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The first alignment star it picked was Sirius and nearly slew to it. it was about 2 degrees outside of the FOV
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Mine has always been the same, the alignment stars are never close. I seem to remember reading somewhere that the alignment stars are deliberately placed a little out, and the slewing process to the star is a necessary part of the alignment process (perhaps correction as Jen suggests). I can't remember where I read it though.
As David said, once aligned, tracking and slews are very accurate.
FWIW at my usual place of observing I use true north marked from the shadow of a vertical stick at solar noon as per
this thread.