prop1728.z

#############################################################################
##
#W  prop1728.z             GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

PROPERTIES_SMALL_GROUPS[ 1728 ] := rec(
isNilpotent := [ 2, 127, -179, 186, -188, 816, -952, 2027, -2185, 2642, -2709
, 2713, 10943, -11353, 11416, -11422, 12177, -12229, 20578, -20781, 20788,
29951, -30087, 31074, -31094, 46029, -46096, 46187, -46189, 47833, -47839,
47937 ], 
isSupersolvable := [ 1, -2, 5, -188, 214, -952, 954, -1284, 1295, -2185, 2268
, -2713, 3021, -7242, 7331, -11353, 11396, -11422, 11425, -11808, 11811,
-12229, 13497, -18162, 18334, -20781, 20787, -20788, 21242, -23061, 23304,
-28127, 28145, -30087, 30749, -30883, 30954, -31094, 33794, -39001, 39508,
-44872, 44907, -46096, 46164, -46165, 46181, -46189, 47269, -47413, 47592,
-47758, 47773, -47839, 47915, 47928, -47930, 47934, -47937 ], 
isAbelian := [ 2, 127, 151, 175, 186, 816, 844, 944, 2027, 2099, 2171, 2642,
2696, 2713, 10943, 11027, 11327, 11416, 12177, 12201, 12225, 20578, 20740,
20788, 29951, 29979, 30079, 31074, 46029, 46083, 46187, 47833, 47937 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5, 6, 7, 8, 9 ], pos := [ [ 47863,
47905, -47906, 47915, 47929, -47931, 47935, 47937 ], [ 22749, -23035, 26312,
-26332, 26498, -26770, 26864, -26938, 26940, 27469, -27472, 27476, -27524,
27852, -27857, 27895, -27953, 27973, -27992, 27994, 28110, -28111, 28113,
-28126, 29349, -29380, 29630, -29639, 29641, -29657, 29659, -29664, 29670,
-29686, 29692, -29697, 29911, -29916, 29922, -29924, 29926, 29931, -29932,
29934, 29950, -29978, 31431, -31517, 31856, -31892, 32057, 32131, 32179,
32235, -32237, 32342, -32346, 32473, -32491, 32494, -32507, 32580, -32585,
32634, -32635, 32664, -32669, 32672, -32677, 32706, 33014, -33020, 33166,
-33201, 33279, -33284, 33333, -33335, 33373, -33384, 33413, 33445, -33448,
33528, -33547, 33592, -33595, 33624, -33625, 33646, -33652, 33669, 33724,
-33725, 33746, -33766, 33781, 33786, -33793, 33932, -36542, 36763, -37589,
37790, -39001, 39109, 39392, -39397, 39405, -39407, 39417, -39419, 39469,
-39472, 39486, -39487, 39497, 39507, 41190, -42673, 42846, -42914, 42963,
-43596, 43603, -43611, 43618, -43624, 43631, -43717, 43722, 43726, 43729,
-43765, 43781, -43895, 43902, -43907, 43914, -43917, 43924, -43966, 43976,
-43983, 43999, -44024, 44085, -44498, 44553, -44567, 44580, -44721, 44727,
-44750, 44754, -44762, 44765, -44793, 44799, -44811, 44815, -44818, 44821,
-44829, 44844, -44872, 44881, 44890, 44901, -44906, 45655, -45923, 45970,
-45985, 45989, -45997, 46001, -46005, 46008, -46010, 46015, -46022, 46027,
-46082, 46126, -46137, 46164, -46165, 46176, -46180, 46183, 46185, -46189,
46510, -46544, 46586, -46627, 46670, -46710, 47011, -47015, 47031, -47040,
47045, -47049, 47054, -47060, 47070, -47073, 47121, -47127, 47145, -47154,
47159, -47162, 47167, -47175, 47186, -47193, 47205, -47211, 47215, -47217,
47221, -47226, 47234, -47236, 47249, -47413, 47574, -47576, 47579, -47580,
47583, -47584, 47587, -47588, 47591, 47647, -47758, 47813, -47839, 47852,
-47853, 47855, -47856, 47859, 47861, -47862, 47874, 47880, 47887, -47888,
47894, -47896, 47898, -47900, 47903, -47904, 47909, 47911, -47912, 47914,
47918, 47921, 47927, -47928, 47932, -47934, 47936 ], [ 5487, -5507, 5593,
-5830, 5871, -5947, 5949, -5982, 6063, -6074, 6117, -6243, 6264, -6311, 6313,
-6331, 7153, -7156, 7158, -7203, 7205, -7207, 7209, -7211, 7213, -7239, 7241,
-7242, 7395, -7426, 8477, -8489, 8553, -8566, 8568, -8573, 8671, -8693, 9589,
-9594, 9629, -9632, 9664, -9666, 9737, 9739, -9802, 10295, -10307, 10315,
-10324, 10326, -10342, 10344, -10363, 10365, -10370, 10381, -10403, 10409,
-10425, 10431, -10436, 10861, -10866, 10869, -10874, 10881, -10884, 10890,
-10892, 10894, 10900, -10902, 10907, -10908, 10910, 10941, -11026, 11565,
-11604, 11683, -11728, 11753, -11755, 11761, -11771, 11790, -11801, 11808,
-11810, 12060, -12066, 12071, -12072, 12074, -12079, 12088, -12095, 12132,
-12144, 12146, -12147, 12149, 12152, 12154, 12156, -12157, 12159, -12161,
12163, -12169, 12177, -12200, 12325, 12468, -12488, 12626, -12629, 12674,
-12697, 12746, -12747, 12764, -12771, 12779, 12789, -12797, 12804, 12807,
-12811, 12894, 13015, 13073, -13074, 13285, -13286, 13370, 13381, -13386,
13394, -13396, 13406, -13408, 13458, -13461, 13475, -13476, 13486, 13496,
-15796, 16105, -16159, 16180, -16647, 16666, -16702, 16713, -16977, 16982,
-17125, 17132, -17160, 17193, -17369, 17372, -17451, 17457, -17481, 17499,
-17592, 17597, -17652, 17659, -17674, 17707, -17802, 17805, -17843, 17849,
-17861, 17879, -17923, 18018, -18162, 18179, -18180, 18198, -18199, 18244,
-18246, 18271, -18273, 18304, -18333, 18360, -18372, 18418, -18433, 18490,
-18509, 18570, -18589, 18670, -18699, 18770, -18789, 18830, -18839, 18902,
-18927, 19006, -19031, 19098, -19117, 19172, -19188, 19238, -19253, 19294,
-19305, 19334, -19341, 19380, -19394, 19612, -19621, 19667, -19678, 19719,
-19726, 19778, -19788, 19826, -19827, 19830, -20367, 20458, -20467, 20470,
-20479, 20483, -20500, 20504, -20509, 20513, -20523, 20527, -20531, 20538,
-20548, 20551, -20553, 20558, -20565, 20574, -20739, 20786, -20788, 20824,
-20879, 20906, -20916, 21021, -21074, 21100, -21110, 21134, -21163, 21178,
-21184, 21219, -21241, 21328, -22748, 23036, -23061, 23078, -23079, 23082,
23231, -23232, 23235, -23244, 23247, -23253, 23261, -23266, 23268, -23271,
23280, -23282, 23286, -23290, 23293, -23296, 23299, -23300, 23302, 24131,
-24142, 24235, -24383, 24434, -24477, 24479, 24771, -24773, 24776, -24804,
24844, -25521, 25564, -26263, 26333, -26497, 26771, -26863, 26939, 26941,
-27468, 27473, -27475, 27525, 27537, -27682, 27693, -27839, 27858, -27894,
27954, -27972, 27993, 27995, -28109, 28112, 28127, 28129, -28131, 28134,
-28139, 28141, -28142, 28145, -28176, 28426, -28435, 28437, -28453, 28455,
-28460, 28466, -28482, 28488, -28493, 28707, -28712, 28718, -28720, 28722,
28727, -28728, 28730, 28746, -28778, 29028, -29037, 29039, -29055, 29057,
-29062, 29068, -29084, 29090, -29095, 29309, -29314, 29320, -29322, 29324,
29329, -29330, 29332, 29348, 29381, -29601, 29623, -29629, 29640, 29658,
29665, -29669, 29687, -29691, 29698, -29798, 29801, -29842, 29844, -29855,
29859, -29887, 29891, -29897, 29901, -29910, 29917, -29921, 29925, 29927,
-29930, 29933, 29935, -29949, 29979, -30078, 30380, -30390, 30394, -30396,
30400, -30402, 30410, -30427, 30731, -30733, 30736, -30737, 30740, -30741,
30744, -30745, 30748, -30883, 30962, -30965, 30976, -30978, 30988, -30990,
31002, -31005, 31014, -31015, 31022, -31023, 31030, -31031, 31034, -31094,
31102, -31109, 31122, -31124, 31151, -31157, 31162, -31164, 31169, -31175,
31180, -31182, 31187, -31193, 31198, -31200, 31205, -31410, 31518, -31855,
31893, -31896, 31902, 31983, -31985, 32050, -32056, 32058, -32059, 32124,
-32130, 32132, -32133, 32174, -32178, 32232, -32234, 32267, -32270, 32277,
32284, -32285, 32287, 32289, 32298, -32341, 32347, -32462, 32492, -32493,
32508, -32579, 32586, -32633, 32636, -32663, 32670, -32671, 32678, -32705,
32738, -32741, 32821, -32840, 32885, -32888, 32917, -32918, 32939, -32945,
32962, 32972, -33013, 33021, -33156, 33202, -33278, 33285, -33332, 33336,
-33372, 33385, -33412, 33420, -33444, 33449, -33521, 33548, -33591, 33596,
-33623, 33626, -33645, 33653, -33668, 33677, 33687, -33695, 33702, 33705,
-33723, 33726, -33745, 33767, -33780, 33782, -33785, 33794, -33931, 36543,
-36762, 37590, -37789, 39013, 39061, 39098, 39110, 39123, -39126, 39145,
39159, -39160, 39200, 39214, -39215, 39255, 39266, -39271, 39279, -39281,
39291, -39293, 39343, -39346, 39360, -39361, 39371, 39381, -39391, 39398,
-39404, 39408, -39416, 39423, -39431, 39433, -39448, 39451, -39468, 39473,
-39485, 39488, -39496, 39499, -39506, 39508, -40323, 40432, -40469, 40498,
-40849, 40856, -40864, 40870, -40919, 40924, 40927, -40947, 40955, -41021,
41028, -41033, 41039, -41063, 41070, -41075, 41083, -41099, 41134, -41189,
42674, -42845, 42915, -42962, 43597, -43602, 43612, -43617, 43625, -43630,
43718, -43721, 43723, -43725, 43727, -43728, 43766, -43780, 43896, -43901,
43908, -43913, 43918, -43923, 43967, -43975, 43984, -43998, 44025, -44084,
44499, -44552, 44568, -44579, 44722, -44726, 44751, -44753, 44763, -44764,
44794, -44798, 44812, -44814, 44819, -44820, 44830, -44843, 44873, -44876,
44882, -44883, 44889, 44907, -45175, 45222, -45237, 45241, -45249, 45253,
-45257, 45260, -45262, 45267, -45274, 45279, -45549, 45596, -45611, 45615,
-45623, 45627, -45631, 45634, -45636, 45641, -45648, 45653, -45654, 45924,
-45969, 45986, -45988, 45998, -46000, 46006, -46007, 46011, -46014, 46023,
-46026, 46083, -46096, 46098, -46101, 46108, 46110, -46112, 46114, -46125,
46139, -46140, 46144, -46147, 46151, -46154, 46158, 46162, -46163, 46166,
-46175, 46181, -46182, 46184, 46195, -46225, 46235, -46236, 46240, -46241,
46254, -46256, 46266, -46267, 46276, -46277, 46282, 46297, -46375, 46401,
-46405, 46411, -46414, 46423, -46430, 46439, -46441, 46459, -46509, 46545,
-46585, 46628, -46669, 46713, -46714, 46725, 46796, -46942, 46980, -46984,
47001, -47003, 47005, 47007, 47010, 47016, -47030, 47041, -47044, 47050,
-47053, 47061, -47069, 47074, -47077, 47089, -47095, 47099, -47101, 47105,
-47110, 47118, -47120, 47128, -47144, 47155, -47158, 47163, -47166, 47176,
-47185, 47194, -47204, 47212, -47214, 47218, -47220, 47227, -47233, 47237,
-47248, 47456, -47476, 47491, -47497, 47553, -47555, 47558, -47559, 47562,
-47563, 47566, -47567, 47570, -47573, 47577, -47578, 47581, -47582, 47585,
-47586, 47589, -47590, 47592, -47646, 47759, -47812, 47847, -47848, 47850,
-47851, 47854, 47858, 47860, 47868, -47871, 47877, -47879, 47881, -47882,
47884, -47886, 47889, -47890, 47893, 47897, 47901, -47902, 47908, 47910,
47913, 47916, -47917, 47919, -47920, 47922, -47926 ], [ 214, -245, 496, -522,
524, -529, 540, -562, 776, -781, 788, -791, 797, -799, 815, -843, 983, -1046,
1169, -1241, 1280, -1294, 1319, -1320, 1345, -1349, 1354, -1355, 1374, -1375,
1387, -1390, 1443, -1450, 1607, -1608, 1617, -1619, 1629, -1631, 1641, -1643,
1649, 1653, 1661, 1665, 1677, 1685, 1691, 1701, -1702, 1716, -1718, 1740,
-1746, 1793, -1801, 1806, -1812, 1817, -1818, 1820, -1821, 1823, -1832, 1849,
-1864, 1937, -1962, 1965, -1968, 1971, 1974, 1977, -1979, 1982, -1984, 1987,
-1988, 1990, -1992, 1994, -1996, 1998, -2004, 2006, -2012, 2027, -2098, 2197,
2242, 2251, 2262, -2536, 2583, -2592, 2596, -2607, 2611, -2618, 2625, -2635,
2640, -2695, 2730, -2739, 2744, -2749, 2760, -2775, 2780, -2784, 2791, -2801,
2814, -2815, 2824, 2834, -2835, 2838, 2842, -2845, 2850, -2851, 2891, -2896,
2921, -2922, 2925, -2926, 2928, 2948, -2949, 2952, -2961, 2964, -2970, 2978,
-2983, 2985, -2988, 2997, -2999, 3003, -3007, 3010, -3013, 3016, -3017, 3019,
3082, -4131, 4174, -4777, 4802, -5277, 5354, -5486, 5508, -5592, 5831, -5870,
5948, 5983, -6062, 6075, -6116, 6244, -6263, 6312, 6332, -7152, 7157, 7204,
7208, 7212, 7240, 7245, -7250, 7256, -7269, 7272, -7275, 7283, -7291, 7298,
-7315, 7319, -7324, 7331, -7394, 7427, -7458, 7505, -7527, 7585, -7601, 7663,
-7684, 7715, -7718, 7735, -7740, 7759, -7764, 7835, -7866, 7963, -7994, 8043,
-8050, 8107, -8130, 8195, -8214, 8275, -8294, 8329, -8335, 8442, -8461, 8463,
-8476, 8498, -8524, 8526, -8539, 8541, -8552, 8567, 8574, -8587, 8589, -8594,
8610, -8643, 8649, -8670, 8704, -8726, 8751, -8762, 8801, -8813, 8851, -8862,
8877, 8899, -8908, 8939, -8948, 8961, 8981, -8989, 9013, -9019, 9043, -9050,
9095, -9112, 9175, -9193, 9261, -9283, 9320, -9324, 9364, -9375, 9425, -9441,
9492, -9503, 9532, -9533, 9547, -9550, 9563, -9566, 9575, -9588, 9597, -9602,
9614, -9619, 9621, -9628, 9639, -9642, 9652, -9655, 9657, -9663, 9672, -9674,
9693, -9701, 9719, -9722, 9731, -9732, 9735, -9736, 9738, 9803, -10244, 10287
, -10294, 10308, -10314, 10325, 10343, 10364, 10371, -10380, 10404, -10408,
10426, -10430, 10437, -10638, 10641, -10659, 10662, -10726, 10728, -10732,
10734, -10738, 10742, -10760, 10764, -10802, 10806, -10824, 10828, -10832,
10836, -10839, 10843, -10860, 10867, -10868, 10875, -10880, 10885, -10889,
10893, 10895, -10899, 10903, -10906, 10909, 10911, -10940, 11027, -11326,
11396, -11422, 11436, -11459, 11504, -11530, 11545, -11546, 11605, -11682,
11729, -11752, 11772, -11789, 11802, -11807, 11816, -11822, 11827, -11828,
11830, -11835, 11844, -11851, 11888, -11900, 11902, -11903, 11905, 11908,
11910, 11912, -11913, 11915, -11917, 11919, -11925, 11938, -11944, 11949,
-11950, 11952, -11957, 11966, -11973, 12010, -12022, 12024, -12025, 12027,
12030, 12032, 12034, -12035, 12037, -12039, 12041, -12047, 12067, -12070,
12073, 12080, -12087, 12096, -12106, 12109, -12127, 12145, 12148, 12150,
-12151, 12153, 12155, 12158, 12162, 12170, -12176, 12201, -12224, 12230,
-12233, 12238, -12241, 12246, -12249, 12314, -12324, 12454, -12467, 12491,
-12494, 12507, -12509, 12511, 12515, 12522, -12546, 12553, -12625, 12630,
-12673, 12698, -12745, 12748, -12763, 12772, -12778, 12780, -12788, 12798,
-12803, 12805, -12806, 12823, 12861, 12892, -12893, 12897, 12943, -12946,
13003, -13004, 13016, 13029, -13032, 13051, -13052, 13075, -13076, 13097,
13100, -13102, 13105, -13109, 13146, -13147, 13175, -13178, 13260, -13262,
13283, -13284, 13289, -13290, 13293, -13294, 13317, -13318, 13327, -13330,
13368, -13369, 13371, -13380, 13387, -13393, 13397, -13405, 13412, -13420,
13422, -13437, 13440, -13457, 13462, -13474, 13477, -13485, 13488, -13495,
15797, -16104, 16160, -16179, 16648, -16665, 16703, -16712, 16978, -16981,
17126, -17131, 17161, -17192, 17370, -17371, 17452, -17456, 17482, -17498,
17593, -17596, 17653, -17658, 17675, -17706, 17803, -17804, 17844, -17848,
17862, -17878, 17924, -18017, 18163, -18170, 18181, -18185, 18196, -18197,
18220, -18231, 18247, -18252, 18268, -18270, 18334, -18359, 18373, -18417,
18434, -18489, 18510, -18569, 18590, -18669, 18700, -18769, 18790, -18829,
18840, -18901, 18928, -19005, 19032, -19097, 19118, -19171, 19189, -19237,
19254, -19293, 19306, -19333, 19342, -19379, 19395, -19409, 19424, -19430,
19450, -19455, 19472, -19476, 19490, -19493, 19508, -19512, 19526, -19529,
19544, -19548, 19562, -19565, 19578, -19581, 19590, -19611, 19624, -19633,
19637, -19648, 19652, -19666, 19682, -19693, 19697, -19702, 19706, -19718,
19730, -19737, 19746, -19751, 19756, -19777, 19795, -19805, 19810, -19811,
19818, -19819, 19822, -19825, 19828, -19829, 20368, -20457, 20468, -20469,
20480, -20482, 20501, -20503, 20510, -20512, 20524, -20526, 20532, -20537,
20549, -20550, 20554, -20557, 20566, -20573, 20740, -20785, 20789, 20792,
-20819, 20880, -20905, 20917, -20924, 20940, -20969, 20984, -20990, 20995,
-21016, 21075, -21099, 21111, -21130, 21164, -21177, 21185, -21188, 21195,
-21218, 21242, -21327, 23062, -23063, 23066, 23070, -23071, 23074, 23080,
23083, 23086, -23091, 23098, -23108, 23115, -23119, 23139, -23140, 23143,
-23152, 23155, -23161, 23169, -23174, 23176, -23179, 23188, -23190, 23194,
-23198, 23201, -23204, 23207, -23208, 23210, 23214, -23230, 23233, -23234,
23254, -23260, 23267, 23272, -23279, 23283, -23285, 23291, -23292, 23297,
-23298, 23301, 23303, 23327, -23698, 23723, -24102, 24143, -24234, 24384,
-24433, 24478, 24480, -24770, 24774, -24775, 24805, -24843, 25522, -25563,
26264, -26311, 27526, -27536, 27683, -27692, 27840, -27851, 28128, 28132,
-28133, 28177, -28397, 28419, -28425, 28436, 28454, 28461, -28465, 28483,
-28487, 28494, -28594, 28597, -28638, 28640, -28651, 28655, -28683, 28687,
-28693, 28697, -28706, 28713, -28717, 28721, 28723, -28726, 28729, 28731,
-28745, 28779, -28999, 29021, -29027, 29038, 29056, 29063, -29067, 29085,
-29089, 29096, -29196, 29199, -29240, 29242, -29253, 29257, -29285, 29289,
-29295, 29299, -29308, 29315, -29319, 29323, 29325, -29328, 29331, 29333,
-29347, 29602, -29622, 29799, -29800, 29843, 29856, -29858, 29888, -29890,
29898, -29900, 30079, -30087, 30118, 30122, 30126, 30128, -30355, 30359,
-30361, 30363, 30365, 30368, -30379, 30391, -30393, 30397, -30399, 30403,
-30409, 30457, -30460, 30465, -30466, 30477, -30481, 30490, -30493, 30498,
-30499, 30504, -30505, 30510, -30574, 30586, -30587, 30596, -30599, 30602,
-30623, 30670, -30673, 30676, -30677, 30683, -30687, 30692, -30695, 30698,
-30699, 30702, -30703, 30706, -30707, 30720, -30721, 30724, -30725, 30727,
-30730, 30734, -30735, 30738, -30739, 30742, -30743, 30746, -30747, 30884,
-30961, 30966, -30975, 30979, -30987, 30991, -31001, 31006, -31013, 31016,
-31021, 31024, -31029, 31032, -31033, 31096, 31098, -31101, 31110, -31117,
31125, -31139, 31144, -31146, 31158, -31161, 31165, -31168, 31176, -31179,
31183, -31186, 31194, -31197, 31201, -31204, 31411, -31430, 31897, -31898,
31909, -31911, 31976, -31982, 31986, -32049, 32060, -32123, 32134, -32173,
32180, -32186, 32227, -32231, 32240, -32243, 32250, 32257, -32258, 32260,
32262, 32271, -32274, 32278, -32283, 32286, 32288, 32290, -32297, 32463,
-32472, 32713, -32737, 32742, -32814, 32841, -32884, 32889, -32916, 32919,
-32938, 32946, -32961, 32963, -32971, 33157, -33165, 33414, -33419, 33522,
-33527, 33670, -33676, 33678, -33686, 33696, -33701, 33703, -33704, 39002,
39014, 39027, -39030, 39049, -39050, 39062, 39075, -39078, 39097, 39099,
-39108, 39111, -39122, 39127, -39144, 39146, -39148, 39161, -39164, 39177,
-39180, 39199, 39201, -39203, 39216, -39219, 39232, -39235, 39254, 39256,
-39265, 39272, -39278, 39282, -39290, 39297, -39305, 39307, -39322, 39325,
-39342, 39347, -39359, 39362, -39370, 39373, -39380, 39420, -39422, 39432,
39449, -39450, 39498, 40324, -40431, 40470, -40497, 40850, -40855, 40865,
-40869, 40920, -40923, 40925, -40926, 40948, -40954, 41022, -41027, 41034,
-41038, 41064, -41069, 41076, -41082, 41100, -41133, 44877, -44880, 44884,
-44888, 44891, -44900, 45176, -45221, 45238, -45240, 45250, -45252, 45258,
-45259, 45263, -45266, 45275, -45278, 45550, -45595, 45612, -45614, 45624,
-45626, 45632, -45633, 45637, -45640, 45649, -45652, 46097, 46104, 46106,
-46107, 46109, 46113, 46138, 46141, -46143, 46148, -46150, 46155, -46157,
46159, -46161, 46237, -46239, 46242, -46253, 46257, -46265, 46268, -46275,
46278, -46281, 46289, -46290, 46296, 46390, -46400, 46406, -46410, 46415,
-46422, 46431, -46438, 46442, -46458, 46711, -46712, 46715, -46724, 46728,
-46729, 46740, -46795, 46943, -46979, 46988, -46990, 46992, 46994, 46997,
-47000, 47004, 47006, 47008, -47009, 47078, -47088, 47096, -47098, 47102,
-47104, 47111, -47117, 47414, -47455, 47477, -47490, 47498, -47552, 47556,
-47557, 47560, -47561, 47564, -47565, 47568, -47569, 47840, -47843, 47845,
-47846, 47849, 47857, 47864, 47866, -47867, 47872, -47873, 47875, -47876,
47883, 47891, -47892, 47907 ], [ 3, -4, 10, -16, 21, -22, 24, -29, 38, -45,
82, -94, 96, -97, 99, 102, -103, 105, -106, 109, -111, 113, -119, 127, -150,
189, -190, 193, 198, -200, 203, -208, 210, -211, 246, -466, 488, -495, 523,
530, -539, 563, -663, 666, -707, 709, -713, 717, -745, 749, -760, 764, -775,
782, -787, 792, -796, 800, -814, 844, -943, 1047, -1168, 1242, -1279, 1315,
-1318, 1321, -1327, 1332, -1336, 1341, -1344, 1350, -1353, 1356, -1360, 1365,
-1366, 1369, -1373, 1377, -1386, 1391, -1394, 1403, -1406, 1415, -1416, 1423,
-1424, 1427, -1442, 1451, -1458, 1463, -1464, 1475, -1478, 1493, -1497, 1531,
-1541, 1571, -1578, 1603, -1606, 1609, -1616, 1620, -1628, 1632, -1640, 1644,
-1648, 1650, -1652, 1654, 1657, 1659, -1660, 1662, -1664, 1666, 1669, 1671,
1674, 1678, -1680, 1683, -1684, 1686, -1687, 1690, 1692, -1693, 1695, -1696,
1699, -1700, 1703, -1705, 1709, -1715, 1720, -1722, 1725, -1739, 1748, -1754,
1757, 1763, -1764, 1771, -1772, 1779, -1780, 1802, -1805, 1813, -1816, 1819,
1822, 1833, -1848, 1865, -1886, 1889, -1899, 1902, -1928, 1963, -1964, 1969,
-1970, 1972, -1973, 1975, -1976, 1980, -1981, 1985, -1986, 1989, 1993, 1997,
2005, 2013, -2026, 2099, -2170, 2186, 2198, 2211, -2214, 2233, -2237, 2243,
-2244, 2250, 2537, -2582, 2593, -2595, 2608, -2610, 2619, -2624, 2636, -2639,
2696, -2709, 2718, -2729, 2740, -2743, 2750, -2759, 2776, -2779, 2785, -2790,
2802, -2803, 2806, 2810, -2813, 2818, 2822, -2823, 2827, 2836, 2839, 2846,
-2847, 2852, -2853, 2858, -2871, 2885, -2890, 2897, -2904, 2908, -2910, 2917,
-2920, 2923, -2924, 2927, 2931, -2947, 2950, -2951, 2971, -2977, 2984, 2989,
-2996, 3000, -3002, 3008, -3009, 3014, -3015, 3018, 3020, -3081, 4132, -4173,
4778, -4801, 5278, -5353, 7243, -7244, 7251, -7255, 7280, -7282, 7292, -7297,
7459, -7504, 7528, -7584, 7602, -7662, 7685, -7714, 7719, -7734, 7741, -7758,
7765, -7834, 7867, -7962, 7995, -8042, 8051, -8106, 8131, -8194, 8215, -8274,
8295, -8328, 8336, -8342, 8357, -8363, 8379, -8382, 8393, -8395, 8407, -8410,
8421, -8423, 8427, -8441, 8462, 8490, -8497, 8525, 8540, 8588, 8595, -8609,
8644, -8648, 8694, -8703, 8727, -8750, 8763, -8800, 8814, -8850, 8863, -8876,
8878, -8898, 8909, -8938, 8949, -8960, 8962, -8980, 8990, -9012, 9020, -9042,
9051, -9094, 9113, -9130, 9135, -9174, 9196, -9260, 9284, -9306, 9309, -9319,
9326, -9330, 9334, -9347, 9351, -9363, 9379, -9424, 9442, -9458, 9462, -9475,
9479, -9491, 9507, -9518, 9522, -9525, 9529, -9531, 9537, -9546, 9551, -9562,
9567, -9574, 9595, -9596, 9603, -9613, 9620, 9633, -9638, 9643, -9651, 9656,
9667, -9671, 9675, -9692, 9702, -9718, 9723, -9730, 9733, -9734, 10245,
-10286, 10639, -10640, 10660, -10661, 10727, 10733, 10739, -10741, 10761,
-10763, 10803, -10805, 10825, -10827, 10833, -10835, 10840, -10842, 11327,
-11395, 11460, -11503, 11531, -11544, 11547, -11564, 11756, -11760, 11823,
-11826, 11829, 11836, -11843, 11852, -11862, 11865, -11883, 11901, 11904,
11906, -11907, 11909, 11911, 11914, 11918, 11926, -11932, 11945, -11948,
11951, 11958, -11965, 11974, -11984, 11987, -12005, 12023, 12026, 12028,
-12029, 12031, 12033, 12036, 12040, 12048, -12059, 12107, -12108, 12128,
-12131, 12225, -12229, 12234, -12237, 12242, -12245, 12250, -12313, 12326,
-12453, 12495, -12498, 12501, -12506, 12510, 12512, -12514, 12516, -12521,
12547, -12552, 12812, 12824, 12837, -12840, 12859, -12860, 12882, -12891,
12895, -12896, 12908, -12912, 12923, -12928, 12933, -12942, 12951, -12952,
12965, -12970, 12981, -12982, 12985, -12988, 12993, -12994, 12999, -13002,
13005, -13014, 13017, -13028, 13033, -13050, 13053, -13072, 13077, -13096,
13098, -13099, 13103, -13104, 13110, -13145, 13148, -13154, 13179, -13188,
13213, -13220, 13257, -13259, 13273, -13282, 13287, -13288, 13291, -13292,
13300, -13304, 13310, -13316, 13321, -13326, 13333, -13334, 13341, -13346,
13352, -13353, 13355, -13358, 13361, -13362, 13365, -13367, 13409, -13411,
13421, 13438, -13439, 13487, 18171, -18178, 18186, -18195, 18200, -18219,
18232, -18243, 18253, -18267, 18274, -18303, 19410, -19423, 19431, -19449,
19456, -19471, 19477, -19489, 19494, -19507, 19513, -19525, 19530, -19543,
19549, -19561, 19566, -19577, 19582, -19589, 19622, -19623, 19634, -19636,
19649, -19651, 19679, -19681, 19694, -19696, 19703, -19705, 19727, -19729,
19738, -19745, 19752, -19755, 19789, -19794, 19806, -19809, 19812, -19817,
19820, -19821, 20820, -20823, 20925, -20936, 20970, -20983, 20991, -20994,
21017, -21020, 21131, -21133, 21189, -21194, 23064, 23067, 23072, 23075,
23081, 23084, -23085, 23092, -23094, 23109, -23111, 23122, -23138, 23141,
-23142, 23162, -23168, 23175, 23180, -23187, 23191, -23193, 23199, -23200,
23205, -23206, 23209, 23211, -23213, 23245, -23246, 23304, -23326, 23699,
-23722, 24103, -24130, 28140, 28143, -28144, 28398, -28418, 28595, -28596,
28639, 28652, -28654, 28684, -28686, 28694, -28696, 29000, -29020, 29197,
-29198, 29241, 29254, -29256, 29286, -29288, 29296, -29298, 30092, -30093,
30100, -30101, 30106, 30110, 30114, 30116, -30117, 30119, -30121, 30123,
-30125, 30127, 30356, -30358, 30362, 30364, 30366, -30367, 30428, -30456,
30461, -30464, 30467, -30476, 30482, -30489, 30494, -30497, 30500, -30503,
30506, -30509, 30575, -30585, 30588, -30595, 30600, -30601, 30624, -30669,
30674, -30675, 30678, -30682, 30688, -30691, 30696, -30697, 30700, -30701,
30704, -30705, 30708, -30719, 30722, -30723, 30726, 31118, -31121, 31140,
-31143, 31147, -31150, 31899, -31901, 31903, -31905, 31912, -31975, 32187,
-32226, 32244, -32247, 32251, -32256, 32259, 32261, 32263, -32266, 32275,
-32276, 32707, -32712, 32815, -32820, 39003, -39012, 39015, -39026, 39031,
-39048, 39051, -39060, 39063, -39074, 39079, -39096, 39149, -39158, 39165,
-39176, 39181, -39198, 39204, -39213, 39220, -39231, 39236, -39253, 39294,
-39296, 39306, 39323, -39324, 39372, 46102, -46103, 46105, 46190, -46194,
46226, -46228, 46232, -46234, 46283, -46288, 46291, -46295, 46376, -46389,
46726, -46727, 46730, -46739, 46985, -46987, 46991, 46993, 46995, -46996,
47844, 47865 ], [ 17, -20, 23, 30, -37, 46, -56, 59, -77, 95, 98, 100, -101,
104, 107, -108, 112, 120, -126, 151, -174, 191, 194, 197, 201, -202, 467,
-487, 664, -665, 708, 714, -716, 746, -748, 761, -763, 944, -952, 954, -982,
1305, -1309, 1328, -1331, 1337, -1340, 1361, -1364, 1367, -1368, 1376, 1395,
-1402, 1407, -1414, 1417, -1422, 1425, -1426, 1459, -1462, 1465, -1474, 1479,
-1492, 1498, -1502, 1507, -1530, 1544, -1570, 1579, -1586, 1591, -1592, 1599,
-1600, 1655, -1656, 1658, 1667, -1668, 1670, 1672, -1673, 1675, -1676, 1681,
-1682, 1688, -1689, 1694, 1697, -1698, 1706, -1708, 1719, 1723, -1724, 1747,
1755, -1756, 1758, -1762, 1765, -1770, 1773, -1778, 1781, -1792, 1887, -1888,
1900, -1901, 1929, -1936, 2171, -2185, 2187, -2196, 2199, -2210, 2215, -2232,
2238, -2241, 2245, -2249, 2252, -2261, 2712, -2713, 2715, -2717, 2804, 2807,
2816, -2817, 2821, 2825, -2826, 2830, 2833, 2837, 2840, -2841, 2848, -2849,
2854, -2857, 2872, -2878, 2905, -2907, 2912, 2914, 2916, 2929, -2930, 2962,
-2963, 7270, -7271, 7276, -7279, 7316, -7318, 7325, -7330, 8343, -8356, 8364,
-8378, 8383, -8392, 8396, -8406, 8411, -8420, 8424, -8426, 9131, -9134, 9194,
-9195, 9307, -9308, 9325, 9331, -9333, 9348, -9350, 9376, -9378, 9459, -9461,
9476, -9478, 9504, -9506, 9519, -9521, 9526, -9528, 9534, -9536, 11424,
-11435, 11811, -11815, 11863, -11864, 11884, -11887, 11933, -11937, 11985,
-11986, 12006, -12009, 12489, -12490, 12499, -12500, 12813, -12822, 12825,
-12836, 12841, -12858, 12862, -12881, 12898, -12907, 12913, -12922, 12929,
-12932, 12947, -12950, 12953, -12964, 12971, -12980, 12983, -12984, 12989,
-12992, 12995, -12998, 13155, -13174, 13189, -13212, 13221, -13256, 13263,
-13272, 13295, -13299, 13305, -13309, 13319, -13320, 13331, -13332, 13335,
-13340, 13347, -13351, 13354, 13359, -13360, 13363, -13364, 20791, 20937,
-20939, 23065, 23068, -23069, 23073, 23076, -23077, 23095, -23097, 23112,
-23114, 23120, -23121, 23153, -23154, 30088, -30091, 30094, -30099, 30102,
-30105, 30107, -30109, 30111, -30113, 30115, 31095, 31097, 31906, -31908,
32238, -32239, 32248, -32249, 46229, -46231 ], [ 5, -9, 57, -58, 78, -81, 175
, -179, 182, 184, -188, 192, 195, -196, 209, 212, -213, 953, 1295, -1304,
1310, -1314, 1503, -1506, 1542, -1543, 1587, -1590, 1593, -1598, 1601, -1602,
2710, -2711, 2714, 2805, 2808, -2809, 2819, -2820, 2828, -2829, 2831, -2832,
2879, -2884, 2911, 2913, 2915, 11423, 20790 ], [ 1, -2, 180, -181, 183 ] ] ),
frattFacs := rec( frattFacs := [ 19, 37, 56, 74, 92, 57, 75, 93, 220, 238,
256, 274, 167, 185, 203, 221, 239, 257, 870, 888, 906, 924, 942, 223, 241,
259, 277, 710, 728, 746, 764, 782, 800, 818, 836, 854, 872, 890, 908, 4077,
4095, 4113, 4131, 4149, 4167, 658, 676, 694, 712, 730, 748, 766, 784, 802,
820, 3287, 3305, 3323, 3341, 3359, 3377, 3395, 3413, 3431, 3449, 3467, 3485,
3503, 3521, 3539, 3557, 27678, 27696, 27714, 27732, 27750, 27768, 27786, 2767
, 2785, 2803, 2821, 2839, 2857, 2875, 2893, 2911, 2929, 2947, 2965, 2983,
3001, 3019, 3037, 3055, 3073, 3091, 3109, 3127, 3145, 3163, 3181, 3199, 18446
, 18464, 18482, 18500, 18518, 18536, 18554, 18572, 18590, 18608, 18626, 18644
, 18662, 18680, 18698, 18716, 18734, 18752, 18770, 18788, 18806, 18824, 13227
, 13245, 13263, 13281, 13299, 13317, 13335, 13353, 13371, 13389, 13407, 13425
, 13443, 13461, 13479, 13497, 13515, 13533, 13551, 13569, 13587, 13605, 13623
, 13641, 13659, 13677, 13695, 13713, 13731, 13749, 13767, 13785, 13803, 13821
, 13839, 13857, 13875, 13893, 13911, 13929, 13947, 13965, 155752, 155770,
155788, 155806, 155824, 155842, 155860, 155878, 155896, 155914, 155932,
155950, 155968, 155986, 156004, 156022, 156040, 156058, 156076, 156094,
156112, 156130, 156148, 156166, 156184, 156202, 156220, 156238, 156256,
156274, 83915, 83933, 83951, 83969, 83987, 84005, 84023, 84041, 84059, 84077,
84095, 84113, 84131, 84149, 84167, 84185, 84203, 84221, 84239, 84257, 84275,
84293, 84311, 84329, 84347, 84365, 84383, 84401, 84419, 84437, 84455, 84473,
84491, 84509, 84527, 84545, 84563, 84581, 84599, 84617, 84635, 84653, 84671,
84689, 84707, 84725, 84743, 84761, 84779, 84797, 84815, 84833, 84851, 84869,
84887, 84905, 84923, 84941, 84959, 84977, 84995, 85013, 85031, 85049, 85067 ]
, pos := [ 1, 2, 4, 126, 179, 183, 185, 188, 196, 213, 815, 952, 953, 1284,
1294, 1782, 2026, 2185, 2233, 2261, 2267, 2641, 2709, 2710, 2711, 2712, 2713,
2714, 2784, 2801, 2833, 2857, 2928, 3020, 7242, 7330, 9738, 10942, 11353,
11374, 11381, 11390, 11395, 11415, 11422, 11423, 11424, 11546, 11755, 11808,
11810, 11932, 12054, 12176, 12229, 12247, 12469, 12488, 12515, 12771, 12811,
13003, 13147, 13370, 13496, 18162, 18303, 18333, 19829, 20577, 20781, 20782,
20783, 20784, 20785, 20786, 20787, 20788, 20789, 20790, 20791, 20924, 20994,
21118, 21188, 21205, 21241, 23061, 23069, 23077, 23085, 23102, 23119, 23211,
23303, 24805, 27525, 28127, 28144, 28746, 29348, 29950, 30087, 30115, 30127,
30144, 30161, 30326, 30355, 30368, 30415, 30427, 30511, 30574, 30602, 30623,
30707, 30727, 30748, 30883, 30928, 30953, 31033, 31073, 31094, 31096, 31101,
31132, 31150, 31168, 31186, 31204, 31809, 31896, 31902, 31909, 31983, 32057,
32131, 32179, 32234, 32237, 32264, 32291, 32706, 32962, 33413, 33669, 33709,
33793, 39001, 39049, 39097, 39145, 39200, 39255, 39381, 39507, 41189, 44173,
44872, 44900, 44906, 45280, 45654, 46028, 46096, 46097, 46099, 46101, 46105,
46109, 46112, 46113, 46116, 46119, 46120, 46125, 46132, 46137, 46138, 46139,
46140, 46144, 46147, 46151, 46154, 46158, 46162, 46163, 46165, 46170, 46175,
46180, 46184, 46186, 46189, 46194, 46225, 46228, 46231, 46234, 46236, 46241,
46256, 46267, 46282, 46293, 46296, 46375, 46382, 46389, 46392, 46395, 46400,
46405, 46410, 46441, 46458, 46475, 46492, 46509, 46674, 46710, 46725, 46740,
46795, 46850, 46905, 46942, 46979, 46984, 46997, 47010, 47073, 47120, 47189,
47236, 47248, 47268, 47413, 47434, 47455, 47476, 47483, 47490, 47497, 47518,
47539, 47544, 47549, 47570, 47591, 47646, 47726, 47758, 47767, 47772, 47792,
47812, 47832, 47839 ] ) );