:Well technically, the census was published in 1959. So the 567,000 figure is the official number of the 1957 census. However, due to the political issues that concern northern Iraq, many Kurdish and Arab scholars pushed for a corrupt census. Thus, the government claimed to have counted 136,800 Turks. Nonetheless, I have also placed this into a footnote in the info box of the article. 

 :The problem is that there is not much academia on this community. I have tried to look for journal articles via my university institution and could not find even one online-journal article. Thus, sources are very limited.  Nonetheless, even the sources which  has used, supports what I am telling you here. What Takabeg did was type "136,800" into a google search and just placed whatever they could find into the article without actually reading them (see for example this link were Takabeg wrote in the search engine "only 136800" ).  

 :So to sum up this confusing census debate, the 1957 census counted 567,000 Turkmens. However, due to political issues, the Iraqi government claimed that there were only 136,000 Turks. Furthermore, a year later they admitted that the very same census actually counted 567,000 Turkmen (more than 400% from the previous year’s claim). The census itself was published in 1959. Thus, the published census says that there was 567,000 Iraqi Turkmen in 1957 not 136,800.