Several large values of ζ(1/2+it) are known. In 1989, first time in history, Andrew M. Odlyzko observed values where |Z(t)|>1000 (e.g: Z(5032868769288289111.35)$\approx$1581.7). Recenty many large values of |Z(t)|>1000 have been found by Jonathan Bober and Ghaith Hiary. They have found approximately 141 values where |Z(t)|>1000. These values can be found on their web page. Tens of thousands of large values of |Z(t)|>1000 have been found by applying some results on computing of n-diemsnional simultaneous Diophantine approximation (Download). These values can be found on this database (approximately 21.000 values).