Analysis of Quadratic Residue over Z₃₄₃

Quadratic residue (QR)	x such that x2 = QR mod 343	Occurance
0	0, 49, 98, 147, 196, 245, 294	7
1	1, 342	2
2	108, 235	2
4	2, 341	2
8	127, 216	2
9	3, 340	2
11	131, 212	2
15	155, 188	2
16	4, 339	2
18	19, 324	2
22	85, 258	2
23	87, 256	2
25	5, 338	2
29	83, 260	2
30	67, 276	2
32	89, 254	2
36	6, 337	2
37	123, 220	2
39	72, 271	2
43	27, 316	2
44	81, 262	2
46	135, 208	2
49	7, 42, 56, 91, 105, 140, 154, 189, 203, 238, 252, 287, 301, 336	14
50	146, 197	2
51	59, 284	2
53	100, 243	2
57	20, 323	2
58	46, 297	2
60	33, 310	2
64	8, 335	2
65	53, 290	2
67	79, 264	2
71	62, 281	2
72	38, 305	2
74	93, 250	2
78	113, 230	2
79	116, 227	2
81	9, 334	2
85	153, 190	2
86	171, 172	2
88	170, 173	2
92	169, 174	2
93	130, 213	2
95	110, 233	2
98	21, 28, 70, 77, 119, 126, 168, 175, 217, 224, 266, 273, 315, 322	14
99	50, 293	2
100	10, 333	2
102	145, 198	2
106	167, 176	2
107	95, 248	2
109	65, 278	2
113	139, 204	2
114	102, 241	2
116	166, 177	2
120	134, 209	2
121	11, 332	2
123	152, 191	2
127	34, 309	2
128	165, 178	2
130	107, 236	2
134	43, 300	2
135	122, 221	2
137	75, 268	2
141	22, 321	2
142	164, 179	2
144	12, 331	2
148	97, 246	2
149	39, 304	2
151	47, 296	2
155	29, 314	2
156	144, 199	2
158	163, 180	2
162	57, 286	2
163	151, 192	2
165	68, 275	2
169	13, 330	2
170	60, 283	2
172	54, 289	2
176	162, 181	2
177	129, 214	2
179	138, 205	2
183	104, 239	2
184	73, 270	2
186	23, 320	2
190	125, 218	2
191	115, 228	2
193	86, 257	2
196	14, 35, 63, 84, 112, 133, 161, 182, 210, 231, 259, 280, 308, 329	14
197	99, 244	2
198	88, 255	2
200	51, 292	2
204	118, 225	2
205	150, 193	2
207	82, 261	2
211	90, 253	2
212	143, 200	2
214	30, 313	2
218	160, 183	2
219	109, 234	2
221	44, 299	2
225	15, 328	2
226	80, 263	2
228	40, 303	2
232	92, 251	2
233	24, 319	2
235	121, 222	2
239	71, 272	2
240	66, 277	2
242	159, 184	2
246	48, 295	2
247	137, 206	2
249	149, 194	2
253	78, 265	2
254	101, 242	2
256	16, 327	2
260	106, 237	2
261	94, 249	2
263	128, 215	2
267	36, 307	2
268	158, 185	2
270	142, 201	2
274	132, 211	2
275	31, 312	2
277	58, 285	2
281	55, 288	2
282	25, 318	2
284	124, 219	2
288	76, 267	2
289	17, 326	2
291	61, 282	2
295	148, 195	2
296	157, 186	2
298	96, 247	2
302	69, 274	2
303	52, 291	2
305	114, 229	2
309	41, 302	2
310	45, 298	2
312	117, 226	2
316	111, 232	2
317	136, 207	2
319	103, 240	2
323	64, 279	2
324	18, 325	2
326	156, 187	2
330	141, 202	2
331	74, 269	2
333	26, 317	2
337	120, 223	2
338	32, 311	2
340	37, 306	2

Occurance	Quadratic residues	Total QRs with same occurance
2	1, 2, 4, 8, 9, 11, 15, 16, 18, 22, 23, 25, 29, 30, 32, 36, 37, 39, 43, 44, 46, 50, 51, 53, 57, 58, 60, 64, 65, 67, 71, 72, 74, 78, 79, 81, 85, 86, 88, 92, 93, 95, 99, 100, 102, 106, 107, 109, 113, 114, 116, 120, 121, 123, 127, 128, 130, 134, 135, 137, 141, 142, 144, 148, 149, 151, 155, 156, 158, 162, 163, 165, 169, 170, 172, 176, 177, 179, 183, 184, 186, 190, 191, 193, 197, 198, 200, 204, 205, 207, 211, 212, 214, 218, 219, 221, 225, 226, 228, 232, 233, 235, 239, 240, 242, 246, 247, 249, 253, 254, 256, 260, 261, 263, 267, 268, 270, 274, 275, 277, 281, 282, 284, 288, 289, 291, 295, 296, 298, 302, 303, 305, 309, 310, 312, 316, 317, 319, 323, 324, 326, 330, 331, 333, 337, 338, 340	147
7	0	1
14	49, 98, 196	3