Software is probably not necessary for most purposes. Here is a table I created of the azimuth and elevation angles for Polaris for Local Sidereal times from 0h to 23h in intervals of 2 hours. The first column is your geographic latitude in degrees. The entries are in two rows per latitude; the first row is the azimuth angle for LST = 0h, 2h, 4h, 6h, .... 20h. The second row is the elevation angle above the horizon. Example, at a latitude of +40 degrees, for LST = 10h the entry pair is ( 358.7 and 40.0) or Azimuth = 358.7 and elevation = 40.0. The coordinates for Polaris I used are for epoch 1950.0 at RA = 1h 48m 48.7s and +89d 1' 42". If anyone is interested, I can generate the missing 22h entry, but the values change so slowly that this may not be interesting to add for most purposes. The table shows that Polaris executes a small orbit around the North Equatorial Pole as the Earth rotates.
; 0.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; -0.9 -1.0 -0.8 -0.4 0.0 0.5 0.9 1.0 0.8 0.4 ; ; 1.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; 0.1 0.0 0.2 0.6 1.0 1.5 1.9 2.0 1.8 1.4 ; ; 2.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; 1.1 1.0 1.2 1.6 2.0 2.5 2.9 3.0 2.8 2.4 ; ; 3.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; 2.1 2.0 2.2 2.6 3.0 3.5 3.9 4.0 3.8 3.4 ; ; 4.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 359.9 359.5 359.1 ; 3.1 3.0 3.2 3.6 4.0 4.5 4.9 5.0 4.8 4.4 ; ; 5.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; 4.1 4.0 4.2 4.6 5.0 5.5 5.9 6.0 5.8 5.4 ; ; 6.0 359.6 359.9 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; 5.1 5.0 5.2 5.6 6.0 6.5 6.9 7.0 6.8 6.4 ; ; 7.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; 6.1 6.0 6.2 6.6 7.0 7.5 7.9 8.0 7.8 7.4 ; ; 8.0 359.6 360.0 359.5 359.1 359.0 359.2 359.6 360.0 359.5 359.1 ; 7.1 7.0 7.2 7.6 8.0 8.5 8.9 9.0 8.8 8.4 ; ; 9.0 359.6 360.0 359.5 359.1 359.0 359.2 359.5 360.0 359.5 359.1 ; 8.1 8.0 8.2 8.6 9.0 9.5 9.9 10.0 9.8 9.4 ; ; 10.0 359.5 359.9 359.5 359.1 359.0 359.2 359.5 360.0 359.5 359.1 ; 9.1 9.0 9.2 9.6 10.0 10.5 10.9 11.0 10.8 10.4 ; ; 11.0 359.5 360.0 359.5 359.1 359.0 359.2 359.5 360.0 359.5 359.1 ; 10.1 10.0 10.2 10.6 11.0 11.5 11.9 12.0 11.8 11.4 ; ; 12.0 359.5 360.0 359.5 359.1 359.0 359.2 359.5 360.0 359.5 359.1 ; 11.1 11.0 11.2 11.6 12.0 12.5 12.9 13.0 12.8 12.4 ; ; 13.0 359.5 360.0 359.5 359.1 359.0 359.2 359.5 360.0 359.5 359.1 ; 12.1 12.0 12.2 12.6 13.0 13.5 13.9 14.0 13.8 13.4 ; ; 14.0 359.5 360.0 359.5 359.1 359.0 359.2 359.5 359.9 359.5 359.1 ; 13.1 13.0 13.2 13.6 14.0 14.5 14.9 15.0 14.8 14.4 ; ; 15.0 359.5 360.0 359.5 359.1 359.0 359.2 359.5 359.9 359.5 359.1 ; 14.1 14.0 14.2 14.6 15.0 15.5 15.9 16.0 15.8 15.4 ; ; 16.0 359.5 360.0 359.5 359.1 359.0 359.1 359.5 359.9 359.5 359.1 ; 15.1 15.0 15.2 15.6 16.0 16.5 16.9 17.0 16.8 16.4 ; ; 17.0 359.5 359.9 359.5 359.1 359.0 359.1 359.5 359.9 359.4 359.1 ; 16.1 16.0 16.2 16.6 17.0 17.5 17.9 18.0 17.8 17.4 ; ; 18.0 359.5 360.0 359.4 359.1 359.0 359.1 359.5 359.9 359.4 359.1 ; 17.1 17.0 17.2 17.6 18.0 18.5 18.9 19.0 18.8 18.4 ; ; 19.0 359.5 359.9 359.4 359.1 359.0 359.1 359.5 359.9 359.4 359.1 ; 18.1 18.0 18.2 18.6 19.0 19.5 19.9 20.0 19.8 19.4 ; ; 20.0 359.5 359.9 359.4 359.1 359.0 359.1 359.5 359.9 359.4 359.1 ; 19.1 19.0 19.2 19.6 20.0 20.5 20.9 21.0 20.8 20.4 ; ; 21.0 359.5 360.0 359.4 359.1 359.0 359.1 359.5 359.9 359.4 359.1 ; 20.1 20.0 20.2 20.6 21.0 21.5 21.9 22.0 21.8 21.4 ; ; 22.0 359.5 359.9 359.4 359.1 359.0 359.1 359.5 359.9 359.4 359.1 ; 21.1 21.0 21.2 21.6 22.0 22.5 22.9 23.0 22.8 22.4 ; ; 23.0 359.5 359.9 359.4 359.1 358.9 359.1 359.5 359.9 359.4 359.1 ; 22.1 22.0 22.2 22.6 23.0 23.5 23.9 24.0 23.8 23.4 ; ; 24.0 359.5 359.9 359.4 359.1 358.9 359.1 359.5 359.9 359.4 359.1 ; 23.1 23.0 23.2 23.6 24.0 24.5 24.9 25.0 24.8 24.4 ; ; 25.0 359.5 359.9 359.4 359.0 358.9 359.1 359.5 359.9 359.4 359.0 ; 24.1 24.0 24.2 24.6 25.0 25.5 25.9 26.0 25.8 25.4 ; ; 26.0 359.5 360.0 359.4 359.0 358.9 359.1 359.5 359.9 359.4 359.0 ; 25.1 25.0 25.2 25.6 26.0 26.5 26.9 27.0 26.8 26.4 ; ; 27.0 359.5 359.9 359.4 359.0 358.9 359.1 359.5 359.9 359.4 359.0 ; 26.1 26.0 26.2 26.6 27.0 27.5 27.9 28.0 27.8 27.4 ; ; 28.0 359.5 360.0 359.4 359.0 358.9 359.1 359.5 360.0 359.4 359.0 ; 27.1 27.0 27.2 27.6 28.0 28.5 28.9 29.0 28.8 28.4 ; ; 29.0 359.5 359.9 359.4 359.0 358.9 359.1 359.5 359.9 359.4 359.0 ; 28.1 28.0 28.2 28.6 29.0 29.5 29.9 30.0 29.8 29.4 ; ; 30.0 359.5 359.9 359.4 359.0 358.9 359.1 359.5 359.9 359.4 359.0 ; 29.1 29.0 29.2 29.6 30.0 30.5 30.9 31.0 30.8 30.4 ; ; 31.0 359.5 359.9 359.4 359.0 358.9 359.0 359.5 359.9 359.4 359.0 ; 30.1 30.0 30.2 30.6 31.0 31.5 31.9 32.0 31.8 31.4 ; ; 32.0 359.5 359.9 359.4 359.0 358.9 359.0 359.5 359.9 359.4 359.0 ; 31.1 31.0 31.2 31.6 32.0 32.5 32.9 33.0 32.8 32.4 ; ; 33.0 359.5 359.9 359.4 359.0 358.8 359.0 359.5 359.9 359.4 359.0 ; 32.1 32.0 32.2 32.6 33.0 33.5 33.9 34.0 33.8 33.4 ; ; 34.0 359.5 359.9 359.4 359.0 358.8 359.0 359.5 359.9 359.4 359.0 ; 33.1 33.0 33.2 33.6 34.0 34.5 34.9 35.0 34.8 34.4 ; ; 35.0 359.5 360.0 359.4 359.0 358.8 359.0 359.5 359.9 359.4 358.9 ; 34.1 34.0 34.2 34.6 35.0 35.5 35.9 36.0 35.8 35.4 ; ; 36.0 359.5 359.9 359.4 358.9 358.8 359.0 359.4 359.9 359.3 358.9 ; 35.1 35.0 35.2 35.6 36.0 36.5 36.9 37.0 36.8 36.4 ; ; 37.0 359.5 359.9 359.3 358.9 358.8 359.0 359.4 359.9 359.3 358.9 ; 36.1 36.0 36.2 36.6 37.0 37.5 37.9 38.0 37.8 37.4 ; ; 38.0 359.4 359.9 359.3 358.9 358.8 359.0 359.4 359.9 359.3 358.9 ; 37.1 37.0 37.2 37.6 38.0 38.5 38.9 39.0 38.8 38.4 ; ; 39.0 359.4 359.9 359.3 358.9 358.8 358.9 359.4 359.9 359.3 358.9 ; 38.1 38.0 38.2 38.6 39.0 39.5 39.9 40.0 39.8 39.4 ; ; 40.0 359.4 359.9 359.3 358.9 358.7 358.9 359.4 359.9 359.3 358.9 ; 39.1 39.0 39.2 39.6 40.0 40.5 40.9 41.0 40.8 40.4 ; ; 41.0 359.4 359.9 359.3 358.9 358.7 358.9 359.4 359.9 359.3 358.8 ; 40.1 40.0 40.2 40.6 41.0 41.5 41.9 42.0 41.8 41.4 ; ; 42.0 359.4 359.9 359.3 358.8 358.7 358.9 359.4 359.9 359.3 358.8 ; 41.1 41.0 41.2 41.5 42.0 42.5 42.9 43.0 42.8 42.4 ; ; 43.0 359.4 359.9 359.3 358.8 358.7 358.9 359.4 359.9 359.3 358.8 ; 42.1 42.0 42.2 42.5 43.0 43.5 43.9 44.0 43.8 43.4 ; ; 44.0 359.4 359.9 359.3 358.8 358.7 358.9 359.4 359.9 359.3 358.8 ; 43.1 43.0 43.2 43.5 44.0 44.5 44.9 45.0 44.8 44.4 ; ; 45.0 359.4 359.9 359.3 358.8 358.6 358.8 359.4 359.9 359.2 358.8 ; 44.1 44.0 44.2 44.5 45.0 45.5 45.9 46.0 45.8 45.4 ; ; 46.0 359.4 359.9 359.3 358.8 358.6 358.8 359.4 359.9 359.2 358.7 ; 45.1 45.0 45.2 45.5 46.0 46.5 46.9 47.0 46.8 46.4 ; ; 47.0 359.4 359.9 359.2 358.7 358.6 358.8 359.3 359.9 359.2 358.7 ; 46.1 46.0 46.2 46.5 47.0 47.5 47.9 48.0 47.8 47.4 ; ; 48.0 359.3 359.9 359.2 358.7 358.5 358.8 359.3 359.9 359.2 358.7 ; 47.1 47.0 47.2 47.5 48.0 48.5 48.9 49.0 48.8 48.4 ; ; 49.0 359.3 359.9 359.2 358.7 358.5 358.7 359.3 359.9 359.2 358.7 ; 48.1 48.0 48.2 48.5 49.0 49.5 49.9 50.0 49.8 49.4 ; ; 50.0 359.3 359.9 359.2 358.7 358.5 358.7 359.3 359.9 359.2 358.6 ; 49.1 49.0 49.2 49.5 50.0 50.5 50.9 51.0 50.8 50.4 ; ; 51.0 359.3 359.9 359.2 358.6 358.5 358.7 359.3 359.9 359.1 358.6 ; 50.1 50.0 50.2 50.5 51.0 51.5 51.9 52.0 51.8 51.4 ; ; 52.0 359.3 359.9 359.2 358.6 358.4 358.7 359.3 359.9 359.1 358.6 ; 51.1 51.0 51.2 51.5 52.0 52.5 52.9 53.0 52.8 52.4 ; ; 53.0 359.3 359.9 359.1 358.6 358.4 358.6 359.2 359.9 359.1 358.5 ; 52.1 52.0 52.2 52.5 53.0 53.5 53.9 54.0 53.8 53.4 ; ; 54.0 359.3 359.9 359.1 358.5 358.3 358.6 359.2 359.9 359.1 358.5 ; 53.1 53.0 53.2 53.5 54.0 54.5 54.9 55.0 54.8 54.4 ; ; 55.0 359.2 359.9 359.1 358.5 358.3 358.6 359.2 359.9 359.1 358.5 ; 54.1 54.0 54.2 54.5 55.0 55.5 55.9 56.0 55.8 55.4 ; ; 56.0 359.2 359.9 359.1 358.5 358.3 358.5 359.2 359.9 359.0 358.4 ; 55.1 55.0 55.2 55.5 56.0 56.5 56.9 57.0 56.8 56.4 ; ; 57.0 359.2 359.9 359.1 358.4 358.2 358.5 359.2 359.9 359.0 358.4 ; 56.1 56.0 56.2 56.5 57.0 57.5 57.9 58.0 57.8 57.4 ; ; 58.0 359.2 359.9 359.0 358.4 358.2 358.4 359.1 359.9 359.0 358.3 ; 57.1 57.0 57.2 57.5 58.0 58.5 58.9 59.0 58.8 58.4 ; ; 59.0 359.2 359.9 359.0 358.3 358.1 358.4 359.1 359.9 359.0 358.3 ; 58.1 58.0 58.2 58.5 59.0 59.5 59.9 60.0 59.8 59.4 ; ; 60.0 359.1 359.9 359.0 358.3 358.1 358.3 359.1 359.9 358.9 358.2 ; 59.1 59.0 59.2 59.5 60.0 60.5 60.9 61.0 60.8 60.4 ; ; 61.0 359.1 359.9 358.9 358.2 358.0 358.3 359.1 359.9 358.9 358.2 ; 60.1 60.0 60.2 60.5 61.0 61.5 61.9 62.0 61.8 61.4 ; ; 62.0 359.1 359.9 358.9 358.2 357.9 358.2 359.0 359.9 358.8 358.1 ; 61.1 61.0 61.2 61.5 62.0 62.5 62.9 63.0 62.8 62.4 ; ; 63.0 359.0 359.9 358.9 358.1 357.9 358.2 359.0 359.9 358.8 358.1 ; 62.1 62.0 62.2 62.5 63.0 63.5 63.9 64.0 63.8 63.4 ; ; 64.0 359.0 359.9 358.8 358.1 357.8 358.1 359.0 359.9 358.8 358.0 ; 63.1 63.0 63.2 63.5 64.0 64.5 64.9 65.0 64.8 64.4 ; ; 65.0 359.0 359.9 358.8 358.0 357.7 358.0 358.9 359.9 358.7 357.9 ; 64.1 64.0 64.2 64.5 65.0 65.5 65.9 66.0 65.8 65.4 ; ; 66.0 358.9 359.9 358.7 357.9 357.6 358.0 358.9 359.9 358.7 357.8 ; 65.1 65.0 65.2 65.5 66.0 66.5 66.9 67.0 66.8 66.4 ; ; 67.0 358.9 359.9 358.7 357.8 357.5 357.9 358.8 359.9 358.6 357.7 ; 66.1 66.0 66.2 66.5 67.0 67.5 67.9 68.0 67.8 67.4 ; ; 68.0 358.9 359.9 358.6 357.7 357.4 357.8 358.8 359.9 358.5 357.6 ; 67.1 67.0 67.2 67.5 68.0 68.5 68.9 69.0 68.8 68.4 ; ; 69.0 358.8 359.9 358.6 357.6 357.3 357.7 358.7 359.9 358.5 357.5 ; 68.1 68.0 68.2 68.5 69.0 69.5 69.9 70.0 69.8 69.4 ; ; 70.0 358.8 359.9 358.5 357.5 357.2 357.6 358.6 359.8 358.4 357.4 ; 69.1 69.0 69.2 69.5 70.0 70.5 70.9 71.0 70.8 70.4 ; ; 71.0 358.7 359.9 358.4 357.4 357.0 357.4 358.6 359.8 358.3 357.3 ; 70.1 70.0 70.2 70.5 71.0 71.5 71.9 72.0 71.8 71.4 ; ; 72.0 358.6 359.9 358.4 357.3 356.9 357.3 358.5 359.8 358.2 357.1 ; 71.1 71.0 71.2 71.5 72.0 72.5 72.9 73.0 72.8 72.4 ; ; 73.0 358.6 359.9 358.3 357.1 356.7 357.1 358.4 359.8 358.1 357.0 ; 72.1 72.0 72.2 72.5 73.0 73.5 73.9 74.0 73.8 73.4 ; ; 74.0 358.5 359.8 358.2 356.9 356.5 356.9 358.3 359.8 358.0 356.8 ; 73.1 73.0 73.2 73.5 74.0 74.5 74.9 75.0 74.8 74.4 ; ; 75.0 358.4 359.8 358.1 356.8 356.2 356.7 358.2 359.8 357.9 356.6 ; 74.1 74.0 74.2 74.5 75.0 75.5 75.9 76.0 75.8 75.4 ; ; 76.0 358.3 359.8 357.9 356.5 356.0 356.5 358.0 359.8 357.7 356.3 ; 75.1 75.0 75.2 75.5 76.0 76.5 76.9 77.0 76.8 76.4 ; ; 77.0 358.1 359.8 357.8 356.3 355.7 356.2 357.9 359.8 357.5 356.0 ; 76.1 76.0 76.2 76.5 77.0 77.5 77.9 78.0 77.8 77.4 ; ; 78.0 358.0 359.8 357.6 356.0 355.3 355.9 357.7 359.8 357.3 355.7 ; 77.1 77.0 77.2 77.5 78.0 78.5 78.9 79.0 78.8 78.4 ; ; 79.0 357.8 359.8 357.4 355.7 354.9 355.5 357.5 359.7 357.0 355.3 ; 78.1 78.0 78.2 78.5 79.0 79.5 79.9 80.0 79.8 79.4 ; ; 80.0 357.6 359.8 357.2 355.2 354.4 355.0 357.2 359.7 356.7 354.8 ; 79.1 79.0 79.2 79.5 80.0 80.5 80.9 81.0 80.8 80.4 ; ; 81.0 357.4 359.7 356.9 354.7 353.8 354.5 356.9 359.7 356.3 354.2 ; 80.1 80.0 80.2 80.5 81.0 81.5 81.9 82.0 81.8 81.4 ; ; 82.0 357.1 359.7 356.6 354.1 353.0 353.7 356.4 359.6 355.8 353.5 ; 81.1 81.0 81.2 81.5 82.0 82.5 82.9 83.0 82.8 82.4 ; ; 83.0 356.8 359.7 356.1 353.4 352.0 352.8 355.9 359.5 355.1 352.5 ; 82.1 82.0 82.2 82.5 83.0 83.5 83.8 84.0 83.8 83.4 ; ; 84.0 356.3 359.6 355.6 352.3 350.7 351.5 355.0 359.4 354.2 351.1 ; 83.1 83.0 83.2 83.5 84.0 84.5 84.8 85.0 84.8 84.4 ; ; 85.0 355.7 359.6 354.8 351.0 360.0 360.0 353.9 359.3 352.8 360.0 ; 84.1 84.0 84.2 84.5 85.0 85.5 85.8 86.0 85.8 85.4 ; ; 86.0 354.8 359.4 353.8 360.0 360.0 360.0 351.9 359.1 350.6 360.0 ; 85.1 85.0 85.2 85.5 85.9 86.4 86.8 87.0 86.8 86.3 ; ; 87.0 353.4 359.4 352.1 360.0 360.0 360.0 360.0 358.7 360.0 360.0 ; 86.1 86.0 86.1 86.4 86.9 87.4 87.8 88.0 87.8 87.3 ;
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