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Imei repair GS4 LTE work only on rooted phones,
Unlock GS4 LTE codereading work via UART cable without root,
Unlock GS4 work only on rooted phones.
For GS4 LTE - MD2 firmwares use CF autoroot,
For GS4 LTE - MDM/MDN/ME2 fimware use modified CFautoroot.
For M919 root - use CWM and SD card solution.
After rooting you need run SuperSU app. If you not see SuperSU - rooting is wrong.

Samsung tool 14.5 Release. GS4 with additional autorisation added.