Analysis of sixth Residue over Z₁₂₁

sixth residue (6R)	x such that x6 = 6R mod 121	Occurance
0	0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110	11
1	1, 120	2
3	3, 118	2
4	48, 73	2
5	17, 104	2
9	9, 112	2
12	23, 98	2
14	25, 96	2
15	51, 70	2
16	5, 116	2
20	31, 90	2
23	45, 76	2
25	47, 74	2
26	29, 92	2
27	27, 94	2
31	53, 68	2
34	54, 67	2
36	52, 69	2
37	7, 114	2
38	49, 72	2
42	46, 75	2
45	32, 89	2
47	30, 91	2
48	15, 106	2
49	50, 71	2
53	24, 97	2
56	10, 111	2
58	8, 113	2
59	37, 84	2
60	28, 93	2
64	2, 119	2
67	12, 109	2
69	14, 107	2
70	59, 62	2
71	6, 115	2
75	20, 101	2
78	34, 87	2
80	36, 85	2
81	40, 81	2
82	16, 105	2
86	42, 79	2
89	56, 65	2
91	58, 63	2
92	18, 103	2
93	38, 83	2
97	57, 64	2
100	43, 78	2
102	41, 80	2
103	4, 117	2
104	60, 61	2
108	35, 86	2
111	21, 100	2
113	19, 102	2
114	26, 95	2
115	39, 82	2
119	13, 108	2

Occurance	sixth residues	Total 6Rs with same occurance
2	1, 3, 4, 5, 9, 12, 14, 15, 16, 20, 23, 25, 26, 27, 31, 34, 36, 37, 38, 42, 45, 47, 48, 49, 53, 56, 58, 59, 60, 64, 67, 69, 70, 71, 75, 78, 80, 81, 82, 86, 89, 91, 92, 93, 97, 100, 102, 103, 104, 108, 111, 113, 114, 115, 119	55
11	0	1