def euler_p_factor(root_list, PREC): ''' computes the coefficients of the pth Euler factor expanded as a geometric series ax^n is the Dirichlet series coefficient p^(-ns) ''' PREC = floor(PREC) # return satake_list R = PowerSeriesRing(CF, 'x') x = R.gen() ep = ~R.prod([1 - a * x for a in root_list]) return ep.O(PREC + 1)