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Unfortunately, the built-in function spherical_harmonic() has many issues, as explained in this post (see also ticket #25034).

As suggested in the above post, a workaround is to use the function spin_weighted_spherical_harmonic() of the SageMath package kerrgeodesic_gw with a zero weight, so that you get the standard spherical harmonics. A limitation is that this works only for specific values of $(l, m)$, i.e. you cannot keep $l$ and $m$ as symbolic variables. See here for the documentation and examples of use of spin_weighted_spherical_harmonic() . Installing kerrgeodesic_gw in SageMath is easy: open a terminal and run

sage -pip install kerrgeodesic_gw

NB: on CoCalc, you have to add the option --user:

sage -pip install --user kerrgeodesic_gw

Unfortunately, the built-in function spherical_harmonic() has many issues, as explained discussed in this post (see also ticket #25034).

As suggested in the above post, a workaround is to use the function spin_weighted_spherical_harmonic() of the SageMath package kerrgeodesic_gw with a zero weight, so that you get the standard spherical harmonics. A limitation is that this works only for specific values of $(l, m)$, i.e. you cannot keep $l$ and $m$ as symbolic variables. See here for the documentation and examples of use of spin_weighted_spherical_harmonic() . Installing kerrgeodesic_gw in SageMath is easy: open a terminal and run

sage -pip install kerrgeodesic_gw

NB: on CoCalc, you have to add the option --user:

sage -pip install --user kerrgeodesic_gw