# Isn't it just 413?

$$f(x)$$ is a polynomial of degree $$413$$ with non-negative integral coefficients such that $$f(1)=612^{1025}.$$ John is a genie that will tell you $$f(x)$$ for any $$x$$ you tell him. What is the minimum number of $$\textit{additional}$$ values of $$f(x)$$ you must ask John for to be able to uniquely determine the polynomial?

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