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A Table of Complex Cubic Fields

A table of real cubic fields with discriminant less than 20,000 is given by Godwin and Samet [6]. This paper describes the construction of a complementary table of the 3169 non-conjugate complex cubic fields with discriminants greater than -20,000, which extends the existing table for discriminants greater than -1000 given by Delone and Faddeev [3]. The basis of this calculation is the following theorem, similar to one used by Godwin [5].