def _small_conducting_mie(m, x):
    """
    Calculate the efficiencies for a small conducting spheres.

    Typically used for small conducting spheres where x < 0.1 and
    m.real == 0

    Args:
        m: the complex index of refraction of the sphere
        x: the size parameter of the sphere

    Returns:
        qext: the total extinction efficiency
        qsca: the scattering efficiency
        qback: the backscatter efficiency
        g: the average cosine of the scattering phase function
    """
    ahat1 = complex(0, 2.0 / 3.0 * (1 - 0.2 * x**2)) / \
        complex(1 - 0.5 * x**2, 2.0 / 3.0 * x**3)
    bhat1 = complex(0.0, (x**2 - 10.0) / 30.0) / \
        complex(1 + 0.5 * x**2, -x**3 / 3.0)
    ahat2 = complex(0.0, x**2 / 30.)
    bhat2 = complex(0.0, -x**2 / 45.)

    qsca = x**4 * (6 * abs(ahat1)**2 + 6 * abs(bhat1)**2 + 10 * abs(ahat2)**2 +
                   10 * abs(bhat2)**2)
    qext = qsca
    g = ahat1.imag * (ahat2.imag + bhat1.imag)
    g += bhat2.imag * (5.0 / 9.0 * ahat2.imag + bhat1.imag)
    g += ahat1.real * bhat1.real
    g *= 6 * x**4 / qsca

    qback = 9 * x**4 * abs(ahat1 - bhat1 - 5 / 3 * (ahat2 - bhat2))**2

    return [qext, qsca, qback, g]