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primitivepolynomials.c

/* -*- mode: c; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

// This file contains 21200 polinomials, that is all primitive polynomials
// modulo two up to degree 18. Another version does contain
// 8129334 polinomials, that is all primitive polynomials
// modulo two up to degree 27. Both are slightly edited versions of
// PrimitivePolynomialsModuloTwoUpToDegree27.c
//
// © 2002 "Monte Carlo Methods in Finance"
//
//
// =========================================================================
// Copyright (C) 2002 Peter Jäckel "Monte Carlo Methods in Finance".
// All rights reserved.
//
// Permission to use, copy, modify, and distribute this software is freely
// granted, provided that this notice is preserved.
// =========================================================================

#include <ql/RandomNumbers/primitivepolynomials.h>

static const long PrimitivePolynomialDegree01[]={
0, // x+1 (1)(1)
-1 };

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_01
static const long PrimitivePolynomialDegree02[]={
1, // x^2+x+1 (1)1(1)
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_02
static const long PrimitivePolynomialDegree03[]={
1, // x^3    +x+1 (1)01(1)
2, // x^3+x^2  +1 (1)10(1)
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_03
static const long PrimitivePolynomialDegree04[]={
1, // x^4+       +x+1 (1)001(1)
4, // x^4+x^3+     +1 (1)100(1)
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_04
static const long PrimitivePolynomialDegree05[]={
2,  // x^5        +x^2  +1 (1)0010(1)
4,  // x^5    +x^3      +1 (1)0100(1)
7,  // x^5    +x^3+x^2+x+1 (1)0111(1)
11, // x^5+x^4    +x^2+x+1 (1)1011(1)
13, // x^5+x^4+x^3    +x+1 (1)1101(1)
14, // x^5+x^4+x^3+x^2  +1 (1)1110(1)
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_05
static const long PrimitivePolynomialDegree06[]={
1,  // x^6                +x+1 (1)00001(1)
13, // x^6    +x^4+x^3    +x+1 (1)01101(1)
16, // x^6+x^5              +1 (1)10000(1)
19, // x^6            +x^2+x+1 (1)10011(1)
22, // x^6+x^5    +x^3+x^2  +1 (1)10110(1)
25, // x^6+x^5+x^4        +x+1 (1)11001(1)
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_06
static const long PrimitivePolynomialDegree07[]={
1,  // x^7                    +x+1 (1)000001(1)
4,  // x^7            +x^3      +1 (1)000100(1)
7,  // x^7            +x^3+x^2+x+1 (1)000111(1)
8,  // x^7        +x^4          +1 (1)001000(1)
14, // x^7        +x^4+x^3+x^2  +1 (1)001110(1)
19, // x^7    +x^5        +x^2+x+1 (1)010011(1)
21, // x^7    +x^5    +x^3    +x+1 (1)010101(1)
28, // x^7    +x^5+x^4+x^3      +1 (1)011100(1)
31, // x^7    +x^5+x^4+x^3+x^2+x+1 (1)011111(1)
32, // x^7+x^6                  +1 (1)100000(1)
37, // x^7+x^6        +x^3    +x+1 (1)100101(1)
41, // x^7+x^6    +x^4        +x+1 (1)101001(1)
42, // x^7+x^6    +x^4    +x^2  +1 (1)101010(1)
// 32 polynomials so far ... let's go ahead
50, // x^7+x^6+x^5        +x^2  +1 (1)110010(1)
55, // x^7+x^6+x^5    +x^3+x^2+x+1 (1)110111(1)
56, // x^7+x^6+x^5+x^4          +1 (1)111000(1)
59, // x^7+x^6+x^5+x^4    +x^2+x+1 (1)111011(1)
62, // x^7+x^6+x^5+x^4+x^3+x^2  +1 (1)111110(1)
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_07
static const long PrimitivePolynomialDegree08[]={
14,
21,
22,
38,
47,
49,
50,
52,
56,
67,
70,
84,
97,
103,
115,
122,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_08
static const long PrimitivePolynomialDegree09[]={
8,
13,
16,
22,
25,
44,
47,
52,
55,
59,
62,
67,
74,
81,
82,
87,
91,
94,
103,
104,
109,
122,
124,
137,
138,
143,
145,
152,
157,
167,
173,
176,
181,
182,
185,
191,
194,
199,
218,
220,
227,
229,
230,
234,
236,
241,
244,
253,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_09
static const long PrimitivePolynomialDegree10[]={
4,
13,
19,
22,
50,
55,
64,
69,
98,
107,
115,
121,
127,
134,
140,
145,
152,
158,
161,
171,
181,
194,
199,
203,
208,
227,
242,
251,
253,
265,
266,
274,
283,
289,
295,
301,
316,
319,
324,
346,
352,
361,
367,
382,
395,
398,
400,
412,
419,
422,
426,
428,
433,
446,
454,
457,
472,
493,
505,
508,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_10
static const long PrimitivePolynomialDegree11[]={
2,
11,
21,
22,
35,
49,
50,
56,
61,
70,
74,
79,
84,
88,
103,
104,
112,
115,
117,
122,
134,
137,
146,
148,
157,
158,
162,
164,
168,
173,
185,
186,
191,
193,
199,
213,
214,
220,
227,
236,
242,
251,
256,
259,
265,
266,
276,
292,
304,
310,
316,
319,
322,
328,
334,
339,
341,
345,
346,
362,
367,
372,
375,
376,
381,
385,
388,
392,
409,
415,
416,
421,
428,
431,
434,
439,
446,
451,
453,
457,
458,
471,
475,
478,
484,
493,
494,
499,
502,
517,
518,
524,
527,
555,
560,
565,
569,
578,
580,
587,
589,
590,
601,
607,
611,
614,
617,
618,
625,
628,
635,
641,
647,
654,
659,
662,
672,
675,
682,
684,
689,
695,
696,
713,
719,
724,
733,
734,
740,
747,
749,
752,
755,
762,
770,
782,
784,
787,
789,
793,
796,
803,
805,
810,
815,
824,
829,
830,
832,
841,
847,
849,
861,
871,
878,
889,
892,
901,
908,
920,
923,
942,
949,
950,
954,
961,
968,
971,
973,
979,
982,
986,
998,
1001,
1010,
1012,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_11
static const long PrimitivePolynomialDegree12[]={
41,
52,
61,
62,
76,
104,
117,
131,
143,
145,
157,
167,
171,
176,
181,
194,
217,
236,
239,
262,
283,
286,
307,
313,
319,
348,
352,
357,
391,
398,
400,
412,
415,
422,
440,
460,
465,
468,
515,
536,
539,
551,
558,
563,
570,
595,
598,
617,
647,
654,
678,
713,
738,
747,
750,
757,
772,
803,
810,
812,
850,
862,
906,
908,
929,
930,
954,
964,
982,
985,
991,
992,
1067,
1070,
1096,
1099,
1116,
1143,
1165,
1178,
1184,
1202,
1213,
1221,
1240,
1246,
1252,
1255,
1267,
1293,
1301,
1305,
1332,
1349,
1384,
1392,
1402,
1413,
1417,
1423,
1451,
1480,
1491,
1503,
1504,
1513,
1538,
1544,
1547,
1555,
1574,
1603,
1615,
1618,
1629,
1634,
1636,
1639,
1657,
1667,
1681,
1697,
1704,
1709,
1722,
1730,
1732,
1802,
1804,
1815,
1826,
1832,
1843,
1849,
1863,
1905,
1928,
1933,
1939,
1976,
1996,
2013,
2014,
2020,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_12
static const long PrimitivePolynomialDegree13[]={
13,
19,
26,
41,
50,
55,
69,
70,
79,
82,
87,
93,
94,
97,
100,
112,
121,
134,
138,
148,
151,
157,
161,
179,
181,
188,
196,
203,
206,
223,
224,
227,
230,
239,
241,
248,
253,
268,
274,
283,
286,
289,
301,
302,
316,
319,
324,
331,
333,
345,
351,
358,
375,
379,
381,
386,
403,
405,
419,
426,
428,
439,
440,
446,
451,
454,
458,
465,
468,
472,
475,
477,
496,
502,
508,
517,
521,
527,
530,
532,
542,
552,
555,
560,
566,
575,
577,
589,
590,
602,
607,
608,
611,
613,
625,
644,
651,
654,
656,
662,
668,
681,
682,
689,
696,
699,
707,
709,
714,
716,
719,
727,
734,
738,
743,
747,
757,
769,
770,
776,
790,
799,
805,
809,
812,
820,
827,
829,
835,
841,
844,
856,
859,
862,
865,
885,
890,
905,
916,
925,
935,
939,
942,
949,
953,
956,
961,
968,
976,
988,
995,
997,
1007,
1015,
1016,
1027,
1036,
1039,
1041,
1048,
1053,
1054,
1058,
1075,
1082,
1090,
1109,
1110,
1119,
1126,
1130,
1135,
1137,
1140,
1149,
1156,
1159,
1160,
1165,
1173,
1178,
1183,
1184,
1189,
1194,
1211,
1214,
1216,
1225,
1231,
1239,
1243,
1246,
1249,
1259,
1273,
1274,
1281,
1287,
1294,
1296,
1305,
1306,
1318,
1332,
1335,
1336,
1341,
1342,
1362,
1364,
1368,
1378,
1387,
1389,
1397,
1401,
1408,
1418,
1425,
1426,
1431,
1435,
1441,
1444,
1462,
1471,
1474,
1483,
1485,
1494,
1497,
1516,
1522,
1534,
1543,
1552,
1557,
1558,
1567,
1568,
1574,
1592,
1605,
1606,
1610,
1617,
1623,
1630,
1634,
1640,
1643,
1648,
1651,
1653,
1670,
1676,
1684,
1687,
1691,
1693,
1698,
1709,
1715,
1722,
1732,
1735,
1747,
1749,
1754,
1777,
1784,
1790,
1795,
1801,
1802,
1812,
1828,
1831,
1837,
1838,
1840,
1845,
1863,
1864,
1867,
1870,
1877,
1881,
1884,
1903,
1917,
1918,
1922,
1924,
1928,
1931,
1951,
1952,
1957,
1958,
1964,
1967,
1970,
1972,
1994,
2002,
2007,
2008,
2023,
2030,
2035,
2038,
2042,
2047,
2051,
2058,
2060,
2071,
2084,
2087,
2099,
2108,
2111,
2120,
2128,
2138,
2143,
2144,
2153,
2156,
2162,
2167,
2178,
2183,
2202,
2211,
2214,
2223,
2225,
2232,
2237,
2257,
2260,
2267,
2274,
2276,
2285,
2288,
2293,
2294,
2297,
2303,
2308,
2311,
2318,
2323,
2332,
2341,
2345,
2348,
2354,
2368,
2377,
2380,
2383,
2388,
2395,
2397,
2401,
2411,
2413,
2419,
2435,
2442,
2455,
2472,
2478,
2490,
2507,
2509,
2517,
2524,
2528,
2531,
2538,
2545,
2546,
2555,
2557,
2564,
2573,
2579,
2592,
2598,
2607,
2612,
2619,
2621,
2627,
2633,
2636,
2642,
2654,
2660,
2669,
2675,
2684,
2694,
2703,
2706,
2712,
2715,
2722,
2727,
2734,
2742,
2745,
2751,
2766,
2768,
2780,
2790,
2794,
2796,
2801,
2804,
2807,
2816,
2821,
2831,
2834,
2839,
2845,
2852,
2856,
2861,
2873,
2874,
2888,
2893,
2894,
2902,
2917,
2921,
2922,
2929,
2935,
2946,
2951,
2957,
2960,
2966,
2972,
2976,
2979,
2985,
3000,
3003,
3013,
3018,
3020,
3025,
3042,
3047,
3048,
3051,
3054,
3056,
3065,
3073,
3074,
3083,
3086,
3091,
3097,
3109,
3116,
3124,
3128,
3153,
3160,
3165,
3172,
3175,
3184,
3193,
3196,
3200,
3203,
3205,
3209,
3224,
3239,
3251,
3254,
3265,
3266,
3275,
3280,
3283,
3286,
3301,
3302,
3305,
3319,
3323,
3326,
3331,
3348,
3351,
3358,
3368,
3374,
3376,
3379,
3385,
3386,
3396,
3420,
3423,
3430,
3433,
3434,
3439,
3442,
3444,
3453,
3464,
3477,
3478,
3482,
3487,
3497,
3500,
3505,
3506,
3511,
3512,
3515,
3525,
3532,
3538,
3540,
3547,
3549,
3560,
3571,
3577,
3583,
3590,
3593,
3594,
3599,
3601,
3602,
3613,
3623,
3630,
3638,
3649,
3655,
3662,
3667,
3669,
3676,
3683,
3700,
3709,
3710,
3713,
3723,
3725,
3728,
3734,
3737,
3738,
3744,
3750,
3762,
3764,
3774,
3776,
3786,
3800,
3803,
3809,
3816,
3821,
3827,
3829,
3836,
3842,
3844,
3847,
3853,
3861,
3871,
3872,
3881,
3890,
3892,
3909,
3921,
3934,
3938,
3947,
3950,
3952,
3964,
3974,
3980,
3983,
3986,
3995,
3998,
4001,
4002,
4004,
4008,
4011,
4016,
4033,
4036,
4040,
4053,
4058,
4081,
4091,
4094,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_13
static const long PrimitivePolynomialDegree14[]={
21,
28,
41,
47,
61,
84,
87,
93,
94,
103,
117,
121,
134,
137,
157,
161,
205,
206,
211,
214,
218,
234,
236,
248,
262,
299,
304,
319,
322,
334,
355,
357,
358,
369,
372,
375,
388,
400,
415,
446,
451,
458,
471,
484,
501,
502,
517,
545,
569,
617,
618,
623,
625,
637,
661,
668,
684,
695,
716,
719,
722,
731,
738,
747,
755,
761,
767,
775,
782,
787,
794,
803,
812,
817,
824,
829,
850,
866,
871,
877,
920,
935,
959,
979,
992,
1010,
1012,
1015,
1033,
1036,
1053,
1057,
1069,
1072,
1075,
1087,
1089,
1137,
1166,
1174,
1180,
1204,
1211,
1219,
1236,
1255,
1264,
1306,
1330,
1341,
1344,
1347,
1349,
1361,
1380,
1390,
1404,
1435,
1444,
1453,
1461,
1462,
1465,
1468,
1474,
1483,
1488,
1493,
1500,
1509,
1510,
1514,
1519,
1528,
1533,
1540,
1550,
1567,
1571,
1573,
1578,
1598,
1606,
1618,
1630,
1634,
1640,
1643,
1654,
1679,
1688,
1698,
1703,
1704,
1722,
1735,
1750,
1753,
1760,
1789,
1792,
1802,
1819,
1825,
1828,
1832,
1845,
1846,
1857,
1869,
1897,
1906,
1908,
1911,
1934,
1962,
1967,
1972,
1975,
1999,
2004,
2011,
2013,
2037,
2051,
2063,
2066,
2094,
2128,
2154,
2164,
2198,
2217,
2220,
2223,
2238,
2245,
2252,
2258,
2264,
2280,
2285,
2293,
2294,
2298,
2303,
2306,
2311,
2326,
2354,
2373,
2380,
2385,
2392,
2401,
2402,
2408,
2419,
2450,
2452,
2477,
2509,
2510,
2515,
2524,
2527,
2531,
2552,
2561,
2567,
2571,
2586,
2588,
2595,
2607,
2621,
2630,
2639,
2653,
2670,
2672,
2700,
2711,
2715,
2748,
2751,
2753,
2754,
2760,
2774,
2784,
2793,
2804,
2811,
2822,
2826,
2836,
2839,
2840,
2893,
2901,
2902,
2905,
2912,
2915,
2918,
2939,
2965,
2966,
2975,
2988,
2993,
3006,
3017,
3031,
3038,
3041,
3042,
3051,
3073,
3088,
3097,
3098,
3103,
3104,
3146,
3148,
3153,
3159,
3182,
3187,
3189,
3199,
3239,
3263,
3271,
3275,
3278,
3280,
3283,
3290,
3311,
3316,
3343,
3346,
3357,
3358,
3361,
3362,
3364,
3386,
3418,
3424,
3433,
3434,
3436,
3463,
3467,
3477,
3484,
3505,
3508,
3515,
3532,
3553,
3554,
3568,
3573,
3587,
3589,
3596,
3608,
3620,
3630,
3644,
3649,
3664,
3679,
3680,
3685,
3686,
3698,
3714,
3726,
3737,
3767,
3782,
3786,
3793,
3796,
3805,
3815,
3841,
3847,
3853,
3862,
3875,
3902,
3904,
3916,
3947,
3949,
3955,
3962,
3971,
3980,
3985,
3998,
4001,
4002,
4016,
4021,
4026,
4043,
4079,
4102,
4106,
4119,
4126,
4147,
4149,
4164,
4174,
4181,
4185,
4188,
4202,
4228,
4232,
4246,
4252,
4256,
4286,
4303,
4306,
4311,
4317,
4342,
4346,
4377,
4401,
4407,
4414,
4422,
4431,
4434,
4436,
4443,
4459,
4461,
4462,
4473,
4497,
4504,
4507,
4525,
4534,
4538,
4548,
4552,
4560,
4575,
4599,
4612,
4619,
4640,
4643,
4677,
4687,
4723,
4730,
4736,
4741,
4763,
4765,
4770,
4781,
4808,
4822,
4828,
4831,
4842,
4855,
4859,
4867,
4870,
4881,
4893,
4910,
4917,
4929,
4939,
4947,
4949,
4954,
4972,
4975,
5000,
5005,
5029,
5039,
5044,
5051,
5056,
5073,
5096,
5128,
5134,
5161,
5179,
5193,
5199,
5202,
5204,
5218,
5247,
5260,
5271,
5301,
5305,
5319,
5326,
5328,
5333,
5364,
5376,
5399,
5416,
5421,
5427,
5429,
5430,
5434,
5441,
5451,
5465,
5466,
5471,
5477,
5492,
5495,
5505,
5515,
5525,
5529,
5532,
5539,
5541,
5556,
5566,
5568,
5574,
5595,
5602,
5611,
5616,
5622,
5628,
5655,
5662,
5675,
5689,
5722,
5724,
5728,
5731,
5746,
5764,
5771,
5781,
5801,
5809,
5810,
5812,
5841,
5848,
5853,
5854,
5858,
5892,
5907,
5910,
5913,
5920,
5929,
5949,
5952,
5955,
5962,
5975,
5985,
5997,
5998,
6012,
6016,
6026,
6036,
6040,
6045,
6055,
6059,
6088,
6115,
6124,
6127,
6132,
6146,
6158,
6169,
6206,
6228,
6237,
6244,
6247,
6256,
6281,
6282,
6284,
6296,
6299,
6302,
6325,
6349,
6352,
6362,
6383,
6386,
6395,
6397,
6415,
6424,
6429,
6439,
6451,
6489,
6496,
6502,
6511,
6514,
6520,
6523,
6529,
6532,
6547,
6549,
6598,
6601,
6610,
6622,
6632,
6655,
6665,
6666,
6695,
6701,
6709,
6710,
6741,
6745,
6758,
6767,
6772,
6782,
6797,
6800,
6843,
6845,
6860,
6865,
6878,
6887,
6888,
6901,
6906,
6940,
6947,
6953,
6954,
6959,
6961,
6964,
6991,
6993,
6999,
7016,
7029,
7036,
7045,
7076,
7083,
7094,
7097,
7123,
7130,
7139,
7145,
7146,
7178,
7186,
7192,
7198,
7222,
7269,
7270,
7276,
7287,
7307,
7315,
7334,
7340,
7351,
7352,
7357,
7360,
7363,
7384,
7396,
7403,
7406,
7425,
7437,
7445,
7450,
7455,
7461,
7466,
7488,
7494,
7515,
7517,
7521,
7536,
7546,
7569,
7591,
7592,
7598,
7612,
7623,
7632,
7637,
7644,
7657,
7665,
7672,
7682,
7699,
7702,
7724,
7749,
7753,
7754,
7761,
7771,
7777,
7784,
7804,
7807,
7808,
7818,
7835,
7842,
7865,
7868,
7880,
7883,
7891,
7897,
7907,
7910,
7924,
7933,
7934,
7942,
7948,
7959,
7984,
7994,
7999,
8014,
8021,
8041,
8049,
8050,
8068,
8080,
8095,
8102,
8106,
8120,
8133,
8134,
8143,
8162,
8168,
8179,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_14
static const long PrimitivePolynomialDegree15[]={
1,
8,
11,
22,
26,
47,
59,
64,
67,
73,
82,
97,
103,
110,
115,
122,
128,
138,
146,
171,
174,
176,
182,
194,
208,
211,
220,
229,
230,
239,
254,
265,
285,
290,
319,
324,
327,
333,
357,
364,
395,
397,
405,
409,
419,
422,
431,
433,
436,
440,
453,
460,
471,
478,
482,
488,
524,
529,
535,
536,
539,
563,
566,
572,
577,
587,
592,
602,
623,
635,
638,
654,
656,
659,
665,
675,
677,
687,
696,
701,
704,
710,
721,
728,
738,
740,
749,
758,
761,
772,
776,
782,
789,
810,
812,
818,
830,
832,
852,
855,
859,
865,
877,
895,
901,
902,
906,
916,
920,
949,
962,
964,
967,
981,
982,
985,
991,
1007,
1016,
1024,
1051,
1060,
1070,
1072,
1084,
1089,
1095,
1114,
1123,
1132,
1154,
1156,
1163,
1171,
1202,
1228,
1239,
1255,
1256,
1262,
1270,
1279,
1308,
1322,
1329,
1330,
1336,
1341,
1347,
1349,
1359,
1367,
1368,
1390,
1413,
1414,
1437,
1441,
1462,
1465,
1480,
1486,
1504,
1509,
1514,
1522,
1528,
1552,
1555,
1571,
1578,
1585,
1588,
1603,
1609,
1617,
1620,
1629,
1636,
1648,
1667,
1669,
1682,
1697,
1704,
1709,
1727,
1730,
1732,
1741,
1744,
1759,
1765,
1766,
1778,
1780,
1783,
1797,
1807,
1821,
1832,
1835,
1849,
1850,
1863,
1867,
1869,
1872,
1887,
1888,
1897,
1906,
1917,
1927,
1939,
1941,
1948,
1970,
1979,
1982,
2002,
2020,
2024,
2032,
2053,
2060,
2063,
2066,
2075,
2078,
2081,
2091,
2096,
2102,
2106,
2116,
2120,
2125,
2134,
2178,
2180,
2187,
2189,
2190,
2208,
2214,
2237,
2252,
2257,
2260,
2264,
2270,
2279,
2288,
2305,
2312,
2317,
2323,
2329,
2335,
2342,
2345,
2365,
2371,
2378,
2385,
2395,
2404,
2414,
2426,
2428,
2441,
2456,
2466,
2468,
2475,
2489,
2495,
2497,
2510,
2512,
2522,
2533,
2543,
2551,
2552,
2557,
2567,
2581,
2586,
2597,
2601,
2622,
2633,
2636,
2642,
2644,
2653,
2667,
2669,
2672,
2675,
2682,
2687,
2691,
2698,
2708,
2712,
2718,
2722,
2736,
2741,
2756,
2765,
2774,
2799,
2804,
2825,
2826,
2840,
2843,
2846,
2849,
2867,
2876,
2891,
2902,
2912,
2917,
2927,
2941,
2965,
2970,
2982,
2993,
3018,
3023,
3025,
3026,
3028,
3032,
3053,
3054,
3065,
3071,
3076,
3088,
3107,
3146,
3148,
3159,
3165,
3170,
3179,
3182,
3205,
3212,
3218,
3220,
3223,
3227,
3233,
3234,
3254,
3263,
3268,
3272,
3277,
3292,
3295,
3296,
3301,
3306,
3313,
3346,
3367,
3371,
3373,
3374,
3376,
3382,
3388,
3391,
3403,
3406,
3413,
3420,
3427,
3441,
3453,
3464,
3469,
3481,
3488,
3497,
3503,
3511,
3515,
3525,
3529,
3547,
3550,
3573,
3583,
3594,
3607,
3613,
3624,
3630,
3635,
3642,
3644,
3650,
3679,
3690,
3698,
3704,
3707,
3713,
3754,
3756,
3761,
3776,
3781,
3788,
3791,
3794,
3806,
3841,
3848,
3851,
3856,
3868,
3875,
3882,
3884,
3889,
3892,
3919,
3921,
3958,
3961,
3973,
3977,
3985,
3991,
4004,
4007,
4019,
4045,
4054,
4057,
4058,
4070,
4101,
4113,
4114,
4119,
4129,
4141,
4142,
4147,
4149,
4150,
4164,
4168,
4186,
4198,
4207,
4221,
4225,
4231,
4238,
4243,
4249,
4250,
4252,
4259,
4279,
4285,
4288,
4303,
4312,
4322,
4327,
4336,
4359,
4384,
4387,
4401,
4407,
4428,
4436,
4450,
4452,
4459,
4461,
4470,
4483,
4485,
4486,
4492,
4497,
4514,
4533,
4537,
4546,
4551,
4555,
4560,
4569,
4576,
4582,
4586,
4609,
4610,
4612,
4649,
4652,
4672,
4677,
4684,
4690,
4695,
4696,
4702,
4705,
4717,
4726,
4736,
4753,
4754,
4756,
4775,
4801,
4819,
4828,
4838,
4852,
4856,
4873,
4887,
4891,
4904,
4912,
4921,
4936,
4941,
4942,
4963,
4984,
4990,
5005,
5013,
5020,
5039,
5048,
5062,
5080,
5085,
5086,
5095,
5096,
5102,
5107,
5141,
5145,
5148,
5157,
5158,
5162,
5172,
5182,
5184,
5193,
5199,
5201,
5204,
5211,
5223,
5230,
5232,
5253,
5257,
5260,
5284,
5306,
5331,
5334,
5364,
5367,
5371,
5382,
5386,
5399,
5400,
5409,
5415,
5416,
5424,
5436,
5454,
5462,
5468,
5481,
5505,
5511,
5518,
5530,
5532,
5539,
5553,
5573,
5580,
5597,
5602,
5608,
5611,
5613,
5625,
5632,
5635,
5638,
5652,
5659,
5677,
5686,
5689,
5698,
5703,
5707,
5731,
5738,
5743,
5748,
5758,
5762,
5768,
5773,
5776,
5815,
5841,
5847,
5860,
5870,
5875,
5877,
5884,
5892,
5902,
5910,
5916,
5919,
5935,
5937,
5944,
5947,
5958,
5962,
5969,
5981,
5995,
5998,
6003,
6010,
6016,
6025,
6031,
6036,
6039,
6045,
6049,
6052,
6067,
6074,
6087,
6101,
6121,
6129,
6142,
6151,
6157,
6166,
6170,
6175,
6186,
6203,
6217,
6231,
6241,
6242,
6248,
6256,
6265,
6275,
6277,
6302,
6315,
6318,
6330,
6343,
6347,
6350,
6352,
6371,
6383,
6386,
6405,
6409,
6410,
6433,
6436,
6439,
6463,
6468,
6477,
6496,
6511,
6516,
6519,
6523,
6530,
6539,
6547,
6589,
6592,
6601,
6610,
6616,
6619,
6626,
6635,
6637,
6638,
6652,
6656,
6662,
6689,
6699,
6710,
6714,
6719,
6739,
6751,
6775,
6779,
6788,
6798,
6815,
6819,
6825,
6826,
6836,
6843,
6845,
6858,
6868,
6877,
6881,
6891,
6896,
6899,
6901,
6908,
6914,
6916,
6923,
6925,
6928,
6931,
6934,
6937,
6938,
6949,
6956,
6973,
6976,
6981,
6988,
6999,
7016,
7027,
7029,
7055,
7058,
7074,
7083,
7093,
7100,
7105,
7112,
7118,
7120,
7129,
7166,
7207,
7216,
7226,
7234,
7236,
7246,
7248,
7254,
7263,
7273,
7274,
7293,
7297,
7310,
7315,
7317,
7331,
7338,
7340,
7346,
7355,
7366,
7383,
7389,
7393,
7396,
7400,
7414,
7417,
7426,
7432,
7452,
7468,
7488,
7491,
7494,
7497,
7515,
7531,
7552,
7562,
7564,
7569,
7582,
7585,
7588,
7592,
7597,
7603,
7610,
7624,
7642,
7647,
7653,
7654,
7666,
7668,
7684,
7705,
7732,
7741,
7749,
7750,
7759,
7764,
7777,
7790,
7817,
7826,
7831,
7859,
7871,
7873,
7876,
7900,
7904,
7913,
7916,
7922,
7946,
7953,
7956,
7963,
7979,
7981,
7984,
7989,
7999,
8001,
8021,
8056,
8080,
8083,
8089,
8090,
8114,
8128,
8133,
8145,
8155,
8161,
8182,
8186,
8191,
8192,
8195,
8201,
8207,
8210,
8228,
8249,
8252,
8258,
8267,
8270,
8275,
8284,
8293,
8298,
8305,
8317,
8328,
8336,
8345,
8351,
8367,
8379,
8381,
8382,
8393,
8402,
8414,
8417,
8420,
8429,
8435,
8438,
8450,
8452,
8459,
8470,
8486,
8490,
8500,
8524,
8536,
8552,
8558,
8570,
8576,
8582,
8594,
8606,
8619,
8621,
8624,
8633,
8641,
8653,
8654,
8662,
8675,
8689,
8695,
8702,
8706,
8720,
8729,
8739,
8741,
8751,
8759,
8766,
8777,
8783,
8786,
8795,
8802,
8814,
8821,
8828,
8831,
8837,
8842,
8855,
8856,
8868,
8877,
8890,
8892,
8900,
8909,
8912,
8921,
8922,
8927,
8943,
8948,
8951,
8958,
8984,
8994,
9000,
9013,
9018,
9020,
9031,
9035,
9045,
9052,
9056,
9059,
9066,
9076,
9089,
9129,
9132,
9147,
9164,
9167,
9185,
9195,
9197,
9210,
9217,
9229,
9248,
9254,
9263,
9266,
9268,
9290,
9310,
9316,
9338,
9340,
9343,
9344,
9350,
9354,
9359,
9361,
9364,
9368,
9371,
9373,
9389,
9390,
9409,
9443,
9445,
9446,
9452,
9490,
9492,
9495,
9508,
9523,
9543,
9558,
9567,
9580,
9585,
9591,
9611,
9613,
9614,
9621,
9631,
9642,
9656,
9661,
9667,
9694,
9715,
9722,
9738,
9745,
9758,
9764,
9782,
9791,
9793,
9794,
9805,
9808,
9811,
9817,
9824,
9836,
9851,
9853,
9854,
9877,
9881,
9923,
9935,
9937,
9954,
9959,
9963,
9968,
9973,
9974,
9980,
9983,
9985,
10003,
10010,
10034,
10040,
10063,
10077,
10081,
10082,
10084,
10088,
10091,
10105,
10111,
10118,
10127,
10135,
10169,
10172,
10183,
10190,
10192,
10211,
10218,
10228,
10235,
10242,
10244,
10271,
10278,
10296,
10299,
10307,
10309,
10310,
10314,
10316,
10321,
10328,
10338,
10343,
10344,
10347,
10352,
10364,
10373,
10386,
10391,
10398,
10408,
10413,
10422,
10445,
10460,
10463,
10464,
10474,
10476,
10487,
10494,
10499,
10506,
10513,
10516,
10523,
10539,
10549,
10550,
10567,
10576,
10625,
10635,
10643,
10656,
10671,
10676,
10683,
10685,
10688,
10697,
10700,
10712,
10724,
10728,
10734,
10739,
10762,
10772,
10781,
10800,
10805,
10827,
10830,
10837,
10841,
10847,
10848,
10857,
10866,
10868,
10872,
10887,
10899,
10901,
10915,
10924,
10929,
10942,
10971,
10992,
10995,
11002,
11010,
11027,
11029,
11045,
11057,
11070,
11092,
11099,
11106,
11115,
11120,
11126,
11153,
11190,
11199,
11222,
11225,
11226,
11231,
11244,
11259,
11261,
11270,
11273,
11300,
11307,
11318,
11332,
11335,
11341,
11347,
11354,
11360,
11369,
11372,
11378,
11396,
11405,
11417,
11424,
11427,
11430,
11439,
11442,
11448,
11461,
11468,
11471,
11473,
11476,
11480,
11489,
11499,
11516,
11522,
11531,
11539,
11546,
11551,
11564,
11582,
11589,
11593,
11601,
11608,
11617,
11630,
11663,
11666,
11668,
11677,
11682,
11687,
11696,
11713,
11728,
11747,
11750,
11754,
11759,
11761,
11764,
11767,
11797,
11804,
11808,
11831,
11832,
11849,
11855,
11863,
11880,
11883,
11885,
11898,
11916,
11924,
11928,
11947,
11955,
11961,
11962,
11982,
11990,
12010,
12018,
12027,
12029,
12035,
12055,
12062,
12068,
12071,
12072,
12086,
12097,
12098,
12100,
12112,
12118,
12133,
12134,
12137,
12161,
12162,
12171,
12174,
12185,
12204,
12212,
12215,
12216,
12253,
12260,
12277,
12289,
12295,
12314,
12323,
12325,
12335,
12349,
12358,
12372,
12376,
12379,
12386,
12395,
12416,
12421,
12440,
12452,
12455,
12456,
12462,
12467,
12479,
12505,
12521,
12535,
12547,
12556,
12561,
12568,
12578,
12583,
12595,
12604,
12610,
12621,
12622,
12624,
12629,
12630,
12639,
12640,
12650,
12679,
12680,
12698,
12716,
12721,
12722,
12731,
12742,
12745,
12751,
12759,
12763,
12769,
12781,
12793,
12799,
12815,
12824,
12836,
12845,
12853,
12854,
12857,
12866,
12872,
12875,
12878,
12880,
12885,
12901,
12902,
12920,
12926,
12929,
12939,
12941,
12950,
12953,
12992,
13002,
13010,
13058,
13072,
13084,
13087,
13091,
13097,
13108,
13123,
13149,
13150,
13163,
13166,
13178,
13180,
13184,
13204,
13238,
13242,
13249,
13255,
13269,
13270,
13274,
13285,
13289,
13298,
13307,
13312,
13335,
13345,
13357,
13366,
13372,
13380,
13384,
13395,
13407,
13408,
13413,
13414,
13417,
13437,
13441,
13447,
13456,
13459,
13461,
13466,
13484,
13487,
13489,
13492,
13496,
13510,
13531,
13538,
13543,
13547,
13572,
13581,
13590,
13605,
13612,
13624,
13630,
13632,
13638,
13661,
13665,
13668,
13686,
13699,
13701,
13708,
13716,
13725,
13730,
13742,
13747,
13749,
13753,
13754,
13771,
13773,
13782,
13785,
13798,
13802,
13809,
13828,
13832,
13840,
13850,
13861,
13874,
13876,
13886,
13897,
13900,
13915,
13927,
13951,
13955,
13962,
13969,
13979,
13988,
13998,
14000,
14005,
14027,
14037,
14051,
14054,
14060,
14063,
14071,
14078,
14080,
14085,
14086,
14095,
14138,
14145,
14158,
14166,
14179,
14181,
14188,
14193,
14200,
14203,
14215,
14224,
14230,
14233,
14236,
14246,
14267,
14282,
14287,
14301,
14323,
14325,
14329,
14339,
14342,
14351,
14356,
14359,
14370,
14402,
14411,
14421,
14431,
14435,
14442,
14447,
14456,
14459,
14472,
14477,
14490,
14496,
14501,
14505,
14513,
14520,
14534,
14562,
14576,
14579,
14585,
14586,
14606,
14627,
14630,
14634,
14636,
14647,
14653,
14659,
14671,
14674,
14701,
14716,
14719,
14720,
14725,
14730,
14743,
14747,
14786,
14788,
14792,
14795,
14809,
14831,
14834,
14850,
14855,
14859,
14864,
14876,
14889,
14890,
14898,
14909,
14917,
14924,
14929,
14942,
14951,
14969,
14970,
14972,
14982,
14988,
14994,
15005,
15016,
15024,
15030,
15048,
15054,
15066,
15071,
15072,
15075,
15119,
15121,
15133,
15138,
15143,
15170,
15194,
15212,
15223,
15229,
15254,
15263,
15270,
15273,
15287,
15299,
15301,
15306,
15313,
15320,
15323,
15329,
15332,
15341,
15359,
15361,
15364,
15367,
15379,
15391,
15415,
15416,
15419,
15433,
15469,
15478,
15481,
15482,
15498,
15505,
15517,
15518,
15527,
15528,
15545,
15548,
15554,
15565,
15577,
15580,
15587,
15601,
15604,
15611,
15616,
15619,
15625,
15633,
15674,
15681,
15691,
15693,
15696,
15712,
15717,
15724,
15727,
15730,
15746,
15751,
15760,
15770,
15782,
15791,
15796,
15808,
15814,
15825,
15828,
15835,
15844,
15847,
15853,
15856,
15877,
15878,
15887,
15908,
15917,
15923,
15930,
15937,
15958,
15977,
15991,
16007,
16011,
16014,
16021,
16022,
16028,
16035,
16041,
16056,
16069,
16076,
16081,
16087,
16088,
16110,
16112,
16117,
16150,
16153,
16160,
16166,
16172,
16190,
16195,
16204,
16216,
16222,
16228,
16245,
16255,
16265,
16273,
16276,
16283,
16295,
16304,
16313,
16319,
16328,
16345,
16355,
16364,
16372,
16375,
16382,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_15
static const long PrimitivePolynomialDegree16[]={
22,
28,
31,
41,
94,
107,
151,
158,
167,
174,
203,
208,
214,
223,
227,
266,
268,
274,
279,
302,
310,
322,
328,
336,
370,
398,
421,
436,
440,
451,
454,
463,
465,
494,
508,
532,
555,
563,
577,
580,
584,
607,
608,
665,
675,
692,
707,
737,
750,
757,
800,
805,
809,
837,
865,
949,
950,
956,
961,
1016,
1030,
1072,
1119,
1130,
1135,
1137,
1144,
1149,
1180,
1214,
1221,
1234,
1239,
1249,
1250,
1267,
1273,
1342,
1344,
1373,
1378,
1408,
1417,
1418,
1448,
1454,
1510,
1513,
1522,
1543,
1550,
1552,
1588,
1592,
1597,
1606,
1610,
1617,
1623,
1657,
1697,
1729,
1735,
1769,
1778,
1826,
1858,
1870,
1875,
1922,
1924,
1933,
1972,
1979,
1987,
1994,
2008,
2023,
2029,
2053,
2081,
2087,
2094,
2111,
2113,
2114,
2123,
2190,
2231,
2276,
2285,
2297,
2336,
2345,
2353,
2363,
2368,
2373,
2391,
2402,
2413,
2422,
2425,
2461,
2462,
2490,
2492,
2510,
2564,
2573,
2598,
2627,
2633,
2647,
2660,
2664,
2678,
2684,
2691,
2759,
2768,
2773,
2794,
2813,
2831,
2843,
2846,
2849,
2856,
2893,
2901,
2924,
2942,
2975,
2979,
2985,
3020,
3025,
3028,
3051,
3127,
3142,
3145,
3156,
3165,
3196,
3199,
3217,
3218,
3253,
3258,
3260,
3289,
3314,
3326,
3331,
3371,
3381,
3396,
3441,
3442,
3460,
3477,
3491,
3493,
3543,
3549,
3550,
3553,
3563,
3568,
3604,
3632,
3650,
3662,
3674,
3685,
3686,
3700,
3703,
3704,
3723,
3743,
3753,
3756,
3759,
3762,
3771,
3776,
3779,
3839,
3856,
3871,
3887,
3896,
3901,
3916,
3919,
3937,
3943,
3955,
3961,
3988,
3997,
4011,
4026,
4033,
4045,
4060,
4063,
4064,
4126,
4136,
4167,
4173,
4188,
4195,
4226,
4291,
4298,
4308,
4312,
4336,
4371,
4378,
4384,
4393,
4421,
4425,
4439,
4440,
4500,
4514,
4523,
4534,
4593,
4615,
4630,
4636,
4645,
4684,
4687,
4723,
4735,
4746,
4779,
4782,
4793,
4796,
4813,
4850,
4867,
4874,
4881,
4894,
4904,
4927,
4929,
4989,
5000,
5020,
5036,
5041,
5059,
5074,
5090,
5110,
5134,
5152,
5176,
5181,
5204,
5218,
5242,
5253,
5260,
5281,
5282,
5313,
5316,
5326,
5340,
5347,
5354,
5368,
5394,
5396,
5400,
5405,
5439,
5442,
5459,
5478,
5484,
5508,
5523,
5545,
5565,
5566,
5580,
5608,
5613,
5647,
5661,
5671,
5678,
5680,
5685,
5689,
5692,
5724,
5745,
5755,
5757,
5786,
5792,
5810,
5824,
5869,
5872,
5895,
5923,
5925,
5926,
5944,
5986,
6012,
6015,
6046,
6049,
6061,
6067,
6099,
6121,
6155,
6163,
6203,
6208,
6231,
6241,
6254,
6262,
6266,
6275,
6278,
6292,
6329,
6355,
6357,
6374,
6380,
6423,
6427,
6430,
6436,
6443,
6445,
6458,
6478,
6490,
6508,
6519,
6520,
6530,
6541,
6556,
6607,
6612,
6626,
6632,
6649,
6666,
6674,
6733,
6782,
6786,
6798,
6821,
6840,
6846,
6865,
6884,
6891,
6925,
6938,
6967,
6988,
6996,
7009,
7016,
7030,
7043,
7045,
7052,
7073,
7142,
7153,
7168,
7174,
7183,
7195,
7204,
7214,
7222,
7267,
7269,
7279,
7293,
7312,
7327,
7334,
7337,
7343,
7346,
7372,
7387,
7390,
7396,
7423,
7428,
7437,
7466,
7474,
7476,
7483,
7518,
7527,
7545,
7572,
7586,
7597,
7630,
7653,
7657,
7671,
7672,
7715,
7717,
7732,
7735,
7753,
7811,
7817,
7825,
7832,
7838,
7841,
7844,
7859,
7861,
7873,
7880,
7897,
7904,
7910,
7960,
7969,
7970,
7976,
7979,
8007,
8041,
8047,
8052,
8061,
8078,
8128,
8146,
8162,
8250,
8270,
8294,
8324,
8351,
8357,
8361,
8364,
8393,
8396,
8407,
8413,
8414,
8432,
8435,
8441,
8447,
8449,
8456,
8485,
8504,
8512,
8532,
8551,
8560,
8566,
8581,
8609,
8639,
8641,
8671,
8695,
8701,
8711,
8739,
8763,
8778,
8783,
8785,
8797,
8802,
8816,
8828,
8837,
8852,
8859,
8889,
8900,
8903,
8909,
8910,
8922,
8924,
8955,
8958,
8980,
8994,
9006,
9017,
9032,
9040,
9061,
9066,
9071,
9076,
9086,
9104,
9150,
9161,
9164,
9185,
9188,
9212,
9230,
9242,
9247,
9260,
9280,
9300,
9313,
9325,
9343,
9349,
9354,
9367,
9368,
9455,
9458,
9469,
9481,
9482,
9495,
9526,
9530,
9558,
9562,
9573,
9583,
9595,
9597,
9616,
9638,
9649,
9662,
9691,
9700,
9703,
9710,
9721,
9724,
9727,
9743,
9779,
9785,
9811,
9820,
9827,
9851,
9854,
9863,
9884,
9894,
9903,
9908,
9912,
9925,
9926,
9971,
9973,
9977,
10021,
10039,
10048,
10051,
10065,
10071,
10072,
10101,
10106,
10130,
10136,
10148,
10155,
10157,
10160,
10166,
10183,
10192,
10225,
10241,
10247,
10284,
10304,
10322,
10331,
10333,
10340,
10347,
10357,
10371,
10386,
10404,
10414,
10422,
10448,
10451,
10473,
10479,
10501,
10530,
10542,
10544,
10571,
10628,
10643,
10673,
10683,
10736,
10795,
10797,
10815,
10817,
10842,
10844,
10863,
10899,
10902,
10917,
10953,
10967,
11002,
11024,
11029,
11030,
11043,
11087,
11106,
11130,
11156,
11176,
11221,
11267,
11282,
11294,
11332,
11353,
11369,
11372,
11375,
11413,
11429,
11430,
11444,
11462,
11465,
11471,
11473,
11495,
11499,
11519,
11562,
11576,
11582,
11596,
11602,
11611,
11627,
11682,
11687,
11691,
11733,
11747,
11759,
11778,
11852,
11857,
11858,
11893,
11907,
11928,
11931,
11933,
11967,
11976,
11989,
12003,
12024,
12030,
12037,
12044,
12052,
12059,
12075,
12083,
12117,
12138,
12146,
12202,
12230,
12254,
12304,
12316,
12337,
12347,
12367,
12398,
12421,
12428,
12446,
12449,
12467,
12479,
12502,
12521,
12553,
12568,
12573,
12592,
12597,
12601,
12615,
12619,
12694,
12697,
12698,
12713,
12722,
12733,
12736,
12790,
12794,
12803,
12815,
12829,
12833,
12840,
12875,
12877,
12916,
12923,
12935,
12949,
12954,
12956,
12959,
12978,
13001,
13010,
13043,
13049,
13058,
13112,
13140,
13149,
13163,
13187,
13196,
13237,
13244,
13264,
13279,
13292,
13295,
13307,
13312,
13317,
13327,
13348,
13390,
13413,
13417,
13418,
13451,
13475,
13482,
13510,
13527,
13543,
13547,
13627,
13650,
13683,
13696,
13702,
13713,
13739,
13749,
13767,
13774,
13781,
13795,
13821,
13825,
13838,
13852,
13879,
13888,
13897,
13906,
13939,
13962,
13981,
13985,
14020,
14030,
14041,
14047,
14048,
14066,
14092,
14120,
14126,
14131,
14143,
14146,
14152,
14155,
14157,
14188,
14206,
14243,
14278,
14308,
14317,
14335,
14354,
14356,
14379,
14381,
14384,
14389,
14390,
14414,
14425,
14462,
14472,
14508,
14511,
14519,
14528,
14561,
14574,
14588,
14594,
14606,
14614,
14639,
14641,
14648,
14668,
14673,
14679,
14695,
14702,
14704,
14740,
14754,
14774,
14792,
14797,
14806,
14812,
14856,
14876,
14900,
14910,
14912,
14915,
14922,
14939,
14946,
14955,
14966,
14976,
14986,
14993,
15012,
15041,
15053,
15056,
15059,
15110,
15116,
15133,
15134,
15137,
15147,
15182,
15203,
15215,
15245,
15246,
15264,
15269,
15296,
15314,
15323,
15364,
15386,
15391,
15436,
15460,
15464,
15469,
15470,
15477,
15488,
15494,
15548,
15551,
15560,
15563,
15604,
15607,
15616,
15631,
15699,
15701,
15708,
15739,
15746,
15772,
15793,
15832,
15837,
15866,
15899,
15911,
15918,
15952,
15962,
15967,
15973,
15977,
16016,
16035,
16044,
16067,
16082,
16084,
16098,
16107,
16142,
16149,
16165,
16172,
16178,
16197,
16201,
16215,
16221,
16226,
16232,
16246,
16261,
16279,
16280,
16290,
16314,
16345,
16355,
16361,
16393,
16394,
16438,
16450,
16507,
16523,
16533,
16603,
16648,
16653,
16672,
16682,
16709,
16713,
16719,
16733,
16740,
16761,
16767,
16771,
16788,
16811,
16814,
16816,
16828,
16834,
16863,
16864,
16879,
16888,
16904,
16909,
16921,
16934,
16951,
16983,
16999,
17000,
17006,
17020,
17030,
17033,
17044,
17051,
17072,
17078,
17084,
17087,
17090,
17123,
17132,
17140,
17149,
17157,
17164,
17170,
17179,
17237,
17248,
17260,
17272,
17275,
17287,
17294,
17296,
17305,
17312,
17321,
17367,
17368,
17378,
17433,
17455,
17457,
17508,
17559,
17560,
17582,
17596,
17599,
17613,
17619,
17622,
17655,
17661,
17698,
17712,
17715,
17721,
17722,
17742,
17778,
17818,
17836,
17841,
17856,
17883,
17896,
17901,
17926,
17937,
17992,
17995,
17998,
18021,
18039,
18067,
18122,
18129,
18130,
18142,
18148,
18163,
18192,
18211,
18228,
18264,
18347,
18372,
18409,
18412,
18418,
18423,
18433,
18439,
18445,
18451,
18467,
18502,
18514,
18547,
18575,
18593,
18613,
18620,
18637,
18640,
18712,
18728,
18742,
18748,
18753,
18756,
18771,
18814,
18818,
18827,
18835,
18842,
18854,
18858,
18895,
18914,
18925,
18933,
18937,
18944,
18973,
19001,
19012,
19016,
19027,
19040,
19074,
19085,
19093,
19100,
19107,
19128,
19141,
19142,
19156,
19169,
19176,
19222,
19226,
19247,
19259,
19262,
19291,
19309,
19324,
19334,
19338,
19343,
19376,
19408,
19413,
19420,
19441,
19444,
19454,
19461,
19473,
19479,
19489,
19591,
19605,
19616,
19619,
19653,
19654,
19681,
19711,
19719,
19726,
19738,
19767,
19819,
19864,
19867,
19885,
19894,
19900,
19903,
19941,
19951,
19959,
19966,
20009,
20018,
20020,
20038,
20049,
20066,
20108,
20130,
20132,
20167,
20219,
20227,
20263,
20267,
20272,
20289,
20296,
20307,
20316,
20323,
20335,
20344,
20354,
20360,
20368,
20390,
20402,
20413,
20425,
20428,
20434,
20443,
20488,
20502,
20505,
20535,
20541,
20554,
20577,
20583,
20602,
20611,
20614,
20626,
20628,
20635,
20642,
20674,
20716,
20734,
20765,
20801,
20804,
20808,
20831,
20832,
20862,
20877,
20880,
20885,
20889,
20905,
20914,
20967,
21028,
21031,
21043,
21052,
21058,
21087,
21088,
21093,
21106,
21108,
21118,
21122,
21131,
21139,
21141,
21146,
21162,
21164,
21184,
21208,
21211,
21213,
21230,
21270,
21276,
21285,
21297,
21304,
21310,
21330,
21339,
21346,
21391,
21427,
21451,
21465,
21468,
21471,
21533,
21610,
21615,
21630,
21633,
21657,
21658,
21669,
21670,
21673,
21701,
21719,
21720,
21747,
21819,
21839,
21854,
21857,
21864,
21882,
21900,
21903,
21928,
21931,
21946,
21971,
21974,
21978,
21993,
21994,
22030,
22035,
22063,
22068,
22086,
22104,
22119,
22153,
22168,
22183,
22189,
22204,
22230,
22240,
22246,
22269,
22282,
22302,
22330,
22347,
22349,
22383,
22386,
22432,
22450,
22473,
22487,
22527,
22537,
22557,
22561,
22568,
22573,
22591,
22593,
22605,
22620,
22627,
22636,
22647,
22697,
22715,
22725,
22732,
22749,
22766,
22768,
22771,
22788,
22797,
22822,
22828,
22851,
22888,
22893,
22901,
22902,
22921,
22929,
22946,
22948,
22951,
22958,
22975,
22983,
22990,
23032,
23047,
23053,
23054,
23082,
23095,
23116,
23197,
23221,
23257,
23260,
23263,
23267,
23282,
23284,
23314,
23326,
23335,
23368,
23373,
23401,
23415,
23432,
23476,
23479,
23497,
23505,
23508,
23531,
23536,
23542,
23565,
23573,
23590,
23593,
23604,
23621,
23622,
23636,
23662,
23667,
23703,
23725,
23734,
23738,
23752,
23800,
23803,
23818,
23832,
23842,
23851,
23873,
23883,
23888,
23910,
23934,
23938,
23949,
23955,
23967,
23973,
23991,
24024,
24030,
24039,
24067,
24069,
24084,
24112,
24115,
24184,
24187,
24262,
24276,
24279,
24313,
24331,
24336,
24348,
24367,
24372,
24402,
24420,
24444,
24465,
24466,
24471,
24475,
24481,
24488,
24501,
24514,
24531,
24534,
24559,
24602,
24614,
24637,
24664,
24676,
24679,
24697,
24709,
24714,
24716,
24731,
24744,
24762,
24764,
24769,
24806,
24812,
24872,
24878,
24883,
24909,
24943,
24946,
24964,
24992,
25016,
25022,
25024,
25039,
25051,
25060,
25072,
25097,
25122,
25148,
25194,
25201,
25204,
25238,
25241,
25248,
25257,
25275,
25278,
25304,
25307,
25320,
25334,
25348,
25357,
25372,
25394,
25454,
25465,
25472,
25492,
25505,
25517,
25530,
25558,
25562,
25598,
25609,
25612,
25627,
25651,
25653,
25668,
25711,
25765,
25770,
25775,
25777,
25783,
25801,
25802,
25812,
25821,
25897,
25906,
25929,
25940,
25950,
25968,
25971,
25977,
25994,
25996,
25999,
26001,
26030,
26069,
26100,
26109,
26131,
26144,
26149,
26162,
26167,
26173,
26179,
26193,
26230,
26234,
26246,
26267,
26283,
26300,
26341,
26356,
26377,
26397,
26404,
26411,
26422,
26451,
26454,
26463,
26488,
26498,
26509,
26512,
26517,
26534,
26545,
26546,
26636,
26749,
26753,
26759,
26774,
26789,
26808,
26825,
26831,
26859,
26888,
26918,
26929,
26950,
26954,
26973,
26997,
26998,
27008,
27038,
27109,
27127,
27150,
27168,
27178,
27212,
27224,
27229,
27246,
27251,
27257,
27258,
27260,
27287,
27300,
27315,
27329,
27332,
27349,
27350,
27354,
27359,
27377,
27378,
27383,
27384,
27387,
27392,
27402,
27438,
27481,
27482,
27494,
27531,
27542,
27546,
27564,
27567,
27582,
27608,
27611,
27624,
27629,
27655,
27667,
27676,
27710,
27724,
27745,
27752,
27770,
27779,
27781,
27791,
27809,
27810,
27815,
27827,
27834,
27865,
27899,
27901,
27914,
27950,
27994,
28005,
28009,
28033,
28039,
28060,
28067,
28069,
28099,
28113,
28114,
28139,
28142,
28153,
28166,
28172,
28183,
28194,
28232,
28245,
28246,
28252,
28265,
28301,
28323,
28344,
28362,
28400,
28417,
28454,
28466,
28468,
28477,
28498,
28510,
28513,
28571,
28573,
28578,
28587,
28601,
28646,
28663,
28681,
28682,
28699,
28706,
28708,
28717,
28720,
28735,
28761,
28783,
28788,
28811,
28825,
28838,
28850,
28891,
28897,
28932,
28975,
28998,
29052,
29090,
29096,
29104,
29113,
29133,
29142,
29170,
29192,
29221,
29236,
29246,
29293,
29305,
29312,
29339,
29365,
29389,
29402,
29423,
29443,
29445,
29463,
29473,
29493,
29506,
29518,
29532,
29560,
29590,
29594,
29637,
29647,
29650,
29655,
29661,
29680,
29721,
29751,
29755,
29760,
29772,
29778,
29799,
29824,
29841,
29842,
29853,
29867,
29949,
29950,
29964,
29967,
29985,
29992,
30000,
30020,
30024,
30030,
30066,
30071,
30078,
30082,
30096,
30101,
30102,
30122,
30141,
30159,
30168,
30177,
30183,
30197,
30213,
30231,
30232,
30241,
30253,
30259,
30262,
30268,
30297,
30316,
30322,
30344,
30350,
30355,
30429,
30445,
30477,
30513,
30520,
30540,
30551,
30573,
30609,
30622,
30635,
30658,
30667,
30681,
30684,
30703,
30705,
30715,
30742,
30748,
30758,
30767,
30770,
30772,
30807,
30814,
30824,
30857,
30875,
30931,
30933,
30949,
30953,
30982,
31010,
31012,
31039,
31041,
31061,
31082,
31087,
31096,
31115,
31130,
31168,
31171,
31177,
31180,
31191,
31207,
31247,
31249,
31285,
31303,
31310,
31337,
31352,
31357,
31374,
31379,
31388,
31410,
31416,
31467,
31495,
31504,
31507,
31509,
31514,
31516,
31530,
31555,
31567,
31570,
31586,
31598,
31605,
31609,
31612,
31626,
31634,
31655,
31681,
31705,
31706,
31718,
31735,
31741,
31744,
31762,
31774,
31864,
31874,
31900,
31910,
31928,
31965,
31976,
32016,
32032,
32037,
32062,
32069,
32115,
32128,
32171,
32173,
32182,
32191,
32193,
32194,
32229,
32230,
32248,
32263,
32264,
32269,
32298,
32335,
32340,
32356,
32374,
32390,
32401,
32414,
32417,
32442,
32450,
32461,
32473,
32479,
32530,
32536,
32548,
32577,
32628,
32642,
32665,
32666,
32668,
32696,
32722,
32757,
32758,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_16
static const long PrimitivePolynomialDegree17[]={
4,
7,
16,
22,
25,
31,
32,
42,
52,
61,
70,
76,
81,
87,
93,
98,
122,
133,
134,
140,
146,
158,
171,
176,
179,
182,
191,
193,
224,
227,
229,
236,
248,
262,
273,
276,
280,
283,
290,
309,
316,
319,
321,
328,
346,
355,
367,
369,
372,
382,
388,
392,
395,
397,
403,
409,
410,
425,
443,
472,
475,
481,
488,
493,
501,
515,
522,
524,
527,
535,
542,
545,
555,
558,
560,
563,
570,
578,
583,
590,
597,
604,
608,
614,
635,
637,
653,
654,
659,
666,
671,
689,
690,
695,
713,
722,
733,
758,
770,
782,
784,
793,
803,
805,
812,
838,
849,
875,
877,
880,
892,
895,
899,
919,
920,
932,
935,
936,
941,
950,
961,
962,
971,
982,
986,
1012,
1021,
1024,
1029,
1030,
1051,
1054,
1064,
1067,
1082,
1096,
1116,
1119,
1129,
1130,
1132,
1137,
1147,
1150,
1154,
1165,
1166,
1174,
1177,
1184,
1194,
1204,
1208,
1213,
1219,
1233,
1264,
1267,
1281,
1312,
1321,
1330,
1332,
1335,
1341,
1356,
1371,
1377,
1380,
1384,
1395,
1397,
1411,
1414,
1426,
1432,
1435,
1437,
1442,
1454,
1468,
1473,
1488,
1491,
1509,
1524,
1533,
1555,
1567,
1571,
1586,
1592,
1595,
1600,
1606,
1627,
1648,
1651,
1654,
1667,
1669,
1674,
1687,
1698,
1710,
1717,
1722,
1735,
1741,
1749,
1750,
1769,
1775,
1777,
1778,
1792,
1797,
1802,
1822,
1825,
1831,
1838,
1852,
1855,
1860,
1867,
1869,
1875,
1882,
1903,
1908,
1917,
1927,
1941,
1945,
1948,
1962,
1975,
1976,
1987,
1993,
2004,
2020,
2029,
2030,
2038,
2041,
2048,
2054,
2057,
2058,
2068,
2072,
2075,
2077,
2082,
2084,
2087,
2101,
2111,
2113,
2119,
2147,
2154,
2161,
2164,
2177,
2178,
2184,
2198,
2201,
2213,
2217,
2228,
2240,
2245,
2250,
2263,
2267,
2285,
2286,
2291,
2298,
2306,
2325,
2329,
2332,
2335,
2339,
2346,
2351,
2353,
2363,
2378,
2383,
2391,
2401,
2408,
2414,
2419,
2428,
2441,
2444,
2461,
2480,
2483,
2486,
2489,
2490,
2518,
2527,
2540,
2558,
2567,
2571,
2574,
2579,
2585,
2615,
2639,
2641,
2644,
2663,
2667,
2669,
2672,
2687,
2700,
2705,
2724,
2728,
2733,
2741,
2748,
2751,
2756,
2771,
2774,
2793,
2796,
2804,
2814,
2822,
2845,
2846,
2850,
2855,
2856,
2867,
2891,
2894,
2902,
2908,
2951,
2970,
2972,
2975,
2976,
2981,
2986,
2999,
3000,
3006,
3014,
3028,
3031,
3035,
3037,
3053,
3059,
3065,
3080,
3091,
3094,
3109,
3110,
3113,
3116,
3136,
3139,
3141,
3154,
3160,
3169,
3182,
3187,
3189,
3190,
3203,
3217,
3229,
3236,
3248,
3257,
3278,
3283,
3289,
3292,
3302,
3316,
3328,
3333,
3337,
3340,
3368,
3371,
3376,
3385,
3386,
3393,
3399,
3405,
3414,
3433,
3436,
3448,
3467,
3469,
3472,
3477,
3484,
3494,
3505,
3515,
3523,
3530,
3543,
3559,
3568,
3577,
3578,
3594,
3601,
3607,
3608,
3620,
3629,
3644,
3656,
3664,
3670,
3680,
3685,
3686,
3695,
3698,
3703,
3710,
3714,
3726,
3731,
3733,
3737,
3756,
3759,
3767,
3776,
3785,
3793,
3812,
3815,
3824,
3844,
3859,
3866,
3872,
3884,
3889,
3899,
3902,
3909,
3913,
3933,
3938,
3949,
3952,
3980,
3991,
3992,
4002,
4008,
4011,
4016,
4034,
4036,
4063,
4067,
4073,
4082,
4091,
4093,
4101,
4113,
4120,
4125,
4126,
4139,
4142,
4144,
4147,
4153,
4154,
4164,
4174,
4182,
4185,
4188,
4191,
4195,
4219,
4225,
4228,
4232,
4246,
4255,
4274,
4283,
4286,
4306,
4311,
4317,
4321,
4324,
4331,
4333,
4359,
4360,
4368,
4373,
4389,
4394,
4413,
4422,
4431,
4436,
4440,
4445,
4452,
4462,
4469,
4470,
4473,
4479,
4480,
4483,
4489,
4503,
4519,
4520,
4525,
4526,
4533,
4552,
4581,
4585,
4591,
4594,
4596,
4599,
4612,
4621,
4630,
4636,
4640,
4649,
4650,
4660,
4677,
4687,
4696,
4701,
4705,
4706,
4711,
4720,
4723,
4732,
4736,
4742,
4748,
4754,
4759,
4769,
4787,
4807,
4814,
4837,
4867,
4873,
4879,
4884,
4898,
4907,
4910,
4918,
4924,
4953,
4956,
4965,
4966,
4970,
4972,
4983,
4989,
4994,
5000,
5005,
5014,
5018,
5023,
5039,
5053,
5054,
5061,
5065,
5080,
5083,
5107,
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60653,
60671,
60673,
60691,
60697,
60700,
60714,
60724,
60728,
60733,
60736,
60745,
60746,
60753,
60754,
60782,
60784,
60790,
60793,
60805,
60830,
60836,
60846,
60851,
60880,
60896,
60905,
60923,
60925,
60932,
60939,
60942,
60953,
60956,
60959,
60963,
60969,
60978,
60980,
60987,
61007,
61012,
61015,
61025,
61026,
61038,
61040,
61052,
61061,
61074,
61083,
61085,
61086,
61096,
61119,
61124,
61127,
61128,
61133,
61134,
61146,
61155,
61161,
61162,
61169,
61179,
61182,
61190,
61201,
61208,
61238,
61241,
61247,
61259,
61267,
61269,
61295,
61304,
61309,
61310,
61313,
61320,
61325,
61334,
61337,
61386,
61399,
61422,
61429,
61436,
61439,
61466,
61477,
61478,
61490,
61495,
61504,
61514,
61516,
61521,
61527,
61531,
61540,
61550,
61557,
61562,
61577,
61583,
61597,
61602,
61604,
61607,
61622,
61625,
61633,
61640,
61643,
61651,
61658,
61670,
61674,
61676,
61679,
61688,
61693,
61701,
61711,
61714,
61723,
61725,
61726,
61729,
61741,
61761,
61779,
61781,
61782,
61797,
61809,
61810,
61816,
61822,
61849,
61876,
61893,
61905,
61908,
61911,
61912,
61928,
61934,
61957,
61961,
61969,
61979,
61982,
62003,
62006,
62010,
62015,
62020,
62024,
62029,
62032,
62035,
62038,
62047,
62068,
62071,
62082,
62088,
62096,
62108,
62124,
62142,
62147,
62153,
62159,
62161,
62171,
62189,
62207,
62227,
62230,
62234,
62236,
62239,
62257,
62270,
62278,
62287,
62295,
62301,
62306,
62312,
62317,
62330,
62342,
62359,
62365,
62366,
62370,
62375,
62376,
62387,
62404,
62411,
62435,
62441,
62442,
62452,
62459,
62461,
62473,
62474,
62493,
62510,
62518,
62524,
62549,
62556,
62565,
62566,
62580,
62584,
62589,
62596,
62608,
62636,
62642,
62651,
62654,
62659,
62666,
62680,
62692,
62701,
62702,
62714,
62716,
62733,
62762,
62769,
62770,
62787,
62794,
62801,
62807,
62808,
62813,
62817,
62818,
62832,
62841,
62857,
62860,
62871,
62882,
62888,
62913,
62919,
62920,
62925,
62933,
62938,
62940,
62949,
62956,
62971,
62978,
62990,
62995,
62997,
63004,
63011,
63032,
63038,
63067,
63069,
63076,
63083,
63088,
63094,
63097,
63100,
63104,
63114,
63116,
63122,
63128,
63149,
63150,
63157,
63167,
63187,
63200,
63220,
63223,
63229,
63235,
63247,
63252,
63255,
63289,
63298,
63303,
63327,
63328,
63348,
63355,
63357,
63368,
63391,
63402,
63409,
63416,
63419,
63430,
63442,
63457,
63458,
63482,
63487,
63488,
63500,
63511,
63517,
63528,
63531,
63559,
63566,
63578,
63580,
63584,
63587,
63594,
63607,
63611,
63630,
63632,
63641,
63647,
63651,
63666,
63668,
63695,
63697,
63709,
63723,
63737,
63746,
63752,
63755,
63775,
63781,
63794,
63796,
63808,
63817,
63820,
63826,
63838,
63848,
63861,
63862,
63866,
63878,
63889,
63892,
63901,
63915,
63917,
63926,
63932,
63937,
63938,
63943,
63944,
63950,
63952,
63955,
63957,
63961,
63962,
63978,
63983,
63988,
64008,
64013,
64019,
64026,
64028,
64032,
64042,
64044,
64055,
64070,
64079,
64084,
64087,
64093,
64100,
64104,
64109,
64140,
64148,
64151,
64152,
64171,
64179,
64186,
64203,
64206,
64213,
64214,
64220,
64233,
64239,
64248,
64251,
64259,
64268,
64273,
64279,
64283,
64292,
64296,
64301,
64302,
64324,
64331,
64346,
64364,
64382,
64386,
64400,
64409,
64419,
64433,
64454,
64458,
64482,
64494,
64496,
64505,
64514,
64519,
64525,
64528,
64534,
64561,
64571,
64579,
64591,
64606,
64616,
64619,
64640,
64645,
64649,
64652,
64670,
64673,
64674,
64683,
64697,
64703,
64711,
64723,
64736,
64739,
64741,
64748,
64759,
64768,
64771,
64778,
64792,
64821,
64831,
64839,
64848,
64860,
64867,
64870,
64874,
64879,
64887,
64894,
64897,
64898,
64921,
64933,
64940,
64957,
64969,
64972,
64978,
64984,
64993,
64999,
65000,
65006,
65011,
65014,
65036,
65044,
65063,
65067,
65075,
65077,
65082,
65095,
65101,
65104,
65109,
65110,
65116,
65126,
65129,
65138,
65160,
65171,
65173,
65180,
65189,
65193,
65208,
65214,
65216,
65225,
65236,
65239,
65273,
65274,
65281,
65294,
65324,
65335,
65354,
65359,
65373,
65383,
65387,
65397,
65411,
65413,
65418,
65441,
65444,
65447,
65448,
65473,
65476,
65480,
65494,
65509,
65519,
65527,
-1 };
#endif

#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_17
static const long PrimitivePolynomialDegree18[]={
19,
31,
38,
61,
64,
109,
115,
118,
131,
167,
200,
241,
244,
247,
261,
265,
304,
314,
341,
376,
395,
405,
406,
443,
451,
458,
460,
468,
472,
482,
491,
496,
524,
536,
542,
557,
572,
580,
592,
656,
713,
719,
738,
749,
752,
767,
772,
782,
789,
830,
838,
916,
920,
936,
991,
998,
1016,
1024,
1053,
1081,
1090,
1125,
1135,
1143,
1150,
1154,
1171,
1174,
1202,
1213,
1225,
1233,
1234,
1252,
1255,
1294,
1349,
1354,
1378,
1383,
1387,
1392,
1402,
1420,
1428,
1437,
1448,
1459,
1473,
1507,
1516,
1528,
1573,
1592,
1597,
1654,
1663,
1730,
1739,
1741,
1753,
1783,
1804,
1807,
1832,
1850,
1852,
1881,
1894,
1927,
1952,
1969,
1999,
2018,
2047,
2066,
2068,
2093,
2105,
2116,
2149,
2201,
2228,
2245,
2246,
2283,
2288,
2320,
2326,
2386,
2392,
2395,
2413,
2419,
2441,
2466,
2477,
2485,
2492,
2495,
2498,
2504,
2515,
2521,
2561,
2579,
2604,
2657,
2681,
2691,
2731,
2739,
2765,
2790,
2802,
2819,
2891,
2905,
2911,
2912,
2921,
2924,
2945,
2952,
2972,
2986,
3000,
3008,
3011,
3018,
3047,
3071,
3079,
3083,
3086,
3148,
3156,
3194,
3230,
3233,
3254,
3268,
3305,
3323,
3326,
3343,
3345,
3382,
3413,
3420,
3434,
3453,
3472,
3488,
3503,
3506,
3518,
3532,
3543,
3547,
3573,
3574,
3587,
3632,
3664,
3713,
3726,
3768,
3771,
3810,
3848,
3868,
3896,
3910,
3921,
3928,
3940,
3947,
3949,
4001,
4004,
4022,
4026,
4036,
4073,
4093,
4099,
4120,
4136,
4156,
4176,
4182,
4191,
4198,
4252,
4259,
4261,
4294,
4341,
4348,
4356,
4384,
4389,
4401,
4428,
4431,
4445,
4470,
4473,
4474,
4490,
4509,
4510,
4533,
4548,
4558,
4594,
4596,
4603,
4610,
4619,
4630,
4652,
4658,
4682,
4708,
4736,
4753,
4760,
4781,
4784,
4799,
4807,
4808,
4842,
4882,
4897,
4900,
4922,
4936,
4960,
4970,
4978,
4994,
5003,
5044,
5061,
5107,
5127,
5131,
5136,
5145,
5146,
5175,
5218,
5223,
5248,
5294,
5299,
5301,
5311,
5343,
5344,
5396,
5406,
5410,
5424,
5447,
5461,
5468,
5475,
5478,
5523,
5530,
5535,
5548,
5559,
5580,
5604,
5622,
5641,
5649,
5656,
5671,
5689,
5721,
5731,
5734,
5738,
5740,
5748,
5791,
5801,
5807,
5822,
5829,
5834,
5847,
5854,
5878,
5882,
5919,
5947,
5981,
5982,
6025,
6028,
6039,
6056,
6064,
6073,
6081,
6088,
6101,
6139,
6142,
6194,
6199,
6200,
6203,
6214,
6238,
6241,
6244,
6248,
6256,
6266,
6271,
6275,
6295,
6315,
6364,
6368,
6377,
6400,
6430,
6477,
6480,
6490,
6526,
6539,
6556,
6584,
6598,
6601,
6609,
6612,
6645,
6655,
6679,
6683,
6719,
6727,
6734,
6770,
6776,
6791,
6798,
6800,
6826,
6833,
6836,
6858,
6882,
6901,
6923,
6967,
6979,
7022,
7060,
7064,
7083,
7093,
7094,
7120,
7125,
7142,
7151,
7165,
7173,
7188,
7191,
7202,
7216,
7219,
7267,
7358,
7383,
7387,
7396,
7408,
7432,
7462,
7480,
7488,
7497,
7531,
7561,
7582,
7591,
7612,
7677,
7687,
7701,
7705,
7712,
7721,
7736,
7756,
7777,
7783,
7792,
7797,
7802,
7808,
7866,
7885,
7891,
7913,
7936,
7946,
7963,
7996,
7999,
8011,
8014,
8028,
8047,
8077,
8101,
8119,
8125,
8140,
8152,
8209,
8212,
8231,
8258,
8275,
8303,
8308,
8312,
8345,
8346,
8370,
8402,
8411,
8414,
8424,
8435,
8452,
8462,
8479,
8509,
8515,
8522,
8541,
8560,
8563,
8585,
8594,
8596,
8603,
8610,
8647,
8661,
8662,
8672,
8690,
8696,
8739,
8783,
8811,
8813,
8821,
8856,
8877,
8885,
8897,
8898,
8934,
8955,
8972,
8977,
9038,
9045,
9071,
9085,
9110,
9120,
9157,
9164,
9185,
9203,
9235,
9278,
9290,
9292,
9319,
9334,
9362,
9387,
9404,
9407,
9410,
9422,
9478,
9512,
9535,
9604,
9616,
9622,
9631,
9656,
9710,
9721,
9728,
9733,
9738,
9774,
9791,
9803,
9805,
9817,
9823,
9839,
9847,
9854,
9863,
9872,
9884,
9935,
9937,
9974,
9980,
10003,
10015,
10016,
10066,
10093,
10118,
10132,
10135,
10151,
10158,
10169,
10172,
10180,
10187,
10189,
10192,
10197,
10211,
10214,
10256,
10278,
10290,
10301,
10310,
10344,
10473,
10474,
10482,
10499,
10525,
10532,
10535,
10556,
10568,
10579,
10586,
10609,
10612,
10650,
10665,
10685,
10686,
10688,
10711,
10728,
10748,
10751,
10781,
10805,
10823,
10838,
10857,
10865,
10872,
10893,
10899,
10917,
10935,
11001,
11072,
11089,
11090,
11108,
11117,
11136,
11148,
11153,
11181,
11190,
11201,
11204,
11216,
11237,
11259,
11279,
11282,
11304,
11312,
11332,
11341,
11354,
11356,
11365,
11377,
11417,
11427,
11433,
11434,
11439,
11444,
11448,
11461,
11466,
11468,
11473,
11489,
11499,
11516,
11531,
11533,
11557,
11572,
11608,
11635,
11638,
11644,
11684,
11702,
11740,
11749,
11754,
11764,
11767,
11784,
11789,
11795,
11798,
11804,
11818,
11820,
11860,
11869,
11874,
11903,
11916,
11927,
11933,
11962,
12009,
12020,
12035,
12041,
12049,
12065,
12072,
12098,
12100,
12107,
12167,
12202,
12207,
12233,
12269,
12290,
12304,
12314,
12340,
12416,
12425,
12428,
12446,
12462,
12476,
12496,
12511,
12518,
12530,
12532,
12539,
12567,
12597,
12601,
12602,
12622,
12693,
12707,
12713,
12716,
12734,
12763,
12765,
12799,
12843,
12853,
12865,
12866,
12919,
12926,
12936,
12944,
12959,
12965,
12980,
13004,
13016,
13019,
13037,
13055,
13063,
13098,
13103,
13106,
13115,
13143,
13144,
13153,
13171,
13184,
13193,
13199,
13207,
13217,
13227,
13232,
13276,
13283,
13307,
13317,
13330,
13345,
13363,
13387,
13426,
13428,
13431,
13489,
13501,
13533,
13589,
13600,
13603,
13623,
13665,
13672,
13675,
13708,
13713,
13720,
13730,
13735,
13767,
13773,
13792,
13843,
13891,
13946,
13967,
13976,
14017,
14030,
14041,
14054,
14058,
14060,
14063,
14078,
14080,
14089,
14131,
14134,
14137,
14188,
14215,
14222,
14249,
14292,
14320,
14339,
14346,
14353,
14365,
14384,
14414,
14428,
14435,
14483,
14486,
14506,
14513,
14520,
14526,
14528,
14533,
14576,
14599,
14613,
14639,
14644,
14653,
14662,
14695,
14704,
14713,
14725,
14783,
14810,
14816,
14822,
14828,
14883,
14889,
14904,
14917,
14927,
14941,
14946,
14952,
15010,
15012,
15033,
15041,
15047,
15066,
15068,
15072,
15095,
15150,
15152,
15175,
15176,
15210,
15245,
15258,
15263,
15264,
15279,
15301,
15306,
15313,
15329,
15341,
15367,
15368,
15386,
15404,
15422,
15436,
15444,
15467,
15498,
15503,
15528,
15534,
15536,
15559,
15565,
15583,
15599,
15602,
15616,
15626,
15667,
15684,
15711,
15745,
15763,
15779,
15811,
15814,
15817,
15853,
15881,
15890,
15899,
15905,
15915,
15937,
15950,
16002,
16041,
16042,
16052,
16121,
16132,
16136,
16150,
16153,
16180,
16190,
16192,
16195,
16210,
16225,
16256,
16266,
16274,
16302,
16310,
16322,
16339,
16345,
16348,
16357,
16382,
16402,
16461,
16469,
16474,
16483,
16497,
16523,
16534,
16550,
16564,
16582,
16591,
16609,
16642,
16648,
16656,
16662,
16665,
16678,
16701,
16713,
16716,
16758,
16768,
16797,
16804,
16811,
16813,
16881,
16888,
16893,
16922,
16937,
16958,
16965,
16978,
16980,
16989,
17011,
17014,
17023,
17063,
17081,
17084,
17099,
17126,
17129,
17138,
17164,
17170,
17203,
17206,
17224,
17305,
17322,
17327,
17332,
17342,
17387,
17410,
17419,
17429,
17439,
17440,
17457,
17458,
17469,
17477,
17512,
17518,
17532,
17536,
17559,
17569,
17641,
17667,
17674,
17693,
17710,
17729,
17754,
17763,
17780,
17784,
17790,
17830,
17851,
17868,
17879,
17896,
17901,
17916,
17935,
17953,
17991,
18009,
18016,
18034,
18061,
18070,
18079,
18132,
18145,
18169,
18170,
18190,
18192,
18201,
18228,
18243,
18260,
18279,
18285,
18297,
18300,
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124757,
124819,
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124903,
124915,
124938,
124945,
124973,
124986,
124991,
125011,
125014,
125082,
125105,
125163,
125165,
125205,
125219,
125239,
125240,
125257,
125284,
125302,
125327,
125336,
125355,
125363,
125365,
125372,
125378,
125383,
125387,
125390,
125414,
125435,
125466,
125481,
125522,
125531,
125544,
125564,
125588,
125602,
125613,
125621,
125648,
125651,
125681,
125719,
125773,
125774,
125779,
125786,
125792,
125822,
125828,
125831,
125837,
125880,
125891,
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125948,
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125973,
126014,
126016,
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126116,
126125,
126145,
126152,
126175,
126188,
126199,
126205,
126213,
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126286,
126294,
126300,
126322,
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126673,
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126857,
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126982,
127009,
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127027,
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127059,
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127126,
127129,
127145,
127154,
127165,
127171,
127197,
127198,
127207,
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127462,
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127510,
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127567,
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127585,
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127662,
127684,
127687,
127693,
127696,
127708,
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127790,
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127910,
127928,
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127975,
128016,
128031,
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128107,
128122,
128157,
128161,
128200,
128213,
128229,
128233,
128241,
128259,
128295,
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128313,
128345,
128362,
128375,
128376,
128406,
128410,
128416,
128443,
128451,
128465,
128466,
128484,
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128502,
128524,
128536,
128541,
128542,
128592,
128598,
128623,
128632,
128671,
128713,
128724,
128731,
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128805,
128820,
128830,
128842,
128852,
128859,
128866,
128875,
128892,
128896,
128914,
128935,
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128973,
129001,
129007,
129012,
129021,
129026,
129055,
129071,
129093,
129105,
129124,
129148,
129151,
129155,
129161,
129200,
129224,
129230,
129237,
129298,
129300,
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129345,
129351,
129352,
129363,
129393,
129410,
129415,
129449,
129477,
129501,
129518,
129520,
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129563,
129594,
129608,
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129652,
129659,
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129692,
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129782,
129793,
129820,
129824,
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129854,
129861,
129879,
129886,
129907,
129949,
129953,
129980,
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130031,
130043,
130057,
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130087,
130091,
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130101,
130111,
130126,
130137,
130138,
130149,
130177,
130180,
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130228,
130240,
130267,
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130294,
130306,
130325,
130398,
130402,
130421,
130438,
130441,
130475,
130486,
130503,
130551,
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130602,
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130633,
130684,
130688,
130698,
130700,
130712,
130739,
130748,
130774,
130783,
130802,
130811,
130836,
130840,
130856,
130864,
130873,
130918,
130927,
130929,
130958,
130966,
130970,
130976,
131006,
131008,
131020,
131059,
-1 };
#endif

// download the 8129334 polinomials version if you need higher dimensions
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_18
#error too many polynomials requested. not provided by this file
#endif

const long *const PrimitivePolynomials[N_MAX_DEGREE]={
   PrimitivePolynomialDegree01
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_01
 , PrimitivePolynomialDegree02
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_02
 , PrimitivePolynomialDegree03
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_03
 , PrimitivePolynomialDegree04
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_04
 , PrimitivePolynomialDegree05
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_05
 , PrimitivePolynomialDegree06
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_06
 , PrimitivePolynomialDegree07
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_07
 , PrimitivePolynomialDegree08
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_08
 , PrimitivePolynomialDegree09
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_09
 , PrimitivePolynomialDegree10
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_10
 , PrimitivePolynomialDegree11
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_11
 , PrimitivePolynomialDegree12
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_12
 , PrimitivePolynomialDegree13
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_13
 , PrimitivePolynomialDegree14
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_14
 , PrimitivePolynomialDegree15
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_15
 , PrimitivePolynomialDegree16
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_16
 , PrimitivePolynomialDegree17
#endif
#if PPMT_MAX_DIM > N_PRIMITIVES_UP_TO_DEGREE_17
 , PrimitivePolynomialDegree18
#endif
};

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