Hello Florian,
congratulations on acquiring this wonderful instrument. 1997 is a good vintage.
Please make sure to immediately extract the content of the CAL RAM to avoid calibration loss.
You will find tons of information here, how to check your instrument for sanity, especially the U180 drift problem.
If you already infected by the the volt-nuts virus, you might already own a ~ 10V voltage and a ~ 10kOhm resistance reference, for checking and maybe calibration of your 3458A.
Several well equipped volt-nuts are living in UK, watch out for them to exchange amateur grade references, otherwise.
Your 3458A has very high impedance inputs, and very low bias / leakage currents.
Leaving the input open will show a slow rise or decrease of the readings, that's completely normal, and will then cause an overflow, or automatic up-ranging.
I usually put a short on the input jacks, to avoid this self-charging effect. 3.9µV is fine, when the instrument is cold and you're using a simple short.
With a proper, low e.m.f. short and fully warmed up, zero reading should be somewhere @ several tens of nV
Frank