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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def get_lm_f0tau(mass, spin, l, m, nmodes):
 """Return the f0 and the tau of each overtone for a given l, m mode. Parameters mass : float or array Mass of the black hole (in solar masses). spin : float or array Dimensionless spin of the final black hole. l : int or array l-index of the harmonic. m : int or array m-index of the harmonic. nmodes : int The number of overtones to generate. Returns ------- f0 : float or array The frequency of the QNM(s), in Hz. If only a single mode is requested (and mass, spin, l, and m are not arrays), this will be a float. If multiple modes requested, will be an array with shape ``[input shape x] nmodes``, where ``input shape`` is the broadcasted shape of the inputs. tau : float or array The damping time of the QNM(s), in seconds. Return type is same as f0. """

    # convert to arrays
    mass, spin, l, m, input_is_array = ensurearray(
        mass, spin, l, m)
    # we'll ravel the arrays so we can evaluate each parameter combination
    # one at a a time
    origshape = mass.shape
    if nmodes < 1:
        raise ValueError("nmodes must be >= 1")
    if nmodes > 1:
        newshape = tuple(list(origshape)+[nmodes])
    else:
        newshape = origshape
    f0s = numpy.zeros((mass.size, nmodes))
    taus = numpy.zeros((mass.size, nmodes))
    mass = mass.ravel()
    spin = spin.ravel()
    l = l.ravel()
    m = m.ravel()
    qnmfreq = None
    modes = range(nmodes)
    for ii in range(mass.size):
        qnmfreq = _genqnmfreq(mass[ii], spin[ii], l[ii], m[ii], nmodes,
                              qnmfreq=qnmfreq)
        f0s[ii, :] = [qnmfreq.data[n].real/(2 * numpy.pi) for n in modes]
        taus[ii, :] = [1./qnmfreq.data[n].imag for n in modes]
    f0s = f0s.reshape(newshape)
    taus = taus.reshape(newshape)
    return (formatreturn(f0s, input_is_array),
            formatreturn(taus, input_is_array))