How can I use discrete fourier transformation on a set of complex values and real values and use that to determine the missing values?

Question

I know that the time of the sample is

T = 9

and the sample rate is 0.5.

The 10 first values of the DFT-sequence are as follows:

{4, 1+3i, 0, 2, 0, -2i, (1-i)/4, 0, -1/25, 0...}

and I am to find out what the missing samples are (10 known samples, 18 samples in total).

How am I to approach this problem?