Why does negative number show up when I do FFT on a Gaussian?

Question

I'm using this fftw library.

Currently I'm trying to plot a 2D Gaussian in the form e^(-(x^2+y^2)/a^2).

Here is the code:

using namespace std;
int main(int argc, char** argv ){
    fftw_complex *in, *out, *data;
    fftw_plan p;
    int i,j;
    int w=16;
    int h=16;
    double a = 2;
    in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*w*h);
    out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)*w*h);
    for(i=0;i<w;i++){
        for(j=0;j<h;j++){
            in[i*h+j][0] = exp(- (i*i+j*j)/(a*a));
            in[i*h+j][1] = 0;
        }
    }
    p = fftw_plan_dft_2d(w, h, in, out, FFTW_FORWARD, FFTW_ESTIMATE);
    fftw_execute(p);
    //This is something that print what's in the matrix
    print_2d(out,w,h);

    fftw_destroy_plan(p);
    fftw_free(in);
    fftw_free(out);
    return 0;
}

Turns out negative numbers shows up. I thought Fourier transform of a Gaussian is another Gaussian, which shouldn't include any negative numbers.

Also, the current origin is at in[0]