diff --git a/tests/fields/conftest.py b/tests/fields/conftest.py
index 1b30fac64..a60645d0c 100644
--- a/tests/fields/conftest.py
+++ b/tests/fields/conftest.py
@@ -38,6 +38,7 @@
 FIELDS_DIFF_MODES = [
     # Binary field
     pytest.param("GF(2)-jit-calculate"),
+    pytest.param("GF(2)-python-calculate"),
     # Binary extension fields
     pytest.param("GF(2^2)-jit-lookup"),
     pytest.param("GF(2^2)-jit-calculate"),
@@ -52,8 +53,10 @@
     # Prime fields
     pytest.param("GF(5)-jit-lookup"),
     pytest.param("GF(5)-jit-calculate"),
+    pytest.param("GF(5)-python-calculate"),
     pytest.param("GF(7)-jit-lookup"),
     pytest.param("GF(7)-jit-calculate"),
+    pytest.param("GF(7)-python-calculate"),
     pytest.param("GF(31)-jit-lookup"),
     pytest.param("GF(31)-jit-calculate"),
     pytest.param("GF(3191)-jit-lookup"),
@@ -76,7 +79,7 @@ def construct_field(folder):
         ufunc_mode = "auto"
 
     if folder == "GF(2)":
-        GF = galois.GF2
+        GF = galois.GF(2, compile=ufunc_mode)
 
     elif folder == "GF(5)":
         GF = galois.GF(5, compile=ufunc_mode)
diff --git a/tests/fields/test_arithmetic.py b/tests/fields/test_arithmetic.py
index d0eb7e623..5465c8425 100644
--- a/tests/fields/test_arithmetic.py
+++ b/tests/fields/test_arithmetic.py
@@ -5,6 +5,7 @@
 import random
 
 import numpy as np
+import pytest
 
 import galois
 
@@ -218,11 +219,12 @@ def test_log_different_base(field_log):
     assert np.array_equal(beta**z, x)
 
 
-def test_log_pollard_rho():
+@pytest.mark.parametrize("ufunc_mode", ["jit-calculate", "python-calculate"])
+def test_log_pollard_rho(ufunc_mode):
     """
     The Pollard-rho discrete logarithm algorithm is only applicable for fields when p^m - 1 is prime.
     """
-    GF = galois.GF(2**19, compile="jit-calculate")
+    GF = galois.GF(2**5, compile=ufunc_mode)
     assert isinstance(GF._log, galois._domains._calculate.log_pollard_rho)
     dtype = random.choice(GF.dtypes)
     x = GF.Random(10, low=1, dtype=dtype)