#### Green Polynomials for C5 #### W-rep key: # x[1] = [[], [1, 1, 1, 1, 1]] , orbit = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] , A-rep = [] # x[2] = [[1, 1, 1, 1, 1], []] , orbit = [2, 1, 1, 1, 1, 1, 1, 1, 1] , A-rep = [] # x[3] = [[1], [1, 1, 1, 1]] , orbit = [2, 2, 1, 1, 1, 1, 1, 1] , A-rep = [1] # x[4] = [[], [2, 1, 1, 1]] , orbit = [2, 2, 1, 1, 1, 1, 1, 1] , A-rep = [-1] # x[5] = [[1, 1, 1, 1], [1]] , orbit = [2, 2, 2, 1, 1, 1, 1] , A-rep = [] # x[6] = [[1, 1], [1, 1, 1]] , orbit = [2, 2, 2, 2, 1, 1] , A-rep = [1] # x[7] = [[], [2, 2, 1]] , orbit = [2, 2, 2, 2, 1, 1] , A-rep = [-1] # x[8] = [[1, 1, 1], [1, 1]] , orbit = [2, 2, 2, 2, 2] , A-rep = [] # x[9] = [[1], [2, 1, 1]] , orbit = [3, 3, 1, 1, 1, 1] , A-rep = [] # x[10] = [[1, 1, 1], [2]] , orbit = [3, 3, 2, 1, 1] , A-rep = [] # x[11] = [[1, 1], [2, 1]] , orbit = [3, 3, 2, 2] , A-rep = [1] # x[12] = [[1], [2, 2]] , orbit = [3, 3, 2, 2] , A-rep = [-1] # x[13] = [[2, 1, 1, 1], []] , orbit = [4, 1, 1, 1, 1, 1, 1] , A-rep = [] # x[14] = [[2], [1, 1, 1]] , orbit = [4, 2, 1, 1, 1, 1] , A-rep = [1] # x[15] = [[], [3, 1, 1]] , orbit = [4, 2, 1, 1, 1, 1] , A-rep = [-1] # x[16] = [[2, 1, 1], [1]] , orbit = [4, 2, 2, 1, 1] , A-rep = [1] # x[17] = [[2, 2, 1], []] , orbit = [4, 2, 2, 1, 1] , A-rep = [-1] # x[18] = [[2, 1], [1, 1]] , orbit = [4, 2, 2, 2] , A-rep = [1] # x[19] = [[], [3, 2]] , orbit = [4, 2, 2, 2] , A-rep = [-1] # x[20] = [[2, 2], [1]] , orbit = [4, 3, 3] , A-rep = [] # x[21] = [[2], [2, 1]] , orbit = [4, 4, 1, 1] , A-rep = [1] # x[22] = [[1], [3, 1]] , orbit = [4, 4, 1, 1] , A-rep = [-1] # x[23] = [[2, 1], [2]] , orbit = [4, 4, 2] , A-rep = [1] # x[24] = [[1, 1], [3]] , orbit = [4, 4, 2] , A-rep = [-1] # x[25] = [[2], [3]] , orbit = [5, 5] , A-rep = [] # x[26] = [[3, 1, 1], []] , orbit = [6, 1, 1, 1, 1] , A-rep = [] # x[27] = [[3], [1, 1]] , orbit = [6, 2, 1, 1] , A-rep = [1] # x[28] = [[], [4, 1]] , orbit = [6, 2, 1, 1] , A-rep = [-1] # x[29] = [[3, 1], [1]] , orbit = [6, 2, 2] , A-rep = [1] # x[30] = [[3, 2], []] , orbit = [6, 2, 2] , A-rep = [-1] # x[31] = [[3], [2]] , orbit = [6, 4] , A-rep = [1] # x[32] = [[1], [4]] , orbit = [6, 4] , A-rep = [-1] # x[33] = [[4, 1], []] , orbit = [8, 1, 1] , A-rep = [] # x[34] = [[4], [1]] , orbit = [8, 2] , A-rep = [1] # x[35] = [[], [5]] , orbit = [8, 2] , A-rep = [-1] # x[36] = [[5], []] , orbit = [10] , A-rep = [] ### Green Polynomials by Orbit orbit #1 : [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] dim = 0 A(O) = 1 , |A(O)_0| = 1 g_s = 55*V[0] Z_G(x)_0 = C5 # Green Polys by orbit reps #1.1 : x[1] : [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],[] : [[5], []] Qxi[C5,1,1] = (x[1])*q^25 + (x[3])*q^24 + (x[4]+x[6])*q^23 + (x[3]+x[8]+x[9])*q^22 + (x[4]+x[5]+x[6]+x[7]+x[11]+x[14])*q^21 + (x[2]+x[3]+x[8]+2*x[9]+x[10]+x[12]+x[18])*q^20 + (x[4]+x[5]+2*x[6]+x[7]+2*x[11]+x[14]+x[15]+x[16]+x[21])*q^19 + (x[3]+2*x[8]+3*x[9]+x[10]+x[12]+x[13]+2*x[18]+x[22]+x[23])*q^18 + (x[4]+x[5]+2*x[6]+x[7]+3*x[11]+2*x[14]+x[15]+2*x[16]+x[19]+x[20]+2*x[21]+x[24])*q^17 + (x[3]+2*x[8]+3*x[9]+2*x[10]+2*x[12]+x[13]+x[17]+3*x[18]+2*x[22]+2*x[23]+x[27])*q^16 + (x[5]+2*x[6]+x[7]+4*x[11]+2*x[14]+2*x[15]+3*x[16]+x[19]+x[20]+3*x[21]+x[24]+x[25]+x[29])*q^15 + (2*x[8]+3*x[9]+2*x[10]+2*x[12]+x[13]+x[17]+4*x[18]+3*x[22]+3*x[23]+x[26]+x[27]+x[31])*q^14 + (x[5]+x[6]+x[7]+4*x[11]+2*x[14]+x[15]+3*x[16]+x[19]+2*x[20]+4*x[21]+2*x[24]+x[25]+x[28]+2*x[29])*q^13 + (x[8]+2*x[9]+2*x[10]+2*x[12]+x[13]+x[17]+4*x[18]+3*x[22]+4*x[23]+x[26]+2*x[27]+x[30]+x[31]+x[32])*q^12 + (x[6]+3*x[11]+x[14]+x[15]+3*x[16]+x[19]+2*x[20]+4*x[21]+2*x[24]+2*x[25]+x[28]+3*x[29])*q^11 + (x[8]+x[9]+x[10]+x[12]+x[17]+3*x[18]+3*x[22]+4*x[23]+2*x[26]+2*x[27]+x[30]+2*x[31]+x[32])*q^10 + (2*x[11]+x[14]+2*x[16]+x[19]+2*x[20]+3*x[21]+2*x[24]+2*x[25]+x[28]+3*x[29]+x[34])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+2*x[22]+3*x[23]+x[26]+2*x[27]+x[30]+2*x[31]+x[32]+x[33])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+2*x[25]+x[28]+3*x[29]+x[34])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31]+x[32]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34]+x[35])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #1.1 : c = () |O_x_c^F| = 1 Qxc[C5,1,1] = (x[1])*q^25 + (x[3])*q^24 + (x[4]+x[6])*q^23 + (x[3]+x[8]+x[9])*q^22 + (x[4]+x[5]+x[6]+x[7]+x[11]+x[14])*q^21 + (x[2]+x[3]+x[8]+2*x[9]+x[10]+x[12]+x[18])*q^20 + (x[4]+x[5]+2*x[6]+x[7]+2*x[11]+x[14]+x[15]+x[16]+x[21])*q^19 + (x[3]+2*x[8]+3*x[9]+x[10]+x[12]+x[13]+2*x[18]+x[22]+x[23])*q^18 + (x[4]+x[5]+2*x[6]+x[7]+3*x[11]+2*x[14]+x[15]+2*x[16]+x[19]+x[20]+2*x[21]+x[24])*q^17 + (x[3]+2*x[8]+3*x[9]+2*x[10]+2*x[12]+x[13]+x[17]+3*x[18]+2*x[22]+2*x[23]+x[27])*q^16 + (x[5]+2*x[6]+x[7]+4*x[11]+2*x[14]+2*x[15]+3*x[16]+x[19]+x[20]+3*x[21]+x[24]+x[25]+x[29])*q^15 + (2*x[8]+3*x[9]+2*x[10]+2*x[12]+x[13]+x[17]+4*x[18]+3*x[22]+3*x[23]+x[26]+x[27]+x[31])*q^14 + (x[5]+x[6]+x[7]+4*x[11]+2*x[14]+x[15]+3*x[16]+x[19]+2*x[20]+4*x[21]+2*x[24]+x[25]+x[28]+2*x[29])*q^13 + (x[8]+2*x[9]+2*x[10]+2*x[12]+x[13]+x[17]+4*x[18]+3*x[22]+4*x[23]+x[26]+2*x[27]+x[30]+x[31]+x[32])*q^12 + (x[6]+3*x[11]+x[14]+x[15]+3*x[16]+x[19]+2*x[20]+4*x[21]+2*x[24]+2*x[25]+x[28]+3*x[29])*q^11 + (x[8]+x[9]+x[10]+x[12]+x[17]+3*x[18]+3*x[22]+4*x[23]+2*x[26]+2*x[27]+x[30]+2*x[31]+x[32])*q^10 + (2*x[11]+x[14]+2*x[16]+x[19]+2*x[20]+3*x[21]+2*x[24]+2*x[25]+x[28]+3*x[29]+x[34])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+2*x[22]+3*x[23]+x[26]+2*x[27]+x[30]+2*x[31]+x[32]+x[33])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+2*x[25]+x[28]+3*x[29]+x[34])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31]+x[32]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34]+x[35])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #2 : [2, 1, 1, 1, 1, 1, 1, 1, 1] dim = 10 A(O) = 1 , |A(O)_0| = 1 g_s = 8*V[1]+V[2]+36*V[0] Z_G(x)_0 = O1+Sp8 # Green Polys by orbit reps #2.1 : x[2] : [2, 1, 1, 1, 1, 1, 1, 1, 1],[] : [[1, 1, 1, 1, 1], []] Qxi[C5,2,1] = (x[2])*q^20 + (x[5])*q^19 + (x[8]+x[13])*q^18 + (x[5]+x[6]+x[16])*q^17 + (x[3]+x[8]+x[10]+x[13]+x[17]+x[18])*q^16 + (x[5]+x[6]+x[11]+x[14]+2*x[16]+x[20])*q^15 + (2*x[8]+x[9]+x[10]+x[13]+x[17]+2*x[18]+x[23]+x[26])*q^14 + (x[5]+x[6]+2*x[11]+x[14]+3*x[16]+x[20]+x[21]+x[29])*q^13 + (x[8]+x[9]+2*x[10]+x[12]+x[13]+x[17]+3*x[18]+2*x[23]+x[26]+x[27]+x[30])*q^12 + (x[6]+2*x[11]+x[14]+3*x[16]+2*x[20]+2*x[21]+x[24]+2*x[29])*q^11 + (x[8]+x[9]+x[10]+x[17]+3*x[18]+x[22]+3*x[23]+2*x[26]+x[27]+x[30]+x[31])*q^10 + (2*x[11]+x[14]+2*x[16]+2*x[20]+2*x[21]+x[24]+x[25]+3*x[29])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+x[22]+3*x[23]+x[26]+2*x[27]+x[30]+x[31]+x[33])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+x[25]+3*x[29]+x[34])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #2.1 : c = () |O_x_c^F| = q^10-1 Qxc[C5,2,1] = (x[2])*q^20 + (x[5])*q^19 + (x[8]+x[13])*q^18 + (x[5]+x[6]+x[16])*q^17 + (x[3]+x[8]+x[10]+x[13]+x[17]+x[18])*q^16 + (x[5]+x[6]+x[11]+x[14]+2*x[16]+x[20])*q^15 + (2*x[8]+x[9]+x[10]+x[13]+x[17]+2*x[18]+x[23]+x[26])*q^14 + (x[5]+x[6]+2*x[11]+x[14]+3*x[16]+x[20]+x[21]+x[29])*q^13 + (x[8]+x[9]+2*x[10]+x[12]+x[13]+x[17]+3*x[18]+2*x[23]+x[26]+x[27]+x[30])*q^12 + (x[6]+2*x[11]+x[14]+3*x[16]+2*x[20]+2*x[21]+x[24]+2*x[29])*q^11 + (x[8]+x[9]+x[10]+x[17]+3*x[18]+x[22]+3*x[23]+2*x[26]+x[27]+x[30]+x[31])*q^10 + (2*x[11]+x[14]+2*x[16]+2*x[20]+2*x[21]+x[24]+x[25]+3*x[29])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+x[22]+3*x[23]+x[26]+2*x[27]+x[30]+x[31]+x[33])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+x[25]+3*x[29]+x[34])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #3 : [2, 2, 1, 1, 1, 1, 1, 1] dim = 18 A(O) = Z2 , |A(O)_0| = 2 g_s = 12*V[1]+3*V[2]+22*V[0] Z_G(x)_0 = Sp6+O2 # Green Polys by orbit reps #3.1 : x[3] : [2, 2, 1, 1, 1, 1, 1, 1],[1] : [[1], [1, 1, 1, 1]] Qxi[C5,3,1] = (x[3])*q^16 + (x[6]+x[14])*q^15 + (x[8]+x[9]+x[18])*q^14 + (x[5]+x[6]+x[11]+x[14]+x[16]+x[21])*q^13 + (x[8]+x[9]+x[10]+x[12]+x[13]+2*x[18]+x[23]+x[27])*q^12 + (x[6]+2*x[11]+x[14]+2*x[16]+x[20]+2*x[21]+x[29])*q^11 + (x[8]+x[9]+x[10]+x[17]+3*x[18]+x[22]+2*x[23]+x[26]+x[27]+x[31])*q^10 + (2*x[11]+x[14]+2*x[16]+2*x[20]+2*x[21]+x[24]+x[25]+2*x[29])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+x[22]+3*x[23]+x[26]+2*x[27]+x[30]+x[31])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+x[25]+3*x[29]+x[34])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #3.2 : x[4] : [2, 2, 1, 1, 1, 1, 1, 1],[-1] : [[], [2, 1, 1, 1]] Qxi[C5,3,2] = (x[4])*q^16 + (x[9])*q^15 + (x[7]+x[11]+x[15])*q^14 + (x[9]+x[10]+x[12]+x[22])*q^13 + (x[7]+x[11]+x[15]+x[19]+x[21]+x[24])*q^12 + (x[9]+x[12]+2*x[22]+x[23])*q^11 + (x[11]+x[15]+x[19]+x[21]+x[24]+x[25]+x[28])*q^10 + (x[12]+2*x[22]+x[23]+x[32])*q^9 + (x[19]+x[21]+x[24]+x[25]+x[28])*q^8 + (x[22]+x[31]+x[32])*q^7 + (x[25]+x[28])*q^6 + (x[32])*q^5 + (x[35])*q^4 # Green Polys by conj class in A(O) #3.1 : c = () |O_x_c^F| = 1/2*q*(q+1)*(q^2+1)*(q^4+1)*(q^10-1) Qxc[C5,3,1] = (x[3]+x[4])*q^16 + (x[6]+x[9]+x[14])*q^15 + (x[7]+x[8]+x[9]+x[11]+x[15]+x[18])*q^14 + (x[5]+x[6]+x[9]+x[10]+x[11]+x[12]+x[14]+x[16]+x[21]+x[22])*q^13 + (x[7]+x[8]+x[9]+x[10]+x[11]+x[12]+x[13]+x[15]+2*x[18]+x[19]+x[21]+x[23]+x[24]+x[27])*q^12 + (x[6]+x[9]+2*x[11]+x[12]+x[14]+2*x[16]+x[20]+2*x[21]+2*x[22]+x[23]+x[29])*q^11 + (x[8]+x[9]+x[10]+x[11]+x[15]+x[17]+3*x[18]+x[19]+x[21]+x[22]+2*x[23]+x[24]+x[25]+x[26]+x[27]+x[28]+x[31])*q^10 + (2*x[11]+x[12]+x[14]+2*x[16]+2*x[20]+2*x[21]+2*x[22]+x[23]+x[24]+x[25]+2*x[29]+x[32])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+x[19]+x[21]+x[22]+3*x[23]+x[24]+x[25]+x[26]+2*x[27]+x[28]+x[30]+x[31])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[22]+x[24]+x[25]+3*x[29]+x[31]+x[32]+x[34])*q^7 + (x[18]+x[22]+2*x[23]+x[25]+x[26]+x[27]+x[28]+x[30]+2*x[31]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[32]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33]+x[35])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #3.2 : c = (1) |O_x_c^F| = 1/2*q*(q-1)*(q^2+1)*(q^4+1)*(q^10-1) Qxc[C5,3,2] = (x[3]-x[4])*q^16 + (x[6]-x[9]+x[14])*q^15 + (-x[7]+x[8]+x[9]-x[11]-x[15]+x[18])*q^14 + (x[5]+x[6]-x[9]-x[10]+x[11]-x[12]+x[14]+x[16]+x[21]-x[22])*q^13 + (-x[7]+x[8]+x[9]+x[10]-x[11]+x[12]+x[13]-x[15]+2*x[18]-x[19]-x[21]+x[23]-x[24]+x[27])*q^12 + (x[6]-x[9]+2*x[11]-x[12]+x[14]+2*x[16]+x[20]+2*x[21]-2*x[22]-x[23]+x[29])*q^11 + (x[8]+x[9]+x[10]-x[11]-x[15]+x[17]+3*x[18]-x[19]-x[21]+x[22]+2*x[23]-x[24]-x[25]+x[26]+x[27]-x[28]+x[31])*q^10 + (2*x[11]-x[12]+x[14]+2*x[16]+2*x[20]+2*x[21]-2*x[22]-x[23]+x[24]+x[25]+2*x[29]-x[32])*q^9 + (x[10]+x[12]+x[17]+2*x[18]-x[19]-x[21]+x[22]+3*x[23]-x[24]-x[25]+x[26]+2*x[27]-x[28]+x[30]+x[31])*q^8 + (x[11]+x[16]+x[20]+2*x[21]-x[22]+x[24]+x[25]+3*x[29]-x[31]-x[32]+x[34])*q^7 + (x[18]+x[22]+2*x[23]-x[25]+x[26]+x[27]-x[28]+x[30]+2*x[31]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]-x[32]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33]-x[35])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #4 : [2, 2, 2, 1, 1, 1, 1] dim = 24 A(O) = 1 , |A(O)_0| = 1 g_s = 6*V[2]+12*V[1]+13*V[0] Z_G(x)_0 = O3+Sp4 # Green Polys by orbit reps #4.1 : x[5] : [2, 2, 2, 1, 1, 1, 1],[] : [[1, 1, 1, 1], [1]] Qxi[C5,4,1] = (x[5])*q^13 + (x[8]+x[10]+x[13])*q^12 + (x[6]+x[11]+2*x[16])*q^11 + (x[8]+x[9]+x[10]+x[17]+2*x[18]+x[23]+x[26])*q^10 + (2*x[11]+x[14]+2*x[16]+2*x[20]+x[21]+x[24]+x[29])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+x[22]+3*x[23]+x[26]+x[27]+x[30])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+x[25]+3*x[29])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #4.1 : c = () |O_x_c^F| = q^2*(q^2-q+1)*(q^2+q+1)*(q^8-1)*(q^10-1) Qxc[C5,4,1] = (x[5])*q^13 + (x[8]+x[10]+x[13])*q^12 + (x[6]+x[11]+2*x[16])*q^11 + (x[8]+x[9]+x[10]+x[17]+2*x[18]+x[23]+x[26])*q^10 + (2*x[11]+x[14]+2*x[16]+2*x[20]+x[21]+x[24]+x[29])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+x[22]+3*x[23]+x[26]+x[27]+x[30])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+x[25]+3*x[29])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31]+x[33])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #5 : [2, 2, 2, 2, 1, 1] dim = 28 A(O) = Z2 , |A(O)_0| = 2 g_s = 10*V[2]+8*V[1]+9*V[0] Z_G(x)_0 = Sp2+O4 # Green Polys by orbit reps #5.1 : x[6] : [2, 2, 2, 2, 1, 1],[1] : [[1, 1], [1, 1, 1]] Qxi[C5,5,1] = (x[6])*q^11 + (x[8]+x[9]+x[18])*q^10 + (2*x[11]+x[14]+x[16]+x[20]+x[21])*q^9 + (x[10]+x[12]+x[17]+2*x[18]+x[22]+2*x[23]+x[27])*q^8 + (x[11]+x[16]+x[20]+2*x[21]+x[24]+x[25]+2*x[29])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[27]+x[30]+2*x[31])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #5.2 : x[7] : [2, 2, 2, 2, 1, 1],[-1] : [[], [2, 2, 1]] Qxi[C5,5,2] = (x[7])*q^11 + (x[9]+x[12])*q^10 + (x[11]+x[15]+x[19]+x[21])*q^9 + (x[12]+2*x[22]+x[23])*q^8 + (x[19]+x[21]+x[24]+x[25]+x[28])*q^7 + (x[22]+x[31]+x[32])*q^6 + (x[25]+x[28])*q^5 + (x[32])*q^4 + (x[35])*q^3 # Green Polys by conj class in A(O) #5.1 : c = () |O_x_c^F| = 1/2*q^4*(q^2-q+1)*(q^2+q+1)*(q^2+1)*(q^8-1)*(q^10-1) Qxc[C5,5,1] = (x[6]+x[7])*q^11 + (x[8]+2*x[9]+x[12]+x[18])*q^10 + (3*x[11]+x[14]+x[15]+x[16]+x[19]+x[20]+2*x[21])*q^9 + (x[10]+2*x[12]+x[17]+2*x[18]+3*x[22]+3*x[23]+x[27])*q^8 + (x[11]+x[16]+x[19]+x[20]+3*x[21]+2*x[24]+2*x[25]+x[28]+2*x[29])*q^7 + (x[18]+2*x[22]+2*x[23]+x[26]+x[27]+x[30]+3*x[31]+x[32])*q^6 + (x[20]+x[21]+x[24]+2*x[25]+x[28]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+2*x[32]+x[33])*q^4 + (x[25]+x[29]+x[34]+x[35])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #5.2 : c = (1) |O_x_c^F| = 1/2*q^4*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,5,2] = (x[6]-x[7])*q^11 + (x[8]-x[12]+x[18])*q^10 + (x[11]+x[14]-x[15]+x[16]-x[19]+x[20])*q^9 + (x[10]+x[17]+2*x[18]-x[22]+x[23]+x[27])*q^8 + (x[11]+x[16]-x[19]+x[20]+x[21]-x[28]+2*x[29])*q^7 + (x[18]+2*x[23]+x[26]+x[27]+x[30]+x[31]-x[32])*q^6 + (x[20]+x[21]+x[24]-x[28]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[33])*q^4 + (x[25]+x[29]+x[34]-x[35])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #6 : [2, 2, 2, 2, 2] dim = 30 A(O) = 1 , |A(O)_0| = 1 g_s = 15*V[2]+10*V[0] Z_G(x)_0 = O5 # Green Polys by orbit reps #6.1 : x[8] : [2, 2, 2, 2, 2],[] : [[1, 1, 1], [1, 1]] Qxi[C5,6,1] = (x[8])*q^10 + (x[11]+x[16])*q^9 + (x[10]+x[12]+x[17]+x[18]+x[23])*q^8 + (x[11]+x[16]+x[20]+x[21]+x[24]+x[29])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[30]+x[31])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #6.1 : c = () |O_x_c^F| = q^6*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,6,1] = (x[8])*q^10 + (x[11]+x[16])*q^9 + (x[10]+x[12]+x[17]+x[18]+x[23])*q^8 + (x[11]+x[16]+x[20]+x[21]+x[24]+x[29])*q^7 + (x[18]+x[22]+2*x[23]+x[26]+x[30]+x[31])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #7 : [3, 3, 1, 1, 1, 1] dim = 30 A(O) = 1 , |A(O)_0| = 1 g_s = 3*V[4]+9*V[2]+13*V[0] Z_G(x)_0 = Sp4+Sp2 # Green Polys by orbit reps #7.1 : x[9] : [3, 3, 1, 1, 1, 1],[] : [[1], [2, 1, 1]] Qxi[C5,7,1] = (x[9])*q^10 + (x[11]+x[14]+x[15]+x[21])*q^9 + (x[10]+x[12]+x[18]+2*x[22]+x[23]+x[27])*q^8 + (x[11]+x[16]+x[19]+2*x[21]+2*x[24]+x[25]+x[28]+x[29])*q^7 + (x[18]+2*x[22]+2*x[23]+x[26]+x[27]+2*x[31]+x[32])*q^6 + (x[20]+x[21]+x[24]+2*x[25]+x[28]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+2*x[32]+x[33])*q^4 + (x[25]+x[29]+x[34]+x[35])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #7.1 : c = () |O_x_c^F| = q^8*(q^2+q+1)*(q^2-q+1)*(q^8-1)*(q^10-1) Qxc[C5,7,1] = (x[9])*q^10 + (x[11]+x[14]+x[15]+x[21])*q^9 + (x[10]+x[12]+x[18]+2*x[22]+x[23]+x[27])*q^8 + (x[11]+x[16]+x[19]+2*x[21]+2*x[24]+x[25]+x[28]+x[29])*q^7 + (x[18]+2*x[22]+2*x[23]+x[26]+x[27]+2*x[31]+x[32])*q^6 + (x[20]+x[21]+x[24]+2*x[25]+x[28]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+2*x[32]+x[33])*q^4 + (x[25]+x[29]+x[34]+x[35])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #8 : [3, 3, 2, 1, 1] dim = 34 A(O) = 1 , |A(O)_0| = 1 g_s = 3*V[4]+2*V[3]+6*V[2]+4*V[1]+6*V[0] Z_G(x)_0 = O1+2*Sp2 # Green Polys by orbit reps #8.1 : x[10] : [3, 3, 2, 1, 1],[] : [[1, 1, 1], [2]] Qxi[C5,8,1] = (x[10])*q^8 + (x[11]+x[16]+x[24])*q^7 + (x[18]+x[22]+2*x[23]+x[26])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #8.1 : c = () |O_x_c^F| = q^8*(q^2+1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,8,1] = (x[10])*q^8 + (x[11]+x[16]+x[24])*q^7 + (x[18]+x[22]+2*x[23]+x[26])*q^6 + (x[20]+x[21]+x[24]+x[25]+2*x[29])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #9 : [3, 3, 2, 2] dim = 36 A(O) = Z2 , |A(O)_0| = 2 g_s = 3*V[4]+4*V[3]+4*V[2]+4*V[1]+4*V[0] Z_G(x)_0 = Sp2+O2 # Green Polys by orbit reps #9.1 : x[11] : [3, 3, 2, 2],[1] : [[1, 1], [2, 1]] Qxi[C5,9,1] = (x[11])*q^7 + (x[18]+x[22]+x[23])*q^6 + (x[20]+x[21]+x[24]+x[25]+x[29])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #9.2 : x[12] : [3, 3, 2, 2],[-1] : [[1], [2, 2]] Qxi[C5,9,2] = (x[12])*q^7 + (x[19]+x[21])*q^6 + (x[22]+x[31])*q^5 + (x[25]+x[28])*q^4 + (x[32])*q^3 + (x[35])*q^2 # Green Polys by conj class in A(O) #9.1 : c = () |O_x_c^F| = 1/2*q^9*(q+1)*(q^2+1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,9,1] = (x[11]+x[12])*q^7 + (x[18]+x[19]+x[21]+x[22]+x[23])*q^6 + (x[20]+x[21]+x[22]+x[24]+x[25]+x[29]+x[31])*q^5 + (x[23]+x[25]+x[27]+x[28]+x[30]+x[31]+x[32])*q^4 + (x[25]+x[29]+x[32]+x[34])*q^3 + (x[31]+x[33]+x[35])*q^2 + (x[34])*q + x[36] #9.2 : c = (1) |O_x_c^F| = 1/2*q^9*(q-1)*(q^2+1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,9,2] = (x[11]-x[12])*q^7 + (x[18]-x[19]-x[21]+x[22]+x[23])*q^6 + (x[20]+x[21]-x[22]+x[24]+x[25]+x[29]-x[31])*q^5 + (x[23]-x[25]+x[27]-x[28]+x[30]+x[31]+x[32])*q^4 + (x[25]+x[29]-x[32]+x[34])*q^3 + (x[31]+x[33]-x[35])*q^2 + (x[34])*q + x[36] orbit #10 : [4, 1, 1, 1, 1, 1, 1] dim = 26 A(O) = 1 , |A(O)_0| = 1 g_s = V[6]+6*V[3]+V[2]+21*V[0] Z_G(x)_0 = O1+Sp6 # Green Polys by orbit reps #10.1 : x[13] : [4, 1, 1, 1, 1, 1, 1],[] : [[2, 1, 1, 1], []] Qxi[C5,10,1] = (x[13])*q^12 + (x[16])*q^11 + (x[17]+x[18]+x[26])*q^10 + (x[14]+x[16]+x[20]+x[29])*q^9 + (x[17]+x[18]+x[23]+x[26]+x[27]+x[30])*q^8 + (x[16]+x[20]+x[21]+2*x[29])*q^7 + (x[18]+x[23]+x[26]+x[27]+x[30]+x[31]+x[33])*q^6 + (x[20]+x[21]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #10.1 : c = () |O_x_c^F| = q^8*(q^8-1)*(q^10-1) Qxc[C5,10,1] = (x[13])*q^12 + (x[16])*q^11 + (x[17]+x[18]+x[26])*q^10 + (x[14]+x[16]+x[20]+x[29])*q^9 + (x[17]+x[18]+x[23]+x[26]+x[27]+x[30])*q^8 + (x[16]+x[20]+x[21]+2*x[29])*q^7 + (x[18]+x[23]+x[26]+x[27]+x[30]+x[31]+x[33])*q^6 + (x[20]+x[21]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #11 : [4, 2, 1, 1, 1, 1] dim = 32 A(O) = Z2 , |A(O)_0| = 2 g_s = V[6]+V[4]+4*V[3]+3*V[2]+4*V[1]+10*V[0] Z_G(x)_0 = Sp4+2*O1 # Green Polys by orbit reps #11.1 : x[14] : [4, 2, 1, 1, 1, 1],[1] : [[2], [1, 1, 1]] Qxi[C5,11,1] = (x[14])*q^9 + (x[18]+x[27])*q^8 + (x[16]+x[21]+x[29])*q^7 + (x[18]+x[23]+x[26]+x[27]+x[31])*q^6 + (x[20]+x[21]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #11.2 : x[15] : [4, 2, 1, 1, 1, 1],[-1] : [[], [3, 1, 1]] Qxi[C5,11,2] = (x[15])*q^9 + (x[22])*q^8 + (x[19]+x[24]+x[28])*q^7 + (x[22]+x[32])*q^6 + (x[25]+x[28])*q^5 + (x[32])*q^4 + (x[35])*q^3 # Green Polys by conj class in A(O) #11.1 : c = () |O_x_c^F| = 1/2*q^8*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,11,1] = (x[14]+x[15])*q^9 + (x[18]+x[22]+x[27])*q^8 + (x[16]+x[19]+x[21]+x[24]+x[28]+x[29])*q^7 + (x[18]+x[22]+x[23]+x[26]+x[27]+x[31]+x[32])*q^6 + (x[20]+x[21]+x[25]+x[28]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[32]+x[33])*q^4 + (x[25]+x[29]+x[34]+x[35])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #11.2 : c = (1) |O_x_c^F| = 1/2*q^8*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,11,2] = (x[14]-x[15])*q^9 + (x[18]-x[22]+x[27])*q^8 + (x[16]-x[19]+x[21]-x[24]-x[28]+x[29])*q^7 + (x[18]-x[22]+x[23]+x[26]+x[27]+x[31]-x[32])*q^6 + (x[20]+x[21]-x[25]-x[28]+2*x[29]+x[34])*q^5 + (x[23]+x[27]+x[30]+x[31]-x[32]+x[33])*q^4 + (x[25]+x[29]+x[34]-x[35])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #12 : [4, 2, 2, 1, 1] dim = 36 A(O) = Z2 , |A(O)_0| = 2 g_s = V[6]+2*V[4]+2*V[3]+6*V[2]+4*V[1]+4*V[0] Z_G(x)_0 = O2+Sp2+O1 # Green Polys by orbit reps #12.1 : x[16] : [4, 2, 2, 1, 1],[1] : [[2, 1, 1], [1]] Qxi[C5,12,1] = (x[16])*q^7 + (x[18]+x[23]+x[26])*q^6 + (x[20]+x[21]+2*x[29])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #12.2 : x[17] : [4, 2, 2, 1, 1],[-1] : [[2, 2, 1], []] Qxi[C5,12,2] = (x[17])*q^7 + (x[20])*q^6 + (x[30])*q^5 # Green Polys by conj class in A(O) #12.1 : c = () |O_x_c^F| = 1/2*q^9*(q+1)*(q^2+1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,12,1] = (x[16]+x[17])*q^7 + (x[18]+x[20]+x[23]+x[26])*q^6 + (x[20]+x[21]+2*x[29]+x[30])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #12.2 : c = (1) |O_x_c^F| = 1/2*q^9*(q-1)*(q^2+1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,12,2] = (x[16]-x[17])*q^7 + (x[18]-x[20]+x[23]+x[26])*q^6 + (x[20]+x[21]+2*x[29]-x[30])*q^5 + (x[23]+x[27]+x[30]+x[31]+x[33])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #13 : [4, 2, 2, 2] dim = 38 A(O) = Z2 , |A(O)_0| = 2 g_s = V[6]+3*V[4]+10*V[2]+3*V[0] Z_G(x)_0 = O3+O1 # Green Polys by orbit reps #13.1 : x[18] : [4, 2, 2, 2],[1] : [[2, 1], [1, 1]] Qxi[C5,13,1] = (x[18])*q^6 + (x[20]+x[21]+x[29])*q^5 + (x[23]+x[27]+x[30]+x[31])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #13.2 : x[19] : [4, 2, 2, 2],[-1] : [[], [3, 2]] Qxi[C5,13,2] = (x[19])*q^6 + (x[22])*q^5 + (x[25]+x[28])*q^4 + (x[32])*q^3 + (x[35])*q^2 # Green Polys by conj class in A(O) #13.1 : c = () |O_x_c^F| = 1/2*q^10*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,13,1] = (x[18]+x[19])*q^6 + (x[20]+x[21]+x[22]+x[29])*q^5 + (x[23]+x[25]+x[27]+x[28]+x[30]+x[31])*q^4 + (x[25]+x[29]+x[32]+x[34])*q^3 + (x[31]+x[33]+x[35])*q^2 + (x[34])*q + x[36] #13.2 : c = (1) |O_x_c^F| = 1/2*q^10*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,13,2] = (x[18]-x[19])*q^6 + (x[20]+x[21]-x[22]+x[29])*q^5 + (x[23]-x[25]+x[27]-x[28]+x[30]+x[31])*q^4 + (x[25]+x[29]-x[32]+x[34])*q^3 + (x[31]+x[33]-x[35])*q^2 + (x[34])*q + x[36] orbit #14 : [4, 3, 3] dim = 40 A(O) = 1 , |A(O)_0| = 1 g_s = V[6]+2*V[5]+3*V[4]+2*V[3]+2*V[2]+2*V[1]+3*V[0] Z_G(x)_0 = O1+Sp2 # Green Polys by orbit reps #14.1 : x[20] : [4, 3, 3],[] : [[2, 2], [1]] Qxi[C5,14,1] = (x[20])*q^5 + (x[23]+x[30])*q^4 + (x[25]+x[29])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #14.1 : c = () |O_x_c^F| = q^12*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,14,1] = (x[20])*q^5 + (x[23]+x[30])*q^4 + (x[25]+x[29])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #15 : [4, 4, 1, 1] dim = 40 A(O) = Z2 , |A(O)_0| = 2 g_s = 3*V[6]+V[4]+4*V[3]+3*V[2]+4*V[0] Z_G(x)_0 = Sp2+O2 # Green Polys by orbit reps #15.1 : x[21] : [4, 4, 1, 1],[1] : [[2], [2, 1]] Qxi[C5,15,1] = (x[21])*q^5 + (x[23]+x[27]+x[31])*q^4 + (x[25]+x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #15.2 : x[22] : [4, 4, 1, 1],[-1] : [[1], [3, 1]] Qxi[C5,15,2] = (x[22])*q^5 + (x[24]+x[25]+x[28])*q^4 + (2*x[32])*q^3 + (x[35])*q^2 # Green Polys by conj class in A(O) #15.1 : c = () |O_x_c^F| = 1/2*q^13*(q+1)*(q^2+1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,15,1] = (x[21]+x[22])*q^5 + (x[23]+x[24]+x[25]+x[27]+x[28]+x[31])*q^4 + (x[25]+x[29]+2*x[32]+x[34])*q^3 + (x[31]+x[33]+x[35])*q^2 + (x[34])*q + x[36] #15.2 : c = (1) |O_x_c^F| = 1/2*q^13*(q-1)*(q^2+1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,15,2] = (x[21]-x[22])*q^5 + (x[23]-x[24]-x[25]+x[27]-x[28]+x[31])*q^4 + (x[25]+x[29]-2*x[32]+x[34])*q^3 + (x[31]+x[33]-x[35])*q^2 + (x[34])*q + x[36] orbit #16 : [4, 4, 2] dim = 42 A(O) = Z2 , |A(O)_0| = 2 g_s = 3*V[6]+3*V[4]+6*V[2]+V[0] Z_G(x)_0 = O2+O1 # Green Polys by orbit reps #16.1 : x[23] : [4, 4, 2],[1] : [[2, 1], [2]] Qxi[C5,16,1] = (x[23])*q^4 + (x[25]+x[29])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #16.2 : x[24] : [4, 4, 2],[-1] : [[1, 1], [3]] Qxi[C5,16,2] = (x[24])*q^4 + (x[32])*q^3 # Green Polys by conj class in A(O) #16.1 : c = () |O_x_c^F| = 1/2*q^13*(q+1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,16,1] = (x[23]+x[24])*q^4 + (x[25]+x[29]+x[32])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #16.2 : c = (1) |O_x_c^F| = 1/2*q^13*(q-1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,16,2] = (x[23]-x[24])*q^4 + (x[25]+x[29]-x[32])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #17 : [5, 5] dim = 44 A(O) = 1 , |A(O)_0| = 1 g_s = 3*V[8]+V[6]+3*V[4]+V[2]+3*V[0] Z_G(x)_0 = Sp2 # Green Polys by orbit reps #17.1 : x[25] : [5, 5],[] : [[2], [3]] Qxi[C5,17,1] = (x[25])*q^3 + (x[31]+x[32])*q^2 + (x[34]+x[35])*q + x[36] # Green Polys by conj class in A(O) #17.1 : c = () |O_x_c^F| = q^16*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,17,1] = (x[25])*q^3 + (x[31]+x[32])*q^2 + (x[34]+x[35])*q + x[36] orbit #18 : [6, 1, 1, 1, 1] dim = 38 A(O) = 1 , |A(O)_0| = 1 g_s = V[10]+V[6]+4*V[5]+V[2]+10*V[0] Z_G(x)_0 = O1+Sp4 # Green Polys by orbit reps #18.1 : x[26] : [6, 1, 1, 1, 1],[] : [[3, 1, 1], []] Qxi[C5,18,1] = (x[26])*q^6 + (x[29])*q^5 + (x[27]+x[30]+x[33])*q^4 + (x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #18.1 : c = () |O_x_c^F| = q^14*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,18,1] = (x[26])*q^6 + (x[29])*q^5 + (x[27]+x[30]+x[33])*q^4 + (x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #19 : [6, 2, 1, 1] dim = 42 A(O) = Z2 , |A(O)_0| = 2 g_s = V[10]+2*V[6]+2*V[5]+V[4]+2*V[2]+2*V[1]+3*V[0] Z_G(x)_0 = Sp2+2*O1 # Green Polys by orbit reps #19.1 : x[27] : [6, 2, 1, 1],[1] : [[3], [1, 1]] Qxi[C5,19,1] = (x[27])*q^4 + (x[29]+x[34])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #19.2 : x[28] : [6, 2, 1, 1],[-1] : [[], [4, 1]] Qxi[C5,19,2] = (x[28])*q^4 + (x[32])*q^3 + (x[35])*q^2 # Green Polys by conj class in A(O) #19.1 : c = () |O_x_c^F| = 1/2*q^14*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,19,1] = (x[27]+x[28])*q^4 + (x[29]+x[32]+x[34])*q^3 + (x[31]+x[33]+x[35])*q^2 + (x[34])*q + x[36] #19.2 : c = (1) |O_x_c^F| = 1/2*q^14*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,19,2] = (x[27]-x[28])*q^4 + (x[29]-x[32]+x[34])*q^3 + (x[31]+x[33]-x[35])*q^2 + (x[34])*q + x[36] orbit #20 : [6, 2, 2] dim = 44 A(O) = Z2 , |A(O)_0| = 2 g_s = V[10]+3*V[6]+2*V[4]+4*V[2]+V[0] Z_G(x)_0 = O2+O1 # Green Polys by orbit reps #20.1 : x[29] : [6, 2, 2],[1] : [[3, 1], [1]] Qxi[C5,20,1] = (x[29])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #20.2 : x[30] : [6, 2, 2],[-1] : [[3, 2], []] Qxi[C5,20,2] = (x[30])*q^3 # Green Polys by conj class in A(O) #20.1 : c = () |O_x_c^F| = 1/2*q^15*(q+1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,20,1] = (x[29]+x[30])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] #20.2 : c = (1) |O_x_c^F| = 1/2*q^15*(q-1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,20,2] = (x[29]-x[30])*q^3 + (x[31]+x[33])*q^2 + (x[34])*q + x[36] orbit #21 : [6, 4] dim = 46 A(O) = Z2 , |A(O)_0| = 2 g_s = V[10]+V[8]+3*V[6]+V[4]+3*V[2] Z_G(x)_0 = 2*O1 # Green Polys by orbit reps #21.1 : x[31] : [6, 4],[1] : [[3], [2]] Qxi[C5,21,1] = (x[31])*q^2 + (x[34])*q + x[36] #21.2 : x[32] : [6, 4],[-1] : [[1], [4]] Qxi[C5,21,2] = (x[32])*q^2 + (x[35])*q # Green Polys by conj class in A(O) #21.1 : c = () |O_x_c^F| = 1/2*q^16*(q^2-1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,21,1] = (x[31]+x[32])*q^2 + (x[34]+x[35])*q + x[36] #21.2 : c = (1) |O_x_c^F| = 1/2*q^16*(q^2-1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,21,2] = (x[31]-x[32])*q^2 + (x[34]-x[35])*q + x[36] orbit #22 : [8, 1, 1] dim = 46 A(O) = 1 , |A(O)_0| = 1 g_s = V[14]+V[10]+2*V[7]+V[6]+V[2]+3*V[0] Z_G(x)_0 = O1+Sp2 # Green Polys by orbit reps #22.1 : x[33] : [8, 1, 1],[] : [[4, 1], []] Qxi[C5,22,1] = (x[33])*q^2 + (x[34])*q + x[36] # Green Polys by conj class in A(O) #22.1 : c = () |O_x_c^F| = q^18*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,22,1] = (x[33])*q^2 + (x[34])*q + x[36] orbit #23 : [8, 2] dim = 48 A(O) = Z2 , |A(O)_0| = 2 g_s = V[14]+V[10]+V[8]+2*V[6]+2*V[2] Z_G(x)_0 = 2*O1 # Green Polys by orbit reps #23.1 : x[34] : [8, 2],[1] : [[4], [1]] Qxi[C5,23,1] = (x[34])*q + x[36] #23.2 : x[35] : [8, 2],[-1] : [[], [5]] Qxi[C5,23,2] = (x[35])*q # Green Polys by conj class in A(O) #23.1 : c = () |O_x_c^F| = 1/2*q^18*(q^2-1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,23,1] = (x[34]+x[35])*q + x[36] #23.2 : c = (1) |O_x_c^F| = 1/2*q^18*(q^2-1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,23,2] = (x[34]-x[35])*q + x[36] orbit #24 : [10] dim = 50 A(O) = 1 , |A(O)_0| = 1 g_s = V[18]+V[14]+V[10]+V[6]+V[2] Z_G(x)_0 = O1 # Green Polys by orbit reps #24.1 : x[36] : [10],[] : [[5], []] Qxi[C5,24,1] = x[36] # Green Polys by conj class in A(O) #24.1 : c = () |O_x_c^F| = q^20*(q^2-1)*(q^4-1)*(q^6-1)*(q^8-1)*(q^10-1) Qxc[C5,24,1] = x[36]