f = lambda x, e= enumerate :[ sum ( t/1j**( 4 *k*n/len ( x) ) for n, t in e( x) ) for k, _ in e( x) ]
for x in ( [ 1 , 1 , 1 , 1 ] , [ 1 , 0 , 2 , 0 , 3 , 0 , 4 , 0 ] , [ 1 , 2 , 3 , 4 , 5 ] , [ 5 -3.28571j, -0.816474 -0.837162j, 0.523306 -0.303902j, 0.806172 -3.69346j, -4.41953 +2.59494j, -0.360252 +2.59411j, 1.26678 +2.93119j] ) :
print ( f( x) , '\n ' )
ZiA9IGxhbWJkYSB4LGU9ZW51bWVyYXRlOltzdW0odC8xaioqKDQqaypuL2xlbih4KSlmb3Igbix0IGluIGUoeCkpZm9yIGssXyBpbiBlKHgpXQoKZm9yIHggaW4gKFsxLCAxLCAxLCAxXSwgWzEsIDAsIDIsIDAsIDMsIDAsIDQsIDBdLCBbMSwgMiwgMywgNCwgNV0sIFs1LTMuMjg1NzFqLCAtMC44MTY0NzQtMC44MzcxNjJqLCAwLjUyMzMwNi0wLjMwMzkwMmosIDAuODA2MTcyLTMuNjkzNDZqLCAtNC40MTk1MysyLjU5NDk0aiwgLTAuMzYwMjUyKzIuNTk0MTFqLCAxLjI2Njc4KzIuOTMxMTlqXSk6CglwcmludChmKHgpLCAnXG4nKQ==
stdout
[(4+0j), 0j, 0j, 0j]
[(10+0j), (-2+2j), (-2+0j), (-2-2j), (10+0j), (-2+2j), (-2+0j), (-2-2j)]
[(15+0j), (-2.5+3.440954801177933j), (-2.5000000000000004+0.8122992405822647j), (-2.499999999999999-0.8122992405822678j), (-2.4999999999999956-3.440954801177935j)]
[(2.0000019999999994+5.9999999995064e-06j), (-2.1873894540114236e-06-2.9999907158676136j), (4.999996876255548+5.070678220420177e-06j), (-7.704864037894055e-06-6.999998252517274j), (11.000004936866294+2.3649529490299415e-07j), (1.217868931480126e-06-12.99999945557741j), (17.00000486126272+7.116788791061701e-06j)]