Every conductor (and free space, and well really everything) has both capacitance and inductance inherent which cannot be made zero. This means that your coil while being mostly an inductor has a small bit of parasitic capacitance. To find out what it is,
pulse your coil with a sharp square wave.
Record the frequency of the subsequent "ring"
Get the equation for "LC" or "Tank" resonance
Input the variables of frequency, and inductance, and solve for capacitance.
Hope this helps!