Analysis of Quadratic Residue over Z₁₂₁

Quadratic residue (QR)	x such that x2 = QR mod 121	Occurance
0	0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110	11
1	1, 120	2
3	27, 94	2
4	2, 119	2
5	48, 73	2
9	3, 118	2
12	54, 67	2
14	16, 105	2
15	35, 86	2
16	4, 117	2
20	25, 96	2
23	12, 109	2
25	5, 116	2
26	53, 68	2
27	40, 81	2
31	47, 74	2
34	43, 78	2
36	6, 115	2
37	20, 101	2
38	37, 84	2
42	52, 69	2
45	23, 98	2
47	17, 104	2
48	13, 108	2
49	7, 114	2
53	30, 91	2
56	32, 89	2
58	28, 93	2
59	46, 75	2
60	51, 70	2
64	8, 113	2
67	34, 87	2
69	39, 82	2
70	42, 79	2
71	26, 95	2
75	14, 107	2
78	21, 100	2
80	50, 71	2
81	9, 112	2
82	18, 103	2
86	36, 85	2
89	45, 76	2
91	60, 61	2
92	24, 97	2
93	59, 62	2
97	58, 63	2
100	10, 111	2
102	49, 72	2
103	57, 64	2
104	15, 106	2
108	41, 80	2
111	56, 65	2
113	38, 83	2
114	31, 90	2
115	29, 92	2
119	19, 102	2

Occurance	Quadratic residues	Total QRs 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