fft: characteristic function to distribution

The characteristic function is the inverse Fourier transform of the
distribution function. The characteristic function of a normaly
distributed random variable is exp(-t^2/2).

x=seq(-2,2,length=100)
fft(pnorm(x),inverse=T)/length(x)
exp(-x^2/2)

Why aren't the inverse fft and the mentioned function the same?
Thanks for help,
Thomas

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