diff --git a/ho_basis.jl b/ho_basis.jl
index b8992f6..a5f44e5 100644
--- a/ho_basis.jl
+++ b/ho_basis.jl
@@ -59,13 +59,11 @@ function sp_T_matrix(ns, ls; ω=1.0, μ=1.0)
     for idx in CartesianIndices(mat)
         (i, j) = Tuple(idx)
         if ls[i] == ls[j]
-            mat[idx] = ls[i]
             if ns[i] == ns[j]
-                mat[idx] += 1/4 * (4*ns[j] + 3)
-            elseif ns[i] == ns[j] + 1
-                mat[idx] += -1/4 * sqrt((2*ns[j] + 2) * (2*ns[j] + 3))
-            elseif ns[i] == ns[j] - 1
-                mat[idx] += -1/4 * sqrt((2*ns[j] + 1) * 2*ns[j])
+                mat[idx] = ns[j] + ls[i]/2 + 3/4
+            elseif abs(ns[i]-ns[j]) == 1
+                n_max = max(ns[i], ns[j])
+                mat[idx] = -(1/2) * sqrt(n_max * (n_max + ls[i] + 1/2))
             end
         end
     end