An aircraft is flying steadily with an airspeed of $250$ m$/$s at a constant altitude. The Mach number is $0\mathrm{.}8$ and the mean geometric chord is $8$m$.$ The atmosphere conforms to the International Standard Atmosphere. $.$ The original flight altitude is $6938\mathrm{.}94$m$.$ The air density at the flight altitude is $0\mathrm{.}594$kg$/$m$^3.$

Calculate the Mach number of the aircraft if the altitude changes to $10$ km but the airspeed is unchanged. Then calculate the required lift coefficient to fly level at the new altitude as a percentage of the lift coefficient at the original altitude if the weight of the aircraft is unchanged.