No chat gpt!!!! Please do it correctly and HANDWRITTEN.

Use the FFT algorithm to evaluate f(x)=84x+2x2+3x35x44x5+2x6+x7 at the eight 8 th roots of unity mod 17 . You may stop using recursion when evaluating a linear function (a+bx), which is easier to do directly. The eight 8 th roots of unity mod17 are 1,2,4,8,16, 15,13,9; it is easier to calculate with 1,2,4,8,1,2,4,8. Do this by hand, and show your work