We use Nordost Valhalla on ours. It gets out of the way and makes sure that we hear all the lovely detail that the 390s has to offer. Very different sound from the Golden Cross: IMO, more clarity and timeliness, less flavor of its own. Our 390s was originally a No. 39 (bought in '95 or '96) and it lived happily with Nordost Quattrofil for many years.
In my experience, the 390s really benefits from a good aftermarket power cord: we like the Shunyata Anaconda but notice a significant audible difference with the Python and with the Nordost El Dorado too. The Anaconda greatly improves the dynamics and opens up the sound.
If you are in a spot where you can do it I would highly recommend doing some in-home auditions of whichever cables make it onto your short list since it's your ears that need to be pleased.
We are dealers for Nordost and Shunyata but not for Levinson.