import - Importing FITS file from HEALPix

I am trying to read FITS file created by HEALPix software. The file contains a spherical map of a scalar field.

There is the online support on how to use the file in IDL, but not for Mathematica.

I understand FITS is partly binary format, but I expect it is still standardised and contains readable description on how the data is stored.

I tried reading Elements from the file in this way

Import["test.fits", #] & /@ 
  Import["test.fits", "Elements"]

but the output is quite short and mainly empty lists, especially for

Import["test.fits", "Data"]
Import["test.fits", "TableData"]

The size of my file is 12.6 MB. Here is a link to the file.

Is there another way to read the content of FITS file, besides these general 'Elements'?

Do I need to know something about the structure of my FITS file in order to be able to read it with Mathematica? Could it be the problem is that Mathematica does not read all types of FITS files?

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