NavList:

Yes, the tables work.  I assume you do not have a copy of the NA?  FYI, here is the work for both of your examples:

Example 1 :
Lat 45°00'0 N, LHA 89°00'0, Dec 44°00'0 N
Result: H= 30°00'3 , Zn = 303.8°

Using NA's tables:
enter with (Lat, LHA)= (45,89), A= 44 59,  B= 01 00,  Z1= 1.4
F= Dec+B= 44 00 + 01 00 = 45 00
enter with (A, F)= (45, 45), H= 30 00,  P= 35 16,  Z2= 54.7
corrn= +1.  H= 30 01
Z= 1.4+54.7= 56.1, Zn= 360-Z= 303.9
NA result:  H= 30º 01', Zn 303.9º

Example 2:
Lat 45°00'0 N, LHA 45°00'0, Dec 02°10'0 N
Result: H= 31°45'7 , Zn = 236.2°

Using NA's tables:
enter with (Lat, LHA)= (45,45), A= 30 00,  B= 35 16,  Z1= 54.7
F= Dec+B= 02 10 + 35 16 = 37 26
enter with (A, F)= (30, 37), H= 31 25,  P= 54 08,  Z2= 69.4
corrn= +21.  H= 31 46
Z= 54.7+69.4= 124.1, Zn= 360-Z= 235.9
NA result:  H= 31º 46', Zn 235.9º
 

As you can see, for these two examples, the H from the table is within 1' of an exact computation.