A synchronous generator is connected to an infinite bus with excitation voltage $E_f$ = $1.3$ $pu$. The generator has a synchronous reactance of $1.1$ $pu$ and is delivering real power $(P)$ of $0.6$ $pu$ to the bus. Assume the infinite bus voltage to be $1.0$ $pu$. Neglect stator resistance. The reactive power $(Q)$ in $pu$ supplied by the generator to the bus under this condition is _________.