diff --git a/src/fast_wave/C_s_matrix.pickle b/src/fast_wave/C_s_matrix.pickle
index 77d59ec..9684c17 100644
Binary files a/src/fast_wave/C_s_matrix.pickle and b/src/fast_wave/C_s_matrix.pickle differ
diff --git a/tests/test_wavefunction.py b/tests/test_wavefunction.py
index f46a9e2..5299ac6 100644
--- a/tests/test_wavefunction.py
+++ b/tests/test_wavefunction.py
@@ -10,6 +10,19 @@ def initialize_c_s_matrix():
     global c_s_matrix
     c_s_matrix = create_normalized_hermite_coefficients_matrix(60)
 
+def test_hermite_sympy():
+    """
+    Tests the hermite_sympy function to verify the accuracy of Hermite polynomial computation.
+    """
+    x = symbols("x")
+    h0 = hermite_sympy(0)
+    h1 = hermite_sympy(1)
+    h2 = hermite_sympy(2)
+
+    assert h0 == 1
+    assert h1 == 2 * x
+    assert h2 == 4 * x**2 - 2
+
 def test_create_hermite_coefficients_table():
     """
     Tests the create_normalized_hermite_coefficients_table function to verify if the normalized coefficient matrix is correct.