Sharedwww / tables / dimskg1new.gpOpen in CoCalc
Author: William A. Stein
1\\ dimskg1new.gp
2\\ This is a table of dimensions of the spaces
3\\             S_k^{new}(Gamma_1(N))
4\\ of weight k cuspidal newforms for Gamma_1(N).
5\\ William Stein ([email protected]y.edu), September, 1998.
6
7{\\ d[N,k]=dim(S_k^{new}(Gamma_1(N))), k>=2
8d=matrix(100,100,m,n,0);
9
10d[1,]=[-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,2,0,1,0,2,0,2,0,2,0,2,0,3,0,2,0,3,0,3,0,3,0,3,0,4,0,3,0,4,0,4,0,4,0,4,0,5,0,4,0,5,0,5,0,5,0,5,0,6,0,5,0,6,0,6,0,6,0,6,0,7,0,6,0,7,0,7,0,7,0,7,0,8,0,7,0,8];
11d[2,]=[-1,0,0,0,0,0,0,1,0,1,0,0,0,2,0,1,0,1,0,2,0,2,0,1,0,3,0,2,0,2,0,3,0,3,0,2,0,4,0,3,0,3,0,4,0,4,0,3,0,5,0,4,0,4,0,5,0,5,0,4,0,6,0,5,0,5,0,6,0,6,0,5,0,7,0,6,0,6,0,7,0,7,0,6,0,8,0,7,0,7,0,8,0,8,0,7,0,9,0,8];
12d[3,]=[-1,0,0,0,0,1,1,1,2,2,2,1,3,3,4,2,4,3,5,3,6,4,6,3,7,5,8,4,8,5,9,5,10,6,10,5,11,7,12,6,12,7,13,7,14,8,14,7,15,9,16,8,16,9,17,9,18,10,18,9,19,11,20,10,20,11,21,11,22,12,22,11,23,13,24,12,24,13,25,13,26,14,26,13,27,15,28,14,28,15,29,15,30,16,30,15,31,17,32,16];
13d[4,]=[-1,0,0,0,1,1,2,0,3,1,4,1,5,1,6,1,7,2,8,1,9,2,10,2,11,2,12,2,13,3,14,2,15,3,16,3,17,3,18,3,19,4,20,3,21,4,22,4,23,4,24,4,25,5,26,4,27,5,28,5,29,5,30,5,31,6,32,5,33,6,34,6,35,6,36,6,37,7,38,6,39,7,40,7,41,7,42,7,43,8,44,7,45,8,46,8,47,8,48,8];
14d[5,]=[-1,0,0,1,2,3,4,5,6,7,8,7,10,11,12,11,14,13,16,15,18,17,20,17,22,21,24,21,26,23,28,25,30,27,32,27,34,31,36,31,38,33,40,35,42,37,44,37,46,41,48,41,50,43,52,45,54,47,56,47,58,51,60,51,62,53,64,55,66,57,68,57,70,61,72,61,74,63,76,65,78,67,80,67,82,71,84,71,86,73,88,75,90,77,92,77,94,81,96,81];
15d[6,]=[-1,0,0,1,2,1,2,1,2,1,4,3,4,1,4,3,6,3,6,3,6,3,8,5,8,3,8,5,10,5,10,5,10,5,12,7,12,5,12,7,14,7,14,7,14,7,16,9,16,7,16,9,18,9,18,9,18,9,20,11,20,9,20,11,22,11,22,11,22,11,24,13,24,11,24,13,26,13,26,13,26,13,28,15,28,13,28,15,30,15,30,15,30,15,32,17,32,15,32,17];
16d[7,]=[-1,0,1,3,5,7,9,11,13,15,17,17,21,23,25,25,29,29,33,33,37,37,41,39,45,45,49,47,53,51,57,55,61,59,65,61,69,67,73,69,77,73,81,77,85,81,89,83,93,89,97,91,101,95,105,99,109,103,113,105,117,111,121,113,125,117,129,121,133,125,137,127,141,133,145,135,149,139,153,143,157,147,161,149,165,155,169,157,173,161,177,165,181,169,185,171,189,177,193,179];
17d[8,]=[-1,0,1,3,3,5,5,8,7,10,9,13,11,15,13,18,15,20,17,23,19,25,21,28,23,30,25,33,27,35,29,38,31,40,33,43,35,45,37,48,39,50,41,53,43,55,45,58,47,60,49,63,51,65,53,68,55,70,57,73,59,75,61,78,63,80,65,83,67,85,69,88,71,90,73,93,75,95,77,98,79,100,81,103,83,105,85,108,87,110,89,113,91,115,93,118,95,120,97,123];
18d[9,]=[-1,0,2,5,8,9,12,15,16,19,22,24,26,29,30,34,36,38,40,44,44,48,50,53,54,58,58,63,64,67,68,73,72,77,78,82,82,87,86,92,92,96,96,102,100,106,106,111,110,116,114,121,120,125,124,131,128,135,134,140,138,145,142,150,148,154,152,160,156,164,162,169,166,174,170,179,176,183,180,189,184,193,190,198,194,203,198,208,204,212,208,218,212,222,218,227,222,232,226,237];
19d[10,]=[-1,0,2,3,4,5,6,5,8,7,10,11,12,9,14,13,16,15,18,15,20,17,22,21,24,19,26,23,28,25,30,25,32,27,34,31,36,29,38,33,40,35,42,35,44,37,46,41,48,39,50,43,52,45,54,45,56,47,58,51,60,49,62,53,64,55,66,55,68,57,70,61,72,59,74,63,76,65,78,65,80,67,82,71,84,69,86,73,88,75,90,75,92,77,94,81,96,79,98,83];
20d[11,]=[-1,1,5,10,15,20,25,30,35,40,45,48,55,60,65,68,75,78,85,88,95,98,105,106,115,118,125,126,135,136,145,146,155,156,165,164,175,176,185,184,195,194,205,204,215,214,225,222,235,234,245,242,255,252,265,262,275,272,285,280,295,292,305,300,315,310,325,320,335,330,345,338,355,350,365,358,375,368,385,378,395,388,405,396,415,408,425,416,435,426,445,436,455,446,465,454,475,466,485,474];
21d[12,]=[-1,0,3,5,5,8,8,14,11,17,13,22,16,26,19,31,21,34,24,40,27,43,29,48,32,52,35,57,37,60,40,66,43,69,45,74,48,78,51,83,53,86,56,92,59,95,61,100,64,104,67,109,69,112,72,118,75,121,77,126,80,130,83,135,85,138,88,144,91,147,93,152,96,156,99,161,101,164,104,170,107,173,109,178,112,182,115,187,117,190,120,196,123,199,125,204,128,208,131,213];
22d[13,]=[-1,2,8,15,22,29,36,43,50,57,64,69,78,85,92,97,106,111,120,125,134,139,148,151,162,167,176,179,190,193,204,207,218,221,232,233,246,249,260,261,274,275,288,289,302,303,316,315,330,331,344,343,358,357,372,371,386,385,400,397,414,413,428,425,442,439,456,453,470,467,484,479,498,495,512,507,526,521,540,535,554,549,568,561,582,577,596,589,610,603,624,617,638,631,652,643,666,659,680,671];
23d[14,]=[-1,1,4,6,8,10,12,12,16,16,20,22,24,22,28,28,32,32,36,34,40,38,44,44,48,44,52,50,56,54,60,56,64,60,68,66,72,66,76,72,80,76,84,78,88,82,92,88,96,88,100,94,104,98,108,100,112,104,116,110,120,110,124,116,128,120,132,122,136,126,140,132,144,132,148,138,152,142,156,144,160,148,164,154,168,154,172,160,176,164,180,166,184,170,188,176,192,176,196,182];
24d[15,]=[-1,1,8,14,20,24,30,36,40,46,52,60,62,68,72,82,84,92,94,104,104,114,116,128,126,136,136,150,148,160,158,172,168,182,180,196,190,204,200,218,212,228,222,240,232,250,244,264,254,272,264,286,276,296,286,308,296,318,308,332,318,340,328,354,340,364,350,376,360,386,372,400,382,408,392,422,404,432,414,444,424,454,436,468,446,476,456,490,468,500,478,512,488,522,500,536,510,544,520,558];
25d[16,]=[-1,2,7,11,16,20,25,29,34,38,43,47,52,56,61,65,70,74,79,83,88,92,97,101,106,110,115,119,124,128,133,137,142,146,151,155,160,164,169,173,178,182,187,191,196,200,205,209,214,218,223,227,232,236,241,245,250,254,259,263,268,272,277,281,286,290,295,299,304,308,313,317,322,326,331,335,340,344,349,353,358,362,367,371,376,380,385,389,394,398,403,407,412,416,421,425,430,434,439,443];
26d[17,]=[-1,5,16,28,40,52,64,76,88,100,112,122,136,148,160,170,184,194,208,218,232,242,256,264,280,290,304,312,328,336,352,360,376,384,400,406,424,432,448,454,472,478,496,502,520,526,544,548,568,574,592,596,616,620,640,644,664,668,688,690,712,716,736,738,760,762,784,786,808,810,832,832,856,858,880,880,904,904,928,928,952,952,976,974,1000,1000,1024,1022,1048,1046,1072,1070,1096,1094,1120,1116,1144,1142,1168,1164];
27d[18,]=[-1,2,6,7,8,13,14,16,20,22,22,27,28,31,34,36,36,42,42,45,48,51,50,56,56,60,62,65,64,71,70,74,76,80,78,85,84,89,90,94,92,100,98,103,104,109,106,114,112,118,118,123,120,129,126,132,132,138,134,143,140,147,146,152,148,158,154,161,160,167,162,172,168,176,174,181,176,187,182,190,188,196,190,201,196,205,202,210,204,216,210,219,216,225,218,230,224,234,230,239];
28d[19,]=[-1,7,21,36,51,66,81,96,111,126,141,154,171,186,201,214,231,244,261,274,291,304,321,332,351,364,381,392,411,422,441,452,471,482,501,510,531,542,561,570,591,600,621,630,651,660,681,688,711,720,741,748,771,778,801,808,831,838,861,866,891,898,921,926,951,956,981,986,1011,1016,1041,1044,1071,1076,1101,1104,1131,1134,1161,1164,1191,1194,1221,1222,1251,1254,1281,1282,1311,1312,1341,1342,1371,1372,1401,1400,1431,1432,1461,1460];
29d[20,]=[-1,3,10,17,22,29,34,45,46,57,58,71,70,85,82,99,94,111,106,127,118,139,130,153,142,167,154,181,166,193,178,209,190,221,202,235,214,249,226,263,238,275,250,291,262,303,274,317,286,331,298,345,310,357,322,373,334,385,346,399,358,413,370,427,382,439,394,455,406,467,418,481,430,495,442,509,454,521,466,537,478,549,490,563,502,577,514,591,526,603,538,619,550,631,562,645,574,659,586,673];
30d[21,]=[-1,5,18,30,42,52,64,76,86,98,110,124,132,144,154,170,178,192,200,216,222,238,246,264,268,284,290,310,314,332,336,356,358,378,382,404,404,424,426,450,450,472,472,496,494,518,518,544,540,564,562,590,586,612,608,636,630,658,654,684,676,704,698,730,722,752,744,776,766,798,790,824,812,844,834,870,858,892,880,916,902,938,926,964,948,984,970,1010,994,1032,1016,1056,1038,1078,1062,1104,1084,1124,1106,1150];
31d[22,]=[-1,4,10,15,20,25,30,33,40,43,50,55,60,61,70,73,80,83,90,91,100,101,110,113,120,119,130,131,140,141,150,149,160,159,170,171,180,177,190,189,200,199,210,207,220,217,230,229,240,235,250,247,260,257,270,265,280,275,290,287,300,293,310,305,320,315,330,323,340,333,350,345,360,351,370,363,380,373,390,381,400,391,410,403,420,409,430,421,440,431,450,439,460,449,470,461,480,467,490,479];
32d[23,]=[-1,12,33,55,77,99,121,143,165,187,209,229,253,275,297,317,341,361,385,405,429,449,473,491,517,537,561,579,605,623,649,667,693,711,737,753,781,799,825,841,869,885,913,929,957,973,1001,1015,1045,1061,1089,1103,1133,1147,1177,1191,1221,1235,1265,1277,1309,1323,1353,1365,1397,1409,1441,1453,1485,1497,1529,1539,1573,1585,1617,1627,1661,1671,1705,1715,1749,1759,1793,1801,1837,1847,1881,1889,1925,1933,1969,1977,2013,2021,2057,2063,2101,2109,2145,2151];
33d[24,]=[-1,5,12,17,26,31,40,43,54,57,68,69,82,83,96,95,110,109,124,121,138,135,152,147,166,161,180,173,194,187,208,199,222,213,236,225,250,239,264,251,278,265,292,277,306,291,320,303,334,317,348,329,362,343,376,355,390,369,404,381,418,395,432,407,446,421,460,433,474,447,488,459,502,473,516,485,530,499,544,511,558,525,572,537,586,551,600,563,614,577,628,589,642,603,656,615,670,629,684,641];
34d[25,]=[-1,12,36,59,82,105,128,151,174,197,220,244,266,289,312,336,358,382,404,428,450,474,496,521,542,566,588,613,634,659,680,705,726,751,772,798,818,843,864,890,910,936,956,982,1002,1028,1048,1075,1094,1120,1140,1167,1186,1213,1232,1259,1278,1305,1324,1352,1370,1397,1416,1444,1462,1490,1508,1536,1554,1582,1600,1629,1646,1674,1692,1721,1738,1767,1784,1813,1830,1859,1876,1906,1922,1951,1968,1998,2014,2044,2060,2090,2106,2136,2152,2183,2198,2228,2244,2275];
35d[26,]=[-1,6,14,21,28,35,42,47,56,61,70,77,84,87,98,103,112,117,126,129,140,143,154,159,168,169,182,185,196,199,210,211,224,225,238,241,252,251,266,267,280,281,294,293,308,307,322,323,336,333,350,349,364,363,378,375,392,389,406,405,420,415,434,431,448,445,462,457,476,471,490,487,504,497,518,513,532,527,546,539,560,553,574,569,588,579,602,595,616,609,630,621,644,635,658,651,672,661,686,677];
36d[27,]=[-1,13,35,56,77,99,120,141,163,184,205,227,248,269,291,312,333,355,376,397,419,440,461,483,504,525,547,568,589,611,632,653,675,696,717,739,760,781,803,824,845,867,888,909,931,952,973,995,1016,1037,1059,1080,1101,1123,1144,1165,1187,1208,1229,1251,1272,1293,1315,1336,1357,1379,1400,1421,1443,1464,1485,1507,1528,1549,1571,1592,1613,1635,1656,1677,1699,1720,1741,1763,1784,1805,1827,1848,1869,1891,1912,1933,1955,1976,1997,2019,2040,2061,2083,2104];
37d[28,]=[-1,8,22,36,48,62,74,92,100,118,126,146,152,174,178,202,204,228,230,258,256,284,282,312,308,340,334,368,360,394,386,424,412,450,438,478,464,506,490,534,516,560,542,590,568,616,594,644,620,672,646,700,672,726,698,756,724,782,750,810,776,838,802,866,828,892,854,922,880,948,906,976,932,1004,958,1032,984,1058,1010,1088,1036,1114,1062,1142,1088,1170,1114,1198,1140,1224,1166,1254,1192,1280,1218,1308,1244,1336,1270,1364];
38d[29,]=[-1,22,56,91,126,161,196,231,266,301,336,369,406,441,476,509,546,579,616,649,686,719,756,787,826,859,896,927,966,997,1036,1067,1106,1137,1176,1205,1246,1277,1316,1345,1386,1415,1456,1485,1526,1555,1596,1623,1666,1695,1736,1763,1806,1833,1876,1903,1946,1973,2016,2041,2086,2113,2156,2181,2226,2251,2296,2321,2366,2391,2436,2459,2506,2531,2576,2599,2646,2669,2716,2739,2786,2809,2856,2877,2926,2949,2996,3017,3066,3087,3136,3157,3206,3227,3276,3295,3346,3367,3416,3435];
39d[30,]=[-1,7,12,16,20,28,32,40,44,52,52,60,64,76,76,84,84,96,96,108,108,120,116,128,128,144,140,152,148,164,160,176,172,188,180,196,192,212,204,220,212,232,224,244,236,256,244,264,256,280,268,288,276,300,288,312,300,324,308,332,320,348,332,356,340,368,352,380,364,392,372,400,384,416,396,424,404,436,416,448,428,460,436,468,448,484,460,492,468,504,480,516,492,528,500,536,512,552,524,560];
40d[31,]=[-1,26,65,105,145,185,225,265,305,345,385,423,465,505,545,583,625,663,705,743,785,823,865,901,945,983,1025,1061,1105,1141,1185,1221,1265,1301,1345,1379,1425,1461,1505,1539,1585,1619,1665,1699,1745,1779,1825,1857,1905,1939,1985,2017,2065,2097,2145,2177,2225,2257,2305,2335,2385,2417,2465,2495,2545,2575,2625,2655,2705,2735,2785,2813,2865,2895,2945,2973,3025,3053,3105,3133,3185,3213,3265,3291,3345,3373,3425,3451,3505,3531,3585,3611,3665,3691,3745,3769,3825,3851,3905,3929];
41d[32,]=[-1,13,31,49,67,85,103,121,139,157,175,193,211,229,247,265,283,301,319,337,355,373,391,409,427,445,463,481,499,517,535,553,571,589,607,625,643,661,679,697,715,733,751,769,787,805,823,841,859,877,895,913,931,949,967,985,1003,1021,1039,1057,1075,1093,1111,1129,1147,1165,1183,1201,1219,1237,1255,1273,1291,1309,1327,1345,1363,1381,1399,1417,1435,1453,1471,1489,1507,1525,1543,1561,1579,1597,1615,1633,1651,1669,1687,1705,1723,1741,1759,1777];
42d[33,]=[-1,19,50,80,110,138,168,198,226,256,286,318,344,374,402,436,462,494,520,554,578,612,638,674,696,730,754,792,814,850,872,910,930,968,990,1030,1048,1086,1106,1148,1166,1206,1224,1266,1282,1324,1342,1386,1400,1442,1458,1504,1518,1562,1576,1622,1634,1680,1694,1742,1752,1798,1810,1860,1870,1918,1928,1978,1986,2036,2046,2098,2104,2154,2162,2216,2222,2274,2280,2334,2338,2392,2398,2454,2456,2510,2514,2572,2574,2630,2632,2690,2690,2748,2750,2810,2808,2866,2866,2928];
43d[34,]=[-1,11,24,36,48,60,72,82,96,106,120,132,144,152,168,178,192,202,216,224,240,248,264,274,288,294,312,320,336,344,360,366,384,390,408,416,432,436,456,462,480,486,504,508,528,532,552,558,576,578,600,604,624,628,648,650,672,674,696,700,720,720,744,746,768,770,792,792,816,816,840,842,864,862,888,888,912,912,936,934,960,958,984,984,1008,1004,1032,1030,1056,1054,1080,1076,1104,1100,1128,1126,1152,1146,1176,1172];
44d[35,]=[-1,25,70,112,154,196,238,280,322,364,406,452,490,532,574,620,658,704,742,788,826,872,910,960,994,1040,1078,1128,1162,1212,1246,1296,1330,1380,1414,1468,1498,1548,1582,1636,1666,1720,1750,1804,1834,1888,1918,1976,2002,2056,2086,2144,2170,2228,2254,2312,2338,2396,2422,2484,2506,2564,2590,2652,2674,2736,2758,2820,2842,2904,2926,2992,3010,3072,3094,3160,3178,3244,3262,3328,3346,3412,3430,3500,3514,3580,3598,3668,3682,3752,3766,3836,3850,3920,3934,4008,4018,4088,4102,4176];
45d[36,]=[-1,13,28,45,63,78,96,111,129,144,164,176,197,210,230,242,265,275,298,308,331,341,366,373,399,407,432,439,467,472,500,505,533,538,568,570,601,604,634,636,669,669,702,702,735,735,770,767,803,801,836,833,871,866,904,899,937,932,972,964,1005,998,1038,1030,1073,1063,1106,1096,1139,1129,1174,1161,1207,1195,1240,1227,1275,1260,1308,1293,1341,1326,1376,1358,1409,1392,1442,1424,1477,1457,1510,1490,1543,1523,1578,1555,1611,1589,1644,1621];
46d[37,]=[-1,40,96,153,210,267,324,381,438,495,552,607,666,723,780,835,894,949,1008,1063,1122,1177,1236,1289,1350,1405,1464,1517,1578,1631,1692,1745,1806,1859,1920,1971,2034,2087,2148,2199,2262,2313,2376,2427,2490,2541,2604,2653,2718,2769,2832,2881,2946,2995,3060,3109,3174,3223,3288,3335,3402,3451,3516,3563,3630,3677,3744,3791,3858,3905,3972,4017,4086,4133,4200,4245,4314,4359,4428,4473,4542,4587,4656,4699,4770,4815,4884,4927,4998,5041,5112,5155,5226,5269,5340,5381,5454,5497,5568,5609];
47d[38,]=[-1,14,30,45,60,75,90,103,120,133,150,165,180,191,210,223,240,253,270,281,300,311,330,343,360,369,390,401,420,431,450,459,480,489,510,521,540,547,570,579,600,609,630,637,660,667,690,699,720,725,750,757,780,787,810,815,840,845,870,877,900,903,930,935,960,965,990,993,1020,1023,1050,1055,1080,1081,1110,1113,1140,1143,1170,1171,1200,1201,1230,1233,1260,1259,1290,1291,1320,1321,1350,1349,1380,1379,1410,1411,1440,1437,1470,1469];
48d[39,]=[-1,29,72,114,156,196,238,280,320,362,404,448,486,528,568,614,652,696,734,780,816,862,900,948,982,1028,1064,1114,1148,1196,1230,1280,1312,1362,1396,1448,1478,1528,1560,1614,1644,1696,1726,1780,1808,1862,1892,1948,1974,2028,2056,2114,2140,2196,2222,2280,2304,2362,2388,2448,2470,2528,2552,2614,2636,2696,2718,2780,2800,2862,2884,2948,2966,3028,3048,3114,3132,3196,3214,3280,3296,3362,3380,3448,3462,3528,3544,3614,3628,3696,3710,3780,3792,3862,3876,3948,3958,4028,4040,4114];
49d[40,]=[-1,19,44,67,94,117,144,165,194,215,244,263,294,313,344,361,394,411,444,459,494,509,544,557,594,607,644,655,694,705,744,753,794,803,844,851,894,901,944,949,994,999,1044,1047,1094,1097,1144,1145,1194,1195,1244,1243,1294,1293,1344,1341,1394,1391,1444,1439,1494,1489,1544,1537,1594,1587,1644,1635,1694,1685,1744,1733,1794,1783,1844,1831,1894,1881,1944,1929,1994,1979,2044,2027,2094,2077,2144,2125,2194,2175,2244,2223,2294,2273,2344,2321,2394,2371,2444,2419];
50d[41,]=[-1,51,120,190,260,330,400,470,540,610,680,748,820,890,960,1028,1100,1168,1240,1308,1380,1448,1520,1586,1660,1728,1800,1866,1940,2006,2080,2146,2220,2286,2360,2424,2500,2566,2640,2704,2780,2844,2920,2984,3060,3124,3200,3262,3340,3404,3480,3542,3620,3682,3760,3822,3900,3962,4040,4100,4180,4242,4320,4380,4460,4520,4600,4660,4740,4800,4880,4938,5020,5080,5160,5218,5300,5358,5440,5498,5580,5638,5720,5776,5860,5918,6000,6056,6140,6196,6280,6336,6420,6476,6560,6614,6700,6756,6840,6894];
51d[42,]=[-1,13,24,34,44,58,68,82,92,106,112,126,136,154,160,174,180,198,204,222,228,246,248,266,272,294,296,314,316,338,340,362,364,386,384,406,408,434,432,454,452,478,476,502,500,526,520,546,544,574,568,594,588,618,612,642,636,666,656,686,680,714,704,734,724,758,748,782,772,806,792,826,816,854,840,874,860,898,884,922,908,946,928,966,952,994,976,1014,996,1038,1020,1062,1044,1086,1064,1106,1088,1134,1112,1154];
52d[43,]=[-1,57,133,210,287,364,441,518,595,672,749,824,903,980,1057,1132,1211,1286,1365,1440,1519,1594,1673,1746,1827,1902,1981,2054,2135,2208,2289,2362,2443,2516,2597,2668,2751,2824,2905,2976,3059,3130,3213,3284,3367,3438,3521,3590,3675,3746,3829,3898,3983,4052,4137,4206,4291,4360,4445,4512,4599,4668,4753,4820,4907,4974,5061,5128,5215,5282,5369,5434,5523,5590,5677,5742,5831,5896,5985,6050,6139,6204,6293,6356,6447,6512,6601,6664,6755,6818,6909,6972,7063,7126,7217,7278,7371,7434,7525,7586];
53d[44,]=[-1,25,60,95,128,163,196,235,264,303,332,373,400,443,468,513,536,581,604,653,672,721,740,791,808,861,876,931,944,999,1012,1071,1080,1139,1148,1209,1216,1279,1284,1349,1352,1417,1420,1489,1488,1557,1556,1627,1624,1697,1692,1767,1760,1835,1828,1907,1896,1975,1964,2045,2032,2115,2100,2185,2168,2253,2236,2325,2304,2393,2372,2463,2440,2533,2508,2603,2576,2671,2644,2743,2712,2811,2780,2881,2848,2951,2916,3021,2984,3089,3052,3161,3120,3229,3188,3299,3256,3369,3324,3439];
54d[45,]=[-1,39,92,143,194,249,300,351,406,457,508,561,614,665,720,769,822,875,928,977,1034,1083,1136,1187,1242,1291,1348,1395,1450,1501,1556,1603,1662,1709,1764,1813,1870,1917,1976,2021,2078,2127,2184,2229,2290,2335,2392,2439,2498,2543,2604,2647,2706,2753,2812,2855,2918,2961,3020,3065,3126,3169,3232,3273,3334,3379,3440,3481,3546,3587,3648,3691,3754,3795,3860,3899,3962,4005,4068,4107,4174,4213,4276,4317,4382,4421,4488,4525,4590,4631,4696,4733,4802,4839,4904,4943,5010,5047,5116,5151];
55d[46,]=[-1,21,44,66,88,110,132,152,176,196,220,242,264,282,308,328,352,372,396,414,440,458,484,504,528,544,572,590,616,634,660,676,704,720,748,766,792,806,836,852,880,896,924,938,968,982,1012,1028,1056,1068,1100,1114,1144,1158,1188,1200,1232,1244,1276,1290,1320,1330,1364,1376,1408,1420,1452,1462,1496,1506,1540,1552,1584,1592,1628,1638,1672,1682,1716,1724,1760,1768,1804,1814,1848,1854,1892,1900,1936,1944,1980,1986,2024,2030,2068,2076,2112,2116,2156,2162];
56d[47,]=[-1,70,161,253,345,437,529,621,713,805,897,987,1081,1173,1265,1355,1449,1539,1633,1723,1817,1907,2001,2089,2185,2275,2369,2457,2553,2641,2737,2825,2921,3009,3105,3191,3289,3377,3473,3559,3657,3743,3841,3927,4025,4111,4209,4293,4393,4479,4577,4661,4761,4845,4945,5029,5129,5213,5313,5395,5497,5581,5681,5763,5865,5947,6049,6131,6233,6315,6417,6497,6601,6683,6785,6865,6969,7049,7153,7233,7337,7417,7521,7599,7705,7785,7889,7967,8073,8151,8257,8335,8441,8519,8625,8701,8809,8887,8993,9069];
57d[48,]=[-1,23,49,77,103,131,157,185,211,239,265,293,319,347,373,401,427,455,481,509,535,563,589,617,643,671,697,725,751,779,805,833,859,887,913,941,967,995,1021,1049,1075,1103,1129,1157,1183,1211,1237,1265,1291,1319,1345,1373,1399,1427,1453,1481,1507,1535,1561,1589,1615,1643,1669,1697,1723,1751,1777,1805,1831,1859,1885,1913,1939,1967,1993,2021,2047,2075,2101,2129,2155,2183,2209,2237,2263,2291,2317,2345,2371,2399,2425,2453,2479,2507,2533,2561,2587,2615,2641,2669];
58d[49,]=[-1,69,164,258,352,446,540,634,728,822,916,1011,1104,1198,1292,1387,1480,1575,1668,1763,1856,1951,2044,2140,2232,2327,2420,2516,2608,2704,2796,2892,2984,3080,3172,3269,3360,3456,3548,3645,3736,3833,3924,4021,4112,4209,4300,4398,4488,4585,4676,4774,4864,4962,5052,5150,5240,5338,5428,5527,5616,5714,5804,5903,5992,6091,6180,6279,6368,6467,6556,6656,6744,6843,6932,7032,7120,7220,7308,7408,7496,7596,7684,7785,7872,7972,8060,8161,8248,8349,8436,8537,8624,8725,8812,8914,9000,9101,9188,9290];
59d[50,]=[-1,24,46,69,92,115,138,162,184,208,230,253,276,301,322,346,368,392,414,439,460,485,506,530,552,578,598,623,644,669,690,716,736,762,782,807,828,855,874,900,920,946,966,993,1012,1039,1058,1084,1104,1132,1150,1177,1196,1223,1242,1270,1288,1316,1334,1361,1380,1409,1426,1454,1472,1500,1518,1547,1564,1593,1610,1638,1656,1686,1702,1731,1748,1777,1794,1824,1840,1870,1886,1915,1932,1963,1978,2008,2024,2054,2070,2101,2116,2147,2162,2192,2208,2240,2254,2285];
60d[51,]=[-1,55,128,200,272,342,414,486,556,628,700,774,842,914,984,1060,1128,1202,1270,1346,1412,1488,1556,1634,1698,1774,1840,1920,1984,2062,2126,2206,2268,2348,2412,2494,2554,2634,2696,2780,2840,2922,2982,3066,3124,3208,3268,3354,3410,3494,3552,3640,3696,3782,3838,3926,3980,4068,4124,4214,4266,4354,4408,4500,4552,4642,4694,4786,4836,4928,4980,5074,5122,5214,5264,5360,5408,5502,5550,5646,5692,5788,5836,5934,5978,6074,6120,6220,6264,6362,6406,6506,6548,6648,6692,6794,6834,6934,6976,7080];
61d[52,]=[-1,37,86,135,182,231,278,331,374,427,470,525,566,623,662,721,758,817,854,917,950,1013,1046,1111,1142,1209,1238,1307,1334,1403,1430,1503,1526,1599,1622,1697,1718,1795,1814,1893,1910,1989,2006,2089,2102,2185,2198,2283,2294,2381,2390,2479,2486,2575,2582,2675,2678,2771,2774,2869,2870,2967,2966,3065,3062,3161,3158,3261,3254,3357,3350,3455,3446,3553,3542,3651,3638,3747,3734,3847,3830,3943,3926,4041,4022,4139,4118,4237,4214,4333,4310,4433,4406,4529,4502,4627,4598,4725,4694,4823];
62d[53,]=[-1,92,208,325,442,559,676,793,910,1027,1144,1259,1378,1495,1612,1727,1846,1961,2080,2195,2314,2429,2548,2661,2782,2897,3016,3129,3250,3363,3484,3597,3718,3831,3952,4063,4186,4299,4420,4531,4654,4765,4888,4999,5122,5233,5356,5465,5590,5701,5824,5933,6058,6167,6292,6401,6526,6635,6760,6867,6994,7103,7228,7335,7462,7569,7696,7803,7930,8037,8164,8269,8398,8505,8632,8737,8866,8971,9100,9205,9334,9439,9568,9671,9802,9907,10036,10139,10270,10373,10504,10607,10738,10841,10972,11073,11206,11309,11440,11541];
63d[54,]=[-1,22,42,64,86,106,128,150,170,192,214,234,256,278,298,320,342,362,384,406,426,448,470,490,512,534,554,576,598,618,640,662,682,704,726,746,768,790,810,832,854,874,896,918,938,960,982,1002,1024,1046,1066,1088,1110,1130,1152,1174,1194,1216,1238,1258,1280,1302,1322,1344,1366,1386,1408,1430,1450,1472,1494,1514,1536,1558,1578,1600,1622,1642,1664,1686,1706,1728,1750,1770,1792,1814,1834,1856,1878,1898,1920,1942,1962,1984,2006,2026,2048,2070,2090,2112];
64d[55,]=[-1,79,190,298,406,514,622,730,838,946,1054,1166,1270,1378,1486,1598,1702,1814,1918,2030,2134,2246,2350,2466,2566,2678,2782,2898,2998,3114,3214,3330,3430,3546,3646,3766,3862,3978,4078,4198,4294,4414,4510,4630,4726,4846,4942,5066,5158,5278,5374,5498,5590,5714,5806,5930,6022,6146,6238,6366,6454,6578,6670,6798,6886,7014,7102,7230,7318,7446,7534,7666,7750,7878,7966,8098,8182,8314,8398,8530,8614,8746,8830,8966,9046,9178,9262,9398,9478,9614,9694,9830,9910,10046,10126,10266,10342,10478,10558,10698];
65d[56,]=[-1,42,94,144,198,248,302,350,406,454,510,556,614,660,718,762,822,866,926,968,1030,1072,1134,1174,1238,1278,1342,1380,1446,1484,1550,1586,1654,1690,1758,1792,1862,1896,1966,1998,2070,2102,2174,2204,2278,2308,2382,2410,2486,2514,2590,2616,2694,2720,2798,2822,2902,2926,3006,3028,3110,3132,3214,3234,3318,3338,3422,3440,3526,3544,3630,3646,3734,3750,3838,3852,3942,3956,4046,4058,4150,4162,4254,4264,4358,4368,4462,4470,4566,4574,4670,4676,4774,4780,4878,4882,4982,4986,5086,5088];
66d[57,]=[-1,71,162,252,342,430,520,610,698,788,878,970,1056,1146,1234,1328,1414,1506,1592,1686,1770,1864,1950,2046,2128,2222,2306,2404,2486,2582,2664,2762,2842,2940,3022,3122,3200,3298,3378,3480,3558,3658,3736,3838,3914,4016,4094,4198,4272,4374,4450,4556,4630,4734,4808,4914,4986,5092,5166,5274,5344,5450,5522,5632,5702,5810,5880,5990,6058,6168,6238,6350,6416,6526,6594,6708,6774,6886,6952,7066,7130,7244,7310,7426,7488,7602,7666,7784,7846,7962,8024,8142,8202,8320,8382,8502,8560,8678,8738,8860];
67d[58,]=[-1,34,70,105,140,175,210,243,280,313,350,385,420,451,490,523,560,593,630,661,700,731,770,803,840,869,910,941,980,1011,1050,1079,1120,1149,1190,1221,1260,1287,1330,1359,1400,1429,1470,1497,1540,1567,1610,1639,1680,1705,1750,1777,1820,1847,1890,1915,1960,1985,2030,2057,2100,2123,2170,2195,2240,2265,2310,2333,2380,2403,2450,2475,2520,2541,2590,2613,2660,2683,2730,2751,2800,2821,2870,2893,2940,2959,3010,3031,3080,3101,3150,3169,3220,3239,3290,3311,3360,3377,3430,3449];
68d[59,]=[-1,117,261,406,551,696,841,986,1131,1276,1421,1564,1711,1856,2001,2144,2291,2434,2581,2724,2871,3014,3161,3302,3451,3594,3741,3882,4031,4172,4321,4462,4611,4752,4901,5040,5191,5332,5481,5620,5771,5910,6061,6200,6351,6490,6641,6778,6931,7070,7221,7358,7511,7648,7801,7938,8091,8228,8381,8516,8671,8808,8961,9096,9251,9386,9541,9676,9831,9966,10121,10254,10411,10546,10701,10834,10991,11124,11281,11414,11571,11704,11861,11992,12151,12284,12441,12572,12731,12862,13021,13152,13311,13442,13601,13730,13891,14022,14181,14310];
69d[60,]=[-1,34,70,108,150,186,228,258,306,336,386,410,464,486,542,560,622,638,700,710,778,788,858,862,936,938,1014,1012,1094,1090,1172,1162,1250,1240,1330,1314,1408,1390,1486,1464,1566,1542,1644,1614,1722,1692,1802,1766,1880,1842,1958,1916,2038,1994,2116,2066,2194,2144,2274,2218,2352,2294,2430,2368,2510,2446,2588,2518,2666,2596,2746,2670,2824,2746,2902,2820,2982,2898,3060,2970,3138,3048,3218,3122,3296,3198,3374,3272,3454,3350,3532,3422,3610,3500,3690,3574,3768,3650,3846,3724];
70d[61,]=[-1,126,280,435,590,745,900,1055,1210,1365,1520,1673,1830,1985,2140,2293,2450,2603,2760,2913,3070,3223,3380,3531,3690,3843,4000,4151,4310,4461,4620,4771,4930,5081,5240,5389,5550,5701,5860,6009,6170,6319,6480,6629,6790,6939,7100,7247,7410,7559,7720,7867,8030,8177,8340,8487,8650,8797,8960,9105,9270,9417,9580,9725,9890,10035,10200,10345,10510,10655,10820,10963,11130,11275,11440,11583,11750,11893,12060,12203,12370,12513,12680,12821,12990,13133,13300,13441,13610,13751,13920,14061,14230,14371,14540,14679,14850,14991,15160,15299];
71d[62,]=[-1,39,80,120,160,200,240,278,320,358,400,440,480,516,560,598,640,678,720,756,800,836,880,918,960,994,1040,1076,1120,1156,1200,1234,1280,1314,1360,1396,1440,1472,1520,1554,1600,1634,1680,1712,1760,1792,1840,1874,1920,1950,2000,2032,2080,2112,2160,2190,2240,2270,2320,2352,2400,2428,2480,2510,2560,2590,2640,2668,2720,2748,2800,2830,2880,2906,2960,2988,3040,3068,3120,3146,3200,3226,3280,3308,3360,3384,3440,3466,3520,3546,3600,3624,3680,3704,3760,3786,3840,3862,3920,3944];
72d[63,]=[-1,87,197,305,413,525,633,741,853,961,1069,1179,1289,1397,1509,1615,1725,1835,1945,2051,2165,2271,2381,2489,2601,2707,2821,2925,3037,3145,3257,3361,3477,3581,3693,3799,3913,4017,4133,4235,4349,4455,4569,4671,4789,4891,5005,5109,5225,5327,5445,5545,5661,5765,5881,5981,6101,6201,6317,6419,6537,6637,6757,6855,6973,7075,7193,7291,7413,7511,7629,7729,7849,7947,8069,8165,8285,8385,8505,8601,8725,8821,8941,9039,9161,9257,9381,9475,9597,9695,9817,9911,10037,10131,10253,10349,10473,10567,10693,10785];
73d[64,]=[-1,61,133,205,277,349,421,493,565,637,709,781,853,925,997,1069,1141,1213,1285,1357,1429,1501,1573,1645,1717,1789,1861,1933,2005,2077,2149,2221,2293,2365,2437,2509,2581,2653,2725,2797,2869,2941,3013,3085,3157,3229,3301,3373,3445,3517,3589,3661,3733,3805,3877,3949,4021,4093,4165,4237,4309,4381,4453,4525,4597,4669,4741,4813,4885,4957,5029,5101,5173,5245,5317,5389,5461,5533,5605,5677,5749,5821,5893,5965,6037,6109,6181,6253,6325,6397,6469,6541,6613,6685,6757,6829,6901,6973,7045,7117];
74d[65,]=[-1,117,272,424,576,728,880,1032,1184,1336,1488,1644,1792,1944,2096,2252,2400,2556,2704,2860,3008,3164,3312,3472,3616,3772,3920,4080,4224,4384,4528,4688,4832,4992,5136,5300,5440,5600,5744,5908,6048,6212,6352,6516,6656,6820,6960,7128,7264,7428,7568,7736,7872,8040,8176,8344,8480,8648,8784,8956,9088,9256,9392,9564,9696,9868,10000,10172,10304,10476,10608,10784,10912,11084,11216,11392,11520,11696,11824,12000,12128,12304,12432,12612,12736,12912,13040,13220,13344,13524,13648,13828,13952,14132,14256,14440,14560,14740,14864,15048];
75d[66,]=[-1,31,60,88,116,148,176,208,236,268,292,324,352,388,412,444,468,504,528,564,588,624,644,680,704,744,764,800,820,860,880,920,940,980,996,1036,1056,1100,1116,1156,1172,1216,1232,1276,1292,1336,1348,1392,1408,1456,1468,1512,1524,1572,1584,1632,1644,1692,1700,1748,1760,1812,1820,1868,1876,1928,1936,1988,1996,2048,2052,2104,2112,2168,2172,2224,2228,2284,2288,2344,2348,2404,2404,2460,2464,2524,2524,2580,2580,2640,2640,2700,2700,2760,2756,2816,2816,2880,2876,2936];
76d[67,]=[-1,155,341,528,715,902,1089,1276,1463,1650,1837,2022,2211,2398,2585,2770,2959,3144,3333,3518,3707,3892,4081,4264,4455,4640,4829,5012,5203,5386,5577,5760,5951,6134,6325,6506,6699,6882,7073,7254,7447,7628,7821,8002,8195,8376,8569,8748,8943,9124,9317,9496,9691,9870,10065,10244,10439,10618,10813,10990,11187,11366,11561,11738,11935,12112,12309,12486,12683,12860,13057,13232,13431,13608,13805,13980,14179,14354,14553,14728,14927,15102,15301,15474,15675,15850,16049,16222,16423,16596,16797,16970,17171,17344,17545,17716,17919,18092,18293,18464];
77d[68,]=[-1,68,152,236,318,402,484,572,650,738,816,906,982,1074,1148,1242,1314,1408,1480,1578,1646,1744,1812,1912,1978,2080,2144,2248,2310,2414,2476,2584,2642,2750,2808,2918,2974,3086,3140,3254,3306,3420,3472,3590,3638,3756,3804,3924,3970,4092,4136,4260,4302,4426,4468,4596,4634,4762,4800,4930,4966,5098,5132,5266,5298,5432,5464,5602,5630,5768,5796,5936,5962,6104,6128,6272,6294,6438,6460,6608,6626,6774,6792,6942,6958,7110,7124,7278,7290,7444,7456,7614,7622,7780,7788,7948,7954,8116,8120,8284];
78d[69,]=[-1,109,242,374,506,636,768,900,1030,1162,1294,1428,1556,1688,1818,1954,2082,2216,2344,2480,2606,2742,2870,3008,3132,3268,3394,3534,3658,3796,3920,4060,4182,4322,4446,4588,4708,4848,4970,5114,5234,5376,5496,5640,5758,5902,6022,6168,6284,6428,6546,6694,6810,6956,7072,7220,7334,7482,7598,7748,7860,8008,8122,8274,8386,8536,8648,8800,8910,9062,9174,9328,9436,9588,9698,9854,9962,10116,10224,10380,10486,10642,10750,10908,11012,11168,11274,11434,11538,11696,11800,11960,12062,12222,12326,12488,12588,12748,12850,13014];
79d[70,]=[-1,45,84,126,168,210,252,298,336,382,420,462,504,554,588,634,672,718,756,806,840,890,924,970,1008,1062,1092,1142,1176,1226,1260,1314,1344,1398,1428,1478,1512,1570,1596,1650,1680,1734,1764,1822,1848,1906,1932,1986,2016,2078,2100,2158,2184,2242,2268,2330,2352,2414,2436,2494,2520,2586,2604,2666,2688,2750,2772,2838,2856,2922,2940,3002,3024,3094,3108,3174,3192,3258,3276,3346,3360,3430,3444,3510,3528,3602,3612,3682,3696,3766,3780,3854,3864,3938,3948,4018,4032,4110,4116,4190];
80d[71,]=[-1,176,385,595,805,1015,1225,1435,1645,1855,2065,2273,2485,2695,2905,3113,3325,3533,3745,3953,4165,4373,4585,4791,5005,5213,5425,5631,5845,6051,6265,6471,6685,6891,7105,7309,7525,7731,7945,8149,8365,8569,8785,8989,9205,9409,9625,9827,10045,10249,10465,10667,10885,11087,11305,11507,11725,11927,12145,12345,12565,12767,12985,13185,13405,13605,13825,14025,14245,14445,14665,14863,15085,15285,15505,15703,15925,16123,16345,16543,16765,16963,17185,17381,17605,17803,18025,18221,18445,18641,18865,19061,19285,19481,19705,19899,20125,20321,20545,20739];
81d[72,]=[-1,55,119,184,247,312,375,441,503,569,631,698,759,826,887,955,1015,1083,1143,1212,1271,1340,1399,1469,1527,1597,1655,1726,1783,1854,1911,1983,2039,2111,2167,2240,2295,2368,2423,2497,2551,2625,2679,2754,2807,2882,2935,3011,3063,3139,3191,3268,3319,3396,3447,3525,3575,3653,3703,3782,3831,3910,3959,4039,4087,4167,4215,4296,4343,4424,4471,4553,4599,4681,4727,4810,4855,4938,4983,5067,5111,5195,5239,5324,5367,5452,5495,5581,5623,5709,5751,5838,5879,5966,6007,6095,6135,6223,6263,6352];
82d[73,]=[-1,187,408,630,852,1074,1296,1518,1740,1962,2184,2404,2628,2850,3072,3292,3516,3736,3960,4180,4404,4624,4848,5066,5292,5512,5736,5954,6180,6398,6624,6842,7068,7286,7512,7728,7956,8174,8400,8616,8844,9060,9288,9504,9732,9948,10176,10390,10620,10836,11064,11278,11508,11722,11952,12166,12396,12610,12840,13052,13284,13498,13728,13940,14172,14384,14616,14828,15060,15272,15504,15714,15948,16160,16392,16602,16836,17046,17280,17490,17724,17934,18168,18376,18612,18822,19056,19264,19500,19708,19944,20152,20388,20596,20832,21038,21276,21484,21720,21926];
83d[74,]=[-1,56,114,171,228,285,342,397,456,511,570,627,684,737,798,853,912,967,1026,1079,1140,1193,1254,1309,1368,1419,1482,1535,1596,1649,1710,1761,1824,1875,1938,1991,2052,2101,2166,2217,2280,2331,2394,2443,2508,2557,2622,2673,2736,2783,2850,2899,2964,3013,3078,3125,3192,3239,3306,3355,3420,3465,3534,3581,3648,3695,3762,3807,3876,3921,3990,4037,4104,4147,4218,4263,4332,4377,4446,4489,4560,4603,4674,4719,4788,4829,4902,4945,5016,5059,5130,5171,5244,5285,5358,5401,5472,5511,5586,5627];
84d[75,]=[-1,119,256,394,532,671,809,947,1086,1224,1362,1499,1639,1777,1916,2052,2192,2329,2469,2605,2746,2882,3022,3157,3299,3435,3576,3710,3852,3987,4129,4263,4406,4540,4682,4815,4959,5093,5236,5368,5512,5645,5789,5921,6066,6198,6342,6473,6619,6751,6896,7026,7172,7303,7449,7579,7726,7856,8002,8131,8279,8409,8556,8684,8832,8961,9109,9237,9386,9514,9662,9789,9939,10067,10216,10342,10492,10619,10769,10895,11046,11172,11322,11447,11599,11725,11876,12000,12152,12277,12429,12553,12706,12830,12982,13105,13259,13383,13536,13658];
85d[76,]=[-1,87,192,297,400,505,608,717,816,925,1024,1135,1232,1345,1440,1555,1648,1763,1856,1975,2064,2183,2272,2393,2480,2603,2688,2813,2896,3021,3104,3233,3312,3441,3520,3651,3728,3861,3936,4071,4144,4279,4352,4491,4560,4699,4768,4909,4976,5119,5184,5329,5392,5537,5600,5749,5808,5957,6016,6167,6224,6377,6432,6587,6640,6795,6848,7007,7056,7215,7264,7425,7472,7635,7680,7845,7888,8053,8096,8265,8304,8473,8512,8683,8720,8893,8928,9103,9136,9311,9344,9523,9552,9731,9760,9941,9968,10151,10176,10361];
86d[77,]=[-1,179,408,634,860,1086,1312,1538,1764,1990,2216,2446,2668,2894,3120,3350,3572,3802,4024,4254,4476,4706,4928,5162,5380,5610,5832,6066,6284,6518,6736,6970,7188,7422,7640,7878,8092,8326,8544,8782,8996,9234,9448,9686,9900,10138,10352,10594,10804,11042,11256,11498,11708,11950,12160,12402,12612,12854,13064,13310,13516,13758,13968,14214,14420,14666,14872,15118,15324,15570,15776,16026,16228,16474,16680,16930,17132,17382,17584,17834,18036,18286,18488,18742,18940,19190,19392,19646,19844,20098,20296,20550,20748,21002,21200,21458,21652,21906,22104,22362];
87d[78,]=[-1,43,84,124,164,208,248,292,332,376,412,456,496,544,580,624,660,708,744,792,828,876,908,956,992,1044,1076,1124,1156,1208,1240,1292,1324,1376,1404,1456,1488,1544,1572,1624,1652,1708,1736,1792,1820,1876,1900,1956,1984,2044,2068,2124,2148,2208,2232,2292,2316,2376,2396,2456,2480,2544,2564,2624,2644,2708,2728,2792,2812,2876,2892,2956,2976,3044,3060,3124,3140,3208,3224,3292,3308,3376,3388,3456,3472,3544,3556,3624,3636,3708,3720,3792,3804,3876,3884,3956,3968,4044,4052,4124];
88d[79,]=[-1,222,481,741,1001,1261,1521,1781,2041,2301,2561,2819,3081,3341,3601,3859,4121,4379,4641,4899,5161,5419,5681,5937,6201,6459,6721,6977,7241,7497,7761,8017,8281,8537,8801,9055,9321,9577,9841,10095,10361,10615,10881,11135,11401,11655,11921,12173,12441,12695,12961,13213,13481,13733,14001,14253,14521,14773,15041,15291,15561,15813,16081,16331,16601,16851,17121,17371,17641,17891,18161,18409,18681,18931,19201,19449,19721,19969,20241,20489,20761,21009,21281,21527,21801,22049,22321,22567,22841,23087,23361,23607,23881,24127,24401,24645,24921,25167,25441,25685];
89d[80,]=[-1,86,184,284,382,482,580,680,778,878,976,1076,1174,1274,1372,1472,1570,1670,1768,1868,1966,2066,2164,2264,2362,2462,2560,2660,2758,2858,2956,3056,3154,3254,3352,3452,3550,3650,3748,3848,3946,4046,4144,4244,4342,4442,4540,4640,4738,4838,4936,5036,5134,5234,5332,5432,5530,5630,5728,5828,5926,6026,6124,6224,6322,6422,6520,6620,6718,6818,6916,7016,7114,7214,7312,7412,7510,7610,7708,7808,7906,8006,8104,8204,8302,8402,8500,8600,8698,8798,8896,8996,9094,9194,9292,9392,9490,9590,9688,9788];
90d[81,]=[-1,164,356,548,740,932,1124,1316,1508,1700,1892,2084,2276,2468,2660,2852,3044,3236,3428,3620,3812,4004,4196,4388,4580,4772,4964,5156,5348,5540,5732,5924,6116,6308,6500,6692,6884,7076,7268,7460,7652,7844,8036,8228,8420,8612,8804,8996,9188,9380,9572,9764,9956,10148,10340,10532,10724,10916,11108,11300,11492,11684,11876,12068,12260,12452,12644,12836,13028,13220,13412,13604,13796,13988,14180,14372,14564,14756,14948,15140,15332,15524,15716,15908,16100,16292,16484,16676,16868,17060,17252,17444,17636,17828,18020,18212,18404,18596,18788,18980];
91d[82,]=[-1,69,140,210,280,350,420,488,560,628,700,770,840,906,980,1048,1120,1188,1260,1326,1400,1466,1540,1608,1680,1744,1820,1886,1960,2026,2100,2164,2240,2304,2380,2446,2520,2582,2660,2724,2800,2864,2940,3002,3080,3142,3220,3284,3360,3420,3500,3562,3640,3702,3780,3840,3920,3980,4060,4122,4200,4258,4340,4400,4480,4540,4620,4678,4760,4818,4900,4960,5040,5096,5180,5238,5320,5378,5460,5516,5600,5656,5740,5798,5880,5934,6020,6076,6160,6216,6300,6354,6440,6494,6580,6636,6720,6772,6860,6914];
92d[83,]=[-1,247,533,820,1107,1394,1681,1968,2255,2542,2829,3114,3403,3690,3977,4262,4551,4836,5125,5410,5699,5984,6273,6556,6847,7132,7421,7704,7995,8278,8569,8852,9143,9426,9717,9998,10291,10574,10865,11146,11439,11720,12013,12294,12587,12868,13161,13440,13735,14016,14309,14588,14883,15162,15457,15736,16031,16310,16605,16882,17179,17458,17753,18030,18327,18604,18901,19178,19475,19752,20049,20324,20623,20900,21197,21472,21771,22046,22345,22620,22919,23194,23493,23766,24067,24342,24641,24914,25215,25488,25789,26062,26363,26636,26937,27208,27511,27784,28085,28356];
93d[84,]=[-1,72,150,230,314,392,476,548,638,710,802,868,964,1028,1126,1186,1290,1348,1452,1504,1614,1666,1778,1824,1940,1984,2102,2142,2266,2304,2428,2460,2590,2622,2754,2780,2916,2940,3078,3098,3242,3260,3404,3416,3566,3578,3730,3736,3892,3896,4054,4054,4218,4216,4380,4372,4542,4534,4706,4692,4868,4852,5030,5010,5194,5172,5356,5328,5518,5490,5682,5648,5844,5808,6006,5966,6170,6128,6332,6284,6494,6446,6658,6604,6820,6764,6982,6922,7146,7084,7308,7240,7470,7402,7634,7560,7796,7720,7958,7878];
94d[85,]=[-1,215,480,742,1004,1266,1528,1790,2052,2314,2576,2842,3100,3362,3624,3890,4148,4414,4672,4938,5196,5462,5720,5990,6244,6510,6768,7038,7292,7562,7816,8086,8340,8610,8864,9138,9388,9658,9912,10186,10436,10710,10960,11234,11484,11758,12008,12286,12532,12806,13056,13334,13580,13858,14104,14382,14628,14906,15152,15434,15676,15954,16200,16482,16724,17006,17248,17530,17772,18054,18296,18582,18820,19102,19344,19630,19868,20154,20392,20678,20916,21202,21440,21730,21964,22250,22488,22778,23012,23302,23536,23826,24060,24350,24584,24878,25108,25398,25632,25926];
95d[86,]=[-1,76,154,231,308,385,462,537,616,691,770,847,924,997,1078,1153,1232,1307,1386,1459,1540,1613,1694,1769,1848,1919,2002,2075,2156,2229,2310,2381,2464,2535,2618,2691,2772,2841,2926,2997,3080,3151,3234,3303,3388,3457,3542,3613,3696,3763,3850,3919,4004,4073,4158,4225,4312,4379,4466,4535,4620,4685,4774,4841,4928,4995,5082,5147,5236,5301,5390,5457,5544,5607,5698,5763,5852,5917,6006,6069,6160,6223,6314,6379,6468,6529,6622,6685,6776,6839,6930,6991,7084,7145,7238,7301,7392,7451,7546,7607];
96d[87,]=[-1,181,392,602,812,1020,1230,1440,1648,1858,2068,2280,2486,2696,2904,3118,3324,3536,3742,3956,4160,4374,4580,4796,4998,5212,5416,5634,5836,6052,6254,6472,6672,6890,7092,7312,7510,7728,7928,8150,8348,8568,8766,8988,9184,9406,9604,9828,10022,10244,10440,10666,10860,11084,11278,11504,11696,11922,12116,12344,12534,12760,12952,13182,13372,13600,13790,14020,14208,14438,14628,14860,15046,15276,15464,15698,15884,16116,16302,16536,16720,16954,17140,17376,17558,17792,17976,18214,18396,18632,18814,19052,19232,19470,19652,19892,20070,20308,20488,20730];
97d[88,]=[-1,115,248,379,514,645,780,909,1046,1175,1312,1439,1578,1705,1844,1969,2110,2235,2376,2499,2642,2765,2908,3029,3174,3295,3440,3559,3706,3825,3972,4089,4238,4355,4504,4619,4770,4885,5036,5149,5302,5415,5568,5679,5834,5945,6100,6209,6366,6475,6632,6739,6898,7005,7164,7269,7430,7535,7696,7799,7962,8065,8228,8329,8494,8595,8760,8859,9026,9125,9292,9389,9558,9655,9824,9919,10090,10185,10356,10449,10622,10715,10888,10979,11154,11245,11420,11509,11686,11775,11952,12039,12218,12305,12484,12569,12750,12835,13016,13099];
98d[89,]=[-1,287,616,946,1276,1606,1936,2266,2596,2926,3256,3584,3916,4246,4576,4904,5236,5564,5896,6224,6556,6884,7216,7542,7876,8204,8536,8862,9196,9522,9856,10182,10516,10842,11176,11500,11836,12162,12496,12820,13156,13480,13816,14140,14476,14800,15136,15458,15796,16120,16456,16778,17116,17438,17776,18098,18436,18758,19096,19416,19756,20078,20416,20736,21076,21396,21736,22056,22396,22716,23056,23374,23716,24036,24376,24694,25036,25354,25696,26014,26356,26674,27016,27332,27676,27994,28336,28652,28996,29312,29656,29972,30316,30632,30976,31290,31636,31952,32296,32610];
99d[90,]=[-1,53,102,157,212,259,314,367,416,469,526,573,628,679,730,783,840,885,942,993,1044,1095,1154,1199,1256,1305,1358,1409,1468,1511,1570,1619,1672,1721,1782,1825,1884,1931,1986,2035,2096,2137,2198,2245,2300,2347,2410,2451,2512,2557,2614,2661,2724,2763,2826,2871,2928,2973,3038,3077,3140,3183,3242,3287,3352,3389,3454,3497,3556,3599,3666,3703,3768,3809,3870,3913,3980,4015,4082,4123,4184,4225,4294,4329,4396,4435,4498,4539,4608,4641,4710,4749,4812,4851,4922,4955,5024,5061,5126,5165];
100d[91,]=[-1,261,582,900,1218,1536,1854,2172,2490,2808,3126,3448,3762,4080,4398,4720,5034,5356,5670,5992,6306,6628,6942,7268,7578,7900,8214,8540,8850,9176,9486,9812,10122,10448,10758,11088,11394,11720,12030,12360,12666,12996,13302,13632,13938,14268,14574,14908,15210,15540,15846,16180,16482,16816,17118,17452,17754,18088,18390,18728,19026,19360,19662,20000,20298,20636,20934,21272,21570,21908,22206,22548,22842,23180,23478,23820,24114,24456,24750,25092,25386,25728,26022,26368,26658,27000,27294,27640,27930,28276,28566,28912,29202,29548,29838,30188,30474,30820,31110,31460];
101d[92,]=[-1,132,286,440,592,746,898,1056,1204,1362,1510,1670,1816,1978,2122,2286,2428,2592,2734,2902,3040,3208,3346,3516,3652,3824,3958,4132,4264,4438,4570,4748,4876,5054,5182,5362,5488,5670,5794,5978,6100,6284,6406,6594,6712,6900,7018,7208,7324,7516,7630,7824,7936,8130,8242,8440,8548,8746,8854,9054,9160,9362,9466,9670,9772,9976,10078,10286,10384,10592,10690,10900,10996,11208,11302,11516,11608,11822,11914,12132,12220,12438,12526,12746,12832,13054,13138,13362,13444,13668,13750,13978,14056,14284,14362,14592,14668,14900,14974,15208];
102d[93,]=[-1,209,450,690,930,1168,1408,1648,1886,2126,2366,2608,2844,3084,3322,3566,3802,4044,4280,4524,4758,5002,5238,5484,5716,5960,6194,6442,6674,6920,7152,7400,7630,7878,8110,8360,8588,8836,9066,9318,9546,9796,10024,10276,10502,10754,10982,11236,11460,11712,11938,12194,12418,12672,12896,13152,13374,13630,13854,14112,14332,14588,14810,15070,15290,15548,15768,16028,16246,16506,16726,16988,17204,17464,17682,17946,18162,18424,18640,18904,19118,19382,19598,19864,20076,20340,20554,20822,21034,21300,21512,21780,21990,22258,22470,22740,22948,23216,23426,23698];
103d[94,]=[-1,91,184,276,368,460,552,642,736,826,920,1012,1104,1192,1288,1378,1472,1562,1656,1744,1840,1928,2024,2114,2208,2294,2392,2480,2576,2664,2760,2846,2944,3030,3128,3216,3312,3396,3496,3582,3680,3766,3864,3948,4048,4132,4232,4318,4416,4498,4600,4684,4784,4868,4968,5050,5152,5234,5336,5420,5520,5600,5704,5786,5888,5970,6072,6152,6256,6336,6440,6522,6624,6702,6808,6888,6992,7072,7176,7254,7360,7438,7544,7624,7728,7804,7912,7990,8096,8174,8280,8356,8464,8540,8648,8726,8832,8906,9016,9092];
104d[95,]=[-1,275,606,934,1262,1590,1918,2246,2574,2902,3230,3562,3886,4214,4542,4874,5198,5530,5854,6186,6510,6842,7166,7502,7822,8154,8478,8814,9134,9470,9790,10126,10446,10782,11102,11442,11758,12094,12414,12754,13070,13410,13726,14066,14382,14722,15038,15382,15694,16034,16350,16694,17006,17350,17662,18006,18318,18662,18974,19322,19630,19974,20286,20634,20942,21290,21598,21946,22254,22602,22910,23262,23566,23914,24222,24574,24878,25230,25534,25886,26190,26542,26846,27202,27502,27854,28158,28514,28814,29170,29470,29826,30126,30482,30782,31142,31438,31794,32094,32454];
105d[96,]=[-1,98,206,314,422,530,638,746,854,962,1070,1178,1286,1394,1502,1610,1718,1826,1934,2042,2150,2258,2366,2474,2582,2690,2798,2906,3014,3122,3230,3338,3446,3554,3662,3770,3878,3986,4094,4202,4310,4418,4526,4634,4742,4850,4958,5066,5174,5282,5390,5498,5606,5714,5822,5930,6038,6146,6254,6362,6470,6578,6686,6794,6902,7010,7118,7226,7334,7442,7550,7658,7766,7874,7982,8090,8198,8306,8414,8522,8630,8738,8846,8954,9062,9170,9278,9386,9494,9602,9710,9818,9926,10034,10142,10250,10358,10466,10574,10682];
106d[97,]=[-1,345,736,1128,1520,1912,2304,2696,3088,3480,3872,4262,4656,5048,5440,5830,6224,6614,7008,7398,7792,8182,8576,8964,9360,9750,10144,10532,10928,11316,11712,12100,12496,12884,13280,13666,14064,14452,14848,15234,15632,16018,16416,16802,17200,17586,17984,18368,18768,19154,19552,19936,20336,20720,21120,21504,21904,22288,22688,23070,23472,23856,24256,24638,25040,25422,25824,26206,26608,26990,27392,27772,28176,28558,28960,29340,29744,30124,30528,30908,31312,31692,32096,32474,32880,33260,33664,34042,34448,34826,35232,35610,36016,36394,36800,37176,37584,37962,38368,38744];
107d[98,]=[-1,95,188,282,376,470,564,659,752,847,940,1034,1128,1224,1316,1411,1504,1599,1692,1788,1880,1976,2068,2163,2256,2353,2444,2540,2632,2728,2820,2917,3008,3105,3196,3292,3384,3482,3572,3669,3760,3857,3948,4046,4136,4234,4324,4421,4512,4611,4700,4798,4888,4986,5076,5175,5264,5363,5452,5550,5640,5740,5828,5927,6016,6115,6204,6304,6392,6492,6580,6679,6768,6869,6956,7056,7144,7244,7332,7433,7520,7621,7708,7808,7896,7998,8084,8185,8272,8373,8460,8562,8648,8750,8836,8937,9024,9127,9212,9314];
108d[99,]=[-1,240,521,800,1079,1362,1641,1920,2203,2482,2761,3042,3323,3602,3885,4162,4443,4724,5005,5282,5567,5844,6125,6404,6687,6964,7249,7524,7807,8086,8369,8644,8931,9206,9489,9766,10051,10326,10613,10886,11171,11448,11733,12006,12295,12568,12853,13128,13415,13688,13977,14248,14535,14810,15097,15368,15659,15930,16217,16490,16779,17050,17341,17610,17899,18172,18461,18730,19023,19292,19581,19852,20143,20412,20705,20972,21263,21534,21825,22092,22387,22654,22945,23214,23507,23774,24069,24334,24627,24896,25189,25454,25751,26016,26309,26576,26871,27136,27433,27696];
109d[100,]=[-1,141,302,463,625,786,948,1107,1271,1430,1594,1752,1917,2074,2240,2396,2563,2719,2886,3040,3209,3363,3532,3685,3855,4007,4178,4329,4501,4652,4824,4973,5147,5296,5470,5618,5793,5940,6116,6262,6439,6585,6762,6906,7085,7229,7408,7551,7731,7873,8054,8195,8377,8518,8700,8839,9023,9162,9346,9484,9669,9806,9992,10128,10315,10451,10638,10772,10961,11095,11284,11417,11607,11739,11930,12061,12253,12384,12576,12705,12899,13028,13222,13350,13545,13672,13868,13994,14191,14317,14514,14638,14837,14961,15160,15283,15483,15605,15806,15927];
110}
111