Let \(a,b,c\) and \(d\) be non-negative integers satisfying \(a+b+c+d=360 \), and that \(b,c,d\) are multiplies of 2, 3, 5, respectively.

Let \(P \) denote the total number of solutions satisfying the condition above, and

\(Q\) denote the total number of solutions satisfying the condition above with an additional constraint of \(a= 0 \).

Find the sum of the first 7 digits of \(\dfrac QP \) after the decimal point.

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