5958：New Signal Decomposition

We consider a sequence A with p float-point numbers denoted by $a_0,a_1,...,a_{p-1}$ where p is a prime number. To simplify our problem, we guarantee that p must be 13, 103 or 100003.
To make a decomposition for this sequence, we define the kernal functions
$$r(h,k)=2^{sin^{3}(2\pi \frac{hk}{p})}$$
Therefore we can get a new sequence B = {$b_0,b_1,  ... , b_{p-1}$} tranformed from the original sequence A where
$$b_{k}=\sum_{h=0}^{p-1}a_{h}*r(h,k)$$
Your mission is to calculate the new sequence B.

The first line is the number of test cases. Each test case contains two lines. The first line contains an integer p. The second line contains p float-point numbers corresponding to the sequence A.

For each test case, output p float-point numbers rounded to three decimal places in one line corresponding to the sequence B.