This is a not a good circuit for a common-emitter amplifier. It's overly reliant on the transistor's current gain (beta or hFE), which varies wildly with current on this transistor. From the datasheet:
Your collector current varies from about 0.25mA to about 1mA.
You can make the circuit better by adding an emitter resistor. 200 ohms vastly improves the output. You'll need to increase the collector resistor to ~3.3k to keep the bias point from drifting too far. Here are LTSpice FFTs with and without emitter resistors (3.3k collector resistors on both):
The gain is lower, but the second harmonic is now 40dB down instead of <20dB down.
A better circuit uses a voltage divider on the base and an emitter resistor. This way the collector's bias current depends mostly on VBE, which is much better-behaved.