The polynomial $f(z)=a{z}^{2018}+b{z}^{2017}+c{z}^{2016}$ 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 $1000$.