| Cubic residue (CR) | x such that x3 = CR mod 169 | Occurance |
|---|---|---|
| 0 | 0, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156 | 13 |
| 1 | 1, 22, 146 | 3 |
| 5 | 7, 8, 154 | 3 |
| 8 | 2, 44, 123 | 3 |
| 12 | 17, 36, 116 | 3 |
| 14 | 61, 118, 159 | 3 |
| 18 | 60, 137, 141 | 3 |
| 21 | 84, 96, 158 | 3 |
| 25 | 49, 56, 64 | 3 |
| 27 | 3, 66, 100 | 3 |
| 31 | 98, 112, 128 | 3 |
| 34 | 45, 145, 148 | 3 |
| 38 | 12, 62, 95 | 3 |
| 40 | 14, 16, 139 | 3 |
| 44 | 59, 115, 164 | 3 |
| 47 | 6, 31, 132 | 3 |
| 51 | 75, 129, 134 | 3 |
| 53 | 9, 29, 131 | 3 |
| 57 | 20, 47, 102 | 3 |
| 60 | 83, 119, 136 | 3 |
| 64 | 4, 77, 88 | 3 |
| 66 | 42, 48, 79 | 3 |
| 70 | 89, 99, 150 | 3 |
| 73 | 97, 106, 135 | 3 |
| 77 | 25, 43, 101 | 3 |
| 79 | 27, 55, 87 | 3 |
| 83 | 76, 111, 151 | 3 |
| 86 | 18, 58, 93 | 3 |
| 90 | 82, 114, 142 | 3 |
| 92 | 68, 126, 144 | 3 |
| 96 | 34, 63, 72 | 3 |
| 99 | 19, 70, 80 | 3 |
| 103 | 90, 121, 127 | 3 |
| 105 | 81, 92, 165 | 3 |
| 109 | 33, 50, 86 | 3 |
| 112 | 67, 122, 149 | 3 |
| 116 | 38, 140, 160 | 3 |
| 118 | 35, 40, 94 | 3 |
| 122 | 37, 138, 163 | 3 |
| 125 | 5, 54, 110 | 3 |
| 129 | 30, 153, 155 | 3 |
| 131 | 74, 107, 157 | 3 |
| 135 | 21, 24, 124 | 3 |
| 138 | 41, 57, 71 | 3 |
| 142 | 69, 103, 166 | 3 |
| 144 | 105, 113, 120 | 3 |
| 148 | 11, 73, 85 | 3 |
| 151 | 28, 32, 109 | 3 |
| 155 | 10, 51, 108 | 3 |
| 157 | 53, 133, 152 | 3 |
| 161 | 46, 125, 167 | 3 |
| 164 | 15, 161, 162 | 3 |
| 168 | 23, 147, 168 | 3 |
| Occurance | Cubic residues | Total CRs with same occurance |
|---|---|---|
| 3 | 1, 5, 8, 12, 14, 18, 21, 25, 27, 31, 34, 38, 40, 44, 47, 51, 53, 57, 60, 64, 66, 70, 73, 77, 79, 83, 86, 90, 92, 96, 99, 103, 105, 109, 112, 116, 118, 122, 125, 129, 131, 135, 138, 142, 144, 148, 151, 155, 157, 161, 164, 168 | 52 |
| 13 | 0 | 1 |