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A molecular-beam electric-resonance spectrometer has been used to study the radio-frequency spectrum of $\mathrm{<mrow\; data-mjx-texclass="ORD">23</mrow>}Na127$I for transitions between the hfs levels of the first rotational state. Transitions for the first four vibrational states have been observed in near zero electric field and zero magnetic field. The observed rf transitions exhibit a natural line width of 2.5 kHz. The quadrupole coupling constants for the two nuclei have been measured. We find $(eqQ)Na=-4072\pm 5$ kHz in $v=0$ with a decrease of about 0.9% per vibrational state. For iodine, we find $(eqQ)t=-262,140\pm 5$ kHz in $v=0$ with an increase of 1.3% per vibrational state. These values are in minor disagreement with earlier $measurements.1.2$ The constants for the excited vibrational states have been determined with less precision because fewer transitions were observed.