Berry phases for the gamma orbit obtained from direct fitting to LK formula..

Angle(degrees); Berry phase(2pi radians); Error (2pi radians)
112.5;-0.0923;0.0268		
112.5;0.0734;0.0447
94.5;-0.0884;0.0236
81;0.0197;0.0326	
81;-0.0288;0.0304
76.5;-0.00714;0.02724	
72;-0.0305;0.03323
63;0.0604;0.0496
58.8;0.196;0.0156
54;0.348;0.064
49.5;0.564;0.124