This page lists the squares modulo a few powers of 11. See Modular Arithmetic and Quadratic Residue (table) for background.

There are also lists for the squares modulo N and the powers of 2, 3, 5, 7.

```Squares mod 11^1 = 11: 0,1,3,4,5,9
Squares mod 11^2 = 121: 0,1,3,4,5,9,12,14,15,16,20,23,25,26,27,31,34,36,37,38,42,45,47,48,49,53,56,58,59,60,64,67,69,70,71,75,78,80,81,82,86,89,91,92,93,97,100,102,103,104,108,111,113,114,115,119
Squares mod 11^3 = 1331: 0,1,3,4,5,9,12,14,15,16,20,23,25,26,27,31,34,36,37,38,42,45,47,48,49,53,56,58,59,60,64,67,69,70,71,75,78,80,81,82,86,89,91,92,93,97,100,102,103,104,108,111,113,114,115,119,121,122,124,125,126,130,133,135,136,137,141,144,146,147,148,152,155,157,158,159,163,166,168,169,170,174,177,179,180,181,185,188,190,191,192,196,199,201,202,203,207,210,212,213,214,218,221,223,224,225,229,232,234,235,236,240,243,245,246,247,251,254,256,257,258,262,265,267,268,269,273,276,278,279,280,284,287,289,290,291,295,298,300,301,302,306,309,311,312,313,317,320,322,323,324,328,331,333,334,335,339,342,344,345,346,350,353,355,356,357,361,363,364,366,367,368,372,375,377,378,379,383,386,388,389,390,394,397,399,400,401,405,408,410,411,412,416,419,421,422,423,427,430,432,433,434,438,441,443,444,445,449,452,454,455,456,460,463,465,466,467,471,474,476,477,478,482,484,485,487,488,489,493,496,498,499,500,504,507,509,510,511,515,518,520,521,522,526,529,531,532,533,537,540,542,543,544,548,551,553,554,555,559,562,564,565,566,570,573,575,576,577,581,584,586,587,588,592,595,597,598,599,603,605,606,608,609,610,614,617,619,620,621,625,628,630,631,632,636,639,641,642,643,647,650,652,653,654,658,661,663,664,665,669,672,674,675,676,680,683,685,686,687,691,694,696,697,698,702,705,707,708,709,713,716,718,719,720,724,727,729,730,731,735,738,740,741,742,746,749,751,752,753,757,760,762,763,764,768,771,773,774,775,779,782,784,785,786,790,793,795,796,797,801,804,806,807,808,812,815,817,818,819,823,826,828,829,830,834,837,839,840,841,845,848,850,851,852,856,859,861,862,863,867,870,872,873,874,878,881,883,884,885,889,892,894,895,896,900,903,905,906,907,911,914,916,917,918,922,925,927,928,929,933,936,938,939,940,944,947,949,950,951,955,958,960,961,962,966,969,971,972,973,977,980,982,983,984,988,991,993,994,995,999,1002,1004,1005,1006,1010,1013,1015,1016,1017,1021,1024,1026,1027,1028,1032,1035,1037,1038,1039,1043,1046,1048,1049,1050,1054,1057,1059,1060,1061,1065,1068,1070,1071,1072,1076,1079,1081,1082,1083,1087,1089,1090,1092,1093,1094,1098,1101,1103,1104,1105,1109,1112,1114,1115,1116,1120,1123,1125,1126,1127,1131,1134,1136,1137,1138,1142,1145,1147,1148,1149,1153,1156,1158,1159,1160,1164,1167,1169,1170,1171,1175,1178,1180,1181,1182,1186,1189,1191,1192,1193,1197,1200,1202,1203,1204,1208,1211,1213,1214,1215,1219,1222,1224,1225,1226,1230,1233,1235,1236,1237,1241,1244,1246,1247,1248,1252,1255,1257,1258,1259,1263,1266,1268,1269,1270,1274,1277,1279,1280,1281,1285,1288,1290,1291,1292,1296,1299,1301,1302,1303,1307,1310,1312,1313,1314,1318,1321,1323,1324,1325,1329
```