diff --git a/hamilflow/models/harmonic_oscillator_chain.py b/hamilflow/models/harmonic_oscillator_chain.py
index da3ece9..dccd551 100644
--- a/hamilflow/models/harmonic_oscillator_chain.py
+++ b/hamilflow/models/harmonic_oscillator_chain.py
@@ -36,22 +36,29 @@ def __init__(
         :param initial_conditions: a sequence of initial conditions on the Fourier modes.
             The first element in the sequence is that of the zero mode, taking a position and a velocity.
             Rest of the elements are that of the independent travelling waves, taking two amplitudes and two initial phases.
-        :param odd_dof: The system will have `2 * len(initial_conditions) - int(odd_dof)` degrees of freedom.
+        :param odd_dof: The system will have `2 * len(initial_conditions) + int(odd_dof) - 2` degrees of freedom.
         """
+        self.n_dof = 2 * len(initial_conditions) + odd_dof - 2
+        if not odd_dof:
+            prefix = "For even degrees of freedom, "
+            if self.n_dof == 0:
+                raise ValueError(prefix + "at least 1 travelling wave is needed")
+            amp = cast(tuple[float, float], initial_conditions[-1]["amp"])
+            if amp[0] != amp[1]:
+                msg = "k == N // 2 must have equal positive and negative amplitudes."
+                raise ValueError(prefix + msg)
         self.omega = omega
-        self.n_independant_csho_dof = len(initial_conditions) - 1
         self.odd_dof = odd_dof
 
         self.free_mode = FreeParticle(cast(Mapping[str, float], initial_conditions[0]))
 
-        r_wave_modes_ic = initial_conditions[1:]
         self.independent_csho_modes = [
             self._sho_factory(
                 k,
                 cast(tuple[float, float], ic["amp"]),
                 cast(tuple[float, float] | None, ic.get("phi")),
             )
-            for k, ic in enumerate(r_wave_modes_ic, 1)
+            for k, ic in enumerate(initial_conditions[1:], 1)
         ]
 
     def _sho_factory(
@@ -67,10 +74,6 @@ def _sho_factory(
             dict(x0=amp) | (dict(phi=phi) if phi else {}),
         )
 
-    @cached_property
-    def n_dof(self) -> int:
-        return self.n_independant_csho_dof * 2 + self.odd_dof
-
     @cached_property
     def definition(
         self,
@@ -107,7 +110,7 @@ def _z(
                 else (
                     independent_cshos[:-1],
                     independent_cshos[[-1]],
-                    independent_cshos[-1::-1].conj(),
+                    independent_cshos[-2::-1].conj(),
                 )
             )
 
diff --git a/tests/test_models/test_harmonic_oscillator_chain.py b/tests/test_models/test_harmonic_oscillator_chain.py
index 3f0c3d8..35a4f6c 100644
--- a/tests/test_models/test_harmonic_oscillator_chain.py
+++ b/tests/test_models/test_harmonic_oscillator_chain.py
@@ -30,13 +30,21 @@ def free_mode(self, request: pytest.FixtureRequest) -> dict[str, int]:
             product(_possible_wave_modes, repeat=r) for r in range(3)
         )
     )
-    def wave_modes(self, request: pytest.FixtureRequest) -> list[dict[str, int]]:
+    def wave_modes(
+        self, request: pytest.FixtureRequest
+    ) -> list[dict[str, tuple[int, int]]]:
         return request.param
 
     @pytest.fixture(params=(False, True))
     def odd_dof(self, request: pytest.FixtureRequest) -> bool:
         return request.param
 
+    @pytest.fixture()
+    def legal_wave_modes_and_odd_def(
+        self, wave_modes: Iterable[Mapping[str, tuple[int, int]]], odd_dof: bool
+    ) -> tuple[Iterable[Mapping[str, tuple[int, int]]], bool]:
+        return wave_modes if odd_dof else chain(wave_modes, [dict(amp=(1, 1))]), odd_dof
+
     @pytest.fixture(params=(0, 1, (0, 1)))
     def times(self, request: pytest.FixtureRequest) -> int | tuple[int]:
         return request.param
@@ -45,19 +53,46 @@ def test_init(
         self,
         omega: int,
         free_mode: Mapping[str, int],
-        wave_modes: Iterable[Mapping[str, int]],
-        odd_dof: bool,
+        legal_wave_modes_and_odd_def: tuple[
+            Iterable[Mapping[str, tuple[int, int]]], bool
+        ],
     ) -> None:
+        wave_modes, odd_dof = legal_wave_modes_and_odd_def
         assert HarmonicOscillatorsChain(omega, [free_mode, *wave_modes], odd_dof)
 
-    def test_real(
+    @pytest.fixture()
+    def hoc_and_zs(
         self,
         omega: int,
         free_mode: Mapping[str, int],
-        wave_modes: Iterable[Mapping[str, int]],
-        odd_dof: bool,
+        legal_wave_modes_and_odd_def: tuple[
+            Iterable[Mapping[str, tuple[int, int]]], bool
+        ],
         times: int | Sequence[int],
-    ) -> None:
+    ) -> tuple[HarmonicOscillatorsChain, np.ndarray, np.ndarray]:
+        wave_modes, odd_dof = legal_wave_modes_and_odd_def
         hoc = HarmonicOscillatorsChain(omega, [free_mode, *wave_modes], odd_dof)
-        original_zs, _ = hoc._z(times)
+        return (hoc, *hoc._z(times))
+
+    def test_real(
+        self, hoc_and_zs: tuple[HarmonicOscillatorsChain, np.ndarray, np.ndarray]
+    ) -> None:
+        _, original_zs, _ = hoc_and_zs
         assert np.all(original_zs.imag == 0.0)
+
+    def test_dof(
+        self, hoc_and_zs: tuple[HarmonicOscillatorsChain, np.ndarray, np.ndarray]
+    ) -> None:
+        hoc, original_zs, _ = hoc_and_zs
+        assert original_zs.shape[0] == hoc.n_dof
+
+    @pytest.mark.parametrize("wave_mode", [None, *_possible_wave_modes[1:]])
+    def test_raise(
+        self,
+        omega: int,
+        free_mode: Mapping[str, int] | None,
+        wave_mode: Mapping[str, int],
+    ) -> None:
+        ics = [free_mode, *([wave_mode] if wave_mode else [])]
+        with pytest.raises(ValueError):
+            HarmonicOscillatorsChain(omega, ics, False)