Sunday, 18 July 2021

The polynomial \(f(z)=az^{2018}+bz^{2017}+cz^{2016}\) has real coefficients not exceeding \(2019\), and \(f\left(\tfrac{1+\sqrt{3}i}{2}\right)=2015+2019\sqrt{3}i\). Find the remainder when \(f(1)\) is divided by \(1000\).
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