POLARLAC-256 conjugate NTT rejection trace for one r
====================================================

Parameters:
  RL_KEM_N     = 512
  CONJ_NTT_Q   = 769
  CONJ_NTT_T   = 3025
  seed pattern = seed[i] = (uint8_t)(0x51 + 13 * 28 + i)
  nonce        = 28

Decision value:
  folded_abs_sum = |x[0]| + |x[N/2]| + 2 * sum_{i=1}^{N/2-1} |x[i]|
  folded_abs_sum = 6331
  full_abs_sum   = sum_{i=0}^{N-1} |x[i]| = 6331
  pass_current_CONJ_NTT_T = no

r coefficient domain[512] = {
     0,      0,      0,      0,      0,      0,      1,      1,      1,      0,      1,      0,      0,     -1,      0,      0,
     0,      1,     -1,      1,      0,      1,      0,      1,      1,      0,      0,      0,     -1,      1,     -1,     -1,
     0,      0,      0,      0,      0,      0,      0,      1,     -1,      1,      1,     -1,      0,      0,     -1,      1,
     0,      1,      1,      0,     -1,     -1,      0,      1,      1,     -1,      1,      1,      1,      1,     -1,      0,
     0,      0,      0,      1,      0,     -1,     -1,      0,     -1,      0,      0,      0,      0,      0,      1,     -1,
    -1,      0,     -1,      1,      0,      0,      1,      1,      1,     -1,      0,      1,      1,      1,     -1,     -1,
     0,      0,     -1,      0,     -1,      0,      1,      1,      0,      0,      1,      0,      0,     -1,      0,     -1,
     0,     -1,      1,      0,      0,      0,      0,      0,      0,      1,      0,      0,      0,      0,     -1,     -1,
    -1,      0,      0,      0,      1,     -1,      0,     -1,      0,      0,      0,      0,      1,      1,     -1,      1,
     0,     -1,     -1,      0,      1,     -1,      0,     -1,      0,     -1,      0,     -1,     -1,      0,      0,     -1,
    -1,      0,      1,     -1,      0,      1,     -1,      0,     -1,      1,      1,     -1,      0,      1,      0,      1,
    -1,      0,     -1,      0,      1,      0,     -1,      0,      0,      1,      0,     -1,      0,      1,      0,      0,
    -1,      0,      1,      0,      0,      0,      0,      0,      0,      1,      0,      0,      0,      0,     -1,      0,
     0,      0,      0,      1,      1,      0,      0,      0,     -1,     -1,      1,      1,     -1,      0,      0,     -1,
     0,     -1,      1,      1,      0,      0,      0,      1,     -1,     -1,      0,      1,      0,      0,      0,      0,
     1,      0,      1,      0,     -1,      0,      0,      0,      0,      0,      0,     -1,      1,      1,      0,      1,
     1,      1,     -1,      0,     -1,     -1,      1,      0,     -1,      0,      0,     -1,      1,     -1,      1,      0,
    -1,      1,      0,      0,      1,      0,     -1,     -1,      0,     -1,     -1,      0,      0,     -1,     -1,     -1,
     1,      0,      0,      0,      0,     -1,      0,      0,      1,      0,     -1,      0,      0,      0,      0,      1,
     1,      1,      1,      0,      0,     -1,      0,      0,     -1,      1,     -1,      0,      1,      1,      0,     -1,
     0,      0,      0,     -1,      0,      0,      1,      1,      0,      0,      0,      1,      0,     -1,      1,      1,
    -1,      1,     -1,      1,     -1,      1,      0,     -1,      1,     -1,      1,     -1,      0,     -1,      0,      0,
     0,      0,      0,      0,      1,      1,      0,     -1,      1,      0,      0,      0,      1,      0,     -1,     -1,
     0,      0,     -1,      0,      0,      0,     -1,      0,      0,      0,      0,     -1,      0,     -1,      0,      0,
    -1,      0,      0,      0,      0,     -1,     -1,      0,     -1,      1,     -1,     -1,      0,     -1,      1,      1,
     0,      1,      1,      0,      0,     -1,      0,      0,     -1,      0,      0,     -1,      0,      1,      0,      0,
     0,      0,     -1,     -1,     -1,      0,      0,     -1,      1,     -1,      0,      0,     -1,      1,      0,      0,
     0,     -1,      0,     -1,     -1,      0,     -1,     -1,      1,      0,      0,     -1,      0,      0,     -1,      1,
    -1,     -1,      0,     -1,      1,     -1,      0,      0,     -1,      0,      0,      0,      1,     -1,      0,      0,
     0,     -1,      1,     -1,      1,      0,      0,     -1,      0,     -1,     -1,      1,      1,     -1,      1,     -1,
    -1,     -1,      0,      0,     -1,      1,      0,      0,      1,      0,      0,      1,      0,      0,      0,      0,
     0,     -1,      1,     -1,     -1,     -1,     -1,     -1,      0,      0,      1,     -1,      1,     -1,     -1,      1
}

con_NTT(r)[512] = {
  -481,    872,    446,   -252,   -625,    138,     52,    -82,   -205,   1432,    306,   -144,   -417,    902,    460,     74,
   -74,    -26,   -328,   -275,    456,    456,    398,   -301,     -9,   1236,   -186,    292,    -29,    502,     -4,    360,
   590,    542,   -896,    -15,    912,   -218,   -466,   -563,    431,     47,   -125,   -371,      3,    109,    -73,   -143,
   607,    -53,    534,  -1358,     69,   -701,    164,   -628,    408,    553,   -563,   -460,     12,    177,    201,   -854,
 -1142,   -389,     -5,    383,   -604,    347,    387,    957,   -160,   -325,   -270,    899,    -66,  -1057,    272,    173,
  -538,   -659,    520,    348,   -948,  -1179,    614,    162,  -1066,   -579,    527,    916,   -676,  -1087,    -85,    778,
  -545,   -467,   -271,   -533,     11,   -687,   -341,    241,   -129,    409,   -455,   -432,   -493,   -247,   -981,   -656,
    64,    467,   -398,    834,    224,   1223,   -482,    512,   -184,    201,   -153,   -299,   -228,     45,   -783,    437,
  -994,    507,   -537,    491,   -714,   -261,   -365,   -261,    125,   -162,   -169,   -584,   -521,    -92,    171,     26,
   224,   -223,    484,   -494,   -524,   -527,    596,     86,   -683,     55,    -24,    440,   -281,    191,    620,    -40,
   652,    -48,   -280,    345,      8,      2,    -66,    295,   -725,    160,    809,   -130,   -171,   -454,     49,    370,
   709,    224,    352,   -164,    -53,   -154,    540,   -242,    579,     67,    606,    668,    881,    795,   1198,     26,
   648,    -60,   -565,   -788,    220,   -248,  -1039,   -152,    593,     68,   -442,    209,   1051,   -384,    298,   -549,
   845,     19,   -539,    405,   1075,   -249,   -193,     33,    153,   -415,   -310,   -494,    735,   -467,    -34,   -504,
   736,    140,    130,     30,    130,    232,   -418,    650,    833,    141,   -940,   -179,   1089,    175,   -812,   -297,
   333,    861,     -3,    243,    683,    217,   -143,     51,    539,    669,   -451,    462,    625,   1205,   -507,     48,
   246,     -7,     66,   -472,     62,     15,   -142,   -936,    642,   -453,    790,   -408,    690,     85,    270,   -132,
  -192,    247,     64,  -1017,     74,    635,    328,   -413,   -638,    939,    -19,   -573,   -380,    859,   -717,   -337,
   -41,    382,   -869,    -47,   -491,     36,   -395,    539,  -1043,     29,   -379,    395,   -569,   -691,   -697,   -163,
   322,   -493,     85,    148,   -422,  -1047,    -89,    128,   -268,   -375,    -48,    150,    216,   -721,    568,   -494,
   -99,   -168,    674,   -162,    249,   -476,   1414,   -172,   -256,   -498,    540,    403,   -990,  -1154,    932,    227,
   149,    336,    465,    143,   -477,     58,    -51,    163,    833,    336,    399,    -75,     63,   -394,   -293,    473,
  -539,    467,     93,     22,   -929,    493,   -483,    726,   -249,     21,   -592,    -42,   -523,    335,     82,   -686,
  -858,   -347,    208,   1106,  -1298,    377,     50,    452,  -1007,   -454,    -72,    324,  -1077,   -356,   -198,    730,
  -292,   -137,    -99,    437,     14,   -339,   -663,    445,   -116,   -259,  -1229,    459,    558,    275,   -573,    815,
     2,   -852,    251,    532,   -170,   -374,   -387,    -62,   -917,    -52,    -47,    564,   -767,   -550,     -5,    -38,
  -346,   -524,    948,    873,     16,   -466,    490,    305,    207,    164,    689,    663,    623,   -230,   1057,     83,
   363,   -575,    258,   -209,    255,     67,   -128,   -547,    881,    478,   -297,   -148,    361,    206,    295,     68,
   548,   -465,    564,    521,    548,     95,   -108,    475,    330,    524,    231,   -145,    190,    386,   -207,    317,
  -392,    352,    -39,   -350,   -490,   -220,   -201,    220,    124,    484,   -873,    -15,     62,     20,   -607,   -559,
  -443,    679,     48,  -1285,     65,    135,    508,  -1057,    610,    -37,    912,   -615,     84,    307,    844,   -687,
   923,   -705,     -2,   -863,    955,   -489,   -438,   -261,    223,    116,    114,   -192,    823,      2,    678,    256
}

adjoint(con_NTT(r))[512] = {
   823,   -265,    -59,     52,    223,    378,    112,     60,    955,     89,    114,     43,    923,    -35,   -148,    122,
    84,    284,    241,    238,    610,   -177,    330,   -322,     65,    379,    -17,    327,   -443,    122,    -65,    218,
    62,    108,    325,    230,    124,   -212,   -342,   -183,   -490,     16,    279,    -16,   -392,    375,   -123,    282,
   190,    293,     27,    284,    330,    282,     97,   -266,    548,   -104,   -305,    133,    548,   -268,    287,   -118,
   361,    107,     91,   -377,    881,   -129,    162,    -51,    255,   -307,    274,    181,    363,   -147,    336,    199,
   623,   -282,    -52,   -108,    207,    344,     71,   -184,     16,   -153,    145,    380,   -346,     32,   -359,    312,
  -767,    335,   -219,   -251,   -917,   -249,    213,   -337,   -170,    110,   -132,     93,      2,    -98,    -26,     76,
   558,    258,    230,    205,   -116,    301,    273,    249,     14,    126,    386,    260,   -292,   -300,    346,    -96,
 -1077,    359,     48,     63,  -1007,   -271,   -367,    356,  -1298,   -104,   -134,     97,   -858,   -358,    -27,   -284,
  -523,   -131,    130,    231,   -249,   -196,     57,     98,   -929,    119,    210,    120,   -539,     43,      7,    -31,
    63,    -31,    372,   -379,    833,     78,    231,    235,   -477,    225,    274,    382,    149,    331,    146,     41,
  -990,    192,   -228,    213,   -256,    191,    109,     96,    249,   -381,     83,    269,    -99,     28,   -107,     86,
   216,     47,      2,     11,   -268,    254,     11,    134,   -422,    232,     79,    169,    322,    -76,   -106,   -308,
  -569,    102,   -163,    272,  -1043,    200,    178,   -180,   -491,    314,    -96,   -330,    -41,    210,    365,    -87,
  -380,     29,   -203,    -26,   -638,    -63,   -296,    220,     74,    156,    -55,    -76,   -192,    221,     67,   -186,
   690,   -240,   -348,   -195,    642,   -167,   -178,   -225,     62,    -50,     68,    -83,    246,   -356,   -250,    -90,
   625,     55,    140,     51,    539,   -241,    -76,   -334,    683,    318,    194,     -4,    333,    249,   -117,   -257,
  1089,    382,    177,     -5,    833,    -93,     83,     26,    130,    -57,   -323,   -380,    736,   -163,    319,   -248,
   735,    -41,    220,     -9,    153,    -30,   -106,    255,   1075,   -377,     61,    258,    845,   -127,   -262,   -249,
  1051,   -307,   -297,   -345,    593,   -362,    313,     11,    220,    104,   -220,   -316,    648,    -13,    261,   -122,
   881,    289,   -230,    289,    579,    -90,   -229,    113,    -53,    198,   -302,    126,    709,   -274,    288,   -376,
  -171,    125,    214,    387,   -725,    -60,   -159,    133,      8,    160,   -114,    353,    652,    243,    204,     13,
  -281,    -92,   -112,    -99,   -683,   -243,    209,    258,   -524,    348,    -92,    -58,    224,     -4,    116,   -117,
  -521,    113,   -292,    310,    125,    172,    350,    290,   -714,    173,   -256,    173,   -994,   -199,   -188,   -265,
  -228,    135,    -36,   -104,   -184,   -110,    -46,    362,    224,    326,    384,    235,     64,    256,    -65,    -30,
  -493,   -174,    272,   -307,   -129,   -148,   -163,    133,     11,    149,    -80,   -195,   -545,   -114,    359,    193,
  -676,   -163,    -84,    120,  -1066,     99,   -367,   -233,   -948,   -345,     88,    332,   -538,    143,    196,   -136,
   -66,   -183,     99,   -331,   -160,   -347,     70,   -286,   -604,    168,   -325,    261,  -1142,   -195,    119,    184,
    12,   -159,    186,    313,    408,      1,    257,   -374,     69,    312,    232,    265,    607,    158,   -249,    150,
     3,    236,   -342,   -153,    431,   -295,   -373,   -315,    912,    283,    308,    253,    590,     99,    223,    114,
   -29,   -325,   -210,    209,     -9,     50,   -232,   -294,    456,     49,    275,   -110,    -74,     -9,   -268,    -40,
  -417,      1,     27,   -258,   -205,    189,     79,     43,   -625,    -56,     -2,    113,   -481,   -128,    -42,    211
}

adjoint(con_NTT(r)) * con_NTT(r)[512] = {
   314,    544,   -265,    500,   -145,    308,   -272,     32,   -268,    495,   -531,    519,    667,    264,   -524,    131,
    10,    459,   -510,    -10,    443,   -973,    193,   -502,    -45,   -372,    836,   -194,    230,    266,   -480,    -48,
   251,   -103,    431,    254,   -230,    334,     99,    358,    101,   -181,    167,   -819,    275,  -1049,   -106,   -261,
  -419,    -55,    510,    163,    466,   -537,   -112,   -601,    -27,    418,    204,    115,    132,    477,   -893,   -492,
  -168,    504,    670,    283,    513,   -581,    -37,    439,    684,   -396,   -933,   -812,   -115,    -30,    995,   -172,
   -38,    -89,     73,    186,    428,   -856,     22,   -606,     62,   -592,   -202,   -435,    361,   -252,   -641,    313,
   147,   -847,    352,    735,    310,    -99,    341,   -522,   -232,   1083,      6,    376,    150,   -351,    447,    346,
     4,    133,    325,    267,     37,   -480,    317,   -563,   -486,   -235,   1064,   -368,    192,   -112,    -75,   -669,
   -46,   -256,   -169,   -167,   -408,    676,     35,   1423,     60,   -451,    549,   -537,     92,   -319,   1073,    171,
   170,     48,   -497,   -773,   -109,   -462,    467,    510,   -356,    828,   -283,    464,     35,    630,   1076,    723,
    49,    107,    556,    -36,   -218,   -134,     54,     94,     79,   -462,    -95,   -876,   -459,    115,    388,    173,
   523,    -87,    -24,   -108,   -226,    924,    545,    887,    -59,   -697,    252,   -455,   -124,    134,   -704,    482,
   284,     47,    149,    154,    173,    172,     47,    938,    373,    509,   -848,   -453,   -110,   1154,   -482,    673,
  -430,    334,   -943,    183,   -114,   -109,    567,   -716,   -158,     93,   -561,    -99,    387,   -480,     44,   -788,
    15,   1047,   -489,    869,    -97,   -268,    -25,    593,     62,   -769,   -109,  -1472,   -272,    516,   -290,    610,
  -188,    367,   -887,   -702,   -241,    173,    150,    839,     74,     44,   -518,    -11,    706,   -882,    105,  -1861,
   -63,   -290,   -120,  -1299,     74,   -452,   -592,    270,   -241,    346,    302,    174,   -188,    306,   -757,    471,
  -272,   -347,    997,    183,     62,    -86,    -91,      0,    -97,   -136,   -264,    492,     15,    482,    273,    -75,
   387,    -58,   -149,    437,   -158,   -143,    215,    647,   -114,     47,     24,    150,   -430,    273,   -310,     -6,
  -110,    106,    372,    424,    373,   -356,   -680,   -223,    173,    451,   -275,    368,    284,    -97,   -748,   -494,
  -124,   -262,   -431,    543,    -59,   -710,    -80,   -682,   -226,    253,   -376,   -756,    523,    401,   -509,   -211,
  -459,    630,    235,   1130,     79,   -286,   -103,   -509,   -218,    442,    303,   -581,     49,   -567,    298,   -814,
    35,     48,    783,    680,   -356,    317,    574,     95,   -109,    329,   -614,    670,    170,   -109,    491,   -999,
    92,    477,     79,    122,     60,   -121,    128,   -199,   -408,    583,    625,    866,    -46,     16,   -168,    287,
   192,    367,    -83,   -288,   -486,   -372,    340,     55,     37,      5,    325,    175,      4,   -167,    511,    441,
   150,    209,   -559,    -72,   -232,   -156,   -297,   -163,    310,    191,    849,     76,    147,    238,   -926,   -223,
   361,     56,   -353,    -50,     62,   -701,   -497,  -1152,    428,   -162,   -588,    228,    -38,   -202,   -286,    138,
  -115,   -187,    970,    334,    684,    239,   -698,   -410,    513,   -164,    196,    168,   -168,   -122,    203,    155,
   132,    -88,    528,    648,    -27,    192,    695,    -31,    466,  -1019,   -346,  -1041,   -419,     32,    -65,    678,
   275,    -64,   -465,   -764,    101,   -303,   -972,    395,   -230,    671,    192,    974,    251,    323,    539,   -243,
   230,   -213,    177,   -646,    -45,    188,    -57,    305,    443,   -115,   -711,   -396,     10,    517,   -548,   -122,
   667,   -549,   -880,    -38,   -268,   -537,    -24,    648,   -145,    472,   -167,    -71,    314,   -454,    256,    435
}

INTT(product)[512] = {
   263,    -12,      9,     14,    -10,     14,    -25,      2,      7,    -11,     21,      1,    -15,     11,     -4,     18,
    20,      4,     20,      1,      3,     -2,     -1,      3,    -14,     -6,     31,     -5,     33,     10,      6,     17,
   -11,      5,     -1,     -9,     16,     -2,     30,      0,    -19,     16,      5,    -13,     12,    -10,     11,      6,
    -5,     21,    -24,     25,      7,    -15,     42,    -18,      9,     11,      2,      5,    -17,     30,      7,    -29,
    26,     13,      0,     10,    -12,     19,      2,     -4,      4,      3,     -1,    -19,     14,      7,     -1,    -12,
    20,    -11,     26,     17,    -10,      0,     -7,     28,     -2,      4,      4,    -14,      1,     -7,     -5,     20,
     6,      4,     26,     11,     -3,    -13,     -4,     12,    -16,      2,     26,    -22,     19,    -11,     -1,      2,
   -10,     14,     -5,     21,     17,    -24,      7,     -7,    -10,    -11,     -6,     19,     -2,     28,     17,     -6,
     1,    -11,      2,      9,     -9,     12,     40,    -12,     13,     -6,     -6,    -17,    -16,     23,     -6,     -7,
     8,    -13,     -3,     -1,     -5,     -7,      2,     26,     21,      8,     15,    -21,     19,     -3,    -35,     10,
     8,     -6,     13,     -5,     12,      8,    -30,     25,    -34,      6,      8,     -9,     30,    -30,     -2,     -5,
   -22,      4,    -17,     10,      7,     -9,     23,    -13,      5,     -3,     -1,     14,     12,     -3,      1,     -7,
     5,     -6,    -19,     18,    -18,    -23,     16,    -10,     -7,    -12,     -5,     20,    -25,      6,    -16,     -8,
     7,    -19,     14,    -12,     11,     14,     17,    -19,      4,    -11,      7,    -13,      8,     34,    -37,     21,
     2,     -9,     -7,    -34,     11,     15,      1,    -18,     -1,      7,     -1,     -9,     19,    -13,     11,     16,
     1,     11,     -7,     -6,     -4,    -21,     -7,      3,     -2,     17,      8,      7,     10,    -20,      9,     -8,
     0,      8,     -9,     20,    -10,     -7,     -8,    -17,      2,     -3,      7,     21,      4,      6,      7,    -11,
    -1,    -16,    -11,     13,    -19,      9,      1,     -7,      1,     18,     -1,    -15,    -11,     34,      7,      9,
    -2,    -21,     37,    -34,     -8,     13,     -7,     11,     -4,     19,    -17,    -14,    -11,     12,    -14,     19,
    -7,      8,     16,     -6,     25,    -20,      5,     12,      7,     10,    -16,     23,     18,    -18,     19,      6,
    -5,      7,     -1,      3,    -12,    -14,      1,      3,     -5,     13,    -23,      9,     -7,    -10,     17,     -4,
    22,      5,      2,     30,    -30,      9,     -8,     -6,     34,    -25,     30,     -8,    -12,      5,    -13,      6,
    -8,    -10,     35,      3,    -19,     21,    -15,     -8,    -21,    -26,     -2,      7,      5,      1,      3,     13,
    -8,      7,      6,    -23,     16,     17,      6,      6,    -13,     12,    -40,    -12,      9,     -9,     -2,     11,
    -1,      6,    -17,    -28,      2,    -19,      6,     11,     10,      7,     -7,     24,    -17,    -21,      5,    -14,
    10,     -2,      1,     11,    -19,     22,    -26,     -2,     16,    -12,      4,     13,      3,    -11,    -26,     -4,
    -6,    -20,      5,      7,     -1,     14,     -4,     -4,      2,    -28,      7,      0,     10,    -17,    -26,     11,
   -20,     12,      1,     -7,    -14,     19,      1,     -3,     -4,      4,     -2,    -19,     12,    -10,      0,    -13,
   -26,     29,     -7,    -30,     17,     -5,     -2,    -11,     -9,     18,    -42,     15,     -7,    -25,     24,    -21,
     5,     -6,    -11,     10,    -12,     13,     -5,    -16,     19,      0,    -30,      2,    -16,      9,      1,     -5,
    11,    -17,     -6,    -10,    -33,      5,    -31,      6,     14,     -3,      1,      2,     -3,     -1,    -20,     -4,
   -20,    -18,      4,    -11,     15,     -1,    -21,     11,     -7,     -2,     25,    -14,     10,    -14,     -9,     12
}

