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We show, a simple and natural example of a homogeneous polynomial with an orbit that is at the same time $d$-dense (the orbit meets every ball of radius $d$), weakly dense and such that $\\Gamma \\cdot Orb_P(x)$ is dense for every $\\Gamma\\subset \\mathbb C$ that is either unbounded or that has 0 as an accumulation point.\n  Moreover we generalize the construction to arbitrary infinite dimensional separable Fr\\'echet spaces. 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