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# Problem 596

## Number of lattice points in a hyperball

Let T($r$) be the number of integer quadruplets $x$, $y$, $z$, $t$ such that $x^2+y^2+z^2+t^2 \le r^2$. 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(104) = 49348022079085897.

Find T(108) mod 1000000007.