import mpmath


def f(x):
    return (mpmath.pi + x + mpmath.sin(x)) / (2*mpmath.pi)


# Note: 40 digits might be overkill; a few more digits than the default
# might be sufficient.
mpmath.mp.dps = 40
ts = mpmath.taylor(f, -mpmath.pi, 20)
p, q = mpmath.pade(ts, 9, 10)

p = [float(c) for c in p]
q = [float(c) for c in q]
print('p =', p)
print('q =', q)