Percentage of Units in the Set of Integers Mod n for n = 2 through 50

*The Code*

def units(n):
    u = []
    elem = list(range(1,n))
    o = 1
    while o < n:
        for x in elem:
            if (x * o) % n == 1:
                if o not in u:
                    list.append(u,o)
        o += 1
    print("The Units for the Integers Mod ", str(n), " are: ", str(u))

    b = "{:.0%}".format(len(u)/n)

    print("The percentage of which is ", str(b))

a = list(range(2,51))

for x in a:
    units(x)

*********************************************************

*The Results*

The Units for the Integers Mod  2  are:  [1]
The percentage of which is  50%
The Units for the Integers Mod  3  are:  [1, 2]
The percentage of which is  67%
The Units for the Integers Mod  4  are:  [1, 3]
The percentage of which is  50%
The Units for the Integers Mod  5  are:  [1, 2, 3, 4]
The percentage of which is  80%
The Units for the Integers Mod  6  are:  [1, 5]
The percentage of which is  33%
The Units for the Integers Mod  7  are:  [1, 2, 3, 4, 5, 6]
The percentage of which is  86%
The Units for the Integers Mod  8  are:  [1, 3, 5, 7]
The percentage of which is  50%
The Units for the Integers Mod  9  are:  [1, 2, 4, 5, 7, 8]
The percentage of which is  67%
The Units for the Integers Mod  10  are:  [1, 3, 7, 9]
The percentage of which is  40%
The Units for the Integers Mod  11  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
The percentage of which is  91%
The Units for the Integers Mod  12  are:  [1, 5, 7, 11]
The percentage of which is  33%
The Units for the Integers Mod  13  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
The percentage of which is  92%
The Units for the Integers Mod  14  are:  [1, 3, 5, 9, 11, 13]
The percentage of which is  43%
The Units for the Integers Mod  15  are:  [1, 2, 4, 7, 8, 11, 13, 14]
The percentage of which is  53%
The Units for the Integers Mod  16  are:  [1, 3, 5, 7, 9, 11, 13, 15]
The percentage of which is  50%
The Units for the Integers Mod  17  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
The percentage of which is  94%
The Units for the Integers Mod  18  are:  [1, 5, 7, 11, 13, 17]
The percentage of which is  33%
The Units for the Integers Mod  19  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
The percentage of which is  95%
The Units for the Integers Mod  20  are:  [1, 3, 7, 9, 11, 13, 17, 19]
The percentage of which is  40%
The Units for the Integers Mod  21  are:  [1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20]
The percentage of which is  57%
The Units for the Integers Mod  22  are:  [1, 3, 5, 7, 9, 13, 15, 17, 19, 21]
The percentage of which is  45%
The Units for the Integers Mod  23  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]
The percentage of which is  96%
The Units for the Integers Mod  24  are:  [1, 5, 7, 11, 13, 17, 19, 23]
The percentage of which is  33%
The Units for the Integers Mod  25  are:  [1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24]
The percentage of which is  80%
The Units for the Integers Mod  26  are:  [1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25]
The percentage of which is  46%
The Units for the Integers Mod  27  are:  [1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26]
The percentage of which is  67%
The Units for the Integers Mod  28  are:  [1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, 27]
The percentage of which is  43%
The Units for the Integers Mod  29  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]
The percentage of which is  97%
The Units for the Integers Mod  30  are:  [1, 7, 11, 13, 17, 19, 23, 29]
The percentage of which is  27%
The Units for the Integers Mod  31  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]
The percentage of which is  97%
The Units for the Integers Mod  32  are:  [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]
The percentage of which is  50%
The Units for the Integers Mod  33  are:  [1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 17, 19, 20, 23, 25, 26, 28, 29, 31, 32]
The percentage of which is  61%
The Units for the Integers Mod  34  are:  [1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 33]
The percentage of which is  47%
The Units for the Integers Mod  35  are:  [1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 26, 27, 29, 31, 32, 33, 34]
The percentage of which is  69%
The Units for the Integers Mod  36  are:  [1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35]
The percentage of which is  33%
The Units for the Integers Mod  37  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]
The percentage of which is  97%
The Units for the Integers Mod  38  are:  [1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 27, 29, 31, 33, 35, 37]
The percentage of which is  47%
The Units for the Integers Mod  39  are:  [1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22, 23, 25, 28, 29, 31, 32, 34, 35, 37, 38]
The percentage of which is  62%
The Units for the Integers Mod  40  are:  [1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39]
The percentage of which is  40%
The Units for the Integers Mod  41  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]
The percentage of which is  98%
The Units for the Integers Mod  42  are:  [1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41]
The percentage of which is  29%
The Units for the Integers Mod  43  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42]
The percentage of which is  98%
The Units for the Integers Mod  44  are:  [1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 35, 37, 39, 41, 43]
The percentage of which is  45%
The Units for the Integers Mod  45  are:  [1, 2, 4, 7, 8, 11, 13, 14, 16, 17, 19, 22, 23, 26, 28, 29, 31, 32, 34, 37, 38, 41, 43, 44]
The percentage of which is  53%
The Units for the Integers Mod  46  are:  [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45]
The percentage of which is  48%
The Units for the Integers Mod  47  are:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]
The percentage of which is  98%
The Units for the Integers Mod  48  are:  [1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47]
The percentage of which is  33%
The Units for the Integers Mod  49  are:  [1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48]
The percentage of which is  86%
The Units for the Integers Mod  50  are:  [1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49]
The percentage of which is  40%