You should create an equivalent signal in the frequency domain, create the hermitian vector and then do an FFT. Since the each component in frequency should be represented by a phasor, you should adjust the phases of these phasors so that to have the peak at 35dBm.
dBm refers to the total output power, that is 10*log10(Power in mW)
dBm/Hz refers to the power spectrum density and is 10*log10(Power in mW/Bandwidth in Hz)
You actually have non consistent constraints since it is not possible to create a signal with +20dBm total power in that frequency range with only -60dBm/Hz of power density.