restart; with(LinearAlgebra): f := (i,j) -> w^((i-1)*(j-1));

NiM+SSJmRzYiZio2JEkiaUdGJUkiakdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKUkid0dGJSomLCY5JCIiIiEiIkYyRjIsJjklRjJGM0YyRjJGJUYlRiU=

W8 := Matrix(8,8,f);

NiM+SSNXOEc2Ii1JJ1JUQUJMRUdGJTYlIidjcSEpLUknTUFUUklYR0YlNiM3KjcqIiIiRi9GL0YvRi9GL0YvRi83KkYvSSJ3R0YlKiRGMSIiIyokRjEiIiQqJEYxIiIlKiRGMSIiJiokRjEiIicqJEYxIiIoNypGL0YyRjZGOiokRjEiIikqJEYxIiM1KiRGMSIjNyokRjEiIzk3KkYvRjRGOiokRjEiIipGQyokRjEiIzoqJEYxIiM9KiRGMSIjQDcqRi9GNkY/RkMqJEYxIiM7KiRGMSIjPyokRjEiI0MqJEYxIiNHNypGL0Y4RkFGSkZTKiRGMSIjRCokRjEiI0kqJEYxIiNONypGL0Y6RkNGTEZVRmZuKiRGMSIjTyokRjEiI1U3KkYvRjxGRUZORldGaG5GXW8qJEYxIiNcSSdNYXRyaXhHNiRJKnByb3RlY3RlZEdGZG9JKF9zeXNsaWJHRiU=

P8 := Matrix([[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]);

NiM+SSNQOEc2Ii1JJ1JUQUJMRUdGJTYlIignKiopRyMtSSdNQVRSSVhHRiU2IzcqNyoiIiIiIiFGMEYwRjBGMEYwRjA3KkYwRjBGMEYwRi9GMEYwRjA3KkYwRi9GMEYwRjBGMEYwRjA3KkYwRjBGMEYwRjBGL0YwRjA3KkYwRjBGL0YwRjBGMEYwRjA3KkYwRjBGMEYwRjBGMEYvRjA3KkYwRjBGMEYvRjBGMEYwRjA3KkYwRjBGMEYwRjBGMEYwRi9JJ01hdHJpeEc2JEkqcHJvdGVjdGVkR0Y6SShfc3lzbGliR0Yl

Multiply(W8,P8);

NiMtSSdSVEFCTEVHNiI2JSIoKWVzdy1JJ01BVFJJWEdGJTYjNyo3KiIiIkYtRi1GLUYtRi1GLUYtNypGLSokSSJ3R0YlIiIjKiRGMCIiJSokRjAiIidGMCokRjAiIiQqJEYwIiImKiRGMCIiKDcqRi1GMiokRjAiIikqJEYwIiM3Ri9GNCokRjAiIzUqJEYwIiM5NypGLUY0Rj8qJEYwIiM9RjYqJEYwIiIqKiRGMCIjOiokRjAiI0A3KkYtRj0qJEYwIiM7KiRGMCIjQ0YyRj8qJEYwIiM/KiRGMCIjRzcqRi1GQUZTKiRGMCIjSUY4RkoqJEYwIiNEKiRGMCIjTjcqRi1GP0ZRKiRGMCIjT0Y0RkZGWCokRjAiI1U3KkYtRkNGVUZbb0Y6RkxGZm4qJEYwIiNcSSdNYXRyaXhHNiRJKnByb3RlY3RlZEdGYm9JKF9zeXNsaWJHRiU=

Q8i := Matrix([[1,0,0,0,1,0,0,0],[0,1,0,0,0,w,0,0],[0,0,1,0,0,0,w^2,0],[0,0,0,1,0,0,0,w^3],[1,0,0,0,-1,0,0,0],[0,1,0,0,0,-w,0,0],[0,0,1,0,0,0,-w^2,0],[0,0,0,1,0,0,0,-w^3]]);

NiM+SSRROGlHNiItSSdSVEFCTEVHRiU2JSIoLytyKC1JJ01BVFJJWEdGJTYjNyo3KiIiIiIiIUYwRjBGL0YwRjBGMDcqRjBGL0YwRjBGMEkid0dGJUYwRjA3KkYwRjBGL0YwRjBGMCokRjIiIiNGMDcqRjBGMEYwRi9GMEYwRjAqJEYyIiIkNypGL0YwRjBGMCEiIkYwRjBGMDcqRjBGL0YwRjBGMCwkRjJGOkYwRjA3KkYwRjBGL0YwRjBGMCwkRjRGOkYwNypGMEYwRjBGL0YwRjBGMCwkRjdGOkknTWF0cml4RzYkSSpwcm90ZWN0ZWRHRkNJKF9zeXNsaWJHRiU=

Q8 := 2*MatrixInverse(Q8i);

NiM+SSNROEc2Ii1JJ1JUQUJMRUdGJTYlIigzQEcjLUknTUFUUklYR0YlNiM3KjcqIiIiIiIhRjBGMEYvRjBGMEYwNypGMEYvRjBGMEYwRi9GMEYwNypGMEYwRi9GMEYwRjBGL0YwNypGMEYwRjBGL0YwRjBGMEYvNypGL0YwRjBGMCEiIkYwRjBGMDcqRjAqJEkid0dGJUY1RjBGMEYwLCRGN0Y1RjBGMDcqRjBGMCokRjghIiNGMEYwRjAsJEY7RjVGMDcqRjBGMEYwKiRGOCEiJEYwRjBGMCwkRj9GNUknTWF0cml4RzYkSSpwcm90ZWN0ZWRHRkRJKF9zeXNsaWJHRiU=

Multiply(Q8,Multiply(W8,P8));

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TTdSMApJNFJUQUJMRV9TQVZFLzc2NzI1ODhYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISNbbyIpIikiIiJGJ0YnRidGJ0YnRidGJ0YnKiQlIndHCiIiIyokRikiIiUqJEYpIiInKiRGKSIiKSokRikiIzUqJEYpIiM3KiRGKSIjOUYnRitGL0YzKiRGKSIjOyokRikiIz8qJEYpIiNDKiRGKSIKI0dGJ0YtRjMqJEYpIiM9RjsqJEYpIiNJKiRGKSIjTyokRikiI1VGJ0YpRigqJEYpIiIkRisqJEYpIiImRi0qJEYpIiIoRidGR0YtKiRGKQoiIipGMyokRikiIzpGPyokRikiI0BGJ0ZJRjFGT0Y5KiRGKSIjREZBKiRGKSIjTkYnRktGNUZRRj1GVUZFKiRGKSIjXEYmCg==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