Mathematics:
Cohomology
→Theory
→Implementation
Jena:
External links:
Mod-5-Cohomology of Normalizer(SymplecticGroup(6,4),Centre(SylowSubgroup(SymplecticGroup(6,4),5))), a group of order 6000
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
General information on the group
- Normalizer(SymplecticGroup(6,4),Centre(SylowSubgroup(SymplecticGroup(6,4),5))) is a group of order 6000.
- The group order factors as
24 · 3 · 53 . - The group is defined by Group([(1,45,1086,149,889)(2,1193,644,1107,1298)(3,567,833,574,8)(4,703,312,840,1300)(5,132,406,66,526)(6,302,100,101,984)(7,1029,1143,497,295)(9,478,1318,746,1361)(10,558,568,71,683)(11,859,830,1186,389)(12,359,902,812,752)(13,1195,438,1071,1262)(14,885,432,156,1283)(15,777,1305,1133,1313)(16,253,1179,1245,511)(17,1173,505,1215,696)(18,1095,479,564,893)(19,701,1171,309,284)(20,460,278,517,877)(21,1160,139,1108,682)(22,329,687,985,191)(23,1310,989,73,426)(24,774,204,951,1336)(25,901,848,1130,122)(26,188,661,408,30)(27,476,1048,1224,1196)(28,493,861,764,968)(29,887,513,1295,958)(31,1056,922,1164,305)(32,180,1067,686,939)(33,1277,279,363,1059)(34,920,581,858,1267)(35,622,591,1184,590)(36,882,429,356,651)(37,248,624,390,1327)(38,1214,46,663,375)(39,668,1301,1265,414)(40,750,711,268,988)(41,1102,899,761,182)(42,544,1213,602,272)(43,492,1154,794,1282)(44,296,321,873,841)(47,266,795,658,1096)(48,1100,748,725,546)(49,1234,870,844,706)(50,1135,474,163,162)(51,963,251,1115,917)(52,647,983,484,53)(54,1338,1010,119,557)(55,190,1343,151,366)(56,1330,757,160,589)(57,391,776,874,184)(58,318,673,832,157)(59,1020,709,913,393)(60,90,1023,886,326)(61,1045,831,1037,1177)(62,818,1087,280,1176)(63,918,1326,172,1047)(64,1018,483,247,306)(65,843,1050,350,472)(67,293,606,385,1303)(68,1314,749,397,417)(69,271,550,1348,456)(70,1309,286,655,74)(72,770,409,916,1112)(75,428,113,970,996)(76,704,910,355,1312)(77,598,642,816,969)(78,721,313,1185,636)(79,784,362,1249,376)(80,207,1236,208,1140)(81,803,1258,972,86)(82,600,216,411,494)(83,586,1137,144,819)(84,698,308,327,488)(85,1070,1285,575,226)(87,935,1317,399,209)(88,1251,256,1181,324)(89,193,685,332,946)(91,1001,1272,477,347)(92,956,487,543,566)(93,167,361,1208,258)(94,509,277,1124,189)(95,316,339,1033,1017)(96,1355,692,1052,838)(97,555,635,965,827)(98,170,384,304,1134)(99,176,465,1012,292)(102,1342,1293,1198,396)(103,464,1174,1000,538)(104,203,781,290,667)(105,386,948,108,654)(106,1299,462,1031,978)(107,515,643,524,1183)(109,979,1362,165,793)(110,175,734,1323,1225)(111,791,1275,1109,971)(112,1302,684,868,1304)(114,453,735,210,1054)(115,778,1076,398,1005)(116,1162,1226,940,583)(117,183,489,1254,1019)(118,1118,1325,836,702)(120,737,995,754,187)(121,570,342,649,789)(123,607,1363,1103,629)(124,1220,1146,554,957)(125,821,1247,215,294)(126,905,1278,1021,650)(127,595,787,1218,730)(128,934,1089,281,1082)(129,213,244,813,545)(130,751,368,648,700)(131,638,947,1065,1252)(133,440,495,1026,835)(134,763,297,909,322)(135,1360,693,1044,1200)(136,943,334,1008,592)(137,1246,1217,959,630)(138,871,459,1161,1322)(140,331,1088,337,797)(141,1034,147,1120,867)(142,521,805,237,227)(143,866,691,1350,1290)(145,579,419,382,548)(146,519,779,1347,1194)(148,652,240,1296,1264)(150,601,1255,394,1192)(152,640,1104,469,810)(153,1204,243,231,627)(154,716,463,758,537)(155,1157,1144,528,792)(158,1243,717,780,1090)(159,1055,975,178,855)(161,212,1042,625,847)(164,1239,1188,1156,1337)(166,486,676,927,1364)(168,849,520,714,1271)(169,671,220,504,999)(171,475,860,994,1114)(173,533,503,1199,639)(174,1149,267,1093,796)(177,914,383,945,1180)(179,264,733,1297,404)(181,222,869,547,1211)(185,850,1041,1142,1189)(186,736,884,424,276)(192,953,768,634,1344)(194,656,611,616,664)(195,573,235,1175,540)(196,1078,632,990,1092)(197,645,938,1116,377)(198,960,525,1321,782)(199,621,1085,1346,1141)(200,799,1111,829,410)(201,1049,1127,502,1307)(202,1197,1349,431,1329)(205,908,582,353,1328)(206,224,1291,1263,214)(211,1352,846,728,1316)(217,352,1040,620,1170)(218,907,923,695,416)(219,856,707,924,675)(221,596,672,1273,516)(223,1051,234,569,864)(225,973,1294,722,802)(228,576,679,1101,1122)(229,455,1172,898,338)(230,929,854,1038,403)(232,745,1117,1132,369)(233,560,1007,708,853)(236,585,1340,289,932)(238,450,473,623,561)(239,1308,1228,565,1315)(241,837,892,1032,1063)(242,987,1058,443,895)(245,444,729,446,1319)(246,991,451,371,964)(249,633,1281,340,609)(250,790,1145,262,319)(254,974,348,1203,954)(255,481,732,1202,760)(257,300,584,967,1039)(259,320,1178,942,1230)(260,1123,769,881,311)(261,608,1064,1306,878)(263,926,952,815,603)(265,688,628,1365,852)(269,1287,739,740,1069)(270,997,950,445,941)(273,626,344,549,694)(274,705,330,1187,357)(275,690,720,1113,894)(282,496,604,857,1066)(283,962,986,1011,824)(285,1061,336,364,743)(287,490,1028,710,613)(288,1094,919,681,1311)(291,1043,619,1269,998)(298,1046,360,1105,1169)(299,523,1098,744,1077)(301,1075,542,747,418)(303,1027,1210,931,863)(307,897,1257,365,343)(310,593,697,955,912)(314,1241,1079,499,1227)(315,755,507,617,381)(317,678,1158,1003,699)(323,466,421,674,325)(328,828,430,1147,588)(333,741,772,1167,437)(335,539,1083,1099,1351)(341,1097,1153,506,436)(345,1091,865,825,508)(346,1150,1345,660,553)(349,723,1324,1335,1268)(351,1014,925,501,514)(354,512,1025,809,982)(358,670,518,1165,944)(367,441,379,571,1190)(370,1292,1207,1222,1002)(372,808,420,1219,1358)(373,572,814,1009,1166)(374,401,880,1016,1274)(378,1024,415,612,1136)(380,1182,1139,903,1339)(387,631,862,1270,900)(388,413,823,976,599)(392,1106,798,911,906)(395,665,1231,1244,845)(400,872,427,1266,405)(402,637,891,1223,875)(407,1212,1286,961,981)(412,785,1233,641,759)(422,1260,1053,788,1110)(423,904,765,1074,936)(425,653,1015,529,1332)(433,669,1280,876,1250)(434,742,715,1259,879)(435,1084,482,921,1030)(439,1279,578,1036,1191)(442,452,1248,646,605)(447,535,610,536,1261)(448,1168,1232,949,597)(449,1359,1284,1060,883)(454,822,1035,689,773)(457,1057,1062,1331,1121)(458,826,467,937,1238)(461,992,977,1237,1356)(468,1155,1119,915,888)(470,1242,1129,786,738)(471,662,980,1006,731)(480,762,890,556,1354)(485,498,500,522,1073)(491,1320,767,1216,559)(510,1138,563,1229,1206)(527,1151,1131,1072,1125)(530,1240,680,1068,1080)(531,811,1205,726,800)(532,1126,1235,1353,1357)(534,771,1022,713,712)(541,1148,677,1341,820)(551,719,801,756,666)(552,1081,659,1004,1152)(562,1013,1209,615,842)(577,1201,783,753,966)(580,724,1159,817,1256)(587,851,718,1288,1221)(594,806,614,1333,839)(618,993,933,1253,1163)(727,1128,1334,807,804)(766,930,1289,1276,896),(1,889,149,1086,45)(2,1298,1107,644,1193)(3,8,574,833,567)(4,1300,840,312,703)(5,526,66,406,132)(6,984,101,100,302)(7,295,497,1143,1029)(9,1361,746,1318,478)(10,683,71,568,558)(11,389,1186,830,859)(12,752,812,902,359)(13,1262,1071,438,1195)(14,1283,156,432,885)(15,1313,1133,1305,777)(16,511,1245,1179,253)(17,696,1215,505,1173)(18,893,564,479,1095)(19,284,309,1171,701)(20,877,517,278,460)(21,682,1108,139,1160)(22,191,985,687,329)(23,426,73,989,1310)(24,1336,951,204,774)(25,122,1130,848,901)(26,30,408,661,188)(27,1196,1224,1048,476)(28,968,764,861,493)(29,958,1295,513,887)(31,305,1164,922,1056)(32,939,686,1067,180)(33,1059,363,279,1277)(34,1267,858,581,920)(35,590,1184,591,622)(36,651,356,429,882)(37,1327,390,624,248)(38,375,663,46,1214)(39,414,1265,1301,668)(40,988,268,711,750)(41,182,761,899,1102)(42,272,602,1213,544)(43,1282,794,1154,492)(44,841,873,321,296)(47,1096,658,795,266)(48,546,725,748,1100)(49,706,844,870,1234)(50,162,163,474,1135)(51,917,1115,251,963)(52,53,484,983,647)(54,557,119,1010,1338)(55,366,151,1343,190)(56,589,160,757,1330)(57,184,874,776,391)(58,157,832,673,318)(59,393,913,709,1020)(60,326,886,1023,90)(61,1177,1037,831,1045)(62,1176,280,1087,818)(63,1047,172,1326,918)(64,306,247,483,1018)(65,472,350,1050,843)(67,1303,385,606,293)(68,417,397,749,1314)(69,456,1348,550,271)(70,74,655,286,1309)(72,1112,916,409,770)(75,996,970,113,428)(76,1312,355,910,704)(77,969,816,642,598)(78,636,1185,313,721)(79,376,1249,362,784)(80,1140,208,1236,207)(81,86,972,1258,803)(82,494,411,216,600)(83,819,144,1137,586)(84,488,327,308,698)(85,226,575,1285,1070)(87,209,399,1317,935)(88,324,1181,256,1251)(89,946,332,685,193)(91,347,477,1272,1001)(92,566,543,487,956)(93,258,1208,361,167)(94,189,1124,277,509)(95,1017,1033,339,316)(96,838,1052,692,1355)(97,827,965,635,555)(98,1134,304,384,170)(99,292,1012,465,176)(102,396,1198,1293,1342)(103,538,1000,1174,464)(104,667,290,781,203)(105,654,108,948,386)(106,978,1031,462,1299)(107,1183,524,643,515)(109,793,165,1362,979)(110,1225,1323,734,175)(111,971,1109,1275,791)(112,1304,868,684,1302)(114,1054,210,735,453)(115,1005,398,1076,778)(116,583,940,1226,1162)(117,1019,1254,489,183)(118,702,836,1325,1118)(120,187,754,995,737)(121,789,649,342,570)(123,629,1103,1363,607)(124,957,554,1146,1220)(125,294,215,1247,821)(126,650,1021,1278,905)(127,730,1218,787,595)(128,1082,281,1089,934)(129,545,813,244,213)(130,700,648,368,751)(131,1252,1065,947,638)(133,835,1026,495,440)(134,322,909,297,763)(135,1200,1044,693,1360)(136,592,1008,334,943)(137,630,959,1217,1246)(138,1322,1161,459,871)(140,797,337,1088,331)(141,867,1120,147,1034)(142,227,237,805,521)(143,1290,1350,691,866)(145,548,382,419,579)(146,1194,1347,779,519)(148,1264,1296,240,652)(150,1192,394,1255,601)(152,810,469,1104,640)(153,627,231,243,1204)(154,537,758,463,716)(155,792,528,1144,1157)(158,1090,780,717,1243)(159,855,178,975,1055)(161,847,625,1042,212)(164,1337,1156,1188,1239)(166,1364,927,676,486)(168,1271,714,520,849)(169,999,504,220,671)(171,1114,994,860,475)(173,639,1199,503,533)(174,796,1093,267,1149)(177,1180,945,383,914)(179,404,1297,733,264)(181,1211,547,869,222)(185,1189,1142,1041,850)(186,276,424,884,736)(192,1344,634,768,953)(194,664,616,611,656)(195,540,1175,235,573)(196,1092,990,632,1078)(197,377,1116,938,645)(198,782,1321,525,960)(199,1141,1346,1085,621)(200,410,829,1111,799)(201,1307,502,1127,1049)(202,1329,431,1349,1197)(205,1328,353,582,908)(206,214,1263,1291,224)(211,1316,728,846,1352)(217,1170,620,1040,352)(218,416,695,923,907)(219,675,924,707,856)(221,516,1273,672,596)(223,864,569,234,1051)(225,802,722,1294,973)(228,1122,1101,679,576)(229,338,898,1172,455)(230,403,1038,854,929)(232,369,1132,1117,745)(233,853,708,1007,560)(236,932,289,1340,585)(238,561,623,473,450)(239,1315,565,1228,1308)(241,1063,1032,892,837)(242,895,443,1058,987)(245,1319,446,729,444)(246,964,371,451,991)(249,609,340,1281,633)(250,319,262,1145,790)(254,954,1203,348,974)(255,760,1202,732,481)(257,1039,967,584,300)(259,1230,942,1178,320)(260,311,881,769,1123)(261,878,1306,1064,608)(263,603,815,952,926)(265,852,1365,628,688)(269,1069,740,739,1287)(270,941,445,950,997)(273,694,549,344,626)(274,357,1187,330,705)(275,894,1113,720,690)(282,1066,857,604,496)(283,824,1011,986,962)(285,743,364,336,1061)(287,613,710,1028,490)(288,1311,681,919,1094)(291,998,1269,619,1043)(298,1169,1105,360,1046)(299,1077,744,1098,523)(301,418,747,542,1075)(303,863,931,1210,1027)(307,343,365,1257,897)(310,912,955,697,593)(314,1227,499,1079,1241)(315,381,617,507,755)(317,699,1003,1158,678)(323,325,674,421,466)(328,588,1147,430,828)(333,437,1167,772,741)(335,1351,1099,1083,539)(341,436,506,1153,1097)(345,508,825,865,1091)(346,553,660,1345,1150)(349,1268,1335,1324,723)(351,514,501,925,1014)(354,982,809,1025,512)(358,944,1165,518,670)(367,1190,571,379,441)(370,1002,1222,1207,1292)(372,1358,1219,420,808)(373,1166,1009,814,572)(374,1274,1016,880,401)(378,1136,612,415,1024)(380,1339,903,1139,1182)(387,900,1270,862,631)(388,599,976,823,413)(392,906,911,798,1106)(395,845,1244,1231,665)(400,405,1266,427,872)(402,875,1223,891,637)(407,981,961,1286,1212)(412,759,641,1233,785)(422,1110,788,1053,1260)(423,936,1074,765,904)(425,1332,529,1015,653)(433,1250,876,1280,669)(434,879,1259,715,742)(435,1030,921,482,1084)(439,1191,1036,578,1279)(442,605,646,1248,452)(447,1261,536,610,535)(448,597,949,1232,1168)(449,883,1060,1284,1359)(454,773,689,1035,822)(457,1121,1331,1062,1057)(458,1238,937,467,826)(461,1356,1237,977,992)(468,888,915,1119,1155)(470,738,786,1129,1242)(471,731,1006,980,662)(480,1354,556,890,762)(485,1073,522,500,498)(491,559,1216,767,1320)(510,1206,1229,563,1138)(527,1125,1072,1131,1151)(530,1080,1068,680,1240)(531,800,726,1205,811)(532,1357,1353,1235,1126)(534,712,713,1022,771)(541,820,1341,677,1148)(551,666,756,801,719)(552,1152,1004,659,1081)(562,842,615,1209,1013)(577,966,753,783,1201)(580,1256,817,1159,724)(587,1221,1288,718,851)(594,839,1333,614,806)(618,1163,1253,933,993)(727,804,807,1334,1128)(766,896,1276,1289,930),(1,684,435,32,590)(2,342,182,865,688)(3,152,1146,636,1178)(4,167,647,26,1145)(5,774,251,1307,362)(6,46,1026,808,393)(7,874,734,989,310)(8,810,1220,1185,320)(9,1192,719,1008,739)(10,1139,977,1212,29)(11,42,993,650,296)(12,862,920,665,783)(13,1140,717,323,330)(14,911,540,1012,617)(15,493,463,490,910)(16,572,626,88,1276)(17,976,255,162,884)(18,1070,879,453,578)(19,1033,214,787,91)(20,470,934,1032,1322)(21,662,356,239,1053)(22,956,895,504,130)(23,955,497,391,110)(24,963,502,784,526)(25,555,399,1105,1199)(27,1013,275,728,1329)(28,716,287,704,1313)(30,790,1300,93,52)(31,888,681,423,606)(33,940,1345,929,634)(34,395,1201,752,631)(35,45,868,1084,180)(36,1228,1110,139,1006)(37,691,1293,881,522)(38,440,1358,709,101)(39,944,367,382,851)(40,1324,261,891,72)(41,825,628,1193,649)(43,352,103,1092,642)(44,389,272,618,1021)(47,123,1077,56,1364)(48,908,142,1072,745)(49,74,529,229,215)(50,424,1173,599,481)(51,1127,79,66,1336)(53,408,250,840,258)(54,120,890,806,199)(55,1235,96,450,974)(57,1225,426,697,1143)(58,140,374,442,1061)(59,302,663,835,420)(60,147,454,515,531)(61,962,106,611,371)(62,1261,937,1051,586)(63,907,813,970,1167)(64,849,397,221,645)(65,354,802,679,1065)(67,1164,1119,1094,1074)(68,672,1116,483,714)(69,134,446,314,796)(70,1332,455,294,1234)(71,380,461,981,1295)(73,593,1029,184,1323)(75,333,1326,695,129)(76,1133,968,154,613)(77,794,1170,1000,632)(78,942,567,640,554)(80,780,466,1187,1195)(81,491,897,667,488)(82,1142,384,534,975)(83,1176,536,467,223)(84,803,1320,1257,104)(85,1259,114,1279,893)(86,559,307,290,327)(87,298,173,848,965)(89,1204,370,678,1007)(90,1120,822,643,811)(92,443,220,700,191)(94,585,1027,967,1168)(95,224,730,1272,1171)(97,1317,360,503,122)(98,713,159,411,850)(99,315,432,392,573)(100,375,133,1219,1020)(102,1123,498,390,143)(105,1128,410,979,1284)(107,800,326,1034,773)(108,804,1111,793,449)(109,1359,654,727,829)(111,950,219,155,525)(112,921,686,591,149)(113,772,1047,218,244)(115,418,652,1042,817)(116,553,1038,192,279)(117,137,510,427,378)(118,869,1188,1200,541)(119,754,480,839,1346)(121,899,345,852,1107)(124,313,259,574,469)(125,870,1309,425,1172)(126,321,859,544,933)(127,477,309,316,1291)(128,892,1161,877,738)(131,1050,1025,973,1122)(132,204,1115,201,1249)(135,1148,1118,547,1156)(136,1069,1318,601,756)(138,460,1242,1089,1063)(141,689,1183,726,886)(144,1087,535,458,569)(145,1288,1301,670,379)(146,1233,604,914,1080)(148,212,1159,1005,747)(150,801,592,740,478)(151,532,1052,561,954)(153,1002,317,560,946)(156,1106,235,176,755)(157,797,1274,605,285)(158,674,274,1071,1236)(160,676,658,1103,1098)(161,724,398,542,1264)(163,736,696,823,760)(164,693,1341,836,181)(165,883,948,807,799)(166,266,607,299,1330)(168,749,516,197,306)(169,368,687,543,987)(170,712,1055,494,1041)(171,860,1114,475,994)(172,416,213,428,741)(174,271,763,1319,1241)(175,1310,912,295,776)(177,1068,1194,785,496)(178,600,1189,304,771)(179,1331,430,263,291)(183,1246,1138,1266,1024)(185,1134,1022,855,216)(186,1215,413,1202,474)(187,762,594,1141,557)(188,262,703,361,983)(189,236,303,584,448)(190,1353,1355,473,348)(193,243,1292,1158,708)(194,991,1037,824,1031)(195,292,381,885,906)(196,816,492,1040,464)(198,1109,270,924,528)(200,1362,1060,386,1334)(202,476,1209,690,1316)(203,698,1258,767,365)(205,227,1131,232,546)(206,1218,1001,701,1017)(207,1090,421,357,438)(208,1243,325,705,1262)(209,1169,639,901,635)(210,1191,479,575,742)(211,1197,1048,615,720)(217,538,990,598,1282)(222,1239,1044,820,702)(225,1101,1252,843,512)(226,715,1054,439,564)(228,638,350,809,1294)(230,768,1059,1226,1150)(231,1207,1003,853,685)(233,332,627,1222,699)(234,1137,818,447,1238)(237,1151,369,725,1328)(238,254,366,1126,838)(240,625,1256,778,301)(241,871,278,1129,281)(242,999,751,329,487)(245,1079,1149,550,297)(246,831,1011,462,664)(247,1271,1314,1273,377)(248,1350,1198,311,1073)(249,340,633,609,1281)(252,657,775,928,834)(253,814,344,1251,896)(256,766,1179,1009,549)(257,949,277,289,931)(260,485,624,1290,396)(264,1121,1147,926,1043)(265,1298,570,761,1091)(267,1348,909,444,499)(268,349,1306,402,916)(269,746,1255,666,943)(273,324,1289,511,373)(276,505,388,732,1135)(280,610,826,864,819)(282,1180,680,1347,412)(283,978,656,451,1177)(284,339,1263,595,347)(286,653,898,821,844)(288,765,1303,922,1155)(293,305,915,919,936)(300,597,1124,932,863)(308,972,1216,343,781)(312,1208,484,661,319)(318,331,401,452,336)(322,729,1227,1093,456)(328,815,1269,1297,1057)(334,1287,1361,394,551)(335,552,1250,1097,925)(337,1016,646,743,832)(338,1247,706,655,1015)(341,1014,1351,1152,876)(346,403,953,363,1162)(351,1099,1004,1280,436)(353,805,527,1132,748)(355,777,861,758,1028)(358,441,548,718,668)(359,1270,581,1231,753)(364,673,1088,880,1248)(372,913,984,1214,495)(376,406,951,917,1049)(383,530,519,641,857)(385,1056,468,1311,904)(387,1267,845,577,812)(400,612,1254,959,1229)(404,1062,828,603,998)(405,415,489,1217,563)(407,958,683,1182,992)(409,711,1268,1064,875)(414,1165,1190,419,587)(417,596,938,1018,520)(422,1108,731,882,565)(429,1315,1260,682,471)(431,1196,562,894,846)(433,1153,501,539,1081)(434,735,1036,1095,1285)(437,918,923,545,996)(445,856,1157,1321,791)(457,588,952,619,733)(459,517,786,1082,837)(465,507,1283,798,1175)(472,982,722,576,947)(482,1067,622,1086,1304)(486,795,1363,523,757)(500,1327,866,1342,769)(506,514,1083,659,669)(508,1365,644,789,1102)(509,1340,1210,1039,1232)(513,568,1339,1356,961)(518,571,579,1221,1265)(521,1125,1117,1100,582)(524,1205,1023,867,1035)(533,1130,827,935,1046)(537,710,1312,1305,764)(556,614,621,1338,737)(558,903,1237,1286,887)(566,1058,671,648,985)(580,1076,1075,1296,847)(583,660,854,1344,1277)(589,927,1096,629,744)(602,1163,1278,841,1186)(608,1223,770,750,1335)(616,964,1045,986,1299)(620,1174,1078,969,1154)(623,1203,1343,1357,692)(630,1206,872,1136,1019)(637,1112,988,723,878)(651,1308,788,1160,980)(675,792,960,971,997)(677,1325,1211,1337,1360)(694,1181,930,1245,1166)(707,1144,782,1275,941)(721,1230,833,1104,957)(759,1066,945,1240,779)(830,1213,1253,905,873)(842,1113,1352,1349,1224)(858,1244,966,902,900)(889,1302,1030,939,1184)(995,1354,1333,1085,1010),(1,590,32,435,684)(2,688,865,182,342)(3,1178,636,1146,152)(4,1145,26,647,167)(5,362,1307,251,774)(6,393,808,1026,46)(7,310,989,734,874)(8,320,1185,1220,810)(9,739,1008,719,1192)(10,29,1212,977,1139)(11,296,650,993,42)(12,783,665,920,862)(13,330,323,717,1140)(14,617,1012,540,911)(15,910,490,463,493)(16,1276,88,626,572)(17,884,162,255,976)(18,578,453,879,1070)(19,91,787,214,1033)(20,1322,1032,934,470)(21,1053,239,356,662)(22,130,504,895,956)(23,110,391,497,955)(24,526,784,502,963)(25,1199,1105,399,555)(27,1329,728,275,1013)(28,1313,704,287,716)(30,52,93,1300,790)(31,606,423,681,888)(33,634,929,1345,940)(34,631,752,1201,395)(35,180,1084,868,45)(36,1006,139,1110,1228)(37,522,881,1293,691)(38,101,709,1358,440)(39,851,382,367,944)(40,72,891,261,1324)(41,649,1193,628,825)(43,642,1092,103,352)(44,1021,618,272,389)(47,1364,56,1077,123)(48,745,1072,142,908)(49,215,229,529,74)(50,481,599,1173,424)(51,1336,66,79,1127)(53,258,840,250,408)(54,199,806,890,120)(55,974,450,96,1235)(57,1143,697,426,1225)(58,1061,442,374,140)(59,420,835,663,302)(60,531,515,454,147)(61,371,611,106,962)(62,586,1051,937,1261)(63,1167,970,813,907)(64,645,221,397,849)(65,1065,679,802,354)(67,1074,1094,1119,1164)(68,714,483,1116,672)(69,796,314,446,134)(70,1234,294,455,1332)(71,1295,981,461,380)(73,1323,184,1029,593)(75,129,695,1326,333)(76,613,154,968,1133)(77,632,1000,1170,794)(78,554,640,567,942)(80,1195,1187,466,780)(81,488,667,897,491)(82,975,534,384,1142)(83,223,467,536,1176)(84,104,1257,1320,803)(85,893,1279,114,1259)(86,327,290,307,559)(87,965,848,173,298)(89,1007,678,370,1204)(90,811,643,822,1120)(92,191,700,220,443)(94,1168,967,1027,585)(95,1171,1272,730,224)(97,122,503,360,1317)(98,850,411,159,713)(99,573,392,432,315)(100,1020,1219,133,375)(102,143,390,498,1123)(105,1284,979,410,1128)(107,773,1034,326,800)(108,449,793,1111,804)(109,829,727,654,1359)(111,525,155,219,950)(112,149,591,686,921)(113,244,218,1047,772)(115,817,1042,652,418)(116,279,192,1038,553)(117,378,427,510,137)(118,541,1200,1188,869)(119,1346,839,480,754)(121,1107,852,345,899)(124,469,574,259,313)(125,1172,425,1309,870)(126,933,544,859,321)(127,1291,316,309,477)(128,738,877,1161,892)(131,1122,973,1025,1050)(132,1249,201,1115,204)(135,1156,547,1118,1148)(136,756,601,1318,1069)(138,1063,1089,1242,460)(141,886,726,1183,689)(144,569,458,535,1087)(145,379,670,1301,1288)(146,1080,914,604,1233)(148,747,1005,1159,212)(150,478,740,592,801)(151,954,561,1052,532)(153,946,560,317,1002)(156,755,176,235,1106)(157,285,605,1274,797)(158,1236,1071,274,674)(160,1098,1103,658,676)(161,1264,542,398,724)(163,760,823,696,736)(164,181,836,1341,693)(165,799,807,948,883)(166,1330,299,607,266)(168,306,197,516,749)(169,987,543,687,368)(170,1041,494,1055,712)(171,994,475,1114,860)(172,741,428,213,416)(174,1241,1319,763,271)(175,776,295,912,1310)(177,496,785,1194,1068)(178,771,304,1189,600)(179,291,263,430,1331)(183,1024,1266,1138,1246)(185,216,855,1022,1134)(186,474,1202,413,1215)(187,557,1141,594,762)(188,983,361,703,262)(189,448,584,303,236)(190,348,473,1355,1353)(193,708,1158,1292,243)(194,1031,824,1037,991)(195,906,885,381,292)(196,464,1040,492,816)(198,528,924,270,1109)(200,1334,386,1060,1362)(202,1316,690,1209,476)(203,365,767,1258,698)(205,546,232,1131,227)(206,1017,701,1001,1218)(207,438,357,421,1090)(208,1262,705,325,1243)(209,635,901,639,1169)(210,742,575,479,1191)(211,720,615,1048,1197)(217,1282,598,990,538)(222,702,820,1044,1239)(225,512,843,1252,1101)(226,564,439,1054,715)(228,1294,809,350,638)(230,1150,1226,1059,768)(231,685,853,1003,1207)(233,699,1222,627,332)(234,1238,447,818,1137)(237,1328,725,369,1151)(238,838,1126,366,254)(240,301,778,1256,625)(241,281,1129,278,871)(242,487,329,751,999)(245,297,550,1149,1079)(246,664,462,1011,831)(247,377,1273,1314,1271)(248,1073,311,1198,1350)(249,1281,609,633,340)(252,834,928,775,657)(253,896,1251,344,814)(256,549,1009,1179,766)(257,931,289,277,949)(260,396,1290,624,485)(264,1043,926,1147,1121)(265,1091,761,570,1298)(267,499,444,909,1348)(268,916,402,1306,349)(269,943,666,1255,746)(273,373,511,1289,324)(276,1135,732,388,505)(280,819,864,826,610)(282,412,1347,680,1180)(283,1177,451,656,978)(284,347,595,1263,339)(286,844,821,898,653)(288,1155,922,1303,765)(293,936,919,915,305)(300,863,932,1124,597)(308,781,343,1216,972)(312,319,661,484,1208)(318,336,452,401,331)(322,456,1093,1227,729)(328,1057,1297,1269,815)(334,551,394,1361,1287)(335,925,1097,1250,552)(337,832,743,646,1016)(338,1015,655,706,1247)(341,876,1152,1351,1014)(346,1162,363,953,403)(351,436,1280,1004,1099)(353,748,1132,527,805)(355,1028,758,861,777)(358,668,718,548,441)(359,753,1231,581,1270)(364,1248,880,1088,673)(372,495,1214,984,913)(376,1049,917,951,406)(383,857,641,519,530)(385,904,1311,468,1056)(387,812,577,845,1267)(400,1229,959,1254,612)(404,998,603,828,1062)(405,563,1217,489,415)(407,992,1182,683,958)(409,875,1064,1268,711)(414,587,419,1190,1165)(417,520,1018,938,596)(422,565,882,731,1108)(429,471,682,1260,1315)(431,846,894,562,1196)(433,1081,539,501,1153)(434,1285,1095,1036,735)(437,996,545,923,918)(445,791,1321,1157,856)(457,733,619,952,588)(459,837,1082,786,517)(465,1175,798,1283,507)(472,947,576,722,982)(482,1304,1086,622,1067)(486,757,523,1363,795)(500,769,1342,866,1327)(506,669,659,1083,514)(508,1102,789,644,1365)(509,1232,1039,1210,1340)(513,961,1356,1339,568)(518,1265,1221,579,571)(521,582,1100,1117,1125)(524,1035,867,1023,1205)(533,1046,935,827,1130)(537,764,1305,1312,710)(556,737,1338,621,614)(558,887,1286,1237,903)(566,985,648,671,1058)(580,847,1296,1075,1076)(583,1277,1344,854,660)(589,744,629,1096,927)(602,1186,841,1278,1163)(608,1335,750,770,1223)(616,1299,986,1045,964)(620,1154,969,1078,1174)(623,692,1357,1343,1203)(630,1019,1136,872,1206)(637,878,723,988,1112)(651,980,1160,788,1308)(675,997,971,960,792)(677,1360,1337,1211,1325)(694,1166,1245,930,1181)(707,941,1275,782,1144)(721,957,1104,833,1230)(759,779,1240,945,1066)(830,873,905,1253,1213)(842,1224,1349,1352,1113)(858,900,902,966,1244)(889,1184,939,1030,1302)(995,1010,1085,1333,1354),(3,701,173,296,1360)(4,289,862,713,450)(5,951,963,201,79)(6,861,1153,1252,168)(7,115,1324,36,39)(8,19,639,44,135)(9,421,1149,169,667)(10,681,425,1147,107)(11,677,152,1017,848)(12,98,96,1145,277)(13,134,22,972,666)(14,1283,156,432,885)(15,1250,679,247,913)(16,725,642,102,458)(17,673,738,948,187)(18,842,792,656,282)(20,449,54,424,743)(21,579,23,161,916)(24,1115,1127,362,406)(25,1186,541,469,339)(26,949,783,850,1235)(27,856,1299,1233,1191)(28,341,947,714,101)(29,888,1309,1121,773)(30,1232,1201,185,1126)(31,870,264,1034,1212)(33,116,1150,854,953)(34,855,254,93,1210)(37,1176,256,1072,1174)(38,716,1014,472,68)(40,1006,851,310,817)(42,1325,1146,206,965)(43,1123,569,572,1328)(46,758,501,843,749)(48,969,1293,467,1179)(49,404,867,981,1164)(50,646,1322,793,199)(51,1307,376,526,204)(52,1039,395,216,366)(53,967,845,600,151)(55,647,257,665,411)(57,1075,1064,1315,670)(58,1129,105,995,1215)(59,1305,669,1122,64)(60,1237,385,821,619)(61,1068,434,846,111)(62,1181,1125,1000,248)(63,1047,172,1326,918)(65,1314,1214,463,925)(66,774,917,502,1249)(67,215,998,1023,461)(69,130,308,1255,330)(70,1331,689,958,915)(71,1094,529,828,524)(72,139,382,989,1042)(73,625,770,1108,548)(74,1062,1035,1295,1119)(75,996,970,113,428)(76,1004,1294,938,1219)(77,1198,937,1245,1100)(78,730,935,933,181)(80,1319,487,559,334)(81,719,438,297,687)(82,1343,484,584,1244)(83,549,142,620,522)(84,150,274,1348,648)(85,720,198,991,945)(86,551,1195,763,329)(87,993,1211,636,1218)(88,1151,103,390,1087)(89,231,1002,1158,233)(90,1356,1303,1247,1269)(91,1169,1021,1156,320)(92,767,136,208,729)(94,812,304,1052,250)(95,1130,859,1341,640)(97,1213,702,957,1291)(99,292,1012,465,176)(100,968,436,638,520)(104,478,674,267,671)(106,785,1036,1196,219)(108,120,1173,832,470)(109,621,1135,605,138)(110,1264,402,1053,571)(114,1197,270,824,779)(117,1019,1254,489,183)(118,124,1263,555,602)(119,736,336,517,1060)(122,830,820,1104,316)(125,1043,326,977,606)(126,164,942,1272,1046)(127,1317,1253,222,721)(128,807,762,976,1088)(129,545,813,244,213)(131,849,302,764,506)(132,1336,251,1049,784)(133,613,1099,809,596)(137,630,959,1217,1246)(140,281,1128,1354,413)(141,407,305,1234,179)(143,535,1276,369,1092)(144,626,237,352,498)(145,426,847,409,682)(146,210,1329,445,986)(147,1286,1056,844,733)(148,637,788,1190,175)(153,1292,699,1007,685)(154,351,350,417,375)(155,611,496,1095,562)(157,1242,654,737,505)(158,499,1058,1257,740)(159,974,167,931,920)(162,1248,1161,165,1141)(163,452,459,1362,1346)(170,1355,262,1124,359)(171,1114,994,860,475)(174,999,290,1361,466)(177,1285,894,525,371)(178,954,258,1027,1267)(184,301,608,565,358)(186,1061,278,1284,1010)(188,597,753,1041,1353)(189,902,384,692,319)(190,983,300,1231,494)(191,1258,756,1262,322)(192,1059,583,346,929)(193,627,370,1003,560)(194,1066,893,615,528)(195,540,1175,235,573)(196,866,610,896,232)(197,808,355,1081,225)(200,839,760,401,837)(202,941,1011,519,1054)(203,1318,325,1093,220)(205,492,769,864,814)(207,245,543,491,1008)(209,618,547,1185,787)(211,1109,1037,1240,1259)(212,1112,1160,419,1310)(214,635,272,1118,1220)(217,485,1137,273,805)(218,416,695,923,907)(221,835,710,1083,1025)(223,1009,908,1154,881)(224,827,544,836,554)(226,690,782,246,383)(227,1040,500,819,344)(228,1018,1020,1133,1280)(229,603,1205,380,1074)(230,1344,363,940,553)(234,373,353,1282,260)(236,900,534,623,312)(238,1300,1340,631,1022)(239,518,391,542,1306)(240,1223,422,441,1323)(241,410,1333,1202,374)(242,307,1287,780,1241)(243,1222,678,853,946)(253,546,816,1342,826)(255,880,892,799,594)(259,347,1105,1278,1188)(261,1228,944,874,418)(263,726,1182,936,455)(268,662,1221,955,724)(269,717,314,895,343)(271,751,327,394,1187)(275,1321,964,914,575)(276,285,460,1359,1338)(279,1226,660,403,634)(280,1251,1131,464,1327)(283,1347,453,1349,997)(284,1199,841,1200,574)(286,457,454,887,468)(287,1351,982,672,440)(288,1015,328,643,568)(291,886,992,293,294)(295,1005,723,651,414)(298,650,1337,1178,1001)(303,858,975,1203,1208)(306,393,777,433,1101)(309,503,873,1044,833)(311,1051,1166,582,794)(313,595,399,1163,869)(315,381,617,507,755)(317,708,332,1204,1207)(318,786,386,754,696)(321,693,567,1171,533)(323,796,504,781,746)(324,527,538,624,818)(331,1082,1334,480,823)(333,437,1167,772,741)(335,354,1273,495,490)(337,934,804,890,599)(338,815,811,1339,765)(348,361,863,581,1055)(349,356,1265,497,398)(357,550,368,488,1192)(360,905,1239,1230,477)(364,877,883,557,884)(365,1069,1243,1227,443)(367,734,652,891,1110)(372,910,552,802,377)(378,1136,612,415,1024)(379,1225,1296,875,1260)(387,771,561,840,585)(388,797,1089,727,556)(389,1148,810,1033,901)(392,906,911,798,1106)(396,1238,511,748,598)(397,663,537,514,1050)(400,405,1266,427,872)(408,1168,577,1189,532)(412,578,1224,675,978)(420,1312,659,973,645)(423,1172,926,800,1139)(429,1301,1143,1076,1268)(430,1183,683,919,1332)(431,950,962,1194,735)(439,476,707,462,641)(442,871,979,1085,474)(444,566,1320,592,1236)(446,956,1216,943,1140)(447,1289,1132,990,1290)(448,966,1142,1357,661)(451,1180,1070,1113,960)(456,700,698,601,705)(471,1288,697,580,711)(473,703,932,1270,712)(479,1013,1157,616,604)(481,1016,1032,1111,806)(483,709,1313,876,576)(493,1097,1065,1271,984)(509,752,1134,838,790)(510,1206,1229,563,1138)(512,516,1026,1028,539)(513,1155,655,1057,822)(515,558,1311,653,588)(521,1170,1073,586,694)(530,715,1316,1275,831)(531,903,904,898,952)(536,766,745,1078,691)(564,1209,1144,664,857)(587,912,1159,988,980)(593,1256,750,731,718)(614,732,1274,1063,829)(632,1350,1261,930,1117)(668,1029,778,1335,882)(680,879,1352,971,1177)(704,1152,722,1116,1358)(706,1297,1120,961,922)(728,791,1045,1080,742)(739,1090,1079,987,897)(747,878,1308,1165,776)(759,1279,1048,924,1031)(768,1277,1162,1345,1038)(801,1071,909,985,803),(3,1360,296,173,701)(4,450,713,862,289)(5,79,201,963,951)(6,168,1252,1153,861)(7,39,36,1324,115)(8,135,44,639,19)(9,667,169,1149,421)(10,107,1147,425,681)(11,848,1017,152,677)(12,277,1145,96,98)(13,666,972,22,134)(14,885,432,156,1283)(15,913,247,679,1250)(16,458,102,642,725)(17,187,948,738,673)(18,282,656,792,842)(20,743,424,54,449)(21,916,161,23,579)(24,406,362,1127,1115)(25,339,469,541,1186)(26,1235,850,783,949)(27,1191,1233,1299,856)(28,101,714,947,341)(29,773,1121,1309,888)(30,1126,185,1201,1232)(31,1212,1034,264,870)(33,953,854,1150,116)(34,1210,93,254,855)(37,1174,1072,256,1176)(38,68,472,1014,716)(40,817,310,851,1006)(42,965,206,1146,1325)(43,1328,572,569,1123)(46,749,843,501,758)(48,1179,467,1293,969)(49,1164,981,867,404)(50,199,793,1322,646)(51,204,526,376,1307)(52,366,216,395,1039)(53,151,600,845,967)(55,411,665,257,647)(57,670,1315,1064,1075)(58,1215,995,105,1129)(59,64,1122,669,1305)(60,619,821,385,1237)(61,111,846,434,1068)(62,248,1000,1125,1181)(63,918,1326,172,1047)(65,925,463,1214,1314)(66,1249,502,917,774)(67,461,1023,998,215)(69,330,1255,308,130)(70,915,958,689,1331)(71,524,828,529,1094)(72,1042,989,382,139)(73,548,1108,770,625)(74,1119,1295,1035,1062)(75,428,113,970,996)(76,1219,938,1294,1004)(77,1100,1245,937,1198)(78,181,933,935,730)(80,334,559,487,1319)(81,687,297,438,719)(82,1244,584,484,1343)(83,522,620,142,549)(84,648,1348,274,150)(85,945,991,198,720)(86,329,763,1195,551)(87,1218,636,1211,993)(88,1087,390,103,1151)(89,233,1158,1002,231)(90,1269,1247,1303,1356)(91,320,1156,1021,1169)(92,729,208,136,767)(94,250,1052,304,812)(95,640,1341,859,1130)(97,1291,957,702,1213)(99,176,465,1012,292)(100,520,638,436,968)(104,671,267,674,478)(106,219,1196,1036,785)(108,470,832,1173,120)(109,138,605,1135,621)(110,571,1053,402,1264)(114,779,824,270,1197)(117,183,489,1254,1019)(118,602,555,1263,124)(119,1060,517,336,736)(122,316,1104,820,830)(125,606,977,326,1043)(126,1046,1272,942,164)(127,721,222,1253,1317)(128,1088,976,762,807)(129,213,244,813,545)(131,506,764,302,849)(132,784,1049,251,1336)(133,596,809,1099,613)(137,1246,1217,959,630)(140,413,1354,1128,281)(141,179,1234,305,407)(143,1092,369,1276,535)(144,498,352,237,626)(145,682,409,847,426)(146,986,445,1329,210)(147,733,844,1056,1286)(148,175,1190,788,637)(153,685,1007,699,1292)(154,375,417,350,351)(155,562,1095,496,611)(157,505,737,654,1242)(158,740,1257,1058,499)(159,920,931,167,974)(162,1141,165,1161,1248)(163,1346,1362,459,452)(170,359,1124,262,1355)(171,475,860,994,1114)(174,466,1361,290,999)(177,371,525,894,1285)(178,1267,1027,258,954)(184,358,565,608,301)(186,1010,1284,278,1061)(188,1353,1041,753,597)(189,319,692,384,902)(190,494,1231,300,983)(191,322,1262,756,1258)(192,929,346,583,1059)(193,560,1003,370,627)(194,528,615,893,1066)(195,573,235,1175,540)(196,232,896,610,866)(197,225,1081,355,808)(200,837,401,760,839)(202,1054,519,1011,941)(203,220,1093,325,1318)(205,814,864,769,492)(207,1008,491,543,245)(209,787,1185,547,618)(211,1259,1240,1037,1109)(212,1310,419,1160,1112)(214,1220,1118,272,635)(217,805,273,1137,485)(218,907,923,695,416)(221,1025,1083,710,835)(223,881,1154,908,1009)(224,554,836,544,827)(226,383,246,782,690)(227,344,819,500,1040)(228,1280,1133,1020,1018)(229,1074,380,1205,603)(230,553,940,363,1344)(234,260,1282,353,373)(236,312,623,534,900)(238,1022,631,1340,1300)(239,1306,542,391,518)(240,1323,441,422,1223)(241,374,1202,1333,410)(242,1241,780,1287,307)(243,946,853,678,1222)(253,826,1342,816,546)(255,594,799,892,880)(259,1188,1278,1105,347)(261,418,874,944,1228)(263,455,936,1182,726)(268,724,955,1221,662)(269,343,895,314,717)(271,1187,394,327,751)(275,575,914,964,1321)(276,1338,1359,460,285)(279,634,403,660,1226)(280,1327,464,1131,1251)(283,997,1349,453,1347)(284,574,1200,841,1199)(286,468,887,454,457)(287,440,672,982,1351)(288,568,643,328,1015)(291,294,293,992,886)(295,414,651,723,1005)(298,1001,1178,1337,650)(303,1208,1203,975,858)(306,1101,433,777,393)(309,833,1044,873,503)(311,794,582,1166,1051)(313,869,1163,399,595)(315,755,507,617,381)(317,1207,1204,332,708)(318,696,754,386,786)(321,533,1171,567,693)(323,746,781,504,796)(324,818,624,538,527)(331,823,480,1334,1082)(333,741,772,1167,437)(335,490,495,1273,354)(337,599,890,804,934)(338,765,1339,811,815)(348,1055,581,863,361)(349,398,497,1265,356)(357,1192,488,368,550)(360,477,1230,1239,905)(364,884,557,883,877)(365,443,1227,1243,1069)(367,1110,891,652,734)(372,377,802,552,910)(378,1024,415,612,1136)(379,1260,875,1296,1225)(387,585,840,561,771)(388,556,727,1089,797)(389,901,1033,810,1148)(392,1106,798,911,906)(396,598,748,511,1238)(397,1050,514,537,663)(400,872,427,1266,405)(408,532,1189,577,1168)(412,978,675,1224,578)(420,645,973,659,1312)(423,1139,800,926,1172)(429,1268,1076,1143,1301)(430,1332,919,683,1183)(431,735,1194,962,950)(439,641,462,707,476)(442,474,1085,979,871)(444,1236,592,1320,566)(446,1140,943,1216,956)(447,1290,990,1132,1289)(448,661,1357,1142,966)(451,960,1113,1070,1180)(456,705,601,698,700)(471,711,580,697,1288)(473,712,1270,932,703)(479,604,616,1157,1013)(481,806,1111,1032,1016)(483,576,876,1313,709)(493,984,1271,1065,1097)(509,790,838,1134,752)(510,1138,563,1229,1206)(512,539,1028,1026,516)(513,822,1057,655,1155)(515,588,653,1311,558)(521,694,586,1073,1170)(530,831,1275,1316,715)(531,952,898,904,903)(536,691,1078,745,766)(564,857,664,1144,1209)(587,980,988,1159,912)(593,718,731,750,1256)(614,829,1063,1274,732)(632,1117,930,1261,1350)(668,882,1335,778,1029)(680,1177,971,1352,879)(704,1358,1116,722,1152)(706,922,961,1120,1297)(728,742,1080,1045,791)(739,897,987,1079,1090)(747,776,1165,1308,878)(759,1031,924,1048,1279)(768,1038,1345,1162,1277)(801,803,985,909,1071),(1,180)(2,761)(4,753)(6,417)(7,670)(9,717)(10,1119)(11,942)(14,465)(15,512)(18,476)(20,976)(25,1156)(26,1022)(27,893)(28,46)(29,643)(30,771)(31,952)(32,889)(34,300)(36,1064)(37,144)(38,764)(39,1315)(40,441)(41,644)(42,1317)(43,610)(45,1067)(47,1330)(49,726)(50,401)(52,303)(53,863)(54,128)(55,258)(56,1096)(57,115)(59,1099)(62,344)(63,113)(64,613)(65,520)(68,302)(69,136)(70,1311)(71,468)(74,681)(75,172)(78,214)(80,368)(82,974)(83,624)(84,245)(85,1011)(87,602)(88,521)(91,541)(92,1255)(93,190)(95,905)(97,787)(99,156)(100,1314)(101,749)(103,1073)(104,1287)(106,1144)(107,1295)(109,594)(110,471)(112,435)(114,960)(117,415)(118,993)(119,281)(122,1188)(123,523)(124,1211)(126,1017)(127,965)(129,218)(130,208)(131,1014)(133,1122)(137,1266)(138,799)(140,1060)(141,423)(142,324)(143,353)(146,690)(147,765)(148,1221)(149,939)(150,543)(151,361)(152,1046)(154,1153)(155,1031)(158,746)(159,1244)(160,795)(162,374)(163,1274)(164,848)(165,1333)(167,1343)(168,350)(169,343)(174,443)(175,662)(176,1283)(177,997)(178,665)(179,1139)(181,1220)(182,1193)(183,612)(184,1005)(185,585)(186,727)(188,713)(194,1233)(195,1106)(196,572)(198,1054)(199,760)(200,1322)(202,991)(203,739)(205,691)(206,721)(207,648)(209,1213)(210,782)(213,907)(216,1203)(217,1131)(219,1209)(220,897)(221,433)(222,1146)(223,1117)(224,313)(226,986)(227,1181)(228,440)(229,961)(232,569)(234,369)(235,911)(236,1189)(237,256)(238,949)(239,668)(240,851)(241,1248)(242,267)(244,923)(246,1329)(247,1028)(248,819)(252,928)(254,494)(255,621)(257,1267)(259,830)(260,1276)(261,356)(263,1164)(264,903)(265,508)(266,757)(268,1190)(269,667)(270,1180)(271,943)(272,935)(273,280)(274,491)(275,1194)(276,804)(278,388)(282,439)(283,1285)(285,890)(286,1094)(287,1018)(288,1309)(289,1041)(290,1069)(292,432)(295,358)(298,810)(299,629)(301,723)(305,926)(306,710)(307,671)(308,729)(310,1223)(311,1289)(312,577)(314,421)(316,1278)(320,1186)(323,499)(325,1079)(327,446)(328,773)(330,767)(331,883)(334,550)(335,709)(336,1354)(337,1359)(338,1286)(339,1021)(341,758)(345,688)(347,820)(348,600)(349,418)(351,1252)(352,1072)(354,1313)(357,559)(360,640)(364,480)(365,999)(366,1208)(367,988)(371,1349)(373,1092)(375,861)(378,1254)(379,750)(380,1297)(383,445)(387,1126)(389,1178)(390,586)(391,778)(392,540)(393,1083)(394,956)(395,975)(397,984)(398,874)(399,544)(400,1217)(402,697)(404,1182)(405,1246)(407,1172)(408,534)(410,1161)(411,954)(412,616)(413,517)(414,565)(416,545)(422,817)(424,807)(425,1062)(427,630)(428,1047)(429,878)(430,822)(431,964)(436,463)(442,1032)(444,698)(447,794)(448,473)(449,1088)(450,597)(451,1197)(452,1063)(453,525)(454,828)(455,981)(456,592)(457,529)(459,829)(460,599)(462,792)(464,485)(466,1227)(469,1169)(472,849)(474,1016)(477,1341)(478,780)(479,1224)(481,1085)(482,684)(483,490)(484,931)(487,1192)(488,1319)(489,1136)(492,536)(493,663)(495,576)(496,1279)(497,944)(498,1174)(500,1000)(501,947)(504,1257)(506,716)(513,1183)(514,1065)(515,958)(516,1250)(518,1029)(519,720)(522,538)(524,887)(527,620)(528,1299)(531,870)(532,900)(535,1282)(537,1097)(539,913)(542,1335)(547,957)(549,818)(554,869)(555,1218)(556,1061)(557,1082)(558,915)(561,1232)(562,924)(564,1196)(566,601)(568,888)(571,711)(573,798)(575,962)(578,604)(580,1053)(581,967)(582,1290)(584,920)(587,652)(588,689)(589,658)(593,875)(595,827)(596,669)(603,922)(605,892)(607,1098)(608,651)(611,759)(614,1362)(615,856)(618,702)(623,1168)(626,1176)(628,1091)(631,1235)(632,1009)(635,730)(636,1263)(637,955)(638,925)(641,656)(646,837)(647,1027)(650,1033)(653,1331)(655,919)(657,775)(661,712)(664,785)(672,1280)(674,1241)(675,1013)(677,1272)(679,1026)(683,1155)(686,1086)(694,1087)(695,813)(700,1236)(703,966)(705,1320)(706,1205)(707,842)(714,843)(718,1296)(724,788)(731,1225)(732,1346)(733,1339)(734,980)(735,1321)(736,1128)(740,781)(743,762)(744,1363)(745,864)(747,1268)(751,1140)(766,769)(776,1076)(777,1025)(779,1113)(783,1300)(793,839)(796,1058)(797,1284)(800,1234)(805,1251)(806,979)(809,1305)(811,844)(814,1078)(815,1056)(823,877)(824,1070)(825,852)(835,1101)(836,1163)(840,1201)(845,1055)(850,1340)(855,1231)(857,1036)(858,1039)(859,1230)(862,1353)(865,1365)(866,1328)(867,936)(868,921)(871,1111)(872,959)(876,1273)(880,1135)(881,930)(882,1306)(884,1334)(885,1012)(891,912)(894,1347)(895,1149)(896,1123)(898,1212)(899,1298)(901,1337)(904,1034)(906,1175)(908,1350)(914,950)(918,970)(932,1142)(933,1118)(934,1338)(941,945)(968,1214)(978,1157)(982,1133)(983,1210)(987,1093)(990,1166)(996,1326)(1001,1148)(1006,1323)(1008,1348)(1010,1089)(1015,1121)(1019,1024)(1020,1351)(1030,1304)(1035,1147)(1040,1125)(1048,1095)(1050,1271)(1051,1132)(1057,1332)(1066,1191)(1074,1120)(1075,1324)(1077,1103)(1084,1302)(1090,1318)(1102,1107)(1104,1105)(1110,1159)(1130,1239)(1137,1327)(1141,1202)(1143,1165)(1151,1170)(1154,1261)(1185,1291)(1187,1216)(1228,1265)(1243,1361)(1253,1325)(1256,1260)(1264,1288)(1270,1357)(1301,1308),(4,289)(5,79)(6,168)(7,39)(8,44)(9,667)(10,107)(11,1017)(12,1145)(13,134)(14,432)(15,1250)(17,948)(18,792)(19,639)(20,54)(21,579)(22,666)(23,916)(24,1115)(25,1186)(26,850)(28,714)(30,1232)(31,1212)(33,953)(34,1210)(36,115)(38,68)(40,1006)(42,1146)(46,843)(48,1293)(49,981)(50,1322)(51,526)(52,395)(55,647)(57,1064)(58,105)(59,669)(60,1237)(61,1068)(63,172)(64,1122)(67,215)(70,915)(72,382)(73,1108)(74,1035)(75,113)(76,938)(77,937)(78,181)(80,487)(81,687)(82,484)(83,522)(84,274)(85,945)(86,1195)(87,636)(88,103)(89,233)(90,1247)(91,1021)(92,729)(93,855)(94,812)(95,640)(96,98)(97,957)(99,176)(100,638)(102,642)(104,267)(106,219)(108,470)(109,605)(110,1053)(111,434)(114,270)(116,854)(117,1019)(118,124)(119,1060)(120,832)(122,316)(125,977)(126,942)(127,721)(128,976)(129,213)(130,330)(132,1336)(133,613)(140,281)(141,407)(145,847)(148,1190)(151,967)(152,677)(153,1292)(156,1283)(159,920)(163,1362)(165,1161)(169,421)(170,1124)(171,860)(173,296)(174,1361)(179,305)(183,1254)(189,319)(190,1231)(192,929)(193,627)(194,528)(195,235)(196,232)(197,1081)(199,793)(200,401)(201,951)(202,519)(205,814)(206,965)(207,1008)(208,767)(209,618)(210,986)(211,1109)(212,1160)(214,1220)(216,366)(217,1137)(218,907)(220,1318)(221,835)(222,1317)(224,836)(226,782)(227,819)(228,1133)(230,553)(231,1158)(234,260)(236,623)(237,352)(238,1300)(239,542)(240,422)(241,1202)(242,1287)(244,545)(245,491)(246,383)(248,1181)(250,304)(251,784)(253,816)(255,880)(256,1072)(257,411)(258,1027)(259,1105)(261,418)(262,1355)(268,1221)(269,717)(271,327)(273,805)(275,914)(276,1359)(278,1284)(279,403)(280,1251)(282,656)(283,1349)(284,574)(285,460)(286,887)(287,1351)(288,1015)(290,999)(291,294)(292,465)(293,886)(295,723)(297,719)(298,1337)(300,983)(301,358)(302,764)(303,975)(306,777)(308,1255)(309,873)(311,794)(313,1163)(314,343)(315,507)(317,1207)(318,696)(320,1156)(321,693)(322,1258)(323,781)(325,1093)(326,1043)(328,568)(329,763)(331,480)(333,1167)(334,559)(335,354)(337,804)(338,1339)(339,541)(341,947)(346,1059)(348,1055)(349,356)(350,417)(351,375)(355,808)(357,550)(360,905)(361,581)(364,883)(365,1069)(367,1110)(368,1192)(369,1276)(370,560)(371,1285)(372,377)(373,1282)(376,1307)(378,612)(379,875)(380,1205)(381,617)(385,619)(387,840)(388,797)(389,1148)(390,1087)(391,518)(392,906)(394,1187)(396,511)(397,537)(398,1265)(399,595)(400,872)(402,1264)(404,867)(405,427)(406,1127)(408,532)(409,682)(410,1333)(413,1128)(414,651)(415,1024)(416,923)(419,1310)(420,973)(423,1172)(424,743)(429,1143)(430,1183)(431,735)(433,1101)(436,968)(439,641)(440,982)(441,1323)(442,474)(443,1243)(444,1236)(445,1329)(446,943)(447,1289)(450,862)(452,459)(453,1347)(454,457)(455,726)(456,601)(458,725)(461,998)(462,476)(463,1214)(467,1179)(471,580)(472,716)(477,1239)(478,674)(479,1013)(481,1111)(483,876)(490,1273)(492,864)(496,1095)(498,626)(499,740)(500,1040)(501,758)(502,917)(504,796)(505,1242)(506,849)(509,838)(510,1138)(512,516)(513,822)(514,1050)(515,653)(517,736)(521,1073)(524,1094)(525,894)(527,818)(529,828)(530,1275)(531,904)(533,567)(534,900)(535,1092)(536,745)(538,624)(539,1026)(540,1175)(544,827)(547,787)(549,620)(556,1089)(557,884)(558,1311)(561,771)(562,611)(563,1206)(564,664)(565,608)(566,592)(569,572)(578,978)(582,1051)(584,1244)(586,694)(593,750)(594,892)(596,1099)(597,1353)(598,748)(599,890)(600,845)(602,1263)(603,1074)(604,1157)(614,1274)(615,1066)(621,1135)(625,770)(630,1246)(632,930)(635,1118)(637,788)(648,1348)(654,737)(659,1312)(660,1226)(661,966)(668,1335)(670,1315)(673,738)(675,1224)(678,853)(679,913)(680,1352)(681,1147)(683,1332)(685,699)(691,1078)(692,902)(697,1288)(698,700)(701,1360)(702,1213)(703,712)(706,1297)(708,1204)(709,1313)(710,1025)(715,1316)(718,731)(720,991)(722,1116)(724,955)(728,1045)(730,933)(733,1286)(734,891)(741,772)(742,1080)(747,776)(752,1134)(753,1041)(754,786)(756,1262)(759,924)(760,839)(762,807)(768,1345)(773,888)(774,1249)(778,1029)(779,824)(780,1241)(783,949)(785,1196)(801,803)(802,910)(810,901)(811,815)(817,851)(826,1342)(829,1063)(830,1104)(833,1044)(844,1056)(856,1191)(861,1252)(866,896)(870,1034)(871,1085)(874,1228)(878,1165)(881,1009)(897,1090)(898,952)(908,1154)(911,1106)(912,980)(918,1326)(922,1120)(925,1314)(926,1139)(931,974)(932,1270)(936,1182)(940,1344)(941,1011)(946,1222)(950,1194)(954,1267)(956,1216)(958,1331)(959,1217)(960,1180)(964,1321)(970,996)(971,1177)(984,1097)(985,1071)(987,1079)(988,1159)(989,1042)(993,1211)(994,1114)(995,1215)(1000,1125)(1001,1178)(1004,1294)(1010,1061)(1016,1032)(1018,1020)(1022,1340)(1037,1259)(1046,1272)(1048,1279)(1057,1155)(1058,1257)(1065,1271)(1070,1113)(1076,1268)(1082,1334)(1100,1245)(1119,1295)(1121,1309)(1123,1328)(1126,1201)(1130,1341)(1131,1327)(1132,1290)(1141,1248)(1142,1357)(1144,1209)(1152,1358)(1162,1277)(1168,1189)(1174,1176)(1188,1278)(1199,1200)(1203,1208)(1225,1296)(1233,1299)(1261,1350)(1303,1356),(1,686)(2,182)(4,532)(5,1336)(6,1050)(7,670)(8,533)(9,1241)(10,1119)(11,1337)(12,250)(13,803)(14,465)(15,133)(16,1198)(17,754)(18,476)(19,321)(20,1128)(21,419)(22,1071)(23,212)(24,1307)(25,360)(26,387)(27,155)(28,472)(29,71)(30,238)(31,380)(32,149)(33,1162)(34,366)(35,622)(36,1064)(37,344)(38,947)(39,1315)(40,1225)(41,1298)(42,636)(43,1117)(44,567)(45,1067)(46,849)(47,56)(48,253)(49,1139)(50,1202)(51,406)(52,855)(53,167)(54,413)(55,258)(57,115)(58,120)(59,1026)(60,1356)(61,1080)(62,144)(63,113)(64,516)(65,520)(67,1043)(68,341)(69,1320)(70,1183)(72,145)(74,681)(75,172)(76,802)(77,458)(78,214)(79,132)(80,368)(81,329)(82,361)(83,1251)(84,943)(85,779)(86,719)(87,1146)(88,521)(90,619)(91,1130)(92,698)(93,395)(94,98)(95,320)(96,812)(97,313)(99,156)(100,1314)(101,1014)(102,1100)(103,1073)(104,343)(105,832)(106,1013)(107,1295)(108,1215)(109,1274)(110,912)(111,1045)(112,435)(114,720)(116,1345)(117,415)(118,721)(119,762)(121,789)(122,1188)(123,1077)(124,127)(125,461)(126,810)(128,517)(129,218)(130,592)(131,749)(134,801)(135,1171)(136,705)(137,1266)(138,732)(139,426)(140,424)(141,1182)(142,464)(143,1166)(146,177)(147,765)(148,1221)(150,1140)(151,974)(152,1001)(153,1207)(154,493)(158,746)(159,600)(160,795)(161,1112)(162,837)(163,594)(164,1033)(165,760)(166,927)(168,514)(169,1287)(170,692)(174,1090)(175,662)(176,1283)(178,665)(179,726)(180,1086)(181,1220)(183,612)(184,882)(185,631)(186,934)(187,386)(188,312)(189,262)(190,975)(192,660)(193,678)(194,1048)(195,1106)(196,1154)(197,420)(198,1197)(199,1333)(200,1248)(201,784)(202,1180)(203,1227)(204,362)(205,691)(206,993)(207,1187)(208,456)(209,827)(210,1285)(213,907)(215,326)(216,1210)(217,818)(219,479)(220,1243)(221,433)(222,602)(223,610)(224,787)(225,645)(226,1349)(227,1176)(228,490)(229,264)(232,908)(234,1289)(235,911)(236,597)(237,1125)(239,723)(240,593)(241,1322)(242,421)(243,1003)(244,923)(245,271)(246,1347)(247,809)(248,498)(249,633)(251,951)(252,928)(254,1039)(255,452)(256,1040)(257,1267)(259,830)(260,447)(261,1268)(263,1234)(265,825)(266,589)(267,314)(268,1190)(269,478)(270,991)(272,935)(273,538)(274,446)(275,1194)(276,556)(277,1052)(278,890)(279,346)(280,522)(281,743)(282,439)(283,782)(284,833)(285,388)(286,568)(287,709)(288,457)(289,408)(290,987)(292,432)(295,542)(297,1195)(298,1017)(299,629)(300,1208)(301,668)(302,758)(303,1231)(304,1145)(305,455)(306,710)(307,1149)(308,1236)(309,1199)(310,1260)(311,369)(316,1278)(317,1292)(318,738)(319,1355)(323,499)(324,485)(325,365)(327,491)(328,887)(330,566)(331,883)(332,1007)(334,550)(335,1018)(336,1088)(337,1010)(338,1286)(339,477)(345,1365)(347,820)(348,1244)(349,776)(350,1065)(351,1097)(352,1000)(353,990)(354,1020)(355,659)(356,747)(357,559)(358,1335)(359,384)(364,480)(367,697)(370,946)(371,986)(372,1294)(373,1132)(374,646)(375,984)(376,1115)(377,1004)(378,1254)(379,817)(382,847)(383,453)(385,1247)(389,1272)(390,586)(391,414)(392,540)(393,1083)(394,1008)(397,861)(398,1165)(399,702)(400,1217)(401,1141)(402,988)(403,1059)(404,423)(405,1246)(407,936)(409,989)(410,793)(411,954)(412,857)(416,545)(417,1271)(418,1076)(422,750)(425,1062)(427,630)(428,1047)(429,1228)(430,915)(431,964)(434,728)(436,463)(438,551)(440,483)(441,731)(442,1032)(443,1318)(444,1255)(445,525)(448,473)(449,1354)(450,1189)(451,1054)(454,1015)(459,880)(460,797)(462,792)(466,739)(467,1342)(468,643)(469,1230)(470,995)(471,891)(474,1016)(481,1085)(482,868)(484,581)(486,676)(487,1192)(488,1319)(489,1136)(492,536)(494,858)(495,1280)(496,1299)(497,1308)(500,1072)(501,764)(503,841)(504,1257)(506,843)(508,852)(512,1122)(513,1311)(515,1057)(518,651)(519,960)(523,1103)(524,773)(526,1127)(527,1137)(528,1279)(529,1309)(530,1352)(531,1120)(534,1041)(535,582)(537,1252)(539,669)(541,1239)(543,751)(544,618)(546,969)(547,836)(549,1131)(552,1219)(554,1185)(555,1253)(557,1082)(558,822)(560,1222)(561,783)(562,1191)(564,578)(565,778)(569,1350)(570,649)(571,587)(572,1261)(573,798)(574,1044)(575,962)(576,672)(577,713)(579,1310)(580,734)(583,634)(584,1055)(585,1235)(588,655)(590,591)(595,1213)(596,913)(599,1284)(601,767)(603,1034)(604,1196)(605,614)(606,1023)(607,744)(608,1029)(609,1281)(611,856)(613,1250)(615,759)(616,1036)(620,1327)(621,1063)(623,1353)(624,805)(626,1181)(627,853)(628,1091)(632,1123)(635,730)(637,955)(638,925)(639,693)(640,1156)(641,656)(642,1245)(644,899)(647,1027)(648,1216)(650,848)(652,711)(653,1155)(657,775)(658,757)(661,712)(663,1153)(664,978)(666,985)(667,780)(671,895)(673,696)(674,717)(675,1144)(677,1178)(679,1099)(680,1275)(682,1042)(683,1331)(684,921)(685,1204)(687,763)(688,865)(689,919)(690,997)(694,1087)(695,813)(699,708)(700,729)(703,966)(706,898)(707,842)(714,716)(715,971)(718,1323)(724,788)(725,937)(727,1338)(733,1339)(735,1321)(736,976)(740,781)(742,1068)(745,864)(753,900)(761,1193)(766,769)(768,854)(771,949)(777,1025)(785,1157)(786,948)(791,846)(794,1276)(796,1058)(799,1346)(800,1164)(804,1061)(806,979)(807,1060)(808,1312)(811,844)(814,1078)(815,1056)(816,1293)(819,1174)(821,1269)(823,877)(824,945)(826,1179)(828,1121)(829,1135)(831,879)(835,1101)(839,1161)(840,850)(845,920)(851,875)(859,1169)(862,1168)(863,1343)(866,881)(867,1172)(869,1291)(870,1074)(871,1111)(872,959)(873,1200)(874,1143)(876,982)(878,1265)(884,1334)(885,1012)(888,1094)(889,939)(892,1362)(893,1031)(894,1329)(896,1009)(897,1361)(901,942)(902,1124)(903,961)(904,922)(905,1186)(906,1175)(909,972)(910,938)(914,950)(916,1160)(918,970)(924,1066)(926,981)(929,1226)(930,1328)(931,967)(932,1142)(933,1118)(941,1070)(944,1301)(952,1297)(953,1277)(956,1348)(957,1163)(958,1332)(963,1049)(965,1211)(968,1214)(973,1081)(977,998)(980,1053)(983,1203)(996,1326)(999,1079)(1005,1306)(1006,1296)(1011,1113)(1019,1024)(1021,1341)(1022,1126)(1028,1305)(1030,1302)(1035,1147)(1038,1150)(1046,1148)(1051,1092)(1069,1093)(1075,1324)(1084,1304)(1089,1359)(1095,1233)(1096,1330)(1098,1363)(1102,1107)(1104,1105)(1110,1288)(1129,1173)(1133,1273)(1151,1170)(1159,1264)(1177,1316)(1201,1340)(1205,1212)(1209,1224)(1218,1325)(1223,1256)(1232,1300)(1237,1303)(1263,1317)(1270,1357)(1282,1290)(1313,1351),(1,1226,180,660)(2,5,761,79)(4,1060,1041,281)(6,593,350,379)(7,306,1315,1025)(8,555,44,1218)(9,49,269,455)(10,487,1295,368)(11,1213,126,618)(12,732,1145,1346)(13,229,134,961)(14,415,292,1019)(15,1264,516,697)(17,863,948,53)(18,792,462,476)(19,1230,639,859)(20,300,128,1210)(21,672,579,1280)(22,588,666,689)(23,663,916,493)(24,644,1115,41)(25,1156,320,1186)(26,760,1340,793)(27,1275,893,530)(28,1335,843,239)(29,86,643,1195)(30,460,561,890)(31,956,898,1187)(32,1162,889,1277)(33,149,953,939)(34,976,983,54)(35,1150)(36,638,57,1314)(37,816,144,253)(38,471,302,1053)(39,710,670,777)(40,287,1323,1020)(42,1317,222,1146)(43,1245,610,1100)(45,553,1067,230)(46,668,714,542)(47,1207,1330,317)(48,62,1293,344)(50,967,200,361)(51,865,526,1365)(52,109,975,892)(55,883,1027,480)(56,1292,1096,153)(58,494,105,254)(59,518,596,778)(60,705,1237,1320)(61,198,1068,1054)(63,213,75,218)(64,1159,133,367)(65,73,520,1108)(66,342)(67,751,215,1140)(68,110,764,580)(69,1303,136,1356)(70,245,558,274)(71,297,468,719)(72,1014,382,131)(74,781,1147,499)(76,1005,938,184)(77,324,937,142)(78,1104,1220,259)(80,107,1192,1119)(81,1234,687,800)(82,1248,931,1202)(83,1328,538,896)(84,1311,491,915)(85,1011,941,945)(87,602,1263,636)(88,103,1073,521)(89,795,233,160)(90,307,1247,671)(91,127,339,206)(92,141,308,1172)(93,614,1231,163)(94,336,812,1354)(95,640,360,905)(96,1088,98,449)(97,957,547,787)(99,400,1283,959)(100,115,925,1064)(101,145,749,847)(102,223,642,1117)(104,286,242,524)(106,114,1209,1180)(108,713,470,188)(111,412,434,616)(112,1344,435,940)(113,129,172,907)(116,482,854,684)(117,465,1024,432)(118,1239,1211,1341)(119,289,140,753)(120,1039,832,858)(121,1049)(122,316,1278,1188)(123,370,523,560)(124,1130,993,477)(125,1227,977,466)(130,454,767,529)(132,1193,1336,182)(137,617,1266,381)(138,250,799,304)(139,1219)(143,1179,353,467)(146,971,690,1177)(147,756,765,1262)(148,436,268,1214)(150,326,543,1043)(151,1322,581,401)(152,677,1272,1046)(154,1160,1153,212)(155,1352,1031,680)(156,872,176,1217)(157,790)(158,886,746,293)(159,337,584,276)(161,225)(162,170,374,1124)(164,284,848,574)(165,387,410,1201)(166,1003)(167,786,1343,754)(168,875,417,750)(169,888,314,328)(171,657,860,775)(173,347,296,820)(174,958,1243,653)(175,1116,662,722)(177,1316,997,715)(178,505,665,1242)(179,780,926,674)(181,1105,214,830)(183,1106,378,235)(185,318,585,696)(186,189,727,319)(187,384)(190,1274,855,1362)(191,992)(192,1086,929,686)(193,589,627,658)(194,283,1299,371)(195,612,911,1254)(196,572,569,232)(197,1301,1081,1308)(199,1022,839,850)(201,825,951,852)(202,1224,720,1013)(203,461,739,998)(204,649)(205,814,1078,691)(207,706,1348,380)(208,457,330,828)(209,942,702,1017)(210,1279,226,1095)(211,575,1109,962)(216,517,1208,1128)(217,1131,1327,1137)(219,960,1144,270)(220,1332,1090,1155)(221,788,1101,955)(224,836,1163,313)(227,819,248,1181)(228,1076,982,747)(231,299,1158,629)(234,260,1276,369)(236,1063,1168,459)(237,1132,1072,582)(238,278,783,797)(240,1050,817,1065)(241,974,1141,484)(243,927)(244,923,416,545)(246,383,445,1329)(247,989,1028,1042)(251,265,784,508)(252,1114,928,994)(255,1353,1135,450)(256,1290,352,1051)(257,1085,954,1111)(258,364,647,331)(261,483,349,1273)(262,934,1355,1338)(263,329,1164,763)(264,803,903,801)(266,678,757,853)(267,1094,1287,887)(271,1183,446,822)(272,1360,935,701)(273,930,1251,1009)(275,439,950,656)(277,1129)(279,1304,403,1030)(280,632,805,881)(282,1194,641,914)(285,1232,599,771)(288,456,1121,566)(290,922,365,1074)(291,1319,294,488)(295,716,301,849)(298,399,901,827)(303,605,395,594)(305,478,1139,1241)(309,869,873,554)(310,808,1223,355)(311,794,447,1289)(312,995,577,1215)(315,1136,507,489)(321,1169,693,469)(322,425,1258,1062)(323,1035,740,681)(325,904,987,870)(327,513,943,430)(332,676)(333,813,1167,695)(334,1056,357,811)(335,1296,1313,731)(338,1257,733,796)(341,734,501,912)(343,773,421,568)(345,1127,688,406)(346,1302,1059,1084)(348,1089,845,1061)(351,398,861,1228)(354,718,709,1225)(356,876,418,490)(358,472,723,506)(359,386)(362,570)(363,1184)(366,413,1203,736)(372,587,377,652)(373,1125,535,500)(375,874,1252,1265)(376,899,1307,1298)(385,1149,619,895)(388,949,1284,1300)(389,1178,1001,1148)(390,745,694,492)(391,669,1029,1099)(392,1246,1175,427)(393,625,1083,770)(394,952,1216,1212)(396,1151,511,1170)(397,1165,1097,429)(402,1250,1288,512)(404,700,936,444)(405,540,630,906)(407,729,423,1255)(408,762,900,424)(409,809,682,1305)(411,481,1267,871)(414,679,608,539)(419,495,1310,576)(420,497,973,944)(422,1271,851,514)(426,552)(428,741,1047,772)(431,735,1321,964)(433,637,835,724)(438,1269)(440,1268,1133,776)(441,1351,1006,1018)(442,703,1016,661)(443,1331,1361,515)(448,737,473,654)(451,742,1197,1080)(452,1189,829,623)(453,1347,894,525)(458,464,725,485)(463,1221,968,1190)(474,966,1032,712)(475,834)(479,991,675,519)(486,1007)(496,782,1048,986)(498,1174,1176,626)(502,1102,917,1107)(504,1286,1058,1339)(509,806,838,979)(510,885,1138,1012)(522,866,624,1123)(527,620,549,818)(528,1285,1233,1349)(531,1093,1034,1079)(532,743,534,807)(533,1325,567,1253)(536,1087,864,586)(537,1143,984,878)(541,721,1021,965)(544,810,595,1337)(548,704)(550,844,559,815)(551,821)(556,1055,1010,600)(557,1357,1334,932)(562,611,759,924)(563,798,1206,573)(564,1196,785,664)(565,913,651,1026)(571,1294,711,1004)(578,978,1157,604)(583,590)(591,634)(592,1309,601,1015)(597,880,862,621)(598,769,748,766)(603,1069,1120,999)(606,972)(607,699,1098,685)(613,988,1122,1110)(615,856,1191,1066)(622,1038)(628,774,1091,1249)(631,673,1235,738)(635,730,933,1118)(645,1112)(646,692,837,902)(648,1297,1008,1205)(650,833,1033,1044)(655,1071,919,985)(659,1256,1312,1260)(667,726,717,981)(683,1318,1057,897)(698,867,1236,1182)(707,1037,842,1259)(708,744,1204,1363)(728,857,1045,1036)(752,877,1134,823)(755,1229)(758,891,947,980)(768,868,1345,921)(779,824,1070,1113)(789,963)(802,882,910,1306)(804,920,1359,1244)(826,1166,1342,990)(840,1161,1126,1333)(884,1270,1082,1142)(908,1350,1261,1154)(909,1023)(918,1326,996,970)(946,1077,1222,1103)(1000,1282,1040,1092)(1002,1364)(1052,1173)(1075,1152,1324,1358)(1185,1200,1291,1199),(1,33,695,45,953,437)(2,1003,14,852,332,432)(3,4,318,555,1270,410)(5,1136,795,79,1229,266)(6,521,637,377,937,565)(7,968,748,989,1294,83)(8,366,760,635,1142,995)(9,307,80,700,972,446)(10,457,886,898,326,1057)(11,82,186,541,1126,1346)(12,109,618,361,364,1156)(13,985,1093,1241,740,357)(15,826,1005,1101,237,548)(16,471,1050,344,268,287)(17,636,783,614,1105,983)(18,1070,680,1285,1095,1196)(19,812,880,214,258,654)(20,1021,190,1322,547,850)(21,1219,572,1268,520,814)(22,327,290,1287,781,308)(23,1028,1154,1143,65,260)(24,510,1103,502,415,1364)(25,170,138,152,974,877)(26,1362,942,1231,1061,1317)(27,431,1224,1240,1347,1068)(28,103,418,973,866,367)(29,147,404,821,264,867)(30,1129,1341,1244,837,830)(31,1121,1062,1056,60,1023)(32,1059,75,1084,768,545)(34,481,181,319,120,905)(35,634,918,684,363,1326)(36,1214,467,72,516,805)(37,1256,1133,990,587,228)(38,500,115,221,642,382)(39,722,1245,1042,764,694)(40,225,43,1006,493,769)(41,1292,798,1102,153,755)(42,966,452,1200,52,1284)(44,1041,829,1118,55,673)(46,1181,1228,1273,930,891)(47,951,137,658,201,489)(48,1053,613,1137,1064,350)(49,643,1234,981,263,961)(50,126,1168,54,222,967)(51,183,744,251,1246,589)(53,1089,298,577,128,313)(56,204,427,1098,1049,405)(57,335,458,110,501,227)(58,477,300,200,730,949)(59,1290,1306,483,1174,1260)(61,831,453,675,707,735)(62,593,982,1117,912,537)(63,939,583,172,482,1038)(64,626,1075,709,253,571)(66,872,486,362,400,607)(67,215,513,1119,1295,294)(68,1179,295,835,273,73)(69,245,456,466,208,421)(70,1035,107,1356,998,952)(71,305,455,229,922,568)(74,815,1043,461,1183,454)(76,624,356,638,1078,409)(77,402,947,1073,1315,1312)(78,1055,505,360,96,594)(81,897,550,365,1258,325)(84,274,174,104,267,330)(85,1031,1194,479,791,1349)(86,751,207,343,746,729)(87,600,401,259,532,105)(88,1225,910,896,391,1252)(89,392,342,678,617,345)(90,683,1172,1331,338,558)(91,1189,163,787,151,1010)(92,314,488,1008,1195,203)(93,1085,209,902,736,320)(94,108,124,1027,1016,173)(95,159,806,316,1355,1173)(97,257,278,567,597,459)(98,832,1211,348,1111,1278)(99,865,1158,540,121,946)(100,390,419,938,196,778)(101,864,776,645,1328,1323)(102,723,463,1040,1108,512)(106,476,1321,971,530,194)(111,893,779,978,575,1329)(112,553,772,591,660,218)(113,686,346,244,921,1345)(114,720,690,210,604,857)(116,428,1086,854,813,889)(117,676,1127,1217,123,774)(118,1134,255,296,1203,737)(119,965,954,474,574,304)(122,920,157,640,262,799)(125,1332,828,887,1339,1205)(127,581,871,1272,1145,517)(129,868,1344,996,590,279)(130,1361)(131,205,1076,704,569,579)(132,1206,757,376,612,299)(133,725,301,417,819,1190)(134,1090,504,780,322,394)(135,289,1333,272,932,696)(136,566,705,543,592,1149)(139,1250,352,1324,433,1342)(140,833,858,1334,827,790)(141,385,903,1297,888,425)(142,724,1065,1238,1288,355)(143,980,440,464,750,397)(144,662,1018,546,711,1020)(145,539,1251,398,925,1276)(146,202,616,1197,519,198)(148,758,1293,358,354,217)(149,1150,1047)(150,491,169,671,767,601)(154,373,240,809,1009,1165)(155,270,1157,451,986,991)(156,825,1002,1283,789,243)(158,559,763,909,1216,717)(160,1307,563,1077,1336,378)(161,247,311,1301,393,794)(162,848,840,1338,469,387)(164,623,276,1253,1022,1141)(165,1291,712,285,1171,450)(166,406,1019,1363,1249,959)(167,823,389,359,1354,1148)(168,396,1264,372,620,670)(171,775,633,860,928,609)(175,1122,816,184,1313,498)(176,649,1222,1175,508,231)(177,445,578,842,824,434)(178,1082,1044,1052,281,544)(179,328,800,1120,726,588)(180,192,923,435,1277,333)(182,699,1012,899,685,573)(185,1088,901,1343,727,810)(187,1130,1232,732,1104,584)(188,762,224,665,388,309)(189,892,1188,1210,1242,993)(191,956,329,739,334,269)(193,315,688,317,911,1107)(195,265,708,292,1298,560)(197,324,718,984,766,1159)(199,957,661,424,533,395)(206,509,621,284,303,884)(211,715,1316,1233,439,641)(212,1026,1261,668,1314,1125)(213,622,403,970,1302,940)(216,738,1263,1357,1063,701)(219,1037,894,1177,856,282)(220,1255,1243,1192,999,297)(223,817,663,353,851,672)(226,782,611,564,664,960)(230,907,1184,1226,741,1304)(232,682,849,1087,349,1358)(233,381,570,853,906,1091)(234,429,1083,908,916,1014)(235,1193,370,465,1365,1204)(236,1248,1185,1340,1359,1169)(238,786,1230,534,241,935)(239,351,248,875,1099,632)(242,368,1348,666,1318,674)(246,1352,615,1144,785,914)(249,475,252)(250,1135,702,1267,557,321)(254,331,595,384,1128,1001)(256,1112,679,1289,882,777)(261,861,536,1110,802,527)(271,648,443,323,478,719)(275,496,1045,1066,1113,924)(277,413,399,863,480,1178)(280,1160,716,369,1335,1025)(283,1013,1036,950,945,879)(286,681,423,977,904,1311)(288,1269,870,936,689,1286)(291,822)(293,430,1303,1155,811,915)(302,598,651,1116,522,770)(306,447,426,913,1072,497)(310,1280,1166)(312,804,869,631,337,650)(336,1186,931,979,677,1124)(339,484,646,1017,1201,449)(340,1114,834,1281,994,657)(341,511,608,659,549,788)(347,900,754,1218,1300,1202)(371,383,759,792,1209,728)(374,820,771,386,859,561)(375,1092,734,596,1327,874)(379,843,535,542,490,1131)(380,958,1147,529,1247,531)(407,773,765,706,619,919)(408,1274,933,845,948,1239)(411,793,1199,1353,743,1146)(412,962,941,846,997,1011)(414,436,586,625,1004,1100)(416,1067,929,1167,1030,1162)(420,818,1296,714,745,518)(422,749,1282,878,495,881)(438,943,698,1227,487,667)(441,552,1123,747,1153,492)(442,1213,838,1060,693,975)(444,895,1319,1236,551,1140)(448,807,873,1039,797,836)(460,1325,703,1161,841,862)(462,656,1080,1275,525,1048)(468,733,1182,606,1034,1015)(470,639,1208,1032,1220,752)(472,1000,1265,710,1350,847)(473,890,503,713,599,554)(485,1221,514,969,580,1351)(494,556,1163,1235,976,1337)(499,796,687,1071,1187,1069)(506,691,1029,1152,538,1310)(507,644,627,1106,628,1207)(515,1094,524,926,1074,603)(523,784,1254,1330,526,630)(528,742,1191,964,1279,1259)(562,1180)(576,1051,1223,1305,582,1308)(585,934,1033)(602,647,839,1360,753,1215)(605,1046,855,883,721,692)(610,988,1097,1151,731,1081)(629,917,1138,927,1115,1024)(652,669,1176,944,876,1132)(653,1139)(655,844,1309,992,1212,1237)(697,1271,1170,955,808,1198)(756,803,801,987,1257,1058)(761,1007,885)(963,1266,1096)(1079,1262)(1109,1299)]).
- It is non-abelian.
- It has 5-Rank 3.
- The centre of a Sylow 5-subgroup has rank 3.
- Its Sylow 5-subgroup has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 3.
Structure of the cohomology ring
The computation was based on 47 stability conditions for H*(SmallGroup(125,5); GF(5)).General information
- The cohomology ring is of dimension 3 and depth 3.
- The depth coincides with the Duflot bound.
- The Poincaré series is
( − 1)·((1 − t + t2 − t3 + t4 − t5 + t6) · (1 − t + t2 − t3 + t4 − t5 + t6 − t7 + t8 − t9 + t10)) ( − 1 + t)3 · (1 + t + t2) · (1 + t2)3 · (1 − t2 + t4) · (1 + t4) - The a-invariants are -∞,-∞,-∞,-3. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
- The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Ring generators
The cohomology ring has 6 minimal generators of maximal degree 12:
-
a_3_0 , a nilpotent element of degree 3 -
c_4_0 , a Duflot element of degree 4 -
a_7_1 , a nilpotent element of degree 7 -
c_8_1 , a Duflot element of degree 8 -
a_11_3 , a nilpotent element of degree 11 -
c_12_2 , a Duflot element of degree 12
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Ring relations
There are 3 "obvious" relations:
Apart from that, there are no relations.
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Data used for the Hilbert-Poincaré test
- We proved completion in degree 21 using the Hilbert-Poincaré criterion.
- However, the last relation was already found in degree 0 and the last generator in degree 12.
- The following is a filter regular homogeneous system of parameters:
c_4_0 , an element of degree 4c_8_1 , an element of degree 8c_12_2 , an element of degree 12
- The above filter regular HSOP forms a Duflot regular sequence.
- The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, -1, 21].
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
Restriction maps
Expressing the generators as elements of H*(SmallGroup(125,5); GF(5))
-
a_3_0 →c_2_5·a_1_2 + c_2_5·a_1_1 + c_2_4·a_1_2 − 2·c_2_4·a_1_1 − 2·c_2_4·a_1_0 − 2·c_2_3·a_1_1
+ c_2_3·a_1_0 -
c_4_0 →c_2_52 + 2·c_2_4·c_2_5 − 2·c_2_42 + c_2_3·c_2_4 + c_2_32 -
a_7_1 →c_2_4·c_2_52·a_1_1 − c_2_4·c_2_52·a_1_0 + c_2_42·c_2_5·a_1_2
+ 2·c_2_42·c_2_5·a_1_1 − c_2_42·c_2_5·a_1_0 − c_2_43·a_1_2 + 2·c_2_43·a_1_1
+ 2·c_2_43·a_1_0 − c_2_3·c_2_52·a_1_1 − 2·c_2_3·c_2_52·a_1_0
− 2·c_2_3·c_2_4·c_2_5·a_1_2 − 2·c_2_3·c_2_4·c_2_5·a_1_1 − 2·c_2_3·c_2_4·c_2_5·a_1_0
− c_2_3·c_2_42·a_1_2 + c_2_3·c_2_42·a_1_1 − 2·c_2_32·c_2_5·a_1_2
− c_2_32·c_2_5·a_1_1 − c_2_32·c_2_4·a_1_2 − 2·c_2_32·c_2_4·a_1_0 + c_2_33·a_1_1
+ 2·c_2_33·a_1_0 -
c_8_1 →c_2_42·c_2_52 − 2·c_2_43·c_2_5 + c_2_44 − 2·c_2_3·c_2_4·c_2_52
− 2·c_2_3·c_2_42·c_2_5 − c_2_3·c_2_43 − 2·c_2_32·c_2_52 − 2·c_2_32·c_2_4·c_2_5
+ 2·c_2_33·c_2_4 + c_2_34 -
a_11_3 →c_2_42·c_2_53·a_1_1 − c_2_42·c_2_53·a_1_0 + c_2_43·c_2_52·a_1_2
+ c_2_43·c_2_52·a_1_1 − 2·c_2_44·c_2_5·a_1_2 − 2·c_2_44·c_2_5·a_1_0 + c_2_45·a_1_2
− 2·c_2_45·a_1_1 − 2·c_2_45·a_1_0 − 2·c_2_3·c_2_4·c_2_53·a_1_1
− 2·c_2_3·c_2_4·c_2_53·a_1_0 + 2·c_2_3·c_2_42·c_2_52·a_1_2
− c_2_3·c_2_42·c_2_52·a_1_0 + 2·c_2_3·c_2_43·c_2_5·a_1_1
+ 2·c_2_3·c_2_43·c_2_5·a_1_0 − 2·c_2_3·c_2_44·a_1_2 + c_2_3·c_2_44·a_1_0
− c_2_32·c_2_53·a_1_1 + 2·c_2_32·c_2_4·c_2_52·a_1_2 − c_2_32·c_2_4·c_2_52·a_1_1
+ 2·c_2_32·c_2_4·c_2_52·a_1_0 − c_2_32·c_2_42·c_2_5·a_1_2
− 2·c_2_32·c_2_42·c_2_5·a_1_1 − 2·c_2_32·c_2_42·c_2_5·a_1_0
+ c_2_32·c_2_43·a_1_2 + 2·c_2_32·c_2_43·a_1_1 + c_2_32·c_2_43·a_1_0
− c_2_33·c_2_52·a_1_1 − 2·c_2_33·c_2_52·a_1_0 − 2·c_2_33·c_2_4·c_2_5·a_1_2
+ 2·c_2_33·c_2_4·c_2_5·a_1_1 + 2·c_2_33·c_2_4·c_2_5·a_1_0 + c_2_33·c_2_42·a_1_2
+ c_2_33·c_2_42·a_1_1 − c_2_33·c_2_42·a_1_0 − c_2_34·c_2_5·a_1_2
− 2·c_2_34·c_2_5·a_1_1 − 2·c_2_34·c_2_4·a_1_2 + 2·c_2_34·c_2_4·a_1_1 + c_2_35·a_1_1
+ 2·c_2_35·a_1_0 -
c_12_2 →c_2_43·c_2_53 + 2·c_2_44·c_2_52 − 2·c_2_45·c_2_5 − c_2_46
+ 2·c_2_3·c_2_42·c_2_53 − c_2_3·c_2_44·c_2_5 − c_2_3·c_2_45
+ 2·c_2_32·c_2_4·c_2_53 + c_2_32·c_2_42·c_2_52 − 2·c_2_32·c_2_43·c_2_5
− c_2_32·c_2_44 + 2·c_2_33·c_2_4·c_2_52 − 2·c_2_33·c_2_42·c_2_5
+ c_2_33·c_2_43 + c_2_34·c_2_52 − c_2_34·c_2_4·c_2_5 − 2·c_2_34·c_2_42
− 2·c_2_35·c_2_4 + c_2_36
Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 3
-
a_3_0 →c_2_5·a_1_2 + c_2_5·a_1_1 + c_2_4·a_1_2 − 2·c_2_4·a_1_1 − 2·c_2_4·a_1_0 − 2·c_2_3·a_1_1
+ c_2_3·a_1_0 , an element of degree 3 -
c_4_0 →c_2_52 + 2·c_2_4·c_2_5 − 2·c_2_42 + c_2_3·c_2_4 + c_2_32 , an element of degree 4 -
a_7_1 →c_2_4·c_2_52·a_1_1 − c_2_4·c_2_52·a_1_0 + c_2_42·c_2_5·a_1_2
+ 2·c_2_42·c_2_5·a_1_1 − c_2_42·c_2_5·a_1_0 − c_2_43·a_1_2 + 2·c_2_43·a_1_1
+ 2·c_2_43·a_1_0 − c_2_3·c_2_52·a_1_1 − 2·c_2_3·c_2_52·a_1_0
− 2·c_2_3·c_2_4·c_2_5·a_1_2 − 2·c_2_3·c_2_4·c_2_5·a_1_1 − 2·c_2_3·c_2_4·c_2_5·a_1_0
− c_2_3·c_2_42·a_1_2 + c_2_3·c_2_42·a_1_1 − 2·c_2_32·c_2_5·a_1_2
− c_2_32·c_2_5·a_1_1 − c_2_32·c_2_4·a_1_2 − 2·c_2_32·c_2_4·a_1_0 + c_2_33·a_1_1
+ 2·c_2_33·a_1_0 , an element of degree 7 -
c_8_1 →c_2_42·c_2_52 − 2·c_2_43·c_2_5 + c_2_44 − 2·c_2_3·c_2_4·c_2_52
− 2·c_2_3·c_2_42·c_2_5 − c_2_3·c_2_43 − 2·c_2_32·c_2_52 − 2·c_2_32·c_2_4·c_2_5
+ 2·c_2_33·c_2_4 + c_2_34 , an element of degree 8 -
a_11_3 →c_2_42·c_2_53·a_1_1 − c_2_42·c_2_53·a_1_0 + c_2_43·c_2_52·a_1_2
+ c_2_43·c_2_52·a_1_1 − 2·c_2_44·c_2_5·a_1_2 − 2·c_2_44·c_2_5·a_1_0 + c_2_45·a_1_2
− 2·c_2_45·a_1_1 − 2·c_2_45·a_1_0 − 2·c_2_3·c_2_4·c_2_53·a_1_1
− 2·c_2_3·c_2_4·c_2_53·a_1_0 + 2·c_2_3·c_2_42·c_2_52·a_1_2
− c_2_3·c_2_42·c_2_52·a_1_0 + 2·c_2_3·c_2_43·c_2_5·a_1_1
+ 2·c_2_3·c_2_43·c_2_5·a_1_0 − 2·c_2_3·c_2_44·a_1_2 + c_2_3·c_2_44·a_1_0
− c_2_32·c_2_53·a_1_1 + 2·c_2_32·c_2_4·c_2_52·a_1_2 − c_2_32·c_2_4·c_2_52·a_1_1
+ 2·c_2_32·c_2_4·c_2_52·a_1_0 − c_2_32·c_2_42·c_2_5·a_1_2
− 2·c_2_32·c_2_42·c_2_5·a_1_1 − 2·c_2_32·c_2_42·c_2_5·a_1_0
+ c_2_32·c_2_43·a_1_2 + 2·c_2_32·c_2_43·a_1_1 + c_2_32·c_2_43·a_1_0
− c_2_33·c_2_52·a_1_1 − 2·c_2_33·c_2_52·a_1_0 − 2·c_2_33·c_2_4·c_2_5·a_1_2
+ 2·c_2_33·c_2_4·c_2_5·a_1_1 + 2·c_2_33·c_2_4·c_2_5·a_1_0 + c_2_33·c_2_42·a_1_2
+ c_2_33·c_2_42·a_1_1 − c_2_33·c_2_42·a_1_0 − c_2_34·c_2_5·a_1_2
− 2·c_2_34·c_2_5·a_1_1 − 2·c_2_34·c_2_4·a_1_2 + 2·c_2_34·c_2_4·a_1_1 + c_2_35·a_1_1
+ 2·c_2_35·a_1_0 , an element of degree 11 -
c_12_2 →c_2_43·c_2_53 + 2·c_2_44·c_2_52 − 2·c_2_45·c_2_5 − c_2_46
+ 2·c_2_3·c_2_42·c_2_53 − c_2_3·c_2_44·c_2_5 − c_2_3·c_2_45
+ 2·c_2_32·c_2_4·c_2_53 + c_2_32·c_2_42·c_2_52 − 2·c_2_32·c_2_43·c_2_5
− c_2_32·c_2_44 + 2·c_2_33·c_2_4·c_2_52 − 2·c_2_33·c_2_42·c_2_5
+ c_2_33·c_2_43 + c_2_34·c_2_52 − c_2_34·c_2_4·c_2_5 − 2·c_2_34·c_2_42
− 2·c_2_35·c_2_4 + c_2_36 , an element of degree 12
| About the group | Ring generators | Ring relations | Completion information | Restriction maps |
|
Simon King Department of Mathematics and Computer Science Friedrich-Schiller-Universität Jena 07737 Jena GERMANY
|