Using a Texture2D as a Normal Map

I'm trying to modify the normal map of a model on the fly in code. I have created a Texture2D and successfully assigned it to the normal map slot ("_BumpMap") on the standard shader but the normal values don't appear to be producing the correct effect. From other references, I thought the correct conversion was:

(r,g,b) = (0.5 + n.x/2, 0.5 + n.y / 2. 0.5 + n.z / 2)

but this looks wrong in the out. The result is too dark, similar to what happens if you using a texture as a normal map without importing it as one. This makes me think that maybe the texture importer does some filtering on the texture first?

The code I am using:

 Texture2D normalMap = new Texture2D(width, height);
 Color flat = new Color(0.5f, 0.5f, 1.0f);
 
 var pixels = normalMap.GetPixels();
 for (int i = 0; i < pixels.Length; i++) {
     pixels[i] = flat;
 }
 normalMap.SetPixels(pixels);
 normalMap.Apply();
 
 MeshRenderer mr = GetComponent<MeshRenderer>();
 mr.material.SetTexture("_BumpMap", normalMap);