I never heard of symmetric beta having any other name.
It's defined on (0,1) so unless you invert it you can't do much.
I bet 1/T is a gamma.
Do you need an online calulator?
I know of p-value sites that may help you.
Or do you want me to transform it via 1/T?
Then you might get chi-square percentiles and flip them back.
I've never been asked this question b4.