If you wish to avoid looking up tables or carrying out long calculations you could try the following approach.
One method of calculating the TAS at any given mach number is
TAS at any given Mach number (in knots) = Mach number x 38.94 x the square root of the absolute temperature.
If was assume ISA conditions we have
The Tropopause is at approximately 36 000 feet.
Below the Tropopause the temperature decreases at a rate of approximately 2 degrees per 1000 feet altitude increase.
Above the Tropopause the temperature is constant.
FL350 = 35000 feet, which is 1000 feet below the tropopause.
FL410 is above the tropopause.
From the above we should be able to see that the temperature at FL350 is approximately 2 degrees higher than the temperature at FL410.
So the TAS at any given mach number will be greater at FL350 than at FL410.