The 1701 Census is included as series Jb in the archive Realistisk ordnet avdeling (Ea-4070). The National Archives' "Section for digitalization and preservation" has digitalized the series in its entirety. Unfortunately the census lists from many parts of the country have been lost. 

The censuses will in due time be available through the Find source  function. Until then we have created a static list of links to the different volumes of the censuses.