Stainless steel open E string

Hi folks!

On my journey through the world of bass strings I've come to try Rotosound Swing Bass RS66LF. Put them on yesterday and all sounds great except for the open E string which sounds a bit chorusy. Before you all cry out "Another string chorus thread" let me continue.
I've checked all the typical reasons for this problem like pickup height, twisted string, break angle at the bridge/nut. All looks good. A few months ago I've had a set of D'Addario Pro Steels which had the same issue with the open E string. So my question is: Is this normal with new Stainless Steel strings? Does it disappear after they break in?
 
Could be a bad string. Since you have had the same problem on that bass, I would check the bass. Try lowering the pickups in half turns, see if it goes away. Also check the saddle and tuning pegs, with no string attached. May be an issue there. Tuner screws could be loose, etc.
Sometimes the truss rod can be in just the wrong place, for weird vibrations. You could try tightening or loosening it, a teeny bit.
 
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@Toptube: Thanks for your hints!

I replaced the string and this time made sure I leave it a little longer to get more windings on the tuning peg. Et voilá, great sounding open E string again.
I didn't know that the windings around the tuning peg had such an huge impact on the sound. I knew that there need to be some windings and to wind down so that the strings gets enough downward pressure past the nut. I've always cut the strings two tuning pegs further since this is the common recommendation and had no problem so far but it seems like the Rotos want more.
I checked some videos again on how to string a bass and on one video it was even recommended to only cut the excess core on the E and A string.
I know now that too few windings are not good but can too many windings cause a problem?