Above the arctic circle it would never rise on the Summer solstice, by definition.
Think of the Sun doing a full lap of the sky, clockwise in the Northern hemisphere. So at 6:00 it is due East, at 12:00 it is due South, 18:00 it is due West and 24:00 it is due North. So if sunrise is at 3:00 at a particular place on a particular day then the sun will rise in a NE direction.
On the Summer solstice, at a point just below the arctic circle, sunrise will be at 00:01, and the Sun will be just a smidgeon East of due North.
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