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A pioneering experiment in Lambda hypernuclear spectroscopy, undertaken at the Thomas Jefferson National Accelerator Facility (Jlab), was recently reported. The experiment used the high- precision, continuous electron beam at Jlab, and a special arrangement of spectrometer magnets to measure the spectrum from {nat}C and 7Li targets using the (e,e' K+)reaction. The 12B hypernuclear spectrum was previously published. This experiment is now reported in more detail, with improved results for the 12B hypernuclear spectrum. In addition, unpublished results of the 7He hypernuclear spectrum are also shown. This later spectrum indicates the need for a more detailed few-body calculation of the hypernucleus and the reaction process. The success of this experiment demonstrates that the (e,e'K+) reaction can be effectively used as a high resolution tool to study hypernuclear spectra, ant its use should be vigorously pursued.