diff --git a/pyerrors/correlators.py b/pyerrors/correlators.py
index 01a7d61e..ff899dc8 100644
--- a/pyerrors/correlators.py
+++ b/pyerrors/correlators.py
@@ -242,7 +242,9 @@ class Corr:
         Parameters
         ----------
         variant -- log: uses the standard effective mass log(C(t) / C(t+1))
-                   periodic : Solves C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. See, e.g., arXiv:1205.5380
+                   cosh : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
+                   sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
+                   See, e.g., arXiv:1205.5380
         guess -- guess for the root finder, only relevant for the root variant
         """
         if self.N != 1:
diff --git a/tests/test_correlators.py b/tests/test_correlators.py
new file mode 100644
index 00000000..37b59fba
--- /dev/null
+++ b/tests/test_correlators.py
@@ -0,0 +1,48 @@
+import numpy as np
+import pyerrors as pe
+import pytest
+
+np.random.seed(0)
+
+
+def test_function_overloading():
+    corr_content_a = []
+    corr_content_b = []
+    for t in range(24):
+        corr_content_a.append(pe.pseudo_Obs(np.random.normal(1e-10, 1e-8), 1e-4, 't'))
+        corr_content_b.append(pe.pseudo_Obs(np.random.normal(1e8, 1e10), 1e7, 't'))
+
+    corr_a = pe.correlators.Corr(corr_content_a)
+    corr_b = pe.correlators.Corr(corr_content_b)
+
+    fs = [lambda x: x[0] + x[1], lambda x: x[1] + x[0], lambda x: x[0] - x[1], lambda x: x[1] - x[0],
+          lambda x: x[0] * x[1], lambda x: x[1] * x[0], lambda x: x[0] / x[1], lambda x: x[1] / x[0],
+          lambda x: np.exp(x[0]), lambda x: np.sin(x[0]), lambda x: np.cos(x[0]), lambda x: np.tan(x[0]),
+          lambda x: np.log(x[0] + 0.1), lambda x: np.sqrt(np.abs(x[0])),
+          lambda x: np.sinh(x[0]), lambda x: np.cosh(x[0]), lambda x: np.tanh(x[0])]
+
+    for i, f in enumerate(fs):
+        t1 = f([corr_a, corr_b])
+        for o_a, o_b, con in zip(corr_content_a, corr_content_b, t1.content):
+            t2 = f([o_a, o_b])
+            t2.gamma_method()
+            assert np.isclose(con[0].value, t2.value)
+            assert np.isclose(con[0].dvalue, t2.dvalue)
+            assert np.allclose(con[0].deltas['t'], t2.deltas['t'])
+
+def test_modify_correlator():
+    corr_content = []
+    for t in range(24):
+        exponent = np.random.normal(3, 5)
+        corr_content.append(pe.pseudo_Obs(2 + 10 ** exponent, 10 ** (exponent - 1), 't'))
+
+    corr = pe.correlators.Corr(corr_content)
+
+    with pytest.warns(RuntimeWarning):
+        corr.symmetric()
+    with pytest.warns(RuntimeWarning):
+        corr.anti_symmetric()
+    corr.roll(np.random.randint(100))
+    corr.deriv(symmetric=True)
+    corr.deriv(symmetric=False)
+    corr.second_deriv()
diff --git a/tests/test_pyerrors.py b/tests/test_pyerrors.py
index 0835fb08..4c8cf18f 100644
--- a/tests/test_pyerrors.py
+++ b/tests/test_pyerrors.py
@@ -35,7 +35,7 @@ def test_function_overloading():
     fs = [lambda x: x[0] + x[1], lambda x: x[1] + x[0], lambda x: x[0] - x[1], lambda x: x[1] - x[0],
           lambda x: x[0] * x[1], lambda x: x[1] * x[0], lambda x: x[0] / x[1], lambda x: x[1] / x[0],
           lambda x: np.exp(x[0]), lambda x: np.sin(x[0]), lambda x: np.cos(x[0]), lambda x: np.tan(x[0]),
-          lambda x: np.log(x[0]), lambda x: np.sqrt(x[0]),
+          lambda x: np.log(x[0]), lambda x: np.sqrt(np.abs(x[0])),
           lambda x: np.sinh(x[0]), lambda x: np.cosh(x[0]), lambda x: np.tanh(x[0])]
 
     for i, f in enumerate(fs):
@@ -47,8 +47,17 @@ def test_function_overloading():
 
 
 def test_overloading_vectorization():
-    a = np.random.randint(0, 100, 10)
-    b = pe.pseudo_Obs(4, 0.8, 'e1')
+    a = np.random.randint(1, 100, 10)
+    b = pe.pseudo_Obs(4, 0.8, 't')
+
+    assert [o.value for o in a * b] == [o.value for o in b * a]
+    assert [o.value for o in a + b] == [o.value for o in b + a]
+    assert [o.value for o in a - b] == [-1 * o.value for o in b - a]
+    assert [o.value for o in a / b] == [o.value for o in [p / b for p in a]]
+    assert [o.value for o in b / a] == [o.value for o in [b / p for p in a]]
+
+    a = np.random.normal(0.0, 1e10, 10)
+    b = pe.pseudo_Obs(4, 0.8, 't')
 
     assert [o.value for o in a * b] == [o.value for o in b * a]
     assert [o.value for o in a + b] == [o.value for o in b + a]
diff --git a/tests/test_roots.py b/tests/test_roots.py
index c1bdc7ea..8d3a8191 100644
--- a/tests/test_roots.py
+++ b/tests/test_roots.py
@@ -16,4 +16,4 @@ def test_root_linear():
 
     assert np.isclose(my_root.value, value)
     difference = my_obs - my_root
-    assert all(np.isclose(0.0, difference.deltas['t']))
+    assert np.allclose(0.0, difference.deltas['t'])