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The variable X-ray source 1E 1547. 0-5408 was identified by Gelfand & Gaensler (2007) as a likely magnetar in G327. 24-0. 13, an apparent supernova remnant. No X-ray pulsations have been detected from it. Using the Parkes radio telescope, we discovered pulsations with period P = 2. 069 s. Using the Australia Telescope Compact Array, we localized these to 1E 1547. 0-5408. We measure dP/dt = (2. 318+-0. 005) e-11, which for a magnetic dipole rotating in vacuo gives a surface field strength of 2. 2e14 G, a characteristic age of 1. 4 kyr, and a spin-down luminosity of 1. 0e35 ergs/s. Together with its X-ray characteristics, these rotational parameters of 1E 1547. 0-5408 prove that it is a magnetar, only the second known to emit radio waves. The distance is ~9 kpc, derived from the dispersion measure of 830 pc/cc. The pulse profile at a frequency of 1. 4 GHz is extremely broad and asymmetric due to multipath propagation in the ISM, as a result of which only approximately 75% of the total flux at 1. 4 GHz is pulsed. At higher frequencies the profile is more symmetric and has FWHM = 0. 12P. Unlike in normal radio pulsars, but in common with the other known radio-emitting magnetar, XTE J1810-197, the spectrum over 1. 4-6. 6 GHz is flat or rising, and we observe large, sudden changes in the pulse shape. In a contemporaneous Swift X-ray observation, 1E 1547. 0-5408 was detected with record high flux, fX (1-8 keV) ~ 5e-12 ergs/cm²/s, 16 times the historic minimum. The pulsar was undetected in archival radio observations from 1998, implying a flux < 0. 2 times the present level. Together with the transient behavior of XTE J1810-197, these results suggest that radio emission is triggered by X-ray outbursts of usually quiescent magnetars.
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