Define $$P(X_{a,b},X_{a,c},X_{a,d},X_{a,e},X_{b,c},X_{b,d},X_{b,e},X_{c,d},X_{c,e},X_{d,e})$$ as the sum of $2^a{3}^b{5}^c{7}^d{11}^e$ over all quintuples of non-negative integers $(a,b,c,d,e)$ such that the sum of each two of the five variables is restricted by a given value. In other words, $a+b\le X_{a,b}$, $a+d\le X_{a,d}$, $b+e\le X_{b,e}$ etc.

For example, $P(2,2,2,2,2,2,2,2,2,2)=7120$ and $P(1,2,3,4,5,6,7,8,9,10)\equiv 799809376(\mathrm{mod}{10}^9+7)$.

Define a sequence $A$ as follows:

• $A_0=1$, $A_1=7$;
• $A_n=(7A_{n-1}+A_{n-2}^2)mod({10}^9+7)$ for $n\ge 2$.

Also define $Q(n)=P(A_{10n},A_{10n+1},A_{10n+2},\dots ,A_{10n+9})$.

Find ${\displaystyle \sum _{0\le n<100}Q(n)}$. Give your answer modulo ${10}^9+7$.