Analysis of Cubic Residue over Z₁₂₁

Cubic residue (CR)	x such that x3 = CR mod 121	Occurance
0	0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110	11
1	1	1
2	73	1
3	9	1
4	5	1
5	47	1
6	52	1
7	50	1
8	2	1
9	81	1
10	43	1
12	45	1
13	106	1
14	20	1
15	60	1
16	25	1
17	30	1
18	105	1
19	13	1
20	114	1
21	87	1
23	89	1
24	18	1
25	31	1
26	115	1
27	3	1
28	8	1
29	39	1
30	24	1
31	26	1
32	10	1
34	12	1
35	51	1
36	42	1
37	49	1
38	102	1
39	107	1
40	94	1
41	35	1
42	59	1
43	54	1
45	56	1
46	84	1
47	53	1
48	104	1
49	80	1
50	85	1
51	28	1
52	46	1
53	92	1
54	98	1
56	100	1
57	117	1
58	64	1
59	38	1
60	58	1
61	63	1
62	83	1
63	57	1
64	4	1
65	21	1
67	23	1
68	29	1
69	75	1
70	93	1
71	36	1
72	41	1
73	17	1
74	68	1
75	37	1
76	65	1
78	67	1
79	62	1
80	86	1
81	27	1
82	14	1
83	19	1
84	72	1
85	79	1
86	70	1
87	109	1
89	111	1
90	95	1
91	97	1
92	82	1
93	113	1
94	118	1
95	6	1
96	90	1
97	103	1
98	32	1
100	34	1
101	7	1
102	108	1
103	16	1
104	91	1
105	96	1
106	61	1
107	101	1
108	15	1
109	76	1
111	78	1
112	40	1
113	119	1
114	71	1
115	69	1
116	74	1
117	116	1
118	112	1
119	48	1
120	120	1

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