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The stability of beams of laser wakefield accelerated electrons in dielectric capillary tubes is experimentally investigated. These beams are found to be more stable in charge and pointing than the corresponding beams of electrons accelerated in a gas jet. Electron beams with an average charge of 43 pC and a standard deviation of 14% are generated. The fluctuations in charge are partly correlated to fluctuations in laser pulse energy. The pointing scatter of the electron beams is measured to be as low as 0.8 mrad (rms). High laser beam pointing stability improved the stability of the electron beams.