coeffs :: [[Int]]
coeffs = [ [1, 2, 3]
         , [0, 1, 2, 3]
         , [1, 0, 3, 4]
         , [1, 2, 0]
         , [0, 0, 0]
         , [0]
         , [1, 1, 1]
         , [-1, -1, -1]
         , [-1, -2, 0, -3]
         , [-1] ]