  We compute the homotopy groups of the {\eta}-periodic motivic sphere spectrum
over a finite-dimensional field k with characteristic not 2 and in which -1 a
sum of four squares. We also study the general characteristic 0 case and show
that the {\eta}-periodic slice spectral sequence over Q determines the
{\eta}-periodic slice spectral sequence over all extensions of Q. This leads to
a speculation on the role of a "connective Witt-theoretic J-spectrum" in
{\eta}-periodic motivic homotopy theory.
