this sucks because the product of roots are calculated by testing random coefficients and roots but it appears that this is the only way to solve it works for 5, 17, 257, and 65537-gons (65537 only generates the first 3 points and the rest are broken)
https://www.researchgate.net/publication/225263489_The_Simple_and_straightforward_construction_of_the_regular_257-gon
