.167-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.167	$0$	✓	✓	$-0.458$	$0$	$2.36746$	Character $\chi_{363}(167, \cdot)$
1-363-363.17-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.17	$0$	✓	✓	$-0.0582$	$0$	$1.37160$	Character $\chi_{363}(17, \cdot)$
1-363-363.173-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.173	$0$	✓	✓	$-0.474$	$0$	$0.135638$	Character $\chi_{363}(173, \cdot)$
1-363-363.182-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.182	$0$	✓	✓	$-0.0756$	$0$	$1.18170$	Character $\chi_{363}(182, \cdot)$
1-363-363.194-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.194	$0$	✓	✓	$-0.0747$	$0$	$1.16877$	Character $\chi_{363}(194, \cdot)$
1-363-363.197-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.197	$0$	✓	✓	$0.473$	$0$	$1.48007$	Character $\chi_{363}(197, \cdot)$
1-363-363.2-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.2	$0$	✓	✓	$0.0756$	$0$	$1.27330$	Character $\chi_{363}(2, \cdot)$
1-363-363.200-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.200	$0$	✓	✓	$-0.326$	$0$	$0.873230$	Character $\chi_{363}(200, \cdot)$
1-363-363.206-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.206	$0$	✓	✓	$-0.0805$	$0$	$1.02701$	Character $\chi_{363}(206, \cdot)$
1-363-363.227-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.227	$0$	✓	✓	$-0.126$	$0$	$0.654094$	Character $\chi_{363}(227, \cdot)$
1-363-363.230-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.230	$0$	✓	✓	$-0.0805$	$0$	$1.55200$	Character $\chi_{363}(230, \cdot)$
1-363-363.248-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.248	$0$	✓	✓	$0.275$	$0$	$1.05706$	Character $\chi_{363}(248, \cdot)$
1-363-363.260-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.260	$0$	✓	✓	$0.475$	$0$	$2.20430$	Character $\chi_{363}(260, \cdot)$
1-363-363.263-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.263	$0$	✓	✓	$0.274$	$0$	$1.24349$	Character $\chi_{363}(263, \cdot)$
1-363-363.266-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.266	$0$	✓	✓	$-0.273$	$0$	$0.414445$	Character $\chi_{363}(266, \cdot)$
1-363-363.272-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.272	$0$	✓	✓	$0.0805$	$0$	$1.77991$	Character $\chi_{363}(272, \cdot)$
1-363-363.281-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.281	$0$	✓	✓	$-0.0805$	$0$	$0.549314$	Character $\chi_{363}(281, \cdot)$
1-363-363.29-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.29	$0$	✓	✓	$-0.141$	$0$	$1.18996$	Character $\chi_{363}(29, \cdot)$
1-363-363.293-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.293	$0$	✓	✓	$0.341$	$0$	$0.300491$	Character $\chi_{363}(293, \cdot)$
1-363-363.296-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.296	$0$	✓	✓	$-0.324$	$0$	$1.07368$	Character $\chi_{363}(296, \cdot)$
1-363-363.299-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.299	$0$	✓	✓	$0.0582$	$0$	$1.33828$	Character $\chi_{363}(299, \cdot)$
1-363-363.305-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.305	$0$	✓	✓	$0.0747$	$0$	$0.884601$	Character $\chi_{363}(305, \cdot)$
1-363-363.314-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.314	$0$	✓	✓	$0.326$	$0$	$1.91879$	Character $\chi_{363}(314, \cdot)$
1-363-363.32-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.32	$0$	✓	✓	$-0.258$	$0$	$0.614578$	Character $\chi_{363}(32, \cdot)$
1-363-363.326-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.326	$0$	✓	✓	$0.0805$	$0$	$1.09399$	Character $\chi_{363}(326, \cdot)$
1-363-363.329-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.329	$0$	✓	✓	$0.258$	$0$	$1.43684$	Character $\chi_{363}(329, \cdot)$
1-363-363.332-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.332	$0$	✓	✓	$0.0805$	$0$	$1.54216$	Character $\chi_{363}(332, \cdot)$
1-363-363.338-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.338	$0$	✓	✓	$0.141$	$0$	$1.22828$	Character $\chi_{363}(338, \cdot)$
1-363-363.347-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.347	$0$	✓	✓	$0.125$	$0$	$1.73247$	Character $\chi_{363}(347, \cdot)$
1-363-363.35-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.35	$0$	✓	✓	$0.325$	$0$	$1.59724$	Character $\chi_{363}(35, \cdot)$
1-363-363.359-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.359	$0$	✓	✓	$-0.0805$	$0$	$1.27713$	Character $\chi_{363}(359, \cdot)$
1-363-363.41-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.41	$0$	✓	✓	$-0.124$	$0$	$1.14793$	Character $\chi_{363}(41, \cdot)$
1-363-363.50-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.50	$0$	✓	✓	$0.458$	$0$	$0.493193$	Character $\chi_{363}(50, \cdot)$
1-363-363.62-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.62	$0$	✓	✓	$0.124$	$0$	$0.988334$	Character $\chi_{363}(62, \cdot)$
1-363-363.65-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.65	$0$	✓	✓	$0.324$	$0$	$2.20617$	Character $\chi_{363}(65, \cdot)$
1-363-363.68-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.68	$0$	✓	✓	$-0.125$	$0$	$1.37539$	Character $\chi_{363}(68, \cdot)$
1-363-363.74-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.74	$0$	✓	✓	$-0.475$	$0$	$0.445661$	Character $\chi_{363}(74, \cdot)$
1-363-363.8-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.8	$0$	✓	✓	$0.126$	$0$	$1.11885$	Character $\chi_{363}(8, \cdot)$
1-363-363.83-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.83	$0$	✓	✓	$-0.325$	$0$	$0.946852$	Character $\chi_{363}(83, \cdot)$
1-363-363.95-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.95	$0$	✓	✓	$-0.0731$	$0$	$1.71671$	Character $\chi_{363}(95, \cdot)$
1-363-363.98-r0-0-0	$1.68$	$1.68$	$1$	$3 \cdot 11^{2}$	363.98	$0$	✓	✓	$-0.274$	$0$	$0.760682$	Character $\chi_{363}(98, \cdot)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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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.