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 252 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-621-621.11-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.11	$0$	✓	✓	$0.0542$	$0$	$1.08539$	Character $\chi_{621}(11, \cdot)$
1-621-621.113-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.113	$0$	✓	✓	$-0.0542$	$0$	$0.901152$	Character $\chi_{621}(113, \cdot)$
1-621-621.121-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.121	$0$	✓	✓	$0.195$	$0$	$1.59530$	Character $\chi_{621}(121, \cdot)$
1-621-621.122-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.122	$0$	✓	✓	$-0.176$	$0$	$0.691599$	Character $\chi_{621}(122, \cdot)$
1-621-621.124-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.124	$0$	✓	✓	$0.449$	$0$	$1.74727$	Character $\chi_{621}(124, \cdot)$
1-621-621.13-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.13	$0$	✓	✓	$-0.193$	$0$	$0.920065$	Character $\chi_{621}(13, \cdot)$
1-621-621.133-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.133	$0$	✓	✓	$0.198$	$0$	$1.44942$	Character $\chi_{621}(133, \cdot)$
1-621-621.137-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.137	$0$	✓	✓	$0.240$	$0$	$1.71097$	Character $\chi_{621}(137, \cdot)$
1-621-621.14-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.14	$0$	✓	✓	$-0.448$	$0$	$0.645243$	Character $\chi_{621}(14, \cdot)$
1-621-621.142-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.142	$0$	✓	✓	$0.471$	$0$	$1.18369$	Character $\chi_{621}(142, \cdot)$
1-621-621.149-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.149	$0$	✓	✓	$-0.0939$	$0$	$1.33852$	Character $\chi_{621}(149, \cdot)$
1-621-621.151-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.151	$0$	✓	✓	$0.454$	$0$	$0.244889$	Character $\chi_{621}(151, \cdot)$
1-621-621.155-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.155	$0$	✓	✓	$0.246$	$0$	$1.85205$	Character $\chi_{621}(155, \cdot)$
1-621-621.158-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.158	$0$	✓	✓	$0.246$	$0$	$1.77689$	Character $\chi_{621}(158, \cdot)$
1-621-621.16-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.16	$0$	✓	✓	$-0.139$	$0$	$0.925283$	Character $\chi_{621}(16, \cdot)$
1-621-621.169-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.169	$0$	✓	✓	$-0.0640$	$0$	$0.748628$	Character $\chi_{621}(169, \cdot)$
1-621-621.176-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.176	$0$	✓	✓	$-0.402$	$0$	$0.171347$	Character $\chi_{621}(176, \cdot)$
1-621-621.182-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.182	$0$	✓	✓	$-0.239$	$0$	$0.316270$	Character $\chi_{621}(182, \cdot)$
1-621-621.187-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.187	$0$	✓	✓	$-0.287$	$0$	$0.528466$	Character $\chi_{621}(187, \cdot)$
1-621-621.191-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.191	$0$	✓	✓	$0.304$	$0$	$1.87087$	Character $\chi_{621}(191, \cdot)$
1-621-621.193-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.193	$0$	✓	✓	$0.134$	$0$	$1.65402$	Character $\chi_{621}(193, \cdot)$
1-621-621.194-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.194	$0$	✓	✓	$0.0283$	$0$	$1.03779$	Character $\chi_{621}(194, \cdot)$
1-621-621.196-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.196	$0$	✓	✓	$0.0600$	$0$	$0.974136$	Character $\chi_{621}(196, \cdot)$
1-621-621.20-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.20	$0$	✓	✓	$0.0686$	$0$	$1.50247$	Character $\chi_{621}(20, \cdot)$
1-621-621.202-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.202	$0$	✓	✓	$0.217$	$0$	$1.14293$	Character $\chi_{621}(202, \cdot)$
1-621-621.203-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.203	$0$	✓	✓	$0.420$	$0$	$1.30883$	Character $\chi_{621}(203, \cdot)$
1-621-621.211-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.211	$0$	✓	✓	$0.156$	$0$	$1.24281$	Character $\chi_{621}(211, \cdot)$
1-621-621.212-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.212	$0$	✓	✓	$0.299$	$0$	$1.65001$	Character $\chi_{621}(212, \cdot)$
1-621-621.218-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.218	$0$	✓	✓	$0.387$	$0$	$0.360248$	Character $\chi_{621}(218, \cdot)$
1-621-621.220-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.220	$0$	✓	✓	$0.139$	$0$	$1.08652$	Character $\chi_{621}(220, \cdot)$
1-621-621.221-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.221	$0$	✓	✓	$-0.114$	$0$	$0.181318$	Character $\chi_{621}(221, \cdot)$
1-621-621.223-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.223	$0$	✓	✓	$-0.139$	$0$	$1.07379$	Character $\chi_{621}(223, \cdot)$
1-621-621.227-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.227	$0$	✓	✓	$0.0686$	$0$	$0.956489$	Character $\chi_{621}(227, \cdot)$
1-621-621.232-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.232	$0$	✓	✓	$0.245$	$0$	$1.18725$	Character $\chi_{621}(232, \cdot)$
1-621-621.238-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.238	$0$	✓	✓	$-0.378$	$0$	$1.64040$	Character $\chi_{621}(238, \cdot)$
1-621-621.245-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.245	$0$	✓	✓	$0.0794$	$0$	$1.17656$	Character $\chi_{621}(245, \cdot)$
1-621-621.25-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.25	$0$	✓	✓	$-0.411$	$0$	$0.756306$	Character $\chi_{621}(25, \cdot)$
1-621-621.256-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.256	$0$	✓	✓	$-0.269$	$0$	$1.13705$	Character $\chi_{621}(256, \cdot)$
1-621-621.259-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.259	$0$	✓	✓	$-0.156$	$0$	$1.46749$	Character $\chi_{621}(259, \cdot)$
1-621-621.263-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.263	$0$	✓	✓	$-0.156$	$0$	$1.00089$	Character $\chi_{621}(263, \cdot)$
1-621-621.265-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.265	$0$	✓	✓	$-0.245$	$0$	$0.862774$	Character $\chi_{621}(265, \cdot)$
1-621-621.272-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.272	$0$	✓	✓	$-0.0980$	$0$	$0.955743$	Character $\chi_{621}(272, \cdot)$
1-621-621.275-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.275	$0$	✓	✓	$0.0925$	$0$	$1.05996$	Character $\chi_{621}(275, \cdot)$
1-621-621.281-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.281	$0$	✓	✓	$0.114$	$0$	$1.25948$	Character $\chi_{621}(281, \cdot)$
1-621-621.290-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.290	$0$	✓	✓	$-0.299$	$0$	$0.118453$	Character $\chi_{621}(290, \cdot)$
1-621-621.292-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.292	$0$	✓	✓	$-0.454$	$0$	$1.92053$	Character $\chi_{621}(292, \cdot)$
1-621-621.293-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.293	$0$	✓	✓	$0.431$	$0$	$1.26101$	Character $\chi_{621}(293, \cdot)$
1-621-621.301-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.301	$0$	✓	✓	$-0.0600$	$0$	$0.428611$	Character $\chi_{621}(301, \cdot)$
1-621-621.31-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.31	$0$	✓	✓	$-0.378$	$0$	$0.741087$	Character $\chi_{621}(31, \cdot)$
1-621-621.320-r0-0-0	$2.88$	$2.88$	$1$	$3^{3} \cdot 23$	621.320	$0$	✓	✓	$-0.0542$	$0$	$1.37372$	Character $\chi_{621}(320, \cdot)$

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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 $\F_{q}$
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.