How to find the neighbours around a Hilbert Curve cell

Question

I have a pandas dataframe with timestamp, latitude and longitude, and I have added the Hilbert Curve index using HilbertCurve from the hilbertcurve package. My dataframe looks like this:

import pandas as pd
df = pd.DataFrame({'time':['2019-10-19 19:23:00', '2019-10-19 19:24:00', '2019-10-19 19:25:00'],\
'lon':[48.80,48.801, 48.8018], \
'lat':[2.13,2.130,2.12], \
'hilbert'=[4578,4577,4521]})
print(df)

I want to find the neighbours of a specific hilbert cell. For example, for cell 4578, I want to find the 8 cells around it, which are east, north-east, north, north-west, west, south-west, south, south-east.

I looked everywhere but I was not lucky enough to find the answer.