How to find the value of $$1+4\omega+9\omega^{2}+\cdot\cdot\cdot +n ^{2}\omega^{n-1}$$ where $\omega$ is a primitive $n$th root of unity? I am trying to find the value using the fact that $$1+\omega+\omega^{2}+\cdot+\cdot\cdot+\omega^{n-1}=0$$
but did't get the answer. Please suggest me how to solve it. Thanks in advance.