Analysis of Cubic Residue over Z₁₂₅

Cubic residue (CR)	x such that x3 = CR mod 125	Occurance
0	0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120	25
1	1	1
2	53	1
3	87	1
4	59	1
6	111	1
7	43	1
8	2	1
9	69	1
11	21	1
12	8	1
13	67	1
14	29	1
16	106	1
17	73	1
18	32	1
19	64	1
21	116	1
22	113	1
23	22	1
24	49	1
26	51	1
27	3	1
28	37	1
29	109	1
31	36	1
32	118	1
33	77	1
34	119	1
36	71	1
37	83	1
38	17	1
39	79	1
41	31	1
42	23	1
43	107	1
44	114	1
46	41	1
47	63	1
48	97	1
49	99	1
51	101	1
52	78	1
53	112	1
54	34	1
56	86	1
57	68	1
58	27	1
59	44	1
61	121	1
62	33	1
63	92	1
64	4	1
66	81	1
67	98	1
68	57	1
69	39	1
71	91	1
72	13	1
73	47	1
74	24	1
76	26	1
77	28	1
78	62	1
79	84	1
81	11	1
82	18	1
83	102	1
84	94	1
86	46	1
87	108	1
88	42	1
89	54	1
91	6	1
92	48	1
93	7	1
94	89	1
96	16	1
97	88	1
98	122	1
99	74	1
101	76	1
102	103	1
103	12	1
104	9	1
106	61	1
107	93	1
108	52	1
109	19	1
111	96	1
112	58	1
113	117	1
114	104	1
116	56	1
117	123	1
118	82	1
119	14	1
121	66	1
122	38	1
123	72	1
124	124	1

Occurance	Cubic residues	Total CRs with same occurance
1	1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98, 99, 101, 102, 103, 104, 106, 107, 108, 109, 111, 112, 113, 114, 116, 117, 118, 119, 121, 122, 123, 124	100
25	0	1