diff --git a/src/caustics/lenses/func/__init__.py b/src/caustics/lenses/func/__init__.py
index bb8b71c3..0373f357 100644
--- a/src/caustics/lenses/func/__init__.py
+++ b/src/caustics/lenses/func/__init__.py
@@ -53,7 +53,11 @@
     concentration_tnfw,
 )
 
-from .multipole import reduced_deflection_angle_multipole, potential_multipole, convergence_multipole
+from .multipole import (
+    reduced_deflection_angle_multipole,
+    potential_multipole,
+    convergence_multipole,
+)
 
 __all__ = (
     "forward_raytrace",
diff --git a/src/caustics/lenses/func/multipole.py b/src/caustics/lenses/func/multipole.py
index 0028d830..b7e856aa 100644
--- a/src/caustics/lenses/func/multipole.py
+++ b/src/caustics/lenses/func/multipole.py
@@ -34,17 +34,21 @@ def reduced_deflection_angle_multipole(x0, y0, m, a_m, phi_m, x, y):
     Equation (B11) and (B12) https://arxiv.org/pdf/1307.4220, Xu et al. 2014
     """
     x, y = translate_rotate(x, y, x0, y0)
-    
+
     phi = torch.arctan2(y, x)
-    ax = torch.cos(phi) * a_m / (1 - m**2) * torch.cos(m * (phi - phi_m)) + torch.sin(phi) * m * a_m / (1 - m**2) * torch.sin(m * (phi - phi_m))
-    ay = torch.sin(phi) * a_m / (1 - m**2) * torch.cos(m * (phi - phi_m)) - torch.cos(phi) * m * a_m / (1 - m**2) * torch.sin(m * (phi - phi_m))
+    ax = torch.cos(phi) * a_m / (1 - m**2) * torch.cos(m * (phi - phi_m)) + torch.sin(
+        phi
+    ) * m * a_m / (1 - m**2) * torch.sin(m * (phi - phi_m))
+    ay = torch.sin(phi) * a_m / (1 - m**2) * torch.cos(m * (phi - phi_m)) - torch.cos(
+        phi
+    ) * m * a_m / (1 - m**2) * torch.sin(m * (phi - phi_m))
 
     return derotate(ax, ay, phi)
 
 
 def potential_multipole(x0, y0, m, a_m, phi_m, x, y):
     """
-    Compute the lensing potential. 
+    Compute the lensing potential.
 
     Parameters
     ----------
@@ -78,12 +82,12 @@ def potential_multipole(x0, y0, m, a_m, phi_m, x, y):
     x, y = translate_rotate(x, y, x0, y0)
     r = torch.sqrt(x**2 + y**2)
     phi = torch.arctan2(y, x)
-    return r * a_m / (1 - m**2) * torch.cos(m * (phi - phi_m)) 
+    return r * a_m / (1 - m**2) * torch.cos(m * (phi - phi_m))
 
 
 def convergence_multipole(x0, y0, m, a_m, phi_m, x, y):
     """
-    Compute the lensing convergence. 
+    Compute the lensing convergence.
 
     Parameters
     ----------
@@ -117,4 +121,4 @@ def convergence_multipole(x0, y0, m, a_m, phi_m, x, y):
     x, y = translate_rotate(x, y, x0, y0)
     r = torch.sqrt(x**2 + y**2)
     phi = torch.arctan2(y, x)
-    return 1/r * a_m * torch.cos(m * (phi - phi_m)) 
+    return 1 / r * a_m * torch.cos(m * (phi - phi_m))
diff --git a/src/caustics/lenses/multipole.py b/src/caustics/lenses/multipole.py
index 52311129..7381a1c4 100644
--- a/src/caustics/lenses/multipole.py
+++ b/src/caustics/lenses/multipole.py
@@ -31,22 +31,15 @@ class Multipole(ThinLens):
         Orientation of multiple.
     m: Optional[Union[Tensor, int]]
         Order of multipole.
-        
+
     """
 
-    _null_params = {
-        "x0": 0.0,
-        "y0": 0.0,
-        "a_m": 0.1,
-        "phi_m": 0.,
-        "m": 3
-    }
+    _null_params = {"x0": 0.0, "y0": 0.0, "a_m": 0.1, "phi_m": 0.0, "m": 3}
 
     def __init__(
         self,
         cosmology: CosmologyType,
         z_l: ZLType = None,
-
         x0: Annotated[
             Optional[Union[Tensor, float]], "The x-coordinate of the lens center", True
         ] = None,
@@ -228,7 +221,7 @@ def convergence(
             The projected mass density.
 
             *Unit: unitless*
-        
+
         Equation (B10) and (B3) https://arxiv.org/pdf/1307.4220, Xu et al. 2014
 
         """
diff --git a/src/caustics/models/utils.py b/src/caustics/models/utils.py
index 40d1c026..eecb5bd2 100644
--- a/src/caustics/models/utils.py
+++ b/src/caustics/models/utils.py
@@ -48,7 +48,7 @@ def _get_kwargs_field_definitions(
         if k != "name":
             anno = v.annotation
             dtype = anno.__origin__
-            cls_param = ClassParam(*anno.__metadata__) # gooooo
+            cls_param = ClassParam(*anno.__metadata__)  # gooooo
             if cls_param.isParam:
                 kwargs_field_definitions[PARAMS][k] = (
                     dtype,
diff --git a/tests/test_multipole.py b/tests/test_multipole.py
index 6894df9a..3e37637c 100644
--- a/tests/test_multipole.py
+++ b/tests/test_multipole.py
@@ -1,6 +1,11 @@
 import torch
 from lenstronomy.LensModel.lens_model import LensModel
-from utils import lens_test_helper, alpha_test_helper, kappa_test_helper, Psi_test_helper
+from utils import (
+    lens_test_helper,
+    alpha_test_helper,
+    kappa_test_helper,
+    Psi_test_helper,
+)
 import yaml
 
 from caustics.cosmology import FlatLambdaCDM
@@ -37,9 +42,15 @@ def test(sim_source, device, lens_models):
 
     # Parameters  m, a_m ,phi_m
     z_s = torch.tensor(1.2)
-    x = torch.tensor([-0.342, 0.51, 0.1, 3.14/4, 3])
+    x = torch.tensor([-0.342, 0.51, 0.1, 3.14 / 4, 3])
     kwargs_ls = [
-        {"center_x": x[0].item(), "center_y": x[1].item(), "a_m": x[2].item(), "phi_m": x[3].item(), "m": x[4].item()}
+        {
+            "center_x": x[0].item(),
+            "center_y": x[1].item(),
+            "a_m": x[2].item(),
+            "phi_m": x[3].item(),
+            "m": x[4].item(),
+        }
     ]
 
     lens_test_helper(lens, lens_ls, z_s, x, kwargs_ls, rtol, atol, device=device)