Gaussian window and standard deviation
The manual entry does not say that $\alpha = 1/\sigma$. It says $\alpha$ is proportional to the inverse of $\sigma$.

If you look at the example on that page you'll see

stdev = (N-1)/(2*alpha);


which, for your values says

stdev = (100-1)/(2*16.6667) = 825


you should be scaling the relationship by $N-1$.