Sharedwww / Tables / dimskg0n.gpOpen in CoCalc
Author: William A. Stein
1\\ dim_skg0n.gp
2\\ This is a table of dimensions of the spaces
3\\             S_k(Gamma_0(N))
4\\ of weight k cusp forms for Gamma_0(N).
5\\ It was computed using a standard formula.
6\\ William Stein ([email protected]), September, 1998.
7
8{\\ d[N,k]=dim(S_{2k}(Gamma_0(N))), 2k>=2
9d=matrix(100,50,m,n,0);
10
11d[1,]=[0,0,0,0,0,1,0,1,1,1,1,2,1,2,2,2,2,3,2,3,3,3,3,4,3,4,4,4,4,5,4,5,5,5,5,6,5,6,6,6,6,7,6,7,7,7,7,8,7,8];
12d[2,]=[0,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24];
13d[3,]=[0,0,1,1,2,3,3,4,5,5,6,7,7,8,9,9,10,11,11,12,13,13,14,15,15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,26,27,27,28,29,29,30,31,31,32];
14d[4,]=[0,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48];
15d[5,]=[0,1,1,3,3,5,5,7,7,9,9,11,11,13,13,15,15,17,17,19,19,21,21,23,23,25,25,27,27,29,29,31,31,33,33,35,35,37,37,39,39,41,41,43,43,45,45,47,47,49];
16d[6,]=[0,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97];
17d[7,]=[0,1,3,3,5,7,7,9,11,11,13,15,15,17,19,19,21,23,23,25,27,27,29,31,31,33,35,35,37,39,39,41,43,43,45,47,47,49,51,51,53,55,55,57,59,59,61,63,63,65];
18d[8,]=[0,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97];
19d[9,]=[0,1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97];
20d[10,]=[0,3,5,9,11,15,17,21,23,27,29,33,35,39,41,45,47,51,53,57,59,63,65,69,71,75,77,81,83,87,89,93,95,99,101,105,107,111,113,117,119,123,125,129,131,135,137,141,143,147];
21d[11,]=[1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98];
22d[12,]=[0,3,7,11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,87,91,95,99,103,107,111,115,119,123,127,131,135,139,143,147,151,155,159,163,167,171,175,179,183,187,191,195];
23d[13,]=[0,3,5,7,9,13,13,17,19,21,23,27,27,31,33,35,37,41,41,45,47,49,51,55,55,59,61,63,65,69,69,73,75,77,79,83,83,87,89,91,93,97,97,101,103,105,107,111,111,115];
24d[14,]=[1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,160,164,168,172,176,180,184,188,192,196];
25d[15,]=[1,4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,136,140,144,148,152,156,160,164,168,172,176,180,184,188,192,196];
26d[16,]=[0,3,7,11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,87,91,95,99,103,107,111,115,119,123,127,131,135,139,143,147,151,155,159,163,167,171,175,179,183,187,191,195];
27d[17,]=[1,4,6,10,12,16,18,22,24,28,30,34,36,40,42,46,48,52,54,58,60,64,66,70,72,76,78,82,84,88,90,94,96,100,102,106,108,112,114,118,120,124,126,130,132,136,138,142,144,148];
28d[18,]=[0,5,11,17,23,29,35,41,47,53,59,65,71,77,83,89,95,101,107,113,119,125,131,137,143,149,155,161,167,173,179,185,191,197,203,209,215,221,227,233,239,245,251,257,263,269,275,281,287,293];
29d[19,]=[1,4,8,10,14,18,20,24,28,30,34,38,40,44,48,50,54,58,60,64,68,70,74,78,80,84,88,90,94,98,100,104,108,110,114,118,120,124,128,130,134,138,140,144,148,150,154,158,160,164];
30d[20,]=[1,6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198,204,210,216,222,228,234,240,246,252,258,264,270,276,282,288,294];
31d[21,]=[1,6,12,16,22,28,32,38,44,48,54,60,64,70,76,80,86,92,96,102,108,112,118,124,128,134,140,144,150,156,160,166,172,176,182,188,192,198,204,208,214,220,224,230,236,240,246,252,256,262];
32d[22,]=[2,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103,109,115,121,127,133,139,145,151,157,163,169,175,181,187,193,199,205,211,217,223,229,235,241,247,253,259,265,271,277,283,289,295];
33d[23,]=[2,5,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81,85,89,93,97,101,105,109,113,117,121,125,129,133,137,141,145,149,153,157,161,165,169,173,177,181,185,189,193,197];
34d[24,]=[1,8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144,152,160,168,176,184,192,200,208,216,224,232,240,248,256,264,272,280,288,296,304,312,320,328,336,344,352,360,368,376,384,392];
35d[25,]=[0,5,9,15,19,25,29,35,39,45,49,55,59,65,69,75,79,85,89,95,99,105,109,115,119,125,129,135,139,145,149,155,159,165,169,175,179,185,189,195,199,205,209,215,219,225,229,235,239,245];
36d[26,]=[2,9,15,23,29,37,43,51,57,65,71,79,85,93,99,107,113,121,127,135,141,149,155,163,169,177,183,191,197,205,211,219,225,233,239,247,253,261,267,275,281,289,295,303,309,317,323,331,337,345];
37d[27,]=[1,6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198,204,210,216,222,228,234,240,246,252,258,264,270,276,282,288,294];
38d[28,]=[2,9,17,25,33,41,49,57,65,73,81,89,97,105,113,121,129,137,145,153,161,169,177,185,193,201,209,217,225,233,241,249,257,265,273,281,289,297,305,313,321,329,337,345,353,361,369,377,385,393];
39d[29,]=[2,7,11,17,21,27,31,37,41,47,51,57,61,67,71,77,81,87,91,97,101,107,111,117,121,127,131,137,141,147,151,157,161,167,171,177,181,187,191,197,201,207,211,217,221,227,231,237,241,247];
40d[30,]=[3,14,26,38,50,62,74,86,98,110,122,134,146,158,170,182,194,206,218,230,242,254,266,278,290,302,314,326,338,350,362,374,386,398,410,422,434,446,458,470,482,494,506,518,530,542,554,566,578,590];
41d[31,]=[2,7,13,17,23,29,33,39,45,49,55,61,65,71,77,81,87,93,97,103,109,113,119,125,129,135,141,145,151,157,161,167,173,177,183,189,193,199,205,209,215,221,225,231,237,241,247,253,257,263];
42d[32,]=[1,8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144,152,160,168,176,184,192,200,208,216,224,232,240,248,256,264,272,280,288,296,304,312,320,328,336,344,352,360,368,376,384,392];
43d[33,]=[3,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,146,154,162,170,178,186,194,202,210,218,226,234,242,250,258,266,274,282,290,298,306,314,322,330,338,346,354,362,370,378,386,394];
44d[34,]=[3,12,20,30,38,48,56,66,74,84,92,102,110,120,128,138,146,156,164,174,182,192,200,210,218,228,236,246,254,264,272,282,290,300,308,318,326,336,344,354,362,372,380,390,398,408,416,426,434,444];
45d[35,]=[3,10,18,26,34,42,50,58,66,74,82,90,98,106,114,122,130,138,146,154,162,170,178,186,194,202,210,218,226,234,242,250,258,266,274,282,290,298,306,314,322,330,338,346,354,362,370,378,386,394];
46d[36,]=[1,12,24,36,48,60,72,84,96,108,120,132,144,156,168,180,192,204,216,228,240,252,264,276,288,300,312,324,336,348,360,372,384,396,408,420,432,444,456,468,480,492,504,516,528,540,552,564,576,588];
47d[37,]=[2,9,15,21,27,35,39,47,53,59,65,73,77,85,91,97,103,111,115,123,129,135,141,149,153,161,167,173,179,187,191,199,205,211,217,225,229,237,243,249,255,263,267,275,281,287,293,301,305,313];
48d[38,]=[4,13,23,33,43,53,63,73,83,93,103,113,123,133,143,153,163,173,183,193,203,213,223,233,243,253,263,273,283,293,303,313,323,333,343,353,363,373,383,393,403,413,423,433,443,453,463,473,483,493];
49d[39,]=[3,12,22,30,40,50,58,68,78,86,96,106,114,124,134,142,152,162,170,180,190,198,208,218,226,236,246,254,264,274,282,292,302,310,320,330,338,348,358,366,376,386,394,404,414,422,432,442,450,460];
50d[40,]=[3,14,26,38,50,62,74,86,98,110,122,134,146,158,170,182,194,206,218,230,242,254,266,278,290,302,314,326,338,350,362,374,386,398,410,422,434,446,458,470,482,494,506,518,530,542,554,566,578,590];
51d[41,]=[3,10,16,24,30,38,44,52,58,66,72,80,86,94,100,108,114,122,128,136,142,150,156,164,170,178,184,192,198,206,212,220,226,234,240,248,254,262,268,276,282,290,296,304,310,318,324,332,338,346];
52d[42,]=[5,20,36,52,68,84,100,116,132,148,164,180,196,212,228,244,260,276,292,308,324,340,356,372,388,404,420,436,452,468,484,500,516,532,548,564,580,596,612,628,644,660,676,692,708,724,740,756,772,788];
53d[43,]=[3,10,18,24,32,40,46,54,62,68,76,84,90,98,106,112,120,128,134,142,150,156,164,172,178,186,194,200,208,216,222,230,238,244,252,260,266,274,282,288,296,304,310,318,326,332,340,348,354,362];
54d[44,]=[4,15,27,39,51,63,75,87,99,111,123,135,147,159,171,183,195,207,219,231,243,255,267,279,291,303,315,327,339,351,363,375,387,399,411,423,435,447,459,471,483,495,507,519,531,543,555,567,579,591];
55d[45,]=[3,14,26,38,50,62,74,86,98,110,122,134,146,158,170,182,194,206,218,230,242,254,266,278,290,302,314,326,338,350,362,374,386,398,410,422,434,446,458,470,482,494,506,518,530,542,554,566,578,590];
56d[46,]=[5,16,28,40,52,64,76,88,100,112,124,136,148,160,172,184,196,208,220,232,244,256,268,280,292,304,316,328,340,352,364,376,388,400,412,424,436,448,460,472,484,496,508,520,532,544,556,568,580,592];
57d[47,]=[4,11,19,27,35,43,51,59,67,75,83,91,99,107,115,123,131,139,147,155,163,171,179,187,195,203,211,219,227,235,243,251,259,267,275,283,291,299,307,315,323,331,339,347,355,363,371,379,387,395];
58d[48,]=[3,18,34,50,66,82,98,114,130,146,162,178,194,210,226,242,258,274,290,306,322,338,354,370,386,402,418,434,450,466,482,498,514,530,546,562,578,594,610,626,642,658,674,690,706,722,738,754,770,786];
59d[49,]=[1,10,20,28,38,48,56,66,76,84,94,104,112,122,132,140,150,160,168,178,188,196,206,216,224,234,244,252,262,272,280,290,300,308,318,328,336,346,356,364,374,384,392,402,412,420,430,440,448,458];
60d[50,]=[2,17,31,47,61,77,91,107,121,137,151,167,181,197,211,227,241,257,271,287,301,317,331,347,361,377,391,407,421,437,451,467,481,497,511,527,541,557,571,587,601,617,631,647,661,677,691,707,721,737];
61d[51,]=[5,16,28,40,52,64,76,88,100,112,124,136,148,160,172,184,196,208,220,232,244,256,268,280,292,304,316,328,340,352,364,376,388,400,412,424,436,448,460,472,484,496,508,520,532,544,556,568,580,592];
62d[52,]=[5,18,32,46,60,74,88,102,116,130,144,158,172,186,200,214,228,242,256,270,284,298,312,326,340,354,368,382,396,410,424,438,452,466,480,494,508,522,536,550,564,578,592,606,620,634,648,662,676,690];
63d[53,]=[4,13,21,31,39,49,57,67,75,85,93,103,111,121,129,139,147,157,165,175,183,193,201,211,219,229,237,247,255,265,273,283,291,301,309,319,327,337,345,355,363,373,381,391,399,409,417,427,435,445];
64d[54,]=[4,21,39,57,75,93,111,129,147,165,183,201,219,237,255,273,291,309,327,345,363,381,399,417,435,453,471,489,507,525,543,561,579,597,615,633,651,669,687,705,723,741,759,777,795,813,831,849,867,885];
65d[55,]=[5,16,28,40,52,64,76,88,100,112,124,136,148,160,172,184,196,208,220,232,244,256,268,280,292,304,316,328,340,352,364,376,388,400,412,424,436,448,460,472,484,496,508,520,532,544,556,568,580,592];
66d[56,]=[5,20,36,52,68,84,100,116,132,148,164,180,196,212,228,244,260,276,292,308,324,340,356,372,388,404,420,436,452,468,484,500,516,532,548,564,580,596,612,628,644,660,676,692,708,724,740,756,772,788];
67d[57,]=[5,18,32,44,58,72,84,98,112,124,138,152,164,178,192,204,218,232,244,258,272,284,298,312,324,338,352,364,378,392,404,418,432,444,458,472,484,498,512,524,538,552,564,578,592,604,618,632,644,658];
68d[58,]=[6,21,35,51,65,81,95,111,125,141,155,171,185,201,215,231,245,261,275,291,305,321,335,351,365,381,395,411,425,441,455,471,485,501,515,531,545,561,575,591,605,621,635,651,665,681,695,711,725,741];
69d[59,]=[5,14,24,34,44,54,64,74,84,94,104,114,124,134,144,154,164,174,184,194,204,214,224,234,244,254,264,274,284,294,304,314,324,334,344,354,364,374,384,394,404,414,424,434,444,454,464,474,484,494];
70d[60,]=[7,30,54,78,102,126,150,174,198,222,246,270,294,318,342,366,390,414,438,462,486,510,534,558,582,606,630,654,678,702,726,750,774,798,822,846,870,894,918,942,966,990,1014,1038,1062,1086,1110,1134,1158,1182];
71d[61,]=[4,15,25,35,45,57,65,77,87,97,107,119,127,139,149,159,169,181,189,201,211,221,231,243,251,263,273,283,293,305,313,325,335,345,355,367,375,387,397,407,417,429,437,449,459,469,479,491,499,511];
72d[62,]=[7,22,38,54,70,86,102,118,134,150,166,182,198,214,230,246,262,278,294,310,326,342,358,374,390,406,422,438,454,470,486,502,518,534,550,566,582,598,614,630,646,662,678,694,710,726,742,758,774,790];
73d[63,]=[5,20,36,52,68,84,100,116,132,148,164,180,196,212,228,244,260,276,292,308,324,340,356,372,388,404,420,436,452,468,484,500,516,532,548,564,580,596,612,628,644,660,676,692,708,724,740,756,772,788];
74d[64,]=[3,18,34,50,66,82,98,114,130,146,162,178,194,210,226,242,258,274,290,306,322,338,354,370,386,402,418,434,450,466,482,498,514,530,546,562,578,594,610,626,642,658,674,690,706,722,738,754,770,786];
75d[65,]=[5,20,32,48,60,76,88,104,116,132,144,160,172,188,200,216,228,244,256,272,284,300,312,328,340,356,368,384,396,412,424,440,452,468,480,496,508,524,536,552,564,580,592,608,620,636,648,664,676,692];
76d[66,]=[9,32,56,80,104,128,152,176,200,224,248,272,296,320,344,368,392,416,440,464,488,512,536,560,584,608,632,656,680,704,728,752,776,800,824,848,872,896,920,944,968,992,1016,1040,1064,1088,1112,1136,1160,1184];
77d[67,]=[5,16,28,38,50,62,72,84,96,106,118,130,140,152,164,174,186,198,208,220,232,242,254,266,276,288,300,310,322,334,344,356,368,378,390,402,412,424,436,446,458,470,480,492,504,514,526,538,548,560];
78d[68,]=[7,24,42,60,78,96,114,132,150,168,186,204,222,240,258,276,294,312,330,348,366,384,402,420,438,456,474,492,510,528,546,564,582,600,618,636,654,672,690,708,726,744,762,780,798,816,834,852,870,888];
79d[69,]=[7,22,38,54,70,86,102,118,134,150,166,182,198,214,230,246,262,278,294,310,326,342,358,374,390,406,422,438,454,470,486,502,518,534,550,566,582,598,614,630,646,662,678,694,710,726,742,758,774,790];
80d[70,]=[9,32,56,80,104,128,152,176,200,224,248,272,296,320,344,368,392,416,440,464,488,512,536,560,584,608,632,656,680,704,728,752,776,800,824,848,872,896,920,944,968,992,1016,1040,1064,1088,1112,1136,1160,1184];
81d[71,]=[6,17,29,41,53,65,77,89,101,113,125,137,149,161,173,185,197,209,221,233,245,257,269,281,293,305,317,329,341,353,365,377,389,401,413,425,437,449,461,473,485,497,509,521,533,545,557,569,581,593];
82d[72,]=[5,28,52,76,100,124,148,172,196,220,244,268,292,316,340,364,388,412,436,460,484,508,532,556,580,604,628,652,676,700,724,748,772,796,820,844,868,892,916,940,964,988,1012,1036,1060,1084,1108,1132,1156,1180];
83d[73,]=[5,18,30,42,54,68,78,92,104,116,128,142,152,166,178,190,202,216,226,240,252,264,276,290,300,314,326,338,350,364,374,388,400,412,424,438,448,462,474,486,498,512,522,536,548,560,572,586,596,610];
84d[74,]=[8,27,45,65,83,103,121,141,159,179,197,217,235,255,273,293,311,331,349,369,387,407,425,445,463,483,501,521,539,559,577,597,615,635,653,673,691,711,729,749,767,787,805,825,843,863,881,901,919,939];
85d[75,]=[5,24,44,64,84,104,124,144,164,184,204,224,244,264,284,304,324,344,364,384,404,424,444,464,484,504,524,544,564,584,604,624,644,664,684,704,724,744,764,784,804,824,844,864,884,904,924,944,964,984];
86d[76,]=[8,27,47,67,87,107,127,147,167,187,207,227,247,267,287,307,327,347,367,387,407,427,447,467,487,507,527,547,567,587,607,627,647,667,687,707,727,747,767,787,807,827,847,867,887,907,927,947,967,987];
87d[77,]=[7,22,38,54,70,86,102,118,134,150,166,182,198,214,230,246,262,278,294,310,326,342,358,374,390,406,422,438,454,470,486,502,518,534,550,566,582,598,614,630,646,662,678,694,710,726,742,758,774,790];
88d[78,]=[11,38,66,94,122,150,178,206,234,262,290,318,346,374,402,430,458,486,514,542,570,598,626,654,682,710,738,766,794,822,850,878,906,934,962,990,1018,1046,1074,1102,1130,1158,1186,1214,1242,1270,1298,1326,1354,1382];
89d[79,]=[6,19,33,45,59,73,85,99,113,125,139,153,165,179,193,205,219,233,245,259,273,285,299,313,325,339,353,365,379,393,405,419,433,445,459,473,485,499,513,525,539,553,565,579,593,605,619,633,645,659];
90d[80,]=[7,30,54,78,102,126,150,174,198,222,246,270,294,318,342,366,390,414,438,462,486,510,534,558,582,606,630,654,678,702,726,750,774,798,822,846,870,894,918,942,966,990,1014,1038,1062,1086,1110,1134,1158,1182];
91d[81,]=[4,21,39,57,75,93,111,129,147,165,183,201,219,237,255,273,291,309,327,345,363,381,399,417,435,453,471,489,507,525,543,561,579,597,615,633,651,669,687,705,723,741,759,777,795,813,831,849,867,885];
92d[82,]=[9,30,50,72,92,114,134,156,176,198,218,240,260,282,302,324,344,366,386,408,428,450,470,492,512,534,554,576,596,618,638,660,680,702,722,744,764,786,806,828,848,870,890,912,932,954,974,996,1016,1038];
93d[83,]=[7,20,34,48,62,76,90,104,118,132,146,160,174,188,202,216,230,244,258,272,286,300,314,328,342,356,370,384,398,412,426,440,454,468,482,496,510,524,538,552,566,580,594,608,622,636,650,664,678,692];
94d[84,]=[11,42,74,106,138,170,202,234,266,298,330,362,394,426,458,490,522,554,586,618,650,682,714,746,778,810,842,874,906,938,970,1002,1034,1066,1098,1130,1162,1194,1226,1258,1290,1322,1354,1386,1418,1450,1482,1514,1546,1578];
95d[85,]=[7,26,42,62,78,98,114,134,150,170,186,206,222,242,258,278,294,314,330,350,366,386,402,422,438,458,474,494,510,530,546,566,582,602,618,638,654,674,690,710,726,746,762,782,798,818,834,854,870,890];
96d[86,]=[10,31,53,75,97,119,141,163,185,207,229,251,273,295,317,339,361,383,405,427,449,471,493,515,537,559,581,603,625,647,669,691,713,735,757,779,801,823,845,867,889,911,933,955,977,999,1021,1043,1065,1087];
97d[87,]=[9,28,48,68,88,108,128,148,168,188,208,228,248,268,288,308,328,348,368,388,408,428,448,468,488,508,528,548,568,588,608,628,648,668,688,708,728,748,768,788,808,828,848,868,888,908,928,948,968,988];
98d[88,]=[9,32,56,80,104,128,152,176,200,224,248,272,296,320,344,368,392,416,440,464,488,512,536,560,584,608,632,656,680,704,728,752,776,800,824,848,872,896,920,944,968,992,1016,1040,1064,1088,1112,1136,1160,1184];
99d[89,]=[7,22,36,52,66,82,96,112,126,142,156,172,186,202,216,232,246,262,276,292,306,322,336,352,366,382,396,412,426,442,456,472,486,502,516,532,546,562,576,592,606,622,636,652,666,682,696,712,726,742];
100d[90,]=[11,46,82,118,154,190,226,262,298,334,370,406,442,478,514,550,586,622,658,694,730,766,802,838,874,910,946,982,1018,1054,1090,1126,1162,1198,1234,1270,1306,1342,1378,1414,1450,1486,1522,1558,1594,1630,1666,1702,1738,1774];
101d[91,]=[7,26,46,62,82,102,118,138,158,174,194,214,230,250,270,286,306,326,342,362,382,398,418,438,454,474,494,510,530,550,566,586,606,622,642,662,678,698,718,734,754,774,790,810,830,846,866,886,902,922];
102d[92,]=[10,33,57,81,105,129,153,177,201,225,249,273,297,321,345,369,393,417,441,465,489,513,537,561,585,609,633,657,681,705,729,753,777,801,825,849,873,897,921,945,969,993,1017,1041,1065,1089,1113,1137,1161,1185];
103d[93,]=[9,30,52,72,94,116,136,158,180,200,222,244,264,286,308,328,350,372,392,414,436,456,478,500,520,542,564,584,606,628,648,670,692,712,734,756,776,798,820,840,862,884,904,926,948,968,990,1012,1032,1054];
104d[94,]=[11,34,58,82,106,130,154,178,202,226,250,274,298,322,346,370,394,418,442,466,490,514,538,562,586,610,634,658,682,706,730,754,778,802,826,850,874,898,922,946,970,994,1018,1042,1066,1090,1114,1138,1162,1186];
105d[95,]=[9,28,48,68,88,108,128,148,168,188,208,228,248,268,288,308,328,348,368,388,408,428,448,468,488,508,528,548,568,588,608,628,648,668,688,708,728,748,768,788,808,828,848,868,888,908,928,948,968,988];
106d[96,]=[9,40,72,104,136,168,200,232,264,296,328,360,392,424,456,488,520,552,584,616,648,680,712,744,776,808,840,872,904,936,968,1000,1032,1064,1096,1128,1160,1192,1224,1256,1288,1320,1352,1384,1416,1448,1480,1512,1544,1576];
107d[97,]=[7,24,40,56,72,90,104,122,138,154,170,188,202,220,236,252,268,286,300,318,334,350,366,384,398,416,432,448,464,482,496,514,530,546,562,580,594,612,628,644,660,678,692,710,726,742,758,776,790,808];
108d[98,]=[7,34,62,90,118,146,174,202,230,258,286,314,342,370,398,426,454,482,510,538,566,594,622,650,678,706,734,762,790,818,846,874,902,930,958,986,1014,1042,1070,1098,1126,1154,1182,1210,1238,1266,1294,1322,1350,1378];
109d[99,]=[9,32,56,80,104,128,152,176,200,224,248,272,296,320,344,368,392,416,440,464,488,512,536,560,584,608,632,656,680,704,728,752,776,800,824,848,872,896,920,944,968,992,1016,1040,1064,1088,1112,1136,1160,1184];
110d[100,]=[7,36,66,96,126,156,186,216,246,276,306,336,366,396,426,456,486,516,546,576,606,636,666,696,726,756,786,816,846,876,906,936,966,996,1026,1056,1086,1116,1146,1176,1206,1236,1266,1296,1326,1356,1386,1416,1446,1476];
111}
112