## Number of lattice points in a hyperball

### Problem 596

Let T(`r`) be the number of integer quadruplets `x`, `y`, `z`, `t` such that `x`^{2} + `y`^{2} + `z`^{2} + `t`^{2} ≤ `r`^{2}. In other words, T(`r`) is the number of lattice points in the four-dimensional hyperball of radius `r`.

You are given that T(2) = 89, T(5) = 3121, T(100) = 493490641 and T(10^{4}) = 49348022079085897.

Find T(10^{8}) mod 1000000007.