diff --git a/test/test_operator.py b/test/test_operator.py
index 316c316..9ce3dbc 100644
--- a/test/test_operator.py
+++ b/test/test_operator.py
@@ -3,7 +3,6 @@
 import numpy as np
 from netket_fidelity.operator import singlequbit_gates as sg
 from jax import numpy as jnp
-
 import netket_fidelity as nkf
 
 
@@ -29,40 +28,83 @@ def test_operator_dense_and_conversion(operator):
     assert operator.hilbert == operator.to_local_operator().hilbert
 
 
-def test_get_conns():
+def test_get_conns_and_mels():
     hi_spin = nk.hilbert.Spin(s=0.5, N=3)
     hi_qubit = nk.hilbert.Qubit(N=3)
 
     local_state_spin = hi_spin.local_states
     local_state_qubit = hi_qubit.local_states
 
-    sigma_4_qubit = hi_qubit.numbers_to_states(2)
+    sigma_2_qubit = hi_qubit.numbers_to_states(2)
     sigma_7_qubit = hi_qubit.numbers_to_states(7)
-    sigma_4_spin = hi_spin.numbers_to_states(2)
+    sigma_2_spin = hi_spin.numbers_to_states(2)
     sigma_7_spin = hi_spin.numbers_to_states(7)
 
-    sigma_qubit = jnp.array([sigma_4_qubit, sigma_7_qubit])
-    sigma_spin = jnp.array([sigma_4_spin, sigma_7_spin])
+    sigma_qubit = jnp.array([sigma_2_qubit, sigma_7_qubit])
+    sigma_spin = jnp.array([sigma_2_spin, sigma_7_spin])
 
-    conns_rx_qubit, _ = sg.get_conns_and_mels_Rx(sigma_qubit, 0, 0, local_state_qubit)
-    conns_ry_qubit, _ = sg.get_conns_and_mels_Ry(sigma_qubit, 0, 0, local_state_qubit)
-    conns_h_qubit, _ = sg.get_conns_and_mels_Hadamard(sigma_qubit, 0, local_state_qubit)
+    conns_rx_qubit, mels_rx_qubit = sg.get_conns_and_mels_Rx(
+        sigma_qubit, 0, np.pi / 2, local_state_qubit
+    )
+    conns_ry_qubit, mels_ry_qubit = sg.get_conns_and_mels_Ry(
+        sigma_qubit, 0, np.pi / 2, local_state_qubit
+    )
+    conns_h_qubit, mels_h_qubit = sg.get_conns_and_mels_Hadamard(
+        sigma_qubit, 0, local_state_qubit
+    )
 
-    conns_rx_spin, _ = sg.get_conns_and_mels_Rx(sigma_spin, 0, 0, local_state_spin)
-    conns_ry_spin, _ = sg.get_conns_and_mels_Ry(sigma_spin, 0, 0, local_state_spin)
-    conns_h_spin, _ = sg.get_conns_and_mels_Hadamard(sigma_spin, 0, local_state_spin)
+    conns_rx_spin, mels_rx_spin = sg.get_conns_and_mels_Rx(
+        sigma_spin, 0, np.pi / 2, local_state_spin
+    )
+    conns_ry_spin, mels_ry_spin = sg.get_conns_and_mels_Ry(
+        sigma_spin, 0, np.pi / 2, local_state_spin
+    )
+    conns_h_spin, mels_h_spin = sg.get_conns_and_mels_Hadamard(
+        sigma_spin, 0, local_state_spin
+    )
 
-    values_check_qubit = jnp.array(
+    conns_check_qubit = jnp.array(
         [[[0.0, 1.0, 0.0], [1.0, 1.0, 0.0]], [[1.0, 1.0, 1.0], [0.0, 1.0, 1.0]]]
     )
 
-    values_check_spin = jnp.array(
+    conns_check_spin = jnp.array(
         [[[-1.0, 1.0, -1.0], [1.0, 1.0, -1.0]], [[1.0, 1.0, 1.0], [-1.0, 1.0, 1.0]]]
     )
 
-    assert (conns_rx_qubit == values_check_qubit).all()
-    assert (conns_ry_qubit == values_check_qubit).all()
-    assert (conns_h_qubit == values_check_qubit).all()
-    assert (conns_rx_spin == values_check_spin).all()
-    assert (conns_ry_spin == values_check_spin).all()
-    assert (conns_h_spin == values_check_spin).all()
+    mels_check_qubit_rx = jnp.array(
+        [[0.70710678 + 0.0j, 0.0 - 0.70710678j], [0.70710678 + 0.0j, 0.0 - 0.70710678j]]
+    )
+    mels_check_qubit_ry = jnp.array(
+        [
+            [0.70710678 + 0.0j, 0.70710678 + 0.0j],
+            [0.70710678 + 0.0j, -0.70710678 + 0.0j],
+        ]
+    )
+    mels_check_qubit_h = jnp.array(
+        [[0.70710678, 0.70710678], [-0.70710678, 0.70710678]]
+    )
+
+    mels_check_spin_rx = jnp.array(
+        [[0.70710678 + 0.0j, 0.0 - 0.70710678j], [0.70710678 + 0.0j, 0.0 - 0.70710678j]]
+    )
+    mels_check_spin_ry = jnp.array(
+        [
+            [0.70710678 + 0.0j, 0.70710678 + 0.0j],
+            [0.70710678 + 0.0j, -0.70710678 + 0.0j],
+        ]
+    )
+    mels_check_spin_h = jnp.array([[0.70710678, 0.70710678], [-0.70710678, 0.70710678]])
+
+    np.testing.assert_allclose(conns_rx_qubit, conns_check_qubit)
+    np.testing.assert_allclose(conns_ry_qubit, conns_check_qubit)
+    np.testing.assert_allclose(conns_h_qubit, conns_check_qubit)
+    np.testing.assert_allclose(conns_rx_spin, conns_check_spin)
+    np.testing.assert_allclose(conns_ry_spin, conns_check_spin)
+    np.testing.assert_allclose(conns_h_spin, conns_check_spin)
+
+    np.testing.assert_allclose(mels_rx_qubit, mels_check_qubit_rx)
+    np.testing.assert_allclose(mels_ry_qubit, mels_check_qubit_ry)
+    np.testing.assert_allclose(mels_h_qubit, mels_check_qubit_h)
+    np.testing.assert_allclose(mels_rx_spin, mels_check_spin_rx)
+    np.testing.assert_allclose(mels_ry_spin, mels_check_spin_ry)
+    np.testing.assert_allclose(mels_h_spin, mels_check_spin_h)