Help analyzing this coil

I have an Inductor and I ran a scan form 20Hz to 20KHz on an impedance meter and got very strange results. I measured L and |Z| and for starters got very different results than my DVM which is measuring in 270Hz. The plot starts with a value of 770mH @ 20Hz and goes up to around 950mH @ 20KHz, but the higher the freq. the more the inductance changes and it is not a monotonic function as it will jump up and down (the higher the freq.).

I also observed |Z| and I can see a pretty "random" behavior, here is the 1st part of the plot. I will appreciate explanations from people who know about magnetics.

The |Z| plot mainly suggests an unsuitable measurement setup or broken impedance meter.

To determine L and reasonable frequency range for the measurement, you should rather a show complex impedance or magnitude/phase plot.

Before impedance and LCR meters have been become popular, people used to determine complex impedances with a generator, a reference resistor and multiple voltage measurements on pencil and paper. It's still an option.

The strange thing is that is measures resistors and capacitors well, however having trouble with inductance...