I think you might be making your calculation based on the minutes going from 1-60 as opposed to 0-59. 18 deg 54 minutes should get you 18.91666666667, squared to 357.840277778. Perfectly precise? No, but certainly curious, especially in lacking a star based rationale for it's exaltation degree. To n...

To note, the Sun's specific exaltation degree of 18Aries54 is the square root of 360.