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 $T({10}^4)=49348022079085897$.

Find $T({10}^8)mod1000000007$.