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 66 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-585-585.112-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.112	$0$	✓	✓	$-0.264$	$0$	$0.831837$	Character $\chi_{585}(112, \cdot)$
1-585-585.113-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.113	$0$	✓	✓	$-0.0196$	$0$	$0.423533$	Character $\chi_{585}(113, \cdot)$
1-585-585.119-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.119	$0$	✓	✓	$-0.115$	$0$	$1.13520$	Character $\chi_{585}(119, \cdot)$
1-585-585.139-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.139	$0$	✓	✓	$0.0684$	$0$	$1.09127$	Character $\chi_{585}(139, \cdot)$
1-585-585.148-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.148	$0$	✓	✓	$0.153$	$0$	$1.54026$	Character $\chi_{585}(148, \cdot)$
1-585-585.149-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.149	$0$	✓	✓	$-0.478$	$0$	$0.374304$	Character $\chi_{585}(149, \cdot)$
1-585-585.164-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.164	$0$	✓	✓	$-0.241$	$0$	$1.09585$	Character $\chi_{585}(164, \cdot)$
1-585-585.173-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.173	$0$	✓	✓	$0.386$	$0$	$2.08884$	Character $\chi_{585}(173, \cdot)$
1-585-585.187-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.187	$0$	✓	✓	$-0.0595$	$0$	$1.08927$	Character $\chi_{585}(187, \cdot)$
1-585-585.193-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.193	$0$	✓	✓	$-0.220$	$0$	$0.611445$	Character $\chi_{585}(193, \cdot)$
1-585-585.202-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.202	$0$	✓	✓	$-0.296$	$0$	$0.473237$	Character $\chi_{585}(202, \cdot)$
1-585-585.212-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.212	$0$	✓	✓	$0.451$	$0$	$1.39344$	Character $\chi_{585}(212, \cdot)$
1-585-585.218-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.218	$0$	✓	✓	$-0.451$	$0$	$0.492753$	Character $\chi_{585}(218, \cdot)$
1-585-585.223-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.223	$0$	✓	✓	$0.296$	$0$	$1.36859$	Character $\chi_{585}(223, \cdot)$
1-585-585.23-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.23	$0$	✓	✓	$-0.0623$	$0$	$0.613560$	Character $\chi_{585}(23, \cdot)$
1-585-585.232-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.232	$0$	✓	✓	$-0.433$	$0$	$0.0579795$	Character $\chi_{585}(232, \cdot)$
1-585-585.239-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.239	$0$	✓	✓	$0.241$	$0$	$1.71622$	Character $\chi_{585}(239, \cdot)$
1-585-585.254-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.254	$0$	✓	✓	$-0.273$	$0$	$0.442554$	Character $\chi_{585}(254, \cdot)$
1-585-585.257-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.257	$0$	✓	✓	$-0.386$	$0$	$0.693645$	Character $\chi_{585}(257, \cdot)$
1-585-585.259-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.259	$0$	✓	✓	$-0.444$	$0$	$0.370612$	Character $\chi_{585}(259, \cdot)$
1-585-585.263-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.263	$0$	✓	✓	$0.343$	$0$	$1.28182$	Character $\chi_{585}(263, \cdot)$
1-585-585.268-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.268	$0$	✓	✓	$0.170$	$0$	$1.46205$	Character $\chi_{585}(268, \cdot)$
1-585-585.272-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.272	$0$	✓	✓	$-0.356$	$0$	$0.624715$	Character $\chi_{585}(272, \cdot)$
1-585-585.284-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.284	$0$	✓	✓	$-0.132$	$0$	$1.20422$	Character $\chi_{585}(284, \cdot)$
1-585-585.292-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.292	$0$	✓	✓	$0.109$	$0$	$1.73360$	Character $\chi_{585}(292, \cdot)$
1-585-585.302-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.302	$0$	✓	✓	$0.408$	$0$	$1.58309$	Character $\chi_{585}(302, \cdot)$
1-585-585.308-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.308	$0$	✓	✓	$-0.408$	$0$	$0.449731$	Character $\chi_{585}(308, \cdot)$
1-585-585.344-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.344	$0$	✓	✓	$0.132$	$0$	$1.32510$	Character $\chi_{585}(344, \cdot)$
1-585-585.347-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.347	$0$	✓	✓	$-0.343$	$0$	$0.718425$	Character $\chi_{585}(347, \cdot)$
1-585-585.358-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.358	$0$	✓	✓	$0.138$	$0$	$0.834106$	Character $\chi_{585}(358, \cdot)$
1-585-585.38-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.38	$0$	✓	✓	$-0.0325$	$0$	$0.838833$	Character $\chi_{585}(38, \cdot)$
1-585-585.382-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.382	$0$	✓	✓	$-0.170$	$0$	$0.464490$	Character $\chi_{585}(382, \cdot)$
1-585-585.394-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.394	$0$	✓	✓	$-0.0257$	$0$	$0.752099$	Character $\chi_{585}(394, \cdot)$
1-585-585.4-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.4	$0$	✓	✓	$-0.136$	$0$	$0.951836$	Character $\chi_{585}(4, \cdot)$
1-585-585.407-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.407	$0$	✓	✓	$0.0623$	$0$	$1.12850$	Character $\chi_{585}(407, \cdot)$
1-585-585.418-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.418	$0$	✓	✓	$0.185$	$0$	$1.17208$	Character $\chi_{585}(418, \cdot)$
1-585-585.427-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.427	$0$	✓	✓	$0.455$	$0$	$1.76484$	Character $\chi_{585}(427, \cdot)$
1-585-585.428-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.428	$0$	✓	✓	$0.356$	$0$	$1.77862$	Character $\chi_{585}(428, \cdot)$
1-585-585.434-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.434	$0$	✓	✓	$-0.147$	$0$	$0.371020$	Character $\chi_{585}(434, \cdot)$
1-585-585.439-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.439	$0$	✓	✓	$0.136$	$0$	$1.60944$	Character $\chi_{585}(439, \cdot)$
1-585-585.448-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.448	$0$	✓	✓	$-0.455$	$0$	$0.557425$	Character $\chi_{585}(448, \cdot)$
1-585-585.452-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.452	$0$	✓	✓	$0.224$	$0$	$1.10138$	Character $\chi_{585}(452, \cdot)$
1-585-585.454-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.454	$0$	✓	✓	$0.444$	$0$	$1.36227$	Character $\chi_{585}(454, \cdot)$
1-585-585.457-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.457	$0$	✓	✓	$-0.0271$	$0$	$1.33880$	Character $\chi_{585}(457, \cdot)$
1-585-585.463-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.463	$0$	✓	✓	$0.0595$	$0$	$0.891350$	Character $\chi_{585}(463, \cdot)$
1-585-585.479-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.479	$0$	✓	✓	$0.478$	$0$	$1.39794$	Character $\chi_{585}(479, \cdot)$
1-585-585.484-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.484	$0$	✓	✓	$-0.0684$	$0$	$0.941561$	Character $\chi_{585}(484, \cdot)$
1-585-585.49-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.49	$0$	✓	✓	$0.0257$	$0$	$1.39697$	Character $\chi_{585}(49, \cdot)$
1-585-585.497-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.497	$0$	✓	✓	$0.0196$	$0$	$1.09956$	Character $\chi_{585}(497, \cdot)$
1-585-585.502-r0-0-0	$2.71$	$2.71$	$1$	$3^{2} \cdot 5 \cdot 13$	585.502	$0$	✓	✓	$-0.153$	$0$	$0.315511$	Character $\chi_{585}(502, \cdot)$

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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.