diff -r -U1 sympy-0.7.6.1.orig/sympy/functions/special/zeta_functions.py sympy-0.7.6.1/sympy/functions/special/zeta_functions.py
--- sympy-0.7.6.1.orig/sympy/functions/special/zeta_functions.py	2015-09-04 02:34:00.000000000 +0600
+++ sympy-0.7.6.1/sympy/functions/special/zeta_functions.py	2015-12-01 11:27:24.000000000 +0600
@@ -243,3 +243,3 @@
     >>> polylog(s, -1)
-    dirichlet_eta(s)
+    -dirichlet_eta(s)
 
@@ -270,2 +270,3 @@
     def eval(cls, s, z):
+        from sympy import unpolarify
         if z == 1:
@@ -273,6 +274,12 @@
         elif z == -1:
-            return dirichlet_eta(s)
+            return -dirichlet_eta(s)
         elif z == 0:
-            return 0
+            return S.Zero
 
+        # branch handling
+        if (1 - abs(z)).is_nonnegative:
+            newz = unpolarify(z)
+            if newz != z:
+                return cls(s, newz)
+ 
     def fdiff(self, argindex=1):
@@ -479,3 +486,3 @@
 
-    .. math:: \eta(s) = \sum_{n=1}^\infty \frac{(-1)^n}{n^s}.
+    .. math:: \eta(s) = \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n^s}.