# 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 $$\frac {56}{10} and $$a$$ is a real variable $$0.

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

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]