Had the same problem when I bought my 400E due to neglect on the previous owner's part. I use P21S GEL (also comes in liquid but the gel form is heavier duty). P21S products are made in Germany and are fairly neutral pH so won't hurt your wheels (like some domestic products can). The gel form can be left on for an hour as long as the wheels are not in direct sunlight. Repeated applications may be necessary.
Once clean, keep the wheels waxed (I use Zaino) and wash them weekly and you won't have those baked-on spots any more.