How to plot the solutions of $f(z,a)=0$ on the complex plain of $z$?

I have an equation $ f(z,a)=0$ where $ z$ is a complex variable $ \frac {56}{10}<z<2\pi$ and $ a$ is a real variable $ 0<a<\pi$ .

I want to plot solutions of this equation on the complex plain $ z$ as $ a$ increases from $ 0$ to $ \pi$ , and show the behavior of $ z$ by changing the color of the curve (as $ a$ increases, the curve changes from blue to red), something like this plot

enter image description here

f[z_,a_]:=9 + 4 Cos[a - (273 z)/50] - 4 Cos[a - 2 z] - 2 Cos[2 z] -   3 Cos[(173 z)/50] + Cos[4 z] - 2 Cos[(273 z)/50] -   3 Cos[(373 z)/50] - 4 Cos[a + 2 z] + 4 Cos[a + (273 z)/50] -   4 I Sin[a - (273 z)/50] + 4 I Sin[a - 2 z] - 2 I Sin[2 z] -   3 I Sin[(173 z)/50] + I Sin[4 z] - 2 I Sin[(273 z)/50] -   3 I Sin[(373 z)/50] - 4 I Sin[a + 2 z] + 4 I Sin[a + (273 z)/50];   f[z,a]==0  56/10 <z<\[Pi] 0<a<\[Pi]