Question 8The polynomial $f(z) = az^{2018} + bz^{2017} + cz^{2016}$ has real coefficients not exceeding $2019,$ and $f\left(\frac{1 + \sqrt{3}i}{2}\right) = 2015 + 2019\sqrt{3}i.$ Find the remainder when $f(1)$ is divided by $1000.$