Below we use x = RootOf( z^2+z+1 ) and y = 1+x.
GF(2)  GF(3)  GF(4)  GF(5)  
(trace)  
n  1  0  1,2  0  1,x,y  0  1,2,3,4  0 
1  1  1  1  1  1  1  1  1 
2  1  0  1  1  2  0  2  2 
3  1  1  3  2  5  5  8  8 
4  2  1  6  6  16  12  30  30 
5  3  3  16  16  51  51  125  124 
6  5  4  39  38  170  160  516  516 
7  9  9  104  104  585  585  2232  2232 
8  16  14  270  270  2048  2016  9750  9750 
9  28  28  729  726  7280  7280  43400  43400 
10  51  48  1960  1960  26214  26112  195250  195248 
11  93  93  5368  5368  95325  95325  887784  887784 
12  170  165  14742  14736  349520  349180  4068740  4068740 
13  315  315  40880  40880  1290555  1290555  18780048  18780048 
14  585  576  113828  113828  4793490  4792320  87191964  87191964 
15  1091  1091  318864  318848  17895679  17895679  406901000  406900992 
16  2048  2032  896670  896670  67108864  67104768  1907343750  1907343750 
I_{q}(n,1) = 


[gcd(d,q)=1] µ(d) q ^{n/d} . 
Here [P] is 1 if P is true, and is 0 if P is false. If q is the power of prime p, then the condition [gcd(d,q)=1] is equivalent to [p does not divide d].