double letter_a[] = {
0.080334, -0.445639,
-0.050940, -0.447993,
-0.175007, -0.428650,
-0.275208, -0.394296,
-0.349133, -0.348910,
-0.399168, -0.296059,
-0.429146, -0.239705,
-0.444190, -0.184144,
-0.449309, -0.133031,
-0.447807, -0.088260,
-0.441110, -0.049854,
-0.429090, -0.016322,
-0.411267, 0.013977,
-0.387297, 0.042290,
-0.356968, 0.069448,
-0.320038, 0.095734,
-0.276016, 0.120705,
-0.224141, 0.143171,
-0.163786, 0.161366,
-0.096207, 0.173662,
-0.025351, 0.178901,
0.042247, 0.176440,
0.099742, 0.166799,
0.143348, 0.152616,
0.172828, 0.138790,
0.191163, 0.131669,
0.202876, 0.135037,
0.213151, 0.148009,
0.227734, 0.165069,
0.251264, 0.178894,
0.284487, 0.185042,
0.323773, 0.182775,
0.361894, 0.174502,
0.392529, 0.162594,
0.412959, 0.147477,
0.424129, 0.127583,
0.429248, 0.100184,
0.431109, 0.063005,
0.431556, 0.014540,
0.431537, -0.045757,
0.431509, -0.116220,
0.431712, -0.192109,
0.432178, -0.265634,
0.432602, -0.328082,
0.432049, -0.374457,
0.428895, -0.404558,
0.420987, -0.422551,
0.406962, -0.433552,
0.387266, -0.440988,
0.364196, -0.446436,
0.341061, -0.450080,
0.320084, -0.451858,
0.301841, -0.451758,
0.285388, -0.449827,
0.269461, -0.446152,
0.253532, -0.440856,
0.237876, -0.434095,
0.222830, -0.426206,
0.206674, -0.418119,
0.184985, -0.411483,
};