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fillcontinents and aeqd projection
The fillcontinents routine seems to fill the ouside of the continents, not the inside under some specific lat/lon values. (basemap.__version__ = 1.1.0 from conda-forge)
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
clon, clat = 62.426312397000004, -34.6302096207
bmap = Basemap(projection='aeqd', lat_0=clat, lon_0=clon)
fig, ax = plt.subplots()
conts = bmap.fillcontinents(zorder=9)
conts = bmap.drawcoastlines(color='black', zorder=10)
plt.show()

This script shows some more details of the issue:
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
clons, clats = [30, 45, 60, 75, 90], [-40, -40, -40, -40, -40]
fig, axes = plt.subplots(1, len(clons))
for ax, clon, clat in zip(axes, clons, clats):
plt.sca(ax)
bmap = Basemap(projection='aeqd', lat_0=clat, lon_0=clon)
conts = bmap.fillcontinents(zorder=9)
conts = bmap.drawcoastlines(color='black', zorder=10)
ax.set_title('{}/{}'.format(clon, clat))
plt.show()

workaround is using bmap.drawlsmask