X₄₄

X₆-LINE CONJUGATE OF X₁

X₄₄ = crossdifference of PU(55)

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

X₄₄ (X₆-LINE CONJUGATE OF X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 6}, {2, 89}

• Related Centers: X₆ (SYMMEDIAN POINT), X₁ (INCENTER), X₂ (CENTROID), X₈₉ (ISOGONAL CONJUGATE OF X₄₅)

Trilinears: \(b + c - 2a : c + a - 2b : a + b - 2c\)

Barycentrics: \(a(b + c - 2a) : b(c + a - 2b) : c(a + b - 2c)\)

Search Value (6, 9, 13): \(-6.395761927675\)

▸ Linear Combinations2 combinations

• X₄₄ = \((3r^{2} + 6rR + s^{2})\) X₁ - \(18rR\) X₂ - \(6r^{2}\) X₃ (Peter Moses, April 2, 2013)

• X₄₄ = X₁ - \(3\) X₂₃₈, \(2\) X₁ - \(3\) X₁₂₇₉, X₁ + \(3\) X₁₇₅₇, \(4\) X₁ - \(3\) X₄₈₆₄, \(3\) X₂ - \(4\) X₆₆₈₇, \(3\) X₂ + X₂₀₀₇₂, \(6\) X₂ - \(5\) X₃₁₂₄₃, \(3\) X₁₉₀ + X₁₇₁₆₀, \(3\) X₂₃₈ - \(2\) X₃₂₄₆, \(4\) X₂₃₈ - X₄₈₆₄, \(3\) X₂₃₉ - X₁₇₁₆₀, X₃₂₀ - \(4\) X₆₆₈₇(and many more)

X₄₄ lies on the curves K137, K453, K454, K717, K752, K1050, Q043, Q087.

▸ Incident Central Lines533 lines

{1, 6}, {2, 89}, {3, 34877}, {7, 14564}, {8, 4217}, {10, 752}, {15, 11790}, {16, 11791}, {19, 1828}, {21, 4273}, {31, 210}, {32, 25066}, {36, 3196}, {39, 37599}, {40, 21896}, {41, 2267}, {42, 3683}, {43, 4640}, {48, 3204}, {51, 209}, {55, 4849}, {56, 1732}, {57, 16602}, {58, 5044}, {63, 3752}, {65, 374}, {69, 17231}, {71, 2264}, {75, 16816}, {81, 17021}, {86, 4698}, {88, 679}, {100, 2384}, {101, 2718}, {105, 6017}, {141, 4416}, {142, 4896}, {144, 4000}, {169, 16605}, {171, 3740}, {172, 5035}, {181, 375}, {190, 239}, {192, 3759}, {193, 344}, {198, 2261}, {200, 3052}, {212, 1864}, {214, 1017}, {241, 651}, {259, 17641}, {281, 3087}, {292, 660}, {294, 1156}, {312, 37652}, {319, 17229}, {321, 19742}, {329, 3772}, {333, 27064}, {346, 3621}, {350, 17029}, {354, 748}, {386, 31445}, {391, 2345}, {394, 39249}, {480, 21002}, {511, 15977}, {513, 649}, {517, 1168}, {519, 2325}, {524, 3912}, {527, 1086}, {545, 1266}, {572, 2174}, {573, 3579}, {579, 16415}, {580, 5777}, {583, 992}, {584, 2268}, {594, 3626}, {595, 34790}, {597, 4364}, {599, 17284}, {602, 14872}, {610, 37500}, {612, 3715}, {614, 21342}, {645, 19623}, {662, 1931}, {674, 3271}, {678, 902}, {726, 4974}, {742, 17755}, {751, 2276}, {756, 2308}, {758, 21331}, {765, 1252}, {799, 30938}, {872, 2309}, {894, 3739}, {897, 9278}, {908, 23593}, {936, 4252}, {940, 3305}, {941, 28625}, {948, 12848}, {966, 3823}, {971, 13329}, {976, 4005}, {990, 5779}, {991, 31658}, {993, 5114}, {1015, 8610}, {1046, 3812}, {1052, 3509}, {1125, 19898}, {1150, 30818}, {1151, 32555}, {1152, 32556}, {1193, 5109}, {1211, 5294}, {1213, 3454}, {1253, 14100}, {1319, 1404}, {1333, 1778}, {1334, 3780}, {1376, 1707}, {1418, 1445}, {1427, 1708}, {1438, 34893}, {1465, 19619}, {1468, 25917}, {1471, 8581}, {1573, 3997}, {1639, 22086}, {1643, 24457}, {1654, 17239}, {1698, 31151}, {1721, 16112}, {1726, 14557}, {1737, 6128}, {1738, 17768}, {1739, 17960}, {1754, 5927}, {1766, 12702}, {1776, 9371}, {1781, 5356}, {1783, 14571}, {1785, 1990}, {1834, 12572}, {1836, 21949}, {1842, 6047}, {1859, 7076}, {1877, 8756}, {1903, 7118}, {1918, 22271}, {1944, 34852}, {1963, 33766}, {1964, 22343}, {1992, 17316}, {1999, 35652}, {2082, 21872}, {2092, 3647}, {2164, 35251}, {2170, 17444}, {2171, 17443}, {2177, 21870}, {2178, 5120}, {2194, 26890}, {2220, 3965}, {2223, 4557}, {2241, 3991}, {2251, 3285}, {2260, 28352}, {2262, 14737}, {2270, 5128}, {2277, 5069}, {2285, 5221}, {2293, 4878}, {2295, 3691}, {2298, 28615}, {2321, 3625}, {2341, 5127}, {2342, 2361}, {2364, 37525}, {2609, 3709}, {2664, 9359}, {2895, 33157}, {2999, 3929}, {3003, 13006}, {3006, 4144}, {3009, 3248}, {3059, 21059}, {3068, 30412}, {3069, 30413}, {3070, 31562}, {3071, 31561}, {3122, 20456}, {3158, 21000}, {3161, 17314}, {3175, 3187}, {3216, 3916}, {3219, 3666}, {3220, 5096}, {3241, 31722}, {3244, 4029}, {3245, 5540}, {3264, 4506}, {3290, 3999}, {3306, 31197}, {3332, 5817}, {3452, 37646}, {3501, 21868}, {3589, 4357}, {3618, 4657}, {3629, 3879}, {3632, 4873}, {3635, 4982}, {3644, 25269}, {3661, 4690}, {3662, 17345}, {3663, 17334}, {3664, 6666}, {3678, 5007}, {3681, 3744}, {3684, 5524}, {3685, 28581}, {3694, 5301}, {3696, 3923}, {3697, 5264}, {3706, 32864}, {3717, 5846}, {3720, 4722}, {3729, 4361}, {3730, 4266}, {3742, 17123}, {3753, 21373}, {3763, 17272}, {3764, 4735}, {3765, 4377}, {3769, 27538}, {3775, 24295}, {3781, 37516}, {3782, 17781}, {3791, 3971}, {3792, 9037}, {3838, 33096}, {3842, 33682}, {3844, 33082}, {3875, 4718}, {3876, 7296}, {3880, 16561}, {3899, 21338}, {3924, 3962}, {3928, 23511}, {3932, 5847}, {3939, 15733}, {3940, 37817}, {3941, 34247}, {3946, 17246}, {3950, 15828}, {3951, 37549}, {3958, 4016}, {3966, 33163}, {3967, 4362}, {3975, 17790}, {3986, 15808}, {4003, 5282}, {4007, 4816}, {4009, 17763}, {4011, 32853}, {4033, 25298}, {4037, 17162}, {4113, 32945}, {4253, 16604}, {4255, 31424}, {4307, 38057}, {4353, 4989}, {4358, 16704}, {4360, 4681}, {4363, 4384}, {4371, 4461}, {4386, 5782}, {4387, 17156}, {4388, 33118}, {4389, 17333}, {4393, 4664}, {4399, 4431}, {4402, 4488}, {4410, 20913}, {4419, 5222}, {4434, 23552}, {4440, 4912}, {4445, 17286}, {4454, 24599}, {4471, 37586}, {4472, 24603}, {4473, 4725}, {4515, 14974}, {4530, 14584}, {4553, 9025}, {4646, 12514}, {4648, 18230}, {4650, 16569}, {4659, 16833}, {4662, 5255}, {4667, 17392}, {4679, 11269}, {4683, 29850}, {4687, 17379}, {4695, 5183}, {4703, 25453}, {4704, 17393}, {4706, 32845}, {4713, 17026}, {4716, 28484}, {4721, 29433}, {4726, 17117}, {4739, 17116}, {4755, 16826}, {4794, 9321}, {4850, 14997}, {4883, 5284}, {4888, 20195}, {4889, 17315}, {4899, 9053}, {4914, 33162}, {4957, 24209}, {4966, 34379}, {4967, 7227}, {5032, 29585}, {5036, 37572}, {5057, 33139}, {5087, 33140}, {5158, 17102}, {5179, 12019}, {5217, 36744}, {5219, 31187}, {5224, 17331}, {5228, 8545}, {5242, 23302}, {5243, 23303}, {5257, 17398}, {5271, 19723}, {5275, 9349}, {5276, 5297}, {5277, 25068}, {5278, 26223}, {5296, 5550}, {5341, 16547}, {5393, 32787}, {5405, 32788}, {5438, 8951}, {5530, 18253}, {5541, 21885}, {5546, 19622}, {5548, 9456}, {5704, 27382}, {5714, 5746}, {5723, 22464}, {5739, 32777}, {5745, 37662}, {5781, 8544}, {5838, 30332}, {5852, 24231}, {5880, 24695}, {5905, 24789}, {6144, 17311}, {6173, 31183}, {6181, 15855}, {6184, 6594}, {6329, 17045}, {6351, 7585}, {6352, 7586}, {6510, 16578}, {6541, 17772}, {6646, 16706}, {7074, 30223}, {7083, 12329}, {7090, 13911}, {7126, 7127}, {7133, 19038}, {7232, 17282}, {7238, 28333}, {7308, 37674}, {7321, 31300}, {7330, 36745}, {7772, 37592}, {7963, 33804}, {8287, 26012}, {8584, 29574}, {8607, 23980}, {9018, 20670}, {9300, 24239}, {9324, 9325}, {9330, 9347}, {9355, 9441}, {10436, 17259}, {10445, 31673}, {11063, 26744}, {11488, 30414}, {11489, 30415}, {12723, 21867}, {13883, 31595}, {13936, 31594}, {13973, 14121}, {14555, 26065}, {14578, 32641}, {14621, 25384}, {15534, 29573}, {15624, 20992}, {15988, 25099}, {16560, 18735}, {16583, 36283}, {16696, 27644}, {16700, 27643}, {16713, 27058}, {16726, 18198}, {16732, 17895}, {16738, 27078}, {16825, 32935}, {16834, 17318}, {17011, 33761}, {17013, 28606}, {17028, 21264}, {17228, 17343}, {17230, 17342}, {17232, 17341}, {17233, 17339}, {17234, 17338}, {17236, 17329}, {17238, 17328}, {17240, 17373}, {17241, 17375}, {17242, 17377}, {17244, 17378}, {17247, 17380}, {17248, 17381}, {17249, 17383}, {17251, 17308}, {17252, 17307}, {17253, 17306}, {17254, 17305}, {17255, 17304}, {17258, 17302}, {17263, 17300}, {17265, 17298}, {17266, 17297}, {17267, 17296}, {17268, 17295}, {17269, 17294}, {17270, 17293}, {17271, 17292}, {17273, 17291}, {17274, 17290}, {17283, 17288}, {17285, 17287}, {17317, 20090}, {17325, 29598}, {17387, 29572}, {17390, 32455}, {17394, 27268}, {17461, 21886}, {17483, 26724}, {17484, 33129}, {17495, 30579}, {17593, 17779}, {17605, 24892}, {17720, 24597}, {17754, 37673}, {17780, 36872}, {17786, 29542}, {18228, 37642}, {18644, 36949}, {18743, 37683}, {19717, 37869}, {19750, 22034}, {19872, 31252}, {20016, 28329}, {20530, 37686}, {20568, 32012}, {20662, 38989}, {20970, 25092}, {21026, 25621}, {21035, 23659}, {21281, 24735}, {21371, 27623}, {21746, 22277}, {22276, 23638}, {23073, 37618}, {23972, 35091}, {24320, 36741}, {24330, 24592}, {24352, 24600}, {24407, 27918}, {24512, 30950}, {24632, 30906}, {24692, 25351}, {24697, 29633}, {24703, 33137}, {24715, 28534}, {24890, 25651}, {25067, 37659}, {25971, 26671}, {26048, 26076}, {26070, 32851}, {26792, 33133}, {26799, 26971}, {26878, 37528}, {27003, 37687}, {27191, 29607}, {27253, 32088}, {28254, 28283}, {28309, 36522}, {28538, 32847}, {28582, 32922}, {28604, 28633}, {29610, 31144}, {30829, 37684}, {32005, 36857}, {32779, 37656}, {32843, 33115}, {32861, 33164}, {32914, 32938}, {33075, 33166}, {33099, 33132}, {35068, 35079}, {35069, 35090}, {35116, 35508}, {35242, 37499}, {35595, 37633}, {36289, 36294}, {37595, 37685}

▸ Functional Relations37 relations

• X₄₄ = midpoint of X_i and X_j for these {i,j}: {190, 239}, {238, 1757}, {320, 20072}, {1266, 4480}, {2325, 4700}, {3218, 3257}, {3271, 20683}, {3943, 4969}, {4432, 4753}, {9355, 9441}, {39150, 39151}

• X₄₄ = reflection of X_i in X_j for these {i,j}: {1, 3246}, {320, 3834}, {1086, 3008}, {1266, 4395}, {1279, 238}, {3834, 6687}, {3912, 4422}, {3943, 2325}, {4432, 4759}, {4645, 3823}, {4702, 4432}, {4727, 3943}, {4864, 1279}, {4887, 17067}, {4908, 4370}, {4969, 4700}, {17374, 3912}, {24692, 25351}, {31138, 2}

• X₄₄ = isogonal conjugate of X₈₈

• X₄₄ = isotomic conjugate of X₂₀₅₆₈

• X₄₄ = complement of X₃₂₀

• X₄₄ = anticomplement of X₃₈₃₄

• X₄₄ = X_i-Ceva conjugate of X_j for these (i,j): (2, 214), (88, 1), (104, 55)

• X₄₄ = crosspoint of X_i and X_j for these (i,j): (1, 88), (2, 80)

• X₄₄ = crosssum of X_i and X_j for these (i,j): (1, 44), (6, 36), (57, 1465)

• X₄₄ = crossdifference of every pair of points on line X₁X₅₁₃

• X₄₄ = crossdifference of PU(55)

• X₄₄ = X_i-line conjugate of X_j for these (i,j): {6, 1} }, {517, 14190}, {649, 513}, {1643, 24457}, {1739, 17960}

• X₄₄ = X₈₈-cross conjugate of X₄₄

• X₄₄ = bicentric sum of PU(i) for these i: 33, 50

• X₄₄ = midpoint of PU(i) for these i: 33, 50

• X₄₄ = perspector of circumconic centered at X₂₁₄

• X₄₄ = center of circumconic that is locus of trilinear poles of lines passing through X₂₁₄

• X₄₄ = inverse-in-circumconic-centered-at-X₉ of X₁

• X₄₄ = polar conjugate of isotomic conjugate of X₅₄₄₀

• X₄₄ = trilinear pole of line X₆₇₈X₁₆₃₅

• X₄₄ = polar conjugate of isogonal conjugate of X₂₃₂₀₂

• X₄₄ = cevapoint of X_i and X_j for these (i,j): {1, 9324}, {6, 3196}, {1635, 2087}, {2251, 23202}, {4120, 4530}

• X₄₄ = crosspoint of X_i and X_j for these (i,j): {1, 88}, {2, 80}, {57, 8686}, {100, 5376}, {214, 19618}, {519, 3911}, {765, 3257}, {1016, 6079}, {1252, 32641}, {4358, 38462}, {7126, 19551}

• X₄₄ = crosssum of X_i and X_j for these (i,j): {1, 44}, {2, 17495}, {6, 36}, {9, 3880}, {37, 31855}, {57, 1465}, {106, 2316}, {244, 1635}, {513, 2087}, {1015, 6085}, {1086, 10015}, {9456, 36058}, {37772, 37773}

• X₄₄ = trilinear pole of line {678, 1635}

• X₄₄ = crossdifference of every pair of points on line {1, 513}

• X₄₄ = X₃₂₀₁₂-anticomplementary conjugate of X₆₃₂₇

• X₄₄ = X_i-complementary conjugate of X_j for these (i,j): {31, 214}, {32, 16586}, {42, 31845}, {80, 2887}, {759, 3741}, {1168, 21241}, {1402, 6739}, {1411, 2886}, {1807, 1368}, {1918, 35069}, {1989, 21236}, {2006, 17046}, {2161, 141}, {2222, 17072}, {2341, 21246}, {6187, 10}, {11060, 5249}, {14975, 1511}, {18359, 626}, {18815, 17047}, {20566, 21235}, {24624, 21240}, {32671, 21196}, {32675, 4885}, {34079, 3739}, {34857, 3454}, {36804, 21262}, {36815, 20542}, {36910, 21244}

• X₄₄ = X_i-Ceva conjugate of X_j for these (i,j): {1, 678}, {2, 214}, {19, 17465}, {57, 17460}, {88, 1}, {100, 3251}, {104, 55}, {519, 3689}, {1022, 3722}, {1023, 1635}, {2161, 37}, {2743, 4162}, {3218, 517}, {3257, 513}, {3911, 1319}, {4358, 5440}, {4585, 8674}, {5376, 100}, {16704, 519}, {17780, 1960}, {23703, 4895}, {30731, 14425}, {32012, 2}, {36037, 3900}

• X₄₄ = X_i-cross conjugate of X_j for these (i,j): {678, 1}, {902, 1319}, {1635, 1023}, {1960, 17780}, {2087, 1635}, {3251, 100}, {4895, 23703}, {14408, 24004}, {20972, 6}, {21805, 519}, {23202, 5440}

• X₄₄ = X_i-isoconjugate of X_j for these (i,j): {1, 88}, {2, 106}, {3, 6336}, {4, 1797}, {6, 903}, {7, 2316}, {31, 20568}, {44, 679}, {56, 4997}, {57, 1320}, {58, 4080}, {63, 36125}, {69, 8752}, {75, 9456}, {81, 4674}, {89, 4792}, {92, 36058}, {100, 1022}, {101, 6548}, {110, 4049}, {190, 23345}, {244, 5376}, {264, 32659}, {292, 27922}, {312, 1417}, {512, 4615}, {513, 3257}, {514, 901}, {519, 2226}, {523, 4591}, {593, 4013}, {649, 4555}, {651, 23838}, {661, 4622}, {673, 34230}, {693, 32665}, {798, 4634}, {900, 4638}, {908, 10428}, {1086, 9268}, {1168, 3218}, {1252, 6549}, {1293, 2403}, {1318, 3911}, {1635, 4618}, {2163, 4945}, {2291, 36887}, {2712, 17953}, {3261, 32719}, {3445, 31227}, {3676, 5548}, {4462, 36042}, {4510, 30650}, {4588, 23598}, {4604, 23352}, {6545, 6551}, {6635, 21143}, {8046, 39148}, {9325, 9326}, {14190, 37131}, {14260, 34234}, {16489, 36592}, {16944, 18359}, {17109, 36805}, {17969, 35153}, {20332, 36814}

• X₄₄ = X_i-aleph conjugate of X_j for these (i,j): {1, 9324}, {2, 16561}, {366, 5541}, {903, 21372}, {1320, 17613}, {3257, X₄₄ = 1023}

• X₄₄ = X_i-beth conjugate of X_j for these (i,j): {21, 3246}, {333, 24593}, {645, 239}, {3939, 2223}, {5546, 7113}

• X₄₄ = X_i-zayin conjugate of X_j for these (i,j): {1, 88}, {6, 4674}, {9, 106}, {19, 36058}, {43, 903}, {46, 1797}, {57, 2316}, {63, 9456}, {104, 1465}, {106, 16610}, {513, 1022}, {517, 57}, {610, 36125}, {649, 23345}, {650, 23838}, {672, 34230}, {978, 4997}, {1022, 1635}, {1023, 244}, {1052, 5376}, {1054, 3257}, {1575, 36814}, {1635, 513}, {1726, 32659}, {1731, 3}, {1739, 63}, {1740, 20568}, {1743, 1320}, {1745, 6336}, {1763, 8752}, {1766, 1417}, {1769, 905}, {2087, 1054}, {2161, 36}, {2183, 14260}, {2246, 14190}, {2316, 517}, {2640, 4622}, {2664, 27922}, {2827, 3669}, {3216, 4080}, {3218, 6}, {3257, 2087}, {3737, 4049}, {3960, 650}, {4040, 6548}, {4498, 2441}, {4585, 3125}, {4674, 3218}, {4893, 23352}, {5539, 4615}, {5540, 901}, {5541, 2226}, {6909, 1427}, {9324, 679}, {9359, 4555}, {9456, 1739}, {12034, 1319}, {16548, 16944}, {16554, 1168}, {16560, 32665}, {16576, 4582}, {16610, 9}, {16670, 4792}, {17613, 269}, {21214, 31227}, {21372, 31}, {21381, 4591}, {21382, 32719}, {21385, 649}, {21864, 3337}, {23345, 21385}, {23650, 4083}, {23838, 3960}, {24625, 1575}, {32486, 3911}, {35338, 6549}, {36814, 24625}, {37680, 37}, {39150, 37773}, {39151, 37772}

• X₄₄ = barycentric product X_i*X_j for these {i,j}: {1, 519}, {3, 38462}, {4, 5440}, {6, 4358}, {7, 3689}, {8, 1319}, {9, 3911}, {19, 3977}, {31, 3264}, {37, 16704}, {42, 30939}, {56, 4723}, {57, 2325}, {58, 3992}, {63, 8756}, {72, 37168}, {75, 902}, {76, 2251}, {78, 1877}, {80, 214}, {81, 3943}, {86, 21805}, {88, 4370}, {89, 4908}, {92, 22356}, {99, 4730}, {100, 900}, {101, 3762}, {104, 1145}, {106, 4738}, {109, 4768}, {162, 14429}, {190, 1635}, {219, 37790}, {256, 4434}, {264, 23202}, {291, 4432}, {312, 1404}, {321, 3285}, {513, 17780}, {514, 1023}, {517, 36944}, {522, 23703}, {528, 14191}, {561, 9459}, {594, 30576}, {643, 30572}, {644, 30725}, {649, 24004}, {651, 1639}, {653, 14418}, {658, 14427}, {660, 4448}, {662, 4120}, {664, 4895}, {668, 1960}, {673, 14439}, {678, 903}, {679, 8028}, {693, 23344}, {741, 4783}, {765, 1647}, {799, 14407}, {898, 30583}, {899, 36872}, {934, 4528}, {985, 4439}, {1002, 4702}, {1016, 2087}, {1017, 20568}, {1019, 4169}, {1100, 31011}, {1120, 17460}, {1126, 4975}, {1156, 6174}, {1227, 6187}, {1255, 4969}, {1317, 1320}, {1809, 1846}, {1811, 5151}, {2171, 30606}, {2320, 36920}, {2323, 14628}, {2334, 4742}, {2415, 4394}, {2429, 4462}, {3251, 4555}, {3257, 6544}, {3445, 4487}, {3576, 36925}, {3669, 30731}, {3903, 4922}, {4506, 30650}, {4511, 14584}, {4530, 4564}, {4598, 14408}, {4606, 4773}, {4607, 14437}, {4618, 33922}, {4700, 25430}, {4727, 25417}, {4753, 30571}, {4958, 37211}, {4984, 37212}, {5298, 32635}, {5376, 35092}, {6335, 22086}, {7126, 36668}, {8851, 24816}, {9278, 31059}, {9456, 36791}, {13143, 33812}, {14425, 27834}, {14436, 37133}, {16670, 36915}, {17100, 38544}, {17455, 18359}, {19551, 36669}, {20972, 36805}, {23757, 36037}, {28602, 37135}

• X₄₄ = barycentric quotient X_i/X_j for these {i,j}: {1, 903}, {2, 20568}, {6, 88}, {9, 4997}, {19, 6336}, {25, 36125}, {31, 106}, {32, 9456}, {37, 4080}, {41, 2316}, {42, 4674}, {45, 4945}, {48, 1797}, {55, 1320}, {99, 4634}, {100, 4555}, {101, 3257}, {106, 679}, {110, 4622}, {163, 4591}, {184, 36058}, {214, 320}, {238, 27922}, {244, 6549}, {513, 6548}, {519, 75}, {644, 4582}, {649, 1022}, {661, 4049}, {662, 4615}, {663, 23838}, {667, 23345}, {678, 519}, {692, 901}, {750, 4510}, {756, 4013}, {900, 693}, {901, 4618}, {902, 1}, {1023, 190}, {1110, 9268}, {1145, 3262}, {1155, 36887}, {1252, 5376}, {1319, 7}, {1397, 1417}, {1404, 57}, {1635, 514}, {1639, 4391}, {1647, 1111}, {1743, 31227}, {1877, 273}, {1960, 513}, {1973, 8752}, {2087, 1086}, {2177, 4792}, {2223, 34230}, {2251, 6}, {2325, 312}, {2429, 27834}, {3009, 36814}, {3251, 900}, {3264, 561}, {3285, 81}, {3689, 8}, {3762, 3261}, {3911, 85}, {3943, 321}, {3977, 304}, {3992, 313}, {4120, 1577}, {4152, 4723}, {4169, 4033}, {4358, 76}, {4370, 4358}, {4394, 2403}, {4432, 350}, {4434, 1909}, {4439, 33931}, {4448, 3766}, {4528, 4397}, {4530, 4858}, {4543, 4768}, {4700, 19804}, {4702, 4441}, {4723, 3596}, {4727, 28605}, {4730, 523}, {4738, 3264}, {4759, 30963}, {4768, 35519}, {4773, 4801}, {4775, 23352}, {4783, 35544}, {4792, 36594}, {4893, 23598}, {4895, 522}, {4908, 4671}, {4922, 4374}, {4958, 4823}, {4969, 4359}, {4975, 1269}, {4984, 4978}, {5168, 17960}, {5440, 69}, {6174, 30806}, {6187, 1168}, {6544, 3762}, {8028, 4738}, {8661, 764}, {8756, 92}, {9247, 32659}, {9324, 9460}, {9456, 2226}, {9459, 31}, {14122, 17089}, {14191, 18821}, {14407, 661}, {14408, 3835}, {14418, 6332}, {14425, 4462}, {14427, 3239}, {14429, 14208}, {14436, 3250}, {14437, 4728}, {14439, 3912}, {14584, 18815}, {16704, 274}, {17455, 3218}, {17460, 1266}, {17780, 668}, {20972, 16610}, {21781, 9326}, {21805, 10}, {21821, 3943}, {22086, 905}, {22356, 63}, {22371, 5440}, {23202, 3}, {23214, 22067}, {23344, 100}, {23644, 1739}, {23703, 664}, {23757, 36038}, {24004, 1978}, {30572, 4077}, {30576, 1509}, {30725, 24002}, {30731, 646}, {30939, 310}, {31011, 32018}, {32665, 4638}, {32739, 32665}, {34858, 10428}, {36872, 31002}, {36944, 18816}, {37168, 286}, {37790, 331}, {38462, 264}, {39251, 17023}

• X₄₄ = {X_i,X_j}-harmonic conjugate of X_k for these (i,j,k): {1, 6, 16666}, {1, 9, 45}, {1, 45, 37}, {1, 238, 3246}, {1, 1743, 16670}, {1, 3246, 1279}, {1, 16505, 16507}, {1, 16666, 1100}, {1, 16670, 6}, {1, 16676, 16672}, {2, 320, 3834}, {2, 3758, 4670}, {2, 3834, 31243}, {2, 4643, 17237}, {2, 4644, 4675}, {2, 4741, 17227}, {2, 17256, 4708}, {2, 20072, 320}, {2, 26768, 27106}, {2, 26816, 27159}, {6, 9, 37}, {6, 37, 1100}, {6, 45, 1}, {6, 1100, 16668}, {6, 1743, 16669}, {6, 3973, 15492}, {6, 15492, 16814}, {6, 16669, 16671}, {6, 16675, 16884}, {6, 16685, 20228}, {6, 16777, 1449}, {6, 16814, 3723}, {6, 16884, 16667}, {6, 16885, 9}, {6, 17796, 2323}, {7, 37650, 17278}, {9, 37, 16814}, {9, 1449, 3731}, {9, 1743, 6}, {9, 2324, 34524}, {9, 3973, 16885}, {9, 16572, 8557}, {9, 16667, 16675}, {9, 16669, 1100}, {9, 16670, 1}, {9, 16671, 3723}, {9, 16885, 15492}, {10, 3707, 17330}, {37, 1100, 3723}, {37, 1743, 16671}, {37, 15492, 9}, {37, 16666, 1}, {37, 16669, 6}, {37, 16671, 16668}, {41, 2267, 2278}, {43, 7262, 4640}, {45, 16670, 16666}, {45, 16672, 16676}, {48, 3217, 3204}, {57, 37679, 16602}, {63, 4383, 3752}, {69, 17279, 17231}, {69, 26685, 17279}, {71, 2347, 4271}, {72, 1724, 1104}, {75, 17349, 17348}, {75, 17350, 17351}, {75, 21591, 21417}, {86, 17260, 4698}, {88, 9326, 679}, {101, 5053, 7113}, {141, 4416, 17344}, {141, 17353, 17357}, {144, 4000, 17276}, {144, 37681, 4000}, {192, 3759, 4852}, {193, 344, 4851}, {213, 16552, 1107}, {219, 1723, 1108}, {220, 8557, 37}, {238, 4649, 16801}, {241, 651, 6610}, {319, 17280, 17229}, {320, 3834, 31138}, {320, 6687, 31243}, {320, 27637, 28362}, {346, 5839, 17299}, {391, 2345, 17275}, {597, 4364, 17023}, {651, 37787, 241}, {662, 1931, 16702}, {672, 899, 20331}, {672, 2183, 2245}, {672, 2238, 1575}, {672, 2246, 1155}, {672, 2348, 910}, {679, 3257, 9326}, {748, 32912, 354}, {756, 2308, 3745}, {894, 17277, 3739}, {896, 899, 1155}, {896, 2246, 2243}, {899, 20331, 1575}, {902, 21805, 3689}, {966, 5749, 17303}, {966, 26039, 9780}, {984, 16468, 1386}, {992, 1400, 28244}, {992, 28249, 27627}, {1100, 16671, 6}, {1100, 16814, 37}, {1155, 2246, 910}, {1155, 2348, 2246}, {1386, 15481, 984}, {1400, 27627, 28249}, {1404, 22356, 17455}, {1445, 6180, 1418}, {1449, 3731, 16777}, {1654, 17289, 17239}, {1708, 34048, 1427}, {1743, 3973, 9}, {1743, 15492, 1100}, {1743, 16885, 37}, {1778, 2287, 1333}, {2170, 21801, 17444}, {2176, 21384, 17448}, {2182, 2183, 910}, {2183, 2265, 2182}, {2238, 20331, 899}, {2243, 20331, 1155}, {2276, 37657, 21904}, {2316, 12034, 2161}, {2323, 5526, 17796}, {2325, 3943, 4908}, {2325, 4969, 4727}, {3008, 4887, 17067}, {3204, 4268, 48}, {3218, 37680, 16610}, {3219, 32911, 3666}, {3247, 16667, 16884}, {3247, 16675, 37}, {3554, 34524, 37}, {3589, 4357, 17384}, {3589, 17332, 4357}, {3618, 17257, 4657}, {3629, 17243, 3879}, {3661, 17346, 4690}, {3661, 17354, 17359}, {3662, 17347, 17345}, {3662, 17352, 17356}, {3664, 6666, 17245}, {3681, 17127, 3744}, {3686, 17355, 594}, {3723, 16668, 1100}, {3729, 4361, 4686}, {3731, 16777, 37}, {3758, 17335, 2}, {3759, 17336, 192}, {3834, 6687, 2}, {3875, 17262, 4718}, {3875, 25728, 17262}, {3879, 25101, 17243}, {3943, 4370, 2325}, {4360, 17261, 4681}, {4363, 4384, 4688}, {4370, 4700, 4727}, {4370, 4969, 3943}, {4389, 17367, 17382}, {4416, 17353, 141}, {4419, 5222, 17301}, {4440, 29590, 37756}, {4473, 6542, 17264}, {4659, 16833, 17119}, {4663, 15254, 1}, {4667, 29571, 17392}, {4687, 17379, 28639}, {4690, 17359, 3661}, {4727, 4908, 3943}, {4753, 4759, 4702}, {4887, 17067, 1086}, {5222, 6172, 4419}, {5223, 7290, 3242}, {5224, 17368, 17385}, {5278, 26223, 31993}, {5540, 16548, 7297}, {5749, 9780, 26039}, {6646, 16706, 17235}, {6687, 20072, 31138}, {7174, 16469, 38315}, {7277, 17245, 3664}, {8609, 17796, 6603}, {9780, 26039, 17303}, {10436, 17259, 31238}, {14439, 39251, 902}, {15492, 16669, 37}, {15569, 16801, 1279}, {16477, 16521, 16666}, {16505, 23343, 1}, {16669, 16814, 16668}, {16669, 16885, 16814}, {16671, 16814, 1100}, {16672, 16676, 37}, {16673, 16677, 37}, {16675, 16884, 3247}, {17120, 17260, 86}, {17121, 17261, 4360}, {17123, 32913, 3742}, {17233, 17363, 17372}, {17234, 17364, 17376}, {17248, 17381, 25498}, {17254, 29630, 17305}, {17328, 17371, 17238}, {17329, 17370, 17236}, {17330, 17369, 10}, {17331, 17368, 5224}, {17333, 17367, 4389}, {17334, 17366, 3663}, {17337, 17365, 142}, {17338, 17364, 17234}, {17339, 17363, 17233}, {17340, 17362, 2321}, {17341, 17361, 17232}, {17342, 17360, 17230}, {17343, 17358, 17228}, {17344, 17357, 141}, {17345, 17356, 3662}, {17346, 17354, 3661}, {17347, 17352, 3662}, {17348, 17351, 75}, {17349, 17350, 75}, {17781, 26723, 3782}, {20372, 21760, 20363}, {20568, 32091, 32012}, {24597, 31018, 17720}, {25454, 25658, 2}, {26975, 27036, 2}, {27265, 29978, 30823}, {27268, 37677, 17394}, {27627, 28249, 28244}, {30556, 30557, 5289}, {31138, 31243, 3834}, {32091, 32103, 20568}, {32864, 32930, 3706}, {33082, 33159, 3844}, {33096, 33138, 3838}, {34247, 36635, 3941}