A Reciprocity Theorem for the case solved by Gauß using ``Integers'' of the form , when is a root if and , are Integers.
See also Reciprocity Theorem
Ireland, K. and Rosen, M. ``Cubic and Biquadratic Reciprocity.'' Ch. 9 in
A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 108-137, 1990.