Analysis of Quadratic Residue over Z₆₂₅

Quadratic residue (QR)	x such that x2 = QR mod 625	Occurance
0	0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600	25
1	1, 624	2
4	2, 623	2
6	109, 516	2
9	3, 622	2
11	56, 569	2
14	83, 542	2
16	4, 621	2
19	137, 488	2
21	164, 461	2
24	218, 407	2
25	5, 120, 130, 245, 255, 370, 380, 495, 505, 620	10
26	299, 326	2
29	148, 477	2
31	284, 341	2
34	97, 528	2
36	6, 619	2
39	267, 358	2
41	71, 554	2
44	112, 513	2
46	36, 589	2
49	7, 618	2
51	26, 599	2
54	298, 327	2
56	166, 459	2
59	197, 428	2
61	44, 581	2
64	8, 617	2
66	146, 479	2
69	87, 538	2
71	236, 389	2
74	232, 393	2
76	274, 351	2
79	177, 448	2
81	9, 616	2
84	297, 328	2
86	94, 531	2
89	283, 342	2
91	221, 404	2
94	62, 563	2
96	189, 436	2
99	168, 457	2
100	10, 115, 135, 240, 260, 365, 385, 490, 510, 615	10
101	51, 574	2
104	27, 598	2
106	184, 441	2
109	228, 397	2
111	144, 481	2
114	67, 558	2
116	296, 329	2
119	37, 588	2
121	11, 614	2
124	57, 568	2
126	249, 376	2
129	123, 502	2
131	266, 359	2
134	128, 497	2
136	194, 431	2
139	208, 417	2
141	254, 371	2
144	12, 613	2
146	211, 414	2
149	282, 343	2
150	45, 80, 170, 205, 295, 330, 420, 455, 545, 580	10
151	76, 549	2
154	273, 352	2
156	91, 534	2
159	28, 597	2
161	244, 381	2
164	142, 483	2
166	179, 446	2
169	13, 612	2
171	214, 411	2
174	118, 507	2
176	224, 401	2
179	202, 423	2
181	84, 541	2
184	72, 553	2
186	294, 331	2
189	133, 492	2
191	104, 521	2
194	38, 587	2
196	14, 611	2
199	107, 518	2
201	101, 524	2
204	52, 573	2
206	259, 366	2
209	172, 453	2
211	281, 344	2
214	217, 408	2
216	29, 596	2
219	63, 562	2
221	186, 439	2
224	293, 332	2
225	15, 110, 140, 235, 265, 360, 390, 485, 515, 610	10
226	199, 426	2
229	98, 527	2
231	191, 434	2
234	272, 353	2
236	231, 394	2
239	58, 567	2
241	46, 579	2
244	88, 537	2
246	239, 386	2
249	68, 557	2
251	126, 499	2
254	248, 377	2
256	16, 609	2
259	253, 372	2
261	181, 444	2
264	292, 333	2
266	121, 504	2
269	113, 512	2
271	39, 586	2
274	157, 468	2
275	30, 95, 155, 220, 280, 345, 405, 470, 530, 595	10
276	174, 451	2
279	227, 398	2
281	159, 466	2
284	153, 472	2
286	131, 494	2
289	17, 608	2
291	196, 429	2
294	138, 487	2
296	161, 464	2
299	243, 382	2
301	151, 474	2
304	77, 548	2
306	291, 334	2
309	53, 572	2
311	81, 544	2
314	258, 367	2
316	271, 354	2
319	163, 462	2
321	264, 361	2
324	18, 607	2
326	149, 476	2
329	73, 552	2
331	116, 509	2
334	47, 578	2
336	31, 594	2
339	92, 533	2
341	279, 346	2
344	188, 437	2
346	64, 561	2
349	207, 418	2
350	40, 85, 165, 210, 290, 335, 415, 460, 540, 585	10
351	176, 449	2
354	223, 402	2
356	59, 566	2
359	147, 478	2
361	19, 606	2
364	183, 442	2
366	204, 421	2
369	213, 412	2
371	136, 489	2
374	193, 432	2
376	124, 501	2
379	252, 373	2
381	234, 391	2
384	247, 378	2
386	69, 556	2
389	167, 458	2
391	129, 496	2
394	238, 387	2
396	289, 336	2
399	32, 593	2
400	20, 105, 145, 230, 270, 355, 395, 480, 520, 605	10
401	201, 424	2
404	102, 523	2
406	216, 409	2
409	278, 347	2
411	119, 506	2
414	108, 517	2
416	54, 571	2
419	263, 362	2
421	89, 536	2
424	257, 368	2
426	99, 526	2
429	48, 577	2
431	41, 584	2
434	178, 447	2
436	169, 456	2
439	242, 383	2
441	21, 604	2
444	288, 337	2
446	111, 514	2
449	143, 482	2
451	226, 399	2
454	198, 427	2
456	134, 491	2
459	78, 547	2
461	219, 406	2
464	33, 592	2
466	96, 529	2
469	312, 313	2
471	311, 314	2
474	82, 543	2
475	60, 65, 185, 190, 310, 315, 435, 440, 560, 565	10
476	74, 551	2
479	277, 348	2
481	309, 316	2
484	22, 603	2
486	269, 356	2
489	308, 317	2
491	171, 454	2
494	287, 338	2
496	114, 511	2
499	307, 318	2
501	251, 374	2
504	127, 498	2
506	141, 484	2
509	122, 503	2
511	306, 319	2
514	42, 583	2
516	246, 379	2
519	262, 363	2
521	86, 539	2
524	93, 532	2
525	55, 70, 180, 195, 305, 320, 430, 445, 555, 570	10
526	49, 576	2
529	23, 602	2
531	34, 591	2
534	222, 403	2
536	256, 369	2
539	233, 392	2
541	304, 321	2
544	237, 388	2
546	286, 339	2
549	132, 493	2
551	276, 349	2
554	173, 452	2
556	209, 416	2
559	303, 322	2
561	206, 419	2
564	117, 508	2
566	229, 396	2
569	212, 413	2
571	139, 486	2
574	268, 357	2
576	24, 601	2
579	302, 323	2
581	241, 384	2
584	203, 422	2
586	156, 469	2
589	158, 467	2
591	154, 471	2
594	187, 438	2
596	61, 564	2
599	43, 582	2
600	35, 90, 160, 215, 285, 340, 410, 465, 535, 590	10
601	301, 324	2
604	152, 473	2
606	66, 559	2
609	103, 522	2
611	106, 519	2
614	192, 433	2
616	79, 546	2
619	162, 463	2
621	261, 364	2
624	182, 443	2

Occurance	Quadratic residues	Total QRs with same occurance
2	1, 4, 6, 9, 11, 14, 16, 19, 21, 24, 26, 29, 31, 34, 36, 39, 41, 44, 46, 49, 51, 54, 56, 59, 61, 64, 66, 69, 71, 74, 76, 79, 81, 84, 86, 89, 91, 94, 96, 99, 101, 104, 106, 109, 111, 114, 116, 119, 121, 124, 126, 129, 131, 134, 136, 139, 141, 144, 146, 149, 151, 154, 156, 159, 161, 164, 166, 169, 171, 174, 176, 179, 181, 184, 186, 189, 191, 194, 196, 199, 201, 204, 206, 209, 211, 214, 216, 219, 221, 224, 226, 229, 231, 234, 236, 239, 241, 244, 246, 249, 251, 254, 256, 259, 261, 264, 266, 269, 271, 274, 276, 279, 281, 284, 286, 289, 291, 294, 296, 299, 301, 304, 306, 309, 311, 314, 316, 319, 321, 324, 326, 329, 331, 334, 336, 339, 341, 344, 346, 349, 351, 354, 356, 359, 361, 364, 366, 369, 371, 374, 376, 379, 381, 384, 386, 389, 391, 394, 396, 399, 401, 404, 406, 409, 411, 414, 416, 419, 421, 424, 426, 429, 431, 434, 436, 439, 441, 444, 446, 449, 451, 454, 456, 459, 461, 464, 466, 469, 471, 474, 476, 479, 481, 484, 486, 489, 491, 494, 496, 499, 501, 504, 506, 509, 511, 514, 516, 519, 521, 524, 526, 529, 531, 534, 536, 539, 541, 544, 546, 549, 551, 554, 556, 559, 561, 564, 566, 569, 571, 574, 576, 579, 581, 584, 586, 589, 591, 594, 596, 599, 601, 604, 606, 609, 611, 614, 616, 619, 621, 624	250
10	25, 100, 150, 225, 275, 350, 400, 475, 525, 600	10
25	0	1