@theofanidis
in your results (without reduction modulo 17) the 4th and the 6th value are in both examples approximately 2 times the value, that it should be. maybe you copy and paste or calculate something twice there.
the correct values:
[1,12,11,3,4,16,15,6,7,9,5,10,14,2,7,11,9,3,6,0,4,1,16,5,15,12,2,7,3,7,6,13,3,14,4,11,16,8,10]
->[10,13,9,6,6,6,16,6,9,7,5,7,16]
(=[387848,408608,397792,397534,369892,375332,398088,390785,388085,409469,376453,394883,396031] mod 17)
[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0,1,2]
->[7,1,8,6,4,9,9,5,5,0,5,14,1]
(=[392724,414971,394476,389289,395934,381948,419535,376062,412306,394672,397176,386288,391596] mod 17)
here are some further examples to test your equations:
[6,3,15,9,9,7,2,7,6,0,11,14,9,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9]
->[1,1,1,1,1,1,1,1,1,1,1,1,1]
(=[332334,319125,330702,325568,323715,299354,317578,303961,321845,330668,321301,328917,327727] mod 17)
[15,10,13,11,10,16,6,10,11,14,6,13,15,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0,1,2,3,4,5,6,7,8,9]
->[16,16,16,16,16,16,16,16,16,16,16,16,16]
(=[462688,451655,462773,449292,455480,428314,444294,440605,452777,457061,454868,449122,464218] mod 17)
[13,8,9,0,8,5,5,2,16,10,7,9,15,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
->[1,2,3,4,5,6,7,8,9,10,11,12,13]
(=[81193,71980,71794,75705,74074,79770,80723,74332,77036,72124,81067,74880,76326] mod 17)
best regards,
jomandi