# find roots

Algebra Level 5

Given the polynomial $G(x)=16x^4+8x^3+4x^2+2x+1$ has roots $$\quad a_1,a_2,a_3,a_4 \quad$$that can be written as $$\quad x_n (\cos (z_n\pi )+i\sin (z_n\pi))\quad$$, where $$0 \leq z_i < 2 \pi$$. $\sum_{n=1}^4 \dfrac{x_n}{z_n}$ can be written as $$\quad\dfrac{a}{b}\quad$$ where a and be are coprime integers. find $$a+b$$

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