Analysis of Quadratic Residue over Z₁₆₉

Quadratic residue (QR)	x such that x2 = QR mod 169	Occurance
0	0, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156	13
1	1, 168	2
3	61, 108	2
4	2, 167	2
9	3, 166	2
10	32, 137	2
12	47, 122	2
14	77, 92	2
16	4, 165	2
17	37, 132	2
22	23, 146	2
23	19, 150	2
25	5, 164	2
27	14, 155	2
29	69, 100	2
30	76, 93	2
35	49, 120	2
36	6, 163	2
38	57, 112	2
40	64, 105	2
42	35, 134	2
43	54, 115	2
48	75, 94	2
49	7, 162	2
51	60, 109	2
53	27, 142	2
55	30, 139	2
56	15, 154	2
61	68, 101	2
62	20, 149	2
64	8, 161	2
66	51, 118	2
68	74, 95	2
69	24, 145	2
74	42, 127	2
75	33, 136	2
77	44, 125	2
79	40, 129	2
81	9, 160	2
82	63, 106	2
87	16, 153	2
88	46, 123	2
90	73, 96	2
92	38, 131	2
94	56, 113	2
95	67, 102	2
100	10, 159	2
101	59, 110	2
103	21, 148	2
105	53, 116	2
107	48, 121	2
108	28, 141	2
113	36, 133	2
114	72, 97	2
116	31, 138	2
118	25, 144	2
120	17, 152	2
121	11, 158	2
126	62, 107	2
127	84, 85	2
129	83, 86	2
131	66, 103	2
133	82, 87	2
134	50, 119	2
139	81, 88	2
140	71, 98	2
142	34, 135	2
144	12, 157	2
146	22, 147	2
147	80, 89	2
152	55, 114	2
153	58, 111	2
155	18, 151	2
157	79, 90	2
159	43, 126	2
160	41, 128	2
165	29, 140	2
166	45, 124	2
168	70, 99	2

Occurance	Quadratic residues	Total QRs with same occurance
2	1, 3, 4, 9, 10, 12, 14, 16, 17, 22, 23, 25, 27, 29, 30, 35, 36, 38, 40, 42, 43, 48, 49, 51, 53, 55, 56, 61, 62, 64, 66, 68, 69, 74, 75, 77, 79, 81, 82, 87, 88, 90, 92, 94, 95, 100, 101, 103, 105, 107, 108, 113, 114, 116, 118, 120, 121, 126, 127, 129, 131, 133, 134, 139, 140, 142, 144, 146, 147, 152, 153, 155, 157, 159, 160, 165, 166, 168	78
13	0	1