Number of lattice points in a hyperball (noch nicht übersetzt)

Let T(r) be the number of integer quadruplets x, y, z, t such that x² + y² + z² + t² ≤ r². 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(10⁴) = 49348022079085897.

Find T(10⁸) mod 1000000007.