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The former general secretary of the Scottish Police Federation, said that around 3,800 cases had been logged since the controversial new legislation came into force.
Since the controversial legislation was rolled out on Monday almost 4,000 complaints have been made to Police Scotland.
The Scottish Conservatives said that if complaints continue to be made at the same speed over the next 12 months officers 1.38 million crimes could be reported.
Reports were made against the Harry Potter author but police have assessed her tweets against Scotland's new hate crime laws and found they did not breach the legislation.
The Harry Potter author had dared Police Scotland to arrest her on Monday for describing a string of prominent trans women as men before the force confirmed no action would be taken.