diff --git a/galois.py b/galois.py
index 73f09ab..65535af 100755
--- a/galois.py
+++ b/galois.py
@@ -115,8 +115,8 @@ class GaloisFieldLog:
     There only needs to be one instantiation of the field for a given set of parameters,
     but elements from different field instances with the same parameters may be mixed.
     '''
-    field_widths = (4, 8, 12, 16)
-    poly_defaults = {4: 0x13, 8: 0x11d, 12:0x1053, 16: 0x1100b}
+    field_widths = (4, 6, 8, 12, 16)
+    poly_defaults = {4: 0x13, 6: 0x43, 8: 0x11d, 12:0x1053, 16: 0x1100b}
     multiply_test_size = 10000
     def __init__ (self, bits, primitive_polynomial = None, repr_prefix = 'G', alpha = 1):
         '''
@@ -192,8 +192,8 @@ class GaloisFieldDirect:
     There only needs to be one instantiation of the field for a given set of parameters,
     but elements from different field instances with the same parameters may be mixed.
     '''
-    field_widths = (4, 8, 12, 16, 32)
-    poly_defaults = {4: 0x13, 8: 0x11d, 12:0x1053, 16: 0x1100b, 32: 0x1000000c5}
+    field_widths = (4, 6, 8, 12, 16, 32, 64)
+    poly_defaults = {4: 0x13, 6: 0x43, 8: 0x11d, 12:0x1053, 16: 0x1100b, 32: 0x1000000c5, 64: 0x1000000000000001b}
     max_test_size = 5000
     def __init__ (self, bits, primitive_polynomial = None, repr_prefix = 'G', alpha = 1):
         '''