Let $f(n)$ be the number of $6$-tuples $(x_1,x_2,x_3,x_4,x_5,x_6)$ such that:

• All $x_i$ are integers with $0\le x_i<n$
• $gcd(x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2,n^2)=1$

Let ${\displaystyle G(n)={\displaystyle \sum _{k=1}^n\frac{f(k)}{k^2\phi (k)}}}$
where $\phi (n)$ is Euler's totient function.

For example, $G(10)=3053$ and $G({10}^5)\equiv 157612967(\mathrm{mod}1000000007)$.

Find $G({10}^{12})mod1000000007$.