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The spectrometer SPI aboard the ESA INTEGRAL satellite, which will be launched in 2002, will study the gamma ray sky in the 20-keV to 8-MeV energy band. It achieves the excellent spectral resolution of about 2 keV for photons of 1 MeV thanks to its 19 germanium detectors. A coded mask imaging technique provides an angular resolution of 2°. An active BGO veto shield is used for the definition of the field of view and for background rejection. After integration and testing at CNES in Toulouse, the flight model of SPI recently underwent a one-month prelaunch calibration at the CEA center of Bruyeres le Chatel, using an accelerator for homogeneity measurements and high-activity radioactive sources for imaging performance measurements. This paper presents the scientific goals and the different detector components of SPI and reports on the testing and calibration campaigns. The methods used to achieve good timing alignment using the digital front end electronics are described and the first detector performance and imaging capabilities are presented.