alignment of text between 2 lines in align*

I have this:

\begin{align*}  &f(1) = -11 & &\mbox{while q satisfies} &q(1) = 11,\\  &f(-2) = 20 & &\mbox{} &q(-1) = 20  \end{align*}

which puts the text "while" on the same line as the first line (obviously). Is there a way to have it in the (vertical) middle of the two lines? I.e. in between the two lines.