X₆₆₁

CROSSDIFFERENCE OF X₁ AND X₂₁

X₆₆₁ = barycentric product of PU(71)

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

X₆₆₁ (CROSSDIFFERENCE OF X₁ AND X₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {44, 513}, {514, 693}

• Related Centers: X₄₄ (-LINE CONJUGATE OF X₁), X₅₁₃ (ISOGONAL CONJUGATE OF X₁₀₀), X₅₁₄ (ISOGONAL CONJUGATE OF X₁₀₁), X₆₉₃ (ISOTOMIC CONJUGATE OF X₁₀₀)

Trilinears: \(\cot B - \cot C : \cot C - \cot A : \cot A - \cot B\)

Barycentrics: \(\sin A (\cot B - \cot C) : \sin B (\cot C - \cot A) : \sin C (\cot A - \cot B)\)

Search Value (6, 9, 13): \(-49.582382944073\)

▸ Alternate Coordinates4 forms

• Trilinears: \(b^{2} - c^{2} : :\)

• Trilinears: \(S_{B} - S_{C} : :\)

• Trilinears: \(\cos 2B - \cos 2C : :\)

• Trilinears: \(d(a,b,c) : :\), where d(a,b,c) = directed distance from A to line X₂X₆

▸ Linear Combinations1 combination

• X₆₆₁ = X₆₆₁ = \(6\) X₂ - \(5\) X₂₄₉₂₄, \(3\) X₂ - \(4\) X₂₅₆₆₆, \(3\) X₂ + X₃₁₂₉₀, \(5\) X₂ - \(4\) X₄₅₆₆₃, \(2\) X₆₄₉ - \(3\) X₁₆₃₅, \(5\) X₆₄₉ - \(8\) X₂₅₁₆, \(3\) X₆₄₉ - \(4\) X₄₃₉₄, \(3\) X₆₄₉ - \(2\) X₄₇₉₀, X₆₄₉ - \(3\) X₄₈₉₃, \(4\) X₆₅₀ - \(3\) X₁₆₃₅, \(5\) X₆₅₀ - \(4\) X₂₅₁₆, \(3\) X₆₅₀ - \(2\) X₄₃₉₄, \(3\) X₆₅₀ - X₄₇₉₀, \(2\) X₆₅₀ + X₄₈₁₃, \(2\) X₆₅₀ - \(3\) X₄₈₉₃, \(4\) X₆₅₀ - X₄₉₇₉, \(2\) X₆₉₃ - \(3\) X₄₇₂₈, X₆₉₃ - \(3\) X₄₇₇₆, \(15\) X₁₆₃₅ - \(16\) X₂₅₁₆, \(9\) X₁₆₃₅ - \(8\) X₄₃₉₄, \(9\) X₁₆₃₅ - \(4\) X₄₇₉₀, \(3\) X₁₆₃₅ + \(2\) X₄₈₁₃, \(3\) X₁₆₃₅ - X₄₉₇₉, \(8\) X₂₄₉₀ - \(9\) X₆₅₄₄, \(6\) X₂₅₁₆ - \(5\) X₄₃₉₄, \(12\) X₂₅₁₆ - \(5\) X₄₇₉₀, \(8\) X₂₅₁₆ + \(5\) X₄₈₁₃, \(8\) X₂₅₁₆ - \(15\) X₄₈₉₃, \(16\) X₂₅₁₆ - \(5\) X₄₉₇₉, \(2\) X₂₅₂₇ - \(3\) X₁₄₄₂₅, \(2\) X₂₅₃₃ - \(3\) X₂₁₀₅₂, \(3\) X₃₂₃₉ - \(4\) X₁₄₃₅₀, \(2\) X₃₇₀₀ - \(3\) X₄₁₂₀, \(4\) X₃₇₀₀ - X₄₈₃₈, \(4\) X₃₇₀₀ - \(3\) X₄₉₃₁, \(2\) X₃₇₀₀ + X₄₉₈₈, \(4\) X₃₇₇₆ - \(3\) X₂₁₁₁₅, \(2\) X₃₇₇₆ - \(3\) X₄₄₄₃₅, \(4\) X₃₈₃₅ - \(3\) X₄₇₂₈, \(2\) X₃₈₃₅ - \(3\) X₄₇₇₆, X₄₀₂₄ - \(3\) X₄₁₂₀, X₄₀₂₄ + \(2\) X₄₈₄₁, \(2\) X₄₀₂₄ - \(3\) X₄₉₃₁, X₄₀₂₄ - \(4\) X₁₄₃₂₁, \(3\) X₄₀₄₁ - \(2\) X₄₇₃₀, \(3\) X₄₀₄₁ - \(4\) X₄₇₇₀, X₄₀₄₁ + \(2\) X₄₉₈₃, \(2\) X₄₁₀₆ - \(3\) X₃₁₁₄₇, \(6\) X₄₁₂₀ - X₄₈₃₈, \(3\) X₄₁₂₀ + \(2\) X₄₈₄₁, \(3\) X₄₁₂₀ + X₄₉₈₈, \(3\) X₄₁₂₀ - \(4\) X₁₄₃₂₁, \(4\) X₄₃₆₉ - \(5\) X₂₄₉₂₄, \(4\) X₄₃₆₉ - \(3\) X₃₁₁₄₈, \(2\) X₄₃₆₉ + X₃₁₂₉₀, X₄₃₆₉ - \(3\) X₄₅₃₁₅, \(5\) X₄₃₆₉ - \(6\) X₄₅₆₆₃, \(2\) X₄₃₇₈ - \(3\) X₁₄₄₁₃, \(3\) X₄₃₇₉ - \(4\) X₄₈₈₅, \(3\) X₄₃₇₉ - \(5\) X₃₀₈₃₅, \(3\) X₄₃₇₉ - \(2\) X₄₃₀₆₇, X₄₃₈₀ - \(3\) X₃₁₁₅₀, X₄₃₈₂ - \(4\) X₄₉₄₀, X₄₃₈₂ - \(3\) X₃₁₁₄₇, \(4\) X₄₃₉₄ + \(3\) X₄₈₁₃, \(4\) X₄₃₉₄ - \(9\) X₄₈₉₃, \(8\) X₄₃₉₄ - \(3\) X₄₉₇₉, \(2\) X₄₄₁₁ - \(3\) X₂₇₄₈₅, \(3\) X₄₄₅₃ - \(4\) X₂₁₂₁₂, \(4\) X₄₇₀₅ - X₄₇₂₉, \(3\) X₄₇₀₅ - X₄₇₃₀, \(3\) X₄₇₀₅ - \(2\) X₄₇₇₀, \(2\) X₄₇₀₅ + X₄₈₂₂, \(3\) X₄₇₂₉ - \(4\) X₄₇₃₀, \(3\) X₄₇₂₉ - \(8\) X₄₇₇₀, X₄₇₂₉ + \(2\) X₄₈₂₂, X₄₇₂₉ + \(4\) X₄₉₈₃, \(2\) X₄₇₃₀ + \(3\) X₄₈₂₂, X₄₇₃₀ + \(3\) X₄₉₈₃, \(3\) X₄₇₅₀ - \(2\) X₄₈₉₇, \(3\) X₄₇₅₀ - \(4\) X₁₇₀₆₉, \(6\) X₄₇₆₃ - \(5\) X₂₇₀₁₃, \(6\) X₄₇₆₃ - \(7\) X₂₇₁₁₅, \(4\) X₄₇₇₀ + \(3\) X₄₈₂₂, \(2\) X₄₇₇₀ + \(3\) X₄₉₈₃, \(2\) X₄₇₉₀ + \(3\) X₄₈₁₃, \(2\) X₄₇₉₀ - \(9\) X₄₈₉₃, \(4\) X₄₇₉₀ - \(3\) X₄₉₇₉, X₄₈₀₄ - \(4\) X₄₈₀₆, X₄₈₀₄ + \(2\) X₄₈₂₄, \(2\) X₄₈₀₆ + X₄₈₂₄, X₄₈₁₃ + \(3\) X₄₈₉₃, \(2\) X₄₈₁₃ + X₄₉₇₉, X₄₈₃₈ + \(4\) X₄₈₄₁, X₄₈₃₈ - \(3\) X₄₉₃₁, X₄₈₃₈ + \(2\) X₄₉₈₈, X₄₈₃₈ - \(8\) X₁₄₃₂₁, \(4\) X₄₈₄₁ + \(3\) X₄₉₃₁, X₄₈₄₁ + \(2\) X₁₄₃₂₁, \(4\) X₄₈₈₅ - \(5\) X₃₀₈₃₅, \(6\) X₄₈₉₃ - X₄₉₇₉, \(6\) X₄₉₂₈ - \(5\) X₂₆₉₈₅, \(6\) X₄₉₂₈ - \(7\) X₂₇₁₃₈, \(3\) X₄₉₃₁ + \(2\) X₄₉₈₈, \(3\) X₄₉₃₁ - \(8\) X₁₄₃₂₁, \(2\) X₄₉₃₂ - \(5\) X₃₁₂₀₉, \(4\) X₄₉₄₀ - \(3\) X₃₁₁₄₇, \(3\) X₄₉₅₈ + \(4\) X₄₅₇₄₅, X₄₉₈₈ + \(4\) X₁₄₃₂₁, \(3\) X₆₅₄₅ - \(2\) X₂₁₁₀₄, \(3\) X₆₅₄₆ + X₂₃₇₃₁, \(3\) X₆₅₉₀ - \(8\) X₁₄₃₅₀, \(2\) X₇₁₉₂ - \(5\) X₂₄₉₂₄, X₇₁₉₂ - \(4\) X₂₅₆₆₆, \(2\) X₇₁₉₂ - \(3\) X₃₁₁₄₈, X₇₁₉₂ - \(6\) X₄₅₃₁₅, \(5\) X₇₁₉₂ - \(12\) X₄₅₆₆₃, \(3\) X₈₀₂₉ - \(2\) X₁₂₀₇₂, \(2\) X₈₆₈₉ - \(3\) X₄₅₆₇₃, \(4\) X₂₁₀₅₁ - \(3\) X₂₁₀₅₂, \(2\) X₂₁₁₉₆ + X₄₄₄₄₉, \(3\) X₂₁₂₉₇ - \(5\) X₂₆₇₉₈, \(3\) X₂₁₂₉₇ - X₂₆₈₂₄, \(2\) X₂₄₇₂₀ - \(3\) X₄₄₄₂₉, \(5\) X₂₄₉₂₄ - \(8\) X₂₅₆₆₆, \(5\) X₂₄₉₂₄ - \(3\) X₃₁₁₄₈, \(5\) X₂₄₉₂₄ + \(2\) X₃₁₂₉₀, \(5\) X₂₄₉₂₄ - \(12\) X₄₅₃₁₅, \(25\) X₂₄₉₂₄ - \(24\) X₄₅₆₆₃, \(8\) X₂₅₆₆₆ - \(3\) X₃₁₁₄₈, \(4\) X₂₅₆₆₆ + X₃₁₂₉₀, \(2\) X₂₅₆₆₆ - \(3\) X₄₅₃₁₅, \(5\) X₂₅₆₆₆ - \(3\) X₄₅₆₆₃, \(5\) X₂₆₇₇₇ - X₂₆₈₅₃, \(5\) X₂₆₇₉₈ - X₂₆₈₂₄, \(5\) X₂₆₉₈₅ - \(7\) X₂₇₁₃₈, \(5\) X₂₇₀₁₃ - \(7\) X₂₇₁₁₅, \(5\) X₃₀₈₃₅ - \(2\) X₄₃₀₆₇, \(3\) X₃₁₁₄₈ + \(2\) X₃₁₂₉₀, X₃₁₁₄₈ - \(4\) X₄₅₃₁₅, \(5\) X₃₁₁₄₈ - \(8\) X₄₅₆₆₃, \(7\) X₃₁₂₀₇ - \(8\) X₃₁₂₈₇, \(5\) X₃₁₂₀₉ - \(4\) X₃₁₂₈₆, X₃₁₂₉₀ + \(6\) X₄₅₃₁₅, \(5\) X₃₁₂₉₀ + \(12\) X₄₅₆₆₃, \(5\) X₄₅₃₁₅ - \(2\) X₄₅₆₆₃

X₆₆₁ lies on the cubic K1005.

▸ Incident Central Lines243 lines

{1, 4160}, {2, 3572}, {4, 17926}, {6, 4833}, {9, 35354}, {10, 4761}, {11, 20974}, {31, 9256}, {37, 42768}, {38, 3805}, {44, 513}, {63, 8774}, {71, 3657}, {100, 2702}, {101, 1290}, {109, 9090}, {115, 2170}, {125, 1566}, {162, 36084}, {163, 32678}, {190, 35147}, {226, 4077}, {239, 40459}, {244, 3124}, {430, 23615}, {442, 14825}, {512, 4041}, {514, 693}, {522, 4502}, {523, 3700}, {525, 21124}, {647, 3709}, {662, 2644}, {663, 810}, {665, 2530}, {669, 4455}, {756, 3005}, {764, 14434}, {784, 23657}, {786, 1926}, {788, 2978}, {799, 27805}, {812, 17494}, {824, 25259}, {830, 1580}, {832, 3063}, {875, 25836}, {876, 25823}, {900, 4976}, {905, 27674}, {918, 3004}, {923, 36150}, {926, 2499}, {940, 18199}, {1011, 23864}, {1015, 38979}, {1019, 1931}, {1021, 2651}, {1022, 40434}, {1024, 1174}, {1084, 3123}, {1211, 6546}, {1213, 2490}, {1252, 14513}, {1459, 6588}, {1638, 28902}, {1639, 3837}, {1643, 6161}, {1734, 6005}, {1769, 6589}, {1901, 42462}, {1953, 8818}, {1960, 14438}, {1962, 9279}, {1980, 8633}, {2051, 40213}, {2149, 2222}, {2159, 36151}, {2171, 12077}, {2276, 24577}, {2292, 18015}, {2294, 17422}, {2310, 20975}, {2488, 40952}, {2520, 8641}, {2527, 14425}, {2533, 20486}, {2623, 21741}, {2640, 9395}, {2650, 2653}, {2786, 4467}, {3064, 24006}, {3136, 28143}, {3139, 33573}, {3309, 45755}, {3310, 6615}, {3667, 4765}, {3676, 28878}, {3716, 23656}, {3722, 21341}, {3733, 20472}, {3737, 5053}, {3738, 23650}, {3776, 21115}, {3777, 23738}, {3801, 21125}, {3907, 24534}, {3942, 8287}, {3952, 7239}, {4025, 28846}, {4049, 30588}, {4051, 23942}, {4063, 29807}, {4071, 4086}, {4083, 4490}, {4105, 6182}, {4106, 4382}, {4132, 4826}, {4148, 21302}, {4151, 4170}, {4155, 8663}, {4367, 5029}, {4374, 24622}, {4378, 14413}, {4379, 4885}, {4380, 4785}, {4411, 27485}, {4449, 17478}, {4453, 21212}, {4521, 4778}, {4534, 36637}, {4559, 35307}, {4560, 6002}, {4562, 7035}, {4581, 26080}, {4750, 4897}, {4763, 27013}, {4773, 39386}, {4775, 4895}, {4777, 4820}, {4802, 4944}, {4808, 7927}, {4815, 22044}, {4817, 26277}, {4874, 24674}, {4926, 4949}, {4927, 21116}, {4928, 26985}, {4932, 31209}, {4948, 45676}, {4984, 28217}, {5051, 5592}, {5701, 46125}, {5949, 40475}, {6075, 46101}, {6084, 23729}, {6545, 17056}, {6586, 43060}, {6587, 7178}, {6627, 41180}, {6791, 17058}, {7004, 23647}, {7199, 18154}, {7265, 23879}, {7668, 38990}, {8029, 12072}, {8054, 40623}, {8286, 38375}, {8635, 21005}, {8645, 23865}, {8689, 45673}, {8713, 14330}, {8819, 40628}, {9258, 17871}, {9810, 18200}, {10196, 25381}, {10933, 15526}, {11124, 22080}, {14437, 24457}, {14470, 29226}, {14936, 38389}, {15523, 21962}, {16546, 17799}, {17072, 25627}, {17435, 42753}, {17452, 24117}, {17893, 20440}, {18155, 23658}, {18197, 24900}, {18210, 36197}, {18591, 42769}, {18635, 23730}, {19584, 30584}, {20483, 20659}, {20508, 28006}, {20954, 29771}, {20980, 22383}, {21054, 23941}, {21117, 21141}, {21191, 29978}, {21232, 27071}, {21260, 23818}, {21272, 26794}, {21297, 26798}, {21301, 29051}, {21339, 38358}, {21604, 33946}, {21719, 21958}, {22043, 24083}, {22260, 23928}, {22382, 23695}, {23090, 30212}, {23466, 27014}, {23764, 38930}, {23897, 24119}, {24019, 36131}, {24103, 27042}, {24130, 26772}, {24459, 27731}, {24506, 45686}, {24562, 25924}, {24719, 29362}, {26049, 27345}, {26114, 27265}, {26777, 26853}, {27081, 31992}, {27440, 27451}, {27486, 28867}, {27575, 27587}, {27648, 27673}, {28225, 43061}, {28292, 38329}, {28374, 28398}, {29029, 33299}, {30061, 30094}, {31207, 31287}, {33570, 42438}, {35068, 35123}, {35069, 35129}, {37998, 38325}, {38347, 38390}, {40134, 43924}, {40619, 44312}

▸ Functional Relations50 relations

• X₆₆₁ = midpoint of X_i and X_j for these {i,j}: {649, 4813}, {2978, 20983}, {3700, 4841}, {4010, 4824}, {4024, 4988}, {4041, 4822}, {4467, 44449}, {4705, 4983}, {7192, 31290}, {17494, 20295}, {25259, 45746}

• X₆₆₁ = reflection of X_i in X_j for these {i,j}: {2, 45315}, {649, 650}, {693, 3835}, {1019, 14838}, {1577, 4129}, {1635, 4893}, {2254, 1491}, {2484, 2509}, {2533, 21051}, {3700, 14321}, {4010, 4806}, {4024, 3700}, {4041, 4705}, {4106, 4940}, {4122, 18004}, {4369, 25666}, {4382, 4106}, {4467, 21196}, {4728, 4776}, {4729, 4041}, {4730, 4770}, {4761, 10}, {4784, 9508}, {4789, 45661}, {4790, 4394}, {4804, 4010}, {4822, 4983}, {4838, 4024}, {4895, 4775}, {4897, 17069}, {4931, 4120}, {4932, 31286}, {4948, 45676}, {4979, 649}, {4988, 4841}, {6590, 3239}, {7192, 4369}, {7199, 42327}, {16892, 3004}, {21115, 44435}, {21116, 4927}, {21146, 3837}, {21834, 4079}, {23738, 3777}, {23755, 7178}, {31148, 2}, {40471, 3005}, {43067, 4885}

• X₆₆₁ = isogonal conjugate of X₆₆₂

• X₆₆₁ = isotomic conjugate of X₇₉₉

• X₆₆₁ = complement of X₇₁₉₂

• X₆₆₁ = anticomplement of X₄₃₆₉

• X₆₆₁ = polar conjugate of X₈₁₁

• X₆₆₁ = X_i-Ceva conjugate of X_j for these (i,j): (2, 244), (162, 31)

• X₆₆₁ = crosspoint of X_i and X_j for these (i,j): (92, 162), (513, 514)

• X₆₆₁ = crosssum of X_i and X_j for these (i,j): (1, 661), (21, 1021), (48, 656), (81, 1019), (100, 101), (513, 1100), (649, 1193), (667, 1197), (820, 822)

• X₆₆₁ = orthic-isogonal conjugate of X₂₃₁₀

• X₆₆₁ = bicentric difference of PU(i) for these i: 23, 32, 35, 78, 81, 128

• X₆₆₁ = PU(23)-harmonic conjugate of X₃₁

• X₆₆₁ = PU(32)-harmonic conjugate of X₁₉₆₂

• X₆₆₁ = PU(35)-harmonic conjugate of X₃₈

• X₆₆₁ = barycentric product of PU(71)

• X₆₆₁ = PU(78)-harmonic conjugate of X₈₉₆

• X₆₆₁ = trilinear product of PU(79)

• X₆₆₁ = trilinear pole of PU(79) (line X₂₆₄₂X₂₆₄₃)

• X₆₆₁ = PU(81)-harmonic conjugate of X₂₆₅₀

• X₆₆₁ = PU(128)-harmonic conjugate of X₆₃

• X₆₆₁ = perspector of the Stammler hyperbola wrt the excentral triangle

• X₆₆₁ = perspector of circumconic centered at X₂₄₄, which is the hyperbola {A, B, C,X₁,X₁₀}}

• X₆₆₁ = center of circumconic that is locus of trilinear poles of lines passing through X₂₄₄

• X₆₆₁ = intersection of trilinear polars of X₁ and X₁₀

• X₆₆₁ = antigonal image of X₁₃₃₈

• X₆₆₁ = pole wrt polar circle of trilinear polar of X₈₁₁ (line X₁₉X₂₇)

• X₆₆₁ = X₄₈-isoconjugate (polar conjugate) of X₈₁₁

• X₆₆₁ = X₆-isoconjugate of X₉₉

• X₆₆₁ = trilinear square root of X₂₆₄₃

• X₆₆₁ = trilinear product X₆*X₅₂₃

• X₆₆₁ = trilinear product X₃₇*X₅₁₃

• X₆₆₁ = trilinear product X₄*X₆₄₇

• X₆₆₁ = trilinear product of circumcircle intercepts of line X₁₁₅X₁₂₅

• X₆₆₁ = trilinear product of Jerabek hyperbola intercepts of orthic axis

• X₆₆₁ = trilinear product of Kiepert hyperbola intercepts of Lemoine axis

• X₆₆₁ = barycentric product of Kiepert hyperbola intercepts of antiorthic axis

• X₆₆₁ = X_i-anticomplementary conjugate of X_j for these (i,j): {100, 30660}, {256, 150}, {257, 21293}, {805, 30941}, {893, 149}, {904, 4440}, {3573, 25332}, {3903, 69}, {4594, 17137}, {4603, 17135}, {7104, 9263}, {7260, 17138}, {27805, 6327}, {29055, 7}, {30670, 4441}, {32739, 30661}, {34067, 30662}, {37137, 3434}, {40729, 148}

• X₆₆₁ = X_i-complementary conjugate of X_j for these (i,j): {6, 17761}, {10, 21252}, {31, 244}, {37, 116}, {41, 4858}, {42, 11}, {55, 34589}, {65, 17059}, {100, 3741}, {101, 3739}, {109, 3742}, {163, 17045}, {181, 8286}, {190, 21240}, {210, 124}, {212, 34588}, {213, 1086}, {228, 2968}, {594, 21253}, {644, 21246}, {651, 17050}, {692, 1125}, {756, 125}, {765, 512}, {798, 6547}, {872, 115}, {902, 34590}, {1016, 42327}, {1018, 141}, {1020, 21258}, {1110, 523}, {1252, 4369}, {1253, 34591}, {1334, 26932}, {1400, 4904}, {1402, 3756}, {1415, 3946}, {1500, 8287}, {1783, 34830}, {1918, 1015}, {2149, 17069}, {2205, 6377}, {2209, 38986}, {2318, 123}, {3690, 34846}, {3725, 15611}, {3747, 38989}, {3939, 960}, {3949, 127}, {3952, 2887}, {4033, 626}, {4041, 46100}, {4069, 1329}, {4103, 21245}, {4551, 2886}, {4552, 17046}, {4557, 10}, {4559, 142}, {4564, 17066}, {4574, 18589}, {4849, 5510}, {4878, 5511}, {5546, 21233}, {7035, 23301}, {7084, 17463}, {7109, 16592}, {8701, 27798}, {8750, 942}, {15742, 21259}, {18098, 44312}, {20964, 40608}, {21805, 3259}, {21859, 17052}, {23067, 34822}, {23344, 34587}, {23990, 14838}, {27808, 21235}, {28615, 24185}, {30730, 21244}, {31625, 21263}, {32656, 37565}, {32665, 4395}, {32739, 3666}, {34067, 740}, {35309, 21248}, {39258, 35094}, {40521, 3454}, {41333, 35119}

• X₆₆₁ = X_i-Ceva conjugate of X_j for these (i,j): {1, 2643}, {2, 244}, {4, 2310}, {6, 2170}, {10, 3122}, {19, 3708}, {37, 3125}, {57, 2611}, {65, 4516}, {76, 3123}, {87, 4128}, {92, 1109}, {99, 23928}, {100, 1962}, {101, 2294}, {162, 31}, {163, 1953}, {190, 2292}, {226, 3120}, {253, 24010}, {304, 17876}, {502, 21043}, {512, 21834}, {513, 512}, {514, 523}, {523, 4041}, {650, 647}, {651, 2650}, {662, 1}, {664, 23668}, {668, 3728}, {799, 38}, {811, 17872}, {823, 774}, {876, 4155}, {1018, 37}, {1019, 4132}, {1020, 65}, {1022, 4145}, {1292, 42446}, {1427, 18210}, {1577, 656}, {1783, 40977}, {1826, 21044}, {1897, 40973}, {1978, 21020}, {2051, 11}, {2127, 21723}, {2184, 2632}, {2222, 3724}, {2321, 21950}, {2616, 810}, {3064, 2501}, {3223, 4117}, {3239, 6587}, {3257, 758}, {3669, 4139}, {3835, 23301}, {3882, 10459}, {3952, 756}, {4017, 4729}, {4033, 10}, {4052, 21963}, {4083, 22226}, {4103, 1213}, {4129, 31946}, {4444, 2254}, {4551, 42}, {4552, 4642}, {4557, 21808}, {4559, 2171}, {4562, 740}, {4584, 20360}, {4593, 17446}, {4599, 17469}, {4602, 75}, {4605, 1834}, {6010, 17452}, {6011, 55}, {7096, 21340}, {7178, 4017}, {7192, 40471}, {7199, 4151}, {8056, 17476}, {8818, 115}, {13478, 7004}, {14554, 1647}, {15322, 16777}, {15455, 24443}, {16606, 3121}, {17758, 1086}, {18070, 1577}, {18795, 38978}, {20570, 23672}, {20691, 22227}, {21353, 21824}, {21604, 27707}, {21859, 2092}, {23894, 2642}, {24019, 19}, {27805, 2}, {32676, 17442}, {32678, 2173}, {32680, 1725}, {35342, 3723}, {35354, 2610}, {36084, 8772}, {36085, 896}, {36086, 3747}, {36104, 2312}, {36126, 2181}, {36142, 18669}, {36145, 48}, {36146, 44661}, {36148, 17438}, {36632, 23953}, {36907, 4466}, {37134, 1959}, {37212, 3743}, {37216, 36263}, {39733, 17879}, {39735, 1111}, {39748, 3248}, {39797, 17463}, {39798, 1015}, {39957, 4475}, {39979, 27846}, {39981, 2087}, {40011, 23676}, {40515, 2486}, {40521, 16589}, {43739, 38345}

• X₆₆₁ = X_i-cross conjugate of X_j for these (i,j): {1, 9396}, {115, 2171}, {512, 4017}, {810, 656}, {1084, 7148}, {2084, 798}, {2632, 2156}, {2642, 23894}, {2643, 1}, {3122, 10}, {3124, 756}, {3125, 37}, {3708, 19}, {3709, 4041}, {4079, 512}, {4155, 876}, {4516, 65}, {4705, 523}, {4983, 513}, {8034, 244}, {8061, 1577}, {16592, 2}, {20975, 1254}, {20982, 6}, {21051, 21834}, {36197, 1824}, {37754, 2155}

• X₆₆₁ = cevapoint of X_i and X_j for these (i,j): {1, 2640}, {2, 21220}, {6, 21004}, {10, 21100}, {37, 21888}, {512, 3709}, {523, 21051}, {798, 810}, {1577, 20910}, {2084, 8061}, {3124, 8034}, {4024, 21720}, {4079, 4705}

• X₆₆₁ = crosspoint of X_i and X_j for these (i,j): {1, 662}, {2, 3952}, {6, 4559}, {10, 4033}, {19, 24019}, {37, 1018}, {57, 26700}, {65, 1020}, {75, 4602}, {92, 162}, {100, 1255}, {101, 2259}, {163, 2148}, {190, 1220}, {226, 4551}, {513, 514}, {523, 7178}, {650, 3064}, {651, 17097}, {668, 1221}, {799, 3112}, {821, 823}, {1168, 3257}, {1577, 24006}, {2222, 34535}, {2576, 2577}, {2580, 2587}, {2581, 2586}, {4562, 30663}, {22116, 40526}, {32676, 46289}, {36127, 40573}

• X₆₆₁ = crosssum of X_i and X_j for these (i,j): {1, 661}, {2, 4560}, {3, 23090}, {6, 3733}, {9, 35057}, {21, 1021}, {31, 1924}, {48, 656}, {63, 24018}, {81, 1019}, {100, 101}, {110, 5546}, {163, 4575}, {214, 1635}, {284, 3737}, {513, 1100}, {514, 5249}, {523, 5949}, {526, 35069}, {649, 1193}, {650, 2646}, {651, 1813}, {667, 1197}, {693, 17866}, {798, 1964}, {820, 822}, {1577, 14213}, {1930, 14208}, {2238, 38348}, {2578, 2585}, {2579, 2584}, {2582, 2583}, {2642, 42081}, {3687, 6332}, {3738, 34544}, {7192, 17169}, {8061, 17457}, {8300, 8632}, {14838, 40214}

• X₆₆₁ = trilinear pole of line {2642, 2643}

• X₆₆₁ = crossdifference of every pair of points on line {1, 21}

• X₆₆₁ = X_i-isoconjugate of X_j for these (i,j): {1, 662}, {2, 110}, {3, 648}, {4, 4558}, {5, 18315}, {6, 99}, {7, 5546}, {8, 4565}, {9, 1414}, {10, 4556}, {13, 17402}, {14, 17403}, {15, 23895}, {16, 23896}, {19, 4592}, {21, 651}, {22, 44766}, {23, 17708}, {25, 4563}, {27, 1331}, {28, 1332}, {29, 1813}, {30, 44769}, {31, 799}, {32, 670}, {38, 4599}, {39, 4577}, {41, 4625}, {42, 4610}, {44, 4622}, {48, 811}, {49, 38342}, {50, 35139}, {54, 14570}, {55, 4573}, {56, 645}, {57, 643}, {58, 190}, {59, 4560}, {60, 4552}, {61, 32036}, {62, 32037}, {63, 162}, {64, 36841}, {65, 4612}, {66, 4611}, {68, 41679}, {69, 112}, {74, 2407}, {75, 163}, {76, 1576}, {81, 100}, {83, 1634}, {86, 101}, {92, 4575}, {95, 1625}, {97, 35360}, {98, 2421}, {107, 394}, {108, 1812}, {109, 333}, {111, 5468}, {141, 827}, {154, 44326}, {171, 4603}, {172, 4594}, {183, 26714}, {184, 6331}, {187, 892}, {193, 3565}, {200, 4637}, {213, 4623}, {216, 18831}, {220, 4616}, {222, 36797}, {226, 4636}, {230, 10425}, {232, 17932}, {237, 43187}, {238, 4584}, {248, 877}, {249, 523}, {250, 525}, {251, 4576}, {255, 823}, {261, 4559}, {264, 32661}, {265, 14590}, {269, 7259}, {274, 692}, {275, 23181}, {283, 653}, {284, 664}, {286, 906}, {287, 4230}, {290, 14966}, {297, 43754}, {298, 5995}, {299, 5994}, {302, 16806}, {303, 16807}, {304, 32676}, {310, 32739}, {311, 14586}, {314, 1415}, {323, 476}, {324, 15958}, {325, 2715}, {326, 24019}, {328, 14591}, {332, 32674}, {340, 32662}, {343, 933}, {352, 9080}, {385, 805}, {391, 5545}, {395, 10410}, {396, 10409}, {403, 43755}, {418, 42405}, {441, 44770}, {470, 38414}, {471, 38413}, {491, 39384}, {492, 39383}, {511, 2966}, {512, 4590}, {513, 4567}, {514, 4570}, {519, 4591}, {520, 23582}, {524, 691}, {526, 39295}, {538, 32717}, {542, 5649}, {560, 4602}, {571, 46134}, {574, 35138}, {576, 35178}, {577, 6528}, {593, 3952}, {595, 37205}, {597, 12074}, {598, 9145}, {599, 11636}, {604, 7257}, {644, 1014}, {646, 1408}, {647, 18020}, {649, 4600}, {658, 2328}, {661, 24041}, {663, 4620}, {666, 3286}, {667, 4601}, {668, 1333}, {669, 34537}, {671, 5467}, {677, 14953}, {685, 36212}, {687, 13754}, {689, 3051}, {694, 17941}, {729, 23342}, {741, 3570}, {757, 1018}, {758, 37140}, {759, 4585}, {763, 40521}, {765, 1019}, {785, 27164}, {798, 24037}, {801, 1624}, {810, 46254}, {813, 33295}, {822, 23999}, {825, 30966}, {842, 14999}, {843, 9182}, {849, 4033}, {850, 23357}, {859, 13136}, {874, 18268}, {880, 9468}, {886, 33875}, {895, 4235}, {896, 36085}, {897, 23889}, {901, 16704}, {902, 4615}, {905, 5379}, {907, 3618}, {919, 30941}, {923, 24039}, {925, 1993}, {930, 1994}, {931, 940}, {932, 27644}, {934, 2287}, {935, 22151}, {1016, 3733}, {1020, 1098}, {1021, 7045}, {1043, 1461}, {1092, 15352}, {1100, 4596}, {1101, 1577}, {1106, 7258}, {1110, 7199}, {1113, 8116}, {1114, 8115}, {1125, 4629}, {1147, 30450}, {1171, 4427}, {1172, 6516}, {1176, 41676}, {1178, 18047}, {1213, 6578}, {1252, 7192}, {1253, 4635}, {1262, 7253}, {1275, 21789}, {1289, 20806}, {1290, 37783}, {1291, 37779}, {1292, 41610}, {1293, 41629}, {1296, 1992}, {1297, 34211}, {1301, 37669}, {1302, 15066}, {1304, 11064}, {1306, 3068}, {1307, 3069}, {1310, 2303}, {1326, 35148}, {1379, 6189}, {1380, 6190}, {1383, 9146}, {1384, 35179}, {1396, 4571}, {1402, 4631}, {1407, 7256}, {1412, 3699}, {1434, 3939}, {1437, 6335}, {1444, 1783}, {1449, 4614}, {1474, 4561}, {1492, 40773}, {1494, 2420}, {1501, 4609}, {1502, 14574}, {1509, 4557}, {1511, 39290}, {1580, 37134}, {1613, 3222}, {1633, 40403}, {1636, 42308}, {1648, 45773}, {1649, 34539}, {1691, 18829}, {1755, 36036}, {1790, 1897}, {1792, 32714}, {1799, 35325}, {1814, 4238}, {1815, 4241}, {1817, 13138}, {1821, 23997}, {1822, 2581}, {1823, 2580}, {1914, 4589}, {1923, 37204}, {1930, 34072}, {1931, 37135}, {1936, 41206}, {1959, 36084}, {1964, 4593}, {1976, 2396}, {1978, 2206}, {1983, 14616}, {1989, 10411}, {2030, 46144}, {2063, 30249}, {2149, 18155}, {2167, 2617}, {2185, 4551}, {2193, 18026}, {2194, 4554}, {2210, 4639}, {2234, 36133}, {2238, 36066}, {2251, 4634}, {2308, 4632}, {2327, 36118}, {2360, 44327}, {2363, 3882}, {2410, 34210}, {2482, 34574}, {2502, 9170}, {2574, 39298}, {2575, 39299}, {2644, 9395}, {2696, 41617}, {2701, 40882}, {2702, 17731}, {2703, 19623}, {2705, 37792}, {2709, 22329}, {2713, 40888}, {2965, 46139}, {2981, 35314}, {2986, 15329}, {2987, 4226}, {2988, 7450}, {2989, 4243}, {2990, 3658}, {2991, 4236}, {3003, 18878}, {3053, 35136}, {3094, 33514}, {3108, 10330}, {3124, 31614}, {3164, 44828}, {3180, 36515}, {3181, 36514}, {3219, 13486}, {3225, 41337}, {3228, 5118}, {3231, 9150}, {3233, 40384}, {3260, 32640}, {3265, 23964}, {3266, 32729}, {3284, 16077}, {3285, 4555}, {3289, 22456}, {3329, 43357}, {3448, 40173}, {3564, 32697}, {3573, 37128}, {3580, 10420}, {3589, 7953}, {3616, 4627}, {3709, 7340}, {3736, 4586}, {3737, 4564}, {3763, 7954}, {3917, 42396}, {3926, 32713}, {3936, 36069}, {3964, 6529}, {3978, 17938}, {4184, 43190}, {4225, 44765}, {4240, 14919}, {4267, 6648}, {4273, 4597}, {4282, 35174}, {4383, 8690}, {4436, 40408}, {4481, 5384}, {4562, 5009}, {4566, 7054}, {4579, 40432}, {4588, 5235}, {4598, 38832}, {4604, 4653}, {4628, 16887}, {4630, 8024}, {4658, 37211}, {4833, 5385}, {4921, 8697}, {4998, 7252}, {5006, 35147}, {5007, 35137}, {5008, 42367}, {5012, 11794}, {5027, 39292}, {5060, 35154}, {5191, 6035}, {5291, 17929}, {5333, 8652}, {5380, 16702}, {5383, 16695}, {5422, 43351}, {5502, 44877}, {5504, 16237}, {5562, 16813}, {5663, 30528}, {5664, 15395}, {5970, 14607}, {6064, 7180}, {6065, 17096}, {6082, 11580}, {6083, 35466}, {6149, 32680}, {6151, 35315}, {6233, 11163}, {6370, 9273}, {6393, 32696}, {6507, 36126}, {6514, 36127}, {6515, 13398}, {6517, 8748}, {6542, 17940}, {6572, 16285}, {6577, 29767}, {6650, 17943}, {6742, 40214}, {6759, 30441}, {7121, 36860}, {7122, 7260}, {7239, 7305}, {7254, 15742}, {7341, 30730}, {7488, 16039}, {7578, 36829}, {7735, 35575}, {7763, 32734}, {7766, 25424}, {7769, 32737}, {7799, 14560}, {7840, 32694}, {8025, 8701}, {8059, 27398}, {8594, 9197}, {8595, 9196}, {8598, 9190}, {8600, 8860}, {8623, 41209}, {8673, 44183}, {8694, 42028}, {8707, 40153}, {8708, 18166}, {8750, 17206}, {8822, 36049}, {9058, 26637}, {9060, 40112}, {9063, 18899}, {9066, 9463}, {9124, 26613}, {9160, 40879}, {9181, 18823}, {9202, 37786}, {9203, 37785}, {9217, 31998}, {9218, 35511}, {9306, 43188}, {9426, 44168}, {9513, 40866}, {10302, 35357}, {11003, 36886}, {11130, 36840}, {11131, 36839}, {11591, 30527}, {11634, 41909}, {11849, 34357}, {13397, 40571}, {13485, 36830}, {13571, 13578}, {14206, 36034}, {14210, 36142}, {14213, 36134}, {14587, 18314}, {14614, 39639}, {15384, 20580}, {15455, 17104}, {15534, 33638}, {15631, 41932}, {16163, 34568}, {16705, 32736}, {16948, 27834}, {17139, 32641}, {17185, 36098}, {17198, 31616}, {17277, 43076}, {17379, 43359}, {17735, 17930}, {17790, 17939}, {17931, 17966}, {17933, 17963}, {17934, 17962}, {17935, 17961}, {17942, 17947}, {17944, 17946}, {18122, 39448}, {18157, 32666}, {18191, 31615}, {18206, 36086}, {19622, 35156}, {20185, 41628}, {20189, 34545}, {20948, 23995}, {20998, 37880}, {22052, 33513}, {23067, 46103}, {23189, 46102}, {23963, 44173}, {24000, 24018}, {24001, 35200}, {25507, 28148}, {26860, 28210}, {27867, 31296}, {27958, 29055}, {28196, 42025}, {28419, 39417}, {28724, 46151}, {30247, 41614}, {30512, 43756}, {30939, 32665}, {30940, 34067}, {31623, 36059}, {31626, 35311}, {31631, 36082}, {32014, 35327}, {32656, 44129}, {32660, 44130}, {32671, 35550}, {32692, 39113}, {32738, 32833}, {32911, 34594}, {33296, 34071}, {33803, 36953}, {33946, 38813}, {35049, 35057}, {35193, 38340}, {35278, 40802}, {35296, 44768}, {35319, 39287}, {35324, 40410}, {35329, 40707}, {35330, 40706}, {35342, 40438}, {35356, 39389}, {36145, 44179}, {36213, 39291}, {36277, 37216}, {36306, 44718}, {36309, 44719}, {36790, 41173}, {36831, 43768}, {37183, 44767}, {37215, 44119}, {37685, 43356}, {39054, 39137}, {39469, 41174}, {40441, 41677}, {41331, 42371}, {41517, 46294}, {42294, 42296}, {42295, 42297}

• X₆₆₁ = barycentric product X_i*X_j for these {i,j}: {1, 523}, {3, 24006}, {4, 656}, {5, 2616}, {6, 1577}, {7, 4041}, {8, 4017}, {9, 7178}, {10, 513}, {11, 4551}, {12, 3737}, {19, 525}, {25, 14208}, {28, 4064}, {31, 850}, {32, 20948}, {33, 17094}, {37, 514}, {39, 18070}, {42, 693}, {44, 4049}, {48, 14618}, {54, 2618}, {55, 4077}, {56, 4086}, {57, 3700}, {58, 4036}, {63, 2501}, {64, 17898}, {65, 522}, {71, 17924}, {72, 7649}, {73, 44426}, {74, 36035}, {75, 512}, {76, 798}, {81, 4024}, {82, 826}, {83, 8061}, {85, 3709}, {86, 4705}, {87, 21051}, {88, 4120}, {89, 4931}, {91, 924}, {92, 647}, {94, 2624}, {99, 2643}, {100, 3120}, {101, 16732}, {105, 4088}, {107, 2632}, {110, 1109}, {112, 20902}, {115, 662}, {125, 162}, {148, 9396}, {158, 520}, {163, 338}, {181, 18155}, {190, 3125}, {210, 3676}, {213, 3261}, {225, 521}, {226, 650}, {228, 46107}, {238, 35352}, {240, 879}, {244, 3952}, {256, 2533}, {264, 810}, {274, 4079}, {278, 8611}, {279, 4171}, {291, 4010}, {293, 16230}, {304, 2489}, {306, 6591}, {307, 18344}, {308, 2084}, {312, 7180}, {313, 667}, {321, 649}, {330, 21834}, {334, 4455}, {335, 21832}, {336, 17994}, {339, 32676}, {341, 7250}, {346, 7216}, {349, 3063}, {351, 46277}, {393, 24018}, {502, 31947}, {524, 23894}, {526, 2166}, {560, 44173}, {561, 669}, {594, 1019}, {596, 4132}, {643, 1365}, {648, 3708}, {651, 21044}, {652, 40149}, {657, 1446}, {658, 36197}, {659, 43534}, {663, 1441}, {664, 4516}, {668, 3122}, {671, 2642}, {673, 24290}, {684, 36120}, {688, 18833}, {690, 897}, {692, 21207}, {740, 876}, {756, 7192}, {759, 6370}, {799, 3124}, {804, 1581}, {811, 20975}, {822, 2052}, {823, 3269}, {824, 40747}, {868, 36084}, {875, 35544}, {878, 40703}, {881, 1926}, {882, 1966}, {891, 41683}, {896, 5466}, {899, 35353}, {900, 4674}, {903, 4730}, {905, 1826}, {918, 18785}, {923, 35522}, {943, 23752}, {983, 3801}, {985, 4122}, {1002, 4804}, {1015, 4033}, {1018, 1086}, {1020, 1146}, {1021, 6354}, {1022, 3943}, {1027, 3932}, {1042, 4397}, {1084, 4602}, {1088, 4524}, {1089, 3733}, {1096, 3265}, {1100, 31010}, {1101, 23105}, {1111, 4557}, {1126, 30591}, {1156, 30574}, {1214, 3064}, {1221, 40627}, {1245, 2517}, {1254, 7253}, {1255, 4988}, {1268, 4983}, {1292, 21945}, {1320, 30572}, {1334, 24002}, {1358, 4069}, {1400, 4391}, {1402, 35519}, {1409, 46110}, {1414, 4092}, {1427, 3239}, {1432, 4140}, {1459, 41013}, {1491, 40718}, {1500, 7199}, {1502, 1924}, {1510, 2962}, {1576, 23994}, {1635, 4080}, {1637, 2349}, {1648, 36085}, {1725, 15328}, {1733, 35364}, {1734, 15320}, {1737, 3657}, {1755, 43665}, {1757, 18014}, {1758, 18013}, {1769, 38955}, {1783, 4466}, {1784, 14380}, {1821, 3569}, {1822, 39240}, {1823, 39241}, {1824, 4025}, {1861, 10099}, {1880, 6332}, {1897, 18210}, {1903, 14837}, {1910, 2799}, {1918, 40495}, {1919, 27801}, {1928, 9426}, {1929, 18004}, {1930, 18105}, {1934, 5027}, {1953, 15412}, {1956, 6130}, {1959, 2395}, {1962, 4608}, {1967, 14295}, {1969, 3049}, {1973, 3267}, {1978, 3121}, {1989, 32679}, {2088, 32680}, {2148, 18314}, {2153, 23870}, {2154, 23871}, {2156, 33294}, {2157, 9979}, {2159, 41079}, {2160, 7265}, {2161, 4707}, {2167, 12077}, {2169, 23290}, {2170, 4552}, {2171, 4560}, {2173, 2394}, {2184, 6587}, {2186, 23878}, {2190, 6368}, {2214, 23879}, {2238, 4444}, {2247, 14223}, {2250, 10015}, {2254, 13576}, {2292, 4581}, {2298, 21124}, {2310, 4566}, {2312, 43673}, {2321, 3669}, {2333, 15413}, {2334, 4815}, {2357, 17896}, {2401, 21801}, {2422, 46238}, {2433, 14206}, {2491, 46273}, {2509, 36907}, {2530, 18082}, {2574, 2589}, {2575, 2588}, {2578, 2593}, {2579, 2592}, {2582, 8106}, {2583, 8105}, {2605, 6757}, {2606, 7137}, {2607, 2614}, {2610, 24624}, {2611, 6742}, {2617, 8901}, {2623, 14213}, {2627, 18114}, {2631, 16080}, {2640, 9293}, {2648, 18006}, {2652, 2785}, {2786, 9278}, {2970, 4575}, {2972, 36126}, {3005, 3112}, {3221, 18832}, {3223, 23301}, {3224, 20910}, {3248, 27808}, {3293, 40086}, {3445, 4404}, {3456, 18076}, {3500, 21958}, {3565, 17876}, {3566, 8769}, {3572, 3948}, {3668, 3900}, {3701, 43924}, {3710, 43923}, {3800, 23051}, {3835, 16606}, {3837, 18793}, {3949, 17925}, {3954, 10566}, {3971, 43931}, {3992, 23345}, {3994, 43928}, {4052, 4394}, {4063, 40085}, {4082, 43932}, {4083, 42027}, {4103, 16726}, {4117, 4609}, {4129, 39798}, {4139, 34860}, {4145, 39697}, {4151, 13476}, {4155, 18827}, {4170, 7241}, {4373, 4729}, {4453, 34857}, {4475, 4613}, {4492, 4761}, {4559, 4858}, {4562, 39786}, {4567, 21131}, {4580, 17442}, {4592, 8754}, {4594, 21725}, {4599, 39691}, {4610, 21833}, {4695, 23836}, {4770, 39704}, {4782, 34475}, {4791, 28658}, {4822, 5936}, {4823, 28625}, {4824, 30571}, {4832, 40023}, {4838, 25417}, {4841, 25430}, {4876, 7212}, {4893, 30588}, {4979, 6539}, {5379, 21134}, {5489, 24000}, {5620, 8674}, {6003, 41501}, {6011, 8286}, {6057, 7203}, {6129, 39130}, {6149, 10412}, {6164, 21093}, {6358, 7252}, {6367, 40438}, {6521, 32320}, {6544, 30575}, {6548, 21805}, {6724, 6728}, {6741, 26700}, {6791, 37216}, {7018, 7234}, {7035, 8034}, {7148, 17217}, {7237, 7255}, {7260, 21823}, {8029, 24041}, {8056, 14321}, {8599, 36263}, {8672, 31359}, {8714, 40504}, {8808, 14298}, {8809, 14308}, {8811, 14302}, {8818, 14838}, {9033, 36119}, {9148, 37132}, {9178, 14210}, {9255, 16229}, {9258, 30476}, {9267, 21100}, {9292, 17893}, {9307, 17478}, {9309, 21052}, {9395, 10278}, {9402, 18298}, {9404, 43682}, {9508, 11599}, {10693, 21180}, {13212, 36117}, {13486, 21054}, {14207, 21448}, {14220, 36063}, {14398, 33805}, {14404, 31002}, {14407, 20568}, {14417, 36128}, {14429, 36125}, {14431, 37129}, {14554, 21894}, {14616, 42666}, {15232, 21189}, {15313, 23604}, {15352, 37754}, {15451, 40440}, {15455, 20982}, {15523, 18108}, {15526, 24019}, {16186, 36129}, {16592, 27805}, {16892, 18098}, {17197, 21859}, {17205, 40521}, {17415, 46281}, {17431, 19218}, {17432, 19217}, {17438, 39183}, {17467, 42345}, {17469, 31065}, {17763, 18015}, {17768, 35347}, {17879, 32713}, {17881, 32734}, {17926, 37755}, {17954, 18003}, {17955, 34763}, {17956, 18008}, {17957, 18010}, {17990, 18032}, {18001, 20947}, {18359, 21828}, {18691, 46005}, {19604, 44729}, {19611, 44705}, {20332, 21053}, {20571, 34952}, {20906, 23493}, {21186, 43703}, {21192, 21353}, {21727, 39734}, {21836, 42328}, {21867, 26721}, {21888, 42555}, {21950, 27834}, {21951, 25576}, {22260, 24037}, {23285, 46289}, {23503, 40162}, {23785, 40516}, {23800, 41506}, {23838, 40663}, {27807, 40471}, {28161, 31503}, {31946, 39748}, {34920, 38469}, {35235, 36061}, {35354, 35466}, {36036, 44114}, {36037, 42759}, {40327, 40345}, {40437, 42768}, {42653, 44188}

• X₆₆₁ = barycentric quotient X_i/X_j for these {i,j}: {1, 99}, {2, 799}, {3, 4592}, {4, 811}, {6, 662}, {7, 4625}, {8, 7257}, {9, 645}, {10, 668}, {11, 18155}, {19, 648}, {25, 162}, {31, 110}, {32, 163}, {33, 36797}, {37, 190}, {38, 4576}, {41, 5546}, {42, 100}, {48, 4558}, {51, 2617}, {55, 643}, {56, 1414}, {57, 4573}, {63, 4563}, {65, 664}, {71, 1332}, {72, 4561}, {73, 6516}, {75, 670}, {76, 4602}, {81, 4610}, {82, 4577}, {83, 4593}, {86, 4623}, {88, 4615}, {91, 46134}, {92, 6331}, {98, 36036}, {99, 24037}, {100, 4600}, {101, 4567}, {106, 4622}, {107, 23999}, {110, 24041}, {111, 36085}, {115, 1577}, {125, 14208}, {158, 6528}, {162, 18020}, {163, 249}, {181, 4551}, {184, 4575}, {187, 23889}, {190, 4601}, {192, 36860}, {200, 7256}, {210, 3699}, {213, 101}, {220, 7259}, {225, 18026}, {226, 4554}, {228, 1331}, {237, 23997}, {240, 877}, {244, 7192}, {251, 4599}, {256, 4594}, {257, 7260}, {269, 4616}, {279, 4635}, {284, 4612}, {291, 4589}, {292, 4584}, {293, 17932}, {308, 37204}, {313, 6386}, {321, 1978}, {333, 4631}, {335, 4639}, {338, 20948}, {346, 7258}, {351, 896}, {393, 823}, {512, 1}, {513, 86}, {514, 274}, {520, 326}, {521, 332}, {522, 314}, {523, 75}, {524, 24039}, {525, 304}, {560, 1576}, {561, 4609}, {594, 4033}, {604, 4565}, {610, 36841}, {643, 6064}, {647, 63}, {648, 46254}, {649, 81}, {650, 333}, {651, 4620}, {652, 1812}, {656, 69}, {657, 2287}, {659, 33295}, {662, 4590}, {663, 21}, {665, 18206}, {667, 58}, {669, 31}, {688, 1964}, {690, 14210}, {692, 4570}, {693, 310}, {694, 37134}, {729, 36133}, {740, 874}, {741, 36066}, {756, 3952}, {762, 4103}, {764, 17205}, {784, 10471}, {788, 3736}, {798, 6}, {799, 34537}, {804, 1966}, {810, 3}, {812, 30940}, {822, 394}, {826, 1930}, {850, 561}, {872, 4557}, {875, 741}, {876, 18827}, {878, 293}, {879, 336}, {881, 1967}, {882, 1581}, {888, 2234}, {893, 4603}, {896, 5468}, {897, 892}, {900, 30939}, {903, 4634}, {905, 17206}, {918, 18157}, {922, 5467}, {923, 691}, {924, 44179}, {1015, 1019}, {1018, 1016}, {1019, 1509}, {1020, 1275}, {1021, 7058}, {1042, 934}, {1084, 798}, {1086, 7199}, {1089, 27808}, {1096, 107}, {1109, 850}, {1126, 4596}, {1245, 1310}, {1254, 4566}, {1255, 4632}, {1333, 4556}, {1334, 644}, {1357, 7203}, {1365, 4077}, {1400, 651}, {1402, 109}, {1407, 4637}, {1409, 1813}, {1414, 7340}, {1426, 36118}, {1427, 658}, {1441, 4572}, {1459, 1444}, {1491, 30966}, {1500, 1018}, {1576, 1101}, {1577, 76}, {1580, 17941}, {1581, 18829}, {1635, 16704}, {1637, 14206}, {1649, 24038}, {1734, 33297}, {1755, 2421}, {1757, 17934}, {1758, 17933}, {1769, 17139}, {1821, 43187}, {1824, 1897}, {1826, 6335}, {1880, 653}, {1903, 44327}, {1910, 2966}, {1917, 14574}, {1918, 692}, {1919, 1333}, {1924, 32}, {1927, 17938}, {1929, 17930}, {1945, 41206}, {1946, 283}, {1953, 14570}, {1959, 2396}, {1962, 4427}, {1964, 1634}, {1966, 880}, {1967, 805}, {1973, 112}, {1974, 32676}, {1976, 36084}, {1980, 2206}, {1989, 32680}, {1990, 24001}, {2054, 37135}, {2084, 39}, {2088, 32679}, {2092, 3882}, {2148, 18315}, {2151, 17402}, {2152, 17403}, {2153, 23895}, {2154, 23896}, {2156, 44766}, {2157, 17708}, {2159, 44769}, {2166, 35139}, {2170, 4560}, {2171, 4552}, {2172, 4611}, {2173, 2407}, {2179, 1625}, {2181, 35360}, {2184, 44326}, {2190, 18831}, {2194, 4636}, {2200, 906}, {2205, 32739}, {2207, 24019}, {2234, 23342}, {2238, 3570}, {2245, 4585}, {2247, 14999}, {2250, 13136}, {2254, 30941}, {2258, 931}, {2295, 18047}, {2310, 7253}, {2312, 34211}, {2318, 4571}, {2321, 646}, {2333, 1783}, {2334, 4614}, {2356, 4238}, {2357, 13138}, {2394, 33805}, {2395, 1821}, {2422, 1910}, {2433, 2349}, {2451, 1958}, {2484, 2303}, {2485, 1760}, {2486, 20954}, {2488, 17194}, {2489, 19}, {2491, 1755}, {2492, 16568}, {2501, 92}, {2514, 17446}, {2517, 44154}, {2519, 2128}, {2520, 17188}, {2530, 16887}, {2533, 1909}, {2576, 39298}, {2577, 39299}, {2578, 8116}, {2579, 8115}, {2588, 15165}, {2589, 15164}, {2610, 3936}, {2611, 4467}, {2616, 95}, {2618, 311}, {2623, 2167}, {2624, 323}, {2631, 11064}, {2632, 3265}, {2640, 31998}, {2642, 524}, {2643, 523}, {2644, 31632}, {2648, 17931}, {2650, 17136}, {2652, 35154}, {2667, 4436}, {2787, 5209}, {2799, 46238}, {2962, 46139}, {2978, 10458}, {3004, 16739}, {3005, 38}, {3049, 48}, {3050, 18042}, {3063, 284}, {3064, 31623}, {3112, 689}, {3120, 693}, {3121, 649}, {3122, 513}, {3123, 17217}, {3125, 514}, {3221, 1740}, {3223, 3222}, {3248, 3733}, {3250, 40773}, {3261, 6385}, {3267, 40364}, {3269, 24018}, {3271, 3737}, {3287, 27958}, {3402, 26714}, {3563, 36105}, {3566, 18156}, {3569, 1959}, {3572, 37128}, {3589, 18062}, {3668, 4569}, {3669, 1434}, {3675, 23829}, {3700, 312}, {3708, 525}, {3709, 9}, {3721, 33946}, {3733, 757}, {3737, 261}, {3747, 3573}, {3773, 4505}, {3777, 33947}, {3778, 3888}, {3800, 39731}, {3801, 33930}, {3835, 31008}, {3900, 1043}, {3930, 42720}, {3942, 15419}, {3943, 24004}, {3948, 27853}, {3952, 7035}, {3954, 4568}, {3971, 36863}, {3994, 41314}, {4010, 350}, {4014, 17218}, {4017, 7}, {4024, 321}, {4027, 46295}, {4033, 31625}, {4036, 313}, {4041, 8}, {4049, 20568}, {4062, 42721}, {4064, 20336}, {4069, 4076}, {4077, 6063}, {4079, 37}, {4083, 33296}, {4086, 3596}, {4088, 3263}, {4092, 4086}, {4117, 669}, {4120, 4358}, {4122, 33931}, {4128, 4367}, {4129, 18140}, {4132, 4360}, {4139, 3875}, {4140, 17787}, {4145, 17160}, {4151, 17143}, {4155, 740}, {4171, 346}, {4367, 17103}, {4369, 8033}, {4391, 28660}, {4394, 41629}, {4415, 21580}, {4444, 40017}, {4455, 238}, {4466, 15413}, {4501, 4483}, {4515, 6558}, {4516, 522}, {4524, 200}, {4531, 40499}, {4551, 4998}, {4557, 765}, {4559, 4564}, {4602, 44168}, {4642, 21272}, {4674, 4555}, {4705, 10}, {4707, 20924}, {4729, 145}, {4730, 519}, {4750, 16741}, {4770, 3679}, {4775, 4653}, {4790, 42028}, {4804, 4441}, {4806, 30963}, {4808, 33937}, {4813, 5333}, {4814, 4720}, {4822, 3616}, {4825, 4803}, {4826, 16777}, {4832, 1449}, {4834, 4658}, {4838, 28605}, {4841, 19804}, {4843, 4673}, {4849, 43290}, {4893, 5235}, {4931, 4671}, {4977, 16709}, {4979, 8025}, {4983, 1125}, {4988, 4359}, {5027, 1580}, {5029, 1931}, {5075, 2651}, {5113, 17799}, {5466, 46277}, {5489, 17879}, {5620, 35156}, {6004, 33953}, {6041, 2247}, {6129, 8822}, {6140, 1749}, {6149, 10411}, {6186, 13486}, {6367, 4647}, {6368, 18695}, {6370, 35550}, {6372, 17175}, {6373, 18792}, {6377, 18197}, {6520, 15352}, {6524, 36126}, {6544, 16729}, {6545, 16727}, {6587, 18750}, {6591, 27}, {6615, 17183}, {6753, 1748}, {6791, 14207}, {7064, 4069}, {7170, 9425}, {7178, 85}, {7180, 57}, {7192, 873}, {7200, 16737}, {7202, 16755}, {7203, 552}, {7212, 10030}, {7216, 279}, {7234, 171}, {7250, 269}, {7252, 2185}, {7265, 33939}, {7649, 286}, {7745, 18063}, {8029, 1109}, {8034, 244}, {8061, 141}, {8105, 2581}, {8106, 2580}, {8287, 18160}, {8574, 16562}, {8611, 345}, {8639, 1468}, {8640, 38832}, {8641, 2328}, {8643, 16948}, {8644, 36277}, {8646, 44119}, {8651, 1707}, {8653, 4512}, {8655, 39673}, {8663, 1962}, {8664, 17469}, {8672, 10436}, {8678, 1010}, {8680, 15418}, {8750, 5379}, {8754, 24006}, {8769, 35136}, {8772, 4226}, {8818, 15455}, {9009, 36289}, {9178, 897}, {9247, 32661}, {9258, 43188}, {9278, 35148}, {9279, 24342}, {9395, 37880}, {9396, 35511}, {9402, 1045}, {9406, 2420}, {9417, 14966}, {9426, 560}, {9427, 1924}, {9456, 4591}, {9494, 1923}, {9508, 17731}, {9979, 20944}, {10099, 31637}, {10278, 20939}, {11060, 32678}, {11123, 20903}, {12071, 42005}, {12077, 14213}, {14061, 33809}, {14207, 11059}, {14208, 305}, {14270, 6149}, {14295, 1926}, {14298, 27398}, {14321, 18743}, {14398, 2173}, {14399, 18653}, {14404, 899}, {14407, 44}, {14419, 6629}, {14428, 2244}, {14431, 6381}, {14574, 23995}, {14618, 1969}, {14838, 34016}, {14936, 1021}, {15451, 44706}, {15475, 2166}, {16230, 40703}, {16583, 3732}, {16592, 4369}, {16600, 33951}, {16606, 4598}, {16613, 6002}, {16732, 3261}, {16892, 16703}, {17094, 7182}, {17414, 36263}, {17415, 3116}, {17442, 41676}, {17467, 14588}, {17469, 10330}, {17476, 4897}, {17478, 1975}, {17747, 42719}, {17763, 17935}, {17898, 14615}, {17924, 44129}, {17954, 17929}, {17955, 34760}, {17958, 17936}, {17959, 17937}, {17989, 17763}, {17990, 1757}, {17991, 17960}, {17992, 1758}, {17993, 17955}, {17994, 240}, {17995, 18028}, {17997, 34054}, {17999, 17959}, {18000, 2648}, {18001, 1929}, {18002, 17954}, {18004, 20947}, {18014, 18032}, {18070, 308}, {18105, 82}, {18155, 18021}, {18197, 7304}, {18210, 4025}, {18266, 17943}, {18344, 29}, {18384, 36129}, {18785, 666}, {18793, 8709}, {18833, 42371}, {19610, 9396}, {20683, 1026}, {20691, 4595}, {20902, 3267}, {20910, 6374}, {20948, 1502}, {20964, 4579}, {20966, 3909}, {20970, 35342}, {20974, 16751}, {20975, 656}, {20979, 27644}, {20982, 14838}, {20998, 2644}, {21004, 39054}, {21006, 33760}, {21035, 4553}, {21043, 4036}, {21044, 4391}, {21051, 6376}, {21055, 30473}, {21056, 22028}, {21100, 9296}, {21104, 16708}, {21108, 16747}, {21123, 16696}, {21124, 20911}, {21127, 16713}, {21131, 16732}, {21143, 16726}, {21144, 23807}, {21207, 40495}, {21448, 37216}, {21720, 40603}, {21725, 2533}, {21727, 4651}, {21731, 1725}, {21755, 20981}, {21759, 34071}, {21789, 1098}, {21795, 35341}, {21796, 21362}, {21801, 2397}, {21805, 17780}, {21806, 4781}, {21809, 25268}, {21814, 46148}, {21816, 4115}, {21824, 7265}, {21828, 3218}, {21831, 7283}, {21832, 239}, {21833, 4024}, {21834, 192}, {21835, 20979}, {21836, 25264}, {21837, 3730}, {21888, 6631}, {21893, 9362}, {21905, 17466}, {21906, 2642}, {21950, 4462}, {21958, 17786}, {21963, 4106}, {22172, 4499}, {22229, 3501}, {22260, 2643}, {22341, 6517}, {22373, 22093}, {22383, 1790}, {23105, 23994}, {23282, 42714}, {23301, 17149}, {23493, 932}, {23503, 1613}, {23610, 4117}, {23655, 13588}, {23751, 16700}, {23878, 3403}, {23879, 33935}, {23894, 671}, {23928, 21295}, {23994, 44173}, {23996, 15631}, {24006, 264}, {24018, 3926}, {24019, 23582}, {24041, 31614}, {24290, 3912}, {25430, 4633}, {28615, 4629}, {28625, 37211}, {28658, 4604}, {30574, 30806}, {30591, 1269}, {31010, 32018}, {31290, 33779}, {31296, 33764}, {31946, 18133}, {32320, 6507}, {32671, 9273}, {32676, 250}, {32678, 39295}, {32679, 7799}, {32713, 24000}, {32740, 36142}, {33294, 20641}, {34079, 37140}, {34294, 18070}, {34591, 15411}, {34952, 47}, {35347, 35141}, {35352, 334}, {35353, 31002}, {35364, 8773}, {35519, 40072}, {36035, 3260}, {36051, 10425}, {36053, 18878}, {36054, 6514}, {36119, 16077}, {36120, 22456}, {36151, 30528}, {36197, 3239}, {36263, 9146}, {36800, 36806}, {37132, 9150}, {37134, 39292}, {38237, 39337}, {38252, 3565}, {38986, 16695}, {39201, 255}, {39258, 2284}, {39786, 812}, {39798, 37205}, {40148, 34594}, {40345, 40301}, {40352, 36034}, {40354, 36131}, {40471, 17140}, {40608, 3907}, {40627, 1107}, {40718, 789}, {40747, 4586}, {40934, 1633}, {40977, 14543}, {41079, 46234}, {41221, 2618}, {41683, 889}, {42027, 18830}, {42074, 3233}, {42327, 34022}, {42653, 191}, {42661, 2292}, {42663, 8772}, {42664, 28606}, {42666, 758}, {42667, 1822}, {42668, 1823}, {42670, 5127}, {42752, 1769}, {42753, 23788}, {42759, 36038}, {43534, 4583}, {43665, 46273}, {43763, 41209}, {43924, 1014}, {44113, 4242}, {44173, 1928}, {44426, 44130}, {44445, 18064}, {44705, 1895}, {44729, 44720}, {45775, 33919}, {45801, 20941}, {45907, 19591}, {46281, 9063}, {46288, 34072}, {46289, 827}

• X₆₆₁ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {2, 4369, 24924}, {2, 7192, 4369}, {2, 26545, 25008}, {2, 26775, 27114}, {2, 26822, 27167}, {2, 27469, 28372}, {2, 31290, 7192}, {115, 20982, 2170}, {647, 7180, 21828}, {649, 650, 1635}, {649, 4893, 650}, {650, 4790, 4394}, {650, 4813, 4979}, {650, 14298, 657}, {662, 2644, 24041}, {693, 3835, 4728}, {693, 4776, 3835}, {798, 8061, 656}, {1635, 4979, 649}, {2533, 21051, 21052}, {2578, 2579, 2624}, {3124, 16592, 244}, {3700, 4024, 4931}, {3700, 4988, 4838}, {3700, 8611, 4171}, {3700, 14321, 4120}, {3709, 7180, 647}, {3952, 7239, 35309}, {4024, 4120, 3700}, {4024, 42664, 21834}, {4106, 4940, 31147}, {4120, 4841, 4838}, {4120, 4988, 4024}, {4369, 4481, 28372}, {4369, 7192, 31148}, {4369, 25666, 2}, {4369, 27929, 26248}, {4369, 29717, 29402}, {4369, 45315, 25666}, {4379, 30835, 4885}, {4382, 31147, 4106}, {4394, 4790, 649}, {4444, 25666, 30765}, {4455, 7234, 669}, {4705, 4730, 4770}, {4705, 4822, 4729}, {4730, 4770, 4041}, {4806, 4824, 4804}, {4813, 4893, 649}, {4838, 4931, 4024}, {4841, 14321, 4024}, {4885, 43067, 4379}, {4897, 17069, 4750}, {4988, 14321, 4931}, {7192, 25666, 24924}, {7192, 26775, 29402}, {7192, 27647, 28372}, {16751, 24948, 14838}, {18070, 20953, 20948}, {20906, 21438, 20909}, {20949, 21611, 20952}, {24041, 36085, 2644}, {24924, 31148, 4369}, {25666, 29512, 27045}, {25666, 29717, 27114}, {25666, 31290, 31148}, {26798, 26824, 21297}, {26983, 27045, 2}, {26985, 27138, 4928}, {27013, 27115, 4763}, {27167, 29457, 24924}, {27469, 27647, 4481}, {27527, 28758, 2}, {28938, 28983, 26640}, {31290, 45315, 24924}

Notes

X₆₆₁ is the perspector of triangle ABC and the tangential triangle of the conic {A, B, C, X₁, X₁₀}}. (Randy Hutson, 9/23/2011)