I have spent a few hours browsing various tutorials, so I am asking after trying for a bit. I am also unable to get a simple arrow on the offset X and Y axes...
from mpl_toolkits.axes_grid.axislines import SubplotZero
from matplotlib import pylab
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
rcParams.update({'figure.autolayout': True})
ax = plt.subplot(111)
sigma = [-4, -2, 0]
jomega = [0, 0, 0]
plt.plot(sigma, jomega, 'x', mew=2, ms=12, linestyle='None')
plt.xlabel("amaranthus")
plt.ylabel('j$\omega')
plt.xlim(-8,2)
plt.ylim(-8,8)
ax.spines['right'].set_color('none')
ax.spines['left'].set_position(('data',0))
ax.spines['top'].set_color('none')
ax.spines['bottom'].set_position(('data',0))
plt.show()