def find_zetas_from_sigmas(sigmas, m):
    """Find first m complete symmetrical polynomials  zetas  using 'sigmas'.
    For this we use:
    zeta_k = \\sum_{i=1}^k (-1)^(i+1) sigmas[i] zetas_{k-i}."""
    zetas = [0.] * m
    zetas[0] = 1.
    for k in range(1, m):
        zetas[k] = sum([sigmas[i] * zetas[k - i] * (-1) ** (i + 1) for i in range(1, min(len(sigmas), k + 1))])
    return zetas