How do I make polynomial solutions evolve over time?

I have periodic system of zeros for 4th degree polynomial, and I use this relation to make all zeros evolve over timE

$ |f(t)> = exp(i t H)|f(0)> $ where H is:

\begin{align}

%\[

H=

\begin{bmatrix}

1& -1i& 0 & 0 & 0\\

1i & 1 & 0 & 0 & 0 \\

0 & 0 & 2.5 & 0 & 0 \\

0 & 0 & 0 & 2.5 & 0\\

0 & 0 & 0 & 0 & 2.5

\end{bmatrix}

%\]

\end{align}

and f0 = [0.2 + 0.0010i;0.1 + 0.0010i; 0.1 + 0.0020i;-0.3 + 0.001i;0.6 - 0.7i]; and t= 0:0.01:4*pi and I want to show the paths of zeros of this polynomial :

p=[0.2 + 0.0010i 0.2000 + 0.0020i 0.2449 + 0.0049i -0.6000 + 0.0020i 0.6 - 0.7i]; .

I used matlab to show this paths of all zeros of p but when t increases I got this figure where 3 zeros do not move and 1 zero move

How can me solve this problem please? I will appreciate any help?