X₃₂₀

ISOTOMIC CONJUGATE OF X₈₀

X₃₂₀ is the isotomic conjugate of X₈₀.

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

X₃₂₀ (ISOTOMIC CONJUGATE OF X₈₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {7, 8}, {2, 44}

• Related Centers: X₈₀ (REFLECTION OF INCENTER IN FEUERBACH POINT), X₇ (GERGONNE POINT), X₈ (NAGEL POINT), X₂ (CENTROID), X₄₄ (-LINE CONJUGATE OF X₁)

Trilinears: \((1 - 2 \cos A)/a^{2} : :\)

Barycentrics: \((1 - 2 \cos A)/a : :\)

Search Value (6, 9, 13): \(20.679630232817\)

▸ Alternate Coordinates2 forms

• Barycentrics: \(a^{2} - b^{2} - c^{2} + b c : :\)

• Barycentrics: \(b c - 2 S_{A} : :\)

▸ Linear Combinations1 combination

• X₃₂₀ = \(3\) X₁ - \(2\) X₄₉₇₀₀, \(4\) X₄₉₇₀₀ - \(3\) X₄₉₇₀₉, \(3\) X₂ - \(4\) X₃₈₃₄, \(9\) X₂ - \(8\) X₆₆₈₇, \(9\) X₂ - \(10\) X₃₁₂₄₃, \(3\) X₄₄ - \(4\) X₆₆₈₇, X₄₄ - \(3\) X₃₁₁₃₈, \(3\) X₄₄ - \(5\) X₃₁₂₄₃, \(3\) X₃₈₃₄ - \(2\) X₆₆₈₇, \(4\) X₃₈₃₄ - X₂₀₀₇₂, \(2\) X₃₈₃₄ - \(3\) X₃₁₁₃₈, \(6\) X₃₈₃₄ - \(5\) X₃₁₂₄₃, \(8\) X₆₆₈₇ - \(3\) X₂₀₀₇₂, \(4\) X₆₆₈₇ - \(9\) X₃₁₁₃₈, \(4\) X₆₆₈₇ - \(5\) X₃₁₂₄₃, X₂₀₀₇₂ - \(6\) X₃₁₁₃₈, \(3\) X₂₀₀₇₂ - \(10\) X₃₁₂₄₃, \(9\) X₃₁₁₃₈ - \(5\) X₃₁₂₄₃, X₈ - \(3\) X₄₆₄₅, \(2\) X₈ - \(3\) X₃₂₈₅₀, \(7\) X₈ - \(6\) X₄₉₆₉₄, \(4\) X₈ - \(3\) X₄₉₆₉₈, \(3\) X₈ - \(2\) X₄₉₇₀₂, \(5\) X₈ - \(3\) X₄₉₇₀₇, \(7\) X₄₆₄₅ - \(2\) X₄₉₆₉₄, and many others

X₃₂₀ lies on the cubics K311, K636, and K660.

▸ Incident Central Lines570 lines

{1, 752}, {2, 44}, {6, 3662}, {7, 8}, {9, 17234}, {10, 4896}, {31, 29638}, {37, 6646}, {38, 32949}, {42, 24707}, {45, 17244}, {57, 4417}, {58, 86}, {63, 18134}, {72, 33943}, {76, 4911}, {77, 44179}, {79, 314}, {80, 20568}, {81, 17184}, {95, 307}, {141, 894}, {142, 3707}, {144, 344}, {145, 4346}, {150, 18159}, {171, 33064}, {183, 7179}, {190, 527}, {192, 4851}, {193, 3759}, {219, 28965}, {226, 14829}, {239, 524}, {241, 17950}, {244, 32843}, {256, 4022}, {264, 7282}, {269, 326}, {273, 317}, {291, 2228}, {298, 36669}, {299, 36668}, {306, 32939}, {309, 20570}, {312, 5905}, {313, 44139}, {315, 3673}, {318, 44134}, {321, 17483}, {325, 1447}, {329, 18141}, {333, 4001}, {334, 660}, {335, 742}, {340, 1835}, {345, 9965}, {346, 17240}, {350, 513}, {354, 4388}, {369, 3232}, {489, 31549}, {490, 31550}, {491, 32792}, {492, 32791}, {514, 30190}, {516, 4684}, {517, 49779}, {519, 679}, {536, 4440}, {537, 32847}, {540, 30117}, {545, 3943}, {553, 3687}, {573, 29747}, {583, 27678}, {594, 3631}, {597, 29630}, {599, 3661}, {662, 20769}, {664, 22464}, {668, 3264}, {670, 18891}, {674, 3888}, {726, 32846}, {740, 32857}, {750, 33065}, {758, 1227}, {765, 1275}, {896, 29632}, {908, 1797}, {940, 27184}, {942, 1330}, {960, 41874}, {966, 4751}, {982, 3764}, {1043, 4292}, {1088, 7055}, {1100, 17235}, {1104, 20077}, {1119, 32001}, {1150, 31019}, {1193, 33947}, {1203, 33955}, {1213, 17252}, {1215, 33085}, {1232, 34388}, {1267, 1270}, {1271, 5391}, {1278, 17299}, {1279, 3622}, {1439, 46752}, {1443, 1464}, {1444, 5303}, {1449, 17304}, {1478, 20925}, {1647, 27922}, {1654, 3739}, {1698, 1757}, {1730, 29790}, {1738, 34379}, {1743, 17282}, {1760, 7289}, {1764, 29788}, {1836, 4479}, {1931, 25536}, {1944, 7359}, {1959, 3942}, {1964, 7184}, {1992, 5222}, {1999, 3782}, {2234, 3783}, {2239, 37632}, {2245, 3218}, {2260, 28402}, {2308, 33123}, {2321, 17295}, {2323, 4585}, {2345, 3620}, {2481, 3254}, {2796, 4693}, {2887, 29861}, {2895, 4359}, {2911, 26657}, {2968, 40996}, {3008, 27191}, {3120, 32919}, {3187, 19796}, {3219, 18139}, {3241, 49699}, {3242, 50289}, {3244, 3663}, {3246, 3616}, {3260, 34387}, {3263, 8047}, {3296, 30479}, {3306, 5233}, {3509, 4070}, {3570, 24602}, {3589, 7277}, {3593, 32795}, {3595, 32796}, {3598, 37668}, {3618, 17370}, {3619, 5749}, {3623, 3672}, {3625, 50099}, {3626, 49713}, {3629, 17121}, {3630, 4405}, {3632, 50088}, {3633, 3875}, {3644, 17314}, {3666, 17778}, {3675, 24516}, {3679, 24693}, {3684, 4987}, {3685, 4966}, {3686, 24199}, {3693, 40868}, {3702, 14450}, {3705, 7788}, {3717, 5850}, {3720, 4683}, {3729, 4873}, {3741, 33097}, {3744, 20101}, {3751, 4429}, {3760, 4056}, {3761, 7272}, {3763, 17368}, {3769, 33144}, {3770, 20891}, {3771, 4650}, {3772, 37683}, {3775, 24342}, {3791, 33147}, {3821, 4649}, {3823, 5232}, {3824, 25446}, {3840, 33096}, {3873, 4514}, {3874, 5015}, {3882, 20367}, {3883, 5542}, {3886, 4312}, {3894, 4680}, {3896, 33102}, {3916, 25650}, {3923, 33087}, {3932, 5852}, {3946, 4982}, {3957, 4450}, {3980, 33084}, {3999, 5211}, {4009, 20947}, {4014, 6007}, {4021, 49696}, {4029, 29601}, {4033, 40875}, {4038, 4425}, {4062, 32845}, {4080, 51908}, {4089, 4867}, {4118, 18207}, {4273, 21997}, {4277, 4850}, {4285, 17012}, {4295, 4673}, {4310, 51192}, {4358, 8046}, {4361, 17363}, {4362, 33103}, {4364, 16826}, {4373, 20054}, {4384, 6173}, {4392, 33070}, {4393, 17301}, {4406, 37998}, {4407, 36531}, {4409, 28297}, {4418, 33081}, {4419, 4664}, {4422, 17266}, {4430, 5014}, {4432, 28558}, {4439, 24821}, {4445, 17118}, {4447, 21320}, {4452, 20014}, {4454, 29616}, {4465, 30967}, {4472, 29610}, {4473, 41310}, {4569, 35164}, {4640, 29839}, {4648, 4687}, {4654, 11679}, {4657, 17236}, {4659, 17294}, {4660, 49490}, {4665, 22165}, {4667, 16786}, {4672, 29637}, {4676, 24695}, {4679, 24482}, {4686, 17372}, {4688, 4690}, {4691, 4967}, {4697, 32783}, {4699, 17275}, {4700, 17067}, {4702, 28534}, {4703, 26102}, {4713, 31028}, {4722, 29850}, {4725, 20016}, {4740, 20055}, {4742, 5180}, {4749, 7191}, {4753, 25351}, {4766, 9318}, {4772, 28634}, {4799, 17027}, {4860, 26240}, {4892, 33140}, {4902, 17151}, {4908, 17487}, {4938, 14459}, {4945, 9326}, {4973, 7799}, {4996, 52437}, {5088, 10609}, {5231, 36278}, {5263, 49511}, {5278, 27186}, {5280, 17192}, {5308, 51488}, {5718, 24627}, {5739, 19804}, {5741, 27003}, {5744, 30828}, {5745, 41878}, {5750, 17307}, {5805, 48878}, {5839, 20080}, {5847, 24231}, {5902, 33934}, {5904, 33933}, {6163, 33864}, {6172, 29627}, {6224, 36917}, {6356, 41008}, {7058, 52361}, {7081, 37671}, {7113, 27950}, {7122, 18209}, {7185, 12635}, {7222, 48630}, {7227, 48635}, {7229, 48640}, {7231, 48636}, {7262, 29642}, {7291, 16568}, {7779, 33891}, {8822, 18650}, {9025, 20358}, {9055, 49752}, {9776, 14555}, {9791, 15569}, {10025, 51384}, {10446, 12699}, {10889, 41864}, {11160, 50077}, {11246, 32932}, {12586, 21280}, {13476, 17153}, {14616, 35156}, {15523, 32940}, {15533, 17119}, {15668, 17248}, {15988, 26573}, {16666, 17382}, {16669, 17356}, {16672, 24441}, {16704, 33129}, {16777, 17247}, {16815, 17330}, {16816, 50074}, {16817, 49716}, {16823, 25557}, {16884, 17323}, {16885, 17265}, {17011, 42045}, {17018, 32950}, {17026, 24694}, {17028, 30958}, {17045, 17324}, {17056, 38000}, {17062, 17739}, {17126, 33122}, {17132, 49765}, {17133, 49761}, {17135, 20292}, {17140, 20290}, {17144, 17753}, {17145, 21282}, {17152, 25303}, {17155, 32852}, {17165, 33078}, {17167, 29766}, {17170, 18156}, {17178, 26971}, {17179, 49997}, {17181, 36280}, {17202, 18166}, {17230, 17281}, {17231, 17280}, {17232, 17279}, {17238, 17303}, {17239, 28604}, {17242, 17262}, {17243, 17261}, {17245, 17260}, {17246, 17319}, {17251, 29576}, {17259, 17331}, {17267, 17339}, {17268, 17340}, {17269, 29577}, {17270, 25590}, {17278, 17349}, {17283, 17353}, {17284, 17354}, {17285, 17355}, {17293, 48634}, {17306, 17381}, {17318, 17389}, {17325, 17397}, {17326, 17398}, {17341, 26685}, {17342, 29579}, {17359, 29587}, {17383, 37677}, {17395, 29584}, {17399, 26626}, {17449, 23633}, {17499, 21240}, {17555, 42856}, {17579, 49687}, {17720, 37684}, {17731, 24194}, {17755, 27487}, {17762, 33865}, {17763, 32856}, {17776, 20078}, {17787, 18040}, {17789, 34377}, {17790, 52043}, {17863, 21287}, {17889, 32853}, {17923, 22128}, {18025, 35157}, {18041, 18161}, {18042, 18162}, {18049, 18727}, {18133, 20245}, {18145, 49999}, {18147, 18148}, {18151, 30807}, {18194, 25572}, {18480, 21276}, {18653, 30606}, {18690, 45797}, {18713, 18725}, {18714, 18726}, {18715, 18728}, {18716, 18729}, {18717, 18730}, {18718, 18731}, {18719, 18732}, {18720, 18733}, {18721, 18734}, {18722, 18735}, {18750, 26871}, {18816, 20566}, {18827, 35147}, {19742, 26724}, {19808, 32782}, {20017, 50106}, {20073, 29583}, {20086, 33150}, {20142, 25357}, {20335, 37686}, {20345, 25333}, {20349, 21221}, {20878, 23363}, {20886, 30690}, {20888, 33297}, {20920, 48380}, {21061, 29382}, {21290, 36919}, {21342, 29840}, {21356, 29611}, {21358, 29613}, {21873, 27705}, {22003, 22047}, {24165, 32861}, {24214, 33296}, {24215, 34063}, {24220, 29746}, {24248, 49470}, {24325, 33082}, {24330, 31027}, {24331, 50296}, {24352, 31038}, {24470, 41014}, {24512, 31004}, {24514, 30945}, {24589, 37656}, {24603, 31144}, {24628, 24685}, {24712, 30997}, {24725, 30942}, {24789, 37652}, {24833, 29331}, {24851, 35633}, {24864, 35962}, {25284, 28597}, {25384, 27495}, {25957, 32912}, {25959, 33114}, {26132, 37642}, {26223, 33172}, {26540, 26651}, {26580, 37633}, {26756, 27102}, {26772, 27017}, {27002, 37663}, {27396, 40905}, {27509, 28753}, {27526, 40892}, {28538, 50015}, {28580, 49763}, {28609, 30567}, {29570, 41312}, {29571, 50093}, {29572, 41313}, {29573, 49748}, {29575, 49742}, {29578, 49738}, {29586, 41311}, {29588, 50125}, {29596, 50115}, {29605, 50121}, {29607, 40480}, {29619, 50113}, {29620, 49737}, {29643, 36263}, {29649, 33101}, {29658, 36267}, {29660, 50300}, {29674, 32935}, {29687, 32938}, {30596, 44147}, {30598, 30712}, {30829, 31018}, {30854, 52457}, {30966, 30969}, {31017, 32779}, {31134, 33120}, {31145, 49703}, {31252, 51073}, {31289, 34595}, {31637, 36086}, {31993, 37653}, {32771, 33080}, {32774, 37685}, {32793, 32814}, {32801, 32808}, {32802, 32809}, {32803, 32805}, {32804, 32806}, {32858, 32933}, {32866, 42055}, {32915, 33098}, {32942, 41011}, {33076, 49479}, {33086, 46897}, {33095, 42057}, {33112, 46909}, {33133, 37639}, {33142, 48646}, {33149, 49488}, {33170, 48647}, {33869, 49452}, {33890, 44453}, {34255, 42034}, {34282, 50599}, {34920, 40438}, {35102, 49755}, {35160, 43762}, {36479, 51055}, {36480, 50301}, {36534, 47358}, {38989, 39044}, {40940, 41629}, {41138, 41141}, {45222, 50256}, {49508, 49521}

▸ Functional Relations28 relations

• X₃₂₀ = midpoint of X₄₄₄₀ and X₆₅₄₂

• X₃₂₀ = reflection of X_i in X_j for these {i,j}: {2, 31138}, {44, 3834}, {190, 3912}, {238, 49676}, {239, 1086}, {1086, 7238}, {1266, 4887}, {1757, 3836}, {3257, 908}, {3685, 4966}, {4480, 2325}, {4693, 49764}, {4700, 17067}, {4753, 25351}, {4969, 4395}, {6542, 17374}, {17160, 1266}, {17264, 17297}, {17487, 4908}, {20072, 44}, {24715, 24692}, {24821, 4439}, {25048, 20358}, {32850, 4645}, {32922, 24231}, {49695, 49675}, {49698, 32850}, {49704, 4864}, {49708, 3244}, {49709, 1}, {49710, 1125}, {49711, 3664}, {49712, 10}, {49713, 3626}, {49714, 8}, {49715, 75}

• X₃₂₀ = isogonal conjugate of X₆₁₈₇

• X₃₂₀ = isotomic conjugate of X₈₀

• X₃₂₀ = complement of X₂₀₀₇₂

• X₃₂₀ = anticomplement of X₄₄

• X₃₂₀ = anticomplement of the isogonal conjugate of X₈₈

• X₃₂₀ = anticomplement of the isotomic conjugate of X₂₀₅₆₈

• X₃₂₀ = isotomic conjugate of the anticomplement of X₂₁₄

• X₃₂₀ = isotomic conjugate of the complement of X₆₂₂₄

• X₃₂₀ = isotomic conjugate of the isogonal conjugate of X₃₆

• X₃₂₀ = isogonal conjugate of the isotomic conjugate of X₄₀₀₇₅

• X₃₂₀ = isotomic conjugate of the polar conjugate of X₁₇₉₂₃

• X₃₂₀ = polar conjugate of the isogonal conjugate of X₂₂₁₂₈

• X₃₂₀ = anticomplementary isogonal conjugate of X₃₀₅₇₈

• X₃₂₀ = X_i-anticomplementary conjugate of X_j for these (i,j): {1, 30578}, {2, 21290}, {6, 17487}, {56, 30577}, {58, 30579}, {88, 8}, {101, 44009}, {106, 2}, {649, 39349}, {679, 320}, {901, 514}, {903, 69}, {1022, 149}, {1168, 17484}, {1318, 908}, {1320, 329}, {1417, 3210}, {1797, 20}, {2226, 519}, {2316, 144}, {2403, 34548}, {3257, 513}, {4049, 3448}, {4080, 1330}, {4555, 20295}, {4591, 523}, {4615, 512}, {4618, 21297}, {4622, 7192}, {4634, 17217}, {4638, 900}, {4674, 2895}, {4945, 21291}, {4997, 3436}, {5376, 3952}, {5548, 4468}, {6336, 4}, {6548, 150}, {8752, 193}, {9268, 190}, {9456, 192}, {10428, 3218}, {20568, 6327}, {23345, 4440}, {23838, 37781}, {27922, 20345}, {31227, 42020}, {32659, 3164}, {32665, 17494}, {32686, 47773}, {32719, 21225}, {34230, 20533}, {36058, 6360}, {36125, 5905}, {36814, 20355}, {39414, 6548}, {40215, 6224}, {40833, 21283}, {46150, 2896}, {52031, 153}

• X₃₂₀ = X_i-Ceva conjugate of X_j for these (i,j): {7, 41873}, {4615, 514}, {18816, 75}, {20568, 2}, {20924, 32851}, {35156, 693}

• X₃₂₀ = X_i-cross conjugate of X_j for these (i,j): {36, 17923}, {214, 2}, {758, 3218}, {3218, 17078}, {3738, 4585}, {3936, 20924}, {4089, 4453}, {4511, 32851}

• X₃₂₀ = X_i-isoconjugate of X_j for these (i,j): {1, 6187}, {6, 2161}, {19, 52431}, {25, 1807}, {31, 80}, {32, 18359}, {37, 34079}, {41, 2006}, {42, 759}, {55, 1411}, {56, 52371}, {58, 34857}, {106, 40172}, {181, 52380}, {213, 24624}, {265, 14975}, {560, 20566}, {604, 36910}, {650, 32675}, {655, 3063}, {663, 2222}, {667, 51562}, {798, 47318}, {902, 1168}, {1397, 52409}, {1400, 2341}, {1402, 6740}, {1911, 36815}, {1918, 14616}, {1919, 36804}, {1973, 52351}, {1989, 2174}, {2175, 18815}, {2194, 52383}, {2206, 15065}, {2212, 52392}, {2299, 52391}, {3219, 11060}, {3271, 52377}, {3457, 46077}, {3458, 46073}, {4024, 32671}, {4079, 37140}, {4705, 36069}, {6198, 52153}, {9273, 21833}, {9274, 21043}, {11073, 42624}, {11075, 19297}, {18384, 52408}, {34535, 52426}

• X₃₂₀ = X_i-Dao conjugate of X_j for these (i,j): {1, 40612}, {1, 52371}, {2, 80}, {3, 6187}, {6, 40584}, {6, 52431}, {9, 2161}, {10, 34857}, {10, 51583}, {35, 40604}, {36, 20989}, {37, 35069}, {42, 34586}, {55, 35204}, {214, 40172}, {223, 1411}, {226, 52391}, {320, 20072}, {333, 36927}, {484, 3218}, {517, 908}, {519, 3936}, {650, 35128}, {655, 10001}, {663, 38984}, {759, 40592}, {1168, 40594}, {1214, 52383}, {1639, 4530}, {1647, 3960}, {1807, 6505}, {2006, 3160}, {2174, 34544}, {2183, 2245}, {2323, 17796}, {2341, 40582}, {2361, 6149}, {3161, 36910}, {3814, 20962}, {4705, 38982}, {5664, 21054}, {6337, 52351}, {6374, 20566}, {6376, 18359}, {6626, 24624}, {6631, 51562}, {6651, 36815}, {6740, 40605}, {9296, 36804}, {10015, 35015}, {13999, 18344}, {14584, 52659}, {14616, 34021}, {15065, 40603}, {16585, 45926}, {18815, 40593}, {31998, 47318}, {32851, 36926}, {33136, 49758}, {34079, 40589}, {36914, 36920}, {40624, 52356}, {46974, 51361}

• X₃₂₀ = cevapoint of X_i and X_j for these (i,j): {2, 6224}, {7, 36918}, {8, 30578}, {36, 22128}, {519, 908}, {758, 3936}, {3218, 4511}, {4089, 4453}

• X₃₂₀ = crosspoint of X_i and X_j for these (i,j): {75, 40716}, {86, 903}, {4555, 4998}

• X₃₂₀ = crosssum of X_i and X_j for these (i,j): {42, 902}, {1960, 3271}

• X₃₂₀ = trilinear pole of line {3904, 3960}

• X₃₂₀ = crossdifference of every pair of points on line {213, 3063}

• X₃₂₀ = X₃₂₀ = barycentric product X_i*X_j for these {i,j}: {1, 20924}, {6, 40075}, {7, 32851}, {8, 17078}, {36, 76}, {69, 17923}, {75, 3218}, {79, 7799}, {81, 35550}, {85, 4511}, {86, 3936}, {88, 1227}, {99, 4707}, {190, 4453}, {214, 20568}, {264, 22128}, {274, 758}, {304, 1870}, {305, 52413}, {310, 2245}, {312, 1443}, {314, 18593}, {323, 20565}, {333, 41804}, {334, 27950}, {340, 52381}, {348, 5081}, {561, 7113}, {654, 4572}, {664, 3904}, {668, 3960}, {670, 21828}, {693, 4585}, {860, 17206}, {873, 4053}, {903, 51583}, {1016, 4089}, {1231, 17515}, {1464, 28660}, {1502, 52434}, {1969, 52407}, {1983, 40495}, {2323, 6063}, {2361, 20567}, {2610, 4623}, {3264, 40215}, {3724, 6385}, {3738, 4554}, {4242, 15413}, {4358, 52553}, {4597, 23884}, {4610, 6370}, {4631, 51663}, {4867, 20569}, {4881, 40014}, {4973, 32018}, {4997, 41801}, {6386, 21758}, {16586, 18816}, {27757, 39704}, {27836, 43290}, {28659, 52440}, {30608, 36589}, {36923, 40833}, {40612, 40716}, {41283, 52426}, {42666, 52612}

• X₃₂₀ = barycentric quotient X_i/X_j for these {i,j}: {1, 2161}, {2, 80}, {3, 52431}, {6, 6187}, {7, 2006}, {8, 36910}, {9, 52371}, {21, 2341}, {36, 6}, {37, 34857}, {44, 40172}, {57, 1411}, {58, 34079}, {63, 1807}, {69, 52351}, {75, 18359}, {76, 20566}, {79, 1989}, {81, 759}, {85, 18815}, {86, 24624}, {88, 1168}, {99, 47318}, {109, 32675}, {190, 51562}, {214, 44}, {215, 52426}, {226, 52383}, {239, 36815}, {274, 14616}, {312, 52409}, {319, 41226}, {321, 15065}, {323, 35}, {333, 6740}, {340, 52412}, {348, 52392}, {651, 2222}, {654, 663}, {664, 655}, {668, 36804}, {758, 37}, {860, 1826}, {1214, 52391}, {1227, 4358}, {1443, 57}, {1464, 1400}, {1812, 1793}, {1835, 1880}, {1845, 14571}, {1870, 19}, {1983, 692}, {2185, 52380}, {2245, 42}, {2323, 55}, {2361, 41}, {2610, 4705}, {3065, 11075}, {3179, 11072}, {3218, 1}, {3268, 7265}, {3336, 11069}, {3724, 213}, {3738, 650}, {3792, 2276}, {3904, 522}, {3911, 14584}, {3936, 10}, {3960, 513}, {4053, 756}, {4089, 1086}, {4242, 1783}, {4282, 2194}, {4358, 51975}, {4391, 52356}, {4453, 514}, {4511, 9}, {4554, 35174}, {4556, 36069}, {4564, 52377}, {4572, 46405}, {4585, 100}, {4707, 523}, {4736, 4053}, {4867, 45}, {4880, 16777}, {4881, 1743}, {4973, 1100}, {4996, 2323}, {4997, 36590}, {5081, 281}, {5239, 19551}, {5240, 7126}, {5249, 45926}, {5357, 42624}, {6126, 19297}, {6149, 2174}, {6186, 11060}, {6370, 4024}, {7113, 31}, {7799, 319}, {8125, 1128}, {8126, 10215}, {8648, 3063}, {11570, 8609}, {11700, 2182}, {13486, 32678}, {16586, 517}, {16696, 46160}, {16944, 9456}, {17078, 7}, {17080, 34242}, {17455, 902}, {17515, 1172}, {17923, 4}, {18593, 65}, {18815, 34535}, {19619, 34431}, {20565, 94}, {20924, 75}, {21758, 667}, {21828, 512}, {22128, 3}, {22379, 22383}, {22464, 52212}, {23884, 4777}, {24781, 51834}, {27757, 3679}, {27950, 238}, {30578, 36909}, {30690, 2166}, {32851, 8}, {33129, 38938}, {34234, 40437}, {34544, 2361}, {34586, 2183}, {35204, 17796}, {35550, 321}, {36589, 5219}, {36913, 36920}, {36923, 4908}, {37772, 33655}, {37773, 7052}, {39149, 21353}, {39152, 2154}, {39153, 2153}, {40075, 76}, {40215, 106}, {40584, 20989}, {40605, 36927}, {40612, 484}, {40988, 21805}, {41225, 11073}, {41801, 3911}, {41804, 226}, {41873, 37759}, {42666, 4079}, {42701, 3678}, {44113, 2333}, {44428, 3064}, {46398, 35015}, {51402, 4530}, {51583, 519}, {52059, 52434}, {52368, 16548}, {52381, 265}, {52407, 48}, {52413, 25}, {52414, 6198}, {52426, 2175}, {52427, 607}, {52434, 32}, {52440, 604}, {52553, 88}

• X₃₂₀ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {1, 4389, 17320}, {1, 4655, 24723}, {1, 17274, 4389}, {2, 4643, 17256}, {2, 4644, 3758}, {2, 4741, 4643}, {2, 20072, 44}, {2, 32859, 33066}, {6, 3662, 16706}, {6, 7232, 3662}, {6, 17290, 17367}, {7, 8, 42697}, {7, 69, 75}, {7, 75, 7321}, {7, 17361, 319}, {7, 21296, 69}, {7, 32099, 31995}, {8, 69, 17360}, {8, 17360, 319}, {8, 42697, 75}, {8, 49714, 49698}, {9, 17234, 17263}, {9, 17298, 17234}, {10, 4896, 50116}, {31, 33069, 33124}, {37, 6646, 17258}, {37, 17300, 17317}, {37, 17345, 6646}, {37, 17376, 17300}, {38, 32949, 33073}, {42, 33067, 33068}, {44, 3834, 2}, {44, 28362, 27637}, {44, 31138, 3834}, {44, 31243, 6687}, {45, 17313, 17244}, {63, 18134, 33116}, {69, 75, 319}, {69, 7321, 5564}, {69, 21296, 17361}, {69, 42696, 32099}, {69, 42697, 8}, {75, 319, 5564}, {75, 17360, 8}, {75, 17361, 69}, {75, 17791, 3262}, {75, 46749, 1441}, {80, 32097, 20568}, {80, 32109, 32032}, {81, 17184, 19786}, {86, 4357, 17322}, {86, 17273, 4357}, {89, 30991, 2}, {141, 894, 17289}, {141, 17365, 894}, {141, 17369, 17292}, {142, 4416, 17277}, {144, 344, 17336}, {144, 4869, 344}, {145, 4346, 50101}, {171, 33064, 33126}, {190, 3912, 17264}, {190, 17297, 3912}, {192, 4851, 17315}, {192, 17375, 4851}, {193, 4000, 3759}, {239, 1086, 37756}, {319, 7321, 75}, {319, 49715, 49698}, {322, 39126, 75}, {329, 18141, 18743}, {344, 4869, 17241}, {350, 30941, 41851}, {594, 3631, 17287}, {594, 7228, 17116}, {599, 4363, 3661}, {894, 17288, 141}, {894, 17292, 17369}, {903, 9460, 36594}, {903, 17160, 1266}, {982, 32946, 33071}, {1086, 4969, 4395}, {1100, 17235, 17302}, {1125, 49710, 238}, {1266, 4887, 903}, {1278, 17373, 17299}, {1443, 36589, 41804}, {1443, 41804, 17078}, {1449, 17304, 17380}, {1654, 26806, 3739}, {1743, 17282, 17352}, {1944, 26932, 37774}, {2325, 4480, 190}, {2345, 3620, 17228}, {2887, 32913, 33121}, {2895, 4359, 4886}, {2895, 26842, 4359}, {3187, 33146, 19796}, {3218, 3936, 32851}, {3218, 27757, 51583}, {3244, 49708, 49695}, {3262, 30806, 17791}, {3589, 7277, 17120}, {3589, 48632, 17291}, {3619, 5749, 17371}, {3629, 17366, 17121}, {3629, 48631, 17366}, {3630, 7263, 17362}, {3631, 7228, 594}, {3644, 17386, 17314}, {3661, 50128, 4363}, {3662, 17364, 6}, {3662, 17367, 17290}, {3663, 3879, 4360}, {3664, 4357, 86}, {3664, 17273, 17322}, {3729, 17296, 17233}, {3739, 17344, 1654}, {3758, 17227, 2}, {3759, 48629, 4000}, {3834, 6687, 31243}, {3873, 6327, 4514}, {3875, 4862, 4398}, {3912, 4480, 2325}, {3936, 51583, 27757}, {3945, 17321, 17394}, {4001, 5249, 333}, {4357, 49711, 238}, {4361, 40341, 17363}, {4364, 17392, 16826}, {4389, 17378, 1}, {4395, 4969, 239}, {4398, 17377, 3875}, {4407, 50299, 36531}, {4419, 17316, 4664}, {4445, 17118, 48628}, {4454, 29616, 50107}, {4643, 4675, 2}, {4648, 17257, 4687}, {4664, 17387, 17316}, {4667, 17023, 46922}, {4667, 50092, 17023}, {4670, 17237, 2}, {4675, 4741, 17256}, {4687, 17329, 17257}, {4699, 17343, 17275}, {4700, 17067, 41140}, {4751, 17328, 966}, {4851, 17276, 192}, {4888, 17272, 10436}, {5224, 10436, 28653}, {6646, 17300, 37}, {6646, 17376, 17317}, {6687, 31243, 2}, {7232, 17364, 16706}, {7263, 17362, 17117}, {7277, 48632, 3589}, {7768, 33940, 5015}, {10436, 17272, 5224}, {15668, 17253, 17248}, {16777, 17255, 17247}, {16826, 17254, 4364}, {16884, 17323, 17396}, {16885, 17265, 17338}, {17023, 50092, 17305}, {17116, 17287, 594}, {17120, 17291, 3589}, {17139, 30941, 30939}, {17140, 20290, 33075}, {17231, 17351, 17280}, {17232, 17350, 17279}, {17234, 17347, 9}, {17236, 17379, 4657}, {17241, 17336, 344}, {17243, 17334, 17261}, {17244, 17333, 45}, {17245, 17332, 17260}, {17246, 17390, 17319}, {17247, 17391, 16777}, {17249, 17394, 17321}, {17250, 39704, 41847}, {17250, 41847, 2}, {17258, 17317, 37}, {17261, 17312, 17243}, {17262, 17311, 17242}, {17274, 17378, 17320}, {17276, 17375, 17315}, {17280, 31300, 17351}, {17284, 50127, 17354}, {17288, 17365, 17289}, {17290, 17367, 16706}, {17292, 17369, 17289}, {17298, 17347, 17263}, {17300, 17345, 17258}, {17302, 20090, 1100}, {17305, 46922, 17023}, {17330, 34824, 16815}, {17331, 27147, 17259}, {17345, 17376, 37}, {17353, 21255, 17283}, {17363, 48627, 4361}, {17368, 48633, 3763}, {17371, 48638, 3619}, {17483, 32863, 321}, {17491, 29824, 5057}, {17778, 26840, 3666}, {20347, 30941, 350}, {20568, 32032, 80}, {21281, 36854, 24524}, {21356, 29611, 48639}, {22165, 49727, 29615}, {24893, 25658, 2}, {25957, 32912, 33118}, {26768, 26816, 2}, {26975, 27106, 2}, {27036, 27159, 2}, {27265, 27315, 2}, {27757, 51583, 32851}, {29601, 50090, 4029}, {30807, 37788, 18151}, {30939, 39995, 350}, {30946, 30962, 30963}, {31151, 49712, 10}, {31995, 32099, 42696}, {31995, 42696, 75}, {32097, 32109, 80}, {32850, 49714, 8}, {32850, 49715, 5564}, {32858, 32933, 42033}, {36589, 41801, 17078}, {36928, 36929, 36920}, {41801, 41804, 1443}, {49479, 50304, 33076}, {49511, 50307, 5263}, {49675, 49708, 3244}, {49676, 49710, 1125}, {49676, 49711, 86}