diff --git a/dirichlet.h b/dirichlet.h
index 316ed036..6d24988b 100644
--- a/dirichlet.h
+++ b/dirichlet.h
@@ -144,6 +144,12 @@ dirichlet_char_is_real(const dirichlet_group_t G, const dirichlet_char_t chi)
     return G->q <= 4 || (nmod_mul(chi->n, chi->n, G->mod) == 1);
 }
 
+DIRICHLET_INLINE int
+dirichlet_char_is_primitive(const dirichlet_group_t G, const dirichlet_char_t chi)
+{
+    return (dirichlet_conductor_char(G, chi) == G->q);
+}
+
 ulong dirichlet_chi(const dirichlet_group_t G, const dirichlet_char_t chi, ulong n);
 
 void dirichlet_vec_set_null(ulong *v, const dirichlet_group_t G, slong nv);
diff --git a/doc/source/dirichlet.rst b/doc/source/dirichlet.rst
index c66d4078..f0d329f5 100644
--- a/doc/source/dirichlet.rst
+++ b/doc/source/dirichlet.rst
@@ -224,6 +224,10 @@ level of *number* and *char* object. Both case require no discrete log computati
 
    Returns 1 if *chi* is a real character (iff it has order `\leq 2`).
 
+.. function:: int dirichlet_char_is_primitive(const dirichlet_group_t G, const dirichlet_char_t chi)
+
+   Returns 1 if *chi* is primitive (iff its conductor is exactly *q*).
+
 Character evaluation
 -------------------------------------------------------------------------------