Maybe not all roots of w can be found exactly. You may be able to obtain approximations with the following code.
P=CC[x](x^32 - x^30 + 3*x^28 - 3*x^26 + 6*x^24 - 6*x^22 + 9*x^20 - 9*x^18 + 12*x^16 - 9*x^14 + 9*x^12 - 6*x^10 + 6*x^8 - 3*x^6 + 3*x^4 - x^2 + 1)

Here CC denotes the Complex Field and CC[x] denotes the Polynomial Ring over CC.