X₆₆₄

TRILINEAR POLE OF LINE X₂X_7

X₆₆₄ = trilinear pole of line {2, 7}

5, 6, 7 3, 4, 5 Kepler Kimberling

X₆₆₄ (TRILINEAR POLE OF LINE X₂X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 85}, {75, 77}

• Related Centers: X₁ (INCENTER), X₈₅ (ISOTOMIC CONJUGATE OF X₉), X₇₅ (ISOTOMIC CONJUGATE OF INCENTER), X₇₇ (ISOGONAL CONJUGATE OF X₃₃)

Trilinears: \(1/[a(b - c)(b + c - a)] : :\)

Search Value (6, 9, 13): \(0.733614853529\)

▸ Linear Combinations1 combination

• X₆₆₄ = \(3\) X₂ - \(4\) X₁₇₀₄₄, \(6\) X₂ - \(5\) X₃₁₆₄₀, \(9\) X₂ - \(8\) X₄₀₄₈₃, X₁₅₀ - \(3\) X₃₈₉₄₁, \(3\) X₁₁₂₁ - \(4\) X₁₁₄₆, \(3\) X₁₁₂₁ - \(8\) X₁₇₀₄₄, \(3\) X₁₁₂₁ - \(5\) X₃₁₆₄₀, X₁₁₂₁ - \(4\) X₃₅₁₁₀, \(3\) X₁₁₂₁ - \(2\) X₃₉₃₅₁, X₁₁₂₁ + \(2\) X₃₉₃₅₇, \(9\) X₁₁₂₁ - \(16\) X₄₀₄₈₃, \(4\) X₁₁₄₆ - \(5\) X₃₁₆₄₀, X₁₁₄₆ - \(3\) X₃₅₁₁₀, \(2\) X₁₁₄₆ + \(3\) X₃₉₃₅₇, \(3\) X₁₁₄₆ - \(4\) X₄₀₄₈₃, \(3\) X₁₂₇₅ - X₃₅₁₅₇, \(4\) X₁₃₂₃ - \(3\) X₁₇₀₇₈, \(2\) X₁₅₆₅ - \(3\) X₃₈₉₄₁, \(2\) X₉₄₃₆ - \(3\) X₁₇₀₇₈, \(3\) X₁₀₀₀₁ - \(2\) X₃₅₁₅₇, \(8\) X₁₇₀₄₄ - \(5\) X₃₁₆₄₀, \(2\) X₁₇₀₄₄ - \(3\) X₃₅₁₁₀, \(4\) X₁₇₀₄₄ - X₃₉₃₅₁, \(4\) X₁₇₀₄₄ + \(3\) X₃₉₃₅₇, \(3\) X₁₇₀₄₄ - \(2\) X₄₀₄₈₃, \(5\) X₃₁₆₄₀ - \(12\) X₃₅₁₁₀, \(5\) X₃₁₆₄₀ - \(2\) X₃₉₃₅₁, \(5\) X₃₁₆₄₀ + \(6\) X₃₉₃₅₇, \(15\) X₃₁₆₄₀ - \(16\) X₄₀₄₈₃, \(2\) X₃₁₈₅₂ - \(3\) X₃₈₆₉₀, \(6\) X₃₅₁₁₀ - X₃₉₃₅₁, \(2\) X₃₅₁₁₀ + X₃₉₃₅₇, \(9\) X₃₅₁₁₀ - \(4\) X₄₀₄₈₃, X₃₉₃₅₁ + \(3\) X₃₉₃₅₇, \(3\) X₃₉₃₅₁ - \(8\) X₄₀₄₈₃, \(9\) X₃₉₃₅₇ + \(8\) X₄₀₄₈₃

X₆₆₄ lies on the Steiner circumellipse.

▸ Incident Central Lines344 lines

{1, 85}, {2, 1121}, {6, 30627}, {7, 528}, {8, 348}, {9, 31169}, {10, 17095}, {12, 17084}, {20, 7973}, {30, 5195}, {34, 18156}, {37, 35144}, {40, 7183}, {42, 7196}, {43, 25721}, {56, 3212}, {57, 3227}, {65, 1434}, {69, 347}, {73, 290}, {75, 77}, {76, 10571}, {78, 16284}, {86, 1411}, {92, 6505}, {99, 109}, {100, 658}, {101, 514}, {106, 21208}, {108, 1310}, {110, 1305}, {118, 18328}, {141, 17086}, {145, 279}, {150, 952}, {163, 4237}, {175, 490}, {176, 489}, {190, 644}, {192, 6180}, {200, 31627}, {220, 3177}, {221, 1975}, {222, 24282}, {223, 312}, {224, 1847}, {225, 8773}, {226, 671}, {239, 241}, {269, 1120}, {273, 20930}, {274, 37558}, {278, 18134}, {292, 39940}, {304, 7210}, {307, 319}, {316, 38945}, {320, 22464}, {322, 326}, {325, 35149}, {333, 1214}, {345, 18623}, {350, 1457}, {355, 17181}, {385, 17966}, {388, 20539}, {394, 6360}, {515, 4872}, {516, 10697}, {517, 5088}, {518, 14189}, {519, 1323}, {522, 1275}, {523, 35154}, {524, 17950}, {527, 34926}, {536, 6610}, {553, 41823}, {604, 18825}, {648, 653}, {655, 4604}, {663, 14727}, {668, 1026}, {670, 4572}, {673, 2170}, {693, 35174}, {728, 2124}, {738, 2136}, {740, 5018}, {765, 31605}, {789, 29055}, {811, 6528}, {835, 29279}, {874, 18830}, {889, 43924}, {892, 4620}, {914, 17923}, {944, 17170}, {948, 17316}, {1015, 24281}, {1016, 30719}, {1018, 1025}, {1020, 3882}, {1042, 35159}, {1043, 1231}, {1088, 3870}, {1100, 41246}, {1125, 25723}, {1212, 32008}, {1215, 40723}, {1220, 40845}, {1223, 42449}, {1284, 35166}, {1292, 6183}, {1319, 1447}, {1331, 36048}, {1362, 14839}, {1376, 31526}, {1388, 17090}, {1397, 18824}, {1400, 3228}, {1402, 18826}, {1403, 17082}, {1407, 3210}, {1415, 4586}, {1418, 4852}, {1419, 3729}, {1427, 1999}, {1429, 35172}, {1432, 14970}, {1435, 8897}, {1443, 17160}, {1445, 3759}, {1446, 34772}, {1456, 3685}, {1458, 10030}, {1461, 4605}, {1469, 43096}, {1482, 17753}, {1575, 43062}, {1633, 16680}, {1788, 17081}, {1818, 33677}, {1897, 13149}, {1944, 6510}, {1992, 12848}, {2006, 25529}, {2082, 6167}, {2114, 17755}, {2222, 13396}, {2340, 40864}, {2669, 7235}, {2893, 6356}, {2898, 25568}, {2966, 32660}, {3174, 23062}, {3188, 3868}, {3243, 42309}, {3244, 10481}, {3501, 34497}, {3509, 6647}, {3616, 31994}, {3623, 43983}, {3665, 10944}, {3668, 3879}, {3669, 4562}, {3671, 41813}, {3674, 7247}, {3676, 4555}, {3693, 40872}, {3752, 40420}, {3873, 23839}, {3880, 34855}, {3888, 3903}, {3911, 35168}, {3912, 35158}, {3935, 37780}, {3936, 37798}, {3939, 6606}, {3952, 4624}, {3957, 21453}, {3996, 7182}, {4017, 35147}, {4025, 7045}, {4059, 11011}, {4077, 35156}, {4089, 7972}, {4318, 40704}, {4334, 32921}, {4350, 17158}, {4352, 37614}, {4384, 31225}, {4393, 5228}, {4449, 46135}, {4482, 4568}, {4511, 30806}, {4513, 25242}, {4534, 26007}, {4569, 4626}, {4589, 18829}, {4597, 23703}, {4598, 37137}, {4614, 4616}, {4645, 35150}, {4664, 8545}, {4861, 20880}, {4904, 43057}, {4911, 45287}, {4971, 40892}, {5176, 33864}, {5219, 35170}, {5252, 7179}, {5263, 43099}, {5289, 30946}, {5543, 20057}, {5845, 20096}, {5930, 7270}, {6063, 43093}, {6332, 46102}, {6335, 24035}, {6354, 17778}, {6357, 35161}, {6376, 37694}, {6540, 33948}, {6542, 35163}, {6554, 26658}, {6558, 42720}, {6559, 9502}, {6571, 8706}, {6603, 10025}, {6613, 6614}, {6645, 40765}, {6739, 23674}, {7056, 17784}, {7080, 34060}, {7117, 24499}, {7146, 41245}, {7175, 35143}, {7178, 35148}, {7181, 35153}, {7185, 30617}, {7190, 17393}, {7268, 21454}, {7354, 33867}, {7763, 34030}, {9086, 14733}, {9259, 21138}, {9263, 32029}, {9296, 42336}, {9318, 17439}, {9358, 17069}, {9362, 43051}, {10405, 27541}, {10509, 15185}, {10725, 31851}, {11054, 37856}, {11109, 20926}, {11185, 34029}, {12513, 36638}, {12635, 36854}, {13395, 13397}, {14100, 23618}, {14513, 44435}, {14723, 44408}, {14829, 17080}, {15343, 21297}, {15903, 17719}, {16090, 44150}, {16585, 40435}, {16586, 34234}, {16609, 35173}, {16777, 26125}, {17056, 17947}, {17075, 17295}, {17093, 36845}, {17094, 35169}, {17233, 28739}, {17234, 37800}, {17285, 28780}, {17317, 21617}, {17352, 44355}, {17743, 41771}, {17752, 28391}, {17791, 46141}, {17864, 37157}, {18031, 39046}, {18138, 34045}, {18359, 40612}, {18990, 33865}, {20050, 32003}, {20220, 21588}, {20247, 38859}, {20248, 38869}, {20533, 39063}, {20565, 46138}, {21294, 36154}, {21296, 36640}, {21605, 34039}, {21609, 34036}, {23890, 35342}, {24002, 35171}, {24028, 35046}, {24291, 32942}, {24349, 41354}, {24618, 45749}, {25082, 28961}, {25083, 40863}, {25930, 30854}, {26006, 37774}, {26015, 37757}, {26526, 27006}, {26653, 26690}, {27191, 37771}, {28660, 40611}, {29052, 34083}, {30379, 37756}, {30545, 32926}, {30567, 36636}, {30573, 39293}, {30726, 34024}, {31343, 43290}, {31604, 34247}, {31631, 40149}, {31648, 36956}, {31721, 38314}, {31852, 38690}, {31997, 37523}, {32025, 40999}, {32040, 44553}, {32851, 34050}, {34085, 37138}, {34342, 41556}, {35961, 42079}, {35962, 41553}, {36098, 37215}, {36276, 42046}, {36595, 39704}, {36802, 41075}, {37211, 38340}, {37686, 43039}, {38459, 38460}, {39350, 44351}, {40859, 43059}, {45798, 46108}

▸ Functional Relations23 relations

• X₆₆₄ = midpoint of X₂ and X₃₉₃₅₇

• X₆₆₄ = reflection of X_i in X_j for these {i,j}: {2, 35110}, {85, 36905}, {150, 1565}, {190, 40865}, {333, 39035}, {1121, 2}, {1146, 17044}, {1944, 6510}, {1952, 1214}, {3509, 6647}, {3732, 101}, {8777, 6505}, {9436, 1323}, {10001, 1275}, {10025, 6603}, {10725, 31851}, {14942, 1}, {17947, 17056}, {18328, 118}, {31648, 36956}, {39351, 1146}, {40862, 6610}

• X₆₆₄ = reflection of X₉₂₇ in the Soddy line

• X₆₆₄ = isogonal conjugate of X₆₆₃

• X₆₆₄ = isotomic conjugate of X₅₂₂

• X₆₆₄ = complement of X₃₉₃₅₁

• X₆₆₄ = anticomplement of X₁₁₄₆

• X₆₆₄ = polar conjugate of X₃₀₆₄

• X₆₆₄ = cevapoint of X_i and X_j for these (i,j): {1, 514}, {2, 522}, {6, 23865}, {7, 3676}, {8, 6332}, {9, 4105}, {10, 7265}, {57, 43924}, {65, 3669}, {77, 4025}, {100, 651}, {109, 1813}, {145, 30719}, {190, 43290}, {192, 24749}, {223, 8058}, {513, 3752}, {521, 1214}, {523, 17056}, {525, 18641}, {649, 7032}, {650, 14100}, {661, 23668}, {663, 2082}, {693, 1441}, {905, 1071}, {1212, 3900}, {1317, 30725}, {1459, 26934}, {1537, 10015}, {1577, 23555}, {2785, 39035}, {3008, 38371}, {3649, 7178}, {3738, 16586}, {3835, 23669}, {3870, 31605}, {3911, 39771}, {3960, 11570}, {4391, 23528}, {4449, 9312}, {4453, 41801}, {4551, 4552}, {5586, 30723}, {6366, 35110}, {6608, 42449}, {7180, 39780}, {10052, 21188}, {14208, 18697}, {15185, 43049}, {16006, 41800}, {16585, 35057}, {17496, 37558}, {21183, 36595}, {23615, 31648}, {30724, 34502}, {30726, 39777}, {35312, 35338}, {39775, 43041}, {39782, 43052}

• X₆₆₄ = crosspoint of X_i and X_j for these (i,j): {99, 811}, {4554, 4569}, {4573, 4625}

• X₆₆₄ = crosssum of X_i and X_j for these (i,j): {512, 810}, {522, 25128}, {3063, 8641}

• X₆₆₄ = trilinear pole of line {2, 7}

• X₆₆₄ = crossdifference of every pair of points on line {3271, 6139}

• X₆₆₄ = Steiner-circumellipse-antipode of X₁₁₂₁

• X₆₆₄ = Steiner-circumellipse-X₁-antipode of X₂₄₈₁

• X₆₆₄ = trilinear product of circumcircle intercepts of line X₇X₈

• X₆₆₄ = pole wrt polar circle of trilinear polar of X₃₀₆₄

• X₆₆₄ = crossdifference of PU(103)

• X₆₆₄ = Jerabek image of X₇

• X₆₆₄ = X_i-isoconjugate of X_j for these (i,j): {1, 663}, {2, 3063}, {3, 18344}, {4, 1946}, {6, 650}, {7, 8641}, {8, 667}, {9, 649}, {11, 692}, {19, 652}, {21, 512}, {25, 521}, {29, 810}, {31, 522}, {32, 4391}, {33, 1459}, {37, 7252}, {41, 514}, {42, 3737}, {48, 3064}, {55, 513}, {56, 3900}, {57, 657}, {58, 4041}, {60, 4705}, {65, 21789}, {80, 8648}, {81, 3709}, {100, 3271}, {101, 2170}, {105, 926}, {106, 4895}, {108, 3270}, {109, 2310}, {110, 4516}, {163, 21044}, {184, 44426}, {200, 43924}, {210, 3733}, {212, 7649}, {213, 4560}, {219, 6591}, {220, 3669}, {244, 3939}, {259, 6729}, {269, 4105}, {281, 22383}, {284, 661}, {292, 4435}, {294, 665}, {312, 1919}, {314, 669}, {333, 798}, {393, 36054}, {480, 43932}, {518, 884}, {523, 2194}, {525, 2204}, {560, 35519}, {604, 3239}, {607, 905}, {643, 3122}, {644, 1015}, {645, 3121}, {646, 1977}, {647, 1172}, {651, 14936}, {654, 2161}, {656, 2299}, {659, 7077}, {672, 1024}, {693, 2175}, {739, 4526}, {764, 6065}, {822, 8748}, {875, 3685}, {885, 2223}, {890, 36798}, {893, 3287}, {902, 23838}, {904, 3907}, {906, 8735}, {919, 17435}, {923, 14432}, {934, 3022}, {1014, 4524}, {1019, 1334}, {1021, 1400}, {1027, 2340}, {1036, 8678}, {1037, 17115}, {1055, 23893}, {1084, 4631}, {1106, 4163}, {1110, 21132}, {1146, 1415}, {1155, 23351}, {1156, 6139}, {1170, 10581}, {1174, 21127}, {1253, 3676}, {1260, 43923}, {1261, 6363}, {1318, 3251}, {1320, 1960}, {1333, 3700}, {1357, 4578}, {1397, 4397}, {1402, 7253}, {1407, 4130}, {1409, 17926}, {1412, 4171}, {1417, 4528}, {1431, 4477}, {1436, 14298}, {1461, 3119}, {1474, 8611}, {1633, 14935}, {1635, 2316}, {1638, 18889}, {1639, 9456}, {1769, 2342}, {1783, 7117}, {1812, 2489}, {1824, 23189}, {1857, 23224}, {1880, 23090}, {1896, 39201}, {1911, 3716}, {1918, 18155}, {1924, 28660}, {1973, 6332}, {1974, 35518}, {1980, 3596}, {2053, 4083}, {2087, 5548}, {2149, 42462}, {2150, 4024}, {2155, 14331}, {2159, 14400}, {2160, 9404}, {2163, 4814}, {2182, 2432}, {2185, 4079}, {2192, 6129}, {2193, 2501}, {2195, 2254}, {2206, 4086}, {2208, 8058}, {2212, 4025}, {2218, 8676}, {2258, 17418}, {2279, 45755}, {2287, 7180}, {2311, 21832}, {2319, 20979}, {2320, 4775}, {2328, 4017}, {2339, 2484}, {2341, 21828}, {2344, 3250}, {2346, 2488}, {2352, 23289}, {2356, 23696}, {2364, 4893}, {2424, 41339}, {2481, 8638}, {2520, 37741}, {2590, 2591}, {2605, 7073}, {2638, 36127}, {2643, 4636}, {2648, 5075}, {2651, 18000}, {2804, 34858}, {2982, 33525}, {3049, 31623}, {3065, 42657}, {3124, 4612}, {3125, 5546}, {3248, 3699}, {3254, 8645}, {3261, 9447}, {3423, 6182}, {3433, 11934}, {3445, 4162}, {3446, 11193}, {3467, 42649}, {3572, 3684}, {3680, 8643}, {3688, 18108}, {3689, 23345}, {3693, 43929}, {3694, 43925}, {3738, 6187}, {3766, 18265}, {4009, 23349}, {4076, 8027}, {4124, 34067}, {4131, 6059}, {4147, 7121}, {4449, 9439}, {4501, 30651}, {4521, 38266}, {4530, 32665}, {4531, 7255}, {4534, 34080}, {4546, 16945}, {4557, 18191}, {4565, 36197}, {4571, 42067}, {4581, 20967}, {4617, 35508}, {4623, 7063}, {4626, 24012}, {4790, 34820}, {4820, 34819}, {4845, 14413}, {4858, 32739}, {4876, 8632}, {4900, 8656}, {4919, 9262}, {4944, 28607}, {4976, 28615}, {4979, 33635}, {5040, 11609}, {5547, 14419}, {6186, 35057}, {6366, 34068}, {6373, 8851}, {6601, 8642}, {6614, 24010}, {7004, 8750}, {7105, 21761}, {7118, 14837}, {7129, 10397}, {7155, 8640}, {8646, 30479}, {8647, 35355}, {8749, 14395}, {8752, 14418}, {9247, 46110}, {9426, 40072}, {9448, 40495}, {10099, 37908}, {10566, 40972}, {11124, 18771}, {11604, 42670}, {14399, 15627}, {14775, 23207}, {14776, 35014}, {14827, 24002}, {15997, 45878}, {16686, 42552}, {21645, 43743}, {21758, 36910}, {21759, 27527}, {23615, 24027}, {23845, 40528}, {23865, 40505}, {23990, 40166}, {25128, 34248}, {32652, 38357}, {32653, 38345}, {32674, 34591}, {33573, 36141}, {36059, 42069}

• X₆₆₄ = barycentric product X_i*X_j for these {i,j}: {1, 4554}, {6, 4572}, {7, 190}, {8, 658}, {9, 4569}, {10, 4573}, {12, 4610}, {37, 4625}, {56, 1978}, {57, 668}, {59, 3261}, {63, 18026}, {65, 799}, {69, 653}, {73, 6331}, {75, 651}, {76, 109}, {77, 6335}, {78, 13149}, {85, 100}, {86, 4552}, {92, 6516}, {99, 226}, {101, 6063}, {108, 304}, {110, 349}, {142, 6606}, {162, 1231}, {200, 36838}, {210, 4635}, {225, 4563}, {257, 6649}, {261, 4605}, {264, 1813}, {269, 646}, {273, 1332}, {274, 4551}, {278, 4561}, {279, 3699}, {305, 32674}, {307, 648}, {308, 46153}, {310, 4559}, {312, 934}, {313, 4565}, {314, 1020}, {319, 38340}, {320, 655}, {321, 1414}, {322, 37141}, {331, 1331}, {333, 4566}, {341, 4617}, {345, 36118}, {346, 4626}, {347, 44327}, {348, 1897}, {388, 37215}, {479, 6558}, {514, 4998}, {518, 34085}, {522, 1275}, {523, 4620}, {527, 35157}, {552, 4103}, {553, 6540}, {561, 1415}, {604, 6386}, {643, 1446}, {644, 1088}, {645, 3668}, {660, 10030}, {662, 1441}, {666, 9436}, {670, 1400}, {672, 46135}, {673, 883}, {692, 20567}, {693, 4564}, {765, 24002}, {789, 7146}, {811, 1214}, {813, 18033}, {835, 33949}, {873, 21859}, {918, 39293}, {927, 3912}, {932, 30545}, {1014, 4033}, {1016, 3676}, {1025, 2481}, {1026, 34018}, {1111, 31615}, {1254, 4631}, {1262, 35519}, {1284, 4639}, {1292, 21609}, {1305, 18134}, {1358, 6632}, {1402, 4602}, {1412, 27808}, {1423, 18830}, {1427, 7257}, {1429, 4583}, {1434, 3952}, {1442, 15455}, {1443, 36804}, {1447, 4562}, {1458, 36803}, {1461, 3596}, {1469, 37133}, {1476, 21580}, {1783, 7182}, {1847, 4571}, {1909, 37137}, {1920, 29055}, {1937, 15418}, {1969, 36059}, {2052, 6517}, {2149, 40495}, {2171, 4623}, {2222, 20924}, {2283, 18031}, {2321, 4616}, {2406, 34393}, {3212, 4598}, {3218, 35174}, {3262, 37136}, {3263, 36146}, {3452, 6613}, {3570, 7233}, {3616, 4624}, {3649, 4632}, {3669, 7035}, {3671, 4633}, {3674, 8707}, {3701, 4637}, {3718, 32714}, {3732, 8817}, {3882, 31643}, {3903, 7196}, {3911, 4555}, {3926, 36127}, {4017, 4601}, {4024, 7340}, {4025, 46102}, {4032, 4594}, {4077, 4567}, {4130, 24011}, {4163, 23586}, {4357, 6648}, {4391, 7045}, {4556, 34388}, {4576, 18097}, {4578, 23062}, {4585, 18815}, {4586, 7179}, {4589, 16609}, {4592, 40149}, {4597, 5219}, {4600, 7178}, {4607, 43037}, {4615, 40663}, {4619, 34387}, {4621, 7185}, {4654, 32042}, {5930, 44326}, {6168, 14727}, {6528, 40152}, {6604, 37206}, {6742, 17095}, {7012, 15413}, {7128, 35518}, {7153, 36863}, {7176, 27805}, {7249, 18047}, {8709, 43040}, {9312, 30610}, {10436, 32038}, {11608, 17933}, {13136, 22464}, {13138, 40702}, {14612, 39712}, {17950, 35154}, {18022, 32660}, {18816, 24029}, {20568, 23703}, {20911, 36098}, {21105, 31619}, {21272, 40420}, {23067, 44129}, {25716, 42343}, {26700, 33939}, {27818, 43290}, {27834, 39126}, {30806, 37139}, {31618, 35338}, {31625, 43924}, {32008, 35312}, {32028, 43948}, {32041, 40719}, {32675, 40075}, {32739, 41283}, {33298, 43190}, {34019, 42301}, {35171, 37787}, {35341, 42311}, {36086, 40704}, {36796, 41353}, {41206, 44150}, {42719, 43736}, {44717, 46107}

• X₆₆₄ = barycentric quotient X_i/X_j for these {i,j}: {1, 650}, {2, 522}, {3, 652}, {4, 3064}, {6, 663}, {7, 514}, {8, 3239}, {9, 3900}, {10, 3700}, {11, 42462}, {12, 4024}, {19, 18344}, {20, 14331}, {21, 1021}, {29, 17926}, {30, 14400}, {31, 3063}, {34, 6591}, {35, 9404}, {36, 654}, {37, 4041}, {40, 14298}, {41, 8641}, {42, 3709}, {44, 4895}, {45, 4814}, {48, 1946}, {55, 657}, {56, 649}, {57, 513}, {58, 7252}, {59, 101}, {63, 521}, {65, 661}, {69, 6332}, {72, 8611}, {73, 647}, {75, 4391}, {76, 35519}, {77, 905}, {81, 3737}, {85, 693}, {86, 4560}, {88, 23838}, {92, 44426}, {99, 333}, {100, 9}, {101, 55}, {102, 2432}, {105, 1024}, {107, 8748}, {108, 19}, {109, 6}, {110, 284}, {112, 2299}, {142, 6362}, {145, 4521}, {162, 1172}, {163, 2194}, {169, 11934}, {171, 3287}, {174, 6728}, {181, 4079}, {188, 6730}, {190, 8}, {192, 4147}, {194, 25128}, {200, 4130}, {210, 4171}, {220, 4105}, {222, 1459}, {223, 6129}, {225, 2501}, {226, 523}, {238, 4435}, {239, 3716}, {241, 2254}, {249, 4636}, {255, 36054}, {264, 46110}, {266, 6729}, {269, 3669}, {273, 17924}, {274, 18155}, {278, 7649}, {279, 3676}, {283, 23090}, {284, 21789}, {304, 35518}, {307, 525}, {312, 4397}, {320, 3904}, {321, 4086}, {329, 8058}, {331, 46107}, {332, 15411}, {333, 7253}, {344, 44448}, {346, 4163}, {347, 14837}, {348, 4025}, {349, 850}, {354, 21127}, {388, 6590}, {390, 14330}, {513, 2170}, {514, 11}, {519, 1639}, {521, 34591}, {522, 1146}, {523, 21044}, {524, 14432}, {527, 6366}, {536, 14430}, {553, 4977}, {579, 8676}, {603, 22383}, {604, 667}, {643, 2287}, {644, 200}, {645, 1043}, {646, 341}, {648, 29}, {649, 3271}, {650, 2310}, {651, 1}, {652, 3270}, {653, 4}, {655, 80}, {657, 3022}, {658, 7}, {660, 4876}, {661, 4516}, {662, 21}, {663, 14936}, {666, 14942}, {668, 312}, {670, 28660}, {672, 926}, {673, 885}, {677, 2338}, {692, 41}, {693, 4858}, {738, 43932}, {748, 4501}, {765, 644}, {799, 314}, {811, 31623}, {812, 4124}, {813, 7077}, {823, 1896}, {874, 3975}, {883, 3912}, {894, 3907}, {899, 4526}, {900, 4530}, {901, 2316}, {905, 7004}, {906, 212}, {908, 2804}, {919, 2195}, {927, 673}, {932, 2319}, {934, 57}, {940, 17418}, {1001, 45755}, {1014, 1019}, {1016, 3699}, {1018, 210}, {1019, 18191}, {1020, 65}, {1023, 3689}, {1025, 518}, {1026, 3693}, {1038, 2522}, {1042, 7180}, {1055, 6139}, {1071, 40628}, {1086, 21132}, {1088, 24002}, {1111, 40166}, {1125, 4976}, {1146, 23615}, {1156, 23893}, {1212, 6608}, {1214, 656}, {1215, 4140}, {1231, 14208}, {1252, 3939}, {1262, 109}, {1284, 21832}, {1305, 1751}, {1310, 2339}, {1317, 6544}, {1319, 1635}, {1323, 1638}, {1331, 219}, {1332, 78}, {1334, 4524}, {1357, 21143}, {1358, 6545}, {1365, 21131}, {1381, 2591}, {1382, 2590}, {1397, 1919}, {1400, 512}, {1401, 21123}, {1402, 798}, {1403, 20979}, {1404, 1960}, {1405, 4775}, {1407, 43924}, {1409, 810}, {1412, 3733}, {1414, 81}, {1415, 31}, {1416, 43929}, {1420, 4394}, {1423, 4083}, {1427, 4017}, {1428, 8632}, {1429, 659}, {1434, 7192}, {1435, 43923}, {1438, 884}, {1441, 1577}, {1442, 14838}, {1443, 3960}, {1445, 3309}, {1446, 4077}, {1447, 812}, {1457, 3310}, {1458, 665}, {1459, 7117}, {1460, 2484}, {1461, 56}, {1462, 1027}, {1464, 21828}, {1465, 1769}, {1469, 3250}, {1475, 2488}, {1492, 2344}, {1633, 2082}, {1697, 40137}, {1698, 4820}, {1708, 15313}, {1734, 38358}, {1743, 4162}, {1751, 23289}, {1783, 33}, {1790, 23189}, {1804, 4091}, {1813, 3}, {1814, 23696}, {1897, 281}, {1943, 8062}, {1950, 21761}, {1978, 3596}, {1981, 243}, {1983, 2361}, {1996, 30181}, {2002, 8760}, {2003, 2605}, {2078, 22108}, {2082, 17115}, {2099, 4893}, {2124, 17427}, {2149, 692}, {2171, 4705}, {2222, 2161}, {2254, 17435}, {2283, 672}, {2284, 2340}, {2285, 8678}, {2291, 23351}, {2293, 10581}, {2325, 4528}, {2329, 4477}, {2397, 6735}, {2398, 40869}, {2399, 15633}, {2406, 515}, {2701, 17963}, {2720, 909}, {3064, 42069}, {3160, 7658}, {3161, 4546}, {3212, 3835}, {3218, 3738}, {3219, 35057}, {3239, 4081}, {3257, 1320}, {3261, 34387}, {3309, 38375}, {3333, 14300}, {3338, 13401}, {3361, 4790}, {3452, 42337}, {3485, 45745}, {3570, 3685}, {3573, 3684}, {3616, 4765}, {3649, 4988}, {3661, 4522}, {3662, 3810}, {3663, 21120}, {3665, 16892}, {3666, 17420}, {3667, 4534}, {3668, 7178}, {3669, 244}, {3671, 4841}, {3674, 3004}, {3676, 1086}, {3679, 4944}, {3685, 4148}, {3686, 4990}, {3689, 14427}, {3699, 346}, {3718, 15416}, {3732, 497}, {3752, 6615}, {3782, 21119}, {3807, 3790}, {3875, 20317}, {3882, 960}, {3888, 3061}, {3900, 3119}, {3911, 900}, {3939, 220}, {3950, 44729}, {3952, 2321}, {3982, 28175}, {4017, 3125}, {4024, 4092}, {4025, 26932}, {4031, 28209}, {4032, 2533}, {4033, 3701}, {4040, 38347}, {4041, 36197}, {4069, 4515}, {4076, 6558}, {4077, 16732}, {4091, 1364}, {4103, 6057}, {4105, 35508}, {4114, 28213}, {4115, 4046}, {4130, 24010}, {4163, 23970}, {4296, 16612}, {4306, 43060}, {4308, 43061}, {4350, 43049}, {4357, 3910}, {4358, 4768}, {4359, 4985}, {4363, 4474}, {4369, 4459}, {4370, 4543}, {4380, 4965}, {4383, 42312}, {4391, 24026}, {4427, 3686}, {4436, 3691}, {4462, 4939}, {4499, 4051}, {4512, 4827}, {4521, 4953}, {4551, 37}, {4552, 10}, {4553, 33299}, {4554, 75}, {4555, 4997}, {4556, 60}, {4557, 1334}, {4558, 283}, {4559, 42}, {4561, 345}, {4562, 4518}, {4563, 332}, {4564, 100}, {4565, 58}, {4566, 226}, {4567, 643}, {4568, 3703}, {4569, 85}, {4570, 5546}, {4571, 3692}, {4572, 76}, {4573, 86}, {4574, 2318}, {4575, 2193}, {4578, 728}, {4579, 2329}, {4585, 4511}, {4587, 1260}, {4588, 2364}, {4589, 36800}, {4592, 1812}, {4595, 27538}, {4597, 30608}, {4598, 7155}, {4600, 645}, {4601, 7257}, {4602, 40072}, {4604, 2320}, {4605, 12}, {4606, 4866}, {4607, 36798}, {4610, 261}, {4612, 1098}, {4616, 1434}, {4617, 269}, {4619, 59}, {4620, 99}, {4624, 5936}, {4625, 274}, {4626, 279}, {4636, 7054}, {4637, 1014}, {4638, 1318}, {4654, 4802}, {4752, 3711}, {4756, 4007}, {4767, 4873}, {4781, 3707}, {4848, 14321}, {4858, 42455}, {4998, 190}, {5219, 4777}, {5221, 4813}, {5226, 28161}, {5228, 4724}, {5257, 4843}, {5298, 4984}, {5382, 31343}, {5435, 3667}, {5440, 14418}, {5540, 11193}, {5546, 2328}, {5750, 29278}, {5930, 6587}, {6049, 31182}, {6063, 3261}, {6135, 13456}, {6136, 13427}, {6163, 4919}, {6168, 42341}, {6180, 4449}, {6183, 39273}, {6331, 44130}, {6332, 2968}, {6335, 318}, {6357, 11125}, {6358, 4036}, {6366, 33573}, {6386, 28659}, {6510, 14414}, {6516, 63}, {6517, 394}, {6540, 4102}, {6544, 4542}, {6545, 7336}, {6558, 5423}, {6603, 14392}, {6604, 4468}, {6606, 32008}, {6610, 14413}, {6613, 40420}, {6614, 1407}, {6632, 4076}, {6648, 1220}, {6649, 894}, {6733, 259}, {6742, 7110}, {7012, 1783}, {7035, 646}, {7045, 651}, {7055, 30805}, {7078, 10397}, {7081, 4529}, {7113, 8648}, {7115, 8750}, {7125, 23224}, {7128, 108}, {7146, 1491}, {7153, 43931}, {7175, 4367}, {7176, 4369}, {7178, 3120}, {7179, 824}, {7180, 3122}, {7181, 4750}, {7182, 15413}, {7183, 4131}, {7185, 3776}, {7192, 17197}, {7196, 4374}, {7201, 4490}, {7203, 16726}, {7210, 16757}, {7217, 21110}, {7223, 4379}, {7233, 4444}, {7243, 4408}, {7251, 21122}, {7265, 6741}, {7339, 1461}, {7340, 4610}, {7649, 8735}, {8012, 6607}, {8058, 5514}, {8059, 1436}, {8269, 7131}, {8270, 2509}, {8545, 14077}, {8694, 34820}, {8701, 33635}, {8709, 36799}, {8750, 607}, {8804, 14308}, {9268, 5548}, {9312, 4885}, {9316, 20980}, {9358, 9355}, {9436, 918}, {9454, 8638}, {10001, 39351}, {10015, 35015}, {10030, 3766}, {10436, 23880}, {10481, 21104}, {10521, 23729}, {10566, 18101}, {10571, 6589}, {10578, 14282}, {11608, 18013}, {12848, 28292}, {13138, 282}, {13149, 273}, {13397, 39943}, {13444, 18888}, {13588, 21388}, {13589, 1731}, {14027, 14442}, {14543, 950}, {14544, 40942}, {14547, 33525}, {14594, 2345}, {14612, 5263}, {14733, 2291}, {14837, 38357}, {14942, 28132}, {15386, 32653}, {15413, 17880}, {15419, 17219}, {15439, 2259}, {16603, 4122}, {16609, 4010}, {16826, 4913}, {16885, 4959}, {16888, 3801}, {17074, 21173}, {17075, 20517}, {17076, 21178}, {17077, 8714}, {17078, 4453}, {17079, 21183}, {17080, 21189}, {17081, 3798}, {17082, 21191}, {17083, 21194}, {17084, 21196}, {17085, 21200}, {17086, 4142}, {17088, 21205}, {17089, 21204}, {17091, 21206}, {17092, 4905}, {17093, 31605}, {17094, 4466}, {17095, 4467}, {17096, 17205}, {17114, 23751}, {17136, 5745}, {17218, 16759}, {17439, 11124}, {17496, 34589}, {17752, 30584}, {17761, 42454}, {17780, 2325}, {17923, 44428}, {17933, 40882}, {17942, 5060}, {17950, 2785}, {17966, 5075}, {18026, 92}, {18047, 7081}, {18134, 20294}, {18315, 35196}, {18623, 21172}, {18626, 21175}, {18627, 21176}, {18830, 27424}, {19297, 42657}, {19804, 4811}, {20567, 40495}, {20616, 21727}, {21007, 38365}, {21105, 46101}, {21147, 6588}, {21173, 11998}, {21189, 38345}, {21272, 3452}, {21362, 3057}, {21454, 4778}, {21580, 20895}, {21773, 42649}, {21859, 756}, {22003, 21677}, {22341, 822}, {22464, 10015}, {23067, 71}, {23113, 22072}, {23187, 38344}, {23346, 1055}, {23353, 2202}, {23363, 23640}, {23586, 4626}, {23703, 44}, {23706, 14571}, {23845, 2347}, {23865, 38991}, {23890, 1155}, {23891, 4009}, {23971, 6614}, {23973, 43035}, {23978, 23104}, {23981, 2183}, {23984, 36127}, {23987, 8755}, {24002, 1111}, {24004, 4723}, {24011, 36838}, {24013, 4617}, {24027, 1415}, {24029, 517}, {24037, 4631}, {24041, 4612}, {24215, 20508}, {25268, 6736}, {25716, 31287}, {25722, 40465}, {26700, 2160}, {26942, 4064}, {27339, 28623}, {27805, 4451}, {27808, 30713}, {27834, 3680}, {27853, 4087}, {28292, 43960}, {28387, 4139}, {28850, 28143}, {29055, 893}, {29227, 36630}, {30239, 8602}, {30379, 2826}, {30545, 20906}, {30719, 3756}, {30720, 6555}, {30725, 1647}, {30730, 4082}, {31231, 4926}, {31286, 24840}, {31526, 21195}, {31605, 4904}, {31615, 765}, {32038, 31359}, {32042, 42030}, {32577, 17424}, {32636, 4979}, {32641, 2342}, {32652, 7118}, {32660, 184}, {32669, 34858}, {32674, 25}, {32675, 6187}, {32676, 2204}, {32693, 2258}, {32714, 34}, {32735, 1438}, {32739, 2175}, {32939, 20293}, {33296, 27527}, {33298, 25259}, {33946, 3705}, {33949, 45746}, {33951, 4514}, {33952, 3966}, {34056, 35348}, {34071, 2053}, {34085, 2481}, {34234, 43728}, {34393, 2399}, {34921, 19302}, {35049, 13486}, {35154, 17947}, {35157, 1121}, {35174, 18359}, {35307, 21807}, {35310, 21039}, {35312, 142}, {35326, 2293}, {35338, 1212}, {35341, 3059}, {35342, 3683}, {35519, 23978}, {36040, 32677}, {36048, 2982}, {36049, 2192}, {36054, 2638}, {36059, 48}, {36075, 2308}, {36082, 2164}, {36086, 294}, {36098, 2298}, {36099, 1039}, {36118, 278}, {36127, 393}, {36141, 34068}, {36146, 105}, {36538, 29362}, {36589, 23884}, {36797, 2322}, {36802, 6559}, {36838, 1088}, {36863, 4110}, {37136, 104}, {37137, 256}, {37138, 40779}, {37139, 1156}, {37141, 84}, {37143, 3254}, {37206, 6601}, {37212, 32635}, {37215, 30479}, {37771, 21201}, {37787, 3887}, {37789, 2827}, {37798, 21180}, {37800, 21185}, {38340, 79}, {38459, 43050}, {38828, 3445}, {39126, 4462}, {39293, 666}, {39294, 1309}, {39771, 35092}, {39780, 40627}, {40117, 7008}, {40131, 6182}, {40149, 24006}, {40152, 520}, {40166, 1090}, {40573, 14775}, {40576, 169}, {40577, 5540}, {40615, 23760}, {40617, 23764}, {40622, 23775}, {40663, 4120}, {40702, 17896}, {40719, 4762}, {40999, 7265}, {41003, 21124}, {41206, 37142}, {41246, 29051}, {41264, 9313}, {41350, 45902}, {41353, 241}, {41526, 8640}, {41572, 28473}, {41777, 3777}, {41803, 21198}, {41804, 4707}, {41808, 21192}, {42462, 5532}, {42717, 44694}, {42720, 3717}, {43035, 676}, {43037, 4728}, {43038, 14475}, {43040, 3837}, {43041, 27918}, {43048, 24457}, {43051, 3123}, {43069, 43073}, {43192, 7707}, {43290, 3161}, {43760, 35355}, {43924, 1015}, {44326, 5931}, {44327, 280}, {44717, 1331}, {44724, 30720}, {44765, 10570}, {45204, 14284}, {45875, 15997}, {45876, 2090}, {46102, 1897}, {46110, 21666}, {46135, 18031}, {46148, 3688}, {46152, 17442}, {46153, 39}, {46177, 16588}

• X₆₆₄ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {1, 1111, 24203}, {1, 9312, 85}, {2, 1146, 31640}, {2, 39351, 1146}, {7, 17089, 1358}, {8, 348, 33298}, {8, 3160, 348}, {65, 7176, 1434}, {78, 34059, 40702}, {99, 4573, 1414}, {100, 934, 6516}, {100, 35312, 658}, {145, 279, 6604}, {150, 38941, 1565}, {220, 3177, 32024}, {269, 3875, 39126}, {651, 4552, 190}, {668, 4561, 3699}, {934, 4566, 658}, {1121, 31640, 1146}, {1146, 17044, 2}, {1146, 35110, 17044}, {1146, 39351, 1121}, {1214, 1943, 333}, {1317, 43038, 7}, {1319, 43037, 1447}, {1323, 9436, 17078}, {1358, 43038, 17089}, {1441, 1442, 86}, {1897, 36118, 18026}, {2082, 6167, 7131}, {2099, 7223, 7}, {2170, 9317, 673}, {3160, 25718, 8}, {3674, 10106, 7247}, {4551, 14594, 3699}, {4566, 17136, 6516}, {9259, 21138, 26273}, {9312, 25716, 1}, {17044, 39351, 31640}, {17136, 21272, 100}, {17136, 35312, 934}, {17439, 21139, 9318}, {17880, 18689, 75}, {18047, 33946, 190}, {20057, 32086, 5543}, {21272, 35312, 4566}, {30725, 45273, 651}, {35110, 39357, 1121}, {41801, 41803, 903}