\\ VORONOI GRAPH in DIMENSION 7: \\ \\ Contiguous Forms to the 7 perfect 7-Dimensional Forms \\ 357 = (157(E8)+200 (others) Voronoi paths \\ =============================================== \\ \\ We display GRAM MATRICES for the contiguous forms to the P_7^k \\ which are some P_7^l with l>=k. \\ Otherwise, we just list the l B is \\ A+t*(vec2mat(B)-A) \\ HOWEVER, due to the size of the data for dimension7, \\ the previous vector V6 has a diffferent structure, \\ and the explicit command takes the form \\ p7[4]+t*(vec2mat(V7[4][11])-p7[4]) {vec2mat(v,n,a,k,i1,j)= n=floor(sqrt(2*length(v)));a=matrix(n,n,k,l,1); k=0;for(i1=1,n,for(j=i1,n,k=k+1;a[i1,j]=v[k];a[j,i1]=v[k])); a;} \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\ 33 perfect, 7-dimensional forms \\\\\\\\\ \\ The function p7(k) outputs the k-th p7 \\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ p7=vector(33,k,0); p7[1]=[2,1,1,1,1,1,0;1,2,1,1,1,1,0;1,1,2,1,1,1,1;1,1,1,2,1,1,1;1,1,1,1,2,1,1;1,1,1,1,1,2,1;0,0,1,1,1,1,2]; p7[2]=[3,1,1,1,1,1,2;1,3,1,1,1,1,2;1,1,3,1,1,1,2;1,1,1,3,1,1,2;1,1,1,1,3,1,2;1,1,1,1,1,3,0;2,2,2,2,2,0,4]; p7[3]=[4,1,2,2,2,2,2;1,4,2,2,2,2,2;2,2,4,1,1,2,2;2,2,1,4,1,2,2;2,2,1,1,4,2,2;2,2,2,2,2,4,1;2,2,2,2,2,1,4]; p7[4]=[2,1,1,1,1,1,2;1,2,1,1,1,1,2;1,1,2,1,1,1,2;1,1,1,2,1,1,2;1,1,1,1,2,1,2;1,1,1,1,1,2,2;2,2,2,2,2,2,4]; p7[5]=[4,1,2,1,2,2,2;1,4,1,2,2,2,2;2,1,4,1,2,2,2;1,2,1,4,2,2,2;2,2,2,2,4,1,2;2,2,2,2,1,4,1;2,2,2,2,2,1,4]; p7[6]=[6,2,2,2,3,3,3;2,6,2,2,3,3,3;2,2,6,2,3,3,3;2,2,2,6,3,3,3;3,3,3,3,6,2,3;3,3,3,3,2,6,1;3,3,3,3,3,1,6]; p7[7]=[4,2,2,0,1,1,1;2,4,2,1,0,1,2;2,2,4,1,1,0,2;0,1,1,4,2,2,1;1,0,1,2,4,2,2;1,1,0,2,2,4,2;1,2,2,1,2,2,4]; p7[8]=[4,-1,-1,2,-1,2,0;-1,4,1,0,0,0,2;-1,1,4,0,0,0,2;2,0,0,4,1,0,2;-1,0,0,1,4,0,2;2,0,0,0,0,4,0;0,2,2,2,2,0,4]; p7[9]=[10,3,3,3,3,3,8;3,10,3,3,3,3,8;3,3,10,3,3,3,8;3,3,3,10,3,3,8;3,3,3,3,10,5,8;3,3,3,3,5,10,8;8,8,8,8,8,8,16]; p7[10]=[4,1,2,2,0,2,2;1,4,1,2,2,0,2;2,1,4,1,2,2,2;2,2,1,4,1,2,2;0,2,2,1,4,1,2;2,0,2,2,1,4,2;2,2,2,2,2,2,4]; p7[11]=[6,1,3,3,3,2,2;1,6,2,2,2,-1,-1;3,2,6,2,2,-1,-1;3,2,2,6,0,3,1;3,2,2,0,6,1,3;2,-1,-1,3,1,6,3;2,-1,-1,1,3,3,6]; p7[12]=[6,2,2,2,2,2,5;2,6,2,2,2,2,5;2,2,6,2,2,2,5;2,2,2,6,2,2,5;2,2,2,2,6,2,5;2,2,2,2,2,6,5;5,5,5,5,5,5,10]; p7[13]=[8,1,3,3,1,4,4;1,8,1,3,3,4,4;3,1,8,1,3,4,4;3,3,1,8,1,4,4;1,3,3,1,8,4,4;4,4,4,4,4,8,3;4,4,4,4,4,3,8]; p7[14]=[6,-1,0,-3,2,1,2;-1,6,-3,0,1,2,2;0,-3,6,3,0,1,1;-3,0,3,6,1,0,1;2,1,0,1,6,-1,1;1,2,1,0,-1,6,1;2,2,1,1,1,1,6]; p7[15]=[8,-4,0,1,1,0,-4;-4,8,-4,0,1,1,0;0,-4,8,-4,0,1,1;1,0,-4,8,-4,0,1;1,1,0,-4,8,-4,0;0,1,1,0,-4,8,-4;-4,0,1,1,0,-4,8]; p7[16]=[6,1,1,2,3,3,4;1,6,1,1,2,3,4;1,1,6,1,1,2,4;2,1,1,6,1,1,4;3,2,1,1,6,1,4;3,3,2,1,1,6,4;4,4,4,4,4,4,8]; p7[17]=[6,0,2,0,1,1,3;0,6,0,2,1,1,3;2,0,6,3,3,3,1;0,2,3,6,3,3,1;1,1,3,3,6,2,-1;1,1,3,3,2,6,-1;3,3,1,1,-1,-1,6]; p7[18]=[8,-4,3,4,0,1,1;-4,8,1,0,4,1,1;3,1,8,4,0,1,1;4,0,4,8,3,0,4;0,4,0,3,8,4,0;1,1,1,0,4,8,-4;1,1,1,4,0,-4,8]; p7[19]=[6,3,1,1,1,1,4;3,6,1,1,1,1,4;1,1,6,3,1,1,4;1,1,3,6,1,1,4;1,1,1,1,6,3,4;1,1,1,1,3,6,4;4,4,4,4,4,4,8]; p7[20]=[6,3,0,-2,-1,-1,-2;3,6,3,0,-2,-1,-1;0,3,6,3,0,-2,-1;-2,0,3,6,3,0,-2;-1,-2,0,3,6,3,0;-1,-1,-2,0,3,6,3;-2,-1,-1,-2,0,3,6]; p7[21]=[6,2,1,3,3,1,4;2,6,1,1,3,3,4;1,1,6,3,3,3,4;3,1,3,6,3,3,4;3,3,3,3,6,3,4;1,3,3,3,3,6,4;4,4,4,4,4,4,8]; p7[22]=[4,2,2,1,1,2,0;2,4,1,2,2,0,2;2,1,4,2,-1,2,0;1,2,2,4,1,0,2;1,2,-1,1,4,0,2;2,0,2,0,0,4,-1;0,2,0,2,2,-1,4]; p7[23]=[6,3,-1,-1,2,2,1;3,6,-1,-1,2,2,3;-1,-1,6,3,1,3,2;-1,-1,3,6,3,1,2;2,2,1,3,6,0,3;2,2,3,1,0,6,3;1,3,2,2,3,3,6]; p7[24]=[6,3,1,3,1,1,1;3,6,-2,1,3,3,-1;1,-2,6,3,1,-1,3;3,1,3,6,2,1,0;1,3,1,2,6,0,1;1,3,-1,1,0,6,-3;1,-1,3,0,1,-3,6]; p7[25]=[6,2,1,1,3,2,4;2,6,1,3,1,2,4;1,1,6,0,0,1,4;1,3,0,6,3,3,0;3,1,0,3,6,3,0;2,2,1,3,3,6,0;4,4,4,0,0,0,8]; p7[26]=[4,1,2,2,2,2,2;1,4,2,2,2,2,2;2,2,4,1,1,2,2;2,2,1,4,1,2,2;2,2,1,1,4,2,2;2,2,2,2,2,4,2;2,2,2,2,2,2,4]; p7[27]=[4,1,2,2,2,2,3;1,4,2,2,2,2,3;2,2,4,1,2,2,3;2,2,1,4,2,2,3;2,2,2,2,4,1,3;2,2,2,2,1,4,3;3,3,3,3,3,3,6]; p7[28]=[4,1,2,2,2,1,5;1,4,1,2,2,2,5;2,1,4,1,2,2,5;2,2,1,4,1,2,5;2,2,2,1,4,1,5;1,2,2,2,1,4,5;5,5,5,5,5,5,14]; p7[29]=[4,1,1,2,2,2,2;1,4,2,2,2,2,2;1,2,4,2,2,2,2;2,2,2,4,1,2,2;2,2,2,1,4,2,2;2,2,2,2,2,4,1;2,2,2,2,2,1,4]; p7[30]=[4,1,2,2,2,2,1;1,4,1,2,2,2,2;2,1,4,1,2,2,2;2,2,1,4,1,2,2;2,2,2,1,4,1,2;2,2,2,2,1,4,1;1,2,2,2,2,1,4]; p7[31]=[4,1,2,2,2,2,3;1,4,1,2,2,2,3;2,1,4,1,2,2,3;2,2,1,4,1,2,3;2,2,2,1,4,2,3;2,2,2,2,2,4,3;3,3,3,3,3,3,6]; p7[32]=[4,1,2,2,2,2,2;1,4,2,2,2,2,2;2,2,4,1,2,2,2;2,2,1,4,2,2,2;2,2,2,2,4,1,2;2,2,2,2,1,4,2;2,2,2,2,2,2,4]; p7[33]=[2,1,1,1,1,1,1;1,2,1,1,1,1,1;1,1,2,1,1,1,1;1,1,1,2,1,1,1;1,1,1,1,2,1,1;1,1,1,1,1,2,1;1,1,1,1,1,1,2]; \\ V7=vector(33,k,0); \\ V7[k][l] = l-th contiguous form to the k-th one (after D.-O. JAQUET) \\------------------------------------------------------------------- \\ 157 orbits of contiguous forms to E_7=P_7^1; V7[1]--[1,157]: v=W1=[1,1,1,1,1,1,1,1,1,1,1,2,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,12,13,13,13,14,14,14,14,14,14,14,15,16,16,16,17,17,17,17,17,17,18,18,18,18,19,20,20,21,21,22,22,22,22,22,22,22,23,23,24,24,24,24,24,25,25,25,25,25,26,26,26,27,27,27,28,28,28,28,28,29,29,29,29,29,29,30,30,31,31,31,31,32]; \\ P_7^1 -- P_7^1 (11 orbits) v[1]=[4,3,3,3,2,2,1, 4,3,3,2,2,1, 4,3,2,2,2, 4,2,2,2, 2,1,1, 2,1, 2]; v[2]=[6,5,4,5,4,2,0, 6,4,5,4,2,0, 4,4,3,2,1, 6,4,2,1, 4,2,1, 2,1, 2]; v[3]=[4,2,2,2,1,1,-1, 4,3,3,2,2,1, 4,2,2,1,1, 4,1,2,1, 2,1,1, 2,1, 2]; v[4]=[4,2,1,2,3,1,-1, 2,2,1,2,1,0, 4,0,2,1,1, 2,1,1,0, 4,1,0, 2,1, 2]; v[5]=[4,4,2,2,2,2,-1, 6,3,3,2,2,-1, 4,2,1,1,1, 2,1,1,0, 2,1,0, 2,0, 2]; v[6]=[4,5,4,4,3,2,1, 8,6,6,4,2,1, 6,5,3,2,2, 6,3,2,2, 4,1,1, 2,1, 2]; v[7]=[4,4,3,4,3,2,1, 6,4,5,3,2,1, 4,4,2,2,2, 6,3,2,2, 4,1,1, 2,1, 2]; v[8]=[8,7,5,7,3,3,-1, 10,5,7,3,3,-2, 4,5,2,2,0, 8,3,3,0, 2,1,0, 2,0, 2]; v[9]=[6,4,3,4,3,2,-1, 6,4,5,4,3,1, 4,3,3,2,1, 6,3,3,1, 4,2,1, 2,1, 2]; v[10]=[2,2,1,2,1,1,-1, 4,1,3,2,2,-1, 2,1,1,1,1, 4,1,2,0, 2,1,0, 2,1, 4]; v[11]=[2,1,2,2,1,1,0, 2,1,2,1,1,0, 4,2,2,2,2, 4,1,2,1, 2,1,1, 2,2, 4]; \\ P_7^1 -- P_7^2 (1 orb) v[12]=[6,4,4,4,4,4,2, 8,4,4,4,4,0, 8,4,4,4,4, 8,4,4,4, 8,4,4, 8,4, 6]/3; \\ P_7^1 -- P_7^3 (6 orb) v[13]=[4,1,2,2,3,1,1, 4,2,2,3,1,1, 4,1,3,1,2, 4,3,1,2, 6,1,3, 4,2, 4]/2; v[14]=[10,5,4,3,6,5,-2, 10,5,6,6,4,-1, 6,4,5,3,2, 6,4,3,1, 8,4,1, 4,0, 4]/2; v[15]=[6,3,3,3,3,3,0, 4,5,3,3,3,3, 10,5,5,5,9, 6,3,3,5, 6,3,5, 6,5, 12]/2; v[16]=[10,6,2,5,5,5,-2, 6,3,4,4,4,0, 4,2,2,2,2, 6,3,3,1, 6,3,1, 6,1, 4]/2; v[17]=[10,2,2,3,1,4,-3, 4,1,2,2,1,-1, 4,2,2,1,2, 6,3,3,4, 4,1,3, 4,1, 8]/2; v[18]=[6,3,3,3,3,3,0, 8,5,5,4,1,-1, 6,3,3,2,1, 6,3,2,1, 4,2,1, 4,2, 4]/2; \\ P_7^1=E7 -- P_7^4=D7 (4 orb) v[19]=[4,-1,1,1,1,2,0, 4,1,1,1,0,0, 2,1,1,1,1, 2,1,1,1, 2,1,1, 2,1, 2]; v[20]=[4,3,3,2,3,3,1, 4,3,3,2,3,1, 4,2,2,3,1, 4,2,3,2, 4,3,2, 4,2, 2]; v[21]=[12,10,10,6,6,6,-1, 10,8,5,5,5,-2, 10,5,5,5,0, 4,3,3,0, 4,3,0, 4,0, 2]; v[22]=[6,6,6,5,5,4,2, 8,6,6,6,5,2, 8,5,5,4,3, 6,4,4,2, 6,4,2, 4,2, 2]; \\ P_7^1 -- P_7^5 (10 orb) v[23]=[6,2,4,3,3,3,1, 4,2,2,2,2,0, 6,3,3,3,3, 6,4,3,5, 6,3,5, 4,3, 8]/2; v[24]=[12,5,7,7,3,3,-1, 6,6,6,3,3,2, 10,8,4,4,4, 10,4,4,4, 4,2,3, 4,3, 6]/2; v[25]=[10,6,8,4,3,4,-1, 8,6,3,2,3,-2, 10,4,3,4,1, 4,1,2,1, 4,1,1, 4,1, 4]/2; v[26]=[8,2,4,4,2,2,-1, 4,4,4,2,2,2, 8,6,3,3,4, 8,3,3,4, 4,2,3, 4,3, 6]/2; v[27]=[6,3,3,3,3,4,1, 6,5,4,3,5,2, 8,3,4,5,4, 6,1,5,2, 4,3,2, 8,4, 4]/2; v[28]=[4,5,2,2,2,3,-1, 10,3,4,3,4,-2, 4,2,0,1,1, 4,1,2,1, 4,2,0, 6,1, 4]/2; v[29]=[4,4,1,2,2,3,-1, 8,2,4,3,4,-1, 4,2,0,1,2, 4,1,2,1, 4,2,0, 6,1, 4]/2; v[30]=[8,3,4,4,2,2,-1, 6,5,3,1,0,-2, 8,4,2,2,1, 4,2,2,1, 4,2,3, 4,3, 6]/2; v[31]=[8,2,3,3,1,3,-2, 4,2,2,2,2,0, 6,5,3,4,5, 8,4,4,6, 4,2,4, 6,4, 10]/2; v[32]=[4,2,2,2,2,2,0, 4,1,1,2,2,-1, 4,1,1,2,2, 6,3,0,2, 4,2,1, 4,1 ,4]/2; \\ P_7^1 -- P_7^6 (6 orb) v[33]=[6,6,6,6,6,5,2, 12,8,8,8,8,2, 12,8,8,8,6, 12,8,8,6, 12,8,6, 10,6, 8]/3; v[34]=[6,6,3,3,3,3,-4, 12,4,4,4,6,-4, 6,2,2,3,1, 6,2,3,1, 6,3,1, 6,1, 10]/3; v[35]=[8,4,4,6,6,6,2, 8,8,6,6,6,4, 14,7,7,7,7, 10,6,6,5, 10,6,5, 10,5, 6]/3; v[36]=[8,4,4,6,6,6,2, 6,6,5,5,5,3, 12,6,6,6,6, 10,6,6,5, 10,6,5, 10,5, 6]/3; v[37]=[6,6,6,5,5,5,1, 12,8,6,6,8,0, 12,6,6,8,4, 10,6,7,6, 10,7,6, 10,5, 10]/3; v[38]=[14,8,12,5,5,5,-1, 12,10,4,4,4,-2, 16,6,6,6,2, 6,2,2,2, 6,2,2, 6,2, 6]/3; \\ P_7^1 -- P_7^7 (18 orb) v[39]=[8,6,6,4,5,5,1, 8,6,5,4,5,1, 8,5,5,4,3, 8,6,6,6, 8,6,6, 8,5, 8]/2; v[40]=[8,6,6,4,5,5,1, 8,6,4,5,6,1, 8,4,6,5,3, 4,4,4,2, 8,6,4, 8,3, 4]/2; v[41]=[4,2,2,2,2,2,0, 6,2,2,3,3,0, 4,3,2,2,2, 6,3,1,3, 4,2,2, 4,1, 4]/2; v[42]=[6,3,0,3,2,4,-2, 4,2,3,2,3,0, 4,3,2,1,3, 6,2,3,2, 6,2,3, 6,1, 6]/2; v[43]=[8,6,6,5,4,4,0, 8,6,4,3,4,0, 8,5,5,4,3, 8,6,4,4, 8,4,5, 4,2, 6]/2; v[44]=[10,6,4,6,3,5,-3, 8,4,5,4,6,-1, 4,3,2,4,0, 6,3,4,-1, 4,3,1, 8,1, 4]/2; v[45]=[8,6,6,6,7,5,3, 8,6,7,6,5,3, 8,7,7,4,5, 10,8,6,7, 10,6,7, 8,5, 8]/2; v[46]=[8,5,5,4,4,6,0, 8,6,6,4,4,1, 8,6,4,5,3, 8,4,3,3, 4,4,2, 8,2, 4]/2; v[47]=[8,3,4,4,2,3,-1, 4,3,2,2,2,0, 6,3,3,3,2, 4,2,3,1, 4,3,2, 6,3, 4]/2; v[48]=[4,2,2,2,2,2,0, 8,3,4,2,2,-1, 4,2,2,1,1, 4,2,3,1, 4,3,2, 6,3, 4]/2; v[49]=[4,2,2,2,2,2,0, 4,2,2,1,1,-1, 4,2,3,4,3, 4,3,2,2, 6,4,5, 8,6,8]/2; v[50]=[4,2,3,4,4,3,2, 4,3,5,3,3,2, 6,6,5,3,5, 10,7,5,6, 10,4,7, 6,4, 8]/2; v[51]=[8,5,6,6,6,5,3, 8,7,6,5,3,2, 10,7,7,3,5, 8,6,5,5, 8,4,5, 8,4, 6]/2; v[52]=[8,5,4,3,5,4,0, 8,5,6,7,4,2, 8,6,7,3,5, 8,7,3,5, 10,3,5, 4,1, 6]/2; v[53]=[14,7,11,9,8,10,6, 8,6,4,5,6,1, 12,8,8,8,7, 8,6,7,6, 8,7,6, 10,6, 8]/2; v[54]=[8,1,4,3,2,3,1, 4,3,3,2,1,1, 8,5,4,4,6, 6,3,3,4, 4,2,4, 4,4, 8]/2; v[55]=[8,4,4,6,6,5,2, 4,4,4,4,4,2, 8,6,6,7,7, 10,7,8,7, 8,7,6, 10,8, 10]/2; v[56]=[10,6,4,7,5,5,1, 8,4,6,6,4,1, 4,4,4,2,2, 8,5,5,3, 8,3,3, 6,2, 4]/2; \\ P_7^1 -- P_7^8 (10 orb) v[57]=[8,4,5,5,5,5,2, 4,3,3,2,2,0, 6,3,4,4,3, 6,4,4,3, 8,5,5, 8,5, 6]/2; v[58]=[4,3,3,3,3,3,1, 6,5,4,3,4,2, 8,4,4,5,4, 6,3,3,3, 6,3,3, 6,3, 4]/2; v[59]=[8,6,4,5,4,5,0, 8,4,4,3,6,-1, 4,3,3,3,1, 6,4,4,2, 6,3,3, 8,1, 4]/2; v[60]=[8,7,4,5,6,4,0, 10,4,5,7,4,-1, 4,3,3,3,1, 6,5,4,2, 8,4,1, 6,3, 4]/2; v[61]=[12,9,9,5,6,5,1, 12,9,5,6,5,1, 10,5,7,5,3, 4,4,3,2, 8,5,4, 6,3, 4]/2; v[62]=[10,5,7,5,6,6,3, 4,4,3,3,3,1, 8,5,6,6,5, 6,6,6,6, 10,7,8, 10,8, 10]/2; v[63]=[4,1,1,2,2,2,1, 6,3,4,5,2,2, 6,4,5,2,5, 6,6,3,5, 10,4,7, 4,4, 8]/2; v[64]=[8,6,6,4,5,5,1, 8,6,4,4,4,0, 10,4,4,4,3, 4,3,3,2, 6,3,2, 6,2, 4]/2; v[65]=[4,2,2,2,3,5,1, 6,3,3,3,2,0, 6,3,3,2,3, 4,3,3,2, 6,5,3, 10,3, 4]/2; v[66]=[10,5,6,6,7,5,3, 4,4,4,4,3,2, 8,5,5,3,4, 8,5,3,4, 8,5,4, 6,3, 4]/2; \\ P_7^1 -- P_7^9 (1 orb) v[67]=[22,13,13,15,15,15,6, 14,9,9,9,9,1, 14,9,9,9,6, 18,11,11,8, 18,11,8, 18,8, 10]/5; \\ P_7^1 -- P_7^10 (8 orb) v[68]=[6,4,2,2,2,3,-2, 6,4,2,3,3,-1, 6,2,3,2,2, 4,2,2,2, 4,2,2, 4,1, 6]/2; v[69]=[6,4,3,4,2,4,0, 10,6,7,4,7,3, 8,5,4,6,6, 8,4,6,4, 4,4,4, 8,5, 8]/2; v[70]=[6,4,4,5,5,6,3, 6,5,5,6,6,4, 8,5,7,6,6, 8,7,8,7, 10,9,8, 12,9, 10]/2; v[71]=[8,5,7,4,5,6,2, 6,6,4,4,5,2, 10,4,5,7,4, 6,4,5,3, 6,5,3, 8,4, 4]/2; v[72]=[6,3,2,2,3,3,0, 4,3,2,2,2,1, 6,1,2,2,3, 4,1,0,1, 4,2,2, 4,1, 4]/2; v[73]=[6,3,2,3,4,3,1, 4,2,2,3,2,0, 4,1,4,3,3, 4,3,3,3, 8,5,6, 6,6, 10]/2; v[74]=[4,2,4,2,2,4,2, 4,3,2,2,3,1, 8,4,5,6,6, 4,3,3,4, 6,3,5, 8,5, 8]/2; v[75]=[4,3,0,3,2,2,0, 6,2,4,3,3,1, 4,2,2,1,3, 8,4,2,4, 4,2,3, 4,2, 6]/2; \\ P_7^1 -- P_7^11 (9 orb) v[76]=[6,4,4,4,4,3,1, 8,3,5,5,4,2, 8,4,4,3,4, 8,4,5,4, 8,3,4, 10,5, 6]/3; v[77]=[14,9,7,5,7,8,0, 12,8,4,6,7,-1, 12,4,6,5,3, 6,4,4,3, 8,5,3, 8,2, 6]/3; v[78]=[10,4,5,5,4,4,0, 6,4,2,4,3,1, 8,7,5,4,5, 12,5,4,7, 8,3,5, 6,3, 8]/3; v[79]=[8,1,3,1,4,2,0, 6,2,2,5,3,1, 6,2,5,3,5, 6,3,3,5, 10,5,5, 6,5, 10]/3; v[80]=[14,4,7,6,7,7,0, 6,6,3,4,3,0, 12,4,6,6,3, 6,4,5,2, 8,6,3, 10,5, 6]/3; v[81]=[6,4,4,4,4,3,1, 8,4,4,4,3,0, 8,4,4,1,4, 8,2,3,4, 8,1,2, 6,1, 6]/3; v[82]=[10,4,5,4,4,4,0, 6,4,4,4,3,1, 8,3,5,4,5, 8,4,3,3, 8,3,5, 6,3, 8]/3; v[83]=[6,4,4,4,4,4,1, 8,3,5,5,2,-1, 8,4,4,5,5, 8,4,3,3, 8,5,3, 8,5, 8]/3; v[84]=[6,4,4,6,4,4,1, 8,4,5,4,5,1, 8,3,4,3,3, 12,7,7,5, 8,5,5, 8,5, 8]/3; \\ P_7^1 -- P_7^12 (1 orb) v[85]=[14,9,9,9,9,9,3, 10,6,6,6,6,0, 10,6,6,6,4, 10,6,6,4, 10,6,4, 10,4, 6]/3; \\ P_7^1 -- P_7^13 (3 orb) v[86]=[8,3,4,0,1,4,-3, 8,4,3,4,7,0, 8,1,3,6,2, 8,4,4,5, 8,6,5, 14,5, 10]/4; v[87]=[8,6,6,6,6,6,2, 12,5,7,7,5,-1, 12,5,7,7,6, 12,5,7,4, 12,5,4, 12,6, 8]/4; v[88]=[8,8,8,6,6,6,2, 16,11,9,7,9,1, 16,7,9,9,6, 12,5,7,4, 12,7,6, 12,6, 8]/4; \\ P_7^1 -- P_7^14 (7 orb) v[89]=[6,5,2,5,3,5,0, 10,5,7,5,6,1, 6,5,5,3,4, 10,6,5,4, 10,3,6, 10,3, 8]/3; v[90]=[8,4,4,4,4,4,0, 10,3,3,3,3,-3, 12,8,6,4,9, 10,5,5,8, 6,3,5, 6,4, 14]/3; v[91]=[8,4,4,4,4,4,0, 6,3,4,4,3,0, 6,4,3,5,4, 8,7,6,6, 12,4,6, 10,8,12]/3; v[92]=[8,4,4,4,4,4,0, 10,3,3,3,4,-2, 6,3,4,3,3, 6,4,3,2, 8,1,2, 6,2, 6]/3; v[93]=[8,4,4,4,4,4,0, 12,4,2,6,4,-3, 6,3,3,3,2, 6,3,2,3, 6,3,0, 6,1, 6]/3; v[94]=[8,4,4,4,4,4,0, 10,4,5,5,6,0, 6,3,3,4,2, 6,5,4,3, 10,3,4, 8,2, 6]/3; v[95]=[8,4,4,4,4,4,0, 10,3,3,4,5,-2, 6,3,3,3,3, 6,3,2,2, 6,3,2, 6,0, 6]/3; \\ P_7^1 -- P_7^15 (1 orb) v[96]=[12,5,5,5,6,7,0, 12,5,5,4,5,-2, 10,3,5,7,5, 10,5,3,3, 8,6,5, 12,5,10]/4; \\ P_7^1 -- P_7^16 (3 orb) v[97]=[8,4,4,4,4,2,0, 10,5,7,8,4,3, 6,4,6,2,3, 10,8,4,5, 12,4,6, 8,4, 6]/3; v[98]=[10,9,7,6,5,7,-1, 14,7,6,6,8,-3, 10,4,5,5,2, 8,4,6,2, 6,4,1, 10,1, 6]/3; v[99]=[8,4,4,2,2,2,-2, 10,5,6,7,4,2, 6,2,4,2,1, 8,6,4,4, 10,4,5,8,4, 6]/3; \\ P_7^1 -- P_7^17 (6 orb) v[100]=[12,6,4,6,4,8,-2, 6,4,3,3,5,-1, 8,3,3,4,3, 6,4,5,2, 8,4,4, 10,2, 8]/3; v[101]=[12,10,10,9,7,8,2, 14,11,10,7,10,3, 14,10,7,8,4, 12,7,9,5, 8,7,4, 12,6, 6]/3; v[102]=[8,4,4,4,5,5,1, 8,4,4,5,5,1, 6,3,5,3,3, 6,3,5,3, 12,6,5, 12,5, 6]/3; v[103]=[8,4,4,5,4,3,0, 8,4,5,4,3,0, 6,5,3,3,3, 12,6,4,7, 6,4,4, 8,5, 10]/3; v[104]=[8,4,3,4,3,4,-1, 6,4,3,3,3,-1, 8,3,3,3,3, 6,4,3,2, 8,3,4, 6,3, 8]/3; v[105]=[8,4,4,4,5,5,1, 8,4,4,5,5,1, 6,3,3,5,3, 6,5,2,3, 12,4,5, 10,3, 6]/3; \\ P_7^1 -- P_7^18 (4 orb) (Parf non s.e.) v[106]=[8,6,4,6,4,2,0, 12,6,7,5,3,0, 8,6,3,1,2, 12,5,3,5, 8,3,5, 8,5, 10]/4; v[107]=[8,6,8,6,4,4,2, 12,10,7,6,6,3, 16,10,8,8,9, 12,6,6,8, 8, 6,7, 14,10, 14]/4; v[108]=[18,13,11,11,11,14,2, 16,11,12,11,13,4, 14,11,9,12,7, 16,11,13,10, 14,12,7, 18,8, 12]/4; v[109]=[16,8,9,6,9,9,1, 8,6,4,6,4,0, 12,6,7,9,6, 8,6,8,6, 12,9,6, 16,10, 12]/4; \\ P_7^1 -- P_7^19 (1 orb) v[110]=[10,8,5,5,6,6,-1, 12,5,6,6,6,-2, 10,8,6,6,7, 12,6,6,7, 8,5,4, 8,4, 12]/3; \\ P_7^1 -- P_7^20 (2 orb) v[111]=[10,5,5,9,3,3,0, 6,5,7,3,3,2, 10,9,5,3,7, 14,5,5,5, 6,1,5, 6,3, 10]/3; v[112]=[12,7,7,6,4,5,-1, 12,9,6,6,7,1, 12,6,7,8,5, 6,4,4,2, 8,6,5, 10,5, 8]/3; \\ P_7^1 -- P_7^21 (2 orb) v[113]=[10,6,7,5,5,6,0, 8,6,5,5,7,1, 10,5,6,6,3, 8,5,4,4, 8,6,4, 12,3, 6]/3; v[114]=[12,8,9,7,4,6,0, 10,8,8,6,6,2, 12,8,4,6,3, 12,6,6,5, 8,5,4, 8,4, 6]/3; \\ P_7^1 -- P_7^22 (7 orb) v[115]=[6,4,4,4,4,3,1, 6,4,4,3,3,0, 6,3,4,4,3, 6,4,3,2, 6,4,4, 6,4, 6]/2; v[116]=[12,9,8,9,7,6,2, 12,9,8,7,5,1, 10,8,6,5,3, 10,6,6,4, 6,4,2, 6,3, 4]/2; v[117]=[6,4,4,4,4,3,1, 6,4,4,5,5,2, 6,3,2,2,1, 6,5,4,3, 8,6,4, 8,4, 4]/2; v[118]=[4,1,1,1,2,2,0, 6,2,3,3,3,2, 4,2,2,2,3, 4,2,3,3, 4,3,3, 6,4 ,6]/2; v[119]=[14,10,7,10,6,8,0, 10,6,8,5,7,0, 6,6,4,4,1, 10,6,7,2, 6,5,3, 8,2, 4]/2; v[120]=[10,5,6,5,7,5,2, 6,4,4,4,4,1, 6,3,5,4,2, 6,5,4,3, 8,5,4, 6,3, 4]/2; v[121]=[6,5,4,6,6,4,2, 8,5,8,6,4,2, 6,7,6,4,5, 12,9,5,6, 10,5,6, 6,4, 8]/2; \\ P_7^1 -- P_7^23 (2 orb) v[122]=[12,6,8,4,6,6,0, 10,8,6,4,5,1, 12,7,6,6,5, 8,4,4,5, 6,4,3, 8,3, 8]/3; v[123]=[10,5,5,4,6,4,0, 8,3,4,5,4,0, 8,4,5,3,4, 6,4,4,3, 8,2,3, 8,2, 6]/3; \\ P_7^1 -- P_7^24 (5 orb) v[124]=[6,2,3,4,2,2,0, 6,3,2,4,3,1, 6,4,4,2,4, 8,5,4,6, 8,5,7, 10,7, 12]/3; v[125]=[12,5,7,8,6,6,2, 10,8,8,7,7,5, 12,9,7,8,8,12,8,7,7, 10,7,7, 10,7, 10]/3; v[126]=[6,4,5,3,4,3,1, 8,7,3,5,4,2, 12,6,7,6,8, 6,4,4,6, 8,3,5, 10,7, 12]/3; v[127]=[10,5,6,6,8,5,1, 6,4,5,6,5,2, 8,6,5,5,4, 10,8,7,7, 12,7,5, 10,7, 10]/3; v[128]=[14,4,7,5,5,6,1, 6,4,2,3,4,0, 8,4,3,5,3, 6,3,2,3, 6,4,3, 8,3, 6]/3; \\ P_7^1 -- P_7^25 (5 orb) v[129]=[6,5,4,3,4,3,-1, 10,4,4,4,4,-2, 8,6,5,5,5,10,5,7,7, 8,6,5, 10,7, 12]/3; v[130]=[16,13,13,13,10,10,3, 16,13,13,9,9,2, 16,12,8,10,5, 16,10,8,5, 10,7,4, 10,4, 6]/3; v[131]=[16,13,8,9,9,9,-1, 16,9,9,11,9,0, 10,6,8,7,4, 8,6,6,1, 12,8,3, 10,3, 6]/3; v[132]=[8,7,7,4,4,5,0, 12,9,6,5,8,1, 12,5,5,6,3, 6,4,4,3, 8,3,4, 10,2, 6]/3; v[133]=[10,6,8,5,6,7,2, 8,6,5,5,6,1, 12,7,9,8,7, 8,7,5,6, 12,5,8, 10,4,10]/3; \\ P_7^1 -- P_7^26 (3 orb) (Parf s.e.) v[134]=[6,5,6,4,5,4,2, 8,7,5,7,4,3, 10,5,8,5,5, 6,6,4,4, 10,5,6, 6,4, 6]/2; v[135]=[8,4,1,5,5,5,0, 4,2,4,4,4,2, 4,3,3,3,5, 8,5,5,5, 8,5,5, 8,5, 10]/2; v[136]=[18,9,9,9,12,7,-2, 8,5,5,7,4,-2, 8,5,7,4,1, 8,7,4,1, 10,5,0, 4,0,4]/2; \\ P_7^1 -- P_7^27 (3 orb) v[137]=[6,3,4,4,3,3,0, 6,4,4,3,3,0, 6,3,3,3,1, 6,3,3,1, 4,2,1, 4,2, 4]/2; v[138]=[12,8,8,5,8,5,-2, 8,6,5,6,4,-1, 8,4,6,5,1, 6,5,4,2, 8,5,1, 6,3, 6]/2; v[139]=[10,7,5,5,6,7,1, 8,6,5,6,6,2, 8,4,6,4,3, 6,5,5,3, 8,6,4, 8,3, 4]/2; \\ P_7^1 -- P_7^28 (5 orb) v[140]=[8,5,6,6,6,5,2, 8,5,6,6,6,2, 8,5,6,6,4, 8,5,6,3, 8,5,3, 8,4, 4]/2; v[141]=[8,8,8,6,7,6,2, 12,10,7,9,8,2, 12,7,10,8,5, 8,8,6,4, 12,8,6, 8,4, 6]/2; v[142]=[4,2,2,1,1,1,-1, 4,2,2,2,4,1, 4,1,2,1,1, 4,2,3,3, 4,3,3, 10,5, 6]/2; v[143]=[6,3,3,3,4,3,0,4,4,2,3,3,1, 8,2,4,4,4, 4,2,3,2, 6,3,2, 6,4, 6]/2; v[144]=[8,3,4,2,4,5,0, 6,3,3,4,4,1, 4,2,3,3,1, 4,2,2,1, 8,5,4, 6,2, 4]/2; \\ P_7^1 -- P_7^29 (6 orb) (Parf non s.e.) v[145]=[8,8,8,5,5,5,1, 12,10,6,6,6,1, 12,6,6,6,3, 6,3,4,2, 6,4,2, 6,3, 4]/2; v[146]=[4,2,3,1,2,1,0, 4,3,3,4,3,2, 6,3,5,2,4, 6,5,3,5, 8,4,6, 6,4, 8]/2; v[147]=[12,9,6,8,4,4,-3, 12,6,8,4,4,-3, 6,6,3,3,1, 10,4,4,1, 4,2,1, 4,1, 6]/2; v[148]=[6,6,3,3,4,4,-1, 10,4,4,6,4,-1, 4,2,3,2,1, 4,3,2,1, 6,3,1, 6,1, 4]/2; v[149]=[12,8,8,8,9,7,1, 8,6,6,7,5,0, 8,6,6,5,2, 8,6,5,2, 10,6,2, 6,2,4]/2; v[150]=[4,5,3,4,6,3,2, 10,5,7,11,5,4, 6,5,7,3,5, 8,10,4,6, 16,6,8, 6,4, 8]/2; \\ P_7^1 -- P_7^30 (2 orb) v[151]=[10,7,6,7,5,8,2, 10,6,8,7,8,3, 6,5,5,6,3, 10,6,8,4, 8,6,4, 10,4, 4]/2; v[152]=[8,3,3,3,3,4,-1, 4,2,3,2,3,0, 4,3,3,3,2, 6,3,3,2, 6,4,3, 6,2, 4]/2; \\ P_7^1 -- P_7^31 (4 orb) v[153]=[6,4,4,3,3,2,0, 6,4,4,4,4,1, 6,3,4,2,2, 6,4,3,3, 6,3,3, 6, 2, 4]/2; v[154]=[10,9,7,7,6,5,0, 12,7,8,6,5,-1, 8,7,5,5,3, 10,5,5,3, 6,4,2, 6,3, 6]/2; v[155]=[8,6,5,6,4,4,0, 12,8,9,6,7,3, 8,6,5,5,3,10,5,6,3, 6,4,3, 6,3, 4]/2; v[156]=[6,4,4,5,3,3,-1, 6,3,5,3,3,-1, 6,4,3,3,2, 8,3,4,1, 4,2,1, 4,2, 6]/2; \\ P_7^1 -- P_7^32 (1 orb) v[157]=[8,9,6,7,5,5,1, 14,8,10,6,6,1, 8,7,4,4,3, 10,5,5,3, 6,3,2, 6,2, 4]/2; V7[1]=v; \\ P_7^1 -- P_7^33 are not contiguous \\==================================================================== \\ 1 orbit of contiguous forms to E_7^*=P_7^2 (to P_7^1);V7[2] empty: V7[2]=W2=[1]; \\==================================================================== \\ 23 orbits of contiguous forms to P_7^3; V7[3]--[7,23]: v=W3=[1,1,1,1,1,1,3,3,3,4,6,6,6,7,7,7,8,8,9,17,22,26,29]; \\v[1]=[4,2,2,2,2,2,2, 4,2,2,2,2,2, 4,2,0,2,2, 4,0,2,2, 4,2,2, 4,2, 4]; \\v[2]=[4,0,2,0,2,2,0, 4,0,2,2,0,2, 4,0,0,2,0, 4,0,2,2, 4,0,2, 4,0, 4]; \\v[3]=[4,0,2,2,2,2,2, 4,2,2,2,6,0, 4,2,2,4,2, 4,2,4,2, 4,4,2, 12,0, 4]; \\v[4]=[4,0,2,2,2,0,2, 4,2,2,2,2,2, 4,2,2,2,2, 4,2,2,2, 4,2,2, 4,0, 4]; \\v[5]=[4,0,2,2,0,0,2, 4,2,2,0,2,0, 4,2,0,2,2, 4,0,2,2, 4,2,2, 4,2, 4]; \\v[6]=[4,2,2,2,2,2,2, 4,2,2,2,2,2, 4,2,0,2,2, 8,-2,0,4, 4,2,0, 4,0, 4]; v[7]=[4,1,2,2,2,3,2, 4,2,2,2,3,2, 4,1,1,3,2, 4,1,3,2, 4,3,2, 6,3, 4]; v[8]=[4,1,2,2,3,3,2, 4,2,2,3,3,2, 4,1,2,3,2, 4,2,3,2, 6,4,3, 6,2, 4]; v[9]=[4,-1,2,2,1,1,2, 4,1,1,2,2,1, 4,1,1,2,2, 4,1,2,2, 4,2,2, 4,1, 4]; v[10]=[4,0,2,2,2,2,2, 4,2,2,2,2,2, 4,2,2,2,2, 4,2,2,2, 4,2,2, 4,2, 4]; v[11]=[12,2,6,6,6,8,6, 12,6,6,6,8,4, 12,4,4,8,6, 12,4,8,6, 12,8,6, 16,4, 12]/3; v[12]=[12,4,8,6,4,6,6, 12,8,6,4,6,6, 16,4,4,8,8, 12,-2,4,4, 12,6,6, 12,4, 12]/3; v[13]=[12,2,8,4,6,6,6, 12,10,6,2,6,6, 20,8,2,10,10, 12,-2,6,6, 12,4,4, 12,4, 12]/3; v[14]=[4,1,2,2,2,2,2, 4,2,2,1,1,2, 4,1,0,1,2, 4,1,2,2, 4,2,2, 4,1, 4]; v[15]=[4,0,2,1,2,2,2, 4,1,2,3,2,2, 4,0,1,2,2, 4,2,2,2, 6,3,3, 4,2, 4]; v[16]=[4,0,2,1,2,2,1, 4,1,2,2,1,2, 4,1,1,2,2, 4,1,2,2, 4,2,2, 4,1, 4]; v[17]=[4,0,1,1,2,2,1, 4,2,2,2,2,2, 4,1,1,2,2, 4,1,2,2, 4,2,2, 4,1, 4]; v[18]=[4,1,2,2,2,3,1, 4,2,2,2,3,1, 4,2,1,3,2, 4,1,3,2, 4,3,1, 6,1, 4]; v[19]=[20,4,10,10,10,6,10, 20,10,10,10,6,10, 20,6,6,8,10, 20,6,8,10, 20,8,10, 20,0, 20]/5; v[20]=[12,0,4,6,4,6,6, 12,6,4,6,6,4, 12,2,4,6,6, 12,2,6,6, 12,6,6, 12,4, 12]/3; v[21]=[4,1,1,2,2,1,2, 4,2,2,2,2,2, 4,1,1,2,2, 4,1,2,2, 4,2,2, 4,1, 4]; v[22]=[4,1,2,2,2,2,2, 4,2,2,2,2,2, 4,1,1,2,2, 4,1,2,2, 4,2,2, 4,2, 4]; v[23]=[4,1,2,2,2,2,2, 4,2,2,2,2,2, 4,2,1,3,2, 4,1,3,2, 4,2,2, 6,1, 4]; V7[3]=v; \\==================== \\ 17 orbits of contiguous forms to D_7=P_7^4; V7[4]--[6,17]: v=W4= [1,1,1,1,3,4,8,9,12,19,22,26,27,29,31,32,33]; v[6]=[2,1,1,1,2,1,2, 2,1,1,1,1,2, 2,1,1,1,2, 2,1,1,2, 4,2,4, 2,3, 6]; v[7]=[4,1,3,3,3,2,4, 4,3,3,2,2,4, 6,4,3,3,6, 6,3,3,6, 6,3,6, 4,5, 10]/2; v[8]=[14,7,7,7,9,7,14, 14,7,7,7,7,14, 14,7,7,7,14, 14,7,7,14, 14,7,14, 10,12, 24]/5; v[9]=[6,4,4,4,4,3,6, 8,4,4,4,4,8, 8,4,4,4,8, 8,4,4,8, 8,4,8, 6,7, 14]/3; v[10]=[10,5,3,5,7,5,10, 10,3,7,5,5,10, 6,3,3,3,6, 10,5,5,10, 10,5,10, 6,8, 16]/3; v[11]=[4,1,3,2,3,2,4, 4,3,1,2,2,4, 6,3,3,3,6, 4,2,2,4, 6,3,6, 4,5, 10]/2; v[12]=[4,3,3,3,3,2,4, 6,4,4,3,3,6, 6,4,3,3,6, 6,3,3,6, 6,3,6, 4,5, 10]/2; v[13]=[4,2,3,2,3,2,4, 4,3,1,2,2,4, 6,3,3,3,6, 4,2,2,4, 6,3,6, 4,5, 10]/2; v[14]=[4,2,3,3,3,2,4, 4,3,3,2,2,4, 6,4,3,3,6, 6,3,3,6, 6,3,6, 4,5, 10]/2; v[15]=[6,4,3,2,4,3,6, 6,2,3,3,3,6, 4,1,2,2,4, 4,2,2,4, 6,3,6, 4,5, 10]/2; v[16]=[6,4,2,2,4,3,6, 6,2,2,3,3,6, 4,1,2,2,4, 4,2,2,4, 6,3,6, 4,5, 10]/2; v[17]=[4,1,1,1,3,2,4, 2,1,1,1,1,2, 2,1,1,1,2, 2,1,1,2, 4,2,4, 2,3, 6]; V7[4]=v; \\==================== \\ 46 orbits of contiguous forms to P_7^5; V7[5]--[11,46]: v=W5=[1,1,1,1,1,1,1,1,1,1,5,5,5,5,5,5,6,7,7,7,7,7,7,7,8,8,10,10,11,11,11,11,13,14,14,14,16,17,18,18,19,20,21,23,24,24]; v[11]=[4,1,2,1,2,2,2, 4,1,2,2,2,2, 4,1,2,2,2, 4,2,2,2, 4,1,1, 4,2, 4]; v[12]=[4,1,2,0,2,2,2, 4,1,2,2,2,2, 4,0,2,2,2, 4,1,2,1, 4,1,2, 4,1, 4]; v[13]=[4,0,2,0,2,1,2, 4,1,2,2,2,2, 4,1,2,2,2, 4,2,2,2, 4,1,2, 4,2, 4]; v[14]=[4,0,1,1,1,2,1, 4,1,1,2,2,2, 4,2,2,2,2, 4,2,2,2, 4,1,2, 4,1, 4]; v[15]=[4,0,2,0,2,2,1, 4,1,2,2,2,2, 4,0,2,2,2, 4,2,2,1, 4,2,2, 4,1, 4]; v[16]=[4,0,1,0,2,1,1, 4,2,2,2,2,2, 4,1,2,2,2, 4,2,2,1, 4,1,2, 4,0, 4]; v[17]=[12,2,6,4,6,6,6, 12,4,6,6,6,6, 12,2,6,6,6, 12,6,6,6, 12,4,4, 12,4, 12]/3; v[18]=[4,0,2,1,2,2,2, 4,1,2,2,1,2, 4,1,2,2,2, 4,2,2,2, 4,1,2, 4,1, 4]; v[19]=[4,0,2,1,2,2,2, 4,1,2,1,2,2, 4,1,2,2,2, 4,2,2,2, 4,1,1, 4,2, 4]; v[20]=[4,0,2,0,1,2,2, 4,1,2,2,2,2, 4,1,2,2,2, 4,2,2,1, 4,1,1, 4,2, 4]; v[21]=[4,1,2,0,2,2,1, 4,1,1,1,2,2, 4,0,2,2,2, 4,1,1,2, 4,0,2, 4,1, 4]; v[22]=[4,1,2,0,2,2,1, 4,1,1,2,2,2, 4,0,2,2,2, 4,1,2,1, 4,1,2, 4,1, 4]; v[23]=[4,0,1,1,2,2,2, 4,1,2,1,2,2, 4,1,2,2,2, 4,2,2,2, 4,1,2, 4,2, 4]; v[24]=[4,1,1,1,2,2,2, 4,1,2,2,2,2, 4,0,1,2,2, 4,2,2,1, 4,1,2, 4,1, 4]; v[25]=[4,0,2,0,2,1,2, 4,1,2,1,2,2, 4,0,1,2,2, 4,2,1,2, 4,0,2, 4,1, 4]; v[26]=[4,0,1,1,2,1,2, 4,2,2,2,2,2, 4,1,2,2,2, 4,2,2,2, 4,1,2, 4,1, 4]; v[27]=[4,0,2,0,2,2,1, 4,1,2,2,1,2, 4,0,2,2,2, 4,2,1,1, 4,1,2, 4,0, 4]; v[28]=[4,0,1,1,2,1,2, 4,1,2,1,2,2, 4,1,1,2,2, 4,2,2,2, 4,0,2, 4,1, 4]; v[29]=[12,0,6,2,4,6,6, 12,2,6,4,6,6, 12,4,6,6,6, 12,6,6,6, 12,2,4, 12,6, 12]/3; v[30]=[12,2,6,0,6,4,6, 12,4,6,6,6,6, 12,2,6,6,6, 12,6,4,6, 12,2,6, 12,4, 12]/3; v[31]=[12,4,6,2,6,6,6, 12,2,4,6,6,6, 12,0,4,6,6, 12,4,6,4, 12,2,6, 12,4, 12]/3; v[32]=[12,2,4,2,6,6,4, 12,4,6,6,6,6, 12,2,6,6,6, 12,6,6,4, 12,4,6, 12,2, 12]/3; v[33]=[8,1,4,0,4,3,3, 8,3,4,4,4,4, 8,1,4,4,4, 8,4,3,3, 8,2,4, 8,1, 8]/2; v[34]=[12,-2,6,2,6,4,4, 12,2,6,4,4,6, 12,4,6,6,6, 12,6,6,6, 12,2,6, 12,2, 12]/3; v[35]=[12,2,4,2,6,6,2, 12,4,4,6,6,6, 12,4,6,6,6, 12,6,6,6, 12,4,6, 12,2, 12]/3; v[36]=[12,2,6,2,6,6,6, 12,4,6,6,6,6, 12,2,6,6,6, 12,6,6,4, 12,4,4, 12,4, 12]/3; v[37]=[12,0,6,2,6,4,6, 12,2,6,6,4,6, 12,2,4,6,6, 12,6,6,4, 12,2,6, 12,2, 12]/3; v[38]=[12,2,6,2,6,6,4, 12,2,4,4,6,6, 12,2,6,6,6, 12,4,6,6, 12,2,6, 12,4, 12]/3; v[39]=[8,0,4,1,4,3,3, 8,2,4,4,3,4, 8,2,4,4,4, 8,4,4,3, 8,2,4, 8,1, 8]/2; v[40]=[8,0,3,1,2,4,2, 8,2,4,4,4,4, 8,3,4,4,4, 8,4,4,4, 8,2,3, 8,2, 8]/2; v[41]=[12,2,6,2,6,6,6, 12,2,6,6,6,6, 12,2,6,6,6, 12,6,6,6, 12,4,6, 12,6, 12]/3; v[42]=[12,4,6,0,6,6,4, 12,4,4,6,6,6, 12,0,6,6,6, 12,4,4,4, 12,2,6, 12,2, 12]/3; v[43]=[12,2,6,2,6,6,6, 12,2,6,6,6,6, 12,2,6,6,4, 12,6,6,4, 12,4,4, 12,4, 12]/3; v[44]=[12,2,6,2,6,6,6, 12,2,6,4,6,6, 12,2,6,6,4, 12,6,4,6, 12,2,4, 12,4, 12]/3; v[45]=[12,2,6,0,6,4,4, 12,4,4,6,6,6, 12,2,6,6,6, 12,4,6,4, 12,2,6, 12,2, 12]/3; v[46]=[12,2,4,2,6,6,6, 12,4,6,6,6,6, 12,2,6,6,6, 12,6,6,4, 12,4,6, 12,4, 12]/3; V7[5]=v; \\==================== \\ 19 orbits of contiguous forms to P_7^6; V7[6]--[11,19]: v=W6=[1,1,1,1,1,1,3,3,3,5,6,6,7,7,8,9,14,16,17]; v[11]=[6,2,2,2,3,3,3, 6,2,2,3,3,3, 6,2,3,3,3, 6,3,3,3, 6,3,2, 6,1, 6]; v[12]=[6,2,1,2,2,3,3, 6,1,2,2,3,3, 6,1,3,2,3, 6,2,3,3, 6,1,3, 6,1, 6]; v[13]=[12,3,3,6,6,6,6, 12,0,3,3,6,3, 12,3,6,3,6, 12,6,6,6, 12,3,6, 12,0, 12]/2; v[14]=[12,6,3,3,6,6,6, 12,3,3,6,6,6, 12,3,3,6,6, 12,6,6,6, 12,3,6, 12,3, 12]/2; v[15]=[12,3,3,3,6,6,6, 12,3,6,6,6,6, 12,3,6,6,6, 12,6,6,6, 12,6,6, 12,3, 12]/2; v[16]=[30,9,9,9,15,15,15, 30,9,9,15,15,15, 30,9,15,15,15, 30,15,15,15, 30,15,15, 30,6, 30]/5; v[17]=[6,2,2,2,3,3,3, 6,2,1,3,3,3, 6,2,3,3,3, 6,3,3,2, 6,2,3, 6,1, 6]; v[18]=[6,2,2,2,3,3,3, 6,2,0,3,3,3, 6,2,3,3,3, 6,3,1,3, 6,2,3, 6,1, 6]; v[19]=[6,1,2,2,3,3,3, 6,1,2,2,3,2, 6,2,3,3,3, 6,3,3,3, 6,2,3, 6,1, 6]; V7[6]=v; \\==================== \\ 94 orbits of contiguous forms to P_7^7;V7[7]--[31,94]: v=W7=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,5,5,5,5,5,5,5,6,6,\ 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,10,10,10,10,11,11,11,11,11,\ 14,14,14,14,14,15,16,16,14,17,18,20,21,22,22,22,23,23,24,24,24,25,25,25,27,\ 28,28,28,28,31]; v[31]=[4,2,2,1,1,2,1, 4,2,1,0,1,2, 4,2,1,1,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[32]=[4,2,2,2,3,3,1, 4,2,3,2,3,2, 4,3,3,2,2, 8,6,6,3, 8,6,4, 8,4, 4]; v[33]=[4,3,2,0,1,2,2, 6,3,2,1,3,4, 4,1,1,1,3, 4,2,3,2, 4,3,3, 6,4, 6]; v[34]=[4,2,2,-1,1,1,1, 4,2,-1,-1,0,2, 4,-1,0,-1,2, 4,2,2,0, 4,2,1, 4,1, 4]; v[35]=[4,3,2,0,0,1,1, 6,3,2,1,2,3, 4,1,0,0,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[36]=[4,3,2,0,0,1,1, 6,3,3,1,3,3, 4,1,0,0,2, 6,3,4,2, 4,3,2, 6,3, 4]; v[37]=[4,3,2,1,1,2,1, 6,3,2,0,1,2, 4,1,0,0,2, 4,2,3,1, 4,3,2, 6,2, 4]; v[38]=[4,2,2,-1,0,-1,0, 4,2,0,-1,0,1, 4,1,0,-1,1, 4,2,2,1, 4,2,2, 4,2, 4]; v[39]=[4,2,2,-1,1,0,1, 4,2,0,0,1,3, 4,1,1,0,2, 4,2,2,1, 4,2,2, 4,3, 6]; v[40]=[4,3,2,1,1,2,1, 6,3,2,1,2,3, 4,2,1,1,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[41]=[4,2,2,-1,0,0,1, 4,2,1,0,1,2, 4,1,1,0,2, 4,2,2,1, 4,2,3, 4,3, 6]; v[42]=[6,3,4,0,2,1,2, 4,3,0,0,0,2, 6,1,2,0,3, 4,2,2,0, 4,2,2, 4,1, 4]; v[43]=[4,2,2,0,1,1,1, 4,2,2,1,2,2, 4,1,1,0,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[44]=[6,3,3,-1,1,1,1, 4,2,0,0,1,2, 4,0,1,0,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[45]=[4,2,3,1,1,1,1, 4,3,2,0,1,2, 6,3,2,1,3, 4,2,2,2, 4,2,3, 4,3, 6]; v[46]=[4,3,3,1,1,1,1, 6,4,2,0,0,2, 6,2,1,0,3, 4,2,2,1, 4,2,2, 4,1, 4]; v[47]=[4,3,2,0,0,1,1, 6,3,1,0,1,3, 4,2,1,1,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[48]=[4,2,3,0,0,0,0, 4,3,2,0,1,2, 6,2,1,0,2, 4,2,2,2, 4,2,3, 4,3, 6]; v[49]=[4,3,3,0,0,0,1, 6,4,3,1,2,3, 6,2,1,0,3, 6,3,3,2, 4,2,2, 4,2, 4]; v[50]=[4,2,2,1,2,2,2, 4,2,2,1,1,2, 4,1,1,0,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[51]=[4,3,2,0,1,2,2, 6,3,1,0,2,3, 4,1,0,1,2, 4,2,3,1, 4,3,2, 6,3, 4]; v[52]=[4,2,2,0,1,1,1, 4,2,1,0,0,1, 4,1,1,0,2, 4,3,2,1, 6,3,3, 4,2, 4]; v[53]=[4,3,2,0,0,1,1, 6,3,2,0,2,3, 4,1,0,0,2, 4,2,3,2, 4,3,3, 6,4, 6]; v[54]=[4,3,3,0,1,1,2, 6,4,2,1,2,4, 6,2,2,1,4, 4,2,2,2, 4,2,3, 4,3, 6]; v[55]=[4,2,2,1,1,2,1, 4,2,2,0,2,2, 4,2,1,1,2, 4,2,3,2, 4,3,3, 6,4, 6]; v[56]=[4,2,2,-1,0,0,1, 4,2,0,-1,0,1, 4,0,0,-1,2, 4,2,2,0, 4,2,2, 4,1, 4]; v[57]=[4,2,2,0,1,1,1, 4,2,1,1,1,2, 4,0,1,0,2, 4,2,2,0, 4,2,2, 4,2, 4]; v[58]=[4,2,2,0,1,1,1, 4,2,0,0,1,2, 4,0,1,0,2, 4,2,2,0, 4,2,2, 4,2, 4]; v[59]=[4,3,3,0,1,1,2, 6,4,2,1,1,3, 6,1,1,0,3, 4,2,2,1, 4,2,2, 4,2, 4]; v[60]=[16,8,8,0,4,6,4, 12,6,2,0,4,6, 12,0,2,0,6, 12,6,8,2, 12,8,6, 16,6, 12]/3; v[61]=[12,8,6,0,0,4,2, 16,8,4,0,4,8, 12,4,2,2,6, 12,6,6,4, 12,6,6, 12,6, 12]/3; v[62]=[12,8,6,0,0,2,2, 16,8,6,0,4,6, 12,4,2,0,6, 12,6,6,4, 12,6,8, 12,8, 16]/3; v[63]=[12,8,6,0,2,4,4, 16,8,6,2,6,8, 12,2,0,0,6, 12,6,8,4, 12,8,6, 16,8, 12]/3; v[64]=[12,8,6,0,2,4,4, 16,8,4,0,4,8, 12,2,0,0,6, 12,6,6,2, 12,6,4, 12,6, 12]/3; v[65]=[12,6,6,-2,0,-2,0, 12,6,2,-2,0,4, 12,4,2,-2,4, 12,6,6,4, 12,6,6, 12,6, 12]/3; v[66]=[12,8,6,2,4,6,4, 16,8,6,2,6,8, 12,4,2,2,6, 12,6,8,4, 12,8,6, 16,8, 12]/3; v[67]=[16,8,8,0,6,6,6, 12,6,2,2,4,6, 12,0,4,0,6, 12,8,8,2, 16,10,8, 16,8, 12]/3; v[68]=[12,8,6,2,4,6,4, 16,8,4,0,4,8, 12,2,0,0,6, 12,6,8,2, 12,8,4, 16,6, 12]/3; v[69]=[12,6,6,0,4,4,4, 12,6,2,0,2,6, 12,0,2,-2,6, 12,6,6,0, 12,6,4, 12,4, 12]/3; v[70]=[8,5,4,1,2,3,2, 10,5,3,0,3,5, 8,2,0,0,3, 8,4,5,2, 8,5,3, 10,5, 8]/2; v[71]=[12,6,6,-2,2,0,2, 12,6,0,-2,2,6, 12,2,0,-2,4, 12,6,6,2, 12,6,4, 12,6, 12]/3; v[72]=[12,6,8,0,2,2,2, 12,8,4,0,2,6, 16,4,4,0,8, 16,8,8,4, 12,6,6, 12,4, 12]/3; v[73]=[12,8,6,2,4,6,4, 16,8,4,0,4,8, 12,2,0,0,6, 12,6,8,2, 12,8,4, 16,6, 12]/3; v[74]=[12,6,6,2,4,4,4, 12,6,6,2,4,6, 12,4,2,0,6, 12,6,6,4, 12,6,6, 12,6, 12]/3; v[75]=[8,5,4,0,2,3,3, 10,5,3,1,3,5, 8,1,1,0,4, 8,4,5,2, 8,5,4, 10,5, 8]/2; v[76]=[12,6,6,0,2,2,2, 12,6,2,0,4,8, 12,4,2,0,4, 12,6,6,2, 12,6,6, 12,8, 16]/3; v[77]=[12,8,8,2,2,2,2, 16,10,6,0,2,6, 16,6,2,0,6, 12,6,6,4, 12,6,6, 12,6, 12]/3; v[78]=[4,3,3,1,1,1,1, 6,4,3,1,2,3, 6,3,2,1,3, 6,3,3,2, 4,2,2, 4,2, 4]; v[79]=[4,2,2,-1,0,0,0, 4,2,1,0,1,2, 4,1,1,0,2, 4,2,2,2, 4,2,3, 4,3, 6]; v[80]=[6,3,3,0,2,2,2, 4,2,1,1,2,2, 4,0,1,0,2, 4,3,3,1, 6,4,3, 6,3, 4]; v[81]=[12,6,6,-2,2,2,2, 12,6,0,-2,2,6, 12,0,0,-2,6, 12,6,6,2, 12,6,4, 12,4, 12]/3; v[82]=[12,8,6,2,2,4,2, 16,8,4,0,2,6, 12,4,2,0,6, 12,6,6,2, 12,6,6, 12,4, 12]/3; v[83]=[12,8,8,0,2,2,4, 16,10,6,2,4,8, 16,4,2,0,8, 12,6,6,4, 12,6,6, 12,6, 12]/3; v[84]=[12,6,6,0,2,2,2, 12,6,4,0,2,4, 12,4,4,0,6, 12,8,6,4, 16,8,10, 12,8, 16]/3; v[85]=[12,8,6,0,2,4,4, 16,8,4,2,4,8, 12,2,2,0,6, 12,6,6,2, 12,6,6, 12,6, 12]/3; v[86]=[12,8,8,2,4,4,4, 16,10,4,0,2,8, 16,4,2,0,8, 12,6,6,2, 12,6,4, 12,4, 12]/3; v[87]=[16,8,10,0,6,4,6, 12,8,2,2,2,6, 16,2,6,0,8, 12,8,6,2, 16,8,8, 12,6, 12]/3; v[88]=[12,8,6,0,2,4,4, 16,8,4,0,4,8, 12,4,2,2,6, 12,6,8,4, 12,8,6, 16,8, 12]/3; v[89]=[6,3,4,0,2,1,2, 4,3,1,1,1,2, 6,1,2,0,3, 4,3,2,1, 6,3,3, 4,2, 4]; v[90]=[4,2,2,-2,-1,-1,1, 4,2,-1,-2,-1,2, 4,-1,-1,-2,2, 4,2,2,-1, 4,2,0, 4,0, 4]; v[91]=[6,4,4,0,1,1,2, 6,4,2,1,2,3, 6,1,1,0,3, 4,2,2,1, 4,2,2, 4,2, 4]; v[92]=[4,3,2,0,1,1,1, 6,3,1,1,1,3, 4,1,1,0,2, 4,2,2,1, 4,2,2, 4,2, 4]; v[93]=[4,2,2,0,1,1,1, 4,2,1,0,1,2, 4,1,1,0,2, 6,3,4,1, 4,3,2, 6,2, 4]; v[94]=[4,2,2,0,1,1,1, 4,2,2,1,2,2, 4,1,1,0,2, 6,4,4,2, 6,4,3, 6,3, 4]; V7[7]=v; \\==================== \\ 27 orbits of contiguous forms to P_7^8' V7[8]--[19,27]: v=W8=[1,1,1,1,1,1,1,1,1,1,3,3,4,5,5,6,7,7,8,9,10,17,19,22,24,28,29]; v[19]=[4,0,0,2,-1,2,1, 4,1,1,0,0,3, 4,1,0,0,3, 4,1,0,3, 4,0,2, 4,0, 6]; v[20]=[20,-4,-4,8,-6,10,0, 20,4,4,4,0,14, 20,4,4,0,14, 20,6,0,14, 20,0,14, 20,0, 28]/5; v[21]=[4,-1,-1,2,-1,2,0, 4,2,0,-1,0,2, 4,0,-1,0,2, 4,1,0,2, 4,-1,1, 4,-1, 4]; v[22]=[12,-2,-2,6,-4,4,0, 12,4,2,0,0,8, 12,2,0,0,8, 12,2,-2,8, 12,0,6, 12,-2, 16]/3; v[23]=[12,-4,-4,4,-2,6,0, 12,4,0,0,0,6, 12,0,0,0,6, 12,6,0,6, 12,0,6, 12,0, 12]/3; v[24]=[4,0,0,2,-1,2,1, 4,1,0,0,1,2, 4,0,0,1,2, 4,1,0,2, 4,0,2, 4,1, 4]; v[25]=[12,-4,-2,6,-2,6,0, 12,4,0,-2,-2,6, 12,0,-2,0,6, 12,4,0,6, 12,0,4, 12,-2, 12]/3; v[26]=[4,-1,0,2,-1,2,0, 4,1,0,-1,-1,2, 4,0,-1,0,2, 4,1,0,2, 4,0,1, 4,-1, 4]; v[27]=[4,-1,-1,2,-1,2,0, 4,1,0,0,0,2, 4,0,0,-1,2, 4,1,0,2, 4,0,2, 4,0, 4]; V7[8]=v; \\==================== \\ 6 orbits of contiguous forms to P_7^9; V7[9]--[6]: v=W9=[1,3,4,6,8,12]; v[6]=[30,10,10,10,10,10,25, 30,10,10,10,10,25, 30,10,10,10,25, 30, 10,10,25, 30,10,25, 30,25, 50]/3; V7[9]=v; \\==================== \\ 24 orbits of contiguous forms to P_7^10; V7[10]--[16,24]: v=W10=[1,1,1,1,1,1,1,1,5,5,7,7,7,7,8,10,10,11,11,18,23,24,28,30]; v[16]=[4,1,2,2,0,2,2, 4,1,2,2,0,2, 4,1,2,2,2, 4,1,2,3, 4,1,3, 4,3, 6]; v[17]=[4,1,2,2,0,2,2, 4,1,2,2,0,1, 4,1,2,2,2, 4,1,2,2, 4,1,2, 4,2, 4]; v[18]=[16,4,8,8,0,8,8, 12,4,6,6,0,6, 12,4,6,6,8, 12,2,6,8, 12,2,8, 12,8, 16]/3; v[19]=[16,4,8,8,0,8,8, 12,2,6,6,0,6, 12,2,4,6,6, 12,2,6,6, 12,2,6, 12,6, 12]/3; v[20]=[8,2,4,4,1,5,5, 8,1,4,4,0,5, 8,2,4,5,5, 8,3,5,5, 8,3,5, 10,5, 10]/2; v[21]=[12,2,6,6,0,6,6, 12,4,6,8,0,6, 12,4,8,6,8, 12,4,6,8, 16,4,10, 12,8, 16]/3; v[22]=[16,4,8,8,0,8,8, 12,4,6,6,0,6, 12,4,6,6,8, 12,2,6,6, 12,2,8, 12,8, 16]/3; v[23]=[6,2,3,4,0,3,4, 4,2,3,2,1,3, 4,2,2,2,3, 6,1,3,4, 4,1,2, 4,3, 6]; v[24]=[4,2,3,2,1,2,3, 6,3,3,4,1,4, 6,2,4,3,4, 4,2,2,3, 6,2,4, 4,3, 6]; V7[10]=v; \\==================================================================== \\ 31 orbits of contiguous forms to P_7^11; V7[11]--[21,31]: v=W11=[1,1,1,1,1,1,1,1,1,5,5,5,5,7,7,7,7,7,10,10,11,11,11,11,13,14,15,17,18,23,24]; v[21]=[6,1,3,3,3,2,2, 6,3,2,2,-1,-1, 6,2,2,-1,-1, 6,0,3,1, 6,1,3, 6,2, 6]; v[22]=[6,1,2,3,3,3,3, 6,2,2,2,-1,-1, 6,2,2,-1,-1, 6,0,3,1, 6,1,3, 6,3, 6]; v[23]=[6,1,3,3,3,2,2, 6,2,2,2,-1,-1, 6,2,2,-1,-1, 6,0,3,1, 6,1,4, 6,3, 8]; v[24]=[6,1,3,3,3,2,2, 6,2,2,2,-1,-1, 6,2,2,-1,-1, 6,0,3,1, 6,1,4, 6,4, 8]; v[25]=[24,6,12,12,12,6,6, 24,9,9,9,-3,-3, 24,9,9,-3,-3, 24,0,12,3, 24,3,12, 24,9, 24]/4; v[26]=[6,1,2,3,3,2,3, 6,2,2,2,-1,-1, 6,2,2,-1,-1, 6,0,3,1, 6,1,3, 6,3, 6]; v[27]=[24,6,12,12,12,6,9, 24,9,9,9,-3,-3, 24,9,9,-3,-3, 24,0,12,3, 24,3,12, 24,12, 24]/4; v[28]=[6,1,2,3,3,2,2, 6,2,2,2,-1,-1, 6,2,2,-1,-1, 6,0,3,1, 6,1,3, 6,3, 6]; v[29]=[24,6,12,12,12,6,6, 24,9,6,9,-6,-3, 24,6,9,-6,-3, 24,0,12,6, 24,3,12, 24,12, 24]/4; v[30]=[6,1,3,3,3,2,2, 6,3,2,2,-1,-1, 6,2,2,-1,-1, 6,0,3,1, 6,1,3, 6,3, 6]; v[31]=[6,0,2,3,3,3,3, 6,2,1,2,-2,-1, 6,1,2,-2,-1, 6,0,4,2, 6,1,3, 8,4, 6]; V7[11]=v; \\==================================================================== \\ 3 orbits of contiguous forms to P_7^12; V7[12] empty V7[12]=W12=[1,4,9]; \\==================================================================== \\ 6 orbits of contiguous forms to P_7^13; V7[13]--[6]: v=W13=[1,1,1,5,11,17]; v[6]=[24,4,8,8,4,12,12, 24,4,8,8,12,12, 24,4,12,12,12, 24,4,12,12, 24,12,12, 24,8, 24]/3; V7[13]=v; \\==================================================================== \\ 24 orbits of contiguous forms to P_7^14; V7[14]--[18,24]: v=W14=[1,1,1,1,1,1,1,5,5,5,6,7,7,7,7,7,11,14,15,16,18,21,22,25]; v[18]=[6,-1,0,-3,2,1,2, 8,-4,0,2,3,3, 6,3,0,0,0, 6,1,0,1, 6,0,2, 6,1, 6]; v[19]=[24,-3,0,-12,9,6,6, 24,-12,0,6,9,9, 24,12,0,3,3, 24,3,0,6, 24,0,6, 24,3, 24]/4; v[20]=[6,0,-1,-3,3,1,2, 6,-3,-1,1,3,2, 6,3,-1,0,1, 6,0,-1,1, 6,-1,1, 6,1, 6]; v[21]=[24,-3,-3,-12,12,3,6, 24,-12,0,3,9,9, 24,12,-3,3,3, 24,0,0,6, 24,-3,3, 24,3, 24]/4; v[22]=[6,0,-1,-4,2,1,2, 6,-4,-1,1,2,2, 8,5,0,1,1, 8,1,0,1, 6,-1,1, 6,1, 6]; v[23]=[12,-3,0,-6,3,3,3, 12,-6,0,3,3,3, 12,6,-3,3,3, 12,0,0,3, 12,-3,0, 12,3, 12]/2; v[24]=[6,0,-1,-4,2,1,2, 6,-3,-1,1,3,2, 6,4,0,0,1, 8,1,-1,1, 6,-1,1, 6,1, 6]; V7[14]=v; \\==================================================================== \\ 4 orbits of contiguous forms to P_7^15; V7[15] empty V7[15]=W15=[1,7,11,14]; \\==================================================================== \\ 12 orbits of contiguous forms to P_7^16; V7[16]--[9,12]: v=W16=[1,1,1,5,6,7,7,14,18,22,25,27]; v[9]=[24,3,3,9,9,12,15, 24,3,3,12,9,15, 24,3,3,9,15, 24,3,3,15, 24,3,15, 24,15, 30]/4; v[10]=[12,3,3,3,6,6,9, 12,3,3,6,6,9, 12,3,3,6,9, 12,3,3,9, 12,3,9, 12,9, 18]/2; v[11]=[6,1,1,2,3,3,4, 6,1,1,3,2,4, 6,1,1,2,4, 6,1,1,4, 6,1,4, 6,4, 8]; v[12]=[12,3,3,3,6,6,9, 12,3,3,6,6,9, 12,3,3,3,9, 12,3,3,9, 12,3,9, 12,9, 18]/2; V7[16]=v; \\==================================================================== \\ 14 orbits of contiguous forms to P_7^17; V7[17] empty V7[17]=W17=[1,1,1,1,1,1,3,5,6,7,7,8,11,13]; \\==================================================================== \\ 13 orbits of contiguous forms to P_7^18; V7[18]--[12,13]: v=W18=[1,1,1,1,5,5,7,10,11,14,16,24,25]; v[12]=[24,-12,8,12,0,4,4, 24,4,0,12,0,4, 24,12,0,0,4, 24,8,0,12, 24,12,0, 24,-12, 24]/3; v[13]=[24,-12,8,12,0,4,4, 24,4,0,12,4,0, 24,12,0,4,4, 24,8,0,12, 24,12,-4, 24,-12, 24]/3; V7[18]=v; \\==================================================================== \\ 4 orbits of contiguous forms to P_7^19; V7[19] empty V7[19]=W19=[1,4,5,8]; \\==================================================================== \\ 4 orbits of contiguous forms to P_7^20; V7[20] empty V7[20]=[1,1,5,7]; \\==================================================================== \\ 6 orbits of contiguous forms to P_7^21; V7[21]--[6]: v=W21=[1,1,5,7,14,31]; v[6]=[12,3,3,6,6,3,9, 12,3,3,6,6,9, 12,6,6,6,9, 12,6,6,9, 12,6,9, 12,9, 18]/2; V7[21]=v; \\==================================================================== \\ 20 orbits of contiguous forms to P_7^22; V7[22]--[16,20]: v=W22=[1,1,1,1,1,1,1,3,4,7,7,7,8,14,16,22,25,27,29,31]; v[16]=[4,2,2,1,1,1,0, 4,1,2,2,0,2, 4,2,-1,2,0, 4,1,0,2, 4,0,2, 4,-1, 4]; v[17]=[12,6,6,2,2,4,0, 12,2,6,6,-2,6, 12,4,-4,6,-2, 12,4,-2,6, 12,-2,6, 12,-6, 12]/3; v[18]=[4,1,2,0,0,2,-1, 4,0,2,2,-1,2, 4,1,-2,2,-1, 4,1,-1,2, 4,-1,2, 4,-2, 4]; v[19]=[4,2,2,1,1,2,0, 4,1,2,2,1,2, 4,2,-1,2,0, 4,1,1,2, 4,1,2, 4,0, 4]; v[20]=[4,2,2,0,1,2,0, 4,1,2,2,0,2, 4,1,-1,2,0, 4,1,-1,2, 4,0,2, 4,-1, 4]; V7[22]=v; \\==================================================================== \\ 7 orbits of contiguous forms to P_7^23; V7[23] empty V7[23]=W23=[1,1,5,7,7,10,11]; \\==================================================================== \\ 16 orbits of contiguous forms to P_7^24; V7[24]--[15,16]: v=V7[24]=[1,1,1,1,1,5,5,7,7,7,8,10,11,18,28,30]; v[15]=[12,6,3,6,3,0,3, 12,-3,3,6,6,-3, 12,6,3,-3,6, 12,6,0,0, 12,0,0,12,-6, 12]/2; v[16]=[12,3,3,6,0,0,3, 12,-6,0,6,6,-3, 12,6,0,-3,6, 12,3,0,0, 12,0,0, 12,-6, 12]/2; V7[24]=v; \\==================================================================== \\ 14 orbits of contiguous forms to P_7^25; V7[25]--[13,14]: v=W25=[1,1,1,1,1,7,7,7,14,16,18,22,27,28]; v[13]=[12,6,3,3,6,6,9, 12,3,6,3,6,9, 12,0,0,3,9, 12,6,9,0, 12,9,0, 18,0, 18]/2; v[14]=[12,6,3,3,6,3,9, 12,3,6,3,3,9, 12,0,0,0,9, 12,6,6,0, 12,6,0, 12,-3, 18]/2; V7[25]=v; \\==================================================================== \\ 6 orbits of contiguous forms to P_7^26; V7[26]--[6]: v=W26=[1,1,1,3,4,29]; v[6]=[4,1,2,2,2,2,2, 4,2,2,2,2,1, 4,1,1,2,2, 4,1,2,2, 4,2,1, 4,2, 4]; V7[26]=v; \\==================================================================== \\ 10 orbits of contiguous forms to P_7^27; V7[27]--[9,10]: v=W27=[1,1,1,4,7,16,22,25,28,32]; v[9]=[6,2,3,4,4,3,5, 4,2,3,3,2,4, 4,2,3,2,4, 6,4,3,5, 6,2,5, 4,4, 8]; v[10]=[4,1,2,2,2,2,3, 4,2,2,2,2,3, 4,2,2,2,3, 4,2,2,3, 4,1,3, 4,3, 6]; V7[27]=v; \\==================================================================== \\ 16 orbits of contiguous forms to P_7^28; V7[28]--[15,16]: v=W28=[1,1,1,1,1,7,7,7,7,8,10,24,25,27,28,29]; v[15]=[4,0,2,2,2,1,4, 4,0,2,1,2,4, 4,1,2,2,4, 4,1,2,5, 4,1,4, 4,5, 12]; v[16]=[4,0,2,2,2,0,4, 4,0,2,1,2,4, 4,1,2,1,4, 4,1,2,5, 4,0,4, 4,4, 12]; V7[28]=v; \\==================================================================== \\ 14 orbits of contiguous forms to P_7^29; V7[29]--[13,14]: v=W29=[1,1,1,1,1,1,3,4,8,22,26,28,31,32]; v[13]=[4,1,1,2,2,2,2, 4,2,2,2,1,2, 4,2,2,2,2, 4,1,2,2, 4,2,2, 4,1, 4]; v[14]=[4,2,1,2,2,2,2, 4,2,2,2,2,2, 4,2,2,2,2, 4,1,2,2, 4,2,2, 4,1, 4]; V7[29]=v; \\==================================================================== \\ 4 orbits of contiguous forms to P_7^30; V7[30] empty V7[30]=W30=[1,1,10,24]; \\==================================================================== \\ 10 orbits of contiguous forms to P_7^31; V7[31]--[10]: v=W31=[1,1,1,1,4,7,21,22,29,31]; v[10]=[4,1,2,2,2,2,3, 4,1,2,2,2,3, 4,1,2,1,3, 4,1,2,3, 4,2,3, 4,3, 6]; V7[31]=v; \\==================================================================== \\ 4 orbits of contiguous forms to P_7^32; V7[32] empty V7[32]=W32=[1,4,27,29];; \\==================================================================== \\ 1 orbit of contiguous forms to P_7^33; V7[33] empty V7[33]=W33=[4]; \\V7[33]=[[4,2,2,2,2,2,2, 2,1,1,1,1,1, 2,1,1,1,1, 2,1,1,1, 2,1,1, 2,1, 2]]; \\==================================================================== \\ Kissing Numbers of the P_7^k: kn7= [63,28,36,42,36,32,34,32,28,32, 30,28,28,29,28,30,28,28,28,28,\ 28,30,28,28,28,30,30,30,29,28, 28,28,28]; \\ Number of orbits of contiguous forms to the P_7^k: voro7=[11,1,6,4,10,6,18,10,1,8,9,1,3,7,1,3,6,4,1,2,2,7,2,5,5,3,3,5,6,2,4,1,0;\ 1,0,0,0, 0,0, 0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 6,0,3,1, 0,3, 3, 2,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0;\ 4,0,1,1, 0,0, 0, 1,1,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,1,0,1,1,1;\ 10,0,0,0, 6,1, 7, 2,0,2,4,0,1,3,0,1,1,2,1,1,1,0,1,2,0,0,0,0,0,0,0,0,0;\ 6,0,3,0, 1,2, 2, 1,1,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 18,0,3,0, 7,2,23, 2,0,4,5,0,0,5,1,2,2,1,0,1,1,3,2,3,3,0,1,4,0,0,1,0,0;\ 10,0,2,1, 2,1, 2, 1,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0,0;\ 1,0,1,1, 0,1, 0, 1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 8,0,0,0, 2,0, 4, 1,0,2,2,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,1,0,0,0;\ 9,0,0,0, 4,0, 5, 0,0,2,4,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0;\ 1,0,0,1, 0,0, 0, 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 3,0,0,0, 1,0, 0, 0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 7,0,0,0, 3,1, 5, 0,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0;\ 1,0,0,0, 0,0, 1, 0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 3,0,0,0, 1,1, 2, 0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0;\ 6,0,1,0, 1,1, 2, 1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 4,0,0,0, 2,0, 1, 0,0,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0;\ 1,0,0,1, 1,0, 0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 2,0,0,0, 1,0, 1, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 2,0,0,0, 1,0, 1, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0;\ 7,0,1,1, 0,0, 3, 1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0;\ 2,0,0,0, 1,0, 2, 0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;\ 5,0,0,0, 2,0, 3, 1,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0;\ 5,0,0,0, 0,0, 3, 0,0,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0;\ 3,0,1,1, 0,0, 0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0;\ 3,0,0,1, 0,0, 1, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0;\ 5,0,0,0, 0,0, 4, 1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,1,0,0,0,0;\ 6,0,1,1, 0,0, 0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,1,1,0;\ 2,0,0,0, 0,0, 0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0;\ 4,0,0,1, 0,0, 1, 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,0,0;\ 1,0,0,1, 0,0, 0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0;\ 0,0,0,1, 0,0, 0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; \\ or7[k] = number of facets orbits of P_7^k : or7=[157,1,23,17,46,19,94,27, 6,24, 31,3,6,24,4,12,14,13,4,4,\ 6,20,7,16,14,6,10,16,14,4, 10,4,1]; \\ ro7 gives the number of orbits from P_7^k to a P_7^h with hor7[k]), print(" The second integer (",l, ") must be in ",[ro7[k]+1,or7[k]]); [],v2m(V7[k][l]));} \\ Number of the perfect form in the l-th orbit of P_7^k : h=prft(k,l) ; \\ h=Wk[l] = number of orbits for P_7^k=lg(Wk) {prft(k,l,h,s)=; s=0;h=0;while(s= k " \\(symmetry between the paths Ph--Pk and Pk--Ph ); \\ cntg2(h,l) accepts any l (but yields for P_7^h another isometry class \\ when h=prft(k,l) < k ): {cntg2(k,l)=h=prft(k,l); if(h>=k,v2m(V7[k][l]), l=exchange(k,l)[2];p=v2m(V7[h][l]);q=v2m(P7[k]); c=content(p);u=Isom(q,p/c); p=v2m(P7[h]); u~*p*u/c);} \\ \\============================================================== \\ END OF FILE \\==============================================================