input: [0.0 + 0.0i, 1.0 + 0.0i, 0.0 + 0.0i, 0.0 + 0.0i, 0.0 + 0.0i, 0.0 + 0.0i, 0.0 + 0.0i, 0.0 + 0.0i]
output: [1.0 + 0.0i, 0.7071067811865476 + 0.7071067811865475i, 6.123233995736766E-17 + 1.0i, -0.7071067811865475 + 0.7071067811865476i, -1.0 + 1.2246467991473532E-16i, -0.7071067811865477 + -0.7071067811865475i, -1.8369701987210297E-16 + -1.0i, 0.7071067811865474 + -0.7071067811865477i]