Polynomial stellar-mode coefficient reduction

When the amplitudes of uniform-density stellar oscillation are finite even polynomials, their highest coefficients close algebraically. With $L=n(2l+n+1)$ and $x={\omega }^2/{\omega }_d^2$, the nonradial coefficient determinant is $x^2+(4-\gamma L/2)x-l(l+1)$. A degree balance gives a necessary frequency relation without solving every lower coefficient or imposing surface conditions.