Correct chronological order:

Augustus (27 B.C.E.-14 C.E.)
Tiberius (14 C.E.-37 C.E.)
Caligula (37 C.E.-41 C.E.)
Claudius (41 C.E.-54 C.E.)
Nero (54 C.E.-68 C.E.)
Vespasian (69 C.E.-79 C.E.)
Titus (79 C.E.-81 C.E.)
Domitian (81 C.E.-96 C.E.)
Trajan (98 C.E.-117 C.E.)
Hadrian (117 C.E.-138 C.E.)
Valerian (253 C.E.-260 C.E.)
Tacitus (275 C.E.-276 C.E.)
Diocletian (284 C.E.-305 C.E.)
Constantine I (306 C.E.-337 C.E.)
Valens (364 C.E.-378 C.E.)