Last update: 2020-12-06
A line in the plane of a triangle is a central line if it passes through two triangle centers. The Encyclopedia of Triangle Centers (ETC) indexes triangle centers as X(1), X(2), X(3), etc. Thus, for example, X(1)X(2) is a central line. In ETC, the entry for X(8) shows that X(8) lies on X(1)X(2) but does not show other centers collinear with those numbered 1, 2 and 8. The list below shows such collinearities.The first line shown is the line at infinity. Among the centers on this line, the two with least indices in ETC are X(30) and X(511), so that the line is X(30)X(511). Similarly, the Euler line, listed as the second line, is abbreviated as X(2)X(3).
After the first line, the next few are X(2)X(3), then X(3)X(6), then X(230)X(232), then X(44)X(513), . . . ; generally, for k>2, Lines X(i)X(j) such that i + j = k are listed in order of increasing k, with i from 1 up to Floor((k - 1)/2), and skipping lines already listed (e.g., line X(4)X(20) is listed as X(2)X(3).)
You can use this page together with ETC to find collinearities. Suppose you want to find centers collinear with X(316) and X(625). First, in ETC find at X(316) and X(625) the line containing both centers: X(2)X(187). Then on this page, scroll to LINE X(2)X(187) to conclude that X(2), X(187), X(316), X(598), X(625), X(1153), X(1383) are collinear.
If P = p : q : r (barycentrics) is a point, then the trilinear polar of P is the line given by q r x + r q y + p q z = 0. This line is the perspectrix of ABC and the cevian triangle of P. Note that q r : r q : p q = 1/p : 1/q : 1/r is the isotomic conjugate of P.
In the list below, the notation L(n) derives from the triangle center X(n) = p : q : r (trilinears) and is simply the line with trilinear equation
p x + q y + r z = 0 (from TCCT, page 127).
On the other hand, if X(n) = p : q : r (barycentrics), then L(n) is the line with barycentric equation
a^2 p x + b^2 q y + c^2 r z = 0.
For a table of named central lines (e.g., orthic axis, Nagel line, Soddy line) with access to a discussion of each, click MathWorld.
1. LINE X(1)X(2) L(649) Trilinear Polar of X(190) Nagel Line
1, 2, 8, 10, 42, 43, 78, 145, 200, 239, 306, 386, 387, 498, 499, 519, 551, 612, 614, 869, 899, 936, 938, 975, 976, 978, 995, 997, 1026, 1103, 1125, 1149, 1189, 1193, 1198, 1201, 1210, 1644, 1647, 1698, 1714, 1722, 1737, 1961, 1998, 1999, 2000, 2057, 2340, 2398, 2534, 2535, 2664, 2999, 3006, 3008, 3009, 3011, 3017, 3083, 3084, 3085, 3086, 3178, 3187, 3190, 3214, 3216, 3240, 3241, 3244, 3293, 3507, 3582, 3584, 3616, 3617, 3621, 3622, 3623, 3624, 3625, 3626, 3632, 3633, 3634, 3635, 3636, 3661, 3679, 3682, 3687, 3705, 3720, 3741, 3757, 3771, 3783, 3809, 3811, 3828, 3831, 3840, 3870, 3872, 3912, 3920, 3924, 3935, 3938, 3957, 3961, 3979, 4028, 4039, 4061, 4062, 4362, 4384, 4393, 4420, 4489, 4511, 4651, 4666, 4668, 4669, 4677, 4678, 4685, 4691, 4701, 4745, 4746, 4816, 4847, 4853, 4861, 4871, 4882, 4915, 4946, 5121, 5205, 5211, 5212, 5222, 5230, 5231, 5256, 5262, 5268, 5271, 5272, 5287, 5292, 5293, 5297, 5308, 5311, 5312, 5313, 5393, 5405, 5524, 5529, 5530, 5550, 5552, 5554, 5703, 5704, 5705, 6048, 6347, 6348, 6542, 6633, 6685, 6686, 6700, 6734, 6735, 6736, 6737, 6738, 6743, 6744, 6745, 6764, 6765, 6788, 6789, 6790, 7080, 7081, 7172, 7191, 7292, 7360, 8013, 8028, 8183, 8580, 8582, 8583, 8669, 8941, 8945, 9458, 9534, 9623, 9780, 9797, 9843, 10027, 10039, 10056, 10072, 10197, 10198, 10199, 10200, 10320, 10321, 10324, 10327, 10449, 10453, 10459, 10479, 10527, 10528, 10529, 10530, 10573, 10578, 10580, 10582, 10586, 10587, 10915, 10916, 11019, 11239, 11240, 11269, 11519, 11679, 12127, 12447, 12546, 12629, 12647, 12648, 12649, 13405, 13411, 14028, 14112, 14459, 14464, 14469, 14478, 14986, 15519, 15523, 15808, 15865, 15866, 15867, 15868, 15933, 15940, 15953, 15954, 15955, 16020, 16086, 16338, 16569, 16815, 16816, 16817, 16818, 16819, 16820, 16821, 16822, 16823, 16824, 16825, 16826, 16827, 16828, 16829, 16830, 16831, 16832, 16833, 16834, 17011, 17012, 17013, 17014, 17015, 17016, 17017, 17018, 17019, 17020, 17021, 17022, 17023, 17024, 17025, 17026, 17027, 17028, 17029, 17030, 17031, 17032, 17033, 17034, 17135, 17150, 17156, 17162, 17230, 17244, 17266, 17284, 17292, 17294, 17308, 17310, 17316, 17367, 17389, 17397, 17730, 17733, 17734, 17748, 17749, 17751, 17752, 17763, 17779, 17780, 17795, 18120, 18229, 18391, 18395, 19766, 19767, 19783, 19784, 19836, 19843, 19846, 19847, 19851, 19853, 19854, 19855, 19856, 19857, 19858, 19859, 19860, 19861, 19862, 19863, 19864, 19865, 19866, 19867, 19868, 19869, 19870, 19871, 19872, 19874, 19875, 19876, 19877, 19878, 19879, 19880, 19881, 19883, 19974, 19993, 19994, 19998, 20007, 20008, 20009, 20011, 20012, 20013, 20014, 20015, 20016, 20017, 20018, 20019, 20020, 20035, 20036, 20037, 20038, 20039, 20040, 20041, 20042, 20043, 20044, 20045, 20046, 20047, 20048, 20049, 20050, 20051, 20052, 20053, 20054, 20055, 20056, 20057, 20058, 20069, 20083, 20103, 20104, 20106, 20107, 20108, 20340, 20352, 20653, 20971, 21081, 21085, 21214, 21267, 21352, 21625, 21674, 21688, 21712, 21717, 21718, 22166, 22266, 22350, 22836, 22837, 23354, 23485, 23511, 23600, 23691, 23705, 23833, 23869, 23891, 24239, 24331, 24432, 24541, 24550, 24551, 24558, 24559, 24564, 24592, 24599, 24600, 24603, 24640, 24641, 24864, 24869, 24871, 24880, 24883, 24892, 24896, 24898, 24899, 24902, 24931, 24936, 24943, 24946, 24947, 24963, 24968, 24969, 24980, 24982, 24987, 24996, 24997, 25005, 25006, 25007, 25011, 25025, 25030, 25031, 25055, 25352, 25377, 25386, 25390, 25391, 25400, 25441, 25446, 25453, 25459, 25460, 25474, 25479, 25492, 25501, 25502, 25509, 25510, 25512, 25543, 25645, 25650, 25663, 25664, 25665, 25669, 25689, 25690, 25697, 25698, 25741, 25746, 25748, 25755, 25756, 25761, 25768, 25773, 25775, 25782, 25783, 25788, 25790, 25800, 25805, 25806, 25813, 25814, 25821, 25823, 25838, 25843, 25845, 25852, 25853, 25859, 25860, 25864, 25879, 25881, 25889, 25890, 25899, 25904, 25930, 25935, 25941, 25943, 25965, 25967, 25972, 25979, 25980, 25982, 26000, 26001, 26006, 26013, 26015, 26016, 26029, 26030, 26037, 26038, 26046, 26047, 26048, 26093, 26094, 26102, 26103, 26111, 26112, 26113, 26115, 26153, 26157, 26158, 26169, 26181, 26203, 26208, 26227, 26228, 26230, 26237, 26238, 26245, 26246, 26247, 26251, 26363, 26364, 26526, 26531, 26532, 26544, 26548, 26559, 26560, 26570, 26575, 26581, 26593, 26594, 26595, 26597, 26599, 26610, 26621, 26626, 26628, 26639, 26653, 26658, 26660, 26672, 26673, 26676, 26723, 26752, 26757, 26759, 26766, 26767, 26773, 26774, 26779, 26801, 26805, 26807, 26814, 26815, 26820, 26821, 26826, 26959, 26964, 26965, 26973, 26974, 26980, 26981, 26982, 26987, 27020, 27024, 27025, 27026, 27034, 27035, 27043, 27044, 27048, 27091, 27096, 27097, 27104, 27105, 27112, 27113, 27117, 27146, 27148, 27156, 27157, 27158, 27165, 27166, 27198, 27210, 27221, 27233, 27241, 27248, 27253, 27255, 27263, 27264, 27271, 27272, 27274, 27299, 27304, 27313, 27314, 27321, 27324, 27368, 27383, 27385, 27391, 27392, 27399, 27517, 27518, 27525, 27526, 27529, 27558, 27567, 27571, 27572, 27573, 27577, 27595, 27597, 27608, 27625, 27627, 27635, 27636, 27645, 27646, 27690, 27700, 27701, 27708, 27709, 27714, 27741, 27742, 27749, 27750, 27756, 27757, 27760, 27838, 27844, 27846, 27872, 27878, 27880, 27888, 27892, 27896, 27911, 27913, 27919, 27920, 27928, 27954, 27959, 27960, 27968, 27969, 27977, 27978, 27979, 28011, 28016, 28018, 28027, 28043, 28057, 28058, 28060, 28074, 28080, 28082, 28092, 28093, 28096, 28118, 28124, 28125, 28131, 28133, 28247, 28248, 28253, 28254, 28257, 28352, 28360, 28361, 28370, 28371, 28404, 28409, 28410, 28418, 28422, 28663, 28668, 28678, 28681, 28694, 28698, 28700, 28707, 28713, 28716, 28734, 28740, 28742, 28751, 28756, 28757, 28761, 28789, 28795, 28797, 28805, 28812, 28813, 28816, 28916, 28922, 28924, 28932, 28933, 28940, 28961, 28967, 28969, 28976, 28977, 28981, 28982, 28986, 29375, 29381, 29383, 29390, 29391, 29400, 29401, 29406, 29433, 29436, 29438, 29440, 29448, 29449, 29455, 29456, 29460, 29502, 29503, 29510, 29511, 29557, 29560, 29561, 29569, 29570, 29571, 29572, 29573, 29574, 29575, 29576, 29577, 29578, 29579, 29580, 29581, 29582, 29583, 29584, 29585, 29586, 29587, 29588, 29589, 29590, 29591, 29592, 29593, 29594, 29595, 29596, 29597, 29598, 29599, 29600, 29601, 29602, 29603, 29604, 29605, 29606, 29607, 29608, 29609, 29610, 29611, 29612, 29613, 29614, 29615, 29616, 29617, 29618, 29619, 29620, 29621, 29622, 29623, 29624, 29625, 29626, 29627, 29628, 29629, 29630, 29631, 29632, 29633, 29634, 29635, 29636, 29637, 29638, 29639, 29640, 29641, 29642, 29643, 29644, 29645, 29646, 29647, 29648, 29649, 29650, 29651, 29652, 29653, 29654, 29655, 29656, 29657, 29658, 29659, 29660, 29661, 29662, 29663, 29664, 29665, 29666, 29667, 29668, 29669, 29670, 29671, 29672, 29673, 29674, 29675, 29676, 29677, 29678, 29679, 29680, 29681, 29682, 29683, 29684, 29685, 29686, 29687, 29688, 29689, 29690, 29691, 29697, 29699, 29707, 29708, 29715, 29716, 29720, 29742, 29748, 29750, 29758, 29759, 29768, 29769, 29773, 29814, 29815, 29816, 29817, 29818, 29819, 29820, 29821, 29822, 29823, 29824, 29825, 29826, 29827, 29828, 29829, 29830, 29831, 29832, 29833, 29834, 29835, 29836, 29837, 29838, 29839, 29840, 29841, 29842, 29843, 29844, 29845, 29846, 29847, 29848, 29849, 29850, 29851, 29852, 29853, 29854, 29855, 29856, 29857, 29858, 29859, 29860, 29861, 29862, 29863, 29864, 29865, 29866, 29867, 29868, 29869, 29870, 29871, 29872, 29873, 29874, 29880, 29895, 29901, 29918, 29936, 29945, 29960, 29966, 29968, 29976, 29977, 29986, 29987, 29988, 29991, 30030, 30036, 30038, 30047, 30048, 30057, 30058, 30059, 30063, 30103, 30104, 30105, 30106, 30107, 30108, 30109, 30110, 30111, 30112, 30113, 30114, 30115, 30116, 30117, 30118, 30119, 30120, 30121, 30122, 30123, 30124, 30125, 30126, 30127, 30128, 30129, 30130, 30131, 30132, 30133, 30134, 30135, 30136, 30137, 30138, 30139, 30140, 30141, 30142, 30143, 30144, 30145, 30146, 30147, 30148, 30149, 30150, 30151, 30152, 30153, 30154, 30155, 30156, 30157, 30158, 30159, 30160, 30161, 30162, 30163, 30164, 30165, 30166, 30167, 30168, 30169, 30170, 30171, 30172, 30173, 30174, 30175, 30176, 30177, 30178, 30179, 30180, 30286, 30567, 30741, 30751, 30752, 30762, 30763, 30768, 30813, 30821, 30822, 30833, 30884, 30886, 30895, 30896, 30907, 30908, 30915, 30942, 30947, 30948, 30950, 30957, 30967, 30970, 31027, 31028, 31038, 31079, 31081, 31091, 31092, 31093, 31098, 31119, 31136, 31137, 31145, 31146, 31183, 31189, 31191, 31199, 31200, 31211, 31241, 31242, 31249, 31253, 31330, 31339, 31397, 31434, 31520, 31680, 31855, 31996, 32778, 32783, 32842, 32847, 32854, 32858, 32866, 32914, 33077, 33088, 33090, 33091, 33093, 33117, 33120, 33137, 33138, 33139, 33140, 33142, 33171, 33173, 33175, 34255, 34595, 34619, 34625, 34641, 34747, 34772, 35613, 35629, 35633, 36440, 36442, 36443, 36444, 36458, 36460, 36461, 36462, 36478, 36479, 36480, 36499, 36500, 36505, 36531, 36534, 36541, 36542, 36546, 36547, 36565, 36568, 36573, 36574, 36578, 36579, 36634, 36845, 36846, 37743, 37762, 37764, 37782, 37794, 37795, 37854, 38016, 38098, 38314, 38460, 38471, 38473, 38475, 38476, 39567, 39570, 39580, 39581, 39584, 39586, 39587, 39594, 39595, 39597, 39766, 40006.
Number of centers on this line: 13302. LINE X(1)X(3) L(650) Trilinear Polar of X(651) OI Line
1, 3, 35, 36, 40, 46, 55, 56, 57, 65, 165, 171, 241, 260, 354, 484, 517, 559, 940, 942, 980, 982, 986, 988, 999, 1038, 1040, 1060, 1062, 1082, 1155, 1159, 1214, 1319, 1381, 1382, 1385, 1388, 1402, 1403, 1420, 1429, 1454, 1460, 1466, 1467, 1470, 1482, 1617, 1622, 1697, 1715, 1735, 1754, 1758, 1764, 1771, 1936, 2061, 2077, 2078, 2093, 2095, 2098, 2099, 2223, 2283, 2352, 2446, 2447, 2448, 2449, 2556, 2557, 2564, 2565, 2572, 2573, 2646, 2662, 3057, 3072, 3075, 3245, 3256, 3295, 3303, 3304, 3333, 3336, 3337, 3338, 3339, 3340, 3359, 3361, 3428, 3503, 3513, 3514, 3550, 3576, 3579, 3587, 3601, 3612, 3660, 3666, 3670, 3675, 3677, 3744, 3745, 3746, 3748, 3749, 3750, 3931, 3953, 3976, 3999, 4003, 4038, 4424, 4689, 4694, 4860, 4883, 5010, 5045, 5048, 5049, 5061, 5078, 5091, 5119, 5122, 5126, 5128, 5131, 5137, 5143, 5172, 5173, 5183, 5193, 5204, 5217, 5221, 5228, 5255, 5264, 5266, 5269, 5285, 5329, 5337, 5347, 5348, 5363, 5425, 5482, 5535, 5536, 5537, 5538, 5563, 5570, 5584, 5597, 5598, 5662, 5697, 5706, 5707, 5708, 5709, 5710, 5711, 5885, 5902, 5903, 5908, 5919, 6244, 6282, 6583, 6766, 6767, 6769, 7011, 7070, 7146, 7280, 7373, 7688, 7742, 7957, 7962, 7964, 7982, 7987, 7991, 7994, 8069, 8071, 8148, 8158, 8162, 8163, 8171, 8186, 8187, 8193, 8251, 8270, 8273, 8726, 8758, 8924, 9120, 9364, 9371, 9441, 9627, 9630, 9659, 9672, 9819, 9940, 9957, 10202, 10222, 10225, 10246, 10247, 10252, 10253, 10267, 10268, 10269, 10270, 10273, 10284, 10306, 10310, 10319, 10383, 10388, 10389, 10434, 10439, 10441, 10470, 10473, 10474, 10475, 10476, 10480, 10500, 10508, 10618, 10679, 10680, 10831, 10832, 10856, 10857, 10882, 10902, 10965, 10966, 10980, 11009, 11010, 11011, 11012, 11014, 11018, 11021, 11224, 11227, 11248, 11249, 11252, 11253, 11278, 11280, 11366, 11367, 11407, 11492, 11493, 11507, 11508, 11509, 11510, 11518, 11521, 11529, 11531, 11567, 11575, 11822, 11823, 11849, 11873, 11874, 11875, 11876, 11877, 11878, 11879, 11880, 11881, 11882, 11883, 11884, 12000, 12001, 12009, 12410, 12435, 12458, 12459, 12555, 12702, 12703, 12704, 12915, 13145, 13151, 13370, 13373, 13384, 13388, 13389, 13462, 13528, 13600, 13601, 13624, 13750, 13751, 14000, 14110, 14115, 14122, 14131, 14132, 14792, 14793, 14794, 14795, 14796, 14797, 14798, 14799, 14800, 14801, 14802, 14803, 14804, 14882, 15016, 15177, 15178, 15803, 15804, 15931, 15932, 15934, 15941, 16189, 16191, 16192, 16193, 16200, 16201, 16202, 16203, 16204, 16205, 16206, 16207, 16208, 16209, 16215, 16216, 16217, 16218, 16541, 16678, 16687, 16763, 16778, 16877, 16878, 17102, 17437, 17502, 17591, 17592, 17593, 17594, 17595, 17596, 17597, 17598, 17599, 17600, 17601, 17603, 17609, 17642, 17699, 17700, 17715, 17716, 17798, 18115, 18193, 18201, 18208, 18280, 18330, 18398, 18421, 18443, 18447, 18453, 18455, 18758, 18788, 18838, 18839, 18856, 18857, 18955, 18956, 18967, 19758, 19761, 19765, 19782, 20182, 20254, 20323, 20358, 20359, 20367, 20368, 20764, 20788, 20789, 20790, 20878, 21010, 21164, 21334, 21842, 22341, 22765, 22766, 22767, 22768, 22770, 23171, 23207, 23340, 23703, 23832, 23853, 23890, 23960, 23961, 23981, 24299, 24301, 24310, 24464, 24468, 24474, 24806, 24926, 24927, 24928, 24929, 25405, 25413, 25414, 25415, 26086, 26087, 26285, 26286, 26287, 26290, 26291, 26296, 26297, 26319, 26320, 26351, 26352, 26357, 26358, 26365, 26366, 26380, 26393, 26395, 26398, 26399, 26400, 26401, 26402, 26404, 26417, 26419, 26422, 26423, 26424, 26425, 26426, 26437, 26903, 26904, 26908, 27247, 30274, 30282, 30323, 30337, 30343, 30350, 30389, 30392, 30502, 30503, 31393, 31498, 31508, 31511, 31515, 31662, 31663, 31666, 31778, 31779, 31780, 31781, 31785, 31786, 31787, 31788, 31792, 31793, 31794, 31797, 31798, 31849, 32167, 32612, 32613, 32622, 32623, 32636, 32760, 33176, 33177, 33178, 33179, 33281, 33574, 33596, 33649, 33657, 33658, 33795, 33862, 33925, 34339, 34345, 34346, 34471, 34486, 34489, 34556, 34557, 34560, 34561, 34583, 34592, 34593, 34871, 34879, 34880, 34881, 34890, 34891, 34923, 35000, 35004, 35010, 35014, 35046, 35059, 35202, 35238, 35239, 35242, 35244, 35245, 35251, 35252, 35390, 35445, 35448, 35457, 35459, 35460, 35461, 35597, 35612, 35620, 35621, 35631, 35645, 36152, 36274, 36279, 36946, 37080, 37520, 37521, 37522, 37523, 37524, 37525, 37526, 37527, 37528, 37529, 37530, 37531, 37532, 37533, 37534, 37535, 37536, 37537, 37538, 37539, 37540, 37541, 37542, 37543, 37544, 37545, 37546, 37547, 37548, 37549, 37550, 37551, 37552, 37553, 37554, 37555, 37556, 37557, 37558, 37559, 37560, 37561, 37562, 37563, 37564, 37565, 37566, 37567, 37568, 37569, 37570, 37571, 37572, 37573, 37574, 37575, 37576, 37577, 37578, 37579, 37580, 37581, 37582, 37583, 37584, 37585, 37586, 37587, 37588, 37589, 37590, 37591, 37592, 37593, 37594, 37595, 37596, 37597, 37598, 37599, 37600, 37601, 37602, 37603, 37604, 37605, 37606, 37607, 37608, 37609, 37610, 37611, 37612, 37613, 37614, 37615, 37616, 37617, 37618, 37619, 37620, 37621, 37622, 37623, 37624, 37625, 37772, 37773, 38013, 38014, 38284, 38285, 38286, 38287, 38288, 38289, 38290, 38291, 38474, 38483, 39271, 39550, 39578, 39598, 40245, 40255, 40292, 40293, 40294, 40295, 40296.
Number of centers on this line: 7653. LINE X(1)X(4) L(652) Trilinear Polar of X(653)
1, 4, 33, 34, 73, 223, 225, 226, 243, 278, 388, 497, 515, 581, 944, 946, 948, 950, 1056, 1058, 1064, 1066, 1068, 1070, 1072, 1079, 1457, 1478, 1479, 1490, 1519, 1528, 1541, 1543, 1558, 1659, 1699, 1745, 1750, 1785, 1838, 1848, 1870, 1877, 1891, 2356, 2635, 2647, 2654, 2655, 2947, 3465, 3468, 3475, 3476, 3485, 3486, 3487, 3488, 3583, 3585, 3586, 3944, 4857, 5225, 5229, 5236, 5270, 5290, 5307, 5603, 5658, 5691, 5712, 5713, 5714, 5715, 5716, 5717, 5882, 5930, 6198, 6256, 6260, 6261, 6637, 7009, 7718, 7952, 7967, 8555, 8763, 8862, 8923, 9118, 9121, 9577, 9612, 9613, 9614, 10106, 10368, 10382, 10393, 10454, 10478, 10531, 10532, 10571, 10572, 10595, 10596, 10597, 10629, 10805, 10806, 10888, 11254, 11392, 11393, 11522, 12047, 12053, 12115, 12116, 12608, 12650, 12667, 13161, 13390, 13407, 13464, 13607, 14547, 15237, 15500, 15836, 15942, 16869, 16870, 17985, 18283, 18340, 18393, 18446, 18483, 18513, 18514, 20130, 20264, 20277, 21147, 21620, 21740, 23706, 23710, 23987, 24042, 24210, 24268, 26098, 26332, 26333, 26389, 26413, 30384, 31516, 31528, 31529, 31532, 31533, 31673, 31866, 32056, 32082, 32083, 33106, 33144, 33152, 34029, 34036, 34039, 34045, 34231, 34500, 34913, 34936, 34937, 35015, 35635, 36844, 36985, 38295, 38945, 39579, 39599, 40257, 40264, 40270.
Number of centers on this line: 1994. LINE X(1)X(5) L(654) Trilinear Polar of X(655) IN Line
1, 5, 11, 12, 80, 119, 355, 495, 496, 952, 1317, 1387, 1411, 1421, 1483, 1484, 1718, 1807, 1837, 2006, 2594, 2596, 2606, 3614, 4551, 5219, 5252, 5396, 5399, 5400, 5443, 5531, 5533, 5534, 5587, 5660, 5718, 5719, 5720, 5721, 5722, 5723, 5724, 5725, 5726, 5727, 5881, 5886, 5901, 6127, 6264, 6265, 6326, 7173, 7741, 7951, 7958, 7972, 7988, 7989, 7993, 8068, 8070, 8227, 9578, 9581, 9624, 9817, 9897, 10057, 10073, 10283, 10523, 10592, 10593, 10826, 10827, 10886, 10887, 10942, 10943, 10944, 10948, 10949, 10950, 10954, 10955, 10956, 10957, 10958, 10959, 11373, 11374, 11375, 11376, 11698, 11729, 12019, 12025, 12433, 12550, 12735, 12737, 12738, 12739, 12740, 12749, 12750, 12751, 13244, 14204, 14584, 14679, 15017, 15251, 15252, 15253, 15888, 15935, 15943, 15950, 16173, 17602, 17717, 17718, 17719, 17720, 17721, 17722, 17723, 17724, 17725, 17726, 17857, 18357, 19372, 19907, 20586, 22392, 23477, 23513, 23517, 23708, 24217, 24222, 26470, 26475, 26476, 26481, 26482, 31517, 32213, 32214, 32486, 34232, 34465, 34586, 35638, 37630, 37691, 37692, 37693, 37694, 37695, 37696, 37697, 37698, 37699, 37700, 37701, 37702, 37703, 37704, 37705, 37706, 37707, 37708, 37709, 37710, 37711, 37712, 37713, 37714, 37715, 37716, 37717, 37718, 37719, 37720, 37721, 37722, 37723, 37724, 37725, 37726, 37727, 37728, 37729, 37730, 37731, 37732, 37733, 37734, 37735, 37736, 37737, 37738, 37739, 37740, 38044, 38045, 38063, 38109, 38138, 38156, 38157, 38184, 38458, 39692.
Number of centers on this line: 2195. LINE X(1)X(6) L(513) Trilinear Polar of X(100) IK Line
1, 6, 9, 37, 44, 45, 72, 213, 218, 219, 220, 238, 392, 405, 518, 611, 613, 954, 956, 958, 960, 984, 1001, 1023, 1083, 1100, 1104, 1107, 1108, 1124, 1191, 1203, 1212, 1279, 1335, 1386, 1449, 1453, 1616, 1642, 1713, 1723, 1724, 1728, 1736, 1743, 1757, 2087, 2176, 2256, 2257, 2273, 2284, 2300, 2323, 2324, 2329, 2427, 2663, 2911, 3061, 3074, 3191, 3230, 3242, 3243, 3246, 3247, 3294, 3297, 3298, 3299, 3301, 3508, 3553, 3554, 3555, 3640, 3641, 3723, 3731, 3751, 3954, 3970, 3973, 3990, 4053, 4426, 4649, 4663, 4864, 4867, 5220, 5223, 5227, 5234, 5239, 5240, 5247, 5251, 5258, 5259, 5280, 5283, 5288, 5289, 5291, 5299, 5302, 5315, 5336, 5353, 5357, 5436, 5525, 5526, 5572, 5588, 5589, 5604, 5605, 5692, 5701, 5728, 5729, 5730, 5904, 6051, 6603, 6762, 7078, 7174, 7290, 7968, 7969, 8271, 8551, 8557, 8609, 8692, 8965, 9119, 9270, 9303, 9440, 9575, 10040, 10041, 10048, 10049, 10177, 10179, 10396, 10398, 10399, 10477, 10929, 10930, 10931, 10932, 11260, 11370, 11371, 11523, 12513, 12594, 12595, 12635, 13359, 13360, 13887, 13940, 14054, 14523, 14686, 15185, 15254, 15285, 15286, 15296, 15297, 15298, 15299, 15479, 15481, 15485, 15492, 15518, 15569, 15570, 15571, 15600, 15601, 15662, 15829, 15853, 16369, 16466, 16467, 16468, 16469, 16470, 16471, 16472, 16473, 16474, 16475, 16476, 16477, 16478, 16479, 16480, 16481, 16482, 16483, 16484, 16485, 16486, 16487, 16488, 16489, 16490, 16491, 16492, 16493, 16494, 16495, 16496, 16497, 16498, 16499, 16500, 16501, 16502, 16503, 16504, 16505, 16506, 16507, 16514, 16515, 16516, 16517, 16518, 16519, 16520, 16521, 16522, 16523, 16524, 16525, 16526, 16527, 16552, 16572, 16601, 16666, 16667, 16668, 16669, 16670, 16671, 16672, 16673, 16674, 16675, 16676, 16677, 16684, 16685, 16690, 16777, 16779, 16780, 16781, 16782, 16783, 16784, 16785, 16786, 16787, 16788, 16790, 16791, 16792, 16793, 16794, 16795, 16796, 16797, 16798, 16799, 16800, 16801, 16814, 16884, 16885, 16968, 16969, 16970, 16971, 16972, 16973, 16974, 16975, 17435, 17448, 17742, 17744, 17745, 17746, 17796, 18170, 18194, 18216, 18397, 18412, 18991, 18992, 19003, 19004, 19047, 19048, 19049, 19050, 19753, 20228, 20363, 20372, 20669, 20685, 20698, 20811, 20812, 20963, 21061, 21078, 21384, 21760, 21769, 21785, 21788, 21802, 21810, 21816, 21839, 21873, 21874, 21879, 22021, 22122, 22123, 22124, 22131, 22132, 22134, 22202, 23150, 23343, 23488, 23561, 23564, 23576, 23660, 23693, 23704, 23830, 24048, 24053, 24433, 24437, 24491, 24727, 24802, 25087, 26342, 26343, 26349, 26350, 26458, 26459, 26464, 26465, 27785, 30330, 30556, 30557, 30612, 30618, 30621, 31435, 31438, 31453, 31464, 31490, 31518, 31519, 33845, 34522, 34524, 34526, 34791, 34807, 35026, 35227, 35552, 35599, 35628, 35892, 35963, 36404, 36405, 36406, 36407, 36408, 36409, 36410, 36411, 36647, 38048, 38315, 38316, 38485, 38487, 39248, 39252, 39260, 40133.
Number of centers on this line: 4286. LINE X(1)X(7) L(657) Trilinear Polar of X(658) Soddy Line
1, 7, 20, 77, 170, 175, 176, 269, 279, 347, 390, 481, 482, 516, 962, 990, 991, 1042, 1044, 1323, 1371, 1372, 1373, 1374, 1442, 1443, 1448, 1458, 1721, 1742, 1770, 2263, 2293, 2951, 3000, 3007, 3010, 3012, 3019, 3100, 3160, 3188, 3332, 3600, 3638, 3639, 3663, 3664, 3668, 3671, 3672, 3674, 3945, 4021, 4089, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4862, 4887, 4888, 4896, 4902, 4909, 5018, 5088, 5195, 5527, 5542, 5543, 5731, 5732, 5733, 5734, 5735, 6049, 7176, 7184, 7185, 7190, 7221, 7268, 7269, 7271, 7274, 7675, 8236, 8544, 8984, 8986, 9538, 9576, 9589, 9643, 9785, 10004, 10437, 10442, 10444, 10446, 10451, 10465, 10481, 10499, 10507, 10624, 10649, 10650, 10651, 10652, 10884, 10889, 11036, 11037, 11038, 11200, 11201, 11551, 11552, 11795, 12520, 12544, 12545, 12560, 12563, 12565, 12573, 12575, 12577, 12651, 12652, 14116, 14189, 15856, 16038, 17134, 17170, 17220, 17221, 17753, 17801, 17802, 17803, 17804, 17805, 17806, 18119, 18444, 18450, 18458, 18460, 18461, 18467, 18469, 18471, 18473, 18650, 18655, 18656, 18657, 18658, 18659, 18660, 18661, 20121, 20291, 21169, 21170, 21171, 21314, 21578, 22464, 22465, 23603, 23973, 24214, 24215, 24231, 24248, 24728, 30265, 30284, 30305, 30331, 30332, 30333, 30334, 30338, 30339, 30340, 30341, 30342, 30344, 30345, 30353, 30354, 30355, 30356, 30357, 30400, 30401, 30424, 30425, 30426, 30431, 30432, 30433, 30434, 31538, 31539, 31549, 31550, 31551, 31552, 31553, 31554, 31563, 31564, 31565, 31566, 31567, 31568, 31569, 31570, 31573, 31574, 31601, 31602, 31721, 32857, 33865, 33866, 33867, 33868, 33869, 33870, 35031, 36640, 37830, 37833, 38459, 38941, 39553.
Number of centers on this line: 3057. LINE X(1)X(15)
1, 15, 1251, 1276, 1652, 2306, 3179, 7051, 10638, 10648, 11097, 11707, 11753, 11754, 11757, 11762, 11763, 11766, 18423, 30322, 30352, 39153.
Number of centers on this line: 228. LINE X(1)X(16)
1, 16, 1250, 1277, 1653, 10647, 11098, 11708, 11771, 11772, 11775, 11780, 11781, 11784, 18422, 19373, 30321, 30351, 33653, 33654, 39152.
Number of centers on this line: 219. LINE X(1)X(19) L(656) Trilinear Polar of X(162)
1, 19, 28, 48, 240, 284, 380, 610, 1172, 1474, 1582, 1610, 1630, 1781, 1844, 1953, 1955, 1973, 2172, 2173, 2294, 2301, 2302, 2303, 2304, 2332, 2360, 2576, 2577, 2939, 8766, 9417, 14192, 16545, 16546, 16564, 17438, 17442, 17446, 18594, 18595, 18596, 18597, 18598, 18599, 18669, 18670, 18671, 18672, 18673, 18674, 18675, 19559, 23052, 23353, 23692, 38860.
Number of centers on this line: 5710. LINE X(1)X(21) L(661) Trilinear Polar of X(662)
1, 21, 31, 38, 47, 58, 63, 81, 191, 255, 283, 595, 758, 774, 846, 896, 920, 968, 993, 1046, 1468, 1496, 1497, 1580, 1612, 1621, 1707, 1725, 1749, 1780, 1822, 1823, 1923, 1931, 1954, 1959, 1962, 2292, 2328, 2650, 2651, 2964, 2975, 3193, 3561, 3562, 3573, 3647, 3743, 3747, 3794, 3868, 3869, 3873, 3874, 3877, 3878, 3881, 3884, 3889, 3890, 3892, 3894, 3897, 3898, 3899, 3901, 3915, 4512, 4653, 4658, 5127, 5208, 5248, 5250, 5330, 5426, 5429, 5496, 6149, 6763, 8616, 8666, 8772, 10122, 10448, 10457, 10458, 10461, 11020, 11031, 11520, 11533, 11682, 11684, 11688, 12081, 12514, 12526, 12559, 12564, 12567, 16126, 16570, 16585, 16948, 17185, 17194, 17469, 17799, 18169, 18192, 18206, 18389, 18417, 18477, 18756, 20985, 23407, 23478, 23602, 23695, 23831, 23889, 23997, 24635, 25058, 25080, 28606, 30358, 31424, 31880, 32913, 34195, 34997, 35016, 35028, 35193, 35614, 35623, 35632, 35637, 36263, 36277, 37817, 38832, 39673, 39772, 40091.
Number of centers on this line: 14911. LINE X(1)X(24)
1, 24, 1061, 1452, 3422, 9590.
Number of centers on this line: 612. LINE X(1)X(25) L(2522) Trilinear Polar of X(36099)
1, 25, 1036, 1039, 1763, 1773, 1829, 1905, 7713, 8185, 8192, 9798, 10037, 10046, 10834, 10835, 11363, 11365, 11396, 11398, 11399, 11400, 11401, 17441, 26308, 26309, 26377, 26378, 27802.
Number of centers on this line: 2913. LINE X(1)X(29) L(822) Trilinear Polar of X(823)
1, 29, 92, 158, 820, 1047, 1096, 1784, 1895, 1896, 2586, 2587, 2658, 2659, 8747, 17188, 20220, 20221, 20322, 20931, 21457, 24024, 39585.
Number of centers on this line: 2314. LINE X(1)X(30) L(9404) Trilinear Polar of X(38340)
1, 30, 79, 500, 554, 1081, 1464, 1717, 1836, 3058, 3649, 3655, 3656, 3782, 4654, 4854, 5160, 5434, 5441, 5453, 5495, 6147, 6284, 7073, 7100, 7286, 7354, 8144, 9579, 9580, 9610, 9611, 10149, 10404, 10483, 10543, 10910, 10911, 11544, 11553, 11809, 11905, 11906, 12696, 12699, 12701, 13408, 13995, 15170, 15171, 15172, 15174, 16118, 16124, 16132, 16137, 16143, 16152, 16153, 16154, 16155, 16159, 16272, 18481, 18506, 18990, 22791, 24701, 24851, 31162, 32047, 33095, 33097, 33103, 33154, 33668, 33857, 33858, 34628, 34634, 34643, 34657, 34712, 34773, 36975, 37631, 38336, 39542, 39544, 39549, 39552, 39751.
Number of centers on this line: 9215. LINE X(1)X(32) L(1491) Trilinear Polar of X(1492)
1, 32, 172, 609, 760, 985, 1572, 1759, 1914, 2241, 2242, 2243, 2344, 3099, 3235, 3236, 3496, 3509, 3721, 3726, 3727, 3735, 7031, 8624, 9941, 9997, 10038, 10047, 10789, 10800, 10801, 10802, 10803, 10804, 10878, 10879, 11364, 11368, 12194, 13723, 17736, 26317, 26318, 26431, 26432, 34998, 36283, 39254.
Number of centers on this line: 4816. LINE X(1)X(39) L(659) Trilinear Polar of X(660)
1, 39, 291, 292, 1009, 1015, 1018, 1500, 2007, 2008, 2108, 2275, 2276, 2295, 3097, 3208, 3501, 3802, 3864, 4876, 4919, 6166, 6184, 7170, 8299, 9331, 9336, 9451, 9592, 9593, 9619, 9620, 12782, 13006, 14200, 14839, 16549, 17475, 17750, 17754, 19593, 20331, 20467, 20671, 20687, 22116, 24496, 24512, 24578, 40460.
Number of centers on this line: 5017. LINE X(1)X(41) L(2254) Trilinear Polar of X(36086)
1, 41, 101, 105, 169, 294, 1183, 1282, 1438, 1752, 2082, 2112, 2170, 2246, 2280, 2809, 4223, 4251, 5276, 5540, 8300, 9310, 9327, 9502, 10695, 10699, 11028, 11712, 11716, 14760, 16550, 16600, 17439, 17451, 17464, 18413, 18785, 21808, 21840, 22197, 23601, 23623, 26242, 38479, 39048, 39247, 40131.
Number of centers on this line: 4718. LINE X(1)X(60) L(2610) Trilinear Polar of X(37140)
1, 60, 110, 245, 759, 2611, 2613, 2948, 5202, 7984, 9275, 10088, 10091, 11101, 11720, 13217, 13218, 17104, 21381, 37816, 38480, 38482, 38850.
Number of centers on this line: 2319. LINE X(1)X(61)
1, 61, 203, 2307, 6191, 7005, 7052, 7126, 7150, 11752, 11791, 36941, 39150.
Number of centers on this line: 1320. LINE X(1)X(69) L(2484) Trilinear Polar of X(37215)
1, 69, 1245, 1716, 3879, 3883, 4357, 4684, 5847, 10452, 10468, 13725, 17272, 17321, 25573, 30479, 31530, 31531, 33082, 35042, 37819, 39773.
Number of centers on this line: 2221. LINE X(1)X(71)
1, 71, 579, 2215, 2260, 2335, 8274, 10207, 13726.
Number of centers on this line: 922. LINE X(1)X(75) L(798) Trilinear Polar of X(799)
1, 75, 86, 274, 304, 314, 326, 332, 740, 874, 1010, 1043, 1045, 1097, 1733, 1740, 1930, 1964, 1966, 2234, 2274, 2667, 2669, 3403, 3736, 3875, 3886, 3905, 4008, 4360, 4647, 4673, 5209, 5263, 5625, 10436, 10447, 10455, 10456, 10471, 14195, 14210, 15418, 16571, 16709, 17143, 17144, 17151, 17158, 17160, 17175, 17189, 17393, 17394, 17445, 17762, 17858, 17859, 17900, 18051, 18079, 18156, 18157, 18465, 18691, 18692, 18693, 18694, 18695, 18696, 18697, 18698, 18699, 18792, 20932, 24039, 24325, 24342, 24374, 24549, 24661, 25124, 25526, 25528, 25590, 28619, 30939, 30940, 31997, 32092, 32104, 32921, 32922, 32941, 33296, 33781, 33808, 33933, 33935, 33943, 33953, 33954, 33955, 34063, 34996, 35025, 35550, 35956, 36289, 39731, 39774.
Number of centers on this line: 11123. LINE X(1)X(76) Trilinear Polar of X(37133)
1, 76, 350, 730, 870, 1008, 1909, 2230, 3510, 3760, 3761, 4116, 4161, 6196, 7976, 9902, 10063, 10079, 12263, 13109, 13110, 18835, 24291, 25303, 35027, 35548, 37632, 40365.
Number of centers on this line: 2824. LINE X(1)X(82) L(8061) Trilinear Polar of X(4599)
1, 82, 560, 1747, 1760, 2244, 3405, 4118, 5009, 8625, 11102, 16556, 17457, 18041, 18042, 18049, 18713, 18714, 18715, 18716, 18717, 18718, 18719, 18720, 18721, 18722, 21336, 21378, 23495, 34054, 34055, 34065, 34066, 34070, 34081, 34082, 35038.
Number of centers on this line: 3725. LINE X(1)X(84) L(14298) Trilinear Polar of X(37141)
1, 84, 221, 222, 1012, 1071, 1394, 1413, 1422, 1433, 1455, 1498, 1709, 1720, 1777, 1854, 2122, 2192, 2956, 6001, 7959, 7971, 7992, 7995, 9363, 10085, 10391, 10463, 11496, 12114, 12547, 12548, 12672, 12675, 12686, 12687, 12705, 12709, 12710, 12711, 15071, 15524, 17617, 17622, 17624, 17625, 17649, 17650, 18238, 20324, 30304, 34033, 34040, 34043, 34044, 34046, 34049, 36746.
Number of centers on this line: 5826. LINE X(1)X(85) Trilinear Polar of X(34085)
1, 85, 664, 1111, 2481, 3673, 7264, 7278, 9312, 13727, 14828, 14942, 24009, 24014, 24203, 25716, 28850, 31637, 32462, 34018, 36905, 39775.
Number of centers on this line: 2227. LINE X(1)X(87) L(20979) Trilinear Polar of X(4598)
1, 87, 192, 194, 330, 726, 894, 2309, 3494, 3685, 3729, 3923, 3993, 4195, 5145, 7032, 7155, 7283, 14199, 17142, 17148, 17157, 17319, 17379, 17480, 17760, 19565, 23493, 24349, 24502, 24766, 24799, 25242, 25252, 25264, 27340, 31999, 32005, 32033, 32095, 32107, 32453, 33681, 33682, 35032, 39914.
Number of centers on this line: 4628. LINE X(1)X(88) L(1635) Trilinear Polar of X(3257)
1, 88, 100, 106, 214, 244, 404, 678, 750, 1054, 1320, 1772, 2177, 2802, 3306, 3315, 3722, 3754, 3871, 3885, 3895, 4256, 4642, 4674, 4792, 4850, 4855, 4868, 5253, 5541, 5883, 6162, 8715, 9324, 9345, 9347, 10087, 10090, 10700, 11717, 12014, 12653, 12736, 13278, 13279, 13541, 14193, 14923, 15015, 16586, 17099, 17109, 17450, 17460, 18240, 21306, 21806, 24025, 24028, 24046, 24443, 25438, 25439, 25440, 32577, 33771, 33846, 35033, 35262, 35293, 35636, 37633, 38478, 38484, 39776.
Number of centers on this line: 7529. LINE X(1)X(89) L(4893) Trilinear Polar of X(4604)
1, 89, 902, 2163, 2320, 3218, 4084, 4189, 4257, 4392, 4414, 4652, 5267, 14996, 16558, 17010, 17126, 17449, 17461, 25094, 35258.
Number of centers on this line: 2130. LINE X(1)X(90)
1, 90, 155, 912, 1069, 1858, 1935, 2003, 3073, 3157, 3173, 3560, 5693, 5887, 7072, 7330, 22659, 22758, 22759, 22760, 24430, 30223, 36742.
Number of centers on this line: 2331. LINE X(1)X(99)
1, 99, 741, 1509, 4128, 5539, 7983, 10086, 10089, 11104, 11711, 13174, 13189, 13190, 17103, 18827, 20538, 24472, 33770, 38477, 38481.
Number of centers on this line: 2132. LINE X(1)X(102)
1, 102, 108, 208, 1845, 2817, 7412, 10696, 10702, 11713, 11719, 36121.
Number of centers on this line: 1233. LINE X(1)X(104) Trilinear Polar of X(37136)
1, 104, 109, 601, 603, 1158, 1768, 1795, 2342, 2800, 2950, 5083, 5450, 5884, 6906, 7004, 10058, 10074, 10698, 10703, 11570, 11571, 11700, 11715, 12005, 12016, 12551, 12758, 12767, 12775, 12776, 13253, 13539, 15501, 15528, 15558, 16767, 25485, 33810, 34051, 35649, 37469.
Number of centers on this line: 4234. LINE X(1)X(142) Trilinear Polar of X(37206)
1, 142, 277, 443, 1738, 1818, 2191, 2550, 3174, 3189, 3755, 3946, 4000, 4648, 4859, 5082, 5853, 6601, 12437, 17050, 17067, 18261, 20257, 21627, 24154, 24155, 24178, 24181, 24364, 24435, 24439, 24654, 24761, 24779, 24790, 28629, 38052, 38053.
Number of centers on this line: 3835. LINE X(1)X(163) Trilinear Polar of X(36084)
1, 163, 293, 1910, 2083, 2247, 3404, 3708, 9247, 16559, 16562, 16567, 17462, 17468, 17471, 21374.
Number of centers on this line: 1636. LINE X(1)X(164)
1, 164, 258, 266, 1130, 5571, 7588, 7589, 8077, 8078, 8093, 8094, 10231, 11032, 11033, 11534, 11899, 12523, 12656, 15997, 18291, 18399, 18409, 31766, 35624, 35625, 35644.
Number of centers on this line: 2737. LINE X(1)X(167)
1, 167, 174, 177, 503, 2089, 6585, 7590, 8081, 8082, 8089, 8090, 8091, 8092, 8241, 8242, 8351, 8422, 8423, 10235, 10236, 11044, 11191, 11234, 11894, 11895, 11896, 11924, 12554, 12844, 12908, 13092, 13385, 13443, 14596, 16012, 18448, 18454, 18456, 30370, 30374, 30408, 30411, 30420, 30423, 32183.
Number of centers on this line: 4638. LINE X(1)X(168) L(10495)
1, 168, 173, 259, 1129, 3645, 7587, 7707, 8075, 8076, 8083, 8110, 9806, 10232, 10490, 10968, 11027, 11528, 11535, 12445, 12518, 18408, 31767, 31768, 35619, 35627.
Number of centers on this line: 2639. LINE X(1)X(181) Apollonius Line
1, 181, 970, 1682, 6176, 9548, 9549, 10823, 12109, 13731, 21321, 21363.
Number of centers on this line: 1240. LINE X(1)X(182)
1, 182, 983, 1428, 1672, 1673, 1674, 1675, 2330, 6211, 7132, 12197, 13732, 31395, 38029.
Number of centers on this line: 1541. LINE X(1)X(185)
1, 185, 296, 1020, 1425, 1937, 2807, 3270, 13734.
Number of centers on this line: 942. LINE X(1)X(188)
1, 188, 361, 1489, 7028, 10233, 10234, 12646, 16011, 16015, 18258.
Number of centers on this line: 1143. LINE X(1)X(198)
1, 198, 2262, 2270, 4254, 11022, 13737.
Number of centers on this line: 744. LINE X(2)X(3) L(647) Trilinear Polar of X(648) Euler Line
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40277, 40279, 40336.
Number of centers on this line: 502045. LINE X(2)X(6) L(512) Trilinear Polar of X(99) GK Line
2, 6, 69, 81, 86, 141, 183, 193, 230, 298, 299, 302, 303, 323, 325, 333, 343, 352, 385, 391, 394, 395, 396, 491, 492, 524, 590, 591, 597, 599, 615, 940, 965, 966, 992, 1007, 1150, 1184, 1185, 1211, 1213, 1270, 1271, 1611, 1613, 1641, 1648, 1654, 1812, 1963, 1991, 1992, 1993, 1994, 2063, 2086, 2106, 2238, 2287, 2303, 2407, 2421, 2668, 2895, 3051, 3054, 3055, 3068, 3069, 3180, 3181, 3231, 3289, 3314, 3329, 3570, 3578, 3580, 3589, 3593, 3595, 3618, 3619, 3620, 3629, 3630, 3631, 3763, 3815, 3936, 3945, 4383, 4417, 4585, 4648, 4869, 4921, 5032, 5108, 5166, 5224, 5232, 5233, 5235, 5241, 5275, 5276, 5278, 5304, 5306, 5333, 5354, 5359, 5361, 5362, 5367, 5372, 5422, 5468, 5590, 5591, 5712, 5718, 5736, 5737, 5738, 5739, 5740, 5741, 5742, 5743, 5858, 5859, 5860, 5861, 5862, 5863, 5912, 5913, 5971, 6144, 6189, 6190, 6329, 6515, 6703, 6707, 6792, 7585, 7586, 7606, 7610, 7708, 7735, 7736, 7766, 7774, 7777, 7778, 7779, 7788, 7792, 7806, 7837, 7840, 7868, 7875, 7897, 7925, 7931, 8025, 8030, 8115, 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27923, 27926, 27927, 27958, 27973, 27976, 28014, 28047, 28055, 28056, 28078, 28089, 28091, 28122, 28251, 28252, 28289, 28350, 28365, 28368, 28369, 28408, 28419, 28421, 28667, 28675, 28689, 28708, 28711, 28712, 28738, 28753, 28754, 28755, 28793, 28807, 28810, 28811, 28920, 28935, 28965, 28979, 28980, 29379, 29395, 29398, 29399, 29437, 29453, 29507, 29508, 29509, 29551, 29558, 29559, 29695, 29711, 29714, 29746, 29763, 29766, 29767, 29878, 29899, 29922, 29940, 29964, 29981, 29984, 29985, 30029, 30034, 30052, 30055, 30056, 30760, 30761, 30811, 30828, 30831, 30832, 30834, 30882, 30902, 30905, 30906, 30937, 30941, 30945, 30962, 30965, 30966, 31006, 31017, 31034, 31037, 31089, 31090, 31120, 31143, 31144, 31179, 31187, 31204, 31205, 31229, 31232, 31247, 31248, 31281, 31303, 31403, 31463, 31473, 31489, 31631, 32236, 32455, 32525, 32748, 32782, 32785, 32786, 32787, 32788, 32789, 32790, 32805, 32806, 32807, 32808, 32809, 32810, 32811, 32812, 32813, 32814, 32863, 32911, 33172, 33295, 33458, 33459, 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Number of centers on this line: 88846. LINE X(2)X(7) L(663) Trilinear Polar of X(664)
2, 7, 9, 57, 63, 142, 144, 226, 307, 329, 527, 553, 579, 672, 894, 908, 1025, 1400, 1423, 1445, 1447, 1652, 1653, 1708, 1741, 1944, 2002, 2094, 2285, 2406, 3218, 3219, 3305, 3306, 3452, 3509, 3598, 3599, 3662, 3911, 3928, 3929, 3982, 4031, 4114, 4357, 4654, 5219, 5226, 5242, 5243, 5249, 5257, 5273, 5279, 5282, 5294, 5296, 5316, 5325, 5328, 5364, 5435, 5437, 5744, 5745, 5746, 5747, 5748, 5749, 5750, 5905, 6168, 6172, 6173, 6203, 6204, 6646, 6666, 6692, 7013, 7179, 7308, 8012, 8232, 8257, 8545, 8558, 8568, 8732, 9318, 9436, 9446, 9776, 9965, 10025, 10436, 12848, 14477, 16091, 16574, 17077, 17184, 17236, 17248, 17254, 17257, 17260, 17274, 17282, 17291, 17306, 17326, 17333, 17338, 17350, 17353, 17368, 17483, 17484, 17754, 17781, 17950, 18228, 18230, 18634, 20059, 20078, 20195, 20196, 20214, 20245, 20258, 20263, 20266, 20335, 20347, 20348, 20610, 21246, 21371, 21454, 21617, 23958, 24029, 24149, 24318, 24333, 24514, 24627, 24870, 24884, 24909, 24912, 24913, 24922, 24937, 24952, 25019, 25023, 25342, 25353, 25447, 25461, 25521, 25525, 25527, 25538, 25651, 25679, 25680, 25687, 25710, 25747, 25774, 25833, 25844, 25880, 25894, 25928, 25966, 25997, 26059, 26065, 26082, 26125, 26132, 26149, 26223, 26229, 26258, 26265, 26267, 26279, 26573, 26580, 26627, 26651, 26685, 26688, 26699, 26791, 26792, 26799, 26806, 26836, 26840, 26842, 26857, 26997, 27002, 27003, 27017, 27058, 27064, 27065, 27078, 27130, 27131, 27147, 27170, 27184, 27186, 27231, 27242, 27254, 27282, 27286, 27287, 27296, 27305, 27334, 27338, 27339, 27349, 27382, 27384, 27411, 27413, 27420, 27508, 27509, 27539, 27540, 27547, 27557, 27559, 27594, 27596, 27624, 27626, 27659, 27661, 27678, 27689, 27691, 27725, 27734, 27740, 27776, 27843, 27845, 27877, 27879, 27904, 27910, 27912, 27945, 27947, 27965, 27995, 27997, 28008, 28015, 28017, 28038, 28039, 28070, 28079, 28081, 28107, 28108, 28123, 28272, 28274, 28287, 28351, 28387, 28388, 28402, 28434, 28435, 28609, 28610, 28699, 28731, 28739, 28741, 28774, 28776, 28780, 28794, 28796, 28826, 28836, 28921, 28923, 28950, 28951, 28966, 28968, 28996, 28997, 29007, 29380, 29382, 29417, 29418, 29429, 29439, 29472, 29474, 29492, 29497, 29529, 29531, 29552, 29696, 29698, 29740, 29747, 29749, 29788, 29790, 29812, 29879, 29900, 29965, 29967, 30006, 30007, 30035, 30037, 30076, 30078, 30097, 30275, 30276, 30277, 30280, 30281, 30324, 30325, 30327, 30328, 30379, 30380, 30381, 30382, 30383, 30412, 30413, 30414, 30415, 30677, 30740, 30742, 30757, 30782, 30798, 30827, 30852, 30867, 30883, 30885, 30901, 30926, 30935, 30946, 30949, 30961, 30985, 31004, 31018, 31019, 31053, 31071, 31080, 31086, 31117, 31121, 31142, 31164, 31188, 31190, 31224, 31231, 31266, 31300, 33573, 33800, 33864, 35578, 35595, 35596, 36276, 36482, 36483, 36503, 36504, 36538, 36540, 36570, 36572, 36589, 36973, 37761, 37763, 37787, 37789, 37797, 37856, 38000, 38093, 39767, 39930, 40127, 40131, 40152, 40212.
Number of centers on this line: 43047. LINE X(2)X(11) L(665) Trilinear Polar of X(666)
2, 11, 55, 100, 105, 120, 149, 390, 497, 528, 673, 1001, 1376, 1621, 2110, 2550, 2886, 3021, 3035, 3058, 3434, 3816, 3826, 3829, 3925, 4026, 4366, 4413, 4421, 4423, 4428, 4429, 4972, 4995, 5132, 5218, 5263, 5274, 5281, 5284, 5326, 5432, 6154, 6174, 6653, 6654, 6667, 6690, 6714, 8167, 8299, 8301, 9342, 10385, 10584, 10589, 10707, 10712, 10773, 10947, 11235, 11238, 11502, 11680, 13205, 13271, 13274, 13576, 14942, 15813, 15842, 15845, 16593, 17784, 20075, 20095, 20097, 20119, 20172, 20344, 20531, 20533, 20539, 21321, 23404, 23541, 24542, 24552, 24582, 24596, 24646, 24647, 24885, 24916, 24938, 24955, 24988, 25448, 25493, 25531, 25652, 25882, 25893, 25919, 25954, 25968, 25973, 26007, 26031, 26040, 26073, 26095, 26105, 26139, 26231, 26241, 26533, 26565, 26582, 26590, 26629, 26667, 26692, 26795, 26846, 26966, 26977, 27009, 27027, 27038, 27072, 27134, 27149, 27190, 27243, 27256, 27306, 27337, 27394, 27521, 27542, 27560, 27568, 27598, 27628, 27639, 27666, 27692, 27703, 27881, 27972, 27999, 28019, 28040, 28053, 28071, 28083, 28239, 28250, 28353, 28364, 28393, 28411, 28743, 28752, 28798, 28806, 28925, 28934, 28955, 28999, 29384, 29394, 29421, 29441, 29452, 29480, 29506, 29539, 29700, 29732, 29751, 29762, 29797, 29969, 29980, 30016, 30039, 30051, 30086, 30755, 30787, 30825, 30857, 30887, 30899, 30928, 30959, 30993, 31020, 31031, 31058, 31073, 31084, 31126, 31140, 31192, 31203, 31226, 31235, 31245, 31272, 32773, 32942, 33108, 33110, 33970, 34607, 34611, 34612, 34708, 34709, 35023, 36441, 36459, 36475, 36481, 36485, 36488, 36497, 36501, 36506, 36509, 36528, 36544, 36559, 36576, 38025, 38060, 38092, 38202, 38878, 40333, 40565, 40566.
Number of centers on this line: 24548. LINE X(2)X(12) Trilinear Polar of X(6648)
2, 12, 56, 388, 529, 958, 961, 1220, 1329, 1791, 2551, 2975, 3436, 3600, 4999, 5253, 5260, 5261, 5265, 5298, 5433, 5434, 5484, 6645, 6668, 6691, 7288, 7294, 8165, 8169, 10585, 10588, 11194, 11236, 11237, 11681, 15843, 15844, 18962, 20060, 20076, 22759, 24583, 24612, 24953, 25466, 25524, 25914, 25992, 26126, 26259, 26264, 26558, 26561, 26686, 26687, 27283, 27335, 27410, 27657, 27944, 27994, 28036, 28037, 28265, 28271, 28385, 28386, 28771, 28773, 29468, 29471, 29524, 29528, 29730, 29783, 29787, 30001, 30005, 30053, 30075, 30478, 30756, 30778, 30826, 30847, 30900, 30960, 30979, 31032, 31039, 31085, 31108, 31141, 31157, 31221, 31230, 31246, 31260, 34605, 34606, 34610, 34695, 34696, 36451, 36476, 36486, 36487, 36493, 36498, 36507, 36508, 36513, 36529, 36545, 36560, 36577, 38299.
Number of centers on this line: 11849. LINE X(2)X(13) L(6137) Trilinear Polar of X(23895)
2, 13, 16, 530, 616, 618, 622, 624, 2004, 3457, 3643, 5335, 5459, 5463, 5979, 5980, 6108, 6115, 6298, 6302, 6306, 6582, 6669, 6672, 6779, 8014, 8017, 8595, 8838, 9762, 10653, 11078, 11131, 12155, 13084, 14904, 16242, 16770, 16966, 18582, 21466, 22489, 22492, 22687, 23006, 30462, 30468, 33416, 33440, 33441, 33517, 35019, 35315, 35749, 35750, 35751, 35752, 36766, 36767, 36768, 36769, 36770, 36771, 37776, 37831, 37832, 40335.
Number of centers on this line: 6750. LINE X(2)X(14) L(6138) Trilinear Polar of X(23896)
2, 14, 15, 531, 617, 619, 621, 623, 2005, 3458, 3642, 5334, 5460, 5464, 5978, 5981, 6109, 6114, 6295, 6299, 6303, 6307, 6670, 6671, 6780, 8015, 8016, 8594, 8836, 9760, 10654, 11092, 11130, 12154, 13083, 14905, 16241, 16771, 16967, 18581, 21467, 22490, 22491, 22689, 23013, 30459, 30465, 33417, 33442, 33443, 33518, 35020, 35314, 36327, 36329, 36330, 36331, 37775, 37834, 37835, 40334.
Number of centers on this line: 6151. LINE X(2)X(17) Trilinear Polar of X(32036)
2, 17, 62, 532, 627, 629, 634, 636, 6673, 6695, 8018, 11126, 11144, 12097, 16267, 16963, 19779, 21360, 21461, 22113, 22488, 22494, 22495, 22508, 22569, 22666, 22685, 22737, 22844, 22911, 22914, 22916, 22927, 22928, 33438, 33439, 33465, 33530, 33622, 33626, 34509, 36304, 36326, 36352, 36366, 36386.
Number of centers on this line: 4652. LINE X(2)X(18) Trilinear Polar of X(32037)
2, 18, 61, 533, 628, 630, 633, 635, 6674, 6694, 8019, 11127, 11143, 12098, 16268, 16962, 19778, 21359, 21462, 22114, 22487, 22493, 22496, 22506, 22567, 22665, 22683, 22736, 22845, 22866, 22869, 22871, 22882, 22883, 33436, 33437, 33464, 33529, 33624, 33627, 34508, 36305, 36324, 36346, 36368, 36388.
Number of centers on this line: 4653. LINE X(2)X(19)
2, 19, 534, 1848, 2339, 3101, 4329, 8020, 9536, 9816, 10319, 18589, 20061, 24611, 25915, 25993, 26260, 26789, 26837, 26998, 27059, 27127, 27180, 28106, 28266, 30674, 30675, 30686, 30687, 30779, 31158, 31261, 40530.
Number of centers on this line: 3354. LINE X(2)X(31) L(3250) Trilinear Polar of X(4586)
2, 31, 171, 238, 748, 750, 752, 985, 2239, 2887, 3836, 3846, 4307, 4388, 4645, 4766, 5156, 6327, 6652, 6679, 8022, 8032, 8622, 14465, 14621, 17122, 17123, 17124, 17125, 17126, 17127, 17717, 20064, 20101, 24545, 24563, 24586, 24602, 24888, 24901, 24941, 24991, 25010, 25451, 25471, 25496, 25655, 25668, 25751, 25760, 25778, 25789, 25809, 25848, 25863, 25885, 25903, 25938, 25957, 25958, 25959, 25960, 25961, 25970, 26010, 26034, 26098, 26161, 26168, 26188, 26211, 26232, 26250, 26536, 26547, 26585, 26598, 26663, 26675, 26762, 26778, 26810, 26825, 26969, 26986, 27030, 27047, 27100, 27116, 27152, 27169, 27259, 27273, 27309, 27323, 27388, 27401, 27512, 27528, 27563, 27576, 27601, 27631, 27695, 27713, 27745, 27759, 27849, 27856, 27884, 27895, 27916, 27931, 27963, 27982, 28026, 28050, 28059, 28086, 28242, 28256, 28356, 28375, 28414, 28424, 28671, 28680, 28703, 28715, 28746, 28760, 28801, 28815, 28928, 28972, 28985, 29405, 29432, 29444, 29459, 29500, 29514, 29555, 29562, 29703, 29719, 29754, 29772, 29883, 29904, 29917, 29925, 29943, 29972, 29990, 30042, 30062, 30652, 30653, 30746, 30767, 30816, 30837, 30877, 30890, 30914, 30953, 30969, 31023, 31041, 31075, 31097, 31134, 31151, 31195, 31210, 31237, 31252, 31289, 32772, 32781, 32784, 32916, 32917, 32918, 32944, 33083, 33086, 33105, 33107, 33111, 33112, 33174, 36262, 36271, 36554.
Number of centers on this line: 19655. LINE X(2)X(32) L(3005) Trilinear Polar of X(4577)
2, 32, 83, 251, 315, 626, 754, 1078, 1369, 1506, 1627, 1799, 2240, 2548, 2896, 3096, 3785, 5277, 5337, 6292, 6296, 6297, 6308, 6313, 6317, 6680, 6704, 7749, 7752, 7753, 7775, 7785, 7787, 7793, 7800, 7808, 7809, 7810, 7811, 7812, 7815, 7818, 7846, 7857, 7862, 7865, 7867, 7883, 7889, 7899, 7900, 7912, 7914, 7929, 7938, 7944, 8023, 8150, 8570, 8623, 8878, 9481, 9765, 9866, 9889, 9939, 10130, 10292, 10337, 10345, 10346, 10347, 10348, 10350, 10548, 10583, 12150, 12156, 12206, 13086, 14466, 14473, 14968, 15573, 15821, 15870, 16095, 16985, 17941, 18548, 18769, 20022, 20065, 20088, 21248, 22870, 22915, 24546, 24587, 24614, 24889, 24942, 24992, 25452, 25497, 25656, 25752, 25779, 25810, 25849, 25886, 26085, 26099, 26162, 26177, 26189, 26212, 26224, 26233, 26537, 26586, 26664, 26763, 26811, 26843, 26970, 27005, 27031, 27067, 27101, 27153, 27260, 27310, 27389, 27414, 27513, 27564, 27602, 27632, 27662, 27696, 27746, 27850, 27885, 27917, 27964, 28051, 28243, 28277, 28357, 28390, 28415, 28436, 28672, 28688, 28704, 28724, 28747, 28802, 28929, 28973, 29387, 29419, 29445, 29476, 29501, 29534, 29556, 29568, 29704, 29755, 29792, 29884, 29905, 29926, 29944, 29973, 30010, 30043, 30081, 30747, 30785, 30817, 30853, 30891, 30954, 30987, 31024, 31076, 31124, 31168, 31196, 31268, 31404, 31982, 32190, 32816, 33454, 33455, 33468, 33469, 33484, 33485, 33651, 34506, 34604, 34677, 34678, 36282, 36337, 36339, 36351, 36359, 36375, 36379, 36395, 36399, 36414, 36502, 36511, 36537, 36548, 36569, 36580, 38834, 38888, 39603, 39668, 39674, 40003.
Number of centers on this line: 23056. LINE X(2)X(33)
2, 33, 1040, 1861, 3100, 9539, 9817, 34822.
Number of centers on this line: 857. LINE X(2)X(36)
2, 36, 535, 993, 1478, 3814, 3822, 4293, 5080, 5251, 5322, 6681, 7951, 10590, 20067, 24630, 24910, 26262, 27060, 27181, 27284, 27336, 27941, 27993, 28268, 28377, 29469, 29526, 29785, 30003, 30073, 30781, 30849, 30981, 31051, 31110, 31160, 31222, 31263, 40109.
Number of centers on this line: 4058. LINE X(2)X(37) L(667) Trilinear Polar of X(668)
2, 37, 75, 192, 312, 321, 344, 345, 346, 350, 536, 1229, 1267, 1278, 1575, 1646, 1997, 2276, 2277, 2345, 2397, 3175, 3210, 3263, 3290, 3644, 3666, 3672, 3693, 3739, 3752, 3772, 3797, 3995, 3998, 4000, 4037, 4043, 4261, 4358, 4359, 4441, 4452, 4461, 4479, 4506, 4657, 4664, 4671, 4681, 4686, 4687, 4688, 4698, 4699, 4704, 4718, 4726, 4739, 4740, 4751, 4755, 4764, 4772, 4788, 4812, 4821, 4850, 4908, 4980, 5391, 6351, 6352, 8026, 8031, 8620, 14470, 15956, 16085, 16602, 16610, 16706, 17147, 17263, 17264, 17278, 17279, 17280, 17281, 17289, 17301, 17302, 17303, 17320, 17321, 17322, 17341, 17342, 17356, 17357, 17358, 17359, 17370, 17371, 17382, 17383, 17384, 17385, 17399, 17400, 17459, 17490, 17495, 17720, 17737, 17740, 17756, 17759, 17776, 17787, 17790, 17862, 17863, 18046, 18137, 18147, 18743, 19785, 19786, 19787, 19788, 19789, 19790, 19791, 19792, 19793, 19794, 19795, 19796, 19797, 19798, 19799, 19800, 19801, 19802, 19803, 19804, 19805, 19806, 19807, 19808, 19809, 19810, 19811, 19812, 19813, 19814, 19815, 19816, 19817, 19818, 19819, 19820, 19821, 19822, 19823, 19824, 19825, 19826, 19827, 19828, 19829, 19830, 19831, 19832, 19833, 19834, 19835, 19837, 20171, 20173, 20284, 20286, 20336, 20440, 20453, 20530, 20891, 20892, 20905, 20923, 20942, 20946, 20947, 21264, 21814, 21820, 21877, 21883, 22016, 22034, 22040, 24004, 24326, 24357, 24403, 24530, 24547, 24554, 24589, 24620, 24789, 24873, 24874, 24919, 24944, 24958, 24993, 25001, 25034, 25036, 25067, 25091, 25099, 25243, 25245, 25368, 25384, 25392, 25399, 25457, 25470, 25480, 25498, 25505, 25535, 25584, 25660, 25753, 25757, 25780, 25785, 25811, 25817, 25834, 25850, 25856, 25887, 25895, 25922, 25939, 25942, 25971, 25975, 25995, 26011, 26014, 26042, 26077, 26107, 26143, 26163, 26165, 26178, 26191, 26213, 26215, 26234, 26242, 26274, 26538, 26567, 26587, 26591, 26612, 26632, 26635, 26665, 26669, 26724, 26764, 26797, 26812, 26850, 26971, 27011, 27032, 27073, 27102, 27136, 27154, 27192, 27205, 27217, 27226, 27238, 27245, 27261, 27268, 27291, 27311, 27343, 27396, 27514, 27544, 27565, 27569, 27586, 27603, 27605, 27619, 27633, 27641, 27671, 27697, 27705, 27727, 27747, 27754, 27851, 27886, 27890, 27906, 27918, 27924, 27974, 28003, 28022, 28023, 28052, 28054, 28072, 28087, 28090, 28113, 28128, 28130, 28244, 28358, 28366, 28395, 28416, 28420, 28439, 28604, 28605, 28606, 28653, 28673, 28676, 28705, 28709, 28748, 28778, 28803, 28808, 28830, 28930, 28936, 28957, 28974, 28978, 29001, 29388, 29396, 29423, 29446, 29484, 29542, 29705, 29712, 29756, 29764, 29802, 29885, 29887, 29906, 29909, 29982, 30044, 30090, 30699, 30748, 30758, 30791, 30818, 30829, 30861, 30892, 30903, 30931, 30963, 30998, 31025, 31035, 31077, 31087, 31130, 31197, 31228, 31233, 31238, 31497, 31993, 32774, 32777, 32779, 32791, 32792, 32793, 32794, 32795, 32796, 32797, 32798, 32799, 32800, 32801, 32802, 32803, 32804, 32849, 32851, 33113, 33116, 33129, 33133, 33150, 33155, 33157, 33168, 33889, 33891, 33931, 35652, 36268, 36281, 36288, 36847, 37756, 37758, 37759, 37788, 37857, 38312, 38313, 40001.
Number of centers on this line: 44759. LINE X(2)X(38) L(8632) Trilinear Polar of X(4562)
2, 38, 244, 291, 335, 537, 756, 982, 984, 1215, 3842, 3952, 4096, 4283, 4310, 4392, 4438, 4518, 4712, 6682, 7226, 9330, 9335, 17063, 17140, 17154, 17165, 17719, 17755, 17793, 17794, 20068, 20366, 24003, 24325, 24349, 24629, 24631, 24911, 24923, 25024, 25539, 25688, 25832, 25873, 25874, 25916, 25929, 25944, 26061, 26083, 26128, 26150, 26263, 26281, 26574, 26800, 26838, 26859, 26999, 27019, 27061, 27080, 27128, 27182, 27285, 27298, 27351, 27409, 27422, 27538, 27549, 27658, 27680, 27724, 27777, 27942, 28010, 28269, 28288, 28403, 28772, 28837, 29416, 29431, 29470, 29494, 29527, 29550, 29741, 29786, 29813, 30004, 30028, 30074, 30099, 30800, 30801, 30850, 30869, 30925, 30936, 30982, 31005, 31052, 31063, 31111, 31115, 31161, 31178, 31223, 31264, 31302, 31317, 31323, 31349, 32771, 32775, 32780, 32931, 32937, 33115, 33119, 33123, 33127, 33130, 33144, 33148, 33153, 33159, 33163, 33166, 33170, 33888, 40092, 40155, 40217, 40328, 40533.
Number of centers on this line: 13960. LINE X(2)X(39) L(669) Trilinear Polar of X(670)
2, 39, 76, 194, 274, 305, 310, 538, 980, 1180, 1194, 1196, 1228, 1230, 1645, 1655, 2229, 2396, 3117, 3229, 3266, 3291, 3767, 3788, 3926, 3934, 3948, 3978, 4352, 5283, 5286, 5309, 6294, 6309, 6314, 6318, 6392, 6581, 6683, 7739, 7746, 7757, 7763, 7769, 7786, 7795, 7797, 7799, 7801, 7803, 7817, 7822, 7827, 7828, 7832, 7834, 7836, 7852, 7859, 7870, 7874, 7880, 7884, 7886, 7915, 7930, 7932, 7940, 7942, 7943, 7945, 8024, 8149, 8267, 8569, 8891, 8962, 9464, 9465, 9466, 9492, 9764, 9865, 9887, 11052, 11054, 11055, 11056, 11059, 13085, 14472, 14568, 14700, 14711, 15302, 16084, 16589, 16705, 16711, 16712, 16748, 16749, 16750, 16752, 18135, 18140, 18145, 18146, 18152, 18153, 18600, 18768, 19568, 19570, 19577, 20023, 20081, 20105, 20913, 21838, 22254, 22868, 22913, 23106, 24548, 24555, 24598, 24621, 24891, 24897, 24945, 24994, 25002, 25021, 25458, 25499, 25506, 25657, 25661, 25754, 25758, 25781, 25786, 25812, 25818, 25835, 25851, 25857, 25888, 25896, 25976, 26035, 26043, 26100, 26108, 26164, 26166, 26179, 26192, 26199, 26214, 26216, 26235, 26539, 26541, 26569, 26588, 26592, 26633, 26636, 26666, 26765, 26770, 26813, 26852, 26972, 26978, 27033, 27040, 27103, 27109, 27137, 27155, 27162, 27262, 27269, 27312, 27318, 27390, 27397, 27515, 27523, 27566, 27570, 27606, 27634, 27642, 27672, 27698, 27706, 27729, 27748, 27755, 27772, 27852, 27853, 27887, 27891, 27925, 27966, 27975, 28004, 28088, 28129, 28245, 28359, 28367, 28397, 28417, 28441, 28660, 28674, 28677, 28691, 28706, 28710, 28728, 28749, 28809, 28931, 28937, 28975, 29397, 29425, 29447, 29454, 29486, 29544, 29706, 29713, 29736, 29757, 29765, 29805, 29886, 29888, 29907, 29910, 29974, 29983, 30022, 30045, 30054, 30092, 30599, 30749, 30793, 30819, 30830, 30863, 30893, 30904, 30933, 30955, 30964, 31000, 31008, 31026, 31036, 31060, 31078, 31088, 31198, 31234, 31239, 31276, 31400, 31401, 31455, 31981, 32189, 32450, 32526, 32530, 32828, 32829, 32830, 32831, 32832, 32833, 32834, 32835, 32836, 32837, 32838, 32839, 32840, 32841, 32867, 32868, 32869, 32870, 32871, 32872, 32873, 32874, 32875, 32876, 32877, 32878, 32879, 32880, 32881, 32882, 32883, 32884, 32885, 32886, 32887, 32888, 32889, 32890, 32891, 32892, 32893, 32894, 32895, 32896, 32897, 32898, 33452, 33453, 33466, 33467, 33482, 33483, 34020, 34254, 34284, 34511, 36212, 36270, 36336, 36338, 36350, 36358, 36373, 36378, 36393, 36398, 36812, 37803, 37804, 39576, 39593, 39784, 39785, 39998, 40022.
Number of centers on this line: 35961. LINE X(2)X(40)
2, 40, 946, 962, 3646, 5250, 6684, 8227, 11024, 14550, 16533, 20070, 24590, 25522, 26062, 26129, 26790, 26839, 27000, 27129, 27183, 28194, 28270, 30738, 31162, 31423, 31435, 34244, 34632, 38021, 38068, 39592, 39596, 39605.
Number of centers on this line: 3462. LINE X(2)X(44) L(4775) Trilinear Polar of X(4597)
2, 44, 89, 320, 3758, 3834, 4641, 4643, 4644, 4670, 4675, 4708, 4715, 4741, 4747, 4748, 4795, 4796, 4798, 5165, 6687, 16590, 17227, 17237, 17250, 17256, 17335, 17488, 20072, 20093, 24593, 24616, 24690, 24691, 24893, 24998, 25057, 25454, 25658, 25815, 25854, 25891, 26071, 26137, 26239, 26674, 26738, 26768, 26816, 26975, 27036, 27106, 27159, 27265, 27315, 27519, 27637, 27751, 27921, 27970, 28281, 28362, 28658, 28953, 29392, 29450, 29504, 29709, 29760, 29908, 29978, 30014, 30049, 30084, 30563, 30564, 30588, 30589, 30608, 30753, 30823, 30897, 30991, 31029, 31056, 31082, 31138, 31172, 31201, 31243, 32859, 33066, 36275, 37520, 39704.
Number of centers on this line: 9563. LINE X(2)X(45) L(1960) Trilinear Polar of X(4555)
2, 45, 88, 190, 545, 903, 1086, 3782, 4080, 4286, 4346, 4363, 4364, 4370, 4389, 4409, 4415, 4419, 4422, 4440, 4454, 4465, 4470, 4472, 4473, 4713, 4945, 4997, 10022, 16594, 17290, 17305, 17325, 17354, 17369, 17487, 17595, 20073, 20092, 20331, 24183, 24330, 24352, 24407, 24441, 24594, 24894, 24957, 24999, 25035, 25349, 25350, 25355, 25358, 25398, 25455, 25469, 25503, 25529, 25534, 25659, 25892, 25921, 26039, 26070, 26076, 26104, 26136, 26142, 26240, 26272, 26273, 26611, 26659, 26769, 26817, 26844, 26976, 27037, 27070, 27107, 27160, 27191, 27266, 27290, 27316, 27342, 27393, 27520, 27543, 27585, 27618, 27638, 27664, 27670, 27702, 27726, 27752, 27905, 27922, 27949, 27971, 28002, 28112, 28249, 28280, 28283, 28363, 28829, 28952, 28956, 29393, 29451, 29483, 29505, 29537, 29541, 29710, 29761, 29795, 29801, 29979, 30013, 30019, 30050, 30083, 30089, 30566, 30577, 30578, 30579, 30754, 30790, 30824, 30855, 30898, 30930, 30958, 30990, 30997, 31030, 31083, 31129, 31139, 31171, 31202, 31227, 31244, 31271, 31285, 32933, 32939, 33146, 33151, 33761, 34762, 34824, 36522, 36525, 37691, 39104, 39106, 40480.
Number of centers on this line: 16364. LINE X(2)X(51) L(3288)
2, 51, 262, 263, 373, 511, 2979, 3060, 3794, 3819, 3917, 5476, 5640, 5650, 5943, 6194, 6688, 6785, 7605, 7998, 9748, 9752, 9753, 9754, 10219, 10519, 11002, 11261, 11451, 11673, 12045, 13857, 14561, 14853, 15082, 15360, 15819, 16981, 20423, 21849, 21969, 22486, 22503, 22564, 22677, 22684, 22686, 22712, 22714, 22715, 22726, 22727, 23611, 31958, 32149, 32225, 33434, 33435, 33462, 33463, 33478, 33479, 33706, 33852, 33873, 33879, 33884, 34095, 34236, 35275, 35288, 35294, 36322, 36323, 36345, 36347, 36364, 36365, 36384, 36385, 36885, 37521, 38227, 38317, 38889.
Number of centers on this line: 8565. LINE X(2)X(54)
2, 54, 68, 96, 539, 569, 1147, 1209, 2888, 5449, 6193, 6689, 9545, 16032, 16037, 18912, 19179, 19196, 26917, 34835.
Number of centers on this line: 2066. LINE X(2)X(58)
2, 58, 540, 1330, 1724, 3454, 4340, 6693, 20077, 24632, 25526, 26064, 26131, 26266, 26841, 27185, 27232, 27412, 27660, 27946, 27996, 28273, 28775, 29473, 29530, 29789, 30077, 30759, 30851, 30984, 31113, 34281, 37522, 37693.
Number of centers on this line: 3467. LINE X(2)X(65) Trilinear Polar of X(32038)
2, 65, 959, 960, 1788, 3485, 3812, 3869, 4870, 11375, 18231, 24633, 24914, 24954, 25681, 25917, 26066, 26268, 26562, 26689, 27948, 28109, 28275, 28389, 28628, 28629, 28777, 29791, 30008, 30079, 30783, 30812, 30986, 31122, 31165, 31359, 34259, 34647, 34744.
Number of centers on this line: 3968. LINE X(2)X(66)
2, 66, 206, 1176, 5157, 5596, 6697, 8793, 16277, 18711, 20079, 21458, 24634, 26269, 28276, 29475, 29532, 30009, 30080, 30794, 31054, 31123, 31166, 31267, 33652, 40146, 40366, 40404.
Number of centers on this line: 2869. LINE X(2)X(71)
2, 71, 1246, 2282, 17220, 24308, 24310, 34830.
Number of centers on this line: 870. LINE X(2)X(74)
2, 74, 113, 146, 541, 1302, 4550, 4846, 6699, 10706, 12900, 37470, 40387.
Number of centers on this line: 1371. LINE X(2)X(77)
2, 77, 189, 223, 282, 1422, 1440, 5932, 5942, 8808, 13156, 18623, 18652, 20082, 20197, 20198, 20201, 20202, 20205, 20206, 20211, 20212, 20215, 20216, 20262, 34050, 34052, 34488, 38004, 38015.
Number of centers on this line: 3072. LINE X(2)X(80)
2, 80, 214, 2320, 5444, 6224, 6702, 17057, 19640, 20085, 37525, 38104, 40172.
Number of centers on this line: 1373. LINE X(2)X(85) L(8641) Trilinear Polar of X(4569)
2, 85, 241, 279, 348, 948, 1088, 1212, 1427, 1446, 1996, 3177, 6554, 6706, 7187, 7196, 7365, 17078, 17079, 17093, 17095, 18607, 18663, 18750, 20089, 20914, 20921, 24015, 24635, 24915, 25467, 25682, 25918, 25994, 26068, 26134, 26563, 26690, 26793, 27006, 27068, 27132, 27187, 27288, 27340, 27541, 28110, 28278, 28391, 28827, 29477, 29535, 29793, 30011, 30082, 30694, 30695, 30796, 30807, 30854, 30988, 31169, 31225, 31269, 31627, 34852, 37757, 37774, 37780.
Number of centers on this line: 6974. LINE X(2)X(92) L(1946) Trilinear Polar of X(18026)
2, 92, 273, 278, 281, 347, 587, 1214, 1441, 1465, 1880, 1948, 2405, 5089, 6349, 6350, 6360, 6708, 16090, 17073, 17080, 17086, 17913, 17917, 17923, 24035, 33572, 34062, 37695, 37790, 37798, 37799, 37800, 37805, 40149.
Number of centers on this line: 3575. LINE X(2)X(94) L(14270) Trilinear Polar of X(35139)
2, 94, 300, 301, 328, 338, 566, 1272, 1989, 2410, 2493, 14570, 15455, 18301, 18883, 21468, 21469, 30529, 30685, 34834, 34990, 36789.
Number of centers on this line: 2276. LINE X(2)X(95) L(15451) Trilinear Polar of X(18831)
2, 95, 97, 233, 275, 317, 577, 3087, 4993, 6709, 8882, 10311, 10313, 10314, 14590, 14918, 17035, 19188, 21449, 26912, 34836, 36794.
Number of centers on this line: 2277. LINE X(2)X(98) L(3569) Trilinear Polar of X(2966)
2, 98, 110, 114, 125, 147, 182, 184, 287, 542, 1352, 1899, 1976, 2001, 3047, 3410, 3448, 3506, 4027, 5012, 5182, 5613, 5617, 5622, 5642, 5651, 5921, 5967, 5972, 5984, 5985, 5986, 5987, 6036, 6054, 6055, 6230, 6231, 6721, 6723, 6770, 6771, 6773, 6774, 6776, 8593, 9140, 9143, 9306, 9544, 9744, 9759, 9775, 10168, 10334, 10352, 10353, 11003, 11005, 11161, 11177, 11178, 11179, 11180, 11442, 11579, 11653, 12177, 12192, 12827, 13029, 13031, 13198, 13414, 13415, 13642, 13654, 13761, 13774, 14177, 14181, 14355, 14683, 14826, 14834, 15059, 15462, 15595, 15920, 16187, 17974, 18800, 18911, 19662, 19905, 20021, 21243, 22112, 22507, 22509, 23234, 23291, 23293, 24206, 24619, 24981, 25046, 25533, 25559, 25560, 25562, 26075, 26141, 26848, 26913, 27668, 27866, 29481, 29540, 29734, 29799, 30789, 30859, 30995, 31127, 32135, 32235, 32618, 32619, 33430, 33431, 34761, 35021, 35279, 35912, 36213, 36318, 36319, 36320, 36344, 36362, 36363, 36382, 36383, 37527, 38064, 39141, 39805, 40330.
Number of centers on this line: 14978. LINE X(2)X(99) L(351) Trilinear Polar of X(892)
2, 99, 111, 115, 126, 148, 543, 574, 620, 671, 2482, 2549, 3734, 4045, 5106, 5461, 6719, 6722, 6772, 6775, 7615, 7617, 7618, 7619, 7620, 7621, 7622, 7664, 7665, 7790, 7820, 7835, 7844, 7913, 7919, 8178, 8302, 8303, 8566, 8585, 8591, 8596, 9166, 9167, 9172, 9877, 9885, 9886, 9888, 9890, 9892, 9894, 10418, 10487, 10717, 11162, 11185, 11648, 13162, 13653, 13773, 14061, 14360, 14609, 14832, 14931, 14971, 15268, 15269, 15300, 15482, 15483, 15560, 15563, 15871, 16093, 16276, 18362, 18546, 19911, 20094, 20099, 22247, 22568, 22570, 24271, 24275, 24296, 24617, 24636, 24918, 24956, 25468, 25530, 25683, 26072, 26138, 26197, 26198, 26564, 26691, 26794, 26845, 26849, 27008, 27062, 27071, 27133, 27189, 27415, 27665, 27669, 27771, 28001, 28111, 28282, 28392, 28437, 28438, 28690, 28725, 28726, 28828, 28954, 28998, 29420, 29479, 29482, 29538, 29731, 29735, 29796, 29800, 30015, 30018, 30085, 30088, 30786, 30856, 30860, 30927, 30929, 30992, 30996, 31057, 31059, 31125, 31128, 31274, 32480, 32815, 33432, 33433, 33460, 33461, 33476, 33477, 34481, 34760, 35022, 35369, 35606, 35690, 35691, 35692, 35693, 35694, 35695, 35696, 35697, 35903, 36521, 36523, 38862, 39103, 39105.
Number of centers on this line: 17679. LINE X(2)X(101)
2, 101, 116, 150, 544, 675, 2224, 5513, 5773, 6710, 10708, 16788, 20096, 24618, 24917, 25532, 25920, 26074, 26140, 26566, 26693, 26796, 26847, 27010, 27135, 27244, 27667, 27950, 28000, 28394, 29000, 29422, 29733, 29798, 30017, 30087, 30788, 30858, 30994, 31273, 31380, 35024.
Number of centers on this line: 4280. LINE X(2)X(102)
2, 102, 117, 151, 6711, 9056, 10709.
Number of centers on this line: 781. LINE X(2)X(103)
2, 103, 118, 152, 6712, 9057, 10710.
Number of centers on this line: 782. LINE X(2)X(104)
2, 104, 119, 153, 6713, 9058, 10269, 10711, 12115, 22758, 30513, 38069.
Number of centers on this line: 1283. LINE X(2)X(106)
2, 106, 121, 996, 4482, 6715, 9059, 10713, 16499, 20098, 21290, 24222.
Number of centers on this line: 1284. LINE X(2)X(107)
2, 107, 122, 132, 1297, 6330, 6525, 6716, 9530, 10002, 10714, 12384, 14944, 18288, 34186, 34841, 36426.
Number of centers on this line: 17