def a_j(j):
    """The a_j coefficients from the spec
    """
    return [
        0,
        0,
        8.072789087,
        -81.24549382,
        408.0297321,
        -1244.129167,
        2444.046270,
        -3120.635139,
        2506.663551,
        -1151.003178,
        230.2006355,
    ][j]