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)
