 The norm-Euclidean rings of quadratic integers are exactly those where is one of the values −11, −7, −3, −2, −1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, or 73.The cases and yield the Gaussian integers and Eisenstein integers, respectively.If is allowed to be any Euclidean function, then the list of possible values of for which the domain is Euclidean is not yet known.