def evaluate_g8( mu, kappa, nu, sigma, s8 ):
    """
    Evaluate the eighth constraint equation and also return the jacobian

    :param float mu: The value of the modulus mu
    :param float kappa: The value of the modulus kappa
    :param float nu: The value of the modulus nu
    :param float sigma: The value of the modulus sigma
    :param float s8: The value of the constraint
    """

    return 4 * mu * ( kappa + nu - 2 * sigma ) - 2 * sigma - s8**2,\
           { 'mu':4 * ( kappa + nu - 2 * sigma ), 'kappa': 4 * mu, 'nu': 4 * mu, 'sigma':-8 * mu - 2, 's8':-2 * s8 }