The set of all values of $a^{2}$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P\!\left(\dfrac{1+a}{2},\,\dfrac{1-a}{2}\right)$ on the circle $2x^{2}+2y^{2}-(1+a)x-(1-a)y=0$, is equal to: