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 500 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-847-847.10-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.10	$0$	✓	✓	$0.373$	$0$	$2.22716$	Character $\chi_{847}(10, \cdot)$
1-847-847.100-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.100	$0$	✓	✓	$0.163$	$0$	$1.06378$	Character $\chi_{847}(100, \cdot)$
1-847-847.101-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.101	$0$	✓	✓	$-0.219$	$0$	$0.814357$	Character $\chi_{847}(101, \cdot)$
1-847-847.102-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.102	$0$	✓	✓	$0.196$	$0$	$1.50013$	Character $\chi_{847}(102, \cdot)$
1-847-847.114-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.114	$0$	✓	✓	$0.163$	$0$	$0.966922$	Character $\chi_{847}(114, \cdot)$
1-847-847.117-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.117	$0$	✓	✓	$0.426$	$0$	$0.975624$	Character $\chi_{847}(117, \cdot)$
1-847-847.129-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.129	$0$	✓	✓	$0.437$	$0$	$1.39543$	Character $\chi_{847}(129, \cdot)$
1-847-847.13-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.13	$0$	✓	✓	$-0.453$	$0$	$0.0728397$	Character $\chi_{847}(13, \cdot)$
1-847-847.131-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.131	$0$	✓	✓	$0.333$	$0$	$1.21744$	Character $\chi_{847}(131, \cdot)$
1-847-847.135-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.135	$0$	✓	✓	$-0.474$	$0$	$0.583647$	Character $\chi_{847}(135, \cdot)$
1-847-847.137-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.137	$0$	✓	✓	$-0.163$	$0$	$0.696575$	Character $\chi_{847}(137, \cdot)$
1-847-847.138-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.138	$0$	✓	✓	$0.339$	$0$	$2.00208$	Character $\chi_{847}(138, \cdot)$
1-847-847.139-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.139	$0$	✓	✓	$0.139$	$0$	$1.19693$	Character $\chi_{847}(139, \cdot)$
1-847-847.144-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.144	$0$	✓	✓	$-0.163$	$0$	$0.906674$	Character $\chi_{847}(144, \cdot)$
1-847-847.145-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.145	$0$	✓	✓	$0.197$	$0$	$0.976134$	Character $\chi_{847}(145, \cdot)$
1-847-847.150-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.150	$0$	✓	✓	$-0.139$	$0$	$0.668355$	Character $\chi_{847}(150, \cdot)$
1-847-847.153-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.153	$0$	✓	✓	$0.0599$	$0$	$1.19894$	Character $\chi_{847}(153, \cdot)$
1-847-847.158-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.158	$0$	✓	✓	$-0.190$	$0$	$0.467998$	Character $\chi_{847}(158, \cdot)$
1-847-847.16-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.16	$0$	✓	✓	$0.0231$	$0$	$0.828083$	Character $\chi_{847}(16, \cdot)$
1-847-847.160-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.160	$0$	✓	✓	$-0.246$	$0$	$0.934926$	Character $\chi_{847}(160, \cdot)$
1-847-847.163-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.163	$0$	✓	✓	$0.325$	$0$	$1.52020$	Character $\chi_{847}(163, \cdot)$
1-847-847.164-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.164	$0$	✓	✓	$-0.362$	$0$	$0.147814$	Character $\chi_{847}(164, \cdot)$
1-847-847.167-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.167	$0$	✓	✓	$0.259$	$0$	$1.15698$	Character $\chi_{847}(167, \cdot)$
1-847-847.17-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.17	$0$	✓	✓	$0.380$	$0$	$0.166128$	Character $\chi_{847}(17, \cdot)$
1-847-847.170-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.170	$0$	✓	✓	$-0.138$	$0$	$0.977237$	Character $\chi_{847}(170, \cdot)$
1-847-847.171-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.171	$0$	✓	✓	$0.260$	$0$	$1.36385$	Character $\chi_{847}(171, \cdot)$
1-847-847.173-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.173	$0$	✓	✓	$0.159$	$0$	$0.908379$	Character $\chi_{847}(173, \cdot)$
1-847-847.177-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.177	$0$	✓	✓	$0.304$	$0$	$1.26833$	Character $\chi_{847}(177, \cdot)$
1-847-847.178-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.178	$0$	✓	✓	$-0.339$	$0$	$1.07237$	Character $\chi_{847}(178, \cdot)$
1-847-847.179-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.179	$0$	✓	✓	$-0.0231$	$0$	$0.676564$	Character $\chi_{847}(179, \cdot)$
1-847-847.19-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.19	$0$	✓	✓	$0.0199$	$0$	$0.644263$	Character $\chi_{847}(19, \cdot)$
1-847-847.191-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.191	$0$	✓	✓	$-0.196$	$0$	$0.750519$	Character $\chi_{847}(191, \cdot)$
1-847-847.194-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.194	$0$	✓	✓	$0.159$	$0$	$1.42855$	Character $\chi_{847}(194, \cdot)$
1-847-847.195-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.195	$0$	✓	✓	$-0.139$	$0$	$0.616583$	Character $\chi_{847}(195, \cdot)$
1-847-847.206-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.206	$0$	✓	✓	$-0.133$	$0$	$0.486148$	Character $\chi_{847}(206, \cdot)$
1-847-847.207-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.207	$0$	✓	✓	$-0.163$	$0$	$0.821106$	Character $\chi_{847}(207, \cdot)$
1-847-847.208-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.208	$0$	✓	✓	$0.419$	$0$	$0.457695$	Character $\chi_{847}(208, \cdot)$
1-847-847.212-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.212	$0$	✓	✓	$0.396$	$0$	$0.0573370$	Character $\chi_{847}(212, \cdot)$
1-847-847.214-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.214	$0$	✓	✓	$-0.390$	$0$	$0.744411$	Character $\chi_{847}(214, \cdot)$
1-847-847.216-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.216	$0$	✓	✓	$0.317$	$0$	$1.42381$	Character $\chi_{847}(216, \cdot)$
1-847-847.221-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.221	$0$	✓	✓	$-0.0231$	$0$	$0.931721$	Character $\chi_{847}(221, \cdot)$
1-847-847.222-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.222	$0$	✓	✓	$-0.259$	$0$	$0.814103$	Character $\chi_{847}(222, \cdot)$
1-847-847.227-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.227	$0$	✓	✓	$-0.397$	$0$	$0.386204$	Character $\chi_{847}(227, \cdot)$
1-847-847.23-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.23	$0$	✓	✓	$0.0231$	$0$	$0.438462$	Character $\chi_{847}(23, \cdot)$
1-847-847.230-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.230	$0$	✓	✓	$0.146$	$0$	$0.833818$	Character $\chi_{847}(230, \cdot)$
1-847-847.235-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.235	$0$	✓	✓	$-0.0231$	$0$	$1.21061$	Character $\chi_{847}(235, \cdot)$
1-847-847.237-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.237	$0$	✓	✓	$0.282$	$0$	$1.14988$	Character $\chi_{847}(237, \cdot)$
1-847-847.24-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.24	$0$	✓	✓	$0.237$	$0$	$1.55340$	Character $\chi_{847}(24, \cdot)$
1-847-847.240-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.240	$0$	✓	✓	$-0.317$	$0$	$2.28637$	Character $\chi_{847}(240, \cdot)$
1-847-847.244-r0-0-0	$3.93$	$3.93$	$1$	$7 \cdot 11^{2}$	847.244	$0$	✓	✓	$0.339$	$0$	$1.80134$	Character $\chi_{847}(244, \cdot)$

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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 $\F_{q}$

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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.