Interpolating a time series with interp1d using only numpy-CodePudding

I want to plot a time series with numpy and matplotlib, using markers for the exact points, and interpolation. Basically this (data is dummy, but functionality is the same, note that distance between time-points may vary):

import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt

T = [
    np.datetime64('2020-01-01T00:00:00.000000000'),
    np.datetime64('2020-01-02T00:00:00.000000000'),
    np.datetime64('2020-01-03T00:00:00.000000000'),
    np.datetime64('2020-01-05T00:00:00.000000000'),
    np.datetime64('2020-01-06T00:00:00.000000000'),
    np.datetime64('2020-01-09T00:00:00.000000000'),
    np.datetime64('2020-01-13T00:00:00.000000000'),
]
Z = [543, 234, 435, 765, 564, 235, 345]

fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot()
ax.plot(T, Z, 'o-')

However, the interpolation done here is just connecting the points. I want to include spline interpolation and other kinds using scipy's interp1d. So, I tried replacing the last line with the following:

ax.plot(T,Z, 'o')
ax.plot(T,interp1d(T, Z)(T), '-')

and I get the following error:

UFuncTypeError: ufunc 'true_divide' cannot use operands with types dtype('float64') and dtype('<m8[ns]')

Reading

The code that can reproduce the image:

import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt

T = np.array([
    np.datetime64('2020-01-01T00:00:00.000000000'),
    np.datetime64('2020-01-02T00:00:00.000000000'),
    np.datetime64('2020-01-03T00:00:00.000000000'),
    np.datetime64('2020-01-05T00:00:00.000000000'),
    np.datetime64('2020-01-06T00:00:00.000000000'),
    np.datetime64('2020-01-09T00:00:00.000000000'),
    np.datetime64('2020-01-13T00:00:00.000000000'),
], dtype='m')

Z = [543, 234, 435, 765, 564, 235, 345]

fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot()
ax.plot(T, Z, 'o')

f = interp1d(x=T/np.timedelta64(1, 's'), y=Z)

ax.plot(T, f(T/np.timedelta64(1, 's')), '-')
plt.show()