The impedance evaluated at s= 0 is:

Z(0)=1.8k Ohm

Poles at:

P1=2.58*10^6j

P2=-2.58*10^6j

Zeros at:

C1=-2.78*10^5+2.57*10^6j

C2=-2.78*10^5-2.57*10^6j

The only clue I have is that the circuit has a resistor, a capacitor and a coil, but I don't know the topology.

I think that if the poles are imaginary conjugates then the answer has to be without loss or oscillatory, but I'm not sure, the input impedance could be this way