def evaluate_g6( kappa, nu, eta, tau, sigma, l, mu, s6 ):
    """
    Evaluate the sixth constraint equation and also return the jacobians
    
    :param float kappa: The value of the modulus kappa
    :param float nu: The value of the modulus nu
    :param float eta: The value of the modulus eta
    :param float tau: The value of the modulus tau
    :param float sigma: The value of the modulus sigma
    :param float l: The value of the modulus lambda
    :param float mu: The value of the modulus mu
    :param float s6: The value of the constraint
    """

    return ( kappa + nu + 2 * eta - 3 * tau - 2 * sigma ) * ( 3 * l + 2 * mu ) - ( 3 * tau + 2 * sigma )**2 - s6**2,\
           { 'kappa':( 3 * l + 2 * mu ), 'nu':( 3 * l + 2 * mu ), 'eta':2 * ( 3 * l + 2 * mu ),\
             'tau':-3 * ( 3 * l + 2 * mu) - 6 * ( 3 * tau + 2 * sigma ),\
             'sigma':-2 * ( 3 * l + 2 * mu ) - 4 * ( 3 * tau + 2 * sigma ),\
             'lambda':3 * ( kappa + nu + 2 * eta - 3 * tau - 2 * sigma ),\
             'mu':2 * ( kappa + nu + 2 * eta - 3 * tau - 2 * sigma ),\
             's6':-2 * s6 }