# Here follows some code which allows to determine all hyperovals of the line # Grassmannians of the polar spaces Q^+(5,2), Q(6,2) and Q^-(7,2). # Put (v,S1,S2,N1,N2,N3) equal to (105,12,12,7,1,2), (315,18,24,1,1,1) or # (1071,30,48,2,1,1) depending on whether the polar space is isomorphic to # Q^+(5,2), Q(6,2) or Q^-(7,2). # A model of the polar line Grassmannian with point set [1,2,..v], line set # lines and automorphism group g can then be implemented as follows. g:=AllPrimitiveGroups(DegreeOperation,v)[N1]; h:=Stabilizer(g,1); oo:=Orbits(h,[1..v]); O1:=Filtered(oo,x->Size(x)=S1)[N2]; O2:=Filtered(oo,x->Size(x)=S2)[N3]; set1:=Union([1],O1); set2:=OnSets(set1,RepresentativeAction(g,1,O1[1])); plane:=Intersection(set1,set2); planes:=Orbit(g,plane,OnSets); set1:=Union([1],O1,O2); set2:=OnSets(set1,RepresentativeAction(g,1,O2[1])); point:=Intersection(set1,set2); points:=Orbit(g,point,OnSets); i:=1; while Intersection(points[1],planes[i])=[] do i:=i+1; od; line:=Intersection(points[1],planes[i]); lines:=Orbit(g,line,OnSets); # A nonempty set H of points of the line Grassmannian is a hyperoval if its # characteristic vector is orthogonal with the characteristic vectors of all # lines. Based on this observation, the following GAP code allows to determine # all hyperovals. These are stored in an array, called hyperovals. M:=NullMat(v,Size(lines),GF(2)); for i in [1..v] do for j in [1..Size(lines)] do if i in lines[j] then M[i][j]:=Z(2); fi; od; od; Y:=NullspaceMat(M); U:=Subspace(GF(2)^v,Y); hyperovals:=[]; balance:=2^(Dimension(U))-1; while balance>0 do w:=Random(U); if w<>Zero(U) then hyperoval:=Filtered([1..v],i->w[i]=One(GF(2))); new:=true; for i in [1..Length(hyperovals)] do if RepresentativeAction(g,hyperoval,hyperovals[i],OnSets) <> fail then new:=false; break; fi; od; if new then Append(hyperovals,[hyperoval]); balance:=balance-Index(g,Stabilizer(g,hyperoval,OnSets)); fi; fi; od; ############################################################################# # We now list the hyperovals of the line Grassmannian of the hyperbolic # polar space Q^+(5,2). There are up to isomorphism 19 such hyperovals. hyperovals:=0*[1..19]; hyperovals[1]:= [ 1, 4, 6, 7, 8, 13, 15, 16, 18, 20, 21, 22, 23, 30, 33, 40, 44, 45, 46, 48, 51, 61, 62, 63, 70, 71, 72, 73, 77, 78, 81, 85, 86, 88, 93, 95, 96, 98, 99, 101, 102, 103, 104, 105 ]; hyperovals[2]:= [ 1, 2, 4, 5, 7, 13, 14, 16, 17, 18, 19, 20, 22, 25, 26, 27, 29, 30, 32, 33, 34, 38, 39, 41, 42, 44, 45, 46, 49, 51, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 69, 71, 72, 73, 76, 77, 80, 82, 84, 85, 88, 92, 97, 100, 101, 102 ]; hyperovals[3]:= [ 2, 4, 5, 6, 11, 13, 14, 15, 16, 19, 20, 23, 24, 25, 29, 31, 33, 36, 37, 39, 50, 51, 53, 54, 56, 57, 58, 60, 62, 63, 64, 66, 71, 72, 76, 77, 79, 81, 82, 83, 84, 85, 86, 88, 90, 91, 93, 97, 100, 102, 103, 104 ]; hyperovals[4]:= [ 1, 2, 3, 4, 6, 7, 8, 11, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 32, 33, 39, 40, 41, 42, 43, 45, 46, 50, 52, 53, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71, 73, 74, 76, 77, 79, 82, 84, 85, 87, 88, 91, 97, 101, 102 ]; hyperovals[5]:= [ 1, 2, 7, 8, 10, 15, 17, 18, 20, 22, 24, 27, 28, 29, 30, 32, 33, 35, 37, 38, 43, 48, 49, 50, 51, 53, 54, 55, 57, 65, 66, 68, 69, 70, 71, 73, 77, 79, 80, 81, 83, 84, 85, 91, 92, 93, 96, 99, 101, 102, 104, 105 ]; hyperovals[6]:= [ 1, 2, 3, 9, 23, 25, 27, 33, 34, 38, 41, 42, 44, 46, 48, 49, 53, 54, 62, 68, 69, 71, 74, 81, 87, 89, 90, 96, 97, 100, 101, 105 ]; hyperovals[7]:= [ 1, 14, 15, 17, 18, 20, 21, 24, 25, 28, 29, 30, 32, 34, 38, 41, 43, 45, 46, 49, 50, 52, 54, 55, 56, 57, 59, 60, 65, 66, 67, 68, 69, 71, 72, 74, 78, 79, 80, 83, 84, 85, 86, 88, 89, 90, 94, 99, 100, 101, 103, 104 ]; hyperovals[8]:= [ 4, 10, 11, 14, 19, 20, 21, 22, 24, 25, 29, 30, 36, 37, 39, 44, 45, 50, 51, 53, 56, 57, 58, 60, 64, 66, 68, 73, 76, 77, 81, 82, 83, 88, 90, 91, 93, 94, 95, 96, 98, 100, 101, 105 ]; hyperovals[9]:= [ 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 26, 28, 30, 31, 32, 33, 34, 38, 42, 43, 44, 46, 47, 48, 50, 51, 53, 54, 56, 58, 61, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 80, 81, 83, 88, 92, 96, 98, 103, 104 ]; hyperovals[10]:= [ 3, 8, 10, 11, 12, 14, 17, 23, 24, 25, 26, 28, 30, 31, 32, 34, 35, 41, 45, 46, 48, 50, 51, 52, 54, 55, 57, 59, 60, 61, 63, 68, 69, 70, 71, 72, 74, 76, 77, 78, 80, 81, 85, 87, 90, 97, 102, 104 ]; hyperovals[11]:= [ 1, 2, 3, 4, 6, 8, 10, 11, 13, 14, 19, 20, 23, 26, 28, 30, 31, 32, 34, 36, 37, 38, 41, 46, 47, 48, 50, 51, 53, 54, 56, 57, 58, 61, 62, 64, 66, 68, 69, 72, 73, 75, 76, 78, 80, 83, 88, 90, 92, 97, 98, 100, 102, 103, 104, 105 ]; hyperovals[12]:= [ 1, 5, 6, 7, 10, 11, 12, 15, 17, 18, 20, 22, 25, 26, 27, 28, 30, 33, 35, 37, 38, 39, 41, 42, 43, 45, 47, 50, 52, 54, 55, 57, 58, 59, 60, 62, 64, 68, 70, 71, 73, 74, 77, 78, 79, 83, 85, 86, 87, 91, 93, 97, 100, 101, 102, 103 ]; hyperovals[13]:= [ 3, 4, 5, 6, 10, 13, 14, 19, 21, 22, 23, 28, 29, 30, 32, 33, 34, 37, 38, 40, 47, 50, 53, 56, 58, 60, 62, 64, 68, 69, 70, 72, 75, 76, 79, 80, 83, 84, 88, 91, 96, 98, 99, 100, 101, 102, 103, 104 ]; hyperovals[14]:= [ 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 21, 22, 23, 24, 25, 28, 30, 31, 33, 34, 35, 39, 41, 43, 44, 46, 47, 48, 49, 52, 55, 56, 58, 60, 61, 65, 66, 67, 70, 71, 74, 75, 77, 79, 80, 81, 82, 83, 84, 86, 92, 94, 95, 97, 99, 100, 101, 102 ]; hyperovals[15]:= [ 2, 3, 5, 8, 9, 10, 12, 14, 16, 17, 18, 22, 23, 25, 26, 27, 30, 31, 32, 34, 36, 38, 39, 40, 42, 43, 45, 47, 48, 50, 52, 53, 56, 58, 62, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 79, 82, 83, 86, 88, 90, 92, 93, 94, 96, 98, 99, 101, 105 ]; hyperovals[16]:= [ 3, 4, 5, 6, 7, 9, 11, 15, 17, 20, 21, 24, 26, 27, 33, 34, 36, 38, 40, 41, 43, 44, 45, 48, 49, 50, 52, 54, 56, 58, 59, 63, 64, 65, 67, 70, 71, 76, 78, 80, 83, 87, 90, 92, 93, 96, 100, 102 ]; hyperovals[17]:= [ 4, 5, 6, 15, 21, 25, 27, 28, 33, 37, 41, 42, 43, 44, 45, 48, 52, 54, 62, 63, 64, 71, 76, 78, 79, 81, 83, 85, 88, 90, 94, 96, 97, 100, 102, 105 ]; hyperovals[18]:= [ 1, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 20, 21, 22, 24, 25, 28, 31, 33, 34, 35, 36, 37, 39, 40, 42, 44, 47, 49, 51, 52, 54, 55, 56, 57, 58, 60, 65, 67, 68, 71, 73, 74, 76, 78, 80, 81, 84, 86, 88, 90, 92, 93, 95, 98, 101, 103, 104 ]; hyperovals[19]:= [ 3, 5, 7, 8, 11, 17, 18, 19, 24, 25, 36, 37, 43, 47, 48, 49, 52, 53, 54, 55, 63, 64, 65, 72, 82, 83, 95, 98 ]; ############################################################################# # We now list the hyperovals of the line Grassmannian of the parabolic # polar space Q(6,2). There are up to isomorphism 39 such hyperovals. hyperovals:=0*[1..39]; hyperovals[1]:= [ 2, 8, 10, 11, 12, 13, 15, 19, 20, 21, 23, 24, 26, 30, 34, 35, 37, 38, 40, 41, 44, 45, 47, 48, 49, 50, 53, 56, 60, 61, 63, 64, 67, 68, 70, 73, 75, 76, 78, 79, 82, 83, 84, 88, 89, 91, 92, 94, 95, 98, 101, 102, 105, 108, 109, 110, 111, 117, 119, 120, 121, 122, 123, 126, 128, 129, 130, 131, 132, 135, 137, 139, 140, 141, 143, 145, 148, 149, 150, 151, 154, 156, 157, 160, 161, 164, 169, 171, 172, 173, 174, 176, 177, 178, 180, 183, 185, 189, 190, 197, 198, 200, 202, 204, 206, 207, 208, 209, 211, 212, 214, 216, 218, 219, 220, 221, 222, 223, 224, 226, 227, 231, 232, 233, 236, 239, 240, 241, 246, 248, 249, 250, 251, 252, 253, 254, 262, 266, 272, 273, 277, 278, 282, 283, 284, 286, 289, 290, 291, 298, 299, 300, 301, 303, 304, 305, 310, 311, 313, 315 ]; hyperovals[2]:= [ 1, 2, 3, 7, 9, 11, 15, 16, 17, 18, 20, 23, 28, 32, 34, 35, 36, 38, 39, 41, 42, 43, 46, 47, 48, 49, 52, 53, 56, 58, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 76, 78, 81, 82, 84, 86, 89, 90, 91, 92, 94, 99, 104, 108, 112, 114, 117, 119, 121, 123, 130, 133, 134, 137, 138, 139, 140, 141, 142, 143, 144, 145, 148, 150, 154, 156, 157, 158, 159, 160, 162, 163, 164, 166, 170, 172, 173, 174, 175, 176, 180, 181, 182, 183, 184, 187, 188, 189, 191, 194, 195, 198, 202, 203, 207, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 228, 230, 231, 233, 235, 239, 241, 242, 246, 249, 251, 253, 254, 256, 257, 260, 261, 264, 265, 268, 269, 270, 271, 273, 276, 277, 283, 284, 285, 287, 291, 293, 296, 298, 299, 301, 304, 305, 307, 312, 313 ]; hyperovals[3]:= [ 1, 3, 4, 5, 7, 8, 11, 15, 16, 23, 24, 25, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 42, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 58, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 75, 76, 78, 80, 82, 83, 84, 85, 86, 87, 89, 91, 92, 94, 95, 99, 101, 103, 105, 106, 107, 109, 110, 113, 114, 117, 118, 120, 121, 125, 129, 130, 131, 135, 136, 138, 142, 143, 148, 150, 151, 153, 154, 157, 158, 159, 165, 166, 169, 170, 173, 174, 175, 176, 179, 184, 186, 189, 190, 191, 193, 194, 199, 200, 201, 206, 211, 213, 214, 215, 219, 221, 223, 225, 226, 229, 230, 232, 234, 235, 236, 237, 238, 239, 241, 242, 245, 250, 253, 256, 258, 263, 267, 268, 269, 270, 271, 273, 275, 276, 277, 280, 281, 282, 286, 291, 297, 301, 302, 303, 304, 305, 308, 310, 315 ]; hyperovals[4]:= [ 1, 2, 4, 5, 7, 8, 11, 13, 14, 15, 17, 19, 20, 21, 26, 27, 29, 32, 35, 36, 39, 40, 43, 44, 47, 49, 50, 51, 53, 54, 55, 56, 60, 63, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 79, 83, 84, 85, 86, 88, 89, 91, 94, 95, 97, 98, 100, 104, 106, 110, 112, 114, 115, 116, 118, 120, 122, 127, 128, 132, 135, 136, 138, 140, 143, 144, 146, 147, 148, 151, 152, 153, 155, 157, 161, 163, 164, 165, 168, 169, 170, 173, 174, 178, 180, 183, 186, 187, 189, 190, 191, 196, 197, 198, 200, 203, 205, 206, 207, 210, 212, 214, 217, 223, 224, 225, 228, 229, 231, 233, 235, 236, 239, 242, 243, 246, 247, 248, 249, 250, 251, 255, 256, 257, 258, 259, 262, 265, 266, 269, 270, 272, 273, 274, 278, 279, 282, 288, 290, 292, 293, 294, 297, 298, 301, 303, 304, 313, 315 ]; hyperovals[5]:= [ 1, 3, 4, 7, 8, 15, 16, 17, 18, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 41, 45, 46, 50, 51, 52, 54, 56, 62, 64, 66, 67, 69, 70, 71, 74, 75, 78, 79, 80, 81, 84, 85, 86, 87, 88, 92, 93, 97, 99, 100, 101, 102, 104, 105, 107, 109, 111, 114, 116, 122, 123, 124, 126, 127, 128, 129, 131, 132, 139, 140, 141, 144, 145, 146, 149, 154, 155, 157, 158, 159, 162, 168, 169, 170, 174, 180, 181, 182, 187, 189, 192, 193, 194, 195, 196, 198, 201, 203, 204, 206, 207, 209, 211, 213, 214, 216, 219, 220, 223, 224, 225, 226, 228, 230, 231, 232, 235, 236, 239, 240, 246, 247, 248, 251, 252, 254, 255, 258, 259, 260, 261, 264, 265, 271, 273, 274, 275, 276, 277, 279, 280, 281, 287, 294, 300, 301, 305, 306, 313, 314 ]; hyperovals[6]:= [ 2, 5, 8, 10, 11, 12, 15, 22, 24, 25, 26, 27, 29, 31, 32, 33, 35, 36, 37, 40, 43, 44, 45, 48, 50, 54, 56, 57, 58, 60, 61, 62, 67, 70, 71, 72, 75, 78, 82, 83, 84, 87, 88, 90, 91, 93, 94, 96, 97, 99, 102, 108, 111, 112, 114, 115, 116, 117, 118, 120, 121, 123, 126, 129, 130, 131, 133, 134, 137, 138, 139, 142, 143, 145, 148, 149, 154, 155, 157, 158, 162, 163, 165, 166, 168, 169, 175, 176, 179, 181, 182, 184, 188, 190, 191, 192, 193, 196, 197, 199, 200, 201, 202, 204, 207, 209, 210, 214, 217, 218, 221, 224, 225, 226, 227, 229, 231, 233, 234, 236, 237, 241, 243, 244, 245, 246, 248, 253, 255, 256, 257, 258, 260, 264, 266, 267, 269, 271, 273, 274, 276, 277, 278, 279, 280, 282, 283, 284, 289, 290, 291, 295, 298, 305, 307, 309, 310, 311, 312, 313 ]; hyperovals[7]:= [ 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 21, 25, 26, 27, 28, 30, 31, 32, 36, 37, 41, 42, 43, 48, 49, 50, 51, 53, 56, 59, 66, 67, 68, 73, 74, 75, 76, 77, 78, 80, 83, 84, 85, 86, 87, 89, 90, 91, 96, 97, 99, 101, 103, 104, 105, 106, 107, 112, 122, 123, 124, 128, 134, 135, 136, 137, 139, 140, 142, 143, 145, 147, 151, 154, 156, 164, 165, 166, 168, 171, 172, 173, 174, 175, 176, 178, 179, 184, 187, 191, 192, 193, 194, 197, 198, 199, 200, 204, 206, 208, 209, 210, 213, 215, 217, 218, 219, 222, 223, 224, 227, 231, 233, 235, 236, 237, 240, 241, 243, 244, 245, 248, 249, 251, 253, 254, 256, 257, 258, 260, 261, 263, 264, 265, 267, 269, 270, 271, 273, 275, 276, 278, 279, 280, 281, 282, 283, 285, 287, 288, 289, 290, 291, 292, 294, 296, 297, 299, 300, 301, 302, 303, 308, 310, 311, 313 ]; hyperovals[8]:= [ 3, 5, 8, 9, 12, 17, 18, 20, 21, 23, 25, 29, 30, 32, 33, 34, 37, 38, 40, 44, 46, 47, 48, 49, 51, 52, 54, 55, 58, 59, 60, 61, 67, 68, 69, 70, 71, 72, 80, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 101, 104, 107, 109, 110, 112, 113, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 127, 131, 132, 134, 135, 136, 137, 138, 139, 142, 148, 149, 150, 151, 152, 157, 158, 161, 163, 164, 166, 167, 169, 170, 171, 172, 174, 176, 177, 180, 182, 183, 185, 189, 191, 192, 193, 194, 195, 197, 198, 200, 202, 204, 205, 208, 212, 213, 214, 220, 221, 222, 225, 227, 228, 230, 232, 233, 234, 236, 237, 238, 239, 242, 244, 246, 248, 249, 250, 252, 257, 258, 259, 262, 263, 266, 268, 269, 271, 276, 278, 279, 280, 282, 284, 286, 287, 288, 291, 294, 296, 300, 301, 305, 306, 307, 309, 311, 315 ]; hyperovals[9]:= [ 2, 3, 5, 7, 11, 12, 16, 18, 19, 20, 23, 24, 27, 28, 30, 31, 32, 33, 34, 36, 37, 39, 41, 44, 47, 52, 53, 54, 55, 56, 57, 58, 62, 63, 64, 66, 67, 68, 69, 72, 75, 76, 77, 78, 81, 82, 83, 85, 90, 94, 95, 99, 100, 102, 103, 104, 105, 106, 107, 110, 116, 118, 122, 127, 128, 129, 130, 133, 134, 135, 136, 138, 139, 141, 147, 150, 151, 161, 164, 166, 167, 168, 172, 173, 176, 178, 179, 180, 183, 184, 185, 188, 190, 191, 195, 196, 198, 199, 201, 202, 205, 207, 209, 210, 212, 213, 216, 217, 218, 225, 226, 229, 231, 232, 233, 240, 241, 245, 248, 251, 252, 255, 256, 257, 261, 263, 264, 265, 268, 269, 271, 272, 274, 277, 278, 280, 281, 282, 285, 288, 290, 295, 297, 299, 300, 301, 303, 306, 307, 311, 313, 315 ]; hyperovals[10]:= [ 4, 6, 9, 10, 13, 14, 22, 25, 27, 33, 39, 42, 46, 47, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 65, 67, 68, 69, 71, 74, 75, 76, 78, 79, 80, 82, 83, 84, 86, 87, 89, 91, 93, 96, 97, 99, 101, 102, 103, 104, 112, 114, 117, 118, 119, 123, 125, 128, 129, 131, 132, 134, 136, 137, 142, 143, 145, 146, 151, 152, 153, 157, 161, 164, 165, 167, 168, 169, 170, 171, 173, 174, 175, 177, 178, 181, 184, 185, 186, 187, 188, 189, 191, 192, 196, 197, 199, 203, 205, 207, 209, 210, 211, 212, 219, 222, 227, 228, 229, 230, 231, 232, 233, 235, 236, 240, 241, 243, 244, 245, 246, 251, 254, 257, 258, 259, 260, 261, 263, 264, 265, 266, 267, 271, 272, 276, 279, 280, 284, 285, 287, 288, 291, 296, 300, 301, 303, 305, 310, 311, 313, 315 ]; hyperovals[11]:= [ 1, 2, 9, 10, 13, 14, 15, 16, 25, 26, 35, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 55, 56, 59, 62, 63, 66, 68, 71, 73, 74, 77, 80, 81, 84, 85, 87, 88, 90, 91, 95, 97, 98, 101, 104, 105, 107, 108, 110, 111, 113, 114, 117, 123, 124, 129, 130, 138, 141, 142, 143, 145, 147, 149, 150, 151, 154, 155, 157, 160, 161, 164, 167, 172, 176, 177, 180, 181, 182, 185, 187, 188, 189, 190, 192, 194, 195, 197, 199, 201, 203, 204, 205, 208, 209, 210, 213, 214, 216, 218, 220, 221, 222, 223, 224, 225, 226, 228, 231, 232, 233, 234, 235, 236, 238, 241, 243, 246, 248, 249, 250, 252, 254, 255, 257, 260, 261, 262, 265, 266, 267, 268, 273, 275, 282, 288, 289, 290, 291, 294, 296, 300, 301, 302, 303, 308, 310, 312, 313 ]; hyperovals[12]:= [ 2, 4, 5, 8, 9, 12, 13, 16, 17, 21, 22, 30, 31, 33, 34, 40, 45, 48, 51, 59, 61, 64, 65, 73, 74, 76, 78, 83, 86, 89, 91, 92, 93, 94, 95, 96, 99, 100, 103, 104, 106, 108, 110, 112, 113, 114, 115, 122, 129, 130, 133, 135, 137, 139, 141, 142, 146, 147, 148, 149, 152, 154, 156, 160, 162, 165, 166, 167, 168, 171, 172, 174, 180, 185, 187, 191, 193, 196, 199, 201, 202, 203, 204, 205, 207, 210, 213, 214, 215, 220, 221, 222, 224, 230, 236, 239, 240, 241, 242, 243, 245, 247, 248, 249, 251, 252, 253, 254, 256, 258, 260, 261, 262, 264, 265, 267, 268, 272, 273, 277, 278, 282, 283, 285, 286, 289, 290, 291, 292, 295, 297, 298, 300, 301, 302, 303, 304, 306, 307, 308, 309, 310, 313, 314 ]; hyperovals[13]:= [ 2, 3, 6, 7, 8, 9, 12, 13, 14, 15, 16, 20, 24, 26, 27, 28, 31, 33, 34, 35, 36, 38, 40, 41, 43, 44, 47, 49, 52, 55, 56, 58, 60, 65, 68, 70, 72, 73, 75, 76, 78, 79, 81, 84, 86, 89, 90, 93, 94, 95, 96, 98, 105, 106, 110, 111, 113, 115, 116, 117, 121, 122, 124, 127, 128, 129, 132, 135, 136, 137, 138, 141, 144, 145, 146, 147, 148, 149, 152, 153, 154, 155, 156, 158, 160, 165, 166, 167, 169, 170, 171, 172, 174, 175, 177, 180, 181, 183, 184, 187, 188, 189, 190, 193, 195, 197, 198, 199, 204, 206, 208, 211, 212, 213, 214, 218, 219, 221, 223, 224, 227, 229, 230, 231, 232, 234, 236, 237, 240, 241, 243, 246, 247, 250, 252, 253, 255, 257, 258, 260, 261, 264, 267, 269, 271, 280, 284, 285, 289, 292, 293, 295, 297, 299, 302, 306, 307, 308, 313, 314 ]; hyperovals[14]:= [ 2, 3, 5, 6, 8, 12, 13, 15, 16, 17, 19, 20, 22, 23, 26, 28, 30, 32, 33, 38, 40, 41, 42, 43, 46, 47, 48, 49, 50, 51, 52, 53, 57, 58, 59, 61, 62, 63, 67, 68, 69, 72, 74, 75, 77, 78, 80, 81, 82, 85, 87, 90, 91, 93, 94, 97, 99, 100, 106, 108, 111, 112, 113, 114, 119, 120, 123, 125, 127, 130, 131, 133, 136, 138, 139, 140, 144, 145, 146, 147, 152, 153, 154, 158, 159, 161, 162, 163, 164, 165, 168, 170, 173, 176, 177, 179, 180, 185, 188, 189, 190, 191, 193, 194, 195, 196, 198, 199, 202, 208, 213, 216, 217, 218, 221, 223, 224, 226, 227, 228, 229, 231, 232, 233, 234, 237, 239, 240, 242, 246, 247, 248, 249, 250, 253, 254, 256, 260, 263, 266, 268, 269, 272, 274, 278, 279, 281, 282, 283, 284, 287, 288, 290, 292, 293, 294, 296, 299, 300, 302, 303, 304, 305, 306, 308, 309, 312, 314 ]; hyperovals[15]:= [ 2, 4, 6, 10, 11, 15, 16, 17, 20, 25, 27, 30, 31, 34, 37, 38, 44, 45, 46, 47, 52, 53, 56, 57, 59, 61, 62, 63, 65, 70, 71, 79, 80, 85, 92, 93, 94, 96, 97, 100, 104, 105, 106, 107, 108, 110, 117, 119, 120, 121, 122, 123, 124, 127, 129, 130, 133, 134, 136, 138, 140, 141, 142, 146, 149, 151, 152, 153, 156, 158, 161, 166, 169, 170, 171, 177, 178, 179, 180, 181, 184, 186, 189, 190, 192, 193, 194, 195, 197, 202, 203, 204, 205, 206, 207, 209, 212, 221, 225, 227, 233, 239, 240, 243, 245, 248, 249, 255, 256, 257, 259, 262, 264, 267, 268, 270, 273, 277, 279, 280, 281, 285, 287, 288, 289, 292, 293, 297, 298, 300, 303, 304, 307, 309, 310, 311 ]; hyperovals[16]:= [ 2, 6, 10, 11, 12, 13, 15, 19, 21, 22, 30, 31, 32, 33, 34, 35, 37, 38, 40, 45, 46, 50, 51, 52, 54, 56, 63, 64, 65, 66, 67, 68, 69, 71, 74, 75, 78, 79, 80, 81, 85, 87, 91, 93, 95, 96, 97, 99, 101, 102, 105, 107, 109, 111, 116, 118, 120, 122, 123, 124, 127, 128, 130, 132, 133, 136, 137, 140, 144, 145, 147, 153, 157, 158, 159, 162, 163, 166, 167, 169, 170, 171, 172, 173, 176, 177, 178, 180, 181, 182, 183, 185, 187, 188, 189, 191, 192, 193, 194, 195, 196, 200, 201, 202, 203, 204, 205, 206, 207, 210, 211, 212, 213, 215, 216, 217, 218, 220, 221, 223, 224, 226, 230, 231, 232, 233, 236, 237, 238, 239, 240, 242, 245, 246, 248, 250, 253, 254, 258, 259, 261, 262, 264, 269, 270, 271, 273, 274, 275, 279, 286, 287, 289, 292, 293, 294, 295, 299, 300, 301, 303, 304, 306, 308, 309, 313, 314, 315 ]; 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hyperovals[35]:= [ 6, 11, 15, 16, 20, 21, 23, 26, 27, 29, 34, 35, 37, 38, 39, 45, 46, 55, 60, 66, 71, 72, 74, 77, 78, 79, 82, 83, 86, 87, 88, 89, 91, 97, 99, 102, 103, 106, 107, 108, 111, 114, 116, 119, 121, 124, 135, 136, 139, 141, 145, 147, 148, 156, 158, 160, 161, 163, 172, 174, 179, 182, 187, 189, 193, 195, 196, 198, 199, 200, 209, 212, 215, 222, 227, 231, 234, 241, 242, 246, 248, 252, 254, 259, 265, 272, 278, 282, 287, 291, 296, 302, 306, 310, 312, 314 ]; hyperovals[36]:= [ 1, 5, 6, 8, 12, 15, 17, 21, 27, 28, 29, 31, 34, 35, 38, 40, 41, 46, 49, 52, 55, 61, 68, 69, 72, 73, 75, 79, 80, 81, 84, 86, 88, 90, 91, 92, 93, 94, 98, 99, 101, 103, 106, 110, 115, 116, 117, 118, 119, 122, 132, 134, 137, 139, 145, 148, 149, 151, 153, 155, 157, 158, 160, 161, 162, 165, 166, 167, 171, 172, 173, 174, 175, 176, 177, 180, 181, 188, 191, 193, 196, 199, 200, 206, 208, 210, 212, 213, 216, 217, 219, 221, 222, 225, 228, 233, 238, 240, 241, 244, 246, 247, 248, 250, 251, 252, 253, 256, 261, 262, 266, 267, 268, 272, 277, 279, 280, 283, 288, 289, 294, 295, 296, 297, 303, 304, 307, 308 ]; hyperovals[37]:= [ 2, 3, 4, 6, 16, 17, 18, 24, 25, 26, 27, 29, 31, 33, 34, 38, 41, 45, 46, 48, 49, 50, 51, 52, 62, 63, 64, 66, 68, 69, 72, 73, 74, 78, 83, 84, 86, 88, 89, 90, 93, 96, 98, 100, 101, 102, 109, 110, 112, 117, 118, 122, 124, 127, 134, 135, 137, 138, 146, 148, 149, 151, 153, 155, 156, 157, 158, 159, 173, 175, 176, 177, 183, 188, 193, 196, 199, 200, 202, 204, 205, 207, 211, 212, 213, 214, 216, 217, 219, 224, 225, 233, 234, 236, 238, 239, 241, 242, 243, 248, 249, 250, 252, 253, 256, 257, 259, 261, 268, 272, 278, 279, 280, 285, 291, 301, 302, 306, 307, 314 ]; hyperovals[38]:= [ 1, 2, 5, 8, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 27, 30, 35, 38, 41, 44, 51, 52, 55, 56, 59, 60, 64, 68, 72, 75, 76, 78, 79, 81, 83, 88, 90, 91, 94, 96, 97, 98, 99, 109, 110, 113, 116, 119, 121, 125, 128, 129, 131, 135, 137, 138, 145, 149, 153, 155, 157, 158, 161, 165, 168, 169, 171, 172, 175, 180, 181, 183, 189, 194, 196, 201, 203, 206, 213, 217, 219, 221, 223, 224, 226, 227, 231, 232, 234, 249, 251, 252, 258, 259, 265, 266, 267, 268, 269, 274, 275, 276, 277, 279, 280, 281, 282, 284, 291, 293, 295, 297, 298, 299, 300, 301, 313, 314 ]; hyperovals[39]:= [ 1, 2, 7, 9, 10, 14, 15, 16, 19, 20, 21, 23, 27, 30, 31, 33, 34, 35, 39, 42, 43, 49, 51, 52, 54, 55, 57, 59, 61, 62, 63, 65, 66, 67, 71, 73, 75, 76, 80, 82, 83, 84, 85, 87, 88, 89, 92, 95, 97, 98, 99, 100, 104, 105, 108, 109, 110, 115, 116, 119, 121, 122, 123, 128, 129, 135, 136, 138, 140, 142, 143, 144, 147, 148, 149, 153, 154, 155, 159, 164, 165, 167, 171, 172, 174, 177, 178, 179, 181, 184, 186, 187, 188, 189, 190, 192, 194, 196, 198, 200, 202, 207, 210, 211, 215, 216, 218, 223, 224, 225, 226, 228, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 245, 246, 247, 249, 257, 258, 259, 263, 265, 266, 267, 269, 271, 272, 273, 274, 278, 279, 281, 282, 283, 284, 285, 288, 296, 298, 299, 301, 302, 303, 304, 306, 307, 311, 312, 313, 314, 315 ]; fi; ############################################################################# # We now list the hyperovals of the line Grassmannian of the elliptic # polar space Q^-(7,2). There are up to isomorphism 54 such hyperovals. hyperovals:=0*[1..54]; hyperovals[1]:= [ 1, 3, 4, 5, 7, 8, 12, 13, 15, 18, 20, 21, 22, 24, 26, 27, 28, 31, 34, 36, 38, 39, 40, 42, 49, 51, 56, 57, 58, 59, 63, 64, 69, 72, 75, 76, 77, 78, 79, 81, 83, 84, 87, 89, 90, 91, 96, 98, 99, 100, 104, 112, 116, 121, 122, 123, 124, 126, 128, 129, 130, 132, 133, 137, 142, 143, 144, 146, 147, 148, 150, 151, 153, 154, 156, 157, 158, 159, 161, 162, 163, 165, 168, 173, 175, 176, 181, 183, 184, 185, 186, 190, 191, 196, 201, 202, 203, 206, 208, 221, 222, 223, 224, 227, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 241, 242, 243, 244, 245, 247, 249, 251, 252, 256, 257, 258, 259, 260, 261, 262, 263, 267, 268, 269, 270, 271, 274, 276, 277, 280, 282, 284, 286, 288, 289, 290, 291, 292, 293, 297, 298, 299, 301, 304, 306, 307, 309, 310, 311, 313, 316, 318, 319, 320, 324, 325, 327, 331, 333, 334, 335, 338, 339, 344, 345, 346, 347, 351, 357, 359, 361, 364, 365, 366, 368, 371, 378, 380, 382, 383, 384, 386, 389, 391, 392, 393, 394, 398, 400, 401, 402, 403, 405, 406, 417, 418, 420, 421, 422, 424, 425, 426, 429, 432, 433, 435, 437, 440, 441, 444, 447, 449, 450, 453, 456, 459, 460, 463, 464, 465, 472, 476, 477, 479, 480, 482, 483, 484, 486, 487, 490, 491, 492, 494, 496, 498, 499, 501, 502, 505, 512, 514, 518, 519, 522, 523, 526, 527, 528, 529, 531, 534, 535, 536, 540, 541, 542, 543, 544, 546, 547, 549, 550, 551, 556, 557, 559, 562, 563, 564, 565, 568, 570, 574, 576, 577, 578, 581, 582, 584, 589, 590, 593, 600, 601, 602, 606, 608, 610, 613, 616, 618, 621, 625, 626, 627, 629, 630, 631, 635, 636, 643, 645, 648, 649, 652, 655, 656, 658, 659, 662, 665, 667, 669, 670, 671, 674, 675, 679, 680, 681, 682, 684, 685, 686, 687, 696, 697, 705, 706, 712, 716, 718, 724, 726, 727, 731, 732, 734, 736, 737, 738, 740, 746, 748, 749, 752, 753, 754, 755, 756, 757, 760, 761, 762, 763, 767, 768, 769, 771, 772, 774, 775, 776, 777, 779, 782, 785, 798, 800, 801, 806, 808, 811, 812, 813, 814, 815, 818, 820, 821, 824, 826, 828, 830, 832, 836, 837, 841, 842, 843, 844, 845, 849, 851, 854, 855, 857, 860, 861, 864, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 878, 879, 881, 883, 884, 885, 887, 892, 893, 895, 897, 898, 901, 902, 906, 907, 910, 911, 920, 924, 925, 927, 930, 932, 934, 935, 936, 937, 940, 941, 943, 945, 949, 951, 954, 958, 959, 960, 961, 963, 967, 969, 973, 977, 986, 988, 994, 996, 999, 1000, 1001, 1003, 1009, 1010, 1011, 1013, 1015, 1016, 1018, 1021, 1023, 1025, 1026, 1027, 1030, 1031, 1034, 1035, 1036, 1037, 1040, 1041, 1042, 1046, 1047, 1048, 1051, 1052, 1054, 1055, 1056, 1057, 1059, 1063, 1064, 1065, 1068, 1069, 1070, 1071 ]; hyperovals[2]:= [ 1, 3, 5, 6, 7, 8, 12, 15, 16, 17, 19, 20, 24, 26, 27, 31, 35, 37, 40, 48, 49, 52, 57, 59, 60, 61, 64, 66, 67, 68, 69, 70, 71, 73, 77, 78, 80, 83, 85, 87, 91, 96, 99, 100, 101, 103, 104, 109, 110, 111, 113, 114, 119, 121, 125, 128, 130, 131, 133, 134, 137, 138, 139, 142, 147, 148, 151, 152, 154, 155, 157, 158, 160, 162, 164, 165, 168, 169, 170, 172, 178, 179, 181, 183, 184, 186, 191, 192, 194, 197, 202, 203, 205, 207, 208, 209, 210, 212, 215, 216, 220, 226, 228, 231, 234, 235, 237, 239, 240, 241, 242, 243, 245, 247, 248, 251, 253, 258, 259, 262, 264, 265, 268, 271, 273, 274, 275, 277, 279, 284, 285, 286, 287, 289, 292, 294, 296, 298, 299, 302, 303, 305, 308, 312, 316, 319, 321, 322, 324, 326, 327, 330, 334, 338, 339, 341, 343, 345, 347, 349, 353, 355, 357, 358, 363, 365, 367, 368, 373, 376, 377, 379, 380, 381, 382, 383, 384, 386, 387, 388, 391, 392, 393, 394, 396, 397, 398, 399, 401, 405, 406, 407, 412, 414, 418, 419, 422, 423, 427, 429, 430, 431, 434, 435, 440, 441, 444, 449, 450, 451, 452, 456, 459, 460, 461, 467, 470, 471, 472, 474, 475, 476, 480, 482, 483, 484, 486, 488, 489, 491, 492, 494, 497, 498, 499, 502, 503, 505, 507, 512, 514, 517, 518, 520, 521, 524, 527, 534, 537, 538, 540, 541, 543, 544, 546, 548, 549, 550, 555, 557, 560, 562, 565, 569, 570, 572, 575, 576, 579, 580, 582, 587, 589, 591, 593, 594, 596, 597, 598, 599, 601, 604, 605, 606, 607, 608, 609, 610, 617, 618, 619, 620, 622, 624, 631, 632, 633, 637, 640, 642, 644, 645, 647, 649, 651, 654, 656, 657, 658, 659, 660, 661, 662, 663, 664, 669, 671, 673, 674, 678, 679, 680, 681, 682, 683, 687, 690, 691, 692, 693, 694, 698, 699, 701, 703, 704, 705, 706, 708, 709, 711, 715, 718, 719, 721, 723, 724, 725, 730, 731, 735, 736, 740, 741, 742, 743, 745, 746, 747, 750, 751, 754, 755, 756, 757, 759, 762, 765, 767, 768, 769, 772, 776, 779, 781, 783, 784, 788, 789, 790, 793, 794, 795, 797, 800, 801, 802, 805, 807, 808, 810, 811, 812, 814, 815, 817, 819, 822, 823, 825, 829, 834, 835, 836, 838, 840, 841, 842, 843, 847, 850, 851, 853, 854, 855, 857, 860, 862, 863, 864, 865, 866, 867, 869, 870, 871, 872, 873, 876, 878, 880, 881, 882, 884, 888, 890, 891, 894, 895, 896, 898, 899, 902, 903, 905, 907, 909, 910, 912, 914, 918, 919, 920, 921, 922, 925, 926, 931, 932, 933, 934, 935, 937, 938, 939, 942, 944, 949, 951, 952, 954, 956, 959, 961, 962, 963, 964, 970, 971, 972, 973, 975, 976, 977, 978, 982, 983, 984, 985, 987, 988, 993, 995, 997, 999, 1000, 1003, 1004, 1005, 1010, 1014, 1026, 1027, 1028, 1029, 1030, 1031, 1034, 1035, 1036, 1037, 1041, 1045, 1046, 1047, 1049, 1051, 1052, 1053, 1055, 1056, 1057, 1059, 1060, 1062, 1063, 1068, 1070 ]; hyperovals[3]:= [ 2, 7, 8, 11, 14, 15, 18, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 40, 41, 42, 44, 47, 49, 50, 51, 52, 53, 54, 56, 58, 59, 64, 69, 72, 73, 74, 76, 79, 80, 81, 82, 83, 84, 85, 87, 89, 90, 91, 92, 93, 95, 96, 97, 104, 105, 106, 108, 110, 111, 112, 113, 115, 116, 117, 118, 119, 121, 123, 124, 130, 131, 132, 136, 137, 139, 142, 146, 147, 148, 149, 151, 155, 161, 163, 167, 168, 175, 178, 179, 181, 183, 185, 186, 187, 188, 191, 192, 197, 198, 201, 204, 206, 208, 210, 213, 215, 216, 221, 223, 226, 229, 231, 232, 233, 234, 235, 237, 239, 246, 247, 248, 249, 252, 254, 256, 258, 259, 260, 263, 264, 265, 266, 270, 271, 274, 277, 278, 279, 280, 281, 282, 284, 286, 288, 289, 290, 291, 292, 293, 294, 296, 300, 301, 302, 304, 306, 309, 311, 312, 314, 317, 318, 319, 320, 322, 325, 326, 329, 332, 333, 334, 337, 339, 344, 348, 350, 351, 353, 354, 355, 358, 359, 361, 362, 363, 365, 366, 368, 371, 374, 375, 376, 377, 378, 380, 381, 382, 383, 384, 385, 386, 387, 389, 392, 394, 395, 398, 400, 402, 403, 405, 406, 410, 414, 416, 418, 419, 425, 426, 429, 430, 432, 435, 437, 438, 440, 441, 444, 450, 452, 453, 454, 455, 456, 459, 460, 462, 463, 464, 465, 470, 474, 475, 477, 480, 481, 484, 485, 493, 497, 499, 502, 503, 510, 512, 513, 514, 515, 517, 518, 519, 520, 521, 522, 524, 525, 526, 527, 529, 531, 532, 536, 538, 540, 542, 543, 544, 545, 546, 549, 550, 551, 552, 557, 558, 561, 562, 563, 566, 568, 572, 573, 574, 580, 581, 585, 586, 588, 589, 592, 593, 594, 596, 598, 600, 601, 604, 612, 613, 616, 621, 624, 627, 628, 629, 630, 633, 635, 637, 641, 647, 649, 652, 653, 654, 659, 661, 664, 667, 669, 674, 676, 677, 681, 682, 684, 687, 688, 696, 697, 698, 703, 704, 706, 708, 710, 711, 712, 715, 716, 718, 719, 720, 726, 727, 728, 731, 735, 737, 738, 740, 741, 742, 743, 745, 748, 751, 752, 753, 754, 755, 756, 760, 761, 763, 764, 766, 769, 770, 772, 774, 775, 778, 779, 785, 786, 793, 795, 799, 800, 802, 803, 805, 806, 807, 808, 811, 813, 816, 817, 818, 821, 822, 823, 824, 826, 827, 828, 829, 830, 831, 834, 840, 841, 842, 844, 848, 849, 850, 852, 855, 856, 857, 858, 861, 863, 864, 868, 869, 871, 873, 874, 875, 876, 879, 880, 881, 883, 885, 886, 889, 893, 894, 895, 897, 898, 900, 901, 902, 903, 905, 906, 907, 911, 912, 913, 917, 922, 923, 925, 927, 930, 932, 933, 934, 935, 936, 937, 939, 940, 941, 942, 944, 945, 946, 947, 948, 950, 952, 953, 954, 955, 958, 960, 967, 968, 970, 974, 975, 977, 980, 982, 985, 986, 987, 989, 990, 994, 998, 999, 1001, 1002, 1007, 1009, 1010, 1011, 1013, 1016, 1018, 1019, 1020, 1021, 1023, 1025, 1026, 1028, 1029, 1030, 1031, 1032, 1033, 1038, 1039, 1040, 1041, 1045, 1047, 1048, 1050, 1051, 1054, 1056, 1057, 1059, 1062, 1063, 1065, 1066, 1068, 1070 ]; hyperovals[4]:= [ 1, 2, 5, 7, 8, 10, 11, 15, 16, 17, 18, 19, 20, 21, 24, 26, 27, 29, 35, 36, 39, 41, 42, 43, 45, 48, 49, 51, 53, 56, 57, 58, 60, 61, 62, 66, 67, 68, 75, 76, 78, 83, 89, 93, 96, 97, 98, 99, 101, 104, 106, 108, 111, 112, 113, 115, 123, 124, 126, 129, 130, 131, 133, 137, 140, 148, 153, 156, 157, 158, 160, 163, 165, 167, 168, 177, 178, 179, 180, 181, 182, 185, 186, 187, 189, 194, 196, 197, 198, 202, 205, 207, 209, 210, 214, 215, 221, 223, 225, 226, 227, 228, 231, 233, 236, 237, 238, 241, 242, 243, 245, 254, 255, 258, 259, 261, 263, 265, 268, 269, 271, 273, 275, 276, 277, 278, 280, 281, 282, 286, 287, 291, 294, 297, 298, 301, 302, 304, 305, 309, 311, 312, 315, 318, 319, 325, 326, 329, 330, 335, 336, 338, 341, 344, 345, 350, 352, 353, 354, 355, 356, 358, 362, 363, 364, 365, 366, 367, 368, 369, 370, 372, 373, 374, 377, 380, 381, 384, 386, 387, 389, 392, 393, 395, 396, 399, 401, 402, 404, 407, 408, 410, 414, 415, 416, 417, 420, 421, 426, 429, 431, 432, 433, 434, 435, 436, 437, 439, 441, 449, 452, 456, 457, 458, 459, 462, 463, 464, 466, 467, 468, 469, 472, 477, 478, 482, 483, 486, 487, 488, 490, 492, 494, 495, 497, 500, 501, 502, 503, 505, 506, 509, 511, 513, 519, 520, 521, 523, 524, 525, 527, 532, 533, 538, 539, 542, 544, 545, 546, 547, 549, 550, 552, 553, 559, 561, 564, 566, 569, 573, 576, 577, 580, 584, 586, 587, 591, 592, 595, 599, 601, 602, 603, 604, 605, 610, 611, 620, 621, 625, 630, 632, 634, 635, 637, 639, 641, 642, 643, 645, 646, 647, 648, 651, 653, 655, 660, 663, 669, 670, 674, 675, 676, 678, 680, 683, 685, 691, 697, 698, 705, 707, 708, 710, 713, 714, 716, 717, 719, 722, 725, 726, 727, 728, 730, 732, 733, 734, 735, 736, 737, 738, 740, 742, 744, 745, 746, 749, 751, 752, 754, 757, 761, 762, 764, 765, 768, 769, 772, 776, 777, 778, 780, 782, 783, 785, 786, 789, 790, 791, 795, 798, 800, 802, 807, 811, 812, 816, 819, 820, 823, 824, 825, 827, 832, 834, 835, 837, 838, 839, 842, 853, 855, 856, 858, 859, 860, 861, 862, 863, 865, 866, 868, 871, 873, 875, 876, 877, 878, 879, 882, 883, 884, 889, 890, 892, 894, 899, 900, 901, 904, 905, 907, 908, 909, 910, 911, 916, 917, 918, 919, 920, 921, 923, 926, 927, 932, 935, 936, 937, 939, 944, 950, 952, 953, 956, 957, 962, 963, 964, 965, 968, 969, 975, 976, 978, 981, 983, 987, 991, 997, 999, 1003, 1006, 1009, 1011, 1013, 1017, 1018, 1019, 1020, 1021, 1023, 1024, 1025, 1030, 1031, 1035, 1036, 1037, 1039, 1040, 1043, 1044, 1046, 1047, 1048, 1052, 1059, 1060, 1061, 1065, 1066, 1068, 1070, 1071 ]; hyperovals[5]:= [ 2, 5, 6, 7, 8, 9, 12, 14, 18, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 37, 39, 42, 45, 46, 48, 50, 51, 52, 55, 59, 61, 62, 65, 67, 68, 73, 75, 76, 77, 78, 79, 80, 83, 84, 93, 94, 95, 96, 97, 98, 99, 102, 103, 105, 109, 111, 112, 114, 115, 119, 122, 123, 124, 125, 131, 133, 134, 135, 136, 139, 140, 141, 142, 143, 144, 148, 149, 151, 153, 155, 156, 159, 160, 161, 165, 166, 171, 172, 173, 175, 176, 177, 179, 180, 182, 187, 188, 189, 190, 193, 195, 196, 197, 198, 199, 200, 201, 202, 204, 205, 206, 212, 216, 218, 220, 226, 235, 236, 237, 240, 244, 246, 250, 253, 254, 255, 256, 258, 260, 261, 262, 263, 264, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 278, 279, 280, 283, 284, 286, 287, 288, 291, 295, 296, 299, 300, 304, 305, 309, 310, 311, 313, 314, 318, 320, 321, 323, 324, 325, 329, 330, 337, 338, 342, 343, 344, 346, 347, 348, 349, 350, 352, 353, 357, 358, 359, 360, 363, 364, 376, 377, 379, 381, 383, 384, 385, 386, 387, 390, 391, 395, 398, 399, 401, 402, 405, 406, 414, 415, 416, 419, 420, 422, 425, 427, 429, 430, 431, 437, 443, 444, 445, 446, 448, 449, 456, 457, 458, 459, 460, 462, 466, 467, 468, 470, 472, 473, 476, 480, 481, 483, 484, 485, 487, 489, 491, 493, 494, 495, 496, 498, 502, 503, 504, 505, 507, 509, 512, 514, 516, 518, 520, 522, 523, 527, 529, 533, 535, 536, 537, 538, 541, 542, 544, 548, 550, 551, 553, 554, 557, 560, 561, 562, 563, 564, 569, 570, 571, 573, 574, 575, 581, 584, 585, 590, 591, 593, 601, 602, 603, 604, 606, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 620, 622, 623, 625, 627, 629, 630, 631, 632, 634, 635, 638, 639, 642, 648, 649, 652, 654, 658, 660, 661, 662, 666, 668, 670, 672, 675, 676, 680, 681, 682, 683, 684, 685, 686, 687, 690, 691, 692, 693, 696, 698, 700, 703, 704, 707, 708, 709, 710, 711, 713, 715, 716, 718, 719, 721, 722, 725, 729, 730, 731, 733, 734, 735, 736, 739, 740, 741, 742, 745, 746, 747, 749, 754, 756, 757, 758, 759, 760, 761, 762, 765, 766, 768, 772, 773, 774, 776, 777, 781, 784, 787, 788, 789, 791, 793, 794, 795, 796, 799, 800, 801, 803, 804, 805, 810, 811, 813, 816, 818, 820, 821, 824, 825, 829, 830, 836, 837, 838, 840, 842, 843, 845, 846, 849, 851, 852, 854, 856, 859, 863, 864, 865, 866, 867, 872, 874, 875, 876, 877, 879, 887, 889, 893, 895, 896, 897, 899, 902, 908, 909, 911, 912, 914, 917, 920, 921, 922, 923, 925, 926, 927, 931, 932, 933, 934, 935, 937, 938, 940, 942, 943, 944, 948, 951, 952, 956, 959, 960, 962, 963, 964, 965, 966, 971, 972, 974, 978, 983, 987, 989, 991, 992, 993, 994, 997, 1000, 1001, 1003, 1004, 1008, 1009, 1010, 1013, 1014, 1015, 1016, 1017, 1018, 1021, 1022, 1023, 1031, 1033, 1036, 1040, 1041, 1044, 1048, 1052, 1053, 1054, 1057, 1058, 1062, 1063, 1064, 1065, 1068, 1070 ]; hyperovals[6]:= [ 1, 2, 3, 4, 8, 9, 12, 14, 17, 18, 19, 21, 23, 25, 26, 28, 32, 34, 35, 36, 38, 43, 46, 48, 49, 51, 52, 53, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 71, 72, 76, 77, 80, 81, 83, 85, 86, 89, 91, 93, 94, 95, 96, 99, 101, 103, 105, 106, 108, 109, 110, 111, 112, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 129, 130, 132, 134, 136, 137, 139, 142, 144, 149, 154, 156, 157, 158, 160, 165, 166, 168, 170, 172, 174, 176, 177, 179, 182, 183, 186, 189, 190, 193, 197, 198, 199, 201, 202, 208, 213, 214, 216, 218, 220, 221, 224, 226, 227, 228, 229, 230, 231, 237, 238, 239, 240, 241, 245, 246, 247, 248, 249, 252, 253, 254, 255, 259, 261, 263, 265, 266, 269, 271, 273, 276, 277, 281, 285, 288, 289, 290, 291, 292, 293, 294, 296, 297, 299, 300, 301, 304, 305, 306, 307, 309, 311, 318, 320, 321, 323, 324, 326, 328, 330, 332, 333, 336, 340, 348, 349, 351, 353, 355, 356, 359, 362, 366, 367, 369, 370, 373, 377, 380, 382, 389, 390, 391, 393, 394, 398, 399, 400, 402, 404, 405, 407, 409, 411, 414, 416, 417, 419, 421, 424, 425, 426, 430, 431, 432, 434, 436, 440, 441, 442, 443, 444, 447, 448, 449, 452, 453, 456, 458, 460, 463, 466, 469, 470, 472, 475, 476, 482, 483, 484, 487, 488, 490, 491, 492, 493, 495, 499, 500, 501, 502, 503, 504, 507, 509, 510, 512, 513, 515, 516, 519, 520, 523, 524, 525, 527, 528, 533, 534, 537, 538, 539, 542, 545, 549, 550, 551, 553, 555, 556, 557, 558, 563, 565, 567, 571, 573, 578, 582, 583, 584, 585, 587, 588, 589, 592, 593, 595, 597, 598, 600, 601, 602, 603, 604, 606, 607, 610, 611, 612, 614, 616, 619, 622, 626, 627, 628, 630, 631, 632, 634, 635, 639, 640, 641, 642, 646, 647, 648, 650, 652, 653, 655, 660, 663, 668, 669, 671, 672, 674, 675, 678, 679, 680, 682, 686, 689, 693, 695, 699, 700, 701, 702, 706, 707, 708, 711, 714, 718, 719, 720, 722, 723, 724, 725, 728, 729, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 744, 746, 749, 750, 752, 753, 754, 756, 758, 759, 760, 762, 767, 770, 771, 772, 776, 777, 778, 779, 782, 783, 785, 788, 789, 791, 792, 793, 795, 796, 797, 798, 802, 804, 805, 806, 808, 812, 813, 814, 815, 817, 819, 824, 830, 831, 832, 833, 836, 837, 838, 842, 843, 845, 846, 847, 848, 850, 852, 854, 856, 858, 860, 862, 864, 867, 868, 869, 870, 871, 872, 877, 878, 879, 880, 881, 882, 883, 887, 889, 890, 893, 895, 896, 897, 898, 901, 906, 907, 910, 912, 913, 915, 917, 920, 921, 922, 925, 926, 927, 928, 930, 931, 932, 933, 934, 936, 938, 939, 941, 942, 944, 946, 951, 954, 957, 958, 961, 964, 968, 971, 974, 975, 978, 980, 981, 982, 983, 985, 986, 992, 994, 995, 996, 998, 999, 1005, 1010, 1013, 1014, 1016, 1019, 1020, 1024, 1025, 1026, 1027, 1028, 1030, 1031, 1032, 1033, 1034, 1036, 1038, 1039, 1040, 1041, 1044, 1045, 1046, 1048, 1049, 1050, 1051, 1053, 1054, 1056, 1058, 1059, 1060, 1061, 1062, 1064, 1065, 1068 ]; hyperovals[7]:= [ 1, 4, 8, 9, 17, 18, 19, 21, 22, 25, 27, 28, 30, 31, 33, 36, 38, 42, 43, 45, 48, 50, 51, 54, 55, 56, 58, 62, 63, 64, 66, 68, 69, 70, 71, 72, 74, 75, 76, 78, 79, 82, 83, 84, 86, 89, 92, 94, 96, 97, 98, 101, 102, 103, 108, 109, 110, 111, 113, 114, 115, 116, 118, 119, 125, 127, 129, 130, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 151, 153, 155, 156, 159, 160, 161, 162, 164, 166, 167, 168, 169, 170, 173, 175, 178, 179, 180, 182, 183, 184, 186, 187, 188, 190, 195, 201, 203, 204, 205, 208, 209, 218, 219, 221, 222, 224, 225, 227, 228, 234, 235, 237, 238, 239, 240, 241, 242, 245, 246, 248, 251, 253, 263, 266, 267, 269, 270, 271, 275, 277, 283, 286, 287, 290, 291, 292, 293, 294, 296, 299, 300, 301, 304, 307, 308, 312, 313, 314, 315, 316, 318, 322, 324, 325, 326, 327, 328, 330, 331, 332, 333, 338, 339, 341, 342, 344, 347, 348, 349, 350, 353, 354, 357, 358, 361, 362, 365, 368, 369, 371, 373, 374, 376, 377, 381, 383, 385, 387, 389, 395, 396, 397, 399, 400, 403, 405, 409, 411, 412, 413, 414, 415, 417, 419, 420, 422, 423, 424, 428, 429, 430, 432, 437, 438, 443, 445, 449, 451, 452, 456, 457, 459, 460, 462, 463, 466, 469, 476, 477, 481, 484, 487, 488, 493, 494, 496, 501, 504, 505, 506, 507, 508, 510, 512, 515, 516, 517, 518, 521, 522, 524, 525, 526, 527, 528, 529, 530, 532, 534, 535, 538, 542, 546, 548, 551, 553, 554, 556, 557, 560, 561, 562, 563, 564, 566, 568, 569, 570, 571, 574, 576, 577, 578, 579, 583, 585, 590, 591, 594, 598, 603, 604, 605, 611, 614, 615, 616, 617, 620, 621, 624, 625, 626, 630, 631, 632, 636, 639, 640, 641, 643, 644, 645, 647, 650, 651, 653, 655, 659, 660, 662, 663, 666, 667, 668, 675, 679, 680, 683, 684, 690, 691, 692, 693, 698, 699, 702, 703, 704, 706, 707, 708, 709, 710, 711, 712, 713, 716, 717, 720, 721, 723, 725, 726, 730, 731, 732, 736, 737, 738, 739, 740, 744, 748, 751, 759, 760, 762, 763, 764, 765, 766, 769, 771, 772, 774, 776, 777, 779, 780, 781, 783, 786, 788, 790, 791, 792, 793, 794, 797, 798, 799, 804, 805, 807, 809, 810, 812, 814, 815, 816, 817, 818, 822, 828, 829, 830, 832, 833, 834, 837, 838, 839, 841, 842, 843, 845, 846, 849, 850, 852, 854, 855, 856, 857, 858, 859, 861, 863, 866, 869, 871, 873, 875, 876, 879, 880, 882, 885, 887, 888, 890, 893, 896, 898, 899, 904, 906, 907, 912, 914, 915, 916, 917, 919, 920, 922, 923, 925, 928, 929, 931, 932, 934, 936, 939, 940, 941, 944, 945, 946, 947, 949, 950, 951, 953, 954, 955, 957, 960, 962, 963, 964, 965, 966, 969, 970, 971, 972, 974, 975, 978, 979, 980, 981, 982, 983, 989, 992, 995, 996, 997, 998, 1003, 1004, 1007, 1008, 1010, 1013, 1018, 1028, 1030, 1031, 1032, 1033, 1034, 1038, 1039, 1041, 1046, 1047, 1051, 1056, 1058, 1060, 1061, 1062, 1067, 1068, 1069, 1070, 1071 ]; hyperovals[8]:= [ 1, 3, 5, 7, 11, 12, 13, 14, 15, 17, 21, 28, 29, 35, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 58, 59, 62, 66, 67, 68, 70, 71, 73, 75, 76, 77, 78, 81, 83, 84, 85, 86, 88, 89, 90, 93, 94, 98, 99, 101, 102, 106, 107, 110, 111, 114, 116, 119, 124, 131, 133, 135, 136, 137, 139, 145, 146, 147, 149, 154, 156, 157, 159, 162, 163, 164, 165, 166, 168, 170, 171, 172, 174, 178, 179, 181, 182, 184, 187, 188, 191, 195, 196, 204, 206, 208, 210, 211, 214, 217, 219, 220, 222, 224, 227, 231, 235, 239, 241, 242, 243, 244, 246, 247, 248, 249, 251, 252, 254, 255, 256, 261, 262, 263, 265, 266, 267, 269, 270, 271, 272, 273, 274, 275, 276, 279, 281, 282, 283, 285, 286, 287, 291, 293, 296, 301, 302, 306, 307, 309, 315, 316, 321, 322, 324, 325, 326, 331, 332, 333, 334, 335, 336, 338, 339, 340, 342, 343, 351, 352, 355, 358, 360, 362, 363, 364, 365, 366, 368, 372, 376, 379, 380, 382, 383, 386, 388, 390, 392, 395, 398, 401, 404, 405, 406, 411, 413, 414, 415, 417, 418, 419, 423, 427, 430, 432, 433, 436, 437, 438, 441, 442, 443, 445, 448, 449, 454, 455, 457, 458, 459, 460, 462, 463, 464, 465, 468, 469, 470, 471, 472, 473, 474, 478, 479, 481, 482, 484, 485, 486, 487, 488, 489, 490, 491, 493, 494, 497, 500, 504, 506, 507, 510, 511, 513, 514, 519, 524, 525, 527, 528, 529, 530, 531, 532, 533, 535, 536, 538, 541, 543, 546, 548, 549, 553, 554, 562, 563, 564, 567, 570, 572, 573, 575, 580, 584, 587, 589, 590, 592, 594, 596, 599, 603, 605, 606, 610, 613, 615, 617, 618, 619, 621, 624, 625, 626, 627, 629, 632, 633, 634, 635, 636, 637, 639, 640, 641, 643, 646, 647, 648, 650, 651, 652, 653, 655, 658, 659, 662, 663, 665, 668, 671, 673, 675, 676, 678, 679, 680, 682, 684, 685, 688, 689, 692, 693, 694, 696, 697, 699, 700, 706, 707, 709, 710, 711, 713, 715, 716, 717, 720, 721, 722, 724, 731, 732, 733, 735, 737, 738, 740, 742, 744, 745, 746, 747, 751, 756, 760, 761, 762, 763, 764, 769, 770, 775, 778, 779, 780, 783, 786, 792, 793, 794, 796, 797, 800, 803, 804, 806, 807, 811, 813, 816, 820, 825, 828, 829, 836, 837, 840, 841, 848, 849, 852, 855, 863, 866, 867, 869, 870, 871, 872, 876, 879, 880, 884, 885, 887, 891, 893, 896, 898, 899, 900, 901, 902, 909, 910, 914, 915, 916, 919, 922, 925, 926, 927, 929, 932, 938, 939, 940, 941, 944, 947, 948, 949, 950, 952, 954, 955, 956, 957, 961, 964, 967, 968, 971, 972, 973, 976, 978, 979, 980, 983, 987, 990, 991, 992, 995, 997, 1002, 1004, 1006, 1008, 1009, 1011, 1012, 1013, 1015, 1016, 1017, 1018, 1024, 1028, 1034, 1038, 1046, 1053, 1055, 1057, 1062, 1063, 1064, 1065, 1067, 1070, 1071 ]; hyperovals[9]:= [ 1, 2, 5, 6, 9, 12, 13, 14, 19, 20, 21, 22, 24, 25, 32, 35, 37, 41, 42, 52, 53, 54, 58, 59, 60, 61, 65, 66, 69, 70, 75, 76, 83, 84, 85, 87, 88, 89, 90, 93, 103, 104, 107, 108, 109, 111, 113, 114, 118, 119, 120, 123, 124, 126, 127, 129, 130, 133, 134, 135, 136, 138, 139, 140, 144, 145, 148, 149, 150, 151, 154, 155, 158, 160, 161, 162, 163, 164, 165, 167, 170, 172, 176, 177, 179, 180, 183, 184, 185, 187, 188, 193, 197, 199, 201, 203, 205, 206, 207, 208, 211, 212, 215, 216, 217, 219, 220, 221, 222, 227, 228, 232, 233, 235, 243, 244, 245, 246, 249, 251, 258, 259, 260, 261, 266, 267, 270, 271, 275, 276, 277, 281, 285, 287, 293, 295, 296, 297, 298, 300, 304, 305, 312, 313, 314, 315, 316, 317, 318, 319, 324, 325, 326, 327, 330, 332, 336, 337, 338, 341, 344, 345, 346, 348, 351, 354, 355, 357, 358, 360, 362, 363, 364, 367, 370, 371, 372, 373, 378, 379, 384, 390, 392, 393, 394, 396, 399, 400, 401, 402, 403, 406, 408, 409, 410, 411, 416, 417, 418, 422, 423, 426, 427, 428, 429, 430, 435, 436, 439, 441, 442, 445, 447, 449, 451, 452, 453, 454, 458, 461, 463, 465, 467, 471, 473, 474, 475, 479, 482, 484, 485, 486, 487, 489, 493, 499, 500, 502, 503, 505, 506, 509, 511, 512, 514, 515, 516, 517, 518, 521, 524, 525, 527, 530, 532, 535, 536, 539, 541, 543, 544, 545, 550, 551, 558, 559, 560, 561, 562, 563, 564, 565, 566, 568, 569, 573, 575, 577, 579, 580, 581, 583, 586, 587, 588, 590, 592, 600, 603, 604, 607, 608, 609, 611, 615, 616, 618, 619, 623, 627, 628, 630, 631, 632, 634, 635, 636, 639, 640, 644, 645, 648, 649, 650, 652, 653, 656, 658, 659, 662, 663, 665, 668, 669, 671, 672, 673, 674, 676, 680, 682, 683, 684, 691, 692, 693, 696, 697, 698, 700, 701, 703, 705, 715, 718, 720, 727, 729, 730, 731, 733, 734, 735, 736, 739, 740, 741, 742, 743, 744, 746, 747, 749, 754, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 770, 771, 775, 776, 779, 782, 783, 787, 788, 790, 791, 792, 793, 797, 802, 807, 808, 809, 816, 817, 818, 819, 820, 824, 828, 829, 831, 832, 835, 836, 837, 843, 845, 846, 847, 849, 850, 851, 852, 853, 856, 858, 859, 862, 865, 866, 869, 870, 871, 873, 874, 875, 880, 885, 886, 889, 890, 892, 894, 895, 897, 901, 902, 903, 912, 913, 914, 915, 917, 919, 920, 922, 923, 925, 928, 931, 932, 934, 936, 938, 942, 944, 946, 948, 949, 954, 957, 958, 959, 960, 961, 964, 967, 971, 973, 976, 977, 978, 979, 983, 988, 990, 992, 993, 995, 996, 998, 1000, 1001, 1002, 1003, 1005, 1006, 1007, 1010, 1011, 1014, 1016, 1017, 1020, 1021, 1022, 1023, 1025, 1026, 1027, 1029, 1030, 1031, 1033, 1036, 1038, 1039, 1040, 1041, 1042, 1044, 1047, 1048, 1050, 1052, 1053, 1054, 1056, 1057, 1058, 1060, 1065, 1066, 1067, 1069, 1070, 1071 ]; hyperovals[10]:= [ 2, 4, 10, 13, 14, 16, 17, 20, 22, 25, 32, 33, 35, 38, 41, 43, 44, 45, 46, 48, 49, 51, 57, 59, 61, 62, 63, 65, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88, 89, 90, 92, 93, 96, 97, 100, 101, 102, 104, 106, 107, 108, 109, 110, 111, 112, 115, 117, 118, 119, 120, 123, 124, 125, 128, 129, 132, 135, 137, 142, 144, 145, 146, 147, 153, 154, 158, 159, 163, 167, 169, 170, 176, 179, 181, 183, 185, 186, 187, 188, 189, 191, 194, 195, 196, 197, 199, 200, 201, 204, 205, 206, 209, 212, 216, 217, 219, 220, 221, 225, 226, 228, 230, 231, 232, 236, 237, 239, 240, 241, 242, 243, 244, 247, 251, 253, 255, 257, 258, 259, 264, 265, 266, 268, 270, 275, 276, 279, 280, 282, 285, 286, 288, 289, 290, 295, 296, 297, 298, 299, 301, 302, 304, 305, 306, 307, 308, 309, 310, 311, 317, 318, 320, 321, 322, 323, 324, 325, 326, 328, 330, 331, 332, 334, 335, 338, 340, 342, 347, 349, 352, 354, 355, 357, 361, 362, 364, 366, 369, 371, 372, 374, 375, 376, 383, 389, 391, 393, 394, 395, 396, 399, 400, 401, 404, 405, 408, 409, 413, 414, 416, 417, 419, 420, 421, 424, 425, 426, 427, 428, 429, 431, 433, 434, 435, 438, 439, 441, 442, 443, 447, 448, 449, 451, 452, 454, 455, 456, 459, 460, 461, 462, 465, 467, 469, 470, 471, 472, 482, 483, 487, 488, 495, 496, 499, 503, 504, 505, 508, 509, 510, 511, 517, 518, 519, 520, 522, 524, 525, 528, 529, 534, 536, 537, 539, 541, 542, 543, 544, 545, 550, 552, 554, 560, 561, 562, 564, 565, 567, 569, 573, 574, 575, 576, 577, 578, 579, 580, 582, 583, 585, 586, 589, 590, 595, 596, 598, 601, 605, 606, 607, 610, 612, 614, 615, 618, 619, 621, 622, 625, 626, 628, 630, 631, 632, 636, 641, 642, 645, 649, 650, 651, 652, 654, 657, 658, 663, 665, 666, 667, 668, 669, 671, 672, 674, 677, 678, 679, 682, 684, 685, 689, 691, 693, 696, 702, 703, 704, 706, 708, 711, 713, 714, 716, 719, 720, 723, 728, 729, 730, 732, 733, 736, 737, 739, 740, 741, 742, 743, 747, 750, 752, 754, 755, 756, 757, 759, 760, 765, 769, 770, 771, 772, 773, 776, 777, 778, 779, 785, 786, 787, 792, 796, 798, 799, 800, 801, 804, 805, 807, 810, 811, 814, 816, 817, 819, 820, 822, 824, 825, 826, 828, 829, 832, 836, 838, 839, 841, 842, 843, 845, 849, 850, 851, 854, 856, 857, 858, 867, 868, 870, 874, 877, 880, 881, 882, 884, 885, 887, 888, 892, 898, 899, 900, 901, 905, 906, 907, 908, 909, 914, 915, 916, 917, 921, 922, 924, 925, 928, 930, 931, 932, 935, 936, 940, 943, 945, 947, 949, 952, 954, 956, 963, 965, 966, 967, 968, 969, 971, 972, 973, 974, 975, 977, 983, 986, 987, 989, 992, 993, 994, 995, 996, 999, 1000, 1001, 1002, 1006, 1007, 1008, 1010, 1013, 1018, 1019, 1025, 1031, 1033, 1034, 1035, 1037, 1038, 1039, 1041, 1043, 1045, 1047, 1049, 1050, 1053, 1057, 1058, 1061, 1062, 1063, 1068, 1069, 1070, 1071 ]; hyperovals[11]:= [ 1, 4, 6, 8, 9, 10, 11, 12, 17, 19, 20, 21, 22, 30, 35, 41, 42, 43, 44, 46, 48, 49, 51, 54, 55, 57, 58, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 77, 79, 80, 81, 84, 85, 90, 91, 97, 100, 102, 103, 104, 105, 106, 107, 115, 117, 119, 120, 121, 122, 123, 124, 127, 133, 134, 135, 136, 139, 140, 142, 144, 147, 149, 150, 153, 156, 157, 160, 161, 165, 166, 167, 168, 172, 178, 179, 180, 181, 184, 185, 186, 187, 189, 190, 195, 196, 197, 198, 199, 200, 201, 202, 204, 206, 208, 210, 211, 212, 219, 220, 221, 222, 223, 224, 227, 228, 232, 233, 237, 238, 239, 240, 241, 242, 243, 247, 250, 254, 256, 259, 261, 265, 267, 268, 269, 271, 272, 273, 275, 276, 279, 280, 281, 282, 286, 287, 288, 291, 292, 293, 295, 301, 302, 305, 307, 312, 313, 316, 317, 318, 319, 320, 321, 324, 329, 330, 331, 333, 334, 335, 339, 341, 344, 345, 351, 358, 360, 363, 364, 365, 370, 371, 372, 375, 377, 378, 380, 385, 386, 387, 393, 395, 396, 397, 399, 401, 403, 407, 408, 410, 412, 417, 418, 419, 420, 421, 423, 427, 429, 432, 438, 440, 441, 442, 450, 452, 453, 456, 458, 459, 460, 461, 463, 467, 469, 471, 473, 475, 476, 477, 479, 481, 482, 485, 489, 492, 493, 495, 496, 498, 499, 502, 503, 504, 505, 507, 508, 509, 511, 513, 516, 517, 519, 520, 521, 524, 529, 530, 537, 539, 543, 544, 547, 550, 553, 557, 558, 559, 561, 563, 564, 567, 568, 569, 570, 571, 573, 574, 575, 577, 582, 586, 587, 588, 589, 595, 596, 598, 600, 601, 606, 609, 610, 611, 613, 614, 617, 618, 620, 625, 628, 630, 632, 634, 636, 637, 638, 640, 641, 643, 645, 646, 648, 650, 651, 652, 654, 655, 656, 657, 659, 660, 662, 669, 670, 671, 675, 677, 681, 684, 688, 692, 698, 700, 703, 704, 705, 708, 710, 711, 712, 713, 714, 715, 717, 719, 720, 721, 723, 728, 731, 732, 737, 740, 744, 746, 748, 750, 753, 754, 758, 760, 761, 765, 770, 771, 775, 776, 778, 779, 780, 781, 782, 784, 785, 788, 797, 798, 800, 802, 803, 804, 807, 808, 816, 820, 823, 824, 825, 827, 831, 835, 840, 843, 846, 851, 856, 861, 862, 865, 866, 867, 870, 873, 874, 875, 876, 877, 879, 883, 884, 886, 889, 890, 891, 893, 898, 900, 901, 902, 908, 909, 912, 917, 920, 923, 926, 927, 929, 934, 935, 937, 941, 942, 943, 944, 947, 949, 950, 953, 954, 956, 957, 958, 959, 960, 961, 963, 972, 973, 978, 979, 981, 984, 988, 989, 991, 994, 995, 996, 999, 1001, 1002, 1004, 1007, 1008, 1010, 1012, 1015, 1016, 1017, 1018, 1022, 1027, 1029, 1030, 1032, 1035, 1038, 1039, 1043, 1046, 1048, 1049, 1051, 1052, 1053, 1057, 1058, 1059, 1060, 1061, 1062, 1068, 1070 ]; hyperovals[12]:= [ 1, 3, 5, 8, 10, 12, 15, 18, 19, 20, 26, 28, 29, 34, 35, 37, 41, 42, 46, 50, 51, 54, 55, 56, 57, 59, 60, 64, 66, 67, 73, 79, 80, 81, 84, 85, 87, 88, 90, 92, 94, 96, 103, 104, 105, 106, 108, 109, 110, 111, 114, 120, 121, 123, 128, 130, 131, 132, 134, 136, 137, 145, 146, 147, 148, 149, 150, 151, 153, 156, 160, 161, 162, 165, 166, 167, 169, 174, 176, 179, 181, 184, 186, 189, 191, 192, 198, 199, 200, 202, 203, 204, 209, 211, 212, 214, 217, 219, 223, 224, 225, 226, 228, 232, 233, 234, 236, 237, 241, 243, 244, 245, 248, 250, 252, 253, 255, 260, 261, 263, 264, 266, 267, 268, 271, 272, 274, 275, 278, 280, 281, 284, 286, 287, 288, 291, 292, 293, 294, 296, 299, 300, 302, 303, 304, 307, 308, 311, 314, 317, 318, 321, 322, 324, 326, 327, 329, 330, 331, 332, 333, 334, 335, 336, 338, 343, 345, 347, 355, 356, 359, 363, 365, 367, 368, 369, 370, 372, 375, 378, 379, 381, 383, 385, 388, 390, 391, 393, 394, 398, 400, 401, 404, 407, 408, 411, 412, 413, 417, 418, 419, 427, 428, 429, 430, 432, 436, 437, 438, 439, 442, 443, 445, 447, 448, 451, 453, 455, 456, 457, 462, 463, 464, 465, 468, 470, 472, 474, 476, 478, 482, 483, 484, 487, 488, 489, 492, 494, 496, 497, 499, 501, 502, 504, 506, 508, 510, 511, 512, 513, 514, 515, 516, 518, 523, 524, 525, 526, 527, 531, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 546, 547, 551, 554, 555, 557, 559, 560, 561, 563, 564, 565, 569, 571, 573, 576, 577, 579, 580, 581, 584, 585, 586, 587, 590, 591, 592, 593, 594, 595, 596, 598, 603, 605, 606, 607, 608, 609, 611, 613, 615, 616, 617, 619, 620, 622, 624, 625, 626, 627, 630, 631, 634, 635, 637, 638, 639, 640, 642, 643, 644, 645, 647, 649, 650, 652, 658, 660, 662, 663, 665, 666, 667, 668, 669, 670, 671, 672, 673, 676, 678, 679, 680, 681, 682, 683, 686, 687, 689, 690, 691, 692, 694, 697, 698, 699, 701, 702, 703, 704, 705, 706, 709, 710, 713, 715, 717, 718, 720, 721, 723, 724, 725, 727, 728, 732, 733, 735, 737, 738, 739, 741, 743, 744, 746, 747, 748, 749, 750, 751, 753, 755, 756, 758, 761, 762, 763, 764, 765, 766, 768, 769, 770, 771, 775, 779, 782, 783, 784, 786, 789, 790, 793, 795, 798, 803, 809, 810, 817, 819, 820, 821, 822, 824, 826, 829, 831, 833, 836, 838, 841, 845, 849, 851, 853, 856, 859, 861, 862, 869, 871, 872, 873, 878, 880, 881, 882, 883, 885, 886, 887, 889, 891, 894, 895, 896, 901, 904, 905, 906, 907, 908, 909, 912, 914, 915, 917, 918, 920, 925, 926, 927, 928, 929, 934, 937, 940, 943, 944, 946, 947, 948, 949, 950, 957, 960, 962, 963, 965, 967, 968, 969, 971, 972, 975, 976, 980, 981, 983, 986, 988, 989, 990, 991, 992, 993, 994, 995, 997, 998, 999, 1000, 1001, 1005, 1006, 1008, 1009, 1010, 1011, 1012, 1013, 1016, 1020, 1021, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1036, 1037, 1038, 1041, 1044, 1045, 1046, 1047, 1048, 1051, 1052, 1057, 1059, 1062, 1063, 1067, 1069, 1070, 1071 ]; hyperovals[13]:= [ 1, 5, 10, 11, 12, 13, 14, 17, 19, 21, 24, 27, 28, 31, 32, 34, 39, 42, 45, 47, 50, 56, 57, 59, 60, 62, 63, 64, 66, 70, 72, 73, 74, 75, 83, 84, 85, 86, 88, 90, 91, 92, 96, 99, 100, 105, 107, 108, 110, 116, 119, 130, 131, 133, 135, 137, 140, 141, 142, 143, 146, 147, 149, 152, 153, 154, 155, 158, 160, 162, 163, 165, 171, 174, 176, 180, 181, 182, 183, 187, 188, 191, 194, 195, 198, 202, 204, 205, 206, 207, 208, 214, 215, 216, 220, 221, 225, 230, 232, 233, 234, 235, 240, 242, 244, 246, 250, 251, 252, 253, 256, 257, 258, 261, 265, 267, 268, 269, 270, 271, 272, 273, 276, 277, 279, 285, 286, 287, 291, 292, 295, 296, 297, 298, 300, 302, 303, 304, 305, 315, 316, 318, 323, 327, 329, 330, 334, 335, 336, 338, 341, 342, 344, 345, 346, 348, 349, 355, 358, 359, 361, 362, 363, 364, 365, 369, 370, 371, 372, 377, 378, 379, 381, 382, 383, 384, 386, 390, 392, 393, 394, 399, 400, 401, 403, 404, 410, 411, 412, 413, 415, 417, 418, 422, 423, 425, 428, 429, 431, 432, 433, 437, 440, 444, 445, 449, 451, 452, 454, 459, 463, 464, 465, 469, 470, 471, 473, 474, 475, 477, 478, 482, 483, 484, 485, 486, 487, 488, 490, 491, 494, 496, 498, 499, 505, 506, 507, 510, 512, 514, 515, 516, 517, 518, 519, 520, 521, 523, 525, 531, 532, 538, 539, 541, 545, 546, 547, 548, 549, 550, 552, 554, 557, 562, 563, 564, 565, 566, 567, 569, 571, 572, 578, 580, 581, 582, 583, 584, 585, 586, 587, 588, 595, 598, 602, 603, 604, 605, 606, 610, 614, 620, 624, 627, 628, 629, 631, 633, 635, 636, 637, 643, 644, 645, 652, 653, 655, 657, 659, 662, 663, 665, 666, 670, 671, 672, 673, 674, 675, 676, 677, 679, 680, 681, 686, 687, 689, 692, 693, 695, 696, 697, 698, 700, 701, 703, 706, 708, 710, 713, 714, 715, 716, 720, 722, 724, 726, 727, 731, 735, 737, 741, 742, 748, 749, 752, 754, 757, 759, 760, 763, 766, 768, 769, 770, 771, 772, 773, 774, 777, 778, 779, 781, 782, 783, 786, 790, 791, 792, 795, 796, 802, 803, 804, 806, 808, 811, 812, 813, 817, 818, 819, 821, 825, 830, 834, 836, 841, 842, 846, 848, 851, 858, 859, 861, 865, 866, 868, 869, 871, 872, 875, 876, 877, 879, 880, 881, 883, 885, 886, 887, 891, 893, 895, 897, 898, 900, 901, 902, 904, 908, 910, 914, 915, 917, 919, 922, 923, 924, 925, 926, 927, 928, 932, 933, 935, 938, 939, 940, 941, 944, 946, 948, 949, 954, 955, 961, 962, 966, 969, 970, 973, 974, 976, 977, 978, 979, 981, 983, 985, 986, 989, 990, 995, 997, 999, 1001, 1002, 1004, 1005, 1008, 1010, 1011, 1013, 1014, 1016, 1017, 1020, 1021, 1023, 1026, 1027, 1028, 1032, 1033, 1034, 1035, 1037, 1038, 1040, 1046, 1051, 1052, 1053, 1054, 1056, 1059, 1062, 1063, 1067, 1068, 1071 ]; hyperovals[14]:= [ 1, 2, 8, 9, 12, 14, 15, 16, 19, 21, 24, 25, 27, 31, 35, 41, 42, 43, 48, 50, 52, 54, 55, 62, 63, 64, 66, 67, 68, 74, 76, 77, 78, 79, 81, 83, 85, 86, 92, 95, 97, 98, 105, 106, 108, 109, 110, 115, 116, 117, 118, 119, 120, 121, 122, 125, 126, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 148, 151, 152, 154, 156, 160, 163, 164, 165, 166, 167, 170, 171, 172, 175, 180, 183, 187, 189, 190, 191, 192, 194, 195, 200, 201, 203, 209, 211, 217, 221, 222, 227, 228, 229, 231, 232, 235, 237, 242, 244, 245, 248, 249, 250, 251, 252, 253, 256, 257, 261, 262, 263, 264, 265, 267, 270, 274, 275, 276, 280, 283, 287, 290, 291, 295, 298, 299, 301, 302, 304, 306, 307, 309, 310, 312, 315, 317, 324, 325, 326, 328, 329, 331, 332, 335, 338, 341, 342, 343, 348, 350, 352, 353, 354, 360, 361, 363, 365, 366, 370, 371, 372, 375, 376, 378, 381, 382, 383, 388, 390, 392, 398, 399, 400, 405, 407, 408, 412, 413, 414, 415, 417, 418, 419, 422, 424, 425, 426, 427, 431, 432, 436, 438, 439, 440, 441, 442, 443, 445, 447, 448, 451, 453, 454, 457, 458, 462, 463, 464, 465, 466, 469, 471, 473, 474, 477, 478, 479, 482, 484, 485, 486, 487, 488, 489, 493, 497, 505, 507, 508, 509, 510, 511, 512, 514, 516, 518, 521, 525, 526, 528, 533, 534, 536, 537, 541, 542, 543, 544, 545, 546, 547, 548, 549, 551, 552, 555, 556, 558, 559, 561, 563, 564, 568, 569, 571, 572, 574, 575, 577, 579, 582, 584, 585, 586, 588, 589, 591, 592, 593, 595, 596, 600, 606, 608, 609, 610, 614, 615, 617, 620, 621, 623, 624, 628, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 643, 644, 651, 656, 657, 659, 662, 663, 665, 666, 668, 669, 670, 677, 679, 687, 688, 690, 691, 692, 693, 695, 698, 701, 702, 703, 713, 714, 718, 720, 721, 722, 723, 724, 725, 727, 728, 729, 730, 731, 732, 733, 736, 738, 741, 743, 745, 748, 749, 751, 755, 757, 758, 759, 762, 764, 765, 766, 771, 773, 778, 780, 782, 786, 788, 789, 790, 795, 797, 798, 799, 801, 804, 805, 807, 809, 812, 814, 815, 816, 817, 818, 820, 821, 823, 825, 831, 834, 836, 840, 841, 843, 844, 846, 847, 848, 850, 851, 852, 853, 854, 856, 857, 859, 860, 861, 866, 868, 869, 870, 872, 875, 878, 883, 888, 892, 894, 897, 898, 900, 901, 904, 905, 907, 908, 909, 910, 911, 919, 923, 925, 926, 927, 928, 929, 931, 932, 933, 935, 936, 937, 938, 939, 940, 941, 942, 944, 949, 952, 955, 957, 961, 963, 964, 968, 970, 975, 978, 980, 981, 983, 984, 985, 986, 989, 991, 992, 993, 994, 996, 997, 998, 999, 1002, 1003, 1006, 1008, 1009, 1013, 1014, 1015, 1018, 1020, 1023, 1026, 1027, 1028, 1030, 1032, 1035, 1036, 1041, 1045, 1046, 1047, 1049, 1050, 1051, 1052, 1055, 1056, 1058, 1059, 1067, 1068, 1069, 1071 ]; hyperovals[15]:= [ 1, 2, 3, 4, 7, 8, 10, 20, 22, 24, 27, 28, 30, 31, 34, 36, 43, 44, 46, 47, 48, 51, 52, 55, 56, 58, 59, 60, 62, 63, 65, 67, 69, 70, 71, 73, 74, 75, 78, 81, 86, 87, 89, 91, 94, 95, 96, 97, 98, 99, 103, 104, 105, 107, 109, 110, 111, 112, 117, 122, 124, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 139, 142, 144, 146, 147, 150, 151, 152, 155, 157, 161, 164, 166, 168, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 186, 187, 188, 190, 191, 193, 194, 196, 201, 203, 205, 210, 213, 214, 216, 217, 218, 219, 222, 224, 225, 227, 230, 235, 237, 239, 241, 243, 245, 246, 248, 249, 250, 251, 252, 253, 255, 256, 257, 258, 259, 261, 262, 266, 268, 269, 271, 276, 278, 281, 285, 287, 288, 292, 294, 300, 301, 302, 304, 307, 311, 313, 314, 316, 321, 324, 325, 326, 328, 329, 330, 332, 334, 335, 338, 341, 345, 349, 351, 353, 359, 360, 361, 365, 366, 373, 374, 375, 377, 378, 379, 380, 382, 383, 384, 386, 392, 394, 399, 400, 401, 403, 406, 407, 409, 411, 412, 414, 415, 419, 421, 424, 426, 428, 430, 432, 435, 436, 437, 438, 440, 442, 449, 452, 454, 455, 456, 458, 464, 465, 467, 468, 469, 477, 478, 479, 480, 481, 483, 486, 487, 489, 492, 493, 499, 501, 502, 503, 505, 506, 507, 508, 509, 510, 512, 513, 515, 517, 518, 519, 523, 524, 526, 527, 530, 531, 532, 534, 535, 541, 543, 544, 546, 548, 549, 553, 554, 556, 557, 558, 560, 561, 562, 563, 566, 567, 569, 571, 572, 573, 575, 577, 578, 579, 580, 581, 589, 590, 592, 595, 598, 600, 604, 606, 608, 609, 610, 613, 614, 618, 619, 620, 621, 626, 629, 630, 632, 634, 640, 641, 642, 644, 646, 647, 648, 649, 650, 655, 657, 658, 659, 661, 664, 666, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 686, 687, 688, 689, 693, 694, 695, 696, 697, 699, 701, 705, 706, 712, 714, 715, 716, 718, 721, 722, 733, 734, 735, 736, 737, 743, 744, 745, 747, 748, 751, 753, 755, 756, 759, 762, 763, 765, 767, 768, 769, 771, 774, 775, 776, 779, 780, 781, 784, 786, 790, 791, 793, 794, 795, 796, 798, 799, 801, 806, 807, 808, 811, 812, 813, 818, 820, 822, 823, 825, 827, 829, 831, 834, 837, 839, 840, 841, 842, 843, 844, 845, 847, 848, 849, 850, 853, 854, 855, 856, 859, 861, 862, 864, 868, 871, 875, 876, 877, 878, 879, 883, 884, 885, 886, 890, 891, 893, 895, 897, 898, 899, 902, 904, 910, 912, 914, 915, 916, 917, 923, 924, 927, 931, 932, 934, 935, 936, 940, 941, 946, 947, 950, 956, 958, 962, 963, 968, 969, 970, 973, 975, 976, 977, 981, 984, 986, 988, 989, 993, 996, 997, 998, 999, 1004, 1007, 1008, 1010, 1011, 1012, 1013, 1018, 1019, 1020, 1022, 1023, 1028, 1029, 1033, 1037, 1038, 1040, 1041, 1042, 1044, 1048, 1050, 1051, 1054, 1055, 1057, 1058, 1061, 1064, 1066, 1068, 1069 ]; hyperovals[16]:= [ 2, 4, 6, 7, 9, 11, 13, 14, 15, 16, 17, 20, 21, 23, 25, 30, 31, 32, 36, 38, 39, 41, 42, 44, 45, 46, 50, 51, 54, 56, 61, 64, 67, 69, 70, 73, 75, 76, 77, 78, 79, 82, 83, 84, 85, 92, 96, 97, 99, 100, 101, 102, 103, 105, 106, 107, 108, 112, 113, 118, 119, 122, 123, 124, 125, 127, 133, 135, 136, 137, 138, 139, 140, 143, 144, 145, 146, 149, 151, 156, 158, 159, 163, 165, 168, 169, 170, 171, 173, 181, 184, 186, 187, 190, 193, 194, 196, 197, 198, 202, 207, 208, 209, 210, 211, 212, 214, 215, 217, 218, 219, 221, 222, 225, 227, 229, 231, 232, 235, 237, 239, 241, 242, 245, 246, 250, 251, 252, 254, 255, 256, 258, 260, 261, 262, 266, 267, 271, 275, 276, 282, 284, 288, 289, 290, 291, 292, 295, 299, 300, 301, 303, 304, 307, 308, 310, 311, 316, 317, 319, 320, 321, 323, 324, 325, 327, 329, 330, 331, 332, 333, 334, 337, 340, 345, 346, 347, 348, 350, 353, 354, 356, 358, 360, 361, 362, 364, 372, 373, 374, 376, 379, 382, 383, 385, 386, 387, 389, 391, 395, 396, 398, 399, 403, 405, 407, 408, 409, 411, 413, 417, 420, 422, 426, 431, 432, 436, 437, 440, 441, 442, 445, 447, 448, 451, 452, 454, 455, 456, 457, 458, 459, 460, 462, 463, 465, 466, 467, 469, 473, 474, 475, 477, 480, 481, 482, 487, 490, 492, 494, 495, 497, 498, 500, 502, 505, 506, 508, 510, 512, 513, 516, 520, 521, 527, 528, 537, 539, 540, 542, 548, 549, 551, 552, 553, 556, 558, 559, 560, 563, 564, 565, 566, 567, 569, 570, 572, 574, 575, 579, 583, 584, 590, 592, 594, 595, 596, 597, 600, 604, 608, 611, 614, 616, 617, 620, 624, 626, 627, 628, 630, 632, 633, 638, 639, 640, 641, 644, 646, 649, 650, 653, 654, 655, 656, 659, 662, 663, 665, 669, 673, 677, 683, 686, 687, 688, 690, 692, 693, 694, 695, 696, 697, 699, 702, 703, 706, 710, 711, 712, 713, 714, 717, 719, 720, 721, 722, 727, 729, 731, 732, 733, 735, 737, 739, 741, 742, 743, 744, 746, 747, 749, 751, 752, 753, 755, 756, 758, 759, 766, 772, 774, 776, 778, 780, 781, 782, 783, 787, 790, 797, 798, 800, 801, 803, 804, 805, 809, 810, 812, 815, 822, 823, 824, 829, 830, 831, 834, 835, 836, 837, 838, 839, 840, 842, 843, 844, 847, 848, 849, 850, 851, 852, 853, 855, 858, 859, 860, 865, 866, 867, 870, 871, 872, 873, 877, 879, 882, 883, 884, 885, 886, 887, 892, 893, 895, 897, 899, 902, 908, 910, 911, 913, 917, 919, 920, 924, 925, 926, 931, 933, 935, 936, 937, 938, 939, 942, 943, 946, 948, 949, 950, 951, 952, 953, 958, 961, 962, 971, 975, 977, 980, 981, 982, 983, 985, 986, 987, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 1002, 1004, 1006, 1008, 1009, 1010, 1013, 1016, 1018, 1024, 1025, 1026, 1027, 1028, 1029, 1031, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1042, 1044, 1045, 1046, 1047, 1048, 1050, 1051, 1052, 1053, 1054, 1055, 1057, 1058, 1059, 1062, 1063, 1065, 1066, 1067, 1069, 1071 ]; hyperovals[17]:= [ 1, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 26, 27, 28, 29, 32, 33, 35, 36, 39, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 67, 68, 70, 73, 77, 78, 81, 82, 85, 86, 89, 90, 94, 95, 102, 105, 106, 109, 110, 111, 114, 117, 118, 123, 125, 126, 128, 130, 132, 133, 134, 141, 142, 146, 147, 150, 151, 152, 157, 158, 163, 164, 165, 170, 171, 173, 176, 179, 180, 183, 184, 186, 192, 193, 194, 195, 196, 199, 200, 201, 202, 205, 207, 209, 211, 212, 218, 220, 221, 224, 226, 227, 230, 233, 236, 237, 240, 241, 242, 243, 244, 246, 249, 251, 252, 256, 257, 258, 261, 264, 265, 268, 270, 271, 272, 274, 275, 277, 278, 280, 282, 284, 285, 286, 287, 288, 290, 291, 292, 295, 296, 298, 299, 300, 306, 308, 311, 314, 318, 319, 320, 322, 327, 330, 331, 333, 334, 335, 337, 340, 343, 345, 352, 355, 358, 360, 363, 364, 365, 369, 372, 375, 378, 382, 383, 387, 388, 391, 393, 394, 397, 398, 399, 400, 401, 402, 404, 405, 406, 407, 408, 409, 411, 413, 416, 421, 423, 425, 429, 431, 433, 434, 435, 439, 441, 442, 448, 449, 451, 454, 459, 461, 462, 465, 466, 468, 470, 472, 474, 475, 476, 477, 478, 480, 483, 484, 487, 489, 490, 492, 494, 495, 497, 498, 499, 500, 504, 505, 507, 509, 510, 511, 512, 514, 516, 518, 520, 522, 524, 525, 526, 529, 532, 535, 537, 538, 539, 540, 542, 546, 548, 549, 550, 553, 555, 557, 559, 560, 562, 563, 564, 567, 568, 570, 572, 574, 575, 577, 578, 580, 581, 582, 584, 585, 588, 590, 591, 592, 593, 596, 597, 598, 600, 602, 604, 605, 606, 608, 611, 615, 616, 618, 619, 621, 624, 627, 631, 634, 636, 637, 638, 640, 642, 643, 647, 648, 650, 651, 652, 655, 661, 662, 663, 664, 665, 668, 669, 670, 674, 675, 680, 685, 686, 689, 691, 692, 693, 694, 696, 697, 700, 701, 703, 705, 706, 708, 709, 710, 712, 714, 715, 716, 717, 720, 721, 723, 725, 726, 727, 731, 735, 736, 739, 740, 742, 743, 744, 746, 748, 749, 751, 752, 756, 757, 760, 764, 765, 766, 769, 771, 772, 773, 775, 776, 777, 778, 779, 780, 781, 784, 785, 786, 788, 790, 791, 792, 793, 794, 795, 796, 798, 799, 801, 802, 803, 804, 805, 806, 807, 813, 817, 818, 819, 821, 822, 828, 831, 833, 834, 837, 844, 846, 847, 851, 853, 858, 859, 861, 862, 864, 867, 869, 870, 871, 873, 874, 875, 879, 880, 882, 890, 893, 896, 900, 901, 903, 904, 906, 907, 908, 910, 911, 912, 913, 914, 915, 918, 919, 921, 923, 924, 925, 927, 928, 930, 931, 932, 933, 934, 935, 936, 938, 940, 943, 944, 945, 946, 948, 950, 951, 955, 957, 958, 959, 960, 961, 962, 963, 965, 967, 971, 972, 973, 974, 975, 978, 979, 981, 983, 984, 985, 986, 987, 988, 989, 990, 991, 995, 996, 997, 998, 999, 1001, 1007, 1008, 1011, 1012, 1013, 1016, 1020, 1023, 1024, 1025, 1027, 1029, 1031, 1033, 1038, 1040, 1042, 1043, 1046, 1047, 1048, 1050, 1052, 1053, 1056, 1057, 1058, 1059, 1063, 1064, 1066, 1069, 1070, 1071 ]; hyperovals[18]:= [ 2, 4, 5, 6, 12, 15, 22, 24, 26, 28, 30, 32, 33, 37, 38, 39, 40, 41, 46, 47, 49, 50, 53, 54, 55, 56, 62, 63, 64, 65, 67, 68, 69, 74, 75, 77, 78, 79, 80, 81, 85, 87, 88, 89, 97, 98, 101, 106, 107, 108, 111, 112, 113, 117, 120, 121, 122, 123, 126, 127, 129, 131, 132, 133, 134, 135, 139, 140, 144, 146, 149, 151, 152, 156, 158, 160, 161, 163, 164, 166, 169, 172, 174, 175, 178, 183, 184, 189, 192, 196, 198, 200, 202, 205, 207, 209, 211, 212, 213, 214, 215, 216, 220, 221, 222, 226, 227, 228, 229, 230, 231, 237, 238, 241, 244, 246, 247, 248, 249, 250, 251, 252, 254, 255, 256, 258, 261, 262, 263, 266, 268, 269, 272, 275, 276, 277, 278, 282, 284, 285, 286, 287, 289, 290, 291, 293, 295, 296, 299, 302, 304, 306, 307, 308, 311, 313, 314, 316, 320, 321, 322, 323, 328, 329, 330, 331, 332, 334, 335, 337, 338, 341, 346, 347, 350, 353, 354, 355, 356, 359, 360, 366, 369, 375, 376, 378, 379, 381, 382, 384, 386, 387, 390, 391, 392, 394, 395, 396, 398, 399, 401, 402, 404, 405, 407, 409, 412, 414, 415, 419, 420, 421, 426, 427, 429, 430, 431, 437, 442, 443, 446, 448, 449, 451, 452, 454, 455, 456, 458, 465, 467, 469, 471, 474, 477, 478, 479, 480, 482, 485, 487, 491, 493, 495, 496, 497, 500, 502, 505, 507, 508, 509, 510, 511, 512, 514, 516, 518, 521, 523, 525, 526, 528, 530, 532, 533, 535, 536, 537, 538, 539, 542, 543, 544, 545, 547, 548, 550, 552, 553, 554, 555, 557, 558, 559, 562, 564, 566, 567, 568, 569, 570, 573, 575, 576, 584, 585, 587, 588, 589, 592, 594, 596, 601, 602, 603, 604, 606, 608, 611, 612, 614, 615, 622, 625, 628, 633, 634, 635, 636, 639, 642, 643, 645, 646, 647, 648, 649, 650, 652, 655, 657, 662, 663, 664, 665, 667, 671, 672, 674, 675, 678, 679, 680, 682, 684, 685, 686, 687, 688, 691, 692, 696, 697, 703, 705, 711, 712, 713, 714, 715, 717, 718, 721, 722, 726, 727, 729, 730, 731, 733, 734, 741, 742, 743, 745, 746, 749, 755, 756, 757, 758, 759, 760, 761, 762, 764, 766, 768, 771, 775, 776, 779, 781, 784, 786, 787, 788, 791, 793, 794, 795, 797, 798, 799, 801, 802, 803, 804, 805, 806, 814, 815, 817, 818, 821, 822, 823, 826, 827, 828, 830, 831, 833, 835, 836, 838, 839, 841, 842, 843, 845, 848, 849, 851, 852, 854, 856, 857, 858, 859, 860, 862, 863, 865, 866, 869, 872, 873, 877, 881, 886, 888, 889, 890, 896, 897, 899, 903, 904, 905, 906, 908, 909, 910, 912, 915, 917, 918, 920, 921, 923, 924, 925, 928, 929, 931, 932, 936, 939, 940, 941, 942, 943, 945, 946, 947, 949, 952, 955, 958, 959, 963, 964, 967, 972, 974, 975, 981, 985, 986, 987, 988, 989, 990, 992, 994, 995, 997, 998, 1000, 1001, 1002, 1003, 1004, 1007, 1010, 1011, 1012, 1013, 1015, 1017, 1018, 1019, 1025, 1027, 1028, 1030, 1035, 1036, 1040, 1041, 1043, 1044, 1046, 1047, 1050, 1052, 1054, 1059, 1063, 1064, 1065, 1067 ]; hyperovals[19]:= [ 1, 5, 6, 13, 15, 20, 21, 24, 25, 26, 27, 30, 31, 32, 33, 35, 39, 41, 43, 44, 45, 48, 49, 51, 52, 53, 54, 57, 59, 60, 61, 63, 64, 65, 66, 67, 68, 71, 73, 74, 79, 80, 83, 84, 86, 88, 89, 91, 93, 95, 96, 99, 101, 103, 105, 108, 109, 111, 112, 114, 117, 118, 119, 120, 121, 122, 124, 125, 132, 134, 135, 137, 138, 141, 143, 144, 148, 151, 152, 153, 155, 161, 163, 167, 170, 171, 174, 176, 177, 180, 183, 184, 185, 189, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 206, 207, 208, 210, 214, 216, 218, 219, 224, 225, 226, 227, 229, 231, 232, 237, 240, 241, 242, 246, 247, 248, 249, 250, 252, 256, 258, 260, 262, 263, 265, 267, 269, 270, 272, 273, 274, 275, 276, 278, 280, 281, 282, 285, 286, 287, 288, 289, 290, 293, 295, 297, 298, 299, 300, 304, 306, 312, 313, 314, 315, 316, 318, 320, 321, 326, 327, 328, 329, 330, 331, 332, 333, 334, 337, 339, 340, 341, 343, 344, 346, 347, 349, 351, 352, 353, 355, 357, 360, 364, 365, 368, 369, 370, 371, 374, 375, 376, 379, 380, 383, 385, 386, 389, 391, 393, 395, 397, 398, 400, 401, 408, 410, 411, 412, 415, 417, 420, 423, 424, 425, 427, 429, 431, 434, 436, 437, 438, 439, 440, 441, 442, 444, 447, 448, 449, 450, 453, 454, 455, 456, 457, 458, 465, 467, 469, 470, 475, 476, 478, 479, 483, 485, 487, 490, 491, 493, 497, 501, 502, 507, 508, 509, 511, 512, 514, 515, 518, 524, 527, 528, 529, 530, 535, 537, 541, 542, 543, 544, 545, 546, 549, 555, 557, 559, 562, 565, 566, 569, 571, 572, 576, 578, 579, 581, 583, 585, 593, 596, 597, 599, 602, 607, 608, 609, 612, 614, 618, 619, 620, 621, 623, 626, 627, 629, 631, 633, 635, 636, 638, 639, 641, 642, 643, 644, 645, 647, 649, 651, 652, 653, 654, 661, 663, 664, 665, 666, 667, 668, 670, 672, 673, 678, 679, 680, 681, 684, 685, 691, 694, 698, 700, 701, 704, 705, 707, 708, 709, 710, 717, 718, 721, 722, 723, 725, 726, 727, 729, 730, 733, 734, 735, 736, 738, 739, 744, 745, 746, 747, 749, 750, 752, 753, 756, 757, 758, 759, 760, 761, 762, 767, 769, 770, 773, 774, 775, 776, 783, 786, 789, 791, 793, 794, 796, 798, 801, 803, 804, 805, 808, 811, 812, 816, 817, 818, 820, 823, 825, 826, 827, 828, 831, 832, 833, 834, 837, 838, 839, 840, 841, 845, 846, 847, 850, 851, 852, 859, 860, 861, 866, 867, 868, 873, 875, 877, 879, 882, 883, 885, 887, 888, 889, 891, 897, 898, 901, 904, 907, 908, 909, 910, 911, 912, 913, 915, 916, 917, 918, 919, 921, 922, 927, 928, 933, 935, 938, 939, 943, 944, 946, 947, 950, 954, 955, 956, 960, 961, 962, 964, 967, 968, 969, 971, 976, 979, 981, 983, 985, 988, 991, 992, 993, 994, 995, 1000, 1001, 1002, 1004, 1005, 1007, 1011, 1015, 1017, 1018, 1021, 1027, 1029, 1030, 1032, 1035, 1037, 1038, 1040, 1041, 1045, 1046, 1047, 1048, 1050, 1051, 1053, 1055, 1057, 1058, 1063, 1065, 1066, 1068, 1069 ]; hyperovals[20]:= [ 1, 2, 3, 4, 5, 6, 7, 8, 11, 13, 14, 17, 19, 20, 22, 23, 26, 27, 29, 30, 32, 33, 36, 37, 41, 42, 43, 48, 51, 52, 54, 57, 58, 61, 62, 63, 64, 65, 66, 68, 71, 78, 79, 80, 81, 82, 85, 88, 89, 90, 92, 94, 99, 100, 101, 103, 104, 106, 109, 110, 111, 115, 116, 120, 122, 123, 124, 130, 134, 137, 141, 142, 143, 146, 147, 148, 150, 151, 155, 157, 158, 159, 160, 162, 164, 165, 169, 170, 172, 174, 175, 178, 180, 181, 183, 186, 187, 188, 191, 193, 196, 197, 198, 201, 205, 207, 208, 209, 212, 217, 219, 220, 222, 225, 227, 229, 230, 232, 237, 238, 239, 240, 242, 245, 248, 249, 250, 251, 254, 255, 259, 260, 261, 262, 264, 267, 268, 269, 271, 274, 275, 276, 280, 281, 283, 288, 289, 290, 291, 293, 294, 297, 299, 303, 304, 306, 309, 310, 313, 314, 316, 317, 319, 320, 321, 322, 323, 324, 329, 330, 335, 337, 338, 340, 342, 343, 347, 348, 349, 350, 355, 356, 357, 359, 360, 361, 366, 367, 370, 371, 374, 375, 377, 378, 382, 387, 388, 389, 392, 393, 394, 397, 400, 403, 405, 406, 407, 408, 409, 410, 411, 412, 413, 415, 416, 424, 425, 426, 427, 429, 431, 433, 434, 436, 437, 439, 442, 443, 445, 448, 449, 454, 456, 457, 458, 462, 464, 466, 467, 468, 470, 472, 474, 475, 477, 478, 483, 484, 485, 486, 487, 488, 489, 493, 497, 500, 501, 505, 506, 507, 510, 512, 513, 514, 515, 516, 518, 521, 522, 523, 524, 526, 527, 532, 534, 535, 536, 537, 541, 542, 543, 544, 546, 549, 551, 552, 553, 554, 555, 556, 558, 560, 562, 564, 568, 571, 572, 577, 580, 581, 583, 584, 585, 590, 593, 594, 595, 598, 600, 605, 606, 607, 608, 609, 610, 614, 616, 617, 618, 619, 621, 623, 625, 627, 628, 629, 631, 632, 634, 635, 640, 645, 647, 649, 650, 652, 653, 654, 656, 658, 659, 661, 662, 664, 665, 666, 670, 675, 677, 678, 679, 680, 682, 683, 684, 685, 687, 688, 689, 690, 695, 697, 699, 700, 701, 702, 703, 704, 705, 707, 708, 711, 713, 716, 723, 726, 727, 728, 729, 730, 732, 741, 742, 745, 746, 747, 749, 750, 752, 753, 758, 759, 760, 763, 765, 767, 770, 772, 773, 777, 778, 781, 783, 785, 786, 787, 791, 797, 799, 802, 804, 805, 810, 813, 820, 821, 823, 824, 825, 832, 833, 835, 836, 838, 840, 844, 846, 847, 848, 849, 850, 851, 852, 853, 854, 857, 858, 859, 860, 861, 862, 863, 864, 867, 868, 869, 872, 875, 876, 877, 879, 881, 882, 884, 885, 886, 887, 890, 892, 893, 894, 895, 897, 898, 899, 901, 902, 903, 904, 907, 908, 909, 910, 918, 920, 921, 922, 923, 925, 926, 927, 929, 930, 931, 932, 936, 937, 938, 941, 942, 943, 945, 947, 948, 950, 952, 954, 957, 958, 960, 961, 962, 964, 965, 967, 968, 971, 973, 976, 977, 978, 979, 981, 982, 985, 987, 988, 989, 990, 991, 992, 994, 995, 997, 999, 1001, 1002, 1003, 1007, 1010, 1011, 1012, 1013, 1019, 1020, 1021, 1027, 1030, 1031, 1033, 1035, 1036, 1037, 1038, 1039, 1042, 1046, 1048, 1050, 1054, 1055, 1056, 1059, 1061, 1062, 1064, 1066, 1067, 1068, 1071 ]; hyperovals[21]:= [ 1, 2, 3, 4, 5, 8, 9, 10, 11, 14, 16, 17, 20, 21, 27, 32, 35, 36, 37, 38, 42, 43, 45, 48, 51, 53, 54, 56, 57, 58, 60, 62, 63, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81, 83, 84, 86, 90, 91, 94, 96, 97, 98, 102, 103, 107, 108, 111, 112, 115, 119, 120, 125, 126, 131, 134, 136, 138, 142, 145, 146, 147, 149, 150, 153, 154, 155, 156, 158, 159, 164, 165, 167, 169, 174, 175, 177, 178, 180, 181, 182, 184, 185, 190, 191, 195, 202, 209, 210, 211, 213, 215, 218, 220, 222, 224, 225, 226, 227, 230, 231, 237, 238, 244, 247, 248, 249, 250, 252, 255, 257, 259, 260, 261, 267, 268, 274, 277, 280, 283, 286, 288, 290, 292, 293, 294, 295, 297, 300, 302, 303, 304, 307, 308, 309, 311, 315, 316, 317, 319, 321, 322, 328, 331, 332, 334, 335, 337, 341, 342, 343, 344, 346, 348, 352, 356, 357, 359, 361, 362, 364, 368, 369, 371, 373, 376, 380, 381, 382, 384, 385, 386, 389, 398, 400, 405, 406, 408, 409, 410, 411, 412, 413, 414, 415, 417, 418, 419, 420, 423, 424, 428, 434, 436, 437, 439, 442, 443, 444, 449, 451, 452, 455, 456, 458, 459, 461, 467, 471, 477, 479, 482, 483, 484, 485, 489, 491, 492, 494, 496, 497, 499, 500, 502, 503, 506, 507, 511, 512, 515, 516, 517, 519, 520, 521, 522, 523, 524, 525, 526, 530, 531, 532, 533, 538, 543, 544, 549, 550, 553, 557, 559, 561, 562, 564, 573, 574, 576, 579, 580, 582, 583, 587, 589, 590, 593, 594, 598, 599, 601, 603, 604, 607, 608, 609, 610, 613, 618, 621, 622, 623, 624, 625, 627, 628, 631, 632, 633, 638, 639, 640, 642, 644, 648, 649, 651, 653, 654, 655, 657, 660, 663, 669, 670, 672, 674, 676, 677, 678, 679, 680, 682, 684, 686, 687, 689, 690, 691, 692, 693, 695, 696, 697, 703, 705, 708, 709, 710, 713, 715, 716, 718, 723, 726, 730, 732, 733, 734, 735, 739, 740, 748, 751, 752, 758, 759, 760, 764, 766, 767, 769, 773, 775, 777, 780, 781, 782, 784, 785, 786, 787, 789, 793, 799, 801, 805, 806, 807, 809, 810, 812, 813, 815, 818, 821, 822, 823, 824, 829, 831, 834, 836, 837, 838, 839, 840, 843, 848, 852, 853, 856, 857, 860, 863, 864, 867, 869, 871, 872, 874, 876, 877, 879, 881, 882, 883, 888, 890, 891, 892, 894, 896, 899, 901, 903, 904, 905, 906, 908, 909, 910, 911, 913, 914, 917, 918, 919, 921, 922, 923, 924, 927, 931, 933, 934, 935, 936, 939, 944, 945, 946, 947, 950, 954, 960, 962, 963, 968, 969, 972, 973, 976, 978, 979, 982, 983, 984, 985, 988, 989, 992, 993, 994, 996, 997, 998, 999, 1003, 1004, 1005, 1006, 1007, 1010, 1012, 1015, 1018, 1019, 1020, 1022, 1024, 1030, 1031, 1033, 1035, 1039, 1040, 1042, 1044, 1045, 1047, 1050, 1051, 1052, 1053, 1054, 1057, 1063, 1065, 1066, 1069, 1071 ]; hyperovals[22]:= [ 1, 2, 4, 10, 12, 16, 17, 20, 27, 28, 29, 33, 34, 38, 39, 41, 43, 46, 47, 48, 50, 54, 56, 57, 58, 59, 60, 61, 62, 64, 74, 76, 82, 83, 87, 88, 89, 91, 93, 94, 95, 98, 103, 106, 110, 112, 114, 116, 118, 119, 122, 127, 129, 130, 132, 135, 141, 142, 143, 144, 145, 148, 153, 155, 156, 157, 158, 159, 160, 162, 163, 165, 173, 174, 175, 178, 179, 183, 186, 187, 189, 190, 191, 193, 194, 195, 199, 200, 202, 203, 206, 208, 210, 211, 213, 214, 216, 217, 222, 223, 224, 230, 231, 232, 233, 234, 235, 237, 238, 239, 242, 243, 247, 249, 250, 251, 252, 254, 257, 258, 259, 262, 264, 271, 273, 274, 275, 277, 279, 281, 283, 285, 287, 288, 289, 290, 293, 294, 295, 296, 297, 298, 302, 303, 305, 306, 307, 308, 309, 311, 313, 314, 315, 317, 318, 320, 321, 322, 323, 324, 325, 326, 327, 330, 331, 332, 335, 338, 340, 341, 343, 345, 346, 348, 349, 352, 353, 354, 356, 360, 362, 364, 366, 367, 370, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 384, 385, 387, 388, 389, 390, 391, 392, 396, 397, 398, 399, 404, 405, 406, 408, 409, 410, 411, 412, 415, 417, 422, 423, 424, 426, 427, 432, 433, 437, 440, 441, 442, 444, 446, 449, 451, 455, 458, 461, 462, 464, 465, 467, 468, 470, 475, 476, 477, 478, 481, 483, 486, 488, 490, 492, 495, 496, 501, 504, 505, 507, 509, 510, 514, 516, 517, 519, 521, 523, 524, 527, 529, 530, 532, 533, 534, 536, 537, 539, 540, 542, 544, 545, 547, 548, 549, 550, 551, 553, 555, 556, 557, 558, 559, 561, 562, 564, 565, 566, 567, 568, 571, 573, 575, 577, 580, 581, 582, 584, 585, 586, 590, 594, 597, 601, 602, 603, 605, 608, 610, 611, 614, 617, 618, 619, 620, 625, 626, 627, 630, 631, 632, 633, 635, 637, 638, 640, 644, 645, 646, 647, 648, 650, 653, 654, 655, 656, 657, 658, 663, 664, 665, 668, 669, 675, 676, 677, 678, 679, 680, 686, 687, 688, 689, 693, 694, 695, 696, 697, 698, 703, 707, 708, 711, 712, 714, 715, 716, 717, 718, 721, 723, 724, 726, 728, 729, 730, 731, 732, 733, 738, 740, 743, 745, 746, 747, 750, 751, 752, 754, 756, 758, 760, 761, 763, 765, 767, 769, 770, 771, 773, 774, 776, 777, 782, 787, 789, 790, 791, 795, 796, 799, 800, 802, 805, 807, 809, 810, 811, 812, 813, 815, 816, 818, 819, 820, 822, 823, 826, 828, 829, 832, 833, 837, 838, 839, 840, 841, 843, 846, 854, 855, 861, 862, 863, 864, 865, 866, 867, 869, 870, 871, 872, 873, 874, 877, 879, 881, 884, 885, 886, 888, 889, 890, 894, 896, 903, 904, 905, 906, 907, 908, 910, 912, 916, 917, 919, 921, 922, 926, 927, 929, 930, 932, 933, 939, 942, 945, 946, 947, 950, 953, 955, 958, 959, 960, 961, 962, 963, 965, 967, 968, 970, 971, 972, 977, 978, 979, 980, 981, 984, 987, 988, 989, 990, 991, 992, 993, 994, 995, 997, 1001, 1002, 1003, 1004, 1009, 1011, 1012, 1013, 1015, 1019, 1020, 1022, 1023, 1024, 1025, 1027, 1028, 1032, 1034, 1038, 1041, 1043, 1045, 1049, 1051, 1053, 1054, 1056, 1060, 1064, 1065, 1067, 1068 ]; hyperovals[23]:= [ 1, 3, 6, 7, 8, 13, 16, 18, 28, 30, 32, 33, 34, 35, 38, 39, 42, 43, 45, 47, 48, 49, 50, 54, 58, 61, 63, 64, 65, 68, 69, 72, 74, 76, 78, 79, 80, 82, 85, 86, 87, 89, 91, 92, 93, 94, 96, 97, 98, 100, 101, 103, 108, 111, 112, 115, 118, 120, 122, 124, 126, 127, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 151, 152, 154, 156, 157, 158, 159, 160, 161, 163, 166, 178, 180, 184, 185, 186, 187, 188, 189, 190, 194, 195, 196, 198, 200, 204, 205, 207, 208, 211, 213, 214, 218, 221, 224, 225, 228, 229, 230, 231, 233, 234, 235, 236, 238, 240, 241, 246, 247, 251, 252, 253, 254, 257, 258, 262, 265, 268, 272, 274, 275, 276, 277, 278, 279, 282, 284, 285, 286, 287, 293, 295, 299, 301, 307, 309, 311, 312, 313, 315, 318, 319, 323, 324, 331, 332, 333, 334, 336, 337, 338, 339, 341, 342, 345, 347, 352, 353, 354, 355, 356, 357, 358, 359, 363, 368, 369, 373, 375, 383, 384, 385, 391, 396, 399, 401, 402, 404, 407, 408, 410, 411, 412, 414, 416, 418, 421, 424, 425, 426, 427, 428, 429, 433, 434, 439, 440, 441, 444, 446, 447, 455, 456, 458, 459, 462, 465, 466, 467, 468, 471, 473, 474, 475, 476, 478, 479, 481, 487, 490, 491, 496, 498, 499, 501, 505, 506, 507, 509, 510, 511, 512, 513, 514, 515, 522, 525, 526, 528, 531, 532, 533, 534, 535, 536, 537, 541, 542, 543, 544, 545, 547, 548, 549, 552, 555, 556, 557, 559, 563, 565, 567, 571, 572, 573, 577, 578, 579, 583, 584, 585, 587, 588, 589, 590, 591, 592, 594, 595, 596, 599, 600, 601, 606, 607, 610, 611, 612, 615, 616, 618, 619, 621, 622, 626, 627, 628, 629, 630, 631, 633, 636, 637, 638, 639, 640, 641, 642, 646, 647, 648, 649, 650, 652, 653, 657, 661, 666, 667, 668, 669, 673, 676, 678, 679, 681, 682, 683, 686, 690, 693, 697, 700, 701, 703, 708, 711, 712, 714, 715, 716, 719, 720, 721, 722, 729, 734, 735, 738, 740, 743, 744, 745, 747, 748, 750, 752, 753, 754, 755, 757, 758, 759, 760, 762, 764, 766, 768, 769, 770, 771, 772, 776, 777, 779, 780, 781, 783, 785, 793, 797, 798, 800, 801, 803, 804, 805, 808, 810, 813, 818, 819, 820, 822, 823, 824, 829, 831, 835, 838, 839, 840, 844, 845, 846, 847, 850, 855, 856, 858, 861, 862, 863, 866, 869, 873, 874, 875, 876, 879, 880, 881, 884, 885, 887, 888, 890, 891, 893, 894, 896, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 910, 911, 913, 914, 915, 918, 920, 922, 923, 926, 927, 928, 930, 931, 933, 936, 937, 938, 941, 942, 943, 946, 951, 952, 954, 956, 957, 960, 961, 963, 964, 966, 967, 972, 975, 976, 977, 979, 980, 981, 983, 986, 988, 990, 991, 992, 993, 995, 997, 1000, 1002, 1004, 1006, 1007, 1008, 1010, 1014, 1017, 1019, 1024, 1025, 1026, 1027, 1028, 1029, 1031, 1032, 1033, 1034, 1036, 1037, 1038, 1040, 1041, 1045, 1051, 1052, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1067, 1068, 1069, 1070, 1071 ]; hyperovals[24]:= [ 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 31, 32, 33, 39, 40, 43, 44, 47, 50, 55, 58, 61, 62, 63, 65, 67, 68, 69, 71, 73, 76, 77, 78, 79, 81, 85, 88, 91, 92, 93, 94, 103, 104, 105, 106, 107, 108, 109, 112, 116, 117, 122, 123, 126, 127, 128, 136, 138, 139, 140, 143, 146, 150, 151, 152, 153, 158, 159, 161, 162, 163, 165, 167, 171, 173, 176, 178, 184, 187, 189, 190, 191, 192, 194, 195, 197, 199, 200, 201, 204, 206, 209, 211, 212, 214, 215, 216, 219, 221, 222, 224, 227, 229, 230, 232, 235, 236, 239, 241, 244, 245, 247, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 260, 262, 263, 265, 268, 271, 272, 273, 277, 280, 282, 283, 284, 293, 295, 297, 298, 300, 303, 305, 307, 312, 314, 317, 319, 320, 321, 323, 324, 326, 329, 331, 333, 334, 335, 338, 340, 342, 346, 347, 348, 354, 356, 357, 360, 361, 365, 366, 368, 369, 372, 378, 379, 381, 382, 383, 391, 393, 394, 395, 396, 397, 398, 400, 402, 403, 407, 408, 413, 414, 416, 417, 420, 421, 422, 423, 424, 425, 426, 428, 431, 433, 434, 435, 437, 438, 439, 444, 445, 446, 447, 448, 449, 450, 452, 453, 454, 456, 457, 458, 459, 460, 461, 463, 466, 467, 468, 471, 474, 477, 479, 480, 482, 484, 488, 489, 491, 493, 495, 497, 499, 500, 504, 507, 510, 511, 512, 519, 521, 522, 526, 527, 531, 534, 536, 542, 543, 546, 547, 548, 549, 554, 555, 556, 557, 558, 559, 560, 561, 565, 566, 567, 569, 571, 573, 574, 579, 582, 583, 586, 587, 591, 593, 597, 598, 599, 600, 604, 607, 608, 612, 613, 614, 615, 617, 618, 619, 620, 621, 624, 626, 627, 632, 634, 636, 638, 639, 641, 642, 644, 645, 646, 647, 649, 650, 651, 654, 655, 656, 657, 660, 662, 663, 664, 666, 667, 672, 675, 677, 678, 679, 680, 683, 684, 685, 689, 693, 694, 697, 700, 701, 706, 709, 710, 714, 718, 721, 727, 729, 734, 735, 741, 743, 746, 751, 752, 754, 755, 756, 763, 764, 769, 774, 775, 776, 777, 778, 786, 787, 788, 791, 800, 801, 802, 803, 804, 806, 807, 809, 810, 811, 812, 814, 816, 817, 819, 820, 823, 825, 828, 829, 833, 836, 837, 839, 841, 844, 845, 854, 857, 862, 863, 864, 865, 866, 871, 872, 876, 877, 880, 881, 882, 887, 889, 892, 893, 894, 895, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 910, 911, 912, 913, 915, 916, 917, 923, 925, 929, 932, 934, 935, 936, 937, 940, 941, 942, 949, 950, 951, 952, 954, 957, 958, 959, 960, 961, 965, 967, 969, 971, 974, 975, 976, 977, 978, 985, 986, 988, 989, 990, 993, 996, 999, 1000, 1001, 1002, 1003, 1005, 1006, 1010, 1011, 1014, 1017, 1021, 1022, 1023, 1025, 1026, 1028, 1030, 1031, 1033, 1034, 1036, 1038, 1039, 1040, 1041, 1042, 1044, 1045, 1046, 1050, 1051, 1052, 1053, 1056, 1057, 1059, 1060, 1063, 1068, 1070 ]; 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hyperovals[28]:= [ 1, 2, 3, 4, 7, 13, 14, 16, 17, 19, 24, 26, 27, 29, 31, 32, 34, 36, 38, 39, 40, 43, 47, 48, 50, 51, 53, 54, 56, 57, 58, 60, 67, 68, 69, 71, 72, 74, 78, 79, 81, 82, 84, 87, 88, 89, 90, 91, 93, 94, 96, 98, 101, 104, 105, 109, 112, 114, 115, 116, 121, 123, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140, 141, 142, 146, 147, 150, 151, 155, 156, 160, 161, 168, 171, 173, 174, 175, 178, 181, 184, 185, 186, 187, 191, 195, 197, 199, 202, 203, 206, 208, 210, 212, 214, 215, 220, 222, 226, 228, 229, 231, 240, 242, 243, 247, 248, 251, 255, 256, 257, 259, 262, 264, 265, 266, 268, 270, 271, 272, 273, 274, 275, 276, 277, 279, 280, 283, 284, 288, 289, 290, 291, 294, 295, 299, 303, 304, 306, 309, 310, 311, 314, 316, 319, 320, 322, 323, 324, 326, 328, 329, 333, 335, 336, 338, 339, 342, 344, 351, 352, 355, 357, 358, 360, 362, 365, 368, 369, 370, 372, 374, 379, 381, 383, 385, 386, 388, 389, 392, 395, 396, 397, 398, 400, 401, 402, 403, 404, 406, 407, 408, 412, 413, 415, 419, 422, 423, 424, 427, 429, 431, 434, 435, 436, 437, 439, 440, 442, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 458, 459, 461, 462, 463, 467, 468, 469, 473, 474, 475, 478, 479, 481, 482, 485, 489, 490, 493, 494, 495, 496, 497, 498, 500, 506, 508, 510, 511, 515, 517, 519, 522, 525, 529, 530, 537, 538, 541, 542, 543, 544, 549, 551, 554, 555, 556, 557, 558, 561, 564, 566, 567, 568, 570, 572, 573, 577, 579, 581, 582, 588, 592, 594, 595, 596, 597, 602, 605, 606, 608, 610, 613, 617, 620, 623, 624, 625, 626, 630, 632, 634, 637, 638, 639, 640, 641, 642, 644, 645, 647, 648, 649, 651, 653, 654, 655, 656, 660, 661, 663, 666, 667, 671, 675, 676, 678, 679, 684, 686, 687, 689, 692, 693, 694, 695, 699, 701, 704, 706, 709, 714, 715, 716, 717, 718, 720, 721, 723, 724, 725, 726, 730, 731, 732, 734, 736, 737, 738, 739, 741, 742, 744, 745, 748, 749, 754, 756, 757, 761, 765, 766, 767, 769, 771, 773, 776, 777, 778, 780, 781, 783, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 815, 816, 817, 826, 829, 832, 835, 840, 841, 842, 843, 844, 847, 849, 852, 853, 856, 858, 862, 863, 865, 868, 869, 870, 872, 873, 874, 875, 876, 878, 879, 880, 881, 885, 886, 888, 891, 896, 898, 899, 900, 901, 902, 903, 905, 906, 911, 913, 915, 918, 919, 922, 925, 926, 927, 928, 930, 931, 932, 935, 937, 939, 940, 941, 943, 946, 947, 948, 949, 950, 951, 957, 958, 959, 961, 965, 968, 971, 977, 980, 982, 984, 985, 986, 993, 995, 996, 1000, 1001, 1002, 1003, 1005, 1010, 1012, 1014, 1015, 1018, 1019, 1021, 1023, 1024, 1025, 1027, 1028, 1031, 1034, 1037, 1039, 1040, 1041, 1044, 1047, 1050, 1052, 1054, 1056, 1057, 1058, 1059, 1061, 1062, 1063, 1064, 1065, 1068, 1069, 1071 ]; 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hyperovals[30]:= [ 3, 5, 6, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 24, 26, 29, 31, 32, 33, 36, 37, 39, 42, 43, 45, 46, 47, 52, 53, 57, 59, 60, 63, 64, 66, 69, 70, 72, 73, 74, 75, 77, 80, 86, 88, 93, 94, 95, 96, 100, 101, 104, 106, 107, 110, 113, 114, 115, 116, 118, 120, 122, 123, 126, 127, 130, 131, 135, 136, 138, 140, 141, 143, 144, 145, 146, 147, 149, 154, 155, 156, 157, 159, 160, 162, 163, 164, 167, 168, 169, 171, 172, 176, 178, 181, 183, 185, 186, 187, 188, 193, 194, 195, 198, 199, 200, 203, 206, 208, 209, 212, 217, 218, 219, 220, 221, 222, 223, 225, 226, 229, 230, 231, 233, 234, 240, 241, 242, 246, 247, 250, 251, 252, 255, 256, 259, 262, 263, 265, 267, 271, 272, 273, 275, 277, 278, 279, 281, 282, 284, 285, 288, 289, 294, 297, 298, 299, 301, 305, 309, 314, 316, 318, 319, 321, 324, 327, 329, 330, 331, 333, 334, 335, 336, 337, 340, 343, 344, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 358, 360, 367, 368, 371, 372, 373, 374, 376, 377, 378, 379, 380, 381, 383, 384, 387, 389, 390, 391, 394, 397, 398, 402, 404, 405, 406, 407, 408, 410, 412, 416, 417, 418, 419, 421, 424, 425, 426, 427, 428, 430, 433, 434, 435, 436, 437, 438, 439, 440, 441, 443, 444, 446, 447, 448, 452, 454, 456, 457, 459, 464, 466, 468, 472, 473, 474, 477, 480, 483, 485, 486, 489, 490, 491, 493, 494, 500, 502, 503, 505, 506, 509, 513, 515, 518, 519, 521, 523, 524, 526, 530, 531, 533, 536, 537, 538, 539, 542, 545, 548, 549, 550, 551, 552, 555, 556, 557, 559, 560, 561, 564, 565, 569, 570, 572, 573, 575, 576, 577, 578, 579, 582, 583, 584, 587, 588, 599, 601, 602, 603, 608, 609, 611, 612, 616, 617, 621, 623, 624, 628, 630, 631, 632, 633, 634, 635, 636, 638, 640, 641, 644, 645, 646, 649, 653, 654, 657, 659, 661, 662, 665, 669, 670, 671, 672, 674, 675, 681, 683, 684, 685, 687, 688, 689, 691, 693, 694, 696, 697, 700, 702, 703, 705, 706, 707, 708, 709, 710, 711, 712, 713, 717, 718, 723, 724, 725, 727, 728, 729, 731, 732, 736, 741, 744, 745, 747, 748, 750, 751, 756, 758, 759, 760, 763, 765, 771, 772, 775, 776, 777, 785, 786, 792, 793, 795, 797, 799, 807, 809, 813, 814, 816, 817, 819, 825, 827, 829, 831, 835, 836, 837, 838, 840, 841, 842, 844, 845, 848, 849, 853, 854, 855, 858, 859, 866, 868, 869, 870, 873, 875, 876, 878, 879, 880, 882, 883, 884, 885, 886, 889, 891, 892, 897, 898, 899, 901, 902, 905, 906, 908, 912, 917, 918, 923, 924, 928, 931, 932, 933, 937, 943, 945, 946, 948, 950, 955, 958, 959, 962, 965, 968, 972, 973, 977, 978, 979, 983, 986, 987, 989, 992, 993, 995, 996, 997, 998, 999, 1006, 1008, 1011, 1013, 1014, 1015, 1016, 1018, 1019, 1021, 1022, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1032, 1033, 1036, 1038, 1040, 1043, 1044, 1047, 1050, 1051, 1053, 1054, 1057, 1058, 1061, 1063, 1067, 1068, 1069 ]; hyperovals[31]:= [ 1, 2, 3, 4, 7, 9, 10, 16, 17, 18, 21, 22, 24, 26, 27, 29, 30, 31, 32, 34, 36, 39, 40, 41, 43, 47, 51, 52, 53, 55, 57, 60, 64, 65, 67, 68, 69, 70, 73, 74, 75, 77, 78, 82, 83, 85, 86, 87, 88, 92, 93, 95, 98, 106, 110, 112, 115, 121, 122, 123, 124, 125, 128, 136, 138, 139, 141, 145, 146, 147, 149, 151, 152, 154, 157, 158, 161, 163, 164, 165, 166, 169, 170, 172, 173, 180, 181, 182, 183, 184, 186, 187, 189, 191, 192, 195, 198, 200, 201, 208, 210, 215, 220, 223, 224, 225, 226, 228, 230, 232, 234, 237, 238, 239, 245, 247, 248, 251, 252, 253, 254, 258, 259, 262, 264, 265, 266, 267, 268, 272, 277, 278, 280, 281, 283, 285, 286, 289, 293, 296, 298, 300, 301, 304, 305, 306, 307, 308, 309, 312, 313, 314, 315, 316, 317, 320, 321, 323, 324, 325, 327, 331, 335, 336, 342, 345, 346, 347, 348, 349, 350, 351, 352, 354, 356, 357, 358, 359, 360, 361, 363, 370, 371, 372, 374, 375, 376, 380, 381, 383, 384, 387, 390, 391, 392, 394, 395, 400, 401, 402, 405, 408, 410, 414, 419, 420, 421, 422, 425, 434, 436, 437, 438, 439, 440, 441, 442, 445, 446, 449, 451, 454, 458, 460, 461, 466, 472, 473, 474, 477, 478, 483, 484, 488, 489, 493, 496, 502, 503, 511, 514, 515, 516, 521, 522, 523, 525, 529, 530, 533, 539, 540, 541, 542, 543, 544, 546, 548, 550, 552, 553, 555, 556, 557, 558, 563, 564, 568, 569, 570, 571, 572, 574, 577, 579, 582, 587, 590, 596, 603, 606, 609, 611, 614, 616, 617, 618, 622, 623, 625, 628, 629, 630, 632, 633, 636, 637, 640, 641, 644, 647, 648, 649, 651, 653, 656, 657, 658, 660, 663, 664, 666, 667, 668, 669, 672, 673, 674, 675, 677, 678, 680, 682, 685, 695, 696, 697, 698, 702, 703, 705, 706, 707, 709, 711, 715, 716, 717, 719, 720, 721, 722, 723, 724, 725, 727, 728, 729, 736, 738, 739, 741, 742, 745, 746, 749, 750, 751, 752, 754, 758, 759, 760, 761, 762, 765, 766, 768, 769, 772, 773, 775, 778, 779, 780, 784, 785, 788, 789, 790, 795, 796, 797, 800, 801, 807, 808, 809, 812, 813, 814, 817, 818, 819, 820, 821, 824, 825, 827, 830, 832, 833, 834, 836, 837, 839, 840, 842, 844, 845, 849, 850, 852, 853, 854, 858, 859, 860, 861, 864, 866, 867, 871, 872, 873, 875, 876, 877, 881, 884, 886, 887, 890, 899, 900, 901, 904, 905, 906, 910, 911, 912, 914, 915, 917, 918, 919, 920, 923, 924, 926, 927, 933, 935, 938, 941, 948, 950, 951, 955, 958, 959, 960, 961, 963, 964, 965, 970, 973, 977, 979, 981, 984, 986, 987, 991, 992, 993, 996, 997, 1000, 1004, 1005, 1007, 1008, 1009, 1010, 1011, 1013, 1015, 1018, 1020, 1022, 1027, 1032, 1035, 1036, 1040, 1044, 1045, 1046, 1048, 1049, 1050, 1056, 1057, 1058, 1062, 1064, 1065, 1070, 1071 ]; hyperovals[32]:= [ 3, 5, 7, 8, 11, 12, 13, 16, 17, 19, 22, 26, 29, 31, 33, 34, 35, 37, 38, 39, 42, 44, 47, 51, 52, 55, 57, 58, 59, 60, 63, 65, 67, 68, 69, 70, 71, 79, 82, 84, 85, 86, 87, 92, 94, 95, 96, 101, 105, 106, 107, 108, 109, 112, 113, 114, 115, 118, 120, 125, 127, 130, 132, 134, 138, 144, 148, 150, 151, 152, 154, 157, 160, 161, 162, 164, 166, 169, 171, 173, 174, 177, 179, 180, 181, 183, 186, 188, 189, 190, 191, 195, 198, 202, 203, 205, 206, 213, 214, 216, 218, 220, 224, 225, 229, 230, 232, 233, 239, 241, 242, 246, 249, 252, 253, 254, 255, 258, 259, 261, 268, 275, 276, 277, 279, 281, 285, 286, 287, 288, 289, 290, 292, 294, 297, 299, 301, 303, 304, 305, 307, 308, 310, 311, 312, 313, 314, 315, 316, 317, 318, 320, 321, 323, 326, 328, 330, 333, 334, 335, 336, 337, 338, 340, 344, 345, 350, 351, 352, 354, 355, 356, 359, 360, 361, 362, 368, 369, 370, 371, 376, 378, 382, 383, 384, 391, 393, 394, 400, 402, 405, 406, 408, 416, 418, 421, 422, 428, 430, 432, 433, 434, 436, 437, 438, 439, 440, 442, 445, 446, 449, 451, 456, 458, 460, 461, 462, 467, 469, 470, 472, 477, 479, 482, 484, 489, 491, 493, 494, 496, 497, 500, 507, 508, 510, 511, 512, 515, 516, 518, 520, 522, 523, 524, 526, 528, 530, 533, 534, 535, 538, 539, 540, 543, 544, 545, 548, 550, 551, 553, 557, 558, 559, 562, 564, 568, 572, 574, 576, 578, 581, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 596, 597, 599, 602, 603, 605, 606, 607, 608, 616, 618, 620, 623, 626, 629, 632, 635, 636, 638, 640, 641, 645, 649, 651, 655, 656, 657, 658, 659, 660, 661, 663, 667, 668, 671, 672, 673, 674, 676, 678, 685, 688, 690, 691, 692, 694, 695, 698, 699, 700, 706, 710, 714, 718, 719, 720, 722, 727, 728, 730, 738, 739, 740, 742, 743, 746, 748, 750, 752, 753, 754, 757, 758, 759, 760, 761, 763, 764, 765, 766, 767, 770, 771, 772, 778, 780, 781, 785, 789, 792, 795, 796, 799, 801, 802, 803, 807, 808, 809, 813, 817, 819, 828, 830, 833, 838, 840, 845, 848, 853, 855, 856, 858, 859, 860, 864, 865, 870, 871, 873, 874, 875, 877, 879, 880, 881, 882, 886, 889, 890, 892, 899, 900, 901, 904, 905, 906, 911, 912, 914, 920, 927, 932, 934, 936, 938, 940, 941, 942, 946, 952, 953, 957, 961, 962, 963, 964, 966, 970, 972, 978, 980, 984, 985, 986, 988, 989, 990, 991, 992, 993, 996, 997, 1003, 1008, 1012, 1015, 1016, 1018, 1019, 1022, 1025, 1029, 1030, 1033, 1036, 1041, 1045, 1046, 1047, 1050, 1052, 1053, 1055, 1056, 1060, 1065, 1066, 1069 ]; hyperovals[33]:= [ 3, 4, 5, 6, 7, 8, 13, 14, 15, 18, 19, 20, 22, 23, 31, 32, 34, 35, 36, 37, 42, 45, 51, 53, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 75, 77, 79, 80, 81, 84, 86, 88, 90, 92, 95, 100, 102, 104, 105, 108, 110, 112, 113, 115, 116, 117, 120, 121, 122, 123, 125, 127, 134, 135, 136, 138, 139, 140, 141, 145, 146, 148, 149, 151, 152, 154, 155, 156, 159, 161, 163, 164, 171, 172, 176, 177, 179, 182, 185, 187, 188, 190, 195, 198, 203, 205, 207, 209, 210, 212, 213, 214, 219, 221, 226, 231, 233, 236, 237, 238, 240, 242, 243, 244, 247, 250, 251, 252, 253, 254, 257, 260, 262, 263, 264, 265, 266, 267, 269, 272, 275, 276, 279, 280, 281, 282, 283, 284, 286, 288, 289, 292, 293, 297, 298, 299, 300, 304, 307, 308, 309, 311, 316, 317, 318, 319, 321, 325, 326, 327, 328, 331, 332, 334, 335, 336, 337, 338, 340, 342, 343, 344, 346, 347, 348, 349, 350, 356, 357, 358, 359, 360, 361, 363, 368, 369, 370, 371, 375, 376, 377, 379, 381, 382, 383, 384, 385, 389, 390, 391, 392, 395, 397, 399, 400, 401, 404, 407, 409, 412, 413, 416, 420, 421, 425, 427, 428, 429, 430, 433, 434, 435, 436, 442, 443, 444, 445, 447, 448, 449, 450, 452, 457, 464, 466, 467, 469, 473, 474, 477, 479, 480, 482, 487, 488, 490, 494, 495, 498, 499, 500, 502, 503, 504, 505, 508, 509, 513, 516, 517, 518, 519, 520, 522, 523, 527, 532, 534, 537, 538, 540, 541, 544, 546, 550, 551, 552, 555, 556, 558, 559, 560, 562, 565, 566, 570, 571, 573, 575, 578, 580, 582, 583, 584, 587, 588, 589, 591, 594, 598, 602, 603, 605, 607, 610, 616, 618, 619, 620, 623, 625, 626, 628, 630, 633, 634, 636, 639, 640, 641, 645, 646, 648, 649, 653, 654, 655, 657, 658, 661, 662, 664, 668, 669, 671, 672, 673, 675, 676, 677, 678, 681, 683, 684, 685, 686, 690, 693, 694, 695, 703, 706, 707, 709, 711, 712, 713, 714, 716, 718, 722, 725, 726, 729, 730, 733, 735, 738, 740, 742, 743, 744, 747, 750, 751, 754, 756, 757, 758, 760, 762, 765, 766, 768, 770, 771, 773, 775, 776, 777, 780, 786, 788, 789, 790, 792, 793, 795, 799, 800, 802, 804, 805, 806, 807, 808, 809, 812, 813, 816, 818, 822, 824, 825, 826, 829, 830, 834, 837, 838, 839, 843, 844, 847, 849, 850, 851, 853, 856, 858, 861, 863, 864, 867, 868, 876, 878, 879, 881, 883, 885, 886, 889, 891, 892, 893, 897, 899, 903, 905, 906, 908, 909, 910, 914, 915, 917, 918, 921, 922, 924, 926, 927, 928, 932, 934, 935, 937, 940, 941, 942, 944, 945, 946, 949, 950, 951, 952, 961, 963, 965, 969, 972, 973, 975, 979, 980, 981, 982, 986, 988, 989, 992, 998, 999, 1000, 1004, 1005, 1009, 1014, 1015, 1016, 1017, 1018, 1026, 1027, 1036, 1039, 1040, 1041, 1046, 1050, 1053, 1054, 1055, 1056, 1058, 1059, 1061, 1062, 1067, 1068, 1069 ]; hyperovals[34]:= [ 5, 16, 25, 27, 29, 31, 32, 37, 42, 43, 44, 46, 49, 51, 54, 56, 58, 63, 69, 72, 73, 77, 79, 80, 81, 84, 87, 90, 93, 95, 99, 102, 111, 119, 120, 130, 131, 138, 140, 144, 147, 149, 153, 154, 155, 156, 157, 158, 161, 162, 163, 167, 168, 170, 172, 173, 175, 176, 178, 179, 180, 184, 189, 190, 191, 197, 198, 201, 202, 205, 206, 207, 212, 214, 215, 218, 220, 221, 222, 223, 224, 226, 228, 230, 231, 232, 234, 235, 236, 238, 239, 241, 242, 243, 244, 246, 247, 252, 253, 254, 257, 258, 261, 263, 265, 270, 272, 274, 279, 284, 285, 286, 288, 289, 293, 294, 295, 296, 301, 302, 304, 306, 307, 310, 311, 313, 314, 318, 321, 322, 324, 325, 329, 331, 332, 333, 334, 336, 338, 340, 346, 347, 354, 355, 356, 361, 362, 370, 371, 377, 378, 382, 386, 388, 390, 393, 394, 396, 397, 399, 400, 402, 405, 406, 407, 408, 411, 413, 415, 417, 418, 421, 422, 426, 427, 430, 431, 432, 434, 438, 441, 444, 447, 448, 450, 451, 452, 455, 458, 459, 460, 463, 464, 465, 467, 468, 469, 471, 472, 473, 477, 478, 479, 481, 486, 490, 491, 495, 496, 498, 502, 510, 511, 512, 514, 517, 518, 519, 520, 521, 522, 525, 526, 527, 528, 533, 534, 535, 538, 540, 541, 543, 544, 547, 549, 551, 553, 555, 557, 560, 561, 564, 565, 566, 567, 568, 569, 570, 572, 574, 577, 579, 584, 585, 586, 588, 590, 591, 596, 597, 598, 599, 600, 601, 603, 605, 606, 608, 612, 614, 616, 617, 619, 623, 624, 625, 629, 630, 631, 632, 634, 636, 637, 641, 642, 643, 644, 645, 648, 651, 652, 653, 655, 657, 658, 659, 660, 663, 666, 667, 668, 671, 675, 677, 679, 681, 682, 685, 687, 688, 690, 691, 694, 695, 698, 700, 702, 705, 706, 708, 710, 711, 712, 713, 714, 717, 718, 719, 720, 721, 723, 725, 726, 727, 728, 734, 735, 737, 738, 739, 743, 745, 747, 748, 749, 750, 751, 754, 755, 758, 760, 761, 763, 765, 767, 768, 771, 774, 775, 776, 778, 779, 781, 783, 789, 790, 791, 792, 794, 796, 801, 802, 803, 806, 807, 812, 813, 824, 832, 833, 834, 838, 840, 842, 844, 845, 849, 851, 852, 853, 855, 856, 857, 858, 860, 861, 862, 865, 866, 867, 868, 871, 872, 874, 877, 879, 880, 882, 886, 887, 889, 890, 891, 892, 894, 895, 897, 899, 901, 902, 903, 906, 908, 911, 912, 914, 916, 921, 922, 923, 924, 926, 927, 928, 929, 933, 935, 936, 938, 941, 943, 945, 949, 951, 952, 958, 963, 964, 967, 968, 969, 973, 975, 976, 978, 980, 982, 983, 985, 987, 991, 993, 995, 996, 997, 1007, 1008, 1011, 1014, 1018, 1019, 1022, 1025, 1029, 1031, 1034, 1035, 1036, 1037, 1039, 1040, 1041, 1045, 1046, 1048, 1050, 1053, 1056, 1057, 1059, 1060, 1061, 1063, 1064, 1065, 1069 ]; hyperovals[35]:= [ 5, 8, 9, 10, 12, 13, 14, 15, 17, 19, 21, 24, 26, 28, 29, 34, 35, 36, 37, 40, 41, 42, 44, 46, 47, 48, 49, 52, 53, 54, 58, 60, 61, 62, 63, 65, 66, 69, 72, 73, 77, 78, 80, 81, 83, 85, 87, 89, 91, 92, 94, 95, 101, 103, 104, 107, 108, 110, 112, 113, 114, 117, 118, 119, 120, 122, 125, 128, 129, 133, 134, 135, 139, 141, 142, 143, 144, 146, 150, 151, 152, 155, 156, 158, 162, 165, 167, 170, 171, 173, 177, 178, 180, 181, 184, 185, 186, 188, 189, 191, 193, 195, 196, 199, 200, 201, 203, 209, 211, 212, 213, 220, 222, 226, 228, 229, 233, 236, 237, 238, 241, 242, 247, 250, 251, 252, 253, 255, 257, 259, 261, 262, 263, 266, 268, 269, 270, 271, 274, 278, 279, 280, 281, 282, 284, 286, 288, 289, 291, 292, 293, 297, 298, 299, 301, 302, 304, 305, 307, 309, 310, 312, 314, 316, 317, 319, 320, 322, 323, 325, 327, 329, 330, 332, 333, 335, 338, 339, 343, 344, 346, 347, 348, 350, 351, 353, 354, 355, 356, 357, 359, 361, 362, 364, 365, 366, 368, 374, 375, 376, 378, 379, 380, 381, 383, 384, 385, 389, 390, 391, 392, 393, 398, 400, 401, 404, 408, 410, 412, 413, 418, 420, 421, 422, 425, 427, 430, 431, 432, 433, 434, 436, 443, 448, 450, 451, 452, 454, 455, 457, 458, 459, 461, 463, 464, 465, 467, 468, 471, 472, 473, 484, 485, 486, 487, 488, 489, 490, 494, 495, 496, 498, 500, 501, 504, 505, 506, 507, 508, 511, 512, 513, 515, 517, 519, 520, 521, 522, 523, 524, 525, 526, 527, 530, 534, 540, 542, 543, 544, 545, 549, 551, 552, 553, 556, 557, 558, 559, 560, 563, 567, 568, 569, 570, 572, 576, 580, 583, 586, 588, 589, 590, 594, 595, 600, 601, 605, 607, 608, 609, 610, 613, 614, 615, 618, 619, 621, 622, 623, 627, 631, 632, 633, 634, 635, 637, 638, 639, 643, 645, 648, 649, 650, 652, 653, 654, 658, 659, 660, 661, 662, 663, 664, 666, 669, 670, 672, 673, 675, 676, 678, 681, 683, 684, 688, 689, 690, 691, 693, 695, 698, 700, 702, 704, 706, 709, 714, 715, 716, 717, 718, 719, 722, 723, 724, 726, 727, 728, 729, 730, 731, 732, 733, 735, 737, 738, 741, 743, 744, 745, 746, 748, 751, 753, 754, 757, 758, 760, 762, 763, 764, 767, 772, 773, 777, 778, 781, 786, 787, 789, 792, 794, 796, 797, 799, 801, 804, 807, 808, 813, 814, 816, 817, 818, 819, 820, 823, 824, 826, 827, 829, 830, 833, 834, 837, 838, 839, 842, 844, 846, 848, 851, 852, 854, 858, 861, 862, 866, 867, 868, 869, 873, 874, 875, 876, 878, 881, 883, 885, 886, 891, 892, 894, 896, 897, 898, 899, 900, 902, 905, 906, 908, 910, 911, 914, 915, 916, 917, 918, 919, 921, 923, 925, 926, 927, 929, 930, 931, 935, 936, 938, 944, 945, 947, 951, 952, 954, 955, 956, 957, 958, 959, 962, 963, 964, 965, 973, 974, 975, 976, 978, 979, 980, 982, 983, 984, 985, 986, 992, 994, 995, 998, 999, 1000, 1002, 1003, 1004, 1007, 1010, 1011, 1013, 1014, 1015, 1016, 1019, 1020, 1021, 1022, 1027, 1029, 1030, 1035, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1048, 1049, 1051, 1052, 1053, 1054, 1055, 1056, 1058, 1060, 1062, 1065, 1066, 1068, 1069, 1071 ]; hyperovals[36]:= [ 1, 2, 9, 12, 13, 20, 21, 22, 24, 25, 28, 29, 31, 34, 35, 38, 41, 42, 43, 44, 47, 48, 52, 53, 56, 59, 62, 64, 65, 66, 67, 71, 72, 73, 74, 75, 78, 82, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 106, 108, 109, 114, 118, 119, 123, 125, 126, 127, 129, 133, 134, 138, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 153, 154, 155, 157, 158, 160, 161, 164, 166, 169, 170, 171, 172, 174, 175, 176, 178, 180, 182, 185, 186, 191, 192, 193, 196, 197, 199, 200, 203, 205, 206, 208, 210, 212, 213, 214, 215, 216, 220, 222, 224, 226, 229, 230, 231, 232, 233, 234, 236, 237, 241, 243, 247, 251, 254, 257, 260, 267, 270, 271, 274, 279, 283, 290, 297, 299, 303, 304, 307, 308, 309, 311, 317, 320, 326, 327, 329, 330, 332, 334, 335, 336, 342, 344, 349, 353, 354, 355, 357, 358, 359, 360, 362, 363, 364, 365, 366, 369, 373, 380, 381, 382, 384, 388, 389, 390, 391, 394, 396, 397, 399, 404, 408, 409, 410, 411, 412, 414, 415, 420, 421, 423, 427, 428, 431, 432, 434, 437, 439, 440, 444, 445, 449, 450, 453, 458, 459, 460, 461, 463, 466, 471, 472, 473, 474, 476, 478, 479, 482, 485, 486, 488, 489, 491, 493, 494, 495, 496, 500, 503, 504, 507, 508, 510, 512, 513, 514, 517, 519, 520, 522, 524, 527, 528, 529, 530, 531, 532, 533, 538, 539, 543, 544, 547, 548, 553, 554, 555, 559, 560, 564, 565, 567, 569, 570, 571, 573, 576, 581, 582, 583, 584, 586, 588, 593, 594, 601, 602, 603, 607, 611, 612, 614, 618, 620, 621, 622, 626, 628, 631, 634, 635, 637, 638, 639, 640, 641, 643, 646, 651, 655, 656, 657, 658, 659, 662, 665, 666, 667, 670, 674, 676, 677, 678, 684, 687, 689, 692, 693, 694, 695, 698, 700, 701, 703, 704, 707, 708, 711, 712, 713, 716, 719, 721, 723, 726, 727, 729, 732, 735, 739, 740, 741, 743, 744, 745, 747, 748, 750, 751, 754, 756, 761, 762, 765, 766, 767, 768, 770, 771, 773, 776, 778, 780, 783, 786, 788, 790, 794, 797, 800, 802, 806, 808, 810, 813, 819, 820, 826, 827, 829, 833, 839, 840, 841, 844, 847, 848, 849, 851, 853, 854, 855, 857, 858, 860, 863, 865, 866, 867, 868, 870, 871, 874, 875, 877, 878, 879, 881, 882, 883, 892, 893, 895, 896, 897, 899, 901, 902, 903, 904, 905, 907, 908, 910, 911, 913, 914, 915, 916, 919, 921, 924, 926, 928, 929, 931, 933, 935, 938, 943, 944, 945, 947, 950, 954, 955, 957, 959, 960, 962, 963, 967, 970, 972, 974, 975, 976, 985, 987, 992, 994, 995, 996, 997, 998, 1002, 1004, 1005, 1008, 1009, 1010, 1012, 1013, 1014, 1018, 1019, 1020, 1028, 1029, 1031, 1033, 1034, 1037, 1038, 1040, 1042, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1054, 1057, 1059, 1061, 1062, 1063, 1067, 1069, 1070 ]; hyperovals[37]:= [ 5, 9, 10, 11, 13, 15, 17, 19, 24, 26, 27, 30, 39, 40, 41, 43, 44, 46, 48, 55, 56, 58, 59, 60, 62, 64, 70, 71, 74, 75, 77, 78, 84, 85, 86, 87, 90, 94, 95, 97, 98, 99, 101, 103, 104, 111, 114, 115, 116, 117, 120, 123, 125, 126, 127, 128, 130, 135, 136, 138, 141, 143, 146, 149, 151, 155, 159, 160, 167, 169, 173, 175, 178, 179, 183, 184, 186, 189, 193, 200, 203, 207, 210, 214, 216, 217, 220, 222, 228, 229, 232, 234, 235, 238, 239, 243, 244, 245, 246, 248, 250, 251, 254, 256, 257, 258, 260, 261, 265, 266, 268, 272, 273, 274, 275, 276, 280, 281, 284, 287, 294, 295, 304, 305, 308, 309, 310, 312, 313, 315, 320, 321, 323, 325, 327, 328, 333, 334, 335, 337, 340, 344, 345, 347, 348, 349, 350, 351, 352, 353, 354, 358, 361, 362, 369, 370, 375, 378, 381, 383, 388, 391, 399, 400, 401, 405, 408, 411, 412, 413, 422, 424, 425, 427, 430, 431, 434, 435, 436, 437, 442, 444, 447, 448, 449, 453, 457, 458, 461, 466, 468, 469, 470, 471, 472, 474, 475, 477, 478, 479, 480, 488, 489, 491, 493, 494, 498, 499, 504, 505, 508, 509, 510, 512, 513, 516, 520, 525, 526, 527, 530, 535, 536, 537, 538, 539, 540, 541, 543, 545, 547, 550, 551, 553, 558, 559, 563, 564, 565, 567, 568, 572, 573, 574, 576, 578, 580, 582, 584, 586, 587, 589, 590, 598, 599, 601, 603, 606, 613, 615, 616, 619, 621, 622, 625, 627, 628, 633, 634, 635, 639, 642, 643, 646, 647, 651, 652, 653, 654, 656, 658, 660, 662, 663, 670, 671, 675, 682, 683, 684, 685, 687, 693, 694, 695, 698, 701, 702, 708, 709, 710, 712, 714, 719, 720, 725, 726, 727, 728, 729, 730, 732, 733, 734, 737, 742, 743, 744, 745, 748, 752, 756, 763, 767, 769, 774, 777, 785, 788, 793, 801, 802, 803, 808, 810, 812, 813, 814, 815, 818, 819, 820, 821, 823, 825, 826, 831, 834, 837, 840, 842, 843, 846, 848, 849, 850, 851, 852, 853, 855, 859, 862, 864, 865, 866, 873, 874, 875, 877, 881, 883, 885, 886, 889, 893, 898, 900, 902, 904, 906, 916, 921, 922, 923, 924, 925, 927, 931, 933, 935, 936, 937, 938, 942, 944, 950, 955, 956, 957, 966, 967, 969, 970, 971, 973, 974, 977, 980, 983, 986, 993, 994, 996, 999, 1000, 1002, 1003, 1005, 1008, 1009, 1010, 1012, 1014, 1015, 1016, 1023, 1024, 1025, 1026, 1028, 1029, 1031, 1036, 1037, 1038, 1039, 1041, 1042, 1045, 1048, 1049, 1050, 1051, 1052, 1056, 1058, 1063, 1070 ]; hyperovals[38]:= [ 2, 4, 6, 8, 9, 11, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 29, 30, 31, 34, 38, 39, 41, 45, 46, 47, 48, 50, 51, 55, 56, 58, 59, 63, 65, 66, 67, 68, 69, 71, 73, 76, 78, 79, 83, 85, 87, 89, 90, 91, 92, 95, 96, 97, 100, 102, 103, 105, 106, 110, 114, 115, 116, 117, 118, 119, 120, 121, 125, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 147, 150, 151, 152, 154, 157, 158, 159, 163, 164, 165, 166, 167, 168, 170, 171, 172, 175, 179, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 195, 200, 201, 203, 205, 209, 210, 211, 212, 213, 214, 215, 216, 217, 219, 221, 222, 224, 227, 228, 231, 232, 234, 235, 237, 238, 245, 248, 249, 250, 251, 252, 253, 255, 256, 259, 260, 262, 263, 264, 265, 267, 269, 270, 271, 272, 274, 275, 277, 278, 280, 283, 284, 285, 286, 287, 290, 291, 292, 295, 296, 297, 299, 300, 302, 303, 304, 305, 309, 310, 311, 312, 313, 315, 316, 318, 319, 325, 326, 327, 328, 329, 330, 334, 335, 336, 337, 338, 339, 341, 342, 344, 348, 355, 356, 359, 362, 366, 367, 370, 371, 372, 373, 374, 375, 376, 377, 380, 381, 383, 385, 387, 388, 389, 390, 391, 396, 397, 398, 403, 406, 408, 409, 411, 415, 416, 419, 420, 421, 422, 426, 427, 428, 432, 435, 436, 437, 439, 441, 444, 446, 447, 448, 451, 452, 453, 454, 459, 460, 461, 462, 464, 465, 467, 471, 472, 473, 474, 477, 478, 480, 482, 483, 484, 491, 494, 496, 498, 500, 504, 505, 506, 507, 508, 510, 512, 513, 514, 515, 518, 520, 521, 522, 524, 526, 530, 532, 534, 536, 538, 539, 542, 546, 549, 550, 551, 556, 558, 560, 562, 563, 565, 568, 569, 571, 572, 573, 574, 577, 579, 582, 583, 584, 585, 586, 587, 588, 591, 592, 596, 597, 601, 605, 606, 607, 611, 612, 616, 617, 620, 621, 622, 623, 624, 625, 630, 632, 633, 634, 635, 636, 638, 640, 643, 644, 646, 648, 649, 651, 652, 653, 655, 657, 661, 662, 663, 670, 673, 674, 675, 676, 677, 679, 681, 682, 684, 686, 687, 688, 693, 699, 703, 710, 713, 714, 716, 717, 720, 723, 725, 726, 729, 730, 736, 741, 743, 746, 749, 750, 751, 756, 757, 758, 759, 764, 765, 768, 769, 770, 771, 772, 774, 775, 776, 779, 782, 788, 795, 797, 798, 801, 802, 803, 804, 805, 806, 807, 809, 810, 811, 812, 813, 814, 815, 816, 820, 821, 822, 823, 824, 826, 830, 831, 834, 835, 837, 839, 840, 841, 843, 844, 846, 848, 849, 850, 852, 859, 864, 865, 866, 867, 868, 871, 873, 874, 876, 877, 878, 882, 883, 885, 887, 888, 889, 890, 893, 895, 897, 900, 902, 905, 906, 907, 909, 910, 911, 912, 913, 915, 919, 921, 922, 925, 929, 931, 933, 935, 937, 938, 939, 940, 942, 943, 947, 949, 955, 956, 957, 962, 963, 965, 967, 968, 970, 975, 978, 979, 980, 982, 984, 985, 986, 987, 988, 990, 992, 993, 994, 995, 996, 997, 999, 1002, 1003, 1004, 1005, 1007, 1008, 1009, 1013, 1015, 1019, 1020, 1021, 1022, 1023, 1024, 1027, 1028, 1029, 1030, 1032, 1033, 1035, 1036, 1039, 1040, 1042, 1043, 1045, 1046, 1050, 1051, 1052, 1053, 1056, 1058, 1059, 1061, 1062, 1067, 1069, 1070, 1071 ]; hyperovals[39]:= [ 2, 3, 5, 7, 9, 10, 11, 14, 15, 16, 19, 20, 22, 26, 27, 32, 35, 38, 39, 42, 44, 45, 50, 51, 53, 54, 57, 60, 63, 64, 66, 67, 70, 73, 74, 76, 77, 82, 89, 95, 96, 97, 100, 101, 108, 109, 110, 111, 116, 118, 123, 124, 125, 126, 127, 129, 130, 131, 134, 135, 136, 138, 140, 141, 142, 144, 145, 146, 148, 151, 152, 154, 156, 157, 158, 160, 161, 164, 166, 169, 171, 178, 181, 182, 183, 185, 186, 187, 188, 189, 190, 192, 193, 195, 196, 197, 202, 204, 205, 212, 213, 214, 217, 218, 219, 220, 221, 222, 225, 229, 232, 233, 234, 239, 242, 243, 244, 245, 247, 248, 249, 253, 254, 255, 256, 257, 261, 262, 264, 265, 268, 271, 272, 273, 275, 282, 283, 285, 286, 290, 291, 296, 298, 299, 301, 302, 303, 305, 306, 307, 309, 310, 316, 320, 326, 333, 334, 336, 338, 344, 349, 353, 354, 355, 356, 358, 359, 360, 362, 365, 369, 371, 373, 374, 377, 379, 381, 384, 386, 389, 390, 394, 396, 397, 400, 401, 403, 404, 406, 408, 412, 415, 416, 418, 419, 420, 422, 423, 425, 426, 431, 433, 436, 438, 439, 442, 444, 447, 448, 449, 450, 455, 456, 457, 458, 461, 466, 468, 469, 470, 475, 476, 478, 479, 481, 482, 484, 486, 490, 491, 492, 495, 496, 497, 498, 499, 500, 505, 506, 508, 510, 511, 512, 513, 514, 515, 516, 518, 522, 524, 529, 531, 533, 534, 536, 539, 543, 544, 545, 546, 548, 551, 554, 555, 556, 560, 561, 564, 565, 568, 570, 571, 572, 575, 576, 579, 580, 581, 583, 585, 586, 588, 590, 592, 597, 599, 600, 601, 603, 604, 605, 611, 615, 616, 618, 622, 623, 626, 629, 635, 636, 638, 641, 643, 645, 650, 651, 653, 655, 657, 660, 665, 666, 669, 670, 672, 673, 675, 676, 677, 679, 680, 681, 682, 685, 687, 693, 694, 696, 697, 698, 699, 700, 701, 702, 709, 710, 712, 715, 717, 722, 723, 724, 726, 727, 729, 730, 731, 736, 741, 743, 744, 750, 753, 754, 755, 756, 757, 759, 760, 761, 763, 764, 765, 769, 771, 772, 773, 774, 776, 777, 778, 779, 781, 785, 787, 789, 790, 792, 793, 795, 798, 800, 802, 803, 808, 810, 811, 812, 813, 814, 815, 817, 822, 823, 825, 826, 827, 831, 833, 834, 835, 837, 838, 839, 841, 845, 848, 849, 852, 856, 858, 859, 862, 864, 865, 866, 868, 869, 870, 871, 873, 878, 880, 881, 882, 883, 884, 885, 886, 889, 893, 897, 899, 900, 901, 904, 905, 908, 910, 911, 913, 920, 922, 923, 928, 930, 931, 932, 934, 935, 937, 940, 942, 943, 944, 945, 948, 953, 955, 956, 958, 961, 963, 965, 968, 970, 973, 974, 978, 979, 980, 982, 984, 985, 987, 988, 989, 990, 992, 994, 996, 1002, 1008, 1009, 1012, 1014, 1016, 1017, 1018, 1019, 1029, 1031, 1032, 1034, 1035, 1036, 1042, 1044, 1045, 1047, 1048, 1049, 1051, 1053, 1055, 1056, 1057, 1061, 1062, 1069, 1071 ]; 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hyperovals[46]:= [ 3, 4, 5, 6, 12, 15, 16, 20, 21, 22, 23, 24, 26, 27, 34, 35, 38, 39, 41, 42, 43, 44, 45, 46, 48, 52, 54, 56, 57, 58, 59, 62, 63, 64, 66, 68, 70, 74, 75, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 107, 108, 111, 115, 116, 118, 120, 121, 127, 128, 129, 133, 135, 137, 139, 141, 143, 146, 148, 152, 153, 155, 156, 157, 159, 160, 161, 162, 164, 165, 167, 169, 172, 173, 174, 175, 177, 179, 181, 184, 188, 189, 191, 192, 197, 199, 200, 203, 204, 205, 209, 210, 211, 213, 217, 221, 222, 224, 228, 234, 235, 237, 238, 242, 247, 248, 250, 253, 254, 257, 258, 259, 260, 261, 265, 266, 268, 270, 272, 275, 278, 280, 281, 282, 283, 286, 288, 290, 292, 293, 294, 295, 299, 301, 302, 309, 310, 311, 312, 314, 315, 316, 318, 321, 322, 324, 325, 326, 329, 330, 331, 333, 334, 335, 336, 337, 339, 347, 349, 352, 353, 355, 357, 358, 359, 362, 366, 368, 369, 371, 373, 376, 379, 382, 384, 386, 387, 388, 389, 392, 393, 394, 400, 403, 406, 411, 414, 417, 419, 420, 421, 422, 423, 426, 428, 429, 432, 433, 434, 436, 437, 438, 439, 443, 446, 447, 448, 450, 451, 452, 453, 454, 455, 456, 460, 466, 468, 469, 471, 476, 477, 478, 479, 484, 485, 486, 487, 491, 492, 494, 496, 497, 498, 499, 500, 501, 502, 503, 507, 508, 509, 510, 515, 516, 517, 519, 521, 522, 526, 528, 530, 532, 533, 534, 536, 537, 538, 540, 541, 542, 547, 551, 555, 557, 558, 560, 562, 564, 566, 567, 570, 571, 573, 574, 575, 576, 577, 578, 579, 580, 582, 584, 585, 589, 590, 591, 592, 594, 596, 597, 599, 604, 607, 608, 609, 610, 612, 613, 617, 623, 624, 625, 629, 631, 632, 633, 634, 637, 638, 640, 642, 646, 647, 650, 651, 652, 653, 656, 659, 661, 662, 665, 667, 670, 672, 678, 679, 680, 681, 682, 683, 686, 690, 691, 692, 693, 695, 698, 702, 703, 704, 706, 707, 709, 711, 715, 717, 719, 720, 721, 722, 723, 724, 727, 728, 732, 734, 735, 738, 741, 742, 743, 746, 748, 751, 752, 753, 755, 757, 758, 759, 760, 762, 764, 766, 768, 769, 770, 772, 773, 775, 776, 777, 780, 781, 782, 784, 786, 787, 788, 789, 793, 796, 802, 803, 808, 809, 813, 815, 817, 819, 820, 821, 822, 823, 829, 833, 838, 839, 840, 841, 842, 843, 844, 845, 847, 849, 851, 852, 853, 854, 856, 862, 863, 866, 867, 872, 878, 880, 884, 885, 888, 890, 891, 894, 895, 899, 900, 904, 906, 908, 909, 911, 912, 913, 914, 915, 916, 917, 918, 923, 925, 928, 931, 932, 934, 937, 940, 941, 944, 946, 948, 949, 954, 956, 957, 958, 959, 961, 962, 964, 969, 971, 972, 973, 974, 975, 978, 979, 980, 982, 983, 985, 991, 995, 996, 997, 1000, 1001, 1007, 1008, 1010, 1012, 1015, 1016, 1017, 1018, 1019, 1020, 1022, 1028, 1031, 1034, 1035, 1037, 1038, 1042, 1043, 1046, 1047, 1049, 1052, 1053, 1055, 1058, 1059, 1061, 1062, 1064, 1065, 1067, 1069, 1070 ]; hyperovals[47]:= [ 3, 4, 5, 6, 7, 9, 12, 17, 19, 20, 21, 22, 24, 30, 32, 34, 35, 37, 40, 41, 44, 45, 46, 50, 52, 53, 54, 59, 62, 63, 64, 66, 68, 72, 73, 74, 75, 77, 80, 81, 85, 86, 88, 93, 94, 95, 96, 105, 114, 115, 116, 118, 119, 120, 121, 123, 124, 125, 127, 128, 132, 133, 134, 136, 138, 139, 143, 144, 148, 149, 150, 151, 152, 154, 157, 158, 161, 165, 166, 168, 170, 172, 173, 179, 181, 182, 184, 188, 189, 200, 203, 208, 210, 212, 215, 218, 219, 220, 221, 223, 225, 230, 231, 233, 235, 240, 244, 245, 246, 249, 251, 252, 254, 255, 256, 259, 260, 261, 262, 263, 266, 268, 271, 272, 275, 279, 280, 281, 286, 287, 291, 292, 294, 295, 296, 297, 299, 303, 304, 305, 306, 307, 309, 310, 315, 316, 317, 318, 321, 324, 325, 326, 327, 329, 330, 332, 335, 336, 340, 341, 342, 343, 346, 347, 349, 350, 351, 356, 360, 362, 365, 366, 367, 368, 369, 370, 374, 375, 376, 378, 384, 385, 386, 393, 396, 397, 398, 400, 401, 405, 407, 410, 413, 414, 416, 417, 418, 420, 424, 425, 428, 429, 431, 432, 434, 435, 440, 442, 445, 446, 448, 451, 452, 453, 455, 456, 457, 458, 459, 466, 469, 470, 471, 472, 474, 477, 481, 483, 485, 486, 488, 492, 494, 497, 499, 504, 505, 508, 510, 512, 514, 516, 523, 524, 528, 530, 531, 532, 535, 537, 540, 542, 543, 549, 551, 552, 555, 556, 557, 558, 559, 560, 564, 566, 567, 570, 571, 573, 574, 577, 579, 580, 584, 585, 588, 590, 591, 592, 593, 594, 596, 599, 600, 602, 605, 606, 608, 610, 612, 613, 614, 615, 617, 618, 620, 622, 624, 625, 626, 627, 628, 629, 630, 633, 636, 637, 638, 642, 646, 647, 648, 649, 650, 658, 662, 663, 664, 666, 667, 668, 673, 675, 682, 683, 684, 686, 688, 689, 694, 695, 696, 697, 698, 699, 702, 710, 711, 714, 716, 717, 718, 720, 721, 722, 724, 726, 727, 730, 732, 734, 736, 740, 741, 743, 744, 746, 747, 752, 753, 755, 756, 757, 759, 764, 768, 770, 771, 772, 773, 774, 776, 778, 779, 780, 785, 786, 787, 789, 790, 791, 793, 796, 797, 799, 800, 802, 803, 805, 806, 810, 813, 814, 817, 820, 821, 824, 825, 827, 830, 831, 833, 834, 835, 839, 840, 842, 844, 847, 853, 854, 855, 856, 860, 865, 867, 868, 869, 870, 872, 877, 879, 882, 884, 885, 888, 890, 891, 893, 896, 900, 901, 903, 906, 907, 914, 915, 917, 918, 919, 920, 926, 929, 931, 933, 934, 935, 936, 937, 938, 940, 944, 945, 946, 947, 948, 949, 953, 955, 958, 959, 961, 962, 963, 967, 968, 972, 977, 978, 980, 981, 982, 985, 987, 989, 991, 992, 995, 1000, 1001, 1006, 1009, 1010, 1011, 1013, 1014, 1015, 1016, 1019, 1024, 1025, 1027, 1028, 1032, 1033, 1034, 1036, 1037, 1040, 1043, 1045, 1047, 1048, 1049, 1053, 1054, 1058, 1059, 1061, 1063, 1064, 1065, 1068 ]; hyperovals[48]:= [ 1, 2, 3, 6, 8, 12, 15, 16, 21, 23, 24, 26, 28, 29, 32, 34, 35, 36, 37, 38, 39, 41, 43, 44, 47, 48, 49, 52, 53, 54, 58, 64, 68, 70, 72, 77, 78, 82, 83, 85, 87, 91, 92, 96, 97, 98, 103, 104, 109, 110, 112, 115, 116, 117, 118, 119, 120, 121, 122, 126, 129, 130, 132, 133, 134, 136, 138, 141, 143, 144, 146, 147, 151, 152, 155, 156, 157, 158, 160, 162, 166, 169, 172, 173, 178, 180, 184, 187, 188, 189, 191, 192, 198, 199, 202, 203, 205, 206, 211, 212, 217, 220, 221, 225, 227, 230, 232, 233, 234, 235, 237, 238, 240, 242, 244, 247, 250, 251, 252, 254, 255, 257, 258, 260, 261, 263, 264, 265, 268, 269, 270, 272, 274, 275, 277, 280, 282, 283, 285, 291, 292, 293, 294, 295, 298, 299, 300, 301, 302, 307, 308, 309, 310, 311, 312, 313, 319, 320, 323, 324, 327, 328, 331, 334, 338, 339, 344, 345, 349, 351, 352, 356, 358, 360, 362, 363, 364, 365, 367, 369, 370, 372, 374, 375, 376, 377, 378, 382, 384, 385, 388, 390, 391, 393, 394, 395, 397, 399, 404, 406, 407, 408, 410, 412, 415, 418, 419, 420, 421, 422, 423, 424, 429, 430, 431, 432, 434, 435, 439, 441, 442, 445, 447, 450, 452, 453, 454, 455, 458, 459, 461, 463, 465, 466, 470, 473, 474, 475, 476, 477, 478, 482, 484, 486, 487, 490, 491, 494, 496, 505, 506, 509, 511, 513, 514, 515, 519, 521, 522, 523, 525, 527, 528, 535, 536, 537, 539, 541, 543, 544, 545, 546, 547, 548, 552, 553, 556, 557, 559, 562, 565, 568, 570, 571, 572, 573, 574, 577, 580, 582, 585, 588, 593, 595, 596, 600, 601, 602, 603, 605, 608, 610, 612, 614, 615, 617, 619, 622, 623, 625, 626, 628, 629, 634, 636, 637, 638, 639, 641, 642, 644, 648, 650, 652, 653, 654, 655, 657, 660, 661, 662, 664, 666, 667, 672, 674, 675, 676, 678, 679, 680, 681, 683, 684, 686, 688, 689, 691, 693, 695, 696, 697, 702, 703, 705, 706, 712, 713, 714, 715, 716, 719, 720, 721, 722, 724, 725, 729, 730, 733, 734, 735, 736, 738, 740, 741, 742, 743, 744, 745, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 760, 762, 768, 769, 770, 771, 772, 773, 776, 777, 778, 780, 781, 790, 791, 794, 797, 799, 800, 801, 803, 805, 807, 808, 810, 811, 812, 814, 815, 816, 817, 818, 820, 823, 824, 826, 829, 830, 834, 835, 836, 838, 839, 840, 842, 844, 845, 846, 850, 851, 852, 854, 855, 858, 860, 865, 866, 867, 868, 869, 871, 873, 874, 875, 876, 877, 878, 883, 886, 889, 890, 891, 893, 894, 896, 899, 900, 901, 903, 904, 905, 907, 909, 910, 911, 912, 913, 915, 918, 920, 921, 922, 924, 927, 930, 934, 935, 936, 937, 938, 940, 941, 942, 945, 946, 948, 949, 950, 952, 953, 956, 959, 960, 963, 964, 965, 966, 967, 969, 971, 972, 973, 975, 978, 981, 982, 986, 988, 990, 991, 992, 994, 995, 996, 997, 1000, 1001, 1002, 1004, 1007, 1008, 1009, 1010, 1012, 1015, 1016, 1022, 1023, 1027, 1028, 1031, 1033, 1036, 1040, 1043, 1044, 1047, 1051, 1052, 1053, 1059, 1060, 1062, 1063, 1065, 1066, 1067, 1069 ]; hyperovals[49]:= [ 5, 6, 9, 16, 19, 25, 30, 31, 32, 42, 44, 46, 49, 51, 54, 56, 58, 60, 61, 64, 66, 69, 72, 73, 74, 76, 81, 82, 84, 86, 88, 90, 91, 92, 98, 101, 105, 113, 114, 120, 124, 131, 136, 141, 142, 145, 146, 147, 150, 152, 153, 154, 155, 157, 158, 162, 163, 165, 166, 174, 175, 176, 180, 189, 191, 192, 193, 194, 201, 203, 204, 205, 209, 210, 212, 214, 218, 219, 222, 223, 227, 231, 232, 233, 235, 238, 239, 240, 242, 244, 245, 252, 258, 259, 260, 261, 263, 264, 268, 269, 271, 272, 273, 275, 277, 279, 280, 285, 287, 289, 297, 298, 299, 301, 302, 303, 304, 310, 312, 313, 314, 317, 320, 323, 324, 326, 329, 330, 332, 334, 336, 337, 340, 342, 343, 344, 351, 353, 356, 357, 358, 359, 360, 361, 364, 365, 367, 369, 372, 373, 378, 381, 388, 390, 391, 393, 394, 398, 400, 401, 404, 405, 408, 410, 411, 413, 417, 418, 419, 421, 423, 429, 431, 433, 434, 436, 437, 441, 442, 443, 444, 448, 450, 451, 452, 454, 455, 458, 459, 461, 463, 464, 465, 466, 470, 472, 473, 475, 477, 478, 479, 480, 481, 483, 487, 488, 489, 490, 493, 494, 497, 499, 500, 501, 506, 507, 508, 509, 510, 512, 513, 515, 516, 518, 521, 525, 526, 528, 529, 534, 535, 536, 539, 541, 542, 545, 549, 550, 552, 553, 554, 556, 557, 559, 561, 562, 563, 567, 569, 570, 574, 577, 578, 580, 583, 586, 588, 597, 598, 601, 603, 606, 607, 609, 612, 613, 625, 627, 630, 631, 633, 639, 641, 644, 646, 647, 649, 650, 651, 655, 656, 659, 663, 667, 670, 672, 674, 676, 681, 684, 686, 687, 688, 689, 692, 693, 694, 696, 697, 698, 700, 701, 702, 703, 704, 709, 715, 716, 717, 722, 725, 727, 729, 730, 731, 732, 733, 737, 738, 739, 741, 742, 743, 744, 745, 746, 748, 750, 751, 754, 755, 757, 759, 760, 761, 762, 764, 767, 768, 771, 773, 774, 777, 778, 780, 781, 783, 784, 786, 787, 789, 790, 792, 793, 795, 796, 798, 799, 801, 802, 803, 805, 808, 809, 811, 817, 818, 820, 821, 823, 825, 828, 829, 830, 831, 834, 835, 836, 838, 841, 842, 843, 846, 847, 850, 851, 854, 855, 857, 858, 859, 860, 861, 862, 864, 865, 866, 872, 874, 875, 876, 881, 883, 885, 888, 889, 890, 891, 893, 895, 897, 898, 900, 904, 906, 907, 909, 910, 911, 913, 915, 920, 921, 922, 927, 928, 930, 932, 935, 938, 939, 942, 944, 951, 953, 955, 956, 957, 959, 960, 962, 965, 966, 967, 968, 969, 970, 978, 980, 982, 983, 984, 986, 991, 994, 995, 998, 999, 1003, 1004, 1005, 1008, 1011, 1014, 1015, 1017, 1019, 1024, 1025, 1035, 1039, 1040, 1044, 1045, 1047, 1050, 1052, 1062, 1068, 1070 ]; hyperovals[50]:= [ 3, 9, 10, 11, 12, 13, 16, 18, 19, 20, 21, 22, 25, 27, 28, 30, 33, 38, 41, 43, 44, 45, 50, 51, 52, 55, 63, 65, 67, 68, 72, 74, 78, 79, 82, 86, 87, 90, 91, 92, 93, 97, 98, 104, 112, 113, 114, 117, 118, 120, 121, 124, 126, 129, 131, 133, 134, 135, 138, 140, 141, 144, 145, 148, 149, 150, 151, 155, 156, 161, 164, 166, 168, 171, 172, 177, 178, 179, 180, 181, 182, 183, 189, 192, 194, 195, 197, 199, 200, 204, 205, 206, 208, 209, 211, 213, 222, 223, 224, 225, 227, 231, 232, 233, 235, 238, 239, 240, 241, 244, 245, 247, 250, 253, 254, 256, 258, 259, 261, 263, 270, 271, 272, 274, 276, 277, 280, 283, 284, 286, 287, 292, 293, 294, 298, 300, 302, 305, 307, 308, 309, 310, 315, 318, 319, 320, 322, 323, 328, 329, 330, 335, 337, 342, 343, 345, 348, 349, 351, 353, 354, 355, 356, 358, 359, 360, 361, 362, 363, 364, 366, 369, 370, 372, 374, 375, 377, 379, 382, 384, 386, 387, 389, 390, 392, 393, 395, 398, 399, 404, 405, 408, 409, 412, 413, 414, 417, 423, 424, 425, 427, 429, 430, 431, 433, 436, 439, 442, 444, 448, 450, 454, 455, 457, 458, 460, 462, 468, 469, 473, 474, 476, 477, 478, 479, 480, 483, 484, 486, 491, 492, 493, 494, 496, 497, 502, 509, 513, 514, 515, 517, 520, 522, 524, 525, 526, 527, 528, 529, 530, 532, 533, 534, 535, 538, 540, 542, 543, 545, 547, 548, 549, 554, 555, 557, 559, 560, 561, 563, 565, 569, 570, 571, 574, 575, 576, 577, 580, 582, 583, 587, 588, 589, 591, 593, 599, 604, 607, 608, 609, 612, 614, 615, 617, 620, 622, 623, 624, 628, 629, 630, 631, 632, 636, 637, 639, 640, 641, 643, 645, 648, 649, 651, 652, 655, 657, 660, 661, 662, 664, 665, 666, 668, 670, 673, 674, 675, 677, 678, 679, 680, 681, 682, 683, 685, 686, 688, 695, 699, 700, 704, 705, 707, 708, 709, 711, 713, 714, 715, 716, 718, 719, 720, 721, 722, 724, 725, 726, 727, 728, 732, 733, 734, 737, 738, 739, 740, 741, 742, 744, 746, 747, 748, 749, 753, 754, 756, 757, 758, 759, 760, 765, 766, 767, 769, 773, 774, 778, 780, 782, 785, 786, 787, 789, 790, 795, 796, 798, 799, 800, 803, 804, 807, 808, 812, 816, 818, 820, 824, 826, 827, 828, 830, 831, 832, 834, 838, 842, 843, 846, 847, 848, 849, 851, 853, 859, 860, 861, 862, 863, 864, 869, 870, 871, 872, 873, 874, 875, 879, 881, 883, 884, 885, 886, 887, 891, 892, 894, 897, 900, 902, 903, 904, 906, 908, 909, 910, 911, 912, 914, 915, 917, 918, 919, 920, 923, 926, 935, 937, 942, 943, 945, 946, 949, 950, 951, 952, 953, 954, 956, 957, 958, 959, 960, 961, 965, 968, 969, 971, 972, 977, 981, 982, 984, 987, 988, 989, 991, 992, 994, 996, 998, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1013, 1014, 1016, 1019, 1021, 1023, 1024, 1026, 1029, 1032, 1035, 1037, 1038, 1039, 1040, 1041, 1042, 1046, 1048, 1050, 1051, 1054, 1058, 1060, 1061, 1063, 1065, 1066, 1068, 1069, 1070, 1071 ]; hyperovals[51]:= [ 1, 7, 8, 11, 17, 25, 26, 29, 30, 31, 32, 35, 42, 43, 52, 54, 55, 57, 59, 60, 69, 70, 71, 74, 75, 76, 81, 82, 88, 93, 94, 96, 99, 100, 102, 103, 104, 105, 106, 111, 116, 117, 118, 119, 122, 125, 128, 129, 130, 132, 133, 135, 137, 145, 146, 147, 149, 152, 153, 156, 157, 158, 161, 164, 166, 167, 170, 171, 172, 180, 182, 183, 185, 187, 193, 194, 195, 196, 199, 200, 202, 204, 206, 208, 209, 212, 216, 218, 222, 224, 230, 232, 233, 236, 237, 238, 240, 241, 244, 245, 246, 249, 250, 253, 254, 257, 262, 263, 268, 269, 275, 283, 286, 290, 292, 293, 295, 296, 301, 302, 303, 304, 305, 308, 311, 313, 316, 320, 323, 324, 325, 327, 329, 331, 333, 334, 337, 341, 348, 351, 353, 358, 359, 362, 364, 365, 368, 369, 370, 372, 376, 378, 379, 380, 381, 382, 384, 387, 388, 392, 397, 398, 401, 403, 404, 405, 414, 419, 421, 425, 435, 438, 439, 440, 443, 444, 445, 449, 451, 452, 453, 454, 458, 460, 465, 466, 468, 469, 475, 484, 485, 486, 487, 489, 490, 495, 498, 500, 502, 503, 504, 505, 506, 508, 513, 514, 517, 519, 521, 524, 525, 526, 528, 531, 532, 533, 535, 539, 541, 543, 545, 546, 548, 550, 551, 552, 553, 554, 560, 563, 572, 574, 575, 577, 583, 584, 585, 586, 587, 592, 594, 595, 597, 598, 599, 609, 610, 615, 618, 620, 626, 628, 629, 630, 634, 636, 640, 641, 644, 646, 651, 653, 656, 663, 665, 670, 672, 673, 678, 680, 687, 688, 690, 695, 696, 697, 699, 701, 704, 705, 708, 711, 712, 714, 719, 720, 722, 724, 725, 726, 727, 728, 729, 730, 734, 735, 738, 744, 745, 747, 750, 752, 753, 754, 760, 763, 764, 772, 775, 776, 777, 779, 780, 781, 783, 787, 788, 794, 797, 800, 802, 806, 808, 814, 815, 818, 819, 821, 822, 826, 828, 829, 830, 833, 834, 837, 838, 840, 841, 842, 845, 848, 849, 850, 852, 853, 859, 861, 863, 864, 865, 867, 869, 870, 879, 880, 881, 882, 883, 886, 891, 893, 895, 896, 897, 901, 902, 903, 904, 906, 912, 913, 914, 915, 916, 918, 923, 924, 930, 931, 932, 933, 934, 935, 936, 939, 940, 947, 948, 950, 953, 954, 959, 961, 965, 966, 967, 968, 972, 976, 978, 979, 981, 982, 983, 986, 987, 988, 990, 991, 995, 997, 998, 1000, 1003, 1005, 1009, 1010, 1011, 1014, 1015, 1018, 1019, 1020, 1023, 1027, 1030, 1032, 1039, 1042, 1044, 1045, 1047, 1048, 1049, 1050, 1051, 1053, 1055, 1057, 1059, 1060, 1064, 1065, 1067, 1068, 1069, 1070 ]; hyperovals[52]:= [ 6, 9, 15, 23, 24, 33, 35, 36, 37, 38, 43, 48, 49, 54, 56, 60, 67, 79, 81, 82, 87, 88, 91, 97, 98, 99, 102, 113, 124, 131, 133, 134, 136, 139, 147, 149, 150, 151, 154, 156, 161, 168, 172, 179, 182, 184, 186, 188, 195, 196, 202, 203, 206, 210, 212, 219, 221, 226, 228, 229, 233, 235, 239, 240, 241, 242, 252, 254, 259, 264, 271, 278, 284, 290, 293, 301, 303, 320, 322, 323, 329, 330, 342, 343, 344, 345, 348, 350, 355, 356, 359, 360, 361, 365, 366, 369, 370, 371, 372, 373, 375, 378, 379, 383, 384, 385, 392, 396, 405, 408, 410, 415, 417, 419, 420, 421, 422, 423, 424, 425, 427, 431, 432, 435, 436, 438, 441, 448, 452, 462, 463, 464, 468, 472, 473, 476, 478, 480, 483, 485, 486, 489, 492, 495, 504, 512, 513, 515, 517, 518, 519, 522, 526, 528, 531, 534, 536, 540, 541, 542, 545, 550, 551, 553, 556, 557, 559, 561, 568, 569, 570, 571, 578, 588, 591, 593, 596, 600, 602, 603, 606, 609, 610, 611, 612, 614, 615, 616, 619, 625, 627, 628, 629, 630, 631, 632, 633, 634, 639, 640, 642, 644, 651, 652, 653, 657, 658, 659, 660, 662, 665, 667, 671, 672, 673, 676, 677, 678, 682, 685, 689, 691, 693, 698, 700, 701, 704, 705, 709, 711, 716, 717, 718, 723, 726, 727, 730, 733, 735, 736, 743, 744, 745, 746, 748, 749, 754, 758, 759, 762, 763, 765, 766, 767, 771, 772, 773, 774, 776, 778, 780, 781, 787, 788, 791, 796, 799, 800, 801, 802, 808, 812, 814, 819, 820, 822, 825, 826, 832, 833, 834, 835, 836, 837, 839, 840, 842, 844, 847, 856, 857, 858, 861, 862, 863, 866, 872, 874, 876, 883, 886, 888, 889, 891, 896, 898, 899, 900, 902, 905, 907, 913, 917, 918, 919, 920, 922, 924, 926, 927, 928, 931, 934, 935, 938, 939, 945, 947, 948, 949, 951, 954, 956, 957, 958, 959, 961, 966, 967, 968, 969, 972, 977, 981, 984, 989, 990, 991, 992, 994, 995, 996, 999, 1002, 1004, 1006, 1008, 1011, 1013, 1021, 1022, 1025, 1027, 1028, 1033, 1034, 1040, 1042, 1043, 1045, 1046, 1047, 1049, 1050, 1051, 1053, 1057, 1058, 1060, 1063, 1064, 1066, 1068, 1070 ]; hyperovals[53]:= [ 1, 3, 8, 10, 18, 21, 22, 23, 25, 26, 28, 29, 35, 37, 40, 41, 50, 53, 55, 56, 58, 62, 63, 69, 72, 74, 75, 76, 87, 89, 90, 91, 96, 97, 99, 100, 105, 109, 110, 114, 115, 116, 118, 124, 125, 127, 129, 133, 137, 138, 139, 142, 143, 147, 152, 154, 160, 161, 162, 171, 182, 188, 190, 191, 194, 195, 203, 214, 215, 220, 224, 225, 229, 230, 231, 233, 235, 242, 254, 255, 263, 264, 266, 267, 268, 269, 271, 274, 275, 276, 280, 289, 292, 293, 298, 303, 305, 306, 310, 314, 315, 321, 323, 327, 328, 339, 341, 344, 345, 346, 349, 352, 358, 362, 364, 366, 374, 377, 378, 381, 382, 383, 386, 389, 394, 395, 398, 400, 402, 405, 412, 414, 415, 416, 422, 423, 433, 434, 437, 440, 441, 443, 444, 448, 452, 453, 454, 461, 463, 471, 475, 480, 482, 483, 489, 494, 496, 498, 499, 500, 505, 512, 516, 518, 523, 526, 527, 528, 532, 541, 544, 548, 550, 551, 552, 555, 556, 560, 564, 565, 567, 568, 571, 574, 575, 577, 578, 579, 583, 584, 587, 591, 592, 593, 594, 606, 607, 609, 610, 611, 618, 621, 629, 631, 633, 637, 639, 644, 647, 654, 657, 658, 662, 663, 665, 667, 669, 670, 678, 681, 682, 683, 685, 689, 692, 693, 697, 699, 700, 704, 705, 710, 711, 718, 719, 733, 736, 738, 741, 746, 747, 752, 757, 759, 775, 778, 782, 784, 785, 791, 793, 797, 805, 807, 811, 812, 818, 820, 822, 824, 825, 827, 831, 832, 834, 842, 848, 856, 861, 862, 865, 868, 871, 875, 876, 878, 882, 889, 898, 900, 904, 920, 921, 922, 923, 924, 928, 930, 935, 937, 938, 939, 949, 950, 951, 952, 956, 963, 966, 969, 971, 974, 976, 977, 980, 983, 987, 989, 992, 994, 1004, 1007, 1008, 1012, 1013, 1018, 1019, 1022, 1025, 1027, 1029, 1030, 1031, 1032, 1033, 1034, 1037, 1041, 1045, 1054, 1059, 1063, 1065, 1066, 1069, 1071 ]; hyperovals[54]:= [ 1, 7, 8, 9, 12, 13, 15, 17, 20, 21, 22, 23, 29, 30, 31, 36, 39, 40, 41, 45, 46, 48, 50, 54, 59, 61, 65, 71, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 86, 87, 89, 90, 92, 93, 94, 95, 97, 99, 100, 103, 104, 112, 113, 116, 119, 120, 121, 122, 124, 125, 126, 128, 129, 131, 133, 134, 137, 139, 140, 142, 143, 144, 145, 146, 149, 151, 154, 155, 160, 161, 164, 165, 166, 168, 170, 173, 175, 178, 181, 183, 184, 185, 186, 187, 192, 193, 196, 199, 200, 202, 203, 204, 205, 208, 212, 213, 214, 216, 217, 218, 219, 220, 221, 222, 224, 226, 227, 230, 231, 232, 233, 234, 236, 238, 242, 243, 244, 247, 251, 254, 255, 258, 259, 260, 261, 264, 266, 267, 268, 269, 272, 273, 274, 276, 277, 278, 279, 282, 286, 288, 291, 292, 296, 298, 300, 301, 302, 304, 305, 311, 313, 315, 317, 319, 323, 325, 330, 333, 336, 338, 339, 340, 341, 342, 345, 347, 349, 354, 355, 361, 363, 366, 368, 369, 370, 374, 375, 376, 377, 378, 383, 385, 387, 390, 391, 392, 393, 394, 397, 399, 400, 401, 402, 403, 404, 405, 408, 409, 410, 412, 413, 415, 416, 417, 419, 421, 422, 424, 427, 428, 430, 431, 433, 434, 436, 437, 438, 440, 445, 446, 447, 449, 450, 451, 452, 454, 457, 458, 460, 462, 463, 464, 466, 467, 469, 472, 473, 474, 475, 478, 479, 480, 482, 483, 485, 486, 487, 488, 490, 491, 493, 495, 497, 501, 509, 513, 516, 518, 524, 525, 526, 528, 529, 530, 533, 534, 538, 540, 541, 543, 545, 547, 549, 552, 553, 555, 556, 557, 558, 559, 560, 561, 563, 564, 565, 571, 573, 576, 578, 582, 584, 585, 587, 588, 589, 590, 599, 600, 601, 602, 604, 606, 611, 618, 619, 620, 622, 623, 627, 630, 636, 638, 640, 644, 649, 651, 653, 654, 656, 658, 660, 662, 663, 664, 665, 669, 670, 672, 673, 674, 676, 677, 678, 679, 680, 683, 687, 688, 691, 692, 694, 695, 699, 701, 703, 705, 706, 707, 709, 710, 713, 715, 717, 718, 721, 725, 726, 728, 730, 731, 732, 735, 737, 738, 742, 744, 745, 746, 748, 758, 759, 760, 761, 764, 767, 769, 770, 771, 772, 777, 779, 780, 783, 784, 788, 789, 790, 791, 793, 797, 798, 799, 803, 804, 806, 807, 809, 810, 811, 812, 814, 818, 821, 822, 826, 832, 834, 841, 843, 846, 852, 855, 859, 860, 862, 863, 865, 869, 870, 871, 873, 875, 876, 877, 878, 879, 881, 882, 887, 888, 889, 890, 891, 892, 893, 894, 896, 897, 905, 907, 909, 910, 911, 912, 916, 922, 923, 926, 929, 932, 933, 934, 935, 940, 941, 944, 945, 948, 952, 953, 959, 960, 961, 964, 966, 967, 969, 981, 982, 987, 988, 992, 1000, 1001, 1003, 1006, 1015, 1023, 1024, 1025, 1026, 1030, 1031, 1032, 1035, 1041, 1042, 1043, 1044, 1046, 1048, 1050, 1051, 1053, 1055, 1057, 1058, 1063, 1065, 1066, 1068, 1069 ];