Inductance vs. frequency

I'm really interested in, is how does the impedance change as a function of frequency: 600 Hz through 2000 Hz? Yes, w*L will be higher as a linear function of frequency. Given. Is there a non-linearity in the impedance vs. frequency? ...does the coupling coefficient change vs. frequency - and therefore, the transformer does not "reflect" the impedance of the grid as firmly at 1kHz as it does at 60 Hz due to the frequency response of core magnetization?

...I know that 60 Hz is the quantum frequency at which everything in the universe oscillates, but at least humor the questions. Serious replies only, please.

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