diff --git a/examples/bulk_j_an.py b/examples/bulk_j_an.py
index 8c46fac29c7517e4a5e82876a8da70d72f5ad2b7..37882cfe372d279a61f92705ee63fda803e14707 100644
--- a/examples/bulk_j_an.py
+++ b/examples/bulk_j_an.py
@@ -86,17 +86,15 @@ def j_anom(T, h, n=5, alpha_soc=0.01, perturbative=False):
         J[:, :, UP] /= dd[0]
         J[:, :, RIGHT] /= dd[1]
         J[:, :, DOWN] /= dd[0]
-        Jtot += pi * aa * J
+        Jtot += 1j * pi * aa * J
 
         # Analytic
         gp = (ww - 1j * h) / np.sqrt((ww - 1j * h) ** 2 + 1)
         gm = (ww + 1j * h) / np.sqrt((ww + 1j * h) ** 2 + 1)
         fp = 1 / np.sqrt((ww - 1j * h) ** 2 + 1)
         fm = 1 / np.sqrt((ww + 1j * h) ** 2 + 1)
-        # XXX: check the 32*eta
-        Jy_an = (
-            (gp - gm) * (1 + gp * gm + fp * fm) * (-1j * alpha_soc**3) * (32 * eta)
-        )
+        # XXX: check the 8*eta
+        Jy_an = (gp - gm) * (1 + gp * gm + fp * fm) * (-1j * alpha_soc**3) * (8 * eta)
         Jantot += pi * aa * Jy_an
 
     return Jtot, Jantot
diff --git a/src/action.hpp b/src/action.hpp
index 252c1dc9d3eed843c2466263ce52cbbaf15b21a1..2531af08a0b804a0f05b26615569596cc48d7502 100644
--- a/src/action.hpp
+++ b/src/action.hpp
@@ -251,7 +251,7 @@ inline Scalar S_H(const array::ArrayView<const Mask, Shape0>& mask,
         }
     }
 
-    return (2.0*eta/(dd[0]*dd[1])) * S;
+    return (2.0*eta/(Complex(0,4.0)*dd[0]*dd[1])) * S;
 }
 
 /* Function that has the same value as the AD variable,