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(This particular example can be understood from the fact that as d increases Exp[ π √ d ] becomes extremely close to -1728 KleinInvariantJ[(1 + √ -d )/2] , which turns out to be an integer whenever there is unique factorization of numbers of the form a + b √ -d —and d = 163 is the largest of the 9 cases for which this is so.)