X₆₆₃

CROSSDIFFERENCE OF X₂ AND X₇

X₆₆₃ = polar conjugate of the isotomic conjugate of X₆₅₂

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

X₆₆₃ (CROSSDIFFERENCE OF X₂ AND X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {187, 237}, {1, 514}

• Related Centers: X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X), X₂₃₇ (-LINE CONJUGATE OF X₂), X₁ (INCENTER), X₅₁₄ (ISOGONAL CONJUGATE OF X₁₀₁)

Trilinears: \(a(b - c)(b + c - a) : :\)

Search Value (6, 9, 13): \(-7.727124614661\)

▸ Linear Combinations1 combination

• X₆₆₃ = \(2\) X₁ + X₄₇₂₄, X₁ + \(2\) X₄₇₉₄, \(3\) X₅₅₁ - X₂₃₇₈₉, X₆₄₉ - \(4\) X₁₉₆₀, X₆₄₉ + \(2\) X₄₇₇₅, \(3\) X₆₄₉ - \(2\) X₄₈₃₄, X₆₄₉ - \(3\) X₈₆₄₃, \(2\) X₆₄₉ - \(5\) X₈₆₅₆, \(4\) X₆₅₀ - X₄₈₁₄, \(2\) X₆₅₀ + X₄₈₉₅, \(4\) X₆₅₀ + X₄₉₅₉, \(3\) X₆₆₇ - X₄₈₃₄, \(2\) X₆₆₇ - \(3\) X₈₆₄₃, \(4\) X₆₆₇ - \(5\) X₈₆₅₆, \(3\) X₁₆₃₅ - X₄₇₂₉, \(3\) X₁₆₃₅ - \(4\) X₆₀₅₀, \(3\) X₁₉₄₆ - \(2\) X₆₁₃₉, \(2\) X₁₉₆₀ + X₄₇₇₅, \(6\) X₁₉₆₀ - X₄₈₃₄, \(4\) X₁₉₆₀ - \(3\) X₈₆₄₃, \(8\) X₁₉₆₀ - \(5\) X₈₆₅₆, \(4\) X₂₆₀₅ - X₄₃₉₂₄, X₃₂₄₁ + \(2\) X₄₅₆₇₃, \(3\) X₃₂₅₁ + X₄₇₀₅, \(2\) X₃₂₅₁ + X₄₈₉₃, \(5\) X₃₆₁₆ - \(2\) X₂₄₇₂₀, \(2\) X₃₆₆₉ - \(3\) X₁₄₄₁₃, \(4\) X₃₇₁₆ - X₄₄₇₄, \(2\) X₃₇₃₇ + X₄₂₃₁₂, \(2\) X₄₀₄₀ + X₄₄₄₉, X₄₀₄₁ + \(2\) X₄₁₆₂, \(2\) X₄₀₄₁ + X₄₉₅₉, \(4\) X₄₁₆₂ + X₄₈₁₄, \(4\) X₄₁₆₂ - X₄₉₅₉, X₄₃₆₇ - \(3\) X₂₅₅₆₉, X₄₄₄₉ + \(4\) X₄₇₉₄, X₄₄₉₈ + \(2\) X₄₈₇₉, \(2\) X₄₅₂₈ - \(3\) X₄₄₇₂₉, \(3\) X₄₅₄₃ - \(4\) X₄₅₄₆, \(2\) X₄₇₀₅ - \(3\) X₄₈₉₃, X₄₇₂₄ - \(4\) X₄₇₉₄, X₄₇₂₉ - \(4\) X₆₀₅₀, \(3\) X₄₇₇₅ + X₄₈₃₄, \(2\) X₄₇₇₅ + \(3\) X₈₆₄₃, \(4\) X₄₇₇₅ + \(5\) X₈₆₅₆, X₄₈₁₄ + \(2\) X₄₈₉₅, \(2\) X₄₈₃₄ - \(9\) X₈₆₄₃, \(4\) X₄₈₃₄ - \(15\) X₈₆₅₆, \(2\) X₆₃₃₂ - \(3\) X₁₄₄₃₂, \(6\) X₈₆₄₃ - \(5\) X₈₆₅₆, \(3\) X₁₄₄₃₀ - \(4\) X₂₀₃₁₇, \(4\) X₁₄₈₃₇ - \(3\) X₃₀₅₇₄, X₁₇₀₇₂ - \(3\) X₄₅₃₁₆, \(4\) X₂₁₂₆₀ - \(5\) X₃₀₈₃₅, X₂₁₃₀₂ - \(6\) X₄₅₃₁₆, \(7\) X₃₁₂₀₇ - \(8\) X₃₁₂₈₈, \(3\) X₃₈₃₁₄ - \(2\) X₄₅₆₆₇

▸ Incident Central Lines173 lines

{1, 514}, {2, 17072}, {6, 9029}, {8, 4147}, {29, 46110}, {31, 2423}, {33, 23615}, {36, 39476}, {41, 884}, {42, 1643}, {56, 2424}, {78, 44448}, {86, 4406}, {101, 919}, {105, 12032}, {106, 840}, {109, 1262}, {110, 2701}, {187, 237}, {200, 4543}, {212, 27780}, {220, 38379}, {238, 37998}, {513, 855}, {521, 17420}, {522, 1944}, {523, 10149}, {551, 23789}, {644, 40499}, {650, 861}, {652, 1951}, {656, 15313}, {657, 853}, {659, 4083}, {660, 9266}, {661, 810}, {664, 14727}, {672, 9320}, {676, 7178}, {692, 32675}, {693, 29051}, {788, 4455}, {814, 4010}, {830, 14349}, {834, 4057}, {875, 23493}, {899, 10006}, {905, 2254}, {928, 4091}, {1015, 35505}, {1019, 6005}, {1193, 1491}, {1201, 2530}, {1400, 9245}, {1575, 40464}, {1577, 29066}, {1618, 39026}, {1633, 46153}, {1635, 4729}, {1734, 3887}, {1912, 23572}, {1919, 2484}, {2082, 6170}, {2170, 38365}, {2176, 21791}, {2320, 23838}, {2440, 7084}, {2499, 7180}, {2517, 8062}, {2520, 4813}, {2533, 4874}, {2785, 4142}, {2821, 22091}, {3022, 7117}, {3241, 45673}, {3248, 42084}, {3616, 24720}, {3667, 21173}, {3676, 8713}, {3700, 4990}, {3716, 3907}, {3720, 4379}, {3768, 9010}, {3801, 29082}, {3810, 3904}, {3835, 4107}, {3938, 6546}, {3939, 5548}, {3960, 4905}, {3961, 10196}, {4024, 21831}, {4063, 4401}, {4069, 30727}, {4122, 29074}, {4163, 4521}, {4170, 29013}, {4336, 42462}, {4369, 24666}, {4374, 17215}, {4378, 6372}, {4382, 29070}, {4491, 9002}, {4502, 20981}, {4528, 44729}, {4564, 9323}, {4666, 21183}, {4707, 20517}, {4800, 29236}, {4804, 23882}, {4810, 29238}, {4843, 4976}, {4844, 30116}, {4922, 29324}, {4978, 29186}, {4992, 24719}, {5272, 44432}, {6003, 21189}, {6006, 18450}, {6182, 21127}, {6366, 21120}, {6373, 23464}, {6586, 19624}, {6589, 17966}, {6614, 24016}, {7190, 30181}, {7191, 44435}, {7265, 29062}, {7649, 14775}, {7662, 17478}, {8750, 14776}, {9032, 23650}, {9313, 21003}, {9817, 14476}, {10015, 28473}, {10459, 29298}, {10570, 23104}, {11193, 14547}, {11707, 35051}, {11708, 35052}, {11712, 39046}, {11918, 35072}, {14077, 23057}, {14430, 20317}, {14837, 28292}, {15283, 21260}, {16466, 22154}, {18000, 21748}, {19372, 44928}, {20295, 31291}, {21146, 29246}, {21204, 29820}, {21261, 30764}, {21300, 25128}, {21343, 29226}, {22383, 23568}, {23056, 24012}, {23226, 34948}, {23345, 41436}, {24533, 28255}, {24675, 28758}, {24749, 25666}, {25259, 29037}, {25299, 30023}, {25901, 25924}, {27416, 27419}, {28373, 28398}, {28468, 44433}, {28521, 44429}, {30804, 43041}, {31207, 31288}, {38314, 45667}, {38357, 38983}, {38986, 40623}

▸ Functional Relations36 relations

• X₆₆₃ = midpoint of X_i and X_j for these {i,j}: {1, 4040}, {650, 4162}, {659, 4879}, {667, 4775}, {2530, 6161}, {4041, 4895}, {4449, 4724}, {4814, 4959}, {17418, 42312}, {20295, 31291}

• X₆₆₃ = reflection of X_i in X_j for these {i,j}: {2, 45316}, {8, 4147}, {649, 667}, {652, 21789}, {667, 1960}, {1459, 2605}, {1734, 14838}, {2254, 905}, {2517, 8062}, {2533, 4874}, {3700, 4990}, {4017, 6129}, {4040, 4794}, {4041, 650}, {4063, 4401}, {4163, 4521}, {4391, 3716}, {4449, 1}, {4474, 4391}, {4498, 659}, {4707, 20517}, {4724, 4040}, {4813, 4983}, {4814, 4041}, {4895, 4162}, {4905, 3960}, {4959, 4895}, {7178, 676}, {17418, 3737}, {18344, 17115}, {20979, 4455}, {21118, 21185}, {21300, 25128}, {21301, 3835}, {21302, 17072}, {23655, 810}, {24719, 4992}, {42649, 8648}, {42666, 42653}, {43924, 1459}

• X₆₆₃ = isogonal conjugate of X₆₆₄

• X₆₆₃ = isotomic conjugate of X₄₅₇₂

• X₆₆₃ = complement of X₂₁₃₀₂

• X₆₆₃ = anticomplement of X₁₇₀₇₂

• X₆₆₃ = polar conjugate of the isotomic conjugate of X₆₅₂

• X₆₆₃ = psi-transform of X₄₁₁₅₇

• X₆₆₃ = X₃₅₀₀-anticomplementary conjugate of X₁₅₀

• X₆₆₃ = X_i-complementary conjugate of X_j for these (i,j): {31, 38991}, {40505, 124}, {40523, 3452}

• X₆₆₃ = X_i-Ceva conjugate of X_j for these (i,j): {1, 2170}, {2, 38991}, {6, 14936}, {29, 21044}, {33, 2310}, {41, 38365}, {55, 3271}, {56, 7117}, {99, 23640}, {100, 2347}, {101, 41}, {108, 1400}, {109, 6}, {110, 21748}, {162, 1195}, {190, 20665}, {282, 3119}, {513, 649}, {522, 652}, {643, 2269}, {644, 1334}, {650, 657}, {651, 1200}, {664, 2082}, {692, 42}, {927, 20459}, {932, 20460}, {934, 1475}, {1415, 40957}, {1897, 40968}, {2191, 244}, {2192, 3270}, {2222, 2183}, {2424, 665}, {2701, 1951}, {2720, 1404}, {3433, 20974}, {3445, 1015}, {3699, 9}, {3737, 650}, {3903, 23544}, {3939, 55}, {4069, 3683}, {4551, 2264}, {4557, 20967}, {4626, 57}, {4636, 284}, {7073, 4516}, {7252, 3063}, {7257, 3691}, {8059, 604}, {8750, 31}, {8761, 39687}, {10570, 1146}, {14733, 1055}, {21789, 1946}, {23351, 6139}, {23838, 654}, {26700, 2260}, {29055, 1193}, {32652, 40958}, {32653, 32}, {32674, 607}, {32676, 40976}, {34435, 20982}, {34921, 7113}, {35348, 22108}, {36082, 48}, {36086, 672}, {36127, 19}, {40519, 23638}, {40523, 16588}

• X₆₆₃ = X_i-cross conjugate of X_j for these (i,j): {512, 18344}, {810, 1946}, {2488, 513}, {3022, 607}, {3063, 649}, {3271, 55}, {3709, 650}, {4516, 42}, {6139, 23351}, {8641, 657}, {14936, 6}

• X₆₆₃ = cevapoint of X_i and X_j for these (i,j): {512, 810}, {522, 25128}, {3063, 8641}

• X₆₆₃ = crosspoint of X_i and X_j for these (i,j): {1, 101}, {6, 109}, {9, 3699}, {19, 36127}, {21, 644}, {33, 8750}, {55, 3939}, {56, 32674}, {57, 4626}, {86, 4603}, {100, 23617}, {108, 1172}, {190, 7033}, {282, 8059}, {284, 4636}, {513, 650}, {514, 26721}, {522, 3064}, {664, 7131}, {692, 2194}, {934, 1170}, {1318, 5548}, {3737, 7252}, {10570, 32653}, {11075, 34921}

• X₆₆₃ = crosssum 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}

• X₆₆₃ = trilinear pole of line {3271, 6139}

• X₆₆₃ = crossdifference of every pair of points on line {2, 7}

• X₆₆₃ = bicentric difference of PU(i) for i in (18, 49, 93, 115)

• X₆₆₃ = PU(18)-harmonic conjugate of X₁₄₀₀

• X₆₆₃ = PU(49)-harmonic conjugate of X₆₇₂

• X₆₆₃ = PU(93)-harmonic conjugate of X₄₁

• X₆₆₃ = trilinear pole of PU(103) (line X₃₂₇₁X₆₁₃₉)

• X₆₆₃ = PU(115)-harmonic conjugate of X₂₀₈₂

• X₆₆₃ = perspector of hyperbola {A, B, C,X₆,X₉}

• X₆₆₃ = intersection of trilinear polars of X₆ and X₉

• X₆₆₃ = pole wrt polar circle of line X₇₅X₂₂₅

• X₆₆₃ = X₉₂-isoconjugate of X₁₈₁₃

• X₆₆₃ = Parry-circle-inverse of X₅₀₇₅

• X₆₆₃ = center of circle {X₁,X₁₅,X₁₆}} (or V(X₁))

• X₆₆₃ = barycentric product of Feuerbach hyperbola intercepts of antiorthic axis

• X₆₆₃ = trilinear product of Feuerbach hyperbola intercepts of Lemoine axis

• X₆₆₃ = intersection of perspectrices of [ABC and Gemini triangle 35] and [ABC and Gemini triangle 36]

• X₆₆₃ = X_i-isoconjugate of X_j for these (i,j): {1, 664}, {2, 651}, {3, 18026}, {4, 6516}, {6, 4554}, {7, 100}, {8, 934}, {9, 658}, {10, 1414}, {21, 4566}, {31, 4572}, {34, 4561}, {36, 35174}, {37, 4573}, {42, 4625}, {55, 4569}, {56, 668}, {57, 190}, {59, 693}, {63, 653}, {65, 99}, {69, 108}, {73, 811}, {75, 109}, {76, 1415}, {77, 1897}, {78, 36118}, {81, 4552}, {85, 101}, {86, 4551}, {92, 1813}, {105, 883}, {110, 1441}, {112, 1231}, {158, 6517}, {162, 307}, {163, 349}, {181, 4623}, {200, 4626}, {210, 4616}, {219, 13149}, {220, 36838}, {222, 6335}, {223, 44327}, {225, 4592}, {226, 662}, {241, 666}, {256, 6649}, {264, 36059}, {269, 3699}, {273, 1331}, {274, 4559}, {278, 1332}, {279, 644}, {286, 23067}, {304, 32674}, {312, 1461}, {319, 26700}, {320, 2222}, {321, 4565}, {322, 8059}, {326, 36127}, {329, 37141}, {331, 906}, {333, 1020}, {341, 6614}, {345, 32714}, {346, 4617}, {347, 13138}, {348, 1783}, {354, 6606}, {377, 13395}, {388, 1310}, {479, 4578}, {497, 8269}, {513, 4998}, {514, 4564}, {518, 927}, {522, 7045}, {527, 37139}, {552, 40521}, {553, 37212}, {604, 1978}, {643, 3668}, {645, 1427}, {646, 1407}, {648, 1214}, {650, 1275}, {655, 3218}, {660, 1447}, {661, 4620}, {670, 1402}, {672, 34085}, {673, 1025}, {692, 6063}, {738, 6558}, {765, 3676}, {789, 1469}, {799, 1400}, {813, 10030}, {823, 40152}, {831, 7247}, {894, 37137}, {898, 43037}, {903, 23703}, {905, 46102}, {908, 37136}, {919, 40704}, {932, 3212}, {940, 32038}, {1014, 3952}, {1016, 3669}, {1018, 1434}, {1042, 7257}, {1086, 31615}, {1088, 3939}, {1119, 4571}, {1121, 23890}, {1122, 8706}, {1155, 35157}, {1252, 24002}, {1262, 4391}, {1284, 4589}, {1292, 6604}, {1293, 39126}, {1305, 3868}, {1317, 4618}, {1319, 4555}, {1334, 4635}, {1397, 6386}, {1403, 18830}, {1408, 27808}, {1409, 6331}, {1412, 4033}, {1423, 4598}, {1428, 4583}, {1429, 4562}, {1432, 18047}, {1439, 36797}, {1442, 6742}, {1445, 37206}, {1446, 5546}, {1449, 4624}, {1462, 42720}, {1463, 8709}, {1465, 13136}, {1476, 21272}, {1492, 7179}, {1509, 21859}, {1633, 8817}, {1758, 35154}, {1799, 46152}, {1847, 4587}, {1880, 4563}, {1909, 29055}, {1945, 15418}, {1969, 32660}, {1981, 40843}, {2003, 15455}, {2006, 4585}, {2078, 35171}, {2099, 4597}, {2149, 3261}, {2171, 4610}, {2185, 4605}, {2223, 46135}, {2254, 39293}, {2283, 2481}, {2284, 34018}, {2285, 37215}, {2321, 4637}, {2338, 24015}, {2346, 35312}, {2397, 34051}, {2398, 43736}, {2406, 36100}, {2550, 6183}, {2652, 17933}, {2720, 3262}, {2742, 38468}, {3057, 6613}, {3112, 46153}, {3219, 38340}, {3257, 3911}, {3263, 32735}, {3451, 21580}, {3573, 7233}, {3598, 37223}, {3649, 4596}, {3666, 6648}, {3671, 4614}, {3674, 36147}, {3732, 7131}, {3779, 34083}, {3903, 7176}, {3912, 36146}, {4017, 4600}, {4025, 7012}, {4032, 4603}, {4059, 8708}, {4076, 43932}, {4077, 4570}, {4105, 24011}, {4130, 23586}, {4146, 6733}, {4163, 24013}, {4357, 36098}, {4397, 7339}, {4556, 6358}, {4558, 40149}, {4567, 7178}, {4579, 7249}, {4584, 16609}, {4586, 7146}, {4595, 7153}, {4601, 7180}, {4604, 5219}, {4606, 21454}, {4612, 6354}, {4619, 4858}, {4621, 41777}, {4622, 40663}, {4654, 37211}, {4705, 7340}, {4968, 29279}, {5061, 35147}, {5172, 35156}, {5221, 32042}, {5228, 32041}, {5252, 13396}, {5376, 30725}, {5377, 43042}, {5378, 43041}, {5379, 17094}, {5380, 7181}, {5382, 30719}, {5383, 43051}, {5385, 43052}, {5389, 7214}, {5435, 27834}, {6012, 30617}, {6135, 13453}, {6136, 13436}, {6180, 30610}, {6332, 7128}, {6528, 22341}, {6540, 32636}, {6734, 36048}, {7035, 43924}, {7115, 15413}, {7132, 33946}, {7175, 27805}, {7182, 8750}, {7235, 36066}, {7265, 35049}, {7316, 42721}, {7672, 43349}, {8047, 40577}, {8680, 41206}, {8685, 33930}, {8687, 20911}, {8707, 24471}, {9357, 10001}, {9436, 36086}, {10509, 35341}, {13486, 40999}, {13577, 40576}, {14612, 39957}, {14733, 30806}, {14942, 41353}, {17080, 44765}, {17090, 29227}, {17097, 17136}, {17791, 34921}, {17924, 44717}, {18033, 34067}, {18743, 38828}, {18816, 23981}, {19604, 43290}, {20567, 32739}, {20924, 32675}, {20930, 36082}, {21362, 40420}, {21453, 35338}, {22464, 36037}, {24027, 35519}, {24029, 34234}, {30456, 44326}, {30545, 34071}, {31618, 35326}, {32018, 36075}, {32693, 34284}, {33864, 36094}, {34855, 36802}, {35516, 36040}, {36049, 40702}, {37138, 40719}, {37143, 37787}

• X₆₆₃ = barycentric product X_i*X_j for these {i,j}: {1, 650}, {3, 3064}, {4, 652}, {6, 522}, {7, 657}, {8, 649}, {9, 513}, {10, 7252}, {11, 101}, {19, 521}, {21, 661}, {25, 6332}, {28, 8611}, {29, 647}, {31, 4391}, {32, 35519}, {33, 905}, {37, 3737}, {41, 693}, {42, 4560}, {44, 23838}, {48, 44426}, {55, 514}, {56, 3239}, {57, 3900}, {58, 3700}, {59, 42462}, {60, 4024}, {63, 18344}, {64, 14331}, {65, 1021}, {73, 17926}, {74, 14400}, {75, 3063}, {78, 6591}, {79, 9404}, {80, 654}, {81, 4041}, {84, 14298}, {85, 8641}, {86, 3709}, {88, 4895}, {89, 4814}, {92, 1946}, {100, 2170}, {106, 1639}, {108, 34591}, {109, 1146}, {110, 21044}, {111, 14432}, {115, 4636}, {124, 32653}, {158, 36054}, {184, 46110}, {188, 6729}, {190, 3271}, {200, 3669}, {210, 1019}, {212, 17924}, {213, 18155}, {219, 7649}, {220, 3676}, {225, 23090}, {226, 21789}, {244, 644}, {256, 3287}, {259, 6728}, {261, 4079}, {266, 6730}, {269, 4130}, {279, 4105}, {281, 1459}, {282, 6129}, {283, 2501}, {284, 523}, {291, 4435}, {292, 3716}, {294, 2254}, {312, 667}, {314, 798}, {318, 22383}, {332, 2489}, {333, 512}, {346, 43924}, {515, 2432}, {518, 1024}, {520, 8748}, {525, 2299}, {527, 23351}, {579, 23289}, {604, 4397}, {607, 4025}, {643, 3125}, {645, 3122}, {646, 3248}, {651, 2310}, {653, 3270}, {656, 1172}, {658, 3022}, {659, 4876}, {662, 4516}, {664, 14936}, {665, 14942}, {669, 28660}, {672, 885}, {673, 926}, {676, 2338}, {692, 4858}, {728, 43932}, {739, 14430}, {749, 4501}, {810, 31623}, {812, 7077}, {813, 4124}, {822, 1896}, {875, 3975}, {876, 3684}, {884, 3912}, {893, 3907}, {900, 2316}, {901, 4530}, {909, 2804}, {918, 2195}, {934, 3119}, {941, 17418}, {1002, 45755}, {1014, 4171}, {1015, 3699}, {1018, 18191}, {1022, 3689}, {1027, 3693}, {1036, 6590}, {1039, 2522}, {1043, 7180}, {1086, 3939}, {1110, 40166}, {1121, 6139}, {1126, 4976}, {1155, 23893}, {1170, 6608}, {1174, 6362}, {1178, 4140}, {1252, 21132}, {1253, 24002}, {1262, 23615}, {1292, 38375}, {1293, 4534}, {1318, 6544}, {1320, 1635}, {1331, 8735}, {1333, 4086}, {1334, 7192}, {1357, 6558}, {1395, 15416}, {1400, 7253}, {1407, 4163}, {1414, 36197}, {1415, 24026}, {1431, 4529}, {1432, 4477}, {1434, 4524}, {1436, 8058}, {1458, 28132}, {1461, 4081}, {1491, 2344}, {1577, 2194}, {1638, 4845}, {1647, 5548}, {1751, 8676}, {1783, 7004}, {1813, 42069}, {1826, 23189}, {1857, 4091}, {1897, 7117}, {1919, 3596}, {1924, 40072}, {1960, 4997}, {1973, 35518}, {1980, 28659}, {2053, 3835}, {2090, 45878}, {2125, 17427}, {2149, 42455}, {2150, 4036}, {2160, 35057}, {2161, 3738}, {2162, 4147}, {2163, 4944}, {2175, 3261}, {2183, 43728}, {2185, 4705}, {2189, 4064}, {2192, 14837}, {2193, 24006}, {2204, 14208}, {2212, 15413}, {2226, 4543}, {2258, 23880}, {2265, 46041}, {2269, 4581}, {2287, 4017}, {2291, 6366}, {2298, 17420}, {2311, 4010}, {2318, 17925}, {2319, 4083}, {2320, 4893}, {2321, 3733}, {2325, 23345}, {2328, 7178}, {2332, 17094}, {2334, 4765}, {2339, 8678}, {2342, 10015}, {2346, 21127}, {2348, 35355}, {2364, 4777}, {2423, 6735}, {2424, 40869}, {2425, 15633}, {2484, 30479}, {2488, 32008}, {2590, 3308}, {2591, 3307}, {2605, 7110}, {2643, 4612}, {2785, 17963}, {2968, 32674}, {2969, 4587}, {3049, 44130}, {3120, 5546}, {3121, 7257}, {3208, 43931}, {3224, 25128}, {3254, 22108}, {3445, 4521}, {3451, 42337}, {3572, 3685}, {3680, 4394}, {3688, 10566}, {3692, 43923}, {3710, 43925}, {3717, 43929}, {3732, 14935}, {3768, 36798}, {3904, 6187}, {4009, 23892}, {4069, 16726}, {4076, 21143}, {4092, 4556}, {4162, 8056}, {4451, 20981}, {4455, 36800}, {4474, 30650}, {4515, 7203}, {4517, 4817}, {4518, 8632}, {4522, 40746}, {4526, 37129}, {4542, 4638}, {4546, 40151}, {4557, 17197}, {4603, 40608}, {4617, 24010}, {4619, 5532}, {4626, 35508}, {4724, 40779}, {4750, 5547}, {4768, 9456}, {4775, 30608}, {4778, 34820}, {4790, 4866}, {4825, 30607}, {4834, 42030}, {4885, 9439}, {4913, 25426}, {4919, 6164}, {4939, 34080}, {4953, 38828}, {4959, 26745}, {4977, 33635}, {4979, 32635}, {4985, 28615}, {5060, 18013}, {5075, 17947}, {5089, 23696}, {5452, 26721}, {5514, 8059}, {5540, 42552}, {6059, 30805}, {6065, 6545}, {6066, 23100}, {6169, 42341}, {6182, 39273}, {6364, 13456}, {6365, 13427}, {6373, 36799}, {6506, 36082}, {6557, 8643}, {6589, 10570}, {6603, 35348}, {6607, 10509}, {6614, 23970}, {6615, 23617}, {6740, 21828}, {7072, 21188}, {7073, 14838}, {7091, 40137}, {7106, 8062}, {7108, 21761}, {7118, 17896}, {7131, 17115}, {7152, 14302}, {7155, 20979}, {7160, 14300}, {7162, 13401}, {7255, 20684}, {7707, 10495}, {8602, 30201}, {8638, 18031}, {8640, 27424}, {8648, 18359}, {8750, 26932}, {9447, 40495}, {10397, 40836}, {10482, 21104}, {10492, 16012}, {10579, 14282}, {10581, 21453}, {11125, 15627}, {11934, 44178}, {12032, 28143}, {12077, 35196}, {14304, 32677}, {14392, 34056}, {14395, 36119}, {14399, 44693}, {14413, 41798}, {14418, 36125}, {14571, 37628}, {14733, 33573}, {15313, 39943}, {15420, 40976}, {15997, 45877}, {17435, 36086}, {18000, 40882}, {18101, 46148}, {18108, 33299}, {21172, 30457}, {21185, 40141}, {21362, 40528}, {21390, 40505}, {21666, 32660}, {21739, 42657}, {21807, 39177}, {23104, 23979}, {23493, 27527}, {24012, 36838}, {24225, 40523}, {28291, 43960}, {29226, 36630}, {30731, 43922}, {31182, 33963}, {32641, 35015}, {32739, 34387}, {35072, 36127}, {36049, 38357}, {36050, 38345}, {39924, 45902}, {39956, 42312}, {42064, 43050}

• X₆₆₃ = barycentric quotient X_i/X_j for these {i,j}: {1, 4554}, {2, 4572}, {6, 664}, {8, 1978}, {9, 668}, {11, 3261}, {19, 18026}, {21, 799}, {25, 653}, {29, 6331}, {31, 651}, {32, 109}, {33, 6335}, {34, 13149}, {41, 100}, {42, 4552}, {48, 6516}, {55, 190}, {56, 658}, {57, 4569}, {58, 4573}, {60, 4610}, {81, 4625}, {101, 4998}, {105, 34085}, {109, 1275}, {110, 4620}, {172, 6649}, {181, 4605}, {184, 1813}, {200, 646}, {210, 4033}, {212, 1332}, {213, 4551}, {219, 4561}, {220, 3699}, {244, 24002}, {269, 36838}, {283, 4563}, {284, 99}, {312, 6386}, {314, 4602}, {333, 670}, {480, 6558}, {512, 226}, {513, 85}, {514, 6063}, {521, 304}, {522, 76}, {523, 349}, {560, 1415}, {577, 6517}, {604, 934}, {607, 1897}, {608, 36118}, {643, 4601}, {644, 7035}, {647, 307}, {649, 7}, {650, 75}, {652, 69}, {654, 320}, {656, 1231}, {657, 8}, {659, 10030}, {661, 1441}, {665, 9436}, {667, 57}, {669, 1400}, {672, 883}, {673, 46135}, {692, 4564}, {693, 20567}, {788, 7146}, {798, 65}, {810, 1214}, {812, 18033}, {834, 33949}, {872, 21859}, {884, 673}, {885, 18031}, {904, 37137}, {905, 7182}, {919, 39293}, {926, 3912}, {1014, 4635}, {1015, 3676}, {1021, 314}, {1024, 2481}, {1027, 34018}, {1036, 37215}, {1098, 4631}, {1106, 4617}, {1110, 31615}, {1146, 35519}, {1172, 811}, {1174, 6606}, {1253, 644}, {1333, 1414}, {1334, 3952}, {1364, 30805}, {1395, 32714}, {1397, 1461}, {1400, 4566}, {1402, 1020}, {1407, 4626}, {1408, 4637}, {1412, 4616}, {1415, 7045}, {1438, 927}, {1456, 24015}, {1459, 348}, {1475, 35312}, {1639, 3264}, {1802, 4571}, {1918, 4559}, {1919, 56}, {1924, 1402}, {1936, 15418}, {1946, 63}, {1960, 3911}, {1973, 108}, {1974, 32674}, {1977, 43924}, {1980, 604}, {2053, 4598}, {2161, 35174}, {2170, 693}, {2175, 101}, {2185, 4623}, {2192, 44327}, {2193, 4592}, {2194, 662}, {2195, 666}, {2200, 23067}, {2204, 162}, {2206, 4565}, {2207, 36127}, {2208, 37141}, {2212, 1783}, {2223, 1025}, {2251, 23703}, {2254, 40704}, {2258, 32038}, {2287, 7257}, {2291, 35157}, {2299, 648}, {2310, 4391}, {2311, 4589}, {2316, 4555}, {2319, 18830}, {2321, 27808}, {2328, 645}, {2330, 18047}, {2332, 36797}, {2334, 4624}, {2340, 42720}, {2342, 13136}, {2344, 789}, {2347, 21272}, {2361, 4585}, {2364, 4597}, {2432, 34393}, {2483, 7247}, {2484, 388}, {2488, 142}, {2489, 225}, {2605, 17095}, {3022, 3239}, {3049, 73}, {3051, 46153}, {3056, 33946}, {3057, 21580}, {3063, 1}, {3064, 264}, {3119, 4397}, {3121, 4017}, {3122, 7178}, {3125, 4077}, {3208, 36863}, {3239, 3596}, {3248, 3669}, {3249, 1357}, {3250, 7179}, {3261, 41283}, {3270, 6332}, {3271, 514}, {3287, 1909}, {3309, 21609}, {3310, 22464}, {3451, 6613}, {3572, 7233}, {3669, 1088}, {3684, 874}, {3685, 27853}, {3688, 4568}, {3689, 24004}, {3699, 31625}, {3700, 313}, {3709, 10}, {3716, 1921}, {3733, 1434}, {3737, 274}, {3738, 20924}, {3768, 43037}, {3900, 312}, {3904, 40075}, {3907, 1920}, {3939, 1016}, {4017, 1446}, {4024, 34388}, {4041, 321}, {4079, 12}, {4083, 30545}, {4086, 27801}, {4091, 7055}, {4105, 346}, {4130, 341}, {4140, 1237}, {4147, 6382}, {4148, 4087}, {4162, 18743}, {4171, 3701}, {4367, 7196}, {4369, 7205}, {4391, 561}, {4394, 39126}, {4397, 28659}, {4435, 350}, {4455, 16609}, {4477, 17787}, {4501, 3760}, {4507, 7201}, {4516, 1577}, {4517, 3807}, {4524, 2321}, {4526, 6381}, {4531, 7239}, {4543, 36791}, {4546, 44723}, {4556, 7340}, {4560, 310}, {4612, 24037}, {4617, 24011}, {4636, 4590}, {4705, 6358}, {4775, 5219}, {4814, 4671}, {4820, 30596}, {4827, 4673}, {4832, 3671}, {4834, 4654}, {4858, 40495}, {4876, 4583}, {4895, 4358}, {4976, 1269}, {5060, 17933}, {5075, 17950}, {5546, 4600}, {6065, 6632}, {6129, 40702}, {6139, 527}, {6169, 14727}, {6186, 38340}, {6187, 655}, {6332, 305}, {6362, 1233}, {6371, 3674}, {6373, 43040}, {6586, 33298}, {6591, 273}, {6602, 4578}, {6608, 1229}, {6614, 23586}, {6615, 26563}, {6729, 4146}, {7004, 15413}, {7063, 4079}, {7064, 4103}, {7073, 15455}, {7077, 4562}, {7083, 3732}, {7104, 29055}, {7117, 4025}, {7118, 13138}, {7180, 3668}, {7234, 4032}, {7252, 86}, {7253, 28660}, {7336, 23100}, {7649, 331}, {8611, 20336}, {8632, 1447}, {8638, 672}, {8640, 1423}, {8641, 9}, {8642, 1445}, {8643, 5435}, {8645, 37787}, {8646, 2285}, {8648, 3218}, {8653, 5257}, {8676, 18134}, {8735, 46107}, {8748, 6528}, {8750, 46102}, {9247, 36059}, {9404, 319}, {9439, 30610}, {9447, 692}, {9448, 32739}, {9449, 46177}, {9454, 2283}, {10581, 4847}, {11124, 20881}, {11193, 18151}, {11934, 20927}, {14298, 322}, {14331, 14615}, {14400, 3260}, {14407, 40663}, {14413, 37780}, {14427, 4723}, {14430, 35543}, {14432, 3266}, {14575, 32660}, {14776, 39294}, {14827, 3939}, {14936, 522}, {14942, 36803}, {17412, 10527}, {17418, 34284}, {17420, 20911}, {17424, 4862}, {17425, 5231}, {17926, 44130}, {17963, 35154}, {18000, 11608}, {18105, 18097}, {18155, 6385}, {18191, 7199}, {18265, 813}, {18344, 92}, {20229, 35338}, {20665, 3888}, {20967, 3882}, {20979, 3212}, {20980, 9312}, {20981, 7176}, {21044, 850}, {21123, 3665}, {21127, 20880}, {21132, 23989}, {21143, 1358}, {21748, 17136}, {21758, 1443}, {21761, 1943}, {21789, 333}, {21828, 41804}, {22383, 77}, {23090, 332}, {23189, 17206}, {23224, 7183}, {23289, 40011}, {23351, 1121}, {23572, 17082}, {23615, 23978}, {23838, 20568}, {24012, 4130}, {25128, 6374}, {28660, 4609}, {32656, 44717}, {32739, 59}, {33525, 6734}, {33635, 6540}, {34068, 37139}, {34591, 35518}, {34858, 37136}, {35057, 33939}, {35508, 4163}, {35518, 40364}, {35519, 1502}, {36054, 326}, {36197, 4086}, {38347, 20954}, {38365, 17494}, {38367, 8850}, {38986, 43051}, {38991, 21302}, {39201, 40152}, {40972, 4553}, {40982, 17906}, {41339, 42719}, {42069, 46110}, {42312, 18135}, {42462, 34387}, {42649, 17483}, {42657, 17484}, {43923, 1847}, {43924, 279}, {43931, 7209}, {43932, 23062}, {44426, 1969}, {45755, 4441}, {46110, 18022}

• X₆₆₃ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {1, 4794, 4724}, {2, 21302, 17072}, {649, 1960, 8656}, {649, 8643, 667}, {650, 4435, 45755}, {650, 4895, 4814}, {667, 1946, 8648}, {667, 1960, 8643}, {667, 8641, 1946}, {667, 8643, 8656}, {669, 2978, 649}, {1919, 4079, 2484}, {1960, 4775, 649}, {2488, 8641, 649}, {3063, 3709, 657}, {3250, 8632, 649}, {4041, 4162, 4959}, {4564, 36086, 9323}, {5638, 5639, 5075}