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Rational Points on Elliptic Curves: x/(y+z)+y/(z+x)+z/(x+y)=n, Y^2=X^3+(4n^2+12n-3)X^2+32(n+3)X (n \in [1..1000])

[2018.02.12]x/(y+z)+y/(z+x)+z/(x+y)=n, Y^2=X^3+(4n^2+12n-3)X^2+32(n+3)X (n \in [1..1000])の有理点

■問題
(1)与えられた非負整数nに対して、以下を満たす自然数x,y,zを求めよ。
     x/(y+z)+y/(z+x)+x/(y+z)=n ------- (*)

(2)与えられた非負整数nに対して、以下を満たす整数x,y,zを求めよ。
     Cn: x/(y+z)+y/(z+x)+x/(y+z)=n

(1)を解くためには、(2)を解くことが本筋である。
一見簡単そうな問題に見えるが、この問題は楕円曲線の有理点を求める問題に帰着できる。

■非負整数nを固定する。 　整数x,y,zの組(x,y,z)が(*)の解であれば、任意の整数t(t!=0)に対して、t(x,y,z)=(tx,ty,tz)が(*)の解であることが直ぐに分かる。

また、(*)の対称性より、x,y,zを任意に入れ替えた(x',y',z')も(*)の解である。

よって、(*)を射影平面の曲線として、その曲線上の点[x:y:z]((x,y,z)!=(0,0,0))を求めれば良い。これは、楕円曲線
     En: Y^2=X^3+(4*n^2+12*n-3)X^2+32*(n+3)*X
の有理点を求めることに、帰着される。

■射影曲線Cnと楕円曲線Enとの間の双有理変換は、簡単な計算により、以下のようになる。
     φ: Cn ----> En
     [x : y : z] ----> [X : Y : Z]
     φ([x : y : z])=[-4*(n+3)*(x+y+2*z) : 4*(n+3)*(2*n+5)*(x-y) : 6*(x+y)-z]

     ψ: En ----> Cn
     [X : Y : Z] ----> [x : y : z]
     ψ([X : Y : Z])=[X-Y-8*(n+3)*Z : X+Y-8*(n+3)*Z : 2*(n+2)*X+8*(n+3)*Z]


■楕円曲線En(n=1,...,1000)のねじれ点群を求めると、以下のようになる。
     En(Q)tors = Z/6Z (n=1, 3,..,1000)
             = Z/6Z+Z/2Z (n=2)
gp > for(n=1,1000,print("tors(E_",n,")=",elltors(ec(n))))
tors(E_1)=[6, [6], [[32, 224]]]
tors(E_2)=[12, [6, 2], [[-8, 24], [0, 0]]]
tors(E_3)=[6, [6], [[48, 528]]]
tors(E_4)=[6, [6], [[56, 728]]]
tors(E_5)=[6, [6], [[64, 960]]]
tors(E_6)=[6, [6], [[72, 1224]]]
tors(E_7)=[6, [6], [[80, 1520]]]
tors(E_8)=[6, [6], [[88, 1848]]]
tors(E_9)=[6, [6], [[96, 2208]]]
tors(E_10)=[6, [6], [[104, 2600]]]
tors(E_11)=[6, [6], [[112, 3024]]]
tors(E_12)=[6, [6], [[120, 3480]]]
tors(E_13)=[6, [6], [[128, 3968]]]
tors(E_14)=[6, [6], [[136, 4488]]]
tors(E_15)=[6, [6], [[144, 5040]]]
tors(E_16)=[6, [6], [[152, 5624]]]
tors(E_17)=[6, [6], [[160, 6240]]]
tors(E_18)=[6, [6], [[168, 6888]]]
tors(E_19)=[6, [6], [[176, 7568]]]
tors(E_20)=[6, [6], [[184, 8280]]]
tors(E_21)=[6, [6], [[192, 9024]]]
tors(E_22)=[6, [6], [[200, 9800]]]
tors(E_23)=[6, [6], [[208, 10608]]]
tors(E_24)=[6, [6], [[216, 11448]]]
tors(E_25)=[6, [6], [[224, 12320]]]
tors(E_26)=[6, [6], [[232, 13224]]]
tors(E_27)=[6, [6], [[240, 14160]]]
tors(E_28)=[6, [6], [[248, 15128]]]
tors(E_29)=[6, [6], [[256, 16128]]]
tors(E_30)=[6, [6], [[264, 17160]]]
tors(E_31)=[6, [6], [[272, 18224]]]
tors(E_32)=[6, [6], [[280, 19320]]]
tors(E_33)=[6, [6], [[288, 20448]]]
tors(E_34)=[6, [6], [[296, 21608]]]
tors(E_35)=[6, [6], [[304, 22800]]]
tors(E_36)=[6, [6], [[312, 24024]]]
tors(E_37)=[6, [6], [[320, 25280]]]
tors(E_38)=[6, [6], [[328, 26568]]]
tors(E_39)=[6, [6], [[336, 27888]]]
tors(E_40)=[6, [6], [[344, 29240]]]
tors(E_41)=[6, [6], [[352, 30624]]]
tors(E_42)=[6, [6], [[360, 32040]]]
tors(E_43)=[6, [6], [[368, 33488]]]
tors(E_44)=[6, [6], [[376, 34968]]]
tors(E_45)=[6, [6], [[384, 36480]]]
tors(E_46)=[6, [6], [[392, 38024]]]
tors(E_47)=[6, [6], [[400, 39600]]]
tors(E_48)=[6, [6], [[408, 41208]]]
tors(E_49)=[6, [6], [[416, 42848]]]
tors(E_50)=[6, [6], [[424, 44520]]]
tors(E_51)=[6, [6], [[432, 46224]]]
tors(E_52)=[6, [6], [[440, 47960]]]
tors(E_53)=[6, [6], [[448, 49728]]]
tors(E_54)=[6, [6], [[456, 51528]]]
tors(E_55)=[6, [6], [[464, 53360]]]
tors(E_56)=[6, [6], [[472, 55224]]]
tors(E_57)=[6, [6], [[480, 57120]]]
tors(E_58)=[6, [6], [[488, 59048]]]
tors(E_59)=[6, [6], [[496, 61008]]]
tors(E_60)=[6, [6], [[504, 63000]]]
tors(E_61)=[6, [6], [[512, 65024]]]
tors(E_62)=[6, [6], [[520, 67080]]]
tors(E_63)=[6, [6], [[528, 69168]]]
tors(E_64)=[6, [6], [[536, 71288]]]
tors(E_65)=[6, [6], [[544, 73440]]]
tors(E_66)=[6, [6], [[552, 75624]]]
tors(E_67)=[6, [6], [[560, 77840]]]
tors(E_68)=[6, [6], [[568, 80088]]]
tors(E_69)=[6, [6], [[576, 82368]]]
tors(E_70)=[6, [6], [[584, 84680]]]
tors(E_71)=[6, [6], [[592, 87024]]]
tors(E_72)=[6, [6], [[600, 89400]]]
tors(E_73)=[6, [6], [[608, 91808]]]
tors(E_74)=[6, [6], [[616, 94248]]]
tors(E_75)=[6, [6], [[624, 96720]]]
tors(E_76)=[6, [6], [[632, 99224]]]
tors(E_77)=[6, [6], [[640, 101760]]]
tors(E_78)=[6, [6], [[648, 104328]]]
tors(E_79)=[6, [6], [[656, 106928]]]
tors(E_80)=[6, [6], [[664, 109560]]]
tors(E_81)=[6, [6], [[672, 112224]]]
tors(E_82)=[6, [6], [[680, 114920]]]
tors(E_83)=[6, [6], [[688, 117648]]]
tors(E_84)=[6, [6], [[696, 120408]]]
tors(E_85)=[6, [6], [[704, 123200]]]
tors(E_86)=[6, [6], [[712, 126024]]]
tors(E_87)=[6, [6], [[720, 128880]]]
tors(E_88)=[6, [6], [[728, 131768]]]
tors(E_89)=[6, [6], [[736, 134688]]]
tors(E_90)=[6, [6], [[744, 137640]]]
tors(E_91)=[6, [6], [[752, 140624]]]
tors(E_92)=[6, [6], [[760, 143640]]]
tors(E_93)=[6, [6], [[768, 146688]]]
tors(E_94)=[6, [6], [[776, 149768]]]
tors(E_95)=[6, [6], [[784, 152880]]]
tors(E_96)=[6, [6], [[792, 156024]]]
tors(E_97)=[6, [6], [[800, 159200]]]
tors(E_98)=[6, [6], [[808, 162408]]]
tors(E_99)=[6, [6], [[816, 165648]]]
tors(E_100)=[6, [6], [[824, 168920]]]
tors(E_101)=[6, [6], [[832, 172224]]]
tors(E_102)=[6, [6], [[840, 175560]]]
tors(E_103)=[6, [6], [[848, 178928]]]
tors(E_104)=[6, [6], [[856, 182328]]]
tors(E_105)=[6, [6], [[864, 185760]]]
tors(E_106)=[6, [6], [[872, 189224]]]
tors(E_107)=[6, [6], [[880, 192720]]]
tors(E_108)=[6, [6], [[888, 196248]]]
tors(E_109)=[6, [6], [[896, 199808]]]
tors(E_110)=[6, [6], [[904, 203400]]]
tors(E_111)=[6, [6], [[912, 207024]]]
tors(E_112)=[6, [6], [[920, 210680]]]
tors(E_113)=[6, [6], [[928, 214368]]]
tors(E_114)=[6, [6], [[936, 218088]]]
tors(E_115)=[6, [6], [[944, 221840]]]
tors(E_116)=[6, [6], [[952, 225624]]]
tors(E_117)=[6, [6], [[960, 229440]]]
tors(E_118)=[6, [6], [[968, 233288]]]
tors(E_119)=[6, [6], [[976, 237168]]]
tors(E_120)=[6, [6], [[984, 241080]]]
tors(E_121)=[6, [6], [[992, 245024]]]
tors(E_122)=[6, [6], [[1000, 249000]]]
tors(E_123)=[6, [6], [[1008, 253008]]]
tors(E_124)=[6, [6], [[1016, 257048]]]
tors(E_125)=[6, [6], [[1024, 261120]]]
tors(E_126)=[6, [6], [[1032, 265224]]]
tors(E_127)=[6, [6], [[1040, 269360]]]
tors(E_128)=[6, [6], [[1048, 273528]]]
tors(E_129)=[6, [6], [[1056, 277728]]]
tors(E_130)=[6, [6], [[1064, 281960]]]
tors(E_131)=[6, [6], [[1072, 286224]]]
tors(E_132)=[6, [6], [[1080, 290520]]]
tors(E_133)=[6, [6], [[1088, 294848]]]
tors(E_134)=[6, [6], [[1096, 299208]]]
tors(E_135)=[6, [6], [[1104, 303600]]]
tors(E_136)=[6, [6], [[1112, 308024]]]
tors(E_137)=[6, [6], [[1120, 312480]]]
tors(E_138)=[6, [6], [[1128, 316968]]]
tors(E_139)=[6, [6], [[1136, 321488]]]
tors(E_140)=[6, [6], [[1144, 326040]]]
tors(E_141)=[6, [6], [[1152, 330624]]]
tors(E_142)=[6, [6], [[1160, 335240]]]
tors(E_143)=[6, [6], [[1168, 339888]]]
tors(E_144)=[6, [6], [[1176, 344568]]]
tors(E_145)=[6, [6], [[1184, 349280]]]
tors(E_146)=[6, [6], [[1192, 354024]]]
tors(E_147)=[6, [6], [[1200, 358800]]]
tors(E_148)=[6, [6], [[1208, 363608]]]
tors(E_149)=[6, [6], [[1216, 368448]]]
tors(E_150)=[6, [6], [[1224, 373320]]]
tors(E_151)=[6, [6], [[1232, 378224]]]
tors(E_152)=[6, [6], [[1240, 383160]]]
tors(E_153)=[6, [6], [[1248, 388128]]]
tors(E_154)=[6, [6], [[1256, 393128]]]
tors(E_155)=[6, [6], [[1264, 398160]]]
tors(E_156)=[6, [6], [[1272, 403224]]]
tors(E_157)=[6, [6], [[1280, 408320]]]
tors(E_158)=[6, [6], [[1288, 413448]]]
tors(E_159)=[6, [6], [[1296, 418608]]]
tors(E_160)=[6, [6], [[1304, 423800]]]
tors(E_161)=[6, [6], [[1312, 429024]]]
tors(E_162)=[6, [6], [[1320, 434280]]]
tors(E_163)=[6, [6], [[1328, 439568]]]
tors(E_164)=[6, [6], [[1336, 444888]]]
tors(E_165)=[6, [6], [[1344, 450240]]]
tors(E_166)=[6, [6], [[1352, 455624]]]
tors(E_167)=[6, [6], [[1360, 461040]]]
tors(E_168)=[6, [6], [[1368, 466488]]]
tors(E_169)=[6, [6], [[1376, 471968]]]
tors(E_170)=[6, [6], [[1384, 477480]]]
tors(E_171)=[6, [6], [[1392, 483024]]]
tors(E_172)=[6, [6], [[1400, 488600]]]
tors(E_173)=[6, [6], [[1408, 494208]]]
tors(E_174)=[6, [6], [[1416, 499848]]]
tors(E_175)=[6, [6], [[1424, 505520]]]
tors(E_176)=[6, [6], [[1432, 511224]]]
tors(E_177)=[6, [6], [[1440, 516960]]]
tors(E_178)=[6, [6], [[1448, 522728]]]
tors(E_179)=[6, [6], [[1456, 528528]]]
tors(E_180)=[6, [6], [[1464, 534360]]]
tors(E_181)=[6, [6], [[1472, 540224]]]
tors(E_182)=[6, [6], [[1480, 546120]]]
tors(E_183)=[6, [6], [[1488, 552048]]]
tors(E_184)=[6, [6], [[1496, 558008]]]
tors(E_185)=[6, [6], [[1504, 564000]]]
tors(E_186)=[6, [6], [[1512, 570024]]]
tors(E_187)=[6, [6], [[1520, 576080]]]
tors(E_188)=[6, [6], [[1528, 582168]]]
tors(E_189)=[6, [6], [[1536, 588288]]]
tors(E_190)=[6, [6], [[1544, 594440]]]
tors(E_191)=[6, [6], [[1552, 600624]]]
tors(E_192)=[6, [6], [[1560, 606840]]]
tors(E_193)=[6, [6], [[1568, 613088]]]
tors(E_194)=[6, [6], [[1576, 619368]]]
tors(E_195)=[6, [6], [[1584, 625680]]]
tors(E_196)=[6, [6], [[1592, 632024]]]
tors(E_197)=[6, [6], [[1600, 638400]]]
tors(E_198)=[6, [6], [[1608, 644808]]]
tors(E_199)=[6, [6], [[1616, 651248]]]
tors(E_200)=[6, [6], [[1624, 657720]]]
tors(E_201)=[6, [6], [[1632, 664224]]]
tors(E_202)=[6, [6], [[1640, 670760]]]
tors(E_203)=[6, [6], [[1648, 677328]]]
tors(E_204)=[6, [6], [[1656, 683928]]]
tors(E_205)=[6, [6], [[1664, 690560]]]
tors(E_206)=[6, [6], [[1672, 697224]]]
tors(E_207)=[6, [6], [[1680, 703920]]]
tors(E_208)=[6, [6], [[1688, 710648]]]
tors(E_209)=[6, [6], [[1696, 717408]]]
tors(E_210)=[6, [6], [[1704, 724200]]]
tors(E_211)=[6, [6], [[1712, 731024]]]
tors(E_212)=[6, [6], [[1720, 737880]]]
tors(E_213)=[6, [6], [[1728, 744768]]]
tors(E_214)=[6, [6], [[1736, 751688]]]
tors(E_215)=[6, [6], [[1744, 758640]]]
tors(E_216)=[6, [6], [[1752, 765624]]]
tors(E_217)=[6, [6], [[1760, 772640]]]
tors(E_218)=[6, [6], [[1768, 779688]]]
tors(E_219)=[6, [6], [[1776, 786768]]]
tors(E_220)=[6, [6], [[1784, 793880]]]
tors(E_221)=[6, [6], [[1792, 801024]]]
tors(E_222)=[6, [6], [[1800, 808200]]]
tors(E_223)=[6, [6], [[1808, 815408]]]
tors(E_224)=[6, [6], [[1816, 822648]]]
tors(E_225)=[6, [6], [[1824, 829920]]]
tors(E_226)=[6, [6], [[1832, 837224]]]
tors(E_227)=[6, [6], [[1840, 844560]]]
tors(E_228)=[6, [6], [[1848, 851928]]]
tors(E_229)=[6, [6], [[1856, 859328]]]
tors(E_230)=[6, [6], [[1864, 866760]]]
tors(E_231)=[6, [6], [[1872, 874224]]]
tors(E_232)=[6, [6], [[1880, 881720]]]
tors(E_233)=[6, [6], [[1888, 889248]]]
tors(E_234)=[6, [6], [[1896, 896808]]]
tors(E_235)=[6, [6], [[1904, 904400]]]
tors(E_236)=[6, [6], [[1912, 912024]]]
tors(E_237)=[6, [6], [[1920, 919680]]]
tors(E_238)=[6, [6], [[1928, 927368]]]
tors(E_239)=[6, [6], [[1936, 935088]]]
tors(E_240)=[6, [6], [[1944, 942840]]]
tors(E_241)=[6, [6], [[1952, 950624]]]
tors(E_242)=[6, [6], [[1960, 958440]]]
tors(E_243)=[6, [6], [[1968, 966288]]]
tors(E_244)=[6, [6], [[1976, 974168]]]
tors(E_245)=[6, [6], [[1984, 982080]]]
tors(E_246)=[6, [6], [[1992, 990024]]]
tors(E_247)=[6, [6], [[2000, 998000]]]
tors(E_248)=[6, [6], [[2008, 1006008]]]
tors(E_249)=[6, [6], [[2016, 1014048]]]
tors(E_250)=[6, [6], [[2024, 1022120]]]
tors(E_251)=[6, [6], [[2032, 1030224]]]
tors(E_252)=[6, [6], [[2040, 1038360]]]
tors(E_253)=[6, [6], [[2048, 1046528]]]
tors(E_254)=[6, [6], [[2056, 1054728]]]
tors(E_255)=[6, [6], [[2064, 1062960]]]
tors(E_256)=[6, [6], [[2072, 1071224]]]
tors(E_257)=[6, [6], [[2080, 1079520]]]
tors(E_258)=[6, [6], [[2088, 1087848]]]
tors(E_259)=[6, [6], [[2096, 1096208]]]
tors(E_260)=[6, [6], [[2104, 1104600]]]
tors(E_261)=[6, [6], [[2112, 1113024]]]
tors(E_262)=[6, [6], [[2120, 1121480]]]
tors(E_263)=[6, [6], [[2128, 1129968]]]
tors(E_264)=[6, [6], [[2136, 1138488]]]
tors(E_265)=[6, [6], [[2144, 1147040]]]
tors(E_266)=[6, [6], [[2152, 1155624]]]
tors(E_267)=[6, [6], [[2160, 1164240]]]
tors(E_268)=[6, [6], [[2168, 1172888]]]
tors(E_269)=[6, [6], [[2176, 1181568]]]
tors(E_270)=[6, [6], [[2184, 1190280]]]
tors(E_271)=[6, [6], [[2192, 1199024]]]
tors(E_272)=[6, [6], [[2200, 1207800]]]
tors(E_273)=[6, [6], [[2208, 1216608]]]
tors(E_274)=[6, [6], [[2216, 1225448]]]
tors(E_275)=[6, [6], [[2224, 1234320]]]
tors(E_276)=[6, [6], [[2232, 1243224]]]
tors(E_277)=[6, [6], [[2240, 1252160]]]
tors(E_278)=[6, [6], [[2248, 1261128]]]
tors(E_279)=[6, [6], [[2256, 1270128]]]
tors(E_280)=[6, [6], [[2264, 1279160]]]
tors(E_281)=[6, [6], [[2272, 1288224]]]
tors(E_282)=[6, [6], [[2280, 1297320]]]
tors(E_283)=[6, [6], [[2288, 1306448]]]
tors(E_284)=[6, [6], [[2296, 1315608]]]
tors(E_285)=[6, [6], [[2304, 1324800]]]
tors(E_286)=[6, [6], [[2312, 1334024]]]
tors(E_287)=[6, [6], [[2320, 1343280]]]
tors(E_288)=[6, [6], [[2328, 1352568]]]
tors(E_289)=[6, [6], [[2336, 1361888]]]
tors(E_290)=[6, [6], [[2344, 1371240]]]
tors(E_291)=[6, [6], [[2352, 1380624]]]
tors(E_292)=[6, [6], [[2360, 1390040]]]
tors(E_293)=[6, [6], [[2368, 1399488]]]
tors(E_294)=[6, [6], [[2376, 1408968]]]
tors(E_295)=[6, [6], [[2384, 1418480]]]
tors(E_296)=[6, [6], [[2392, 1428024]]]
tors(E_297)=[6, [6], [[2400, 1437600]]]
tors(E_298)=[6, [6], [[2408, 1447208]]]
tors(E_299)=[6, [6], [[2416, 1456848]]]
tors(E_300)=[6, [6], [[2424, 1466520]]]
tors(E_301)=[6, [6], [[2432, 1476224]]]
tors(E_302)=[6, [6], [[2440, 1485960]]]
tors(E_303)=[6, [6], [[2448, 1495728]]]
tors(E_304)=[6, [6], [[2456, 1505528]]]
tors(E_305)=[6, [6], [[2464, 1515360]]]
tors(E_306)=[6, [6], [[2472, 1525224]]]
tors(E_307)=[6, [6], [[2480, 1535120]]]
tors(E_308)=[6, [6], [[2488, 1545048]]]
tors(E_309)=[6, [6], [[2496, 1555008]]]
tors(E_310)=[6, [6], [[2504, 1565000]]]
tors(E_311)=[6, [6], [[2512, 1575024]]]
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tors(E_977)=[6, [6], [[7840, 15358560]]]
tors(E_978)=[6, [6], [[7848, 15389928]]]
tors(E_979)=[6, [6], [[7856, 15421328]]]
tors(E_980)=[6, [6], [[7864, 15452760]]]
tors(E_981)=[6, [6], [[7872, 15484224]]]
tors(E_982)=[6, [6], [[7880, 15515720]]]
tors(E_983)=[6, [6], [[7888, 15547248]]]
tors(E_984)=[6, [6], [[7896, 15578808]]]
tors(E_985)=[6, [6], [[7904, 15610400]]]
tors(E_986)=[6, [6], [[7912, 15642024]]]
tors(E_987)=[6, [6], [[7920, 15673680]]]
tors(E_988)=[6, [6], [[7928, 15705368]]]
tors(E_989)=[6, [6], [[7936, 15737088]]]
tors(E_990)=[6, [6], [[7944, 15768840]]]
tors(E_991)=[6, [6], [[7952, 15800624]]]
tors(E_992)=[6, [6], [[7960, 15832440]]]
tors(E_993)=[6, [6], [[7968, 15864288]]]
tors(E_994)=[6, [6], [[7976, 15896168]]]
tors(E_995)=[6, [6], [[7984, 15928080]]]
tors(E_996)=[6, [6], [[7992, 15960024]]]
tors(E_997)=[6, [6], [[8000, 15992000]]]
tors(E_998)=[6, [6], [[8008, 16024008]]]
tors(E_999)=[6, [6], [[8016, 16056048]]]
tors(E_1000)=[6, [6], [[8024, 16088120]]]
time = 162 ms.
n=2のとき、楕円曲線E2の位数2のねじれ点は、[0,0],[-5,0],[-32,0],[0:1:0](無限遠点)の4個である。

■楕円曲線Enのねじれ点の1つは、位数6の元
     Tn=[8*(n+3) : 8*(n+3)*(2*n+5) : 1]
である。
[2]Tn,...,[6]Tnを求めると、以下のようになる。

     [2]Tn=[4 : 4*(2*n+5) : 1]
     [3]Tn=[0 : 0 : 1]
     [4]Tn=[4 : -4*(2*n+5) : 1]
     [5]Tn=[8*(n+3) : -8*(n+3)*(2*n+5) : 1]
     [6]Tn=[0 : 1 : 0] (無限遠点)
よって、楕円曲線Enのねじれ点群En(Q)torsは、位数6の巡回群Z/6Zを部分群として含む。

これらのねじれ点を双有理変換ψでCnに移すことにより、Cnのねじれ点を求めることができる。
     ψ(Tn)=[-1 : 1 : 1]
     ψ([2]Tn)=[-1 : 0 : 1]
     ψ([3]Tn)=[-1 : -1 : 1]
     ψ([4]Tn)=[0 : 1 : 1]
     ψ([5]Tn)=[1 : -1 : 1]
     ψ([6]Tn)=[-1 : 1 : 0] (無限遠点)

■参考文献[3](Theorem 4.1)によると、曲線Cnの有理点[a:b:c]とEnの有理点(x,y)が対応するならば、
     a,b,c > 0
     　　 ⇔　
     (3-13n-4n2-(2n+5)sqrt(4n2+4n-15))/2 < x < -2(n+3)(n+sqrt(n2+4))
         または、
     -2(n+3)(n-sqrt(n2-4)) < x < -4(n+3)/(n+2)

同じく、参考文献[3](Theorem 5.1)によると、nが奇数の場合、Enの有理点(x,y)のx座標はx >= 0を満たすので、(*)は自然数解を持たない。

よって、(*)の自然数解を求めるためには、nが偶数の場合のみ、調べれば良い。


■1000以下の非負整数nに対して、(*)の整数解、自然数解を求める。
CremonaのmwrankまたはMAGMA 4-descentプログラムにより、楕円曲線EnのMordell-Weil群En(Q)の自由部分群の基底を求める。
En(Q)の自由部分群の基底とねじれ点群En(Q)torsの6元(対称性を考慮すると、実際に必要なのは、無限遠点[0:1:0]とTnの２元だけで良い)から、有理点を求めることができる。
これらを双有理変換ψによって、射影曲線Cn上の有理点[x:y:z]に写して、x,y,zがすべて正整数になるものを見つけると、(*)の自然数解が求まる。

例えば、n=4の場合、Cremonaのmwrankにより、楕円曲線E4はrank 1で、Mordell-Weil群E4(Q)の生成元は、
     P=[-100 : 260 : 1]
である。また、ねじれ点群E4(Q)torsの生成元は、位数6の
     T4 = [56 : 728 : 1]
である。射影曲線C4の最も高さの低い有理点は、[x:y:z]のx,y,zを入れ替えたものを除くと、以下の2つである。
     ψ(P)=[4 : 1 : -11]
     ψ(P+T4)=[-5 : 9 : 11]

また、m=1,2,...に対して、C4の有理点ψ([m]P),ψ([m]P+T)で、x,y,zがすべて正整数になるものを探すと、(*)の自然数解
     ψ([9]P)=[154476802108746166441951315019919837485664325669565431700026634898253202035277999 : 36875131794129999827197811565225474825492979968971970996283137471637224634055579 : 4373612677928697257861252602371390152816537558161613618621437993378423467772036]
が見つかる。
[pari/gpによる実行例]
(20:23) gp > e=ec(4)
%1 = [0, 109, 0, 224, 0, 436, 448, 0, -50176, 179344, -75850048, 8818933760, 1408317602329/2153060, Vecsmall([1]), [Vecsmall([96, 1])], [0, 0, 0, 0, 0, 0, 0, 0]]
(20:23) gp > P=[-100,260]
%2 = [-100, 260]
(20:23) gp > T=[56,728]
%3 = [56, 728]
(20:23) gp > pps([-100,260,1],4)
%4 = [4, -1, 11]
(20:27) gp > C(4,-1,11)
%5 = 4
(20:27) gp > elladd(e,P,T)
%6 = [-56, -392]
(20:27) gp > pps([-56,-392,1],4)
%7 = [-5, 9, 11]
(20:27) gp > C(-5,9,11)
%8 = 4
(20:27) gp > ss(4,[-100,260],10,200)
torsion point T=[56, 728, 1]
generator P=[-100, 260, 1]
R=[4, -1, 11]
R+T=[-5, 9, 11]
[9]R=[154476802108746166441951315019919837485664325669565431700026634898253202035277999, 36875131794129999827197811565225474825492979968971970996283137471637224634055579, 4373612677928697257861252602371390152816537558161613618621437993378423467772036]
time = 4 ms.
%9 = 9
(20:28) gp > Q=ellpow(e,P,9)
%10 = [-66202368404229585264842409883878874707453676645038225/13514400292716288512070907945002943352692578000406921, 58800835157308083307376751727347181330085672850296730351871748713307988700611210/1571068668597978434556364707291896268838086945430031322196754390420280407346469]
(20:30) gp > ps(elladd(e,Q,ellpow(e,T,1)),4)
%11 = [149873336803401113247625861581739438102261891754592894935710516699882406130045705/137211312120705701411473512317968603024979592973551357146751192967446785917250491, -75325962525379922497547802683539615501464274037547624568031470107460639959387061/137211312120705701411473512317968603024979592973551357146751192967446785917250491]
(20:30) gp > ps(elladd(e,Q,ellpow(e,T,2)),4)
%12 = [36875131794129999827197811565225474825492979968971970996283137471637224634055579/154476802108746166441951315019919837485664325669565431700026634898253202035277999, 4373612677928697257861252602371390152816537558161613618621437993378423467772036/154476802108746166441951315019919837485664325669565431700026634898253202035277999]
(20:30) gp > ps(elladd(e,Q,ellpow(e,T,3)),4)
%13 = [-75325962525379922497547802683539615501464274037547624568031470107460639959387061/149873336803401113247625861581739438102261891754592894935710516699882406130045705, 137211312120705701411473512317968603024979592973551357146751192967446785917250491/149873336803401113247625861581739438102261891754592894935710516699882406130045705]
(20:30) gp > ps(elladd(e,Q,ellpow(e,T,4)),4)
%14 = [4373612677928697257861252602371390152816537558161613618621437993378423467772036/36875131794129999827197811565225474825492979968971970996283137471637224634055579, 154476802108746166441951315019919837485664325669565431700026634898253202035277999/36875131794129999827197811565225474825492979968971970996283137471637224634055579]
(20:30) gp > ps(elladd(e,Q,ellpow(e,T,5)),4)
%15 = [-137211312120705701411473512317968603024979592973551357146751192967446785917250491/75325962525379922497547802683539615501464274037547624568031470107460639959387061, -149873336803401113247625861581739438102261891754592894935710516699882406130045705/75325962525379922497547802683539615501464274037547624568031470107460639959387061]
(20:31) gp > ps(elladd(e,Q,ellpow(e,T,6)),4)
%16 = [154476802108746166441951315019919837485664325669565431700026634898253202035277999/4373612677928697257861252602371390152816537558161613618621437993378423467772036, 36875131794129999827197811565225474825492979968971970996283137471637224634055579/4373612677928697257861252602371390152816537558161613618621437993378423467772036]
(20:31) gp > pp(%16)
%17 = [154476802108746166441951315019919837485664325669565431700026634898253202035277999, 36875131794129999827197811565225474825492979968971970996283137471637224634055579, 4373612677928697257861252602371390152816537558161613618621437993378423467772036]
(20:32) gp > pp(%12)
%18 = [36875131794129999827197811565225474825492979968971970996283137471637224634055579, 4373612677928697257861252602371390152816537558161613618621437993378423467772036, 154476802108746166441951315019919837485664325669565431700026634898253202035277999]
(20:32) gp > pp(%14)
%19 = [4373612677928697257861252602371390152816537558161613618621437993378423467772036, 154476802108746166441951315019919837485664325669565431700026634898253202035277999, 36875131794129999827197811565225474825492979968971970996283137471637224634055579]


偶数n(0 ≤ n ≤ 1000)に対して、この方法で、(*)の自然数解[x:y:z]を求めることができなかったものは、
     40,44,50,68,80,104,106,110,124,128, 170,176,180,216,220,224,226,230,234,236,
     238,248,254,256,260,274,290,320,324,328, 330,334,342,346,358,360,370,372,380,382,
     386,390,394,398,404,408,410,420,422,428, 438,440,442,444,450,452,454,458,460,468,
     484,488,490,498,500,524,526,530,534,536, 538,540,544,554,562,564,568,572,598,600,
     602,612,616,622,626,628,630,634,636,644, 650,660,664,670,680,684,688,690,692,698,
     710,714,718,722,726,730,732,736,744,746, 750,754,756,758,762,766,768,
     774,776,778,784,790,794,796,798,802,806, 808,810,812,818,820,824,828,
     832,838,840,846,850,852,860,866,874,876, 880,882,884,886,890,894,896,
     898,900,902,904,906,908,912,916,918,920, 924,928,932,938,946,948,952,
     954,960,966,972,976,984,992,996,998,1000
の190個である。
(2018.02.12計算開始)


- En: Y2Z=X3+(4n2+12n-3)X2Z+32(n+3)XZ2
En(Q)tors=Z/6Z if n!=2;
              =Z/2Z+Z/6Z if n=2
Tn=[8*(n+3) : 8*(n+3)*(2n+5) : 1]
φ:Cn → En
φ([x:y:z])=[-4*(n+3)*(x+y+2*z) : 4*(n+3)*(2*n+5)*(x-y) : 6*(x+y)-z)]
 Cn: x/(y+z)+y/(z+x)+z/(x+y)=n
Cn(Q)tors=Z/6Z if n!=2
              =Z/2Z+Z/6Z if n=2
TC=ψ(Tn)=[-1 : 1 : 1]
ψ:En → Cn
ψ([X:Y:Z])=[X-Y-8*(n+3)*Z : X+Y-8*(n+3)*Z : 2*(n+2)*X+32*Z]
 -
n [a1, a2, a3, a4, a6]
En(Q)torsの生成元Tn
conductor(En)
 rank(En) En(Q)/En(Q)torsの生成元[X:Y:Z]
P=P1,P2,P3,...
 En(Q)/En(Q)torsの生成元の高さ Cn(Q)/Cn(Q)torsの生成元[x:y:z]
Q=Q1,Q2,Q3,...
 [x:y:z]+TC
 [m]Q1+[k]Q2+[j]Q3+[i]TC= [x:y:z] where x,y,z > 0
 [x:y:z](where x,y,z > 0)の高さ
height(En,φ([x:y:z]))
 n
0 [0, -3, 0, 96, 0]
[24, 120]
90
 0 - - - - - - 0
1 [0, 13, 0, 128, 0]
[32, 224]
14
 0 - - - - - - 1
2 [0, 37, 0, 160, 0]
[0, 0],[-8, 24]
30
 0 - - - - T1C=[3 : 1 : 1] 0 2
3 [0, 69, 0, 192, 0]
[48, 528]
198
 0 - - - - - - 3
4 [0, 109, 0, 224, 0]
[56, 728]
910
 1 [-100 : 260 : 1] 1.51870218672685 [4 : -1 : 11] [-5 : 9 : 11] [9]Q= [154476802108746166441951315019919837485664325669565431700026634898253202035277999 : 36875131794129999827197811565225474825492979968971970996283137471637224634055579 : 4373612677928697257861252602371390152816537558161613618621437993378423467772036],
 [13]Q+TC= [184386514670723295219914666691038096275031765336404340516686430257803895506237580602582859039981257570380161221662398153794290821569045182385603418867509209632768359835 : 32343421153825592353880655285224263330451946573450847101645239147091638517651250940206853612606768544181415355352136077327300271806129063833025389772729796460799697289 : 16666476865438449865846131095313531540647604679654766832109616387367203990642764342248100534807579493874453954854925352739900051220936419971671875594417036870073291371],
 [17]Q= [1440354387400113353318275132419054375891245413681864837390427511212805748408072838847944629793120889446685643108530381465382074956451566809039119353657601240377236701038904980199109550001860607309184336719930229935342817546146083848277758428344831968440238907935894338978800768226766379 : 9391500403903773267688655787670246245493629218171544262747638036518222364768797479813561509116827252710188014736501391120827705790025300419608858224262849244058466770043809014864245428958116544162335497194996709759345801074510016208346248254582570123358164225821298549533282498545808644 : 1054210182683112310528012408530531909717229064191793536540847847817849001214642792626066010344383473173101972948978951703027097154519698536728956323881063669558925110120619283730835864056709609662983759100063333396875182094245046315497525532634764115913236450532733839386139526489824351],
 [21]Q+TC= [5054729227475450427274369484803239479825091305751388135572448603576037654978196142209886225943055713384230446118035969818320833964792478425568165426513861388534926491015921716410969570164048517748147506388402603496289958758089911825477669004739864966841494437579004665357462952425413032747439063553786897871988705969714829772337356641778138923838273632046383016843421820241871452675269925797080859944523086015293719539167125415529515145 : 23327978912047254535804038142169556127186936756095181398136756224463368530351921955206357565424226029748329737767516130520072674084336131550259761622497092797922739666348144750601917346229515778478878142030504652018159936616800590064485753155232061032607622109441379545719754978549786027663601160534574317253280344812956727894696796553762212813889660906595671851622444601557714326712873901193569743490902166958363537983235022557869209259 : 1161640217306132458900911441651415023972393417197892812143262449233898803422146346627825401856073449291322173894322476243337457486170427505800629028080349908170091219751869674513518143111011120403910142953219728784138582766210837461563508481437266175417187186208008663435889653439706655448626378444301314102088643599567233932299749952837694062004500119197352724794576882305675018438398927991642460037666142140173983786350444307965016411],
 [39]Q+TC,
[43]Q,
[47]Q+TC,
[51]Q,
[55]Q+TC,
[73]Q+TC,
[77]Q,
[85]Q,
[103]Q,
[107]Q+TC,
[111]Q,
...
 123.014877124874,
256.660669556837,
438.904931964060,
669.747664346541,
2309.94602601154,
2808.08034325794,
3354.81313047961,
3950.14438767654,
4594.07411484872,
8093.16395306739,
9964.20504711487,
10972.6232991015,
16111.9114989851,
17387.6213358357,
18711.9296426615,
 ...
 4
5 [0, 157, 0, 256, 0]
[64, 960]
210
 0 - - - - - - 5
6 [0, 213, 0, 288, 0]
[72, 1224]
306
 1 [-200 : 680 : 1] 1.68788702948038 [7 : -3 : 23] [-5 : 7 : 8] [11]Q= [20260869859883222379931520298326390700152988332214525711323500132179943287700005601210288797153868533207131302477269470450828233936557 : 2250324022012683866886426461942494811141200084921223218461967377588564477616220767789632257358521952443049813799712386367623925971447 : 1218343242702905855792264237868803223073090298310121297526752830558323845503910071851999217959704024280699759290559009162035102974023],
 [27]Q+TC,
...
 204.234330567126,
1230.46964449120,
 ...
 6
7 [0, 277, 0, 320, 0]
[80, 1520]
2090
 0 - - - - - - 7
8 [0, 349, 0, 352, 0]
[88, 1848]
6006
 0 - - - - - - 8
9 [0, 429, 0, 384, 0]
[96, 2208]
2070
 0 - - - - - - 9
10 [0, 517, 0, 416, 0]
[104, 2600]
2210
 1 [-416 : 4160 : 1] 1.72166299585030 [9 : -7 : 19] [-16 : 19 : 23] [13]Q= [269103113846520710198086599018316928810831097261381335767926880507079911347095440987749703663156874995907158014866846058485318408629957749519665987782327830143454337518378955846463785600977 : 4862378745380642626737318101484977637219057323564658907686653339599714454790559130946320953938197181210525554039710122136086190642013402927952831079021210585653078786813279351784906397934209 : 221855981602380704196804518854316541759883857932028285581812549404634844243737502744011549757448453135493556098964216532950604590733853450272184987603430882682754171300742698179931849310347],
 [39]Q,
...
 290.961046298702,
2618.64941668832,
 ...
 10
11 [0, 613, 0, 448, 0]
[112, 3024]
798
 0 - - - - - - 11
12 [0, 717, 0, 480, 0]
[120, 3480]
18270
 1 [-605 : 6380 : 1] 3.39075763351921 [49 : -39 : 116] [-187 : 215 : 247] [35]Q+TC,
...
 4153.67810106103,
 ...
 12
13 [0, 829, 0, 512, 0]
[128, 3968]
1426
 0 - - - - - - 13
14 [0, 949, 0, 544, 0]
[136, 4488]
5610
 1 [-612 : 11220 : 1] 1.30258691809007 [8 : -7 : 13] [-33 : 37 : 47] [47]Q+TC,
...
 2877.41450206098,
 ...
 14
15 [0, 1077, 0, 576, 0]
[144, 5040]
630
 0 - - - - - - 15
16 [0, 1213, 0, 608, 0]
[152, 5624]
40774
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 1 [1532644 : -275094123 : 64] 12.1699718804878 [92200901 : -91195181 : 47009104] [-80273777 : 81415905 : 76675457] ???,
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 1 [-21316 : 1106972 : 1] 8.59700068479763 [141115 : -135628 : 415583] [-377629 : 385299 : 392881] [65]Q+TC,
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[27]Q1+[11]Q2+TC,
[37]Q1+[-16]Q2,
...
 2359.40204546388,
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[34]Q1+[-3]Q2+TC,
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 1 [-945 : 193410 : 1] 5.36653589973616 [1859 : -1825 : 1864] [-339 : 391 : 5303] [423]Q,
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 1 [1724373165927130372669702381016360232365855792 : 367603091115045244835172020461595888372484901648 : 902399798148156735409874917553861923858844603] 68.0897051602764 [-335045541107451133320520215689056409825953575 : -117271198029817694437124468970101499652680529 : 333931692439080062170678741143101469262183039] [-155542404522756595318515307735346246153444273 : -157925869256774833215260758758856752611400292 : 157153940674180529296560689968009099749646957] - - 103
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 1 [503756 : 113019285 : 85184] 10.4427155070841 [-12634791 : 2434447 : 12656512] [-12455549 : -12366963 : 12419821] ???,
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 112
113 [0, 52429, 0, 3712, 0]
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2987754
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 [21]Q1,
[1]Q1+[37]Q2,
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 1 [13924 : -3962676 : 1] 5.27481869521019 [5712 : -5675 : 5203] [-2537 : 2553 : 2167] ???,
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18115930
 1 [-154453 : -40579174 : 2197] 11.4331092482069 [-38087113 : 43071235 : 38437984] [-18157547 : -20727585 : 17990159] [707]Q+TC,
...
 5714828.22460699,
 ...
 130
131 [0, 70213, 0, 4288, 0]
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 2 [98496 : -26157312 : 6859],
[173598271920 : 46362967434928 : 44928178875]
 9.39325298032009,
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702090
 1 [-16040808 : -2511331992 : 343] 11.3178982471644 [-11550559 : 11702515 : 19900769] [-28827331 : 29901229 : 29111076] [461]Q+TC,
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20714614
 1 [-70756 : -4931108 : 1] 9.78867069118935 [-607405 : 625372 : 2440943] [-2315929 : 2362039 : 2343501] [65]Q,
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 41357.1336702750,
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 136
137 [0, 76717, 0, 4480, 0]
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1764210
 1 [2465044640 : 826739957280 : 68921] 11.6400860195610 [-55400007 : 55720955 : 46059113] [-51076999 : 47673261 : 51389378] - - 137
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 [27]Q1+[5]Q2+TC,
[37]Q1+[1]Q2+TC,
...
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 ...
 144
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6265210
 1 [37926980 : 19826947868 : 1501123625] 16.9786270855110 [-224639924111 : -219683187144 : 223560113015] [-35075916421 : -62486284069 : 62249184661] - - 145
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167178
 1 [-43061 : 9027612 : 1] 4.22106853857810 [205 : -203 : 288] [-2397 : 2417 : 2513] [307]Q,
...
 397831.488692447,
 ...
 146
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 [15]Q1+[3]Q2,
[35]Q1+[9]Q2+TC,
[45]Q1+[9]Q2,
[16]Q1+[-41]Q2,
[14]Q1+[47]Q2,
[36]Q1+[-35]Q2+TC,
[65]Q1+[15]Q2+TC,
...
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 152
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 8031085.75848313,
 ...
 156
157 [0, 100477, 0, 5120, 0]
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992090
 1 [27403697245818880 : -8692671738804475904 : 344545816407625] 23.0872915956542 [1115174675518391 : -1226601116185401 : 1233215836364785] [1118787561704908 : -1112853932902373 : 987798537634457] - - 157
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32352306
 1 [-2592 : -816192 : 1] 6.86308052090276 [-101539 : 102509 : 103519] [-2952 : 8675 : 3007] [1211]Q,
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 10064851.7085948,
 ...
 158
159 [0, 103029, 0, 5184, 0]
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203490
 1 [849977388 : 286632846396 : 79507] 13.6119671664736 [-441181960 : 443487319 : 422524321] [-1367665429 : 1066139109 : 1374161611] - - 159
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 4.56458860838840,
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 [517, -513 : 623],
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 [-1505 : 1516 : 1619],
[-7979 : 8021 : 7147]
 [3]Q1+[-34]Q2,
...
 7186.88993734462,
 ...
 160
161 [0, 105613, 0, 5248, 0]
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8553666
 1 [46473326477083225044 : 31047749046429497705583 : 136400001978176] 31.3415394948687 [-284417015383073484839 : 285266453358752161135 : 138995260443410336984] [-249822148672637349939 : 246914786458417937891 : 250818688548102532099] - - 161
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34850970
 1 [-45 : -6580 : 729] 4.03820574124298 [-581 : -589 : 576] [-323 : -145 : 143] [457]Q+TC,
...
 843375.230852855,
 ...
 162
163 [0, 108229, 0, 5312, 0]
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17747558
 1 [215645393381532868 : 78131930311978758292 : 9357915116017] 28.8348543185621 [-9741089028733912000 : 9791893549260777573 : 8896925890897489627] [-4326346406220010427 : 3833897340730996027 : 4348590044973058373] - - 163
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4600890
 1 [22186486182976 : 7399681996552640 : 64432972729] 17.2584235917047 [-348138685901 : 342130157061 : 349668111029] [-93706404259 : -55418192836 : 93376720135] - - 165
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 2 [-364 : -119132 : 343],
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 5.44889043048741,
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 [-16451 : -16099 : 15975],
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 [29]Q1+[-4]Q2+TC,
[3]Q1+[-31]Q2+TC,
[27]Q1+[31]Q2,
[59]Q1+[-4]Q2,
...
 4660.03983641973,
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 ...
 166
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4315014
 0 - - - - - - 168
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 0 - - - - - - 169
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40227690
 1 [18873148 : 7842260964 : 343] 10.7556782189066 [-14173664 : 14240325 : 11762387] [-8220673 : 7777265 : 8261791] ???,
 ...
 ?,
 ...
 170
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20468142
 0 - - - - - - 171
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8330630
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43111890
 0 - - - - - - 174
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21926930
 1 [554254768 : 195777885680 : 4330747] 13.8300296547593 [-2517382683 : 2377064459 : 2529664645] [-472779011 : -394679605 : 470607688] - - 175
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44604294
 1 [10118176513142101668 : -1166673327300337388911884 : 761048497] 33.6690270739068 [8578554746145299335043 : -8578405949447897560720 : 26485814998297129717] [-8578440612665857723743 : 8578737286106465313217 : 8578142096432110571663] ???,
 ...
 ?,
 ...
 176
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420030
 0 - - - - - - 177
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2427934
 1 [-9897361664226781536 : -3083067790302174769664 : 54398020955487562683] 30.6394796644954 [-497994499440184491953 : -538561180891528896817 : 494771606213318088237] [-77708818231801355744 : -67474779627418986601 : 67023369979996246775] [2945]Q+TC,
...
 265736973.117160,
 ...
 178
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2132130
 1 [586218416 : 231806240688 : 2622362939] 14.2532379443989 [-7669281177 : -6791227235 : 7633279367] [-1700387149 : -1861545029 : 1852677014] - - 179
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47691630
 1 [207690013274484 : 77636532266143397 : 26039617344] 25.4766567282950 [-77466964252660529 : 77806100279626265 : 75637286831703792] [-21934382185618813 : 15061836115814125 : 22016331252340621] ???,
 ...
 ?,
 ...
 180
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6060638
 0 - - - - - - 181
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864690
 1 [-392 : -143640 : 1] 2.59184764447923 [-1969 : 2021 : 1983] [-105 : -181 : 104] [858]Q,
...
 1885851.67275189,
 ...
 182
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2277198
 0 - - - - - - 183
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50918230
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 13847263.7890614,
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 184
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 0 - - - - - - 185
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1947582
 1 [-133956 : -10929492 : 1] 8.77655577115261 [-149917 : 153680 : 699527] [-2019893 : 2047867 : 2037913] [643]Q,
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 3628658.20702727,
 ...
 186
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3363030
 1 [3679312 : 1453749584 : 2197] 11.4506845498596 [-90846895 : 90871803 : 90820561] [-9133243 : 253541 : 9134530] - - 195
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 1 [-4657940 : -31371956 : 114084125] 5.36155609469103 [-22699401623 : -22707244612 : 22472172845] [-4564188251 : -89273259 : 65985911] [701]Q+TC,
...
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 1115024.30473856,
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32155370
 0 - - - - - - 199
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 47483518.7381300,
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 [7]Q1+[38]Q2,
[37]Q1+[-22]Q2+TC,
[55]Q1+[21]Q2+TC,
[29]Q1+[48]Q2,
[19]Q1+[-65]Q2+TC,
[81]Q1+[-6]Q2,
...
 634.559836600110,
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 214
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 1 [209764 : -132496652 : 1] 6.89261041287225 [37959 : -37840 : 26161] [-27709 : 27811 : 27149] ???,
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 ?,
 ...
 216
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 0 - - - - - - 217
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4019106
 1 [-85697 : 28033782 : 1] 6.53335587744602 [11253 : -11183 : 15088] [-40541 : 40761 : 42025] [471]Q+TC,
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 1449366.20120850,
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 218
219 [0, 194469, 0, 7104, 0]
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42780510
 1 [4997858866572 : 2411531490748996 : 130323843] 21.8886786634178 [-300845635878449 : 302037236808800 : 276160634271249] [-127981793960801 : 116171616467999 : 128486005866401] - - 219
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 ...
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 220
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 1 [244963924250737499136 : -374898371430179626334208 : 73276641703828357303159] 36.0817776208305 [-511471088273070257513389 : -514399981799868535844125 : 513363265013579082858889] [59049950537160670879278 : -202493766777178453369097 : 202758342960850233768347] - - 221
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 ...
 ?,
 ...
 224
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23185890
 1 [207998408 : -162644103245 : 512] 14.3383788896775 [2505402581 : -2499031365 : 1452803248] [-2048701715 : 2055267571 : 2023861043] - - 225
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 ...
 ?,
 ...
 226
227 [0, 208837, 0, 7360, 0]
[1840, 844560]
5290230
 1 [3364 : -1549644 : 1] 6.58833970411242 [64632 : -64505 : 64273] [-12557 : 12573 : 3667] - - 227
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 12.3619954711339,
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 [6]Q1+[-7]Q2+TC= [2172367150814537096448336277467148575317526758092738000260149407851242009858830282188716789432217446627780702211710539569929477716026549139805483420587923608305301319967073747776832833252563329604678254558895494927187840637176024312695159997314595303824559161813520467494389827990861095882758344748098033550410274413022173392001748552207851047867688228548848200124217693856206557480579038339543919163019096044551654502355203667930102752448114271994705850471218382456467031957391 : 6987847197982908593379197899550694745023464495872664374068224086288186308957187970329466565872378011971332425173915787632908769016729670430581152835113756450794488157029383307202902275893252969376593450350270660032621557115732616100458074805389614785919815772386341648192458013954689693014181854892807271066725046823365294149900283748169346630582255731373642252925053732583029620776623126338010484320630265276140287027801718317758322382330914075518328033006141361081931482684 : 2540261881170309361041496744071802534411526327907352024053633737203040763950819608763074385293263647655954142198612230800664313516983791388107513072744108430473978940329157212856791473462690185564535288993206313514692973936800496407673305493073166549294107264369649264654694969403758975928362806184492984046888393709372383790633533594773625175771274569760947841583281756770907406778583077966700154710087293539206020145490491695270054268427903234984253705862045442672470275991],
 [49]Q1+[2]Q2,
[37]Q1+[16]Q2,
[2]Q1+[-55]Q2,
[14]Q1+[-69]Q2,
[45]Q1+[-46]Q2+TC,
...
 733.461781258306,
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 228
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99027330
 1 [22079596 : -10299093420 : 6859] 9.33427363717577 [2771072 : -2766075 : 2757451] [-530915 : 531523 : 141149] ???,
 ...
 ?,
 ...
 230
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 0 - - - - - - 231
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 1 [-315375 : -143277400 : 27] 9.95918412418645 [-4083179 : 4104101 : 4215564] [-1828595 : 2517119 : 1839551] [777]Q,
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 6012648.27211096,
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 232
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25732614
 0 - - - - - - 233
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 1 [6343674428732 : -18351152572513651 : 778688] 20.8535511319910 [38810771185095 : -38783954280079 : 6330265976224] [-38288564509229 : 38334046068989 : 38225302523101] ???,
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 234
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 0 - - - - - - 235
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 1 [1071738369249810050191910142010974076269596 : -555638824505559937766347178801544885603271572 : 24824032116923074435843302514451356559] 63.3924725761451 [437628222740096062026900752004047349595755 : -436017727740344091693770912778255929654672 : 401096640968802783655401383641219568630557] [-182790025556479601175983481631869267216097 : 183462289029520529885055879409751409444927 : 166643790088738526563752363664424975170193] ???,
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 236
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6768270
 1 [29112683538770972576737027788 : 16142441932124623958652495427620 : 303001407432204926735513585881] 43.8599430562997 [-52007309631038562310217627287 : -49198951605268794746081841722 : 51816159098935802385513777329] [-27057460073659470456928526155 : -31440399677471629407435992363 : 31329913459704997095107001447] - - 237
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 ...
 ?,
 ...
 238
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1009470
 1 [2722500 : -1424802225 : 64] 10.0061897812108 [1685243 : -1679107 : 1549432] [-7622925 : 7650589 : 6932861] - - 239
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 1 [1553389055676257797599399914064 : 761562299674338262735953972324016 : 1254646438262087947416268461] 47.8311089771664 [-47654878425572612126179361796325 : 47540409033719670715814884744177 : 47726861341991631869013823388913] [-4412087164658371132871405931751 : -1002860655970486372189771518134 : 4407995688804717864149060084569] - - 243
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7.15782801402155
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 [-12299 : -10971 : 10919],
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 [13]Q1+[-5]Q2,
[23]Q1+[-36]Q2,
[55]Q1+[11]Q2+TC,
[19]Q1+[52]Q2+TC,
[81]Q1+[1]Q2+TC,
...
 1461.33535713979,
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19002.0000661102,
19024.0187377169,
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 ...
 244
245 [0, 243037, 0, 7936, 0]
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 ...
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 248
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4943094
 1 [614122448 : 312623918256 : 148877] 12.1318146852280 [-500500503 : 501499235 : 498475123] [-47112211 : 15973174 : 47175281] - - 251
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 0 - - - - - - 252
253 [0, 259069, 0, 8192, 0]
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514066
 1 [399563912288910531691584369456685122471166980 : 216549810884627580851830451925383219709590005372 : 11529015171225856047884867374042898828625] 68.0243338365472 [-370160716430495446700898862610117421993013463 : 371448224955215446627287616586400453724760528 : 348974668990436715266941946286457966296397575] [-134868291870201422024736788039547982991654417 : 119389021931807848678093496585026102469587247 : 135323503038541973102384944044617347652922737] - - 253
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 1 [3459908 : -220972276281 : 1715932202048] 22.3115203207591 [-1175911877224833 : -1176059192075687 : 1175986126294528] [1663378316219 : -207485385853995 : 207491883422261] ???,
 ...
 ?,
 ...
 254
255 [0, 263157, 0, 8256, 0]
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5181930
 1 [19696656 : 21069491248 : 2102071041] 15.4873901418034 [-272482776451 : -269849090045 : 271799919363] [-13073595869 : -27233055040 : 27182304413] - - 255
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136313254
 1 [1114615595127839616 : 574807368148715456832 : 97113355174136449] 25.1369597884336 [-26765391837330697 : 12942218562552935 : 26815436550386017] [-22062032331330456 : -21847792205430391 : 22006761099588811] ???,
 ...
 ?,
 ...
 256
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 [17]Q1+[10]Q2+TC,
[45]Q1+[-17]Q2,
[51]Q1+[30]Q2+TC,
[79]Q1+[3]Q2,
[5]Q1+[82]Q2,
...
 6396.63594235893,
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 ...
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 ...
 260
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 1 [4818880 : 2531328064 : 166375] 9.28000891797043 [-1450551 : 1101191 : 1454695] [-962629 : -937016 : 959549] - - 261
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[7]Q1+[-5]Q2+TC,
[1]Q1+[48]Q2,
[13]Q1+[-58]Q2,
[69]Q1+[14]Q2+TC,
[83]Q1+[4]Q2+TC,
[9]Q1+[91]Q2+TC,
...
 1670.73706011481,
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 29698920.1846313,
 ...
 270
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11540606
 1 [1222676032053382162555076147000885939043648291840 : 767972954396924786308200876058562338249540930265344 : 12539374860911763544146339572543487127529625] 70.5760241075265 [-87611718998465096290143346513700236247061337627 : 87884842792422651952132904870797555857495547717 : 76280690106357607328697480009006711385010913195] [-22300367224470290774975042159133828338806044664 : 21248903679798732722777165805112909005875143429 : 22372941312302826901896786843671612809129146499] - - 271
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 1 [919271326338476519796692784179195097052 : -507015589079835920601316445291346678230204 : 61524826053220618507796973637020697927] 58.4924287393589 [83995444365333975250414793059649187776 : -145215943102946278185985046583816760791 : 145519165161115716442371724784483173639] [119497814838542933306806319345291946607 : -119184035659154572116619015677382803215 : 118007682847271904593598802794879440303] ???,
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84396630
 0 - - - - - - 275
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18959166
 1 [-298116 : -29657628 : 1] 10.1237966773847 [-407740 : 416083 : 2302087] [-6731543 : 6791283 : 6773177] [1377]Q+TC,
...
 19196024.4700929,
 ...
 276
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21560630
 1 [15255243328 : -9018056527168 : 389017] 6.71092149929637 [141131880819 : -140682385655 : 133020268361] [-49889070881 : 50043839714 : 44351409871] - - 277
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 1 [54671236 : 59223133977 : 64] 14.1614356804707 [-2817552769 : 2822745705 : 1473526904] [-2412562381 ; 2393968829 : 2418379101] - - 281
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 1 [-1683672 : -866040056 : 10503459] 13.8446776302965 [-2885441267 : -3101951281 : 2873945103] [-422218853 : -383157808 : 381611435] [65]Q,
[195]Q,
...
 58493.7629880028,
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 282
283 [0, 323749, 0, 9152, 0]
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 ...
 ?,
 ...
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 2 [1120000 : 1354326400 : 1],
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 6.16911483735038,
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 1 [2019244 : -1214095068 : 6859] 10.4215568886448 [16660319 : -17064544 : 17113281] [4417137 : -4405775 : 3456463] - - 299
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 2 [-4056 : -2432040 : 1],
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 5.85210002344661,
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 [-533 : 2099 : 540],
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 [23]Q1+[18]Q2,
[13]Q1+[-35]Q2+TC,
[51]Q1+[-1]Q2,
[5]Q1+[90]Q2+TC,
[33]Q1+[71]Q2+TC,
...
 7080.22778989051,
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 ...
 300
301 [0, 366013, 0, 9728, 0]
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12526722
 1 [208 : 143248 : 2197] 7.84751316908114 [-345081 : -327175 : 344071] [-51547 : -58277 : 58112] - - 303
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20701010
 1 [-4764988927369959673962543359556313325348901 : -2895918515507626816007488805900862823371686058 : 1914601484477274696722566114082446750362541] 69.2166718653997 [-1811107719295929798817096113645182708844063539 : -7602944750311183430832073725446908355587435655 : 1786088022325771334685545840138025463776873284] [-7386518779336750773023075916207258476295651273 : -7362278493282330919783137781247175955367355163 : 7323080662207290250629024509300934846842164693] [385]Q+TC,
...
 10259641.1872488,
 ...
 304
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57488970
 0 - - - - - - 305
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 0 - - - - - - 309
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1931210
 1 [-376996 : -39756500 : 1] 7.83548763902928 [-39377 : 40136 : 235243] [-229943 : 231737 : 231219] [207]Q+TC,
...
 335742.809844765,
 ...
 310
311 [0, 390613, 0, 10048, 0]
[2512, 1575024]
121867482
 0 - - - - - - 311
312 [0, 393117, 0, 10080, 0]
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9114210
 1 [-1499160 : -939125160 : 2197] 9.29585604610507 [-7767413 : 7884673 : 7799467] [-1198181 : -2090429 : 1191460] [1063]Q,
...
 10504029.1605613,
 ...
 312
313 [0, 395629, 0, 10112, 0]
[2528, 1595168]
62111854
 2 [2843212 : 1790790548 : 300763],
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 13.0127269591150,
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2006610
 1 [-748424392 : -472050277800 : 22188041] 13.7152523032488 [-17293040893 : 22044482257 : 17363972657] [-4735005673 : -4860987248 : 4717733727] [969]Q,
...
 12878087.0179108,
 ...
 314
315 [0, 400677, 0, 10176, 0]
[2544, 1615440]
126610110
 0 - - - - - - 315
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36518482
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1344030
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260493426
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[267]Q+TC,
...
 693910.015612490,
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 ...
 318
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131474210
 0 - - - - - - 319
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37916970
 1 [4212 : 2725884 : 2197] 8.23956647750089 [-1049840 : -368369 : 1048697] [-980253 : -985139 : 983555] ???,
 ...
 ?,
 ...
 320
321 [0, 416013, 0, 10368, 0]
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826866
 1 [920154346996018229792695661509454112 : -595030291190317409198286213554409090144 : 191340136152250228705583686855372363] 55.2996201658523 [115737051655880595628710639915270115 : -1261647881655039333071025965534750927 : 1262006181789421723670086011185454307] [4619410228147151842513898923995988427 : -4617008927461478575734987698470403317 : 4614121812963087512496986893972109282] - - 321
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136461318
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 ???,
 ...
 ?,
 ...
 324
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34750370
 1 [93708218208290585792 : 82508117381165256946496 : 268623284623667] 28.9828718442354 [-9830046997907421143 : 9852232911721695495 : 7309861590615564839] [-6651016870931631329 : 6534788201016246040 : 6668084589431247113] - - 325
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285741046
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 ...
 ?,
 ...
 328
329 [0, 436909, 0, 10624, 0]
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72087990
 0 - - - - - - 329
330 [0, 439557, 0, 10656, 0]
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32330970
 1 [22727933228 : -206849325195149 : 175728920193728] 26.5041282740189 [-467934971342963015 : -468348669993353313 : 468156934743754784] [5307984970072421 : -72745817312382037 : 72761804701190155] ???,
 ...
 ?,
 ...
 330
331 [0, 442213, 0, 10688, 0]
[2672, 1782224]
146810702
 1 [4349416453708653232 : -2909652433845134786864 : 818633651978323] 28.1675208412068 [7912539296686840655 : -7900789148123674491 : 7877442248065350901] [-646730176699580783 : 647370779038611598 : 213477835465720037] - - 331
332 [0, 444877, 0, 10720, 0]
[2680, 1792920]
296280030
 1 [-500 : -333300 : 1] 5.00514503683925 [-2751 : 2804 : 2761] [-905 : -1321 : 901] [2887]Q+TC,
...
 41716727.6935516,
 ...
 332
333 [0, 447549, 0, 10752, 0]
[2688, 1803648]
18684666
 1 [13559679568464046249336075836 : -16548748153234320613935642033916 : 1313997382288512461558977211079] 49.5277407563833 [-439432831969839839001293220658825 : -443570019008148419154777131167304 : 442638743612799050957198239273809] [44716565803387652999591794337771 : -81386544431829223158819867016181 : 81519681840504381434478638457541] - - 333
334 [0, 450229, 0, 10784, 0]
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301645330
 1 [12120300 : 8138330540 : 19683] 13.2599377920025 [-1022409451 : 1012173184 : 1024738371] [-201707855 : -126630127 : 201332447] ???,
 ...
 ?,
 ...
 334
335 [0, 452917, 0, 10816, 0]
[2704, 1825200]
260130
 0 - - - - - - 335
336 [0, 455613, 0, 10848, 0]
[2712, 1836024]
307075014
 1 [-16670226804073608 : -6848880419437692936 : 440757991465326683] 25.1545617706813 [-73147677416379391 : -73990720304050205 : 72874606076711731] [-8735488333345777 : -5322190361313732 : 5296100984147467] [857]Q+TC,
...
 18474742.7379151,
 ...
 336
337 [0, 458317, 0, 10880, 0]
[2720, 1846880]
77453530
 0 - - - - - - 337
338 [0, 461029, 0, 10912, 0]
[2728, 1857768]
312569466
 1 [-3318160595670431292808 : -2084854845338476859378328 : 20144716373489873797169] 33.0751405455273 [-9705075180274884231019 : -10470440395156850772641 : 9672987713257063590229] [-1443077948921172687253 : -1335686913356775315525 : 1331267520675817046368] [1055]Q+TC,
...
 36813458.3056856,
 ...
 338
339 [0, 463749, 0, 10944, 0]
[2736, 1868688]
1167930
 0 - - - - - - 339
340 [0, 466477, 0, 10976, 0]
[2744, 1879640]
6492430
 0 - - - - - - 340
341 [0, 469213, 0, 11008, 0]
[2752, 1890624]
40116678
 0 - - - - - - 341
342 [0, 471957, 0, 11040, 0]
[2760, 1901640]
323754210
 1 [4142646120320 : 11508091400029120 : 571787] 20.3924721543168 [-22122981407771 : 22138908592341 : 5481042517139] [-16959037987808 : 16926589002103 : 16978589580605] ???,
 ...
 ?,
 ...
 342
343 [0, 474709, 0, 11072, 0]
[2768, 1912688]
163295738
 0 - - - - - - 343
344 [0, 477469, 0, 11104, 0]
[2776, 1923768]
109815090
 0 - - - - - - 344
345 [0, 480237, 0, 11136, 0]
[2784, 1934880]
83078910
 0 - - - - - - 345
346 [0, 483013, 0, 11168, 0]
[2792, 1946024]
335202634
 1 [-470596 : -52439212 : 1] 11.6781262063710 [-6495728 : 6614075 : 40941503] [-40114879 : 40392171 : 40315729] ???,
 ...
 ?,
 ...
 346
347 [0, 485797, 0, 11200, 0]
[2800, 1957200]
33810630
 1 [2924100 : 5399615700 : 1] 11.9088245520921 [-26983472 : 27012685 : 10205123] [-125124633 : 124689337 : 125320871] - - 347
348 [0, 488589, 0, 11232, 0]
[2808, 1968408]
12630618
 1 [-1176 : -821016 : 1] 5.63761819775819 [-34043 : 34375 : 34183] [-1421 : -3476 : 1411] [257]Q+TC,
...
 372359.044343730,
 ...
 348
349 [0, 491389, 0, 11264, 0]
[2816, 1979648]
10748870
 0 - - - - - - 349
350 [0, 494197, 0, 11296, 0]
[2824, 1990920]
346917810
 0 - - - - - - 350
351 [0, 497013, 0, 11328, 0]
[2832, 2002224]
174944322
 1 [785548880 : -901411665392 : 56844576125] 17.8519724059797 [-1429300378319 : -1445397015201 : 1442307474065] [84246122717 : -136809333637 : 137047165528] - - 351
352 [0, 499837, 0, 11360, 0]
[2840, 2013560]
352876390
 0 - - - - - - 352
353 [0, 502669, 0, 11392, 0]
[2848, 2024928]
29656758
 1 [2074709421979473715336923464181990297624896756 : -1521777341036779591801859196850870822613228580609 : 6435634563431736209434097520825474119332384064] 71.5824914837524 [-70906477578881120923844361261586065312015933911 : -83748480456828628027657519040918308540819550625 : 83551607283793295621761710543798157819292432536] [43791882709927682096591964529625663649028702339 : -45178841573649464102542105205448533375712959411 : 45292244176125939276088821640180123589426831661] - - 353
354 [0, 505509, 0, 11424, 0]
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358902810
 0 - - - - - - 354
355 [0, 508357, 0, 11456, 0]
[2864, 2047760]
180970790
 1 [1856 : 1506560 : 24389] 6.84684054345267 [-81085 : -77661 : 80881] [-10918 : -12427 : 12397] - - 355
356 [0, 511213, 0, 11488, 0]
[2872, 2059224]
364997454
 0 - - - - - - 356
357 [0, 514077, 0, 11520, 0]
[2880, 2070720]
5112090
 0 - - - - - - 357
358 [0, 516949, 0, 11552, 0]
[2888, 2082248]
19534774
 1 [3771292 : -2740214308 : 343] 12.5085329041641 [342874377 : -342179200 : 339540103] [-62378623 : 62479297 : 36346463] ???,
 ...
 ?,
 ...
 358
359 [0, 519829, 0, 11584, 0]
[2896, 2093808]
187134090
 1 [2434663100679777376 : 3964515412645346851977 : 448037109706059513856] 32.0136161312222 [-1800107262044665310099 : -1789140414430155360301 : 1797058501338090112576] [-131927744954170981453 : -297725219030537444147 : 297360265371126936525] - - 359
360 [0, 522717, 0, 11616, 0]
[2904, 2105400]
6861690
 1 [9535999578851284 : -6896612800861988875 : 33125645336896] 21.3614396373530 [77628406114363 : -79604145629427 : 79797783632336] [224383240091797 : -223881079839749 : 183869137719131] ???,
 ...
 ?,
 ...
 360
361 [0, 525613, 0, 11648, 0]
[2912, 2117024]
95133766
 0 - - - - - - 361
362 [0, 528517, 0, 11680, 0]
[2920, 2128680]
1578990
 1 [-1435295316056 : -1043024116917384 : 3588604291] 15.8932826508792 [-65392573381 : 66903737745 : 65602249211] [-34538218547 : -45519660707 : 34411535952] - - 362
363 [0, 531429, 0, 11712, 0]
[2928, 2140368]
193435758
 1 [15578996109478523371670877341605852502846084 : -15502129562836932036646119576318700322316046316 : 610187120340752801355296215353258823305887681] 67.7381500448617 [-302857417886247912415918181959760863280578016 : -308159103783250967148013298093932785415433025 : 307455635348434255203424599694547555910861281] [48683359212839815686508349410184670711171409 : -66293644442450746729506732078321082907019281 : 66426171007911900316117794410142468398526161] - - 363
364 [0, 534349, 0, 11744, 0]
[2936, 2152088]
78013190
 1 [-504500638456940432004964190124596 : -348950951317245261597339623099544748 : 2402786943209624589734336331431741] 50.4680075181188 [-1143611189390291520173034926700916 : -1262625838543512960008416789968155 : 1140055934159784686090105334568961] [-549711039151859740768651338781987 : -520256519741107789330269544020977 : 518675624876609220070693567331757] [1591]Q+TC,
...
 127748708.538471,
 ...
 364
365 [0, 537277, 0, 11776, 0]
[2944, 2163840]
3511410
 1 [2517168 : 1845990755 : 110592] 11.4890970244631 [-61973041 : 43512145 : 62090976] [-44602559 : -43938049 : 44503679] - - 365
366 [0, 540213, 0, 11808, 0]
[2952, 2175624]
543906
 0 - - - - - - 366
367 [0, 543157, 0, 11840, 0]
[2960, 2187440]
199877330
 0 - - - - - - 367
368 [0, 546109, 0, 11872, 0]
[2968, 2199288]
403019526
 0 - - - - - - 368
369 [0, 549069, 0, 11904, 0]
[2976, 2211168]
14510790
 0 - - - - - - 369
370 [0, 552037, 0, 11936, 0]
[2984, 2223080]
409602490
 1 [6082524294396732 : 4612100578713675676 : 11675917360117647] 28.5025314779194 [-4930869432126292199 : -3777844287447873280 : 4920791934702778407] [-3135496991788565767 : -3198675843505727495 : 3191346103146448519] ???,
 ...
 ?,
 ...
 370
371 [0, 555013, 0, 11968, 0]
[2992, 2235024]
68820114
 0 - - - - - - 371
372 [0, 557997, 0, 12000, 0]
[3000, 2247000]
16650270
 1 [747837933190068 : -558889924336664228 : 30997612361997] 25.8018655749959 [58330615647982912 : -81391865436183145 : 81546951389020233] [57402037956400487 : -57275741015846183 : 56509689352072423] ???,
 ...
 ?,
 ...
 372
373 [0, 560989, 0, 12032, 0]
[3008, 2259008]
52451342
 0 - - - - - - 373
374 [0, 563989, 0, 12064, 0]
[3016, 2271048]
422982690
 0 - - - - - - 374
375 [0, 566997, 0, 12096, 0]
[3024, 2283120]
7895790
 1 [204196437900 : 186922714728420 : 753571] 18.6338367613934 [-2593344404017 : 2598953227328 : 2138422124657] [-4478226366605 : 4369017713779 : 4488713491981] - - 375
376 [0, 570013, 0, 12128, 0]
[3032, 2295224]
429780694
 0 - - - - - - 376
377 [0, 573037, 0, 12160, 0]
[3040, 2307360]
108301710
 0 - - - - - - 377
378 [0, 576069, 0, 12192, 0]
[3048, 2319528]
436651146
 1 [-1376863550173699957990836099827389651130975902131196835213044650108278292 : -1001139396106825549518150597080134979988031990909544465212207164541016940348 : 5349710383108336665592085244813567149310259577541009452645057268387657497] 107.936636607047 [-6598822999833396409599071908255233427128609862583070151895187483899600 : -7462049825383099236655395950974385754660790539780796987020443281235107 : 6578709526068320015387458306311860230287424642739939857117577636468837] [-69424101776623947853198089936249853550836328580345490291404609442752259 : -66523079502804947024810092248221971365333237053524410161883467897486361 : 66328612907587891100841142524593961388255696780639521059470292512794781] [107]Q+TC,
...
 1235766.55251408,
 ...
 378
379 [0, 579109, 0, 12224, 0]
[3056, 2331728]
220056830
 0 - - - - - - 379
380 [0, 582157, 0, 12256, 0]
[3064, 2343960]
147864810
 1 [21316 : -16559028 : 1] 7.67366127305895 [230240 : -229733 : 226229] [-49421 : 49517 : 36915] ???,
 ...
 ?,
 ...
 380
381 [0, 585213, 0, 12288, 0]
[3072, 2356224]
3492918
 1 [123904 : -104338432 : 1] 5.08159528506254 [1729 : -1725 : 1571] [-2959 : 2966 : 2809] - - 381
382 [0, 588277, 0, 12320, 0]
[3080, 2368520]
450610930
 1 [-111443780 : -84643843180 : 103161709] 15.5298843753373 [-5830141608 : -10062333767 : 5803731017] [-18406900087 : -18240525413 : 18179623625] ???,
 ...
 ?,
 ...
 382
383 [0, 591349, 0, 12352, 0]
[3088, 2380848]
227073378
 0 - - - - - - 383
384 [0, 594429, 0, 12384, 0]
[3096, 2393208]
50855670
 2 [-580644 : -68173092 : 1],
[29102442650768036 : 31845037608034471732 : 48268303721]
 10.7893491645270,
23.9668065402108
 [-938741 : 954956 : 6225751],
[-5144903719930793 : 5154267563392128 : 3633123409615337]
 [-18337403 : 18450485 : 18420663],
[-3672926954837321 : 3627659483177911 : 3680714758129865]
 [35]Q1+[28]Q2+TC,
[29]Q1+[-43]Q2,
[19]Q1+[-64]Q2,
...
 51099.7420072837,
29093.8375803634,
78372.3206053560,
 ...
 384
385 [0, 597517, 0, 12416, 0]
[3104, 2405600]
23063690
 1 [128269783767367948670856108466186284 : 118095748829901136337446752251305073140 : 2584190549772762231909496567354143651] 55.7407166204254 [-6563947536726441722770849388072661919 : -6373470522484665696420128819925395672 : 6548877644460158677514774171790395223] [-1437509349063570536937864242384137709 : -1711741824340775115661970191946957773 : 1708073482196657769117238560218247581] - - 385
386 [0, 600613, 0, 12448, 0]
[3112, 2418024]
464865114
 1 [888928866754311401332464 : 702043804408799337398284987 : 1650549698005456340545536] 41.1375971060911 [-833952219390717879682094365 : -633368275273918068996870083 : 832331351542046539887385728] [-537213387195272828121087533 : -547245960133225004491557907 : 546048017832502479430770797] ???,
 ...
 ?,
 ...
 386
387 [0, 603717, 0, 12480, 0]
[3120, 2430480]
234237510
 0 - - - - - - 387
388 [0, 606829, 0, 12512, 0]
[3128, 2442968]
472103566
 1 [-42999924948258557788372658210252 : -33489076252174181919220077615455252 : 737715339824966411034923348131] 48.3455127691535 [-20814507181987585847402717061692 : 23956985133753299071340702210307 : 20877251254458008115784380461927] [-47526459712691006047642624347389 : -49324691570469976477933789633775 : 47390919640092550380917502950579] [97]Q+TC,
...
 454882.929644965,
 ...
 388
389 [0, 609949, 0, 12544, 0]
[3136, 2455488]
188790
 1 [36288 : 29171520 : 1] 5.91186492026339 [-65041 : 65189 : 63349] [-44343 : 37202 : 44437] - - 389
390 [0, 613077, 0, 12576, 0]
[3144, 2468040]
479416770
 1 [90145963691216412851180760318723689051153877236 : -70662429848156930145582617626811786596691017560185 : 9755419626863254284677261401167921180020404544] 72.2784986613803 [51059282171961879092240112792176517319436967581 : -128972386230985713635358913008617843436463714101 : 129102515720728330122740160426944352109667250496] [118817480036279225754215490703127562443238610721 : -118646247790422287822024822626163578799249152561 : 118250300155639071580554941213310243981754538095] ???,
 ...
 ?,
 ...
 390
391 [0, 616213, 0, 12608, 0]
[3152, 2480624]
241550762
 1 [300871225475409069518985156097386639460 : 265897892777636032422333028477587175624397 : 1825472203436754363972792113704000] 58.8250865549738 [-337487643507682155022324378096864274451 : 338237624033959604627823089444653325611 : 300496235212270344716235800423492113880] [-158166687995275911388839256389930805031 : 151873405677690238689636300681800083511 : 158531154936174944642657737588866144151] - - 391
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486805110
 0 - - - - - - 392
393 [0, 622509, 0, 12672, 0]
[3168, 2505888]
4541922
 0 - - - - - - 393
394 [0, 625669, 0, 12704, 0]
[3176, 2518568]
494268970
 1 [42874210292 : 40981402074964 : 148877] 14.8135851230933 [-6453184221 : 6466551616 : 5352592589] [-3666643093 : 3578545963 : 3674846645] ???,
 ...
 ?,
 ...
 394
395 [0, 628837, 0, 12736, 0]
[3184, 2531280]
249014670
 0 - - - - - - 395
396 [0, 632013, 0, 12768, 0]
[3192, 2544024]
501808734
 0 - - - - - - 396
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[3200, 2556800]
6320090
 0 - - - - - - 397
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[3208, 2569608]
169808262
 1 [48724694066807307057898890536404 : 39421485189569213873952410618457516 : 3008118707916148268742545461] 46.6717151622037 [-6145819372708708110259150720000 : 6158014956120634547029366951179 : 6084488966644950163852253201461] [-1158911969743377931125667873771 : 774140229101315651561319274091 : 1160839533519898722747527296789] ???,
 ...
 ?,
 ...
 398
399 [0, 641589, 0, 12864, 0]
[3216, 2582448]
256630770
 0 - - - - - - 399
400 [0, 644797, 0, 12896, 0]
[3224, 2595320]
517117510
 0 - - - - - - 400
401 [0, 648013, 0, 12928, 0]
[3232, 2608224]
130248186
 1 [464417398866333230399488 : -3717156415945059452249954304 : 2278066810514642293946037139] 41.2640231924256 [-758972185514643148540440561 : -759738925699450297767389809 : 759394209159118209428351281] [76857386445876569777448416 : -763130192919479483938075745 : 763320896305234386547303169] - - 401
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[3240, 2621160]
6480090
 1 [-40714877670843802334124517479861743348257662045 : 31897848680196577091793567906941715474629911496400 : 117656269872993705921239693903042990472039740089] 69.9670594010099 [-1260952793256014979868285188756980470775952409 : -1066242978180573101666001815551580019222411769 : 1063067323568062430065601483685485816978792800] [13738297652681896415772433221946393798403195283 : -13303735664139629259781979407249949755610959759 : 13340687219426330827923972754684373272944061681] [1247]Q,
...
 108799407.072105,
 ...
 402
403 [0, 654469, 0, 12992, 0]
[3248, 2634128]
264400598
 0 - - - - - - 403
404 [0, 657709, 0, 13024, 0]
[3256, 2647128]
532734510
 1 [45622669721990636562191730297635408266900 : -37015964582576161624774235641966024543818180 : 81930990751244077250982803020363361629] 60.4497184410220 [5657260139362254235210213309598609601264 : -5725262795009259179542011672555764489701 : 5736835043072332042439865468683003477581] [1131020871174756668773627246536060374495 : -1129059266528493365223373027716848303087 : 800385189947567883339631360625624980607] ???,
 ...
 ?,
 ...
 404
405 [0, 660957, 0, 13056, 0]
[3264, 2660160]
67085910
 1 [368124540319184700 : -781369307997364341116 : 95757609375] 27.2529172041096 [599491656430097029 : -598927527614940304 : 229795773291912075] [-553981918718761021 : 554734980592797571 : 552290098010768221] - - 405
406 [0, 664213, 0, 13088, 0]
[3272, 2673224]
540659554
 2 [-500000 : -202616000 : 1],
[1927613340246861500917818690498203268 : -1589054558324485055854027305509355142396 : 2262491594770849080617827344092569497]
6.94868148542320,
57.3156045942581
[-30923 : 31077 : 62423],
[-16895030018678739169844726586253005955 : -26133719311262954610856513246191117248 : 26092456348057142955030439306155294363]
[-19000 : 19187 : 19063],
[19820221492783418668986031415208558073 : -19999036485596114660121976701418712743 : 20037258319802173577315282754114339863]
[19]Q1+[44]Q2+TC,
[9]Q1+[-59]Q2+TC,
[47]Q1+[29]Q2+TC,
...
 131424.084714145,
188675.555247455,
92821.6710053421,
 ...
 406
407 [0, 667477, 0, 13120, 0]
[3280, 2686320]
90775230
 1 [111268609561856 : -117471070199723136 : 248858189] 21.2993849012866 [188431927170553 : -188077913213175 : 145863043071247] [-60053045068964 : 60179310681811 : 59053161398889] - - 407
408 [0, 670749, 0, 13152, 0]
[3288, 2699448]
548662806
 1 [-80654572681525768135255257728734307284765928027109872520 : -66041894701611194263499284603333422572690774787678888035832 : 374677705222786659510048392255303394560781316509804875] 83.0645866111398 [-3285084238436720765270756710915004603333848959143703803 : 3418315548572129647183494669853714699618929642934949063 : 3293991539995869231345933425894574422056039992567288725] [-523597719642770255352727687690560495740236372907501951 : -597031316265069746248691783648708727993257145592667139 : 522110633216738091342919412858931641345453898878010116] ???,
 ...
 ?,
 ...
 408
409 [0, 674029, 0, 13184, 0]
[3296, 2712608]
138173470
 0 - - - - - - 409
410 [0, 677317, 0, 13216, 0]
[3304, 2725800]
111348930
 1 [5038511840604 : -4156565860001412 : 1556862679] 21.9320421773999 [519557562193825 : -519583902806528 : 519609703868639] [72319267230111 : -72317453086817 : 747427426145] ???,
 ...
 ?,
 ...
 410
411 [0, 680613, 0, 13248, 0]
[3312, 2739024]
31156398
 1 [5290816 : 4460266112 : 12008989] 14.0426331702967 [-2764296679 : -2206763415 : 2758999099] [-823118798 : -840854513 : 839081243] - - 411
412 [0, 683917, 0, 13280, 0]
[3320, 2752280]
564905470
 0 - - - - - - 412
413 [0, 687229, 0, 13312, 0]
[3328, 2765568]
17781738
 1 [261814258361395867937596152187198479298560 : -217097102044331751536868077713062612082239488 : 859893302109357322225423828432825773375] 64.0773429628385 [837879653879973461861091653766505337452133 : -858191455841368347020690203366796319440363 : 860029528708509810767855534439059304654675] [424867806614487593865669420343126525738196 : -424025096227252288815081633842989098737051 : 353581040723510087159699289472467447308359] - - 413
414 [0, 690549, 0, 13344, 0]
[3336, 2778888]
16375590
 0 - - - - - - 414
415 [0, 693877, 0, 13376, 0]
[3344, 2792240]
288647810
 0 - - - - - - 415
416 [0, 697213, 0, 13408, 0]
[3352, 2805624]
64607286
 0 - - - - - - 416
417 [0, 700557, 0, 13440, 0]
[3360, 2819040]
146413890
 0 - - - - - - 417
418 [0, 703909, 0, 13472, 0]
[3368, 2832488]
2905742
 0 - - - - - - 418
419 [0, 707269, 0, 13504, 0]
[3376, 2845968]
297047910
 0 - - - - - - 419
420 [0, 710637, 0, 13536, 0]
[3384, 2859480]
1704690
 1 [180114423223248 : 152022646717490835 : 103029788672] 21.41599191672765 [-260155871964331 : 259579672368971 : 260453377786816] [-113199695206257 : -36052026735695 : 113114309755697] [??]Q+[?]TC= (where ?? > 100)
???,
 ...
 ?,
 ...
 420
421 [0, 714013, 0, 13568, 0]
[3392, 2873024]
6847918
 1 [90962953573440 : -76898235163258432 : 4239729131625] 19.8252071325170 [12704552942849 : -18504146392889 : 18534054370455] [13570809869369 : -13544982283364 : 13405866011851] - - 421
422 [0, 717397, 0, 13600, 0]
[3400, 2886600]
4185570
 1 [-25465812405064 : -15082090115979432 : 686525785714313] 19.6956078065649 [-341450389741621 : -345891523462463 : 340487730051409] [-23346168635041 : -16333075858296 : 16277502920755] [??]Q+[?]TC= (where ?? > 1000)
???,
 ...
 ?,
 ...
 422
423 [0, 720789, 0, 13632, 0]
[3408, 2900208]
305609418
 1 [23718521966396096067057998999450445785432064927037899056727352500 : -27222410058479972013411635763853262183612513703466405411210264973700 : 1037842576636151175719028986505169627099800796317715558954536322673] 97.6232482316747 [-2420323902696328565910425798595663053495972128952393194975527821 : -2457869361585456479513052418153782005217521085032048730593952796 : 2453015952543707133079730891825104246366976692043299542043383121] [5368859516163007613680993533685933505739005952336084250048919375 : -7243071102987199814172935187944118792477874593058328076842012033 : 7255631453777240111313812813135023349066035982484302700537604233] - - 423
424 [0, 724189, 0, 13664, 0]
[3416, 2913848]
47350030
 3 [-324 : -275652 : 1],
[20216 : 17442152 : 1],
[474347548 : -403796154164 : 1092727]
 5.15725762782886,
6.53839777449684,
14.5900866794194
 [-33989 : 34924 : 34079],
[-311167 : 311767 : 307633],
[10934081381 : -10914347611 : 8466362491]
 [-6939 : -8395 : 6919],
[-56107 : 39807 : 56200],
[10934081381 : -10914347611 : 8466362491]
 [1]Q1+[-1]Q2+[2]Q3= [2743260400516683056616306684496286550899825 : 6383088000457968550863626020707964592827 : 86901761472912010754925122912564100123],
 [1]Q1+[-8]Q2+[8]Q3+TC,
[11]Q1+[5]Q2+[5]Q3= [4957388129625954875287359499291510370001214152188372300389381922712857193612227197385652207479221373168020963852951520353342869910911206182746944170239736857587646437677363573663318880194462174567178260295812458952142384582857069058871601 : 4610641311343911571239659170359263831726612581818284235453051232120881574860876806183351262508248552325975019315428112159671204566442793634519193807603437840996840518612787379654710045050705945964714482904092742019978736993840525545917905 : 4056821943283692123846675639019941628773389445713607573536266975388031970031947057604601035587693759442077498248168190111411664989703922824060843314450044018397406871862758846206030475434882828744019780992167046338427248040517576350497852179],
 [11]Q1+[12]Q2+[-1]Q3+TC= [23354103733733685112983458601709944035815455880397856845308400237877295180577666351366045780767108460858900797696273228366939066228504000873395744533549726573852908371651358071284069964874250235366095045555817548303232658786188981959681204713589808550001364162700644904173069139775537158995684548839957902258433095643815142358952370589496721391788638007541948359261093544506869855649084760774407299114553151532983455820146258402073051113135807923111878783092480946866149591293506710703723194307718920564058906500606602857907627776965026983593818393625366633151045227892795571459382240587311425905640949938807326728256659610907031 : 25872911837406102563947167333662646675302917193773475465900746733873688201211660387993586608050275546092880620511864170956314636070740453809007168885307518136221932397121548428115054968435814336292079226516019787514205163560468659828381686361398911552511099491108958820964938694158877607929995513042818235890738043502902595330101004429495575613748152079383932508201516833929505638266276356574488255283949176698861740539472429977878870560972902243929762769487400720338045877156908552153931582462875003686356773585544617593951735747763856624378978052969506886212898798857413497810488709642568652081429209418190803357715488061041701095 : 37667253804736603160680647642420834172394453618624483925954635998301130272048604065230635950028996734253510993066017946581874697104862056336669719919668108780155922536049084356438762928885832483597561916567416873479867285028467608285617249298037149248727284234397794369274158742044997415422528834229118633091935861716583861595102813756879486810278610779993095621592992694422983018313028710574727839178677436698466272710668549461167384608292727154490368024727512382941210238442626486373925537048042464698195792206082736971249847219174842424320197579445683237077454712386293210145917491824120633077570859532884631478670392753748189],
 [11]Q1+[-2]Q2+[11]Q3+TC,
...
 65.1221070359963,
1496.83542162632,
368.041700111125,
969.916642362713,
1663.29744335772,
 ...
 424
425 [0, 727597, 0, 13696, 0]
[3424, 2927520]
4696230
 1 [1520092 : -1300573380 : 343] 9.95407644911496 [10840992 : -10835231 : 10827775] [-1493297 : 1493745 : 191311] - - 425
426 [0, 731013, 0, 13728, 0]
[3432, 2941224]
624274794
 2 [-40923036 : -32078667852 : 347428927],
[-179341531083 : -153310481165556 : 1939096223]
 14.9828189002348,
18.4041171561248
 [-4395220957 : -4638241168 : 4383886207],
[-341436273653 : 373297904275 : 342334201328]
 [-8883595371 : -8146074875 : 8124706871],
[-2999528275233 : -3165537256283 : 2991792760133]
 [83]Q1+[-12]Q2,
[84]Q1+[-13]Q2+TC,
[85]Q1+[-14]Q2,
[86]Q1+[-15]Q2+TC,
...
 113884.514179091,
117619.536481672,
121437.432419227,
125338.201991756,
 ...
 426
427 [0, 734437, 0, 13760, 0]
[3440, 2954960]
314333870
 0 - - - - - - 427
428 [0, 737869, 0, 13792, 0]
[3448, 2968728]
633081246
 1 [12055504356310378455815611892620183303500 : -10357341237917190471444186949507864630718172 : 72690119818939663318825724448248046875] 64.2077110765618 [1264845151142224611347086432937865693549584 : -1324490158337073006513960304439100464129959 : 1327296159945328678890592165693864613329375] [421937186031904340845924240931603640699291 : -421065634827981298982088933686675134141291 : 383188468126723235413822079686537952086459] ???,
 ...
 ?,
 ...
 428
429 [0, 741309, 0, 13824, 0]
[3456, 2982528]
1475730
 0 - - - - - - 429
430 [0, 744757, 0, 13856, 0]
[3464, 2996360]
641970130
 0 - - - - - - 430
431 [0, 748213, 0, 13888, 0]
[3472, 3010224]
19013106
 0 - - - - - - 431
432 [0, 751677, 0, 13920, 0]
[3480, 3024120]
650941830
 0 - - - - - - 432
433 [0, 755149, 0, 13952, 0]
[3488, 3038048]
163864714
 0 - - - - - - 433
434 [0, 758629, 0, 13984, 0]
[3496, 3052008]
219998910
 0 - - - - - - 434
435 [0, 762117, 0, 14016, 0]
[3504, 3066000]
781830
 0 - - - - - - 435
436 [0, 765613, 0, 14048, 0]
[3512, 3080024]
669135214
 0 - - - - - - 436
437 [0, 769117, 0, 14080, 0]
[3520, 3094080]
84216990
 1 [36588558904161428411856086093612 : -32115615206335243090630174202940753 : 3424313783853875981846398263488] 48.6093153771951 [22865323374372879480025834358995 : -50207748767459300475901751995819 : 50259771600704638909794044912024] [44858459564191639067738266064519 : -44794799346857451023494477140759 : 44624545268377871742655594061449] - - 437
438 [0, 772629, 0, 14112, 0]
[3528, 3108168]
10767582
 1 [-599076 : -249573204 : 1] 6.32363540203594 [-3925 : 3944 : 8311] [-21801 : 21991 : 21869] ???,
 ...
 ?,
 ...
 438
439 [0, 776149, 0, 14144, 0]
[3536, 3122288]
13660010
 0 - - - - - - 439
440 [0, 779677, 0, 14176, 0]
[3544, 3136440]
687664470
 1 [4640440913922020046194138668961513879820052118272728 : -4861421041918484970514421404604242602009748528576643144 : 14600309893927885810733843291974754584630632273] 76.1851247797057 [23271653878286255643978375016894523842442326250785 : -23227763058608615329301089005413340507040672262593 : 19618746945925937374521424724062655566300522264959] [-94139956402762523491296388772209052362390166850649 : 94330505587616036035336761960507190173693496415008 : 91875424835177183166881357620306726080514974827305] ???,
 ...
 ?,
 ...
 440
441 [0, 783213, 0, 14208, 0]
[3552, 3150624]
173087406
 1 [6971119879530607590932764907608917511401290357021215602687388754311142672721841759950737886855208698053394599932218776004608514593803416375805132099531391484587164625404896 : 9816154666028013921505509875836703454748922317692904153649326332127839349547413707582525592306353713944926880525226629959650578472531671131599575124495879181420798745425774048 : 5811293813454239176877383675756807805778084715993696101240364950165857927333703465202334090415881889630702981357150150772260490229123478331140809308259786526694689749] 265.533377119318 [-102179210290251132326793056035374071098112991157216605704741568220310741625021351616013367219897788150618181814398793664385224094033324599602279189630739695090603691670191225 : 102324011918665824371238399711223917542489557128052230829619397032352578157216433958622582619817914223234461529876761126440829624144418548972711958796257787855662948859512401 : 64337842239372330364833187256336637534196556042476127433224771271833077053738642589906897567129208996747703997884746001431444656243449174537066450545202872855270527892153399] [-97695144340720858218588260182338171740111059650866649214179686311181682848563936332378239055241144551111310309286797240323713676180635498786429260824579985051311993775405917 : 96949679832879173670095459934974009503370281591299696055197851063976815862175710822403549064181111380278585931262675730273375867160031438541884658389479353049103492680475617 : 97864405609009369357405745058949081385035426574580041555479891772659131125560035314906683474107824232458258186586507962927483196335905921014234710845454869777933476757715308] - - 441
442 [0, 786757, 0, 14240, 0]
[3560, 3164840]
697056010
 1 [15488 : 13872320 : 1] 7.31374907593759 [-247507 : 247933 : 245659] [-14960 : 9351 : 14981] ???,
 ...
 ?,
 ...
 442
443 [0, 790309, 0, 14272, 0]
[3568, 3179088]
12995994
 1 [7366220 : 6578351868 : 3723875] 11.7875611788870 [-75218832 : -25382833 : 75161825] [-70665463 : -70907817 : 70827593] - - 443
444 [0, 793869, 0, 14304, 0]
[3576, 3193368]
706532670
 1 [1619523092479039334015603471289260830282668 : 1450543990459769474101679397639722229018651419 : 944072263371407056341594352827743949283008] 68.1233298617163 [-253943520062286424644484484204233964780231861 : -101254678961258058949570863400052677515110659 : 253716684858287090495761036952738580170956656] [-232314432667423570768723976745297365934833297 : -233304539049849617873455645223102433390312895 : 233007187388929606086513904995040042273070177] ???,
 ...
 ?,
 ...
 444
445 [0, 797437, 0, 14336, 0]
[3584, 3207680]
11114110
 0 - - - - - - 445
446 [0, 801013, 0, 14368, 0]
[3592, 3222024]
716094834
 0 - - - - - - 446
447 [0, 804597, 0, 14400, 0]
[3600, 3236400]
890010
 0 - - - - - - 447
448 [0, 808189, 0, 14432, 0]
[3608, 3250808]
725742886
 0 - - - - - - 448
449 [0, 811789, 0, 14464, 0]
[3616, 3265248]
182649810
 0 - - - - - - 449
450 [0, 815397, 0, 14496, 0]
[3624, 3279720]
735477210
 1 [7715825132279477445243551349619436 : -7042763601336871644392976152775772660 : 434722160500382367549568031219] 50.0240335345935 [973605523944682007753897799665781 : -971909283054453805614327656902112 : 963630021089820579585658847320595] [-170906536751829696016274482571417 : 171155116828241811795805283957831 : 112742154241645819484832814098025] ???,
 ...
 ?,
 ...
 450
451 [0, 819013, 0, 14528, 0]
[3632, 3294224]
370188422
 1 [172678468948819573440718042200954040561302300717146108250779468527273987682919065964681486719823981667 : 156481119504307896830997506015179918128559085614640323239210356228703788254398534213443669063056033049404 : 25883036559034517918966814069441755858743761543351628131696854964480166382093267688013348668546578441] 157.530196435097 [-1102712025628953508102397606489830050074692181671261191653227110093253209543957547975081365376640449187 : 275976251942041177633263239458891695551379057224248264198846513067132590054267423068475190244998608517 : 1103321064537638337528537510723686423028622142621971310350348791703533908107874105757118543314192512282] [-16110192658458892487746395426788258979638220546309837099117925182496390826151246838080652280155271272409 : -16072274104336408198976185910464649591831504637068032123314624559876921386991070512600319097513776519835 : 16095982252767664270573177949833333003019272313389624425564546441877103215038052527929544635212955851589] - - 451
452 [0, 822637, 0, 14560, 0]
[3640, 3308760]
248432730
 1 [130595352093080 : 338251572072750840 : 22188041] 19.3750612551014 [-3985396717175 : 3988473440127 : 1397697553807] [-7816068897563 : 7797494070616 : 7824992874207] ???,
 ...
 ?,
 ...
 452
453 [0, 826269, 0, 14592, 0]
[3648, 3323328]
93780162
 1 [112165824 : -102793299904 : 104487111] 15.0719336467953 [-4347867425 : -7560158047 : 7550623137] [6159012803 : -6195823808 : 6205724413] - - 453
454 [0, 829909, 0, 14624, 0]
[3656, 3337928]
755206210
 1 [99630031789991202500 : -90788342583140592842425 : 3019978228972088384] 35.1100088014330 [79846932209808628913021 : -101729752956472556771829 : 101903629397593931811904] [63850119622811441525425 : -63729029838537830620673 : 62723303175077262760223] ???,
 ...
 ?,
 ...
 454
455 [0, 833557, 0, 14656, 0]
[3664, 3352560]
380096490
 2 [99117290384 : 91773622698960 : 4173281],
[45183825585360 : -41594244904382192 : 42746503582125]
 16.9545888279859,
24.3783326973912
 [-382040817959 : 382739371199 : 377535392969],
[-7186485024683653 : -12385765637731427 : 12370075356870315]
 [-36721890263 : 26855354955 : 36780359828],
[5022541702718881 : -5053064161287301 : 5061147846903164]
 - - 455
456 [0, 837213, 0, 14688, 0]
[3672, 3367224]
28340802
 0 - - - - - - 456
457 [0, 840877, 0, 14720, 0]
[3680, 3381920]
192558070
 0 - - - - - - 457
458 [0, 844549, 0, 14752, 0]
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775284906
 1 [38720 : 141361869 : 32768000] 15.6102675119929 [-40329902383 : -40235661137 : 40294668800] [-1381717777 : -5484628463 : 5481625617] ???,
 ...
 ?,
 ...
 458
459 [0, 848229, 0, 14784, 0]
[3696, 3411408]
390179790
 1 [30228969986776236 : -27881679520291312412 : 12121035004611] 27.7913538208966 [3483388643112630799 : -3487031236960197304 : 3489488709148091481] [467751700690807987 : -467554863671094445 : 90757324806312893] - - 459
460 [0, 851917, 0, 14816, 0]
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157091270
 1 [78867560316275593590091513197212100356791468 : 79890560443531775039362893620662560663922748540 : 927254855033571732165610830390233468907057547] 68.9240865156306 [-2374570051302408915802158998562763592834666967 : -2266609834486825436019236169345652024369906496 : 2369882168092289421904504779702465371325281399] [-675350153000197931359223477735805298339390183 : -741077303631462703725226615599167653637183591 : 739646622930499811155187850144878361405999527] ???,
 ...
 ?,
 ...
 460
461 [0, 855613, 0, 14848, 0]
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16470318
 0 - - - - - - 461
462 [0, 859317, 0, 14880, 0]
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795716370
 0 - - - - - - 462
463 [0, 863029, 0, 14912, 0]
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57205694
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161213070
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465 [0, 870477, 0, 14976, 0]
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22535370
 1 [66491068 : 68596376036 : 343] 14.8984868041351 [-8566396145 : 8582697864 : 7762992713] [-3729908827 : 3581408069 : 3737207755] - - 465
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816503674
 2 [-857476 : -110932948 : 1],
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 12.2773444205621,
24.0737601959052
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 [-98819479 : 99313209 : 99193411],
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 [11]Q1+[8]Q2+TC,
[7]Q1+[-15]Q2,
[29]Q1+[1]Q2,
[3]Q1+[-38]Q2+TC,
...
 1672.05577903255,
7634.02083638289,
9903.04220307721,
36627.3408740000,
 ...
 466
467 [0, 877957, 0, 15040, 0]
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58696890
 1 [94180509433080878656 : 113309443789249188090624 : 165369706597369] 27.5689386964763 [-7535668601565023517 : 7548123170166764035 : 5880054555266684657] [-2380947286013571746 : 2345360027218754159 : 2385334982299297831] - - 467
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827031726
 1 [52040723539794600 : 116906949429915166392 : 14380373566148609375] 27.3910702755233 [-2404450164096454813 : -2394097086747011387 : 2401441988902557875] [-88198211542025273 : -210873310498496827 : 210685824685234248] ???,
 ...
 ?,
 ...
 468
469 [0, 885469, 0, 15104, 0]
[3776, 3560768]
104041190
 1 [7032980 : -6825010156 : 125] 11.1040925055171 [37128104 : -37056789 : 36008365] [-9673609 : 9691289 : 8440279] - - 469
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93072210
 0 - - - - - - 470
471 [0, 893013, 0, 15168, 0]
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421496442
 2 [53936064 : 51665104512 : 2197],
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 13.2163662225640,
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213436734
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432296030
 1 [21814745142064559176272 : 20792320402416304860099280 : 250203847974126422013] 35.3780086725668 [-271591064649091246733759 : 248216945411316374768723 : 272100579752283111149265] [-56993002743181515507941 : -54454507337558447996257 : 56883869018382585564290] - - 475
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 0 - - - - - - 476
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 1 [11209371564094518272 :119337788374967750576128 : 99703702853] 30.6592388217282 [-66588492961085867753 : 66601002993119211015 : 5992510235080785413] [-132654823697498965694 : 132600052427243976901 : 132700542919488119609] - - 477
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892105830
 0 - - - - - - 480
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20401766
 1 [72086913941847884646522906587132072722201026800192465657476462570513026130639740 : -69573048845077818871824911999275302755160055961576927239991017135496016135338400713 : 444270981102781340643573652232087339166536141384626546086015930739120798296000] 122.145729773035 [70242935387993482322129801162791926215749151033025693608276566612455691241434259 : -73651684767286391249379841028056683412296466260825241738137119293430588252543819 : 73791288631494339110147926519764451320474684414092239722406738911000474636194520] [23562827963673037170829756398647864810325010681988322908587199443987243610302711 : -23518989715835469228030647369605071922837292611828552255801464354790851401970631 : 21666636460411372580421364458582496698438737876153880666057849886397061564203609] - - 481
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29137830
 0 - - - - - - 482
483 [0, 938949, 0, 15552, 0]
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1870146
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 1 [10591041289194597999750492670213800311937824304772261533100 : -10309527052444775610611176075474427729550570764125079652951940 : 3203265842760203126795806682447714313933296169779663940259] 92.7988034227992 [-269975703707472646673192033333956679652701661128964849595503 : -2847357466818666549325986052202563612040344352160234762833488 : 2846801982061362579719242713783013608785960887712526115177783] [2833161001119420478044501628368788383847780528671735039217845 : -2834382967614994114819240627500257335547607598989273987760939 : 2835393060282288547843421592019981254028357835521023272350459] ???,
 ...
 ?,
 ...
 484
485 [0, 946717, 0, 15616, 0]
[3904, 3806400]
23004930
 2 [82944 : -84165120 : 1],
[10863616 : -37334082048 : 1]
 5.86380839878356,
12.7041434944726
 [20251 : -20213 : 19421],
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486 [0, 950613, 0, 15648, 0]
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925885314
 2 [3727638531920940 : 3654836595429895252 : 348170767875],
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[-641065629691862913927955 : -668429139579932512984328 : 639625769064257744737793]
[11]Q1+[-47]Q2,
[31]Q1+[49]Q2+TC,
[53]Q1+[-45]Q2+TC,
[36]Q1+[-69]Q2+TC,
...
 97618.2006028782,
78101.8921968590,
206703.035362471,
270642.015751969,
 ...
 486
487 [0, 954517, 0, 15680, 0]
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66542630
 0 - - - - - - 487
488 [0, 958429, 0, 15712, 0]
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312443922
 1 [10869767639811754226146330135001286976336286611600675800696779708 : 15641834792489434410420768589869511076469966438197999856805169486868 : 769541989458729112384164367978199583433322089586413781762951491967] 100.607477931021 [-1161464793432239134595256979999274645839290060415527421233133766496 : -1149506204141345071590348135511606823915383358245651274553619110925 : 1159561661651721510927607431556066217493462816809939601318637731101] [-137049098566095766099498137471413821038448367220377584851558851221 : -201380124734764214696091317326015502628559543578690642951566439051 : 201101421362460532663329312690327650488690954592948814362611370411] ???,
 ...
 ?,
 ...
 488
489 [0, 962349, 0, 15744, 0]
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47154510
 1 [45236682647234580836066043592218752 : -44401771444211068205929781513957547520 : 3056656631601336664677637986879209] 48.1774559647745 [25134611276514342662607827302863 : -43721571024138009838958094455377 : 43772658720789410444932788753253] [162765726713361856919743415440618 : -162525217788293648225879767112917 : 161633581196755046613433374278323] - - 489
490 [0, 966277, 0, 15776, 0]
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948872170
 1 [230752125636 : -228575656885220 : 15438249] 15.4143934602673 [29028619360 : -28985506753 : 28822459401] [-4522844045 : 4528178621 : 2630075027] ???,
 ...
 ?,
 ...
 490
491 [0, 970213, 0, 15808, 0]
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477338862
 0 - - - - - - 491
492 [0, 974157, 0, 15840, 0]
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106722990
 1 [-9329086545 : -9186206137640 : 2679826869] 19.6047845780906 [-287047470029 : -3961529925085 : 278995378956] [-8829215856733 : -8824073132303 : 8790615841201] [1251]Q,
...
 30681507.4694964,
 ...
 492
493 [0, 978109, 0, 15872, 0]
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60397486
 1 [65423667332471791588204380852382238611739428853 : 64712433609133307586949534336480546410007999625438 : 369151765675713844295456115495382276482747587] 74.2917491223169 [-2132638843483937688049216123287543259499348471671 : 2042356873234340220786237704872491992759232149325 : 2136587898882203426015700222907873970925986354506] [-3651728011729334415467634980437172853692544801311 : -3339323505330608508825930858345501584403389285621 : 3645121547361293347932185882093205317270763973691] - - 493
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 0 - - - - - - 496
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1100010
 0 - - - - - - 497
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995980986
 1 [48258809358020972 : -48227013202867421923 : 72053614132928] 24.9972679427616 [47938542584196471 : -48419126152801375 : 48499101142323424] [8699151667712429 : -8686790663155901 : 6206335168215011] ???,
 ...
 ?,
 ...
 498
499 [0, 1001989, 0, 16064, 0]
[4016, 4028048]
500988470
 2 [93488497236 : 93826792634788 : 17779581],
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 17.4848902987120,
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 ...
 ?,
 ...
 500
501 [0, 1010013, 0, 16128, 0]
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4694634
 2 [1127844 : -1649067228 : 1],
[800436928 : -804542679616 : 4330747]
 6.90962061138806,
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1020109090
 0 - - - - - - 502
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513100698
 1 [263601446235301838160 : -267950313882964943404293 : 247417679057826304000] 33.0264412443634 [-2176061867943265974331 : -3766271445883710742309 : 3761970995619393872800] [3062352909999805366539 ; -3079018296516827302859 : 3083466008753382150581] - - 503
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259614670
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348207918
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[11]Q1+[-37]Q2+TC,
[43]Q1+[20]Q2+TC,
[1]Q1+[80]Q2,
[97]Q1+[3]Q2+TC,
...
 38409.6187894875,
37712.3772587881,
202179.797403449,
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 ...
 506
507 [0, 1034277, 0, 16320, 0]
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 1 [56025069723428 : -57876375638654364 : 2263571297] 21.3947006676894 [219405792122520 : -219051599079407 : 216920048656727] [-38900992381157 : 38955187664117 : 27807282304123] - - 509
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7922430
 1 [-1028196 : -139171500 : 1] 8.39665088092256 [-76744 : 77891 : 584927] [-1730729 : 1738573 : 1736743] [2395]Q,
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 48163399.3692438,
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 510
511 [0, 1050613, 0, 16448, 0]
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537907682
 1 [354354703725427617782265920487829414620631632 : 381598521681076086290039884948491670150222114544 : 3249063793597162818328176635049690069093] 67.5895099312171 [-301627790449105957441271032033486681219276577 : 302167338793103039853095874530582417119682465 : 287643422604911398242178639147813531429060257] [-48033406320298732849894768616002763220229249 : 44461478237945918408365663730591317624830016 : 48118096460740104578183656465876765523137729] - - 511
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22084230
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...
 9515336.88718703,
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 512
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 8.18973250709623,
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 [-50207 : -87425 : 87329],
[-32035133 : 31697123 : 32086637]
 [19]Q1+[-84]Q2+TC,
???,
 ...
 180228.647725377,
 ...
 520
521 [0, 1092013, 0, 16768, 0]
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285012246
 0 - - - - - - 521
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...
 134932834.867755,
 ...
 522
523 [0, 1100389, 0, 16832, 0]
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576597518
 1 [301481413585560606528193619471731148643675038128 : 318114941759966658064503029043683865711476052846032 : 232828193425801880726999970864578013827848949587] 76.3119037136427 [-81097156142634713222324419551397276046901297354375 : -41332788422638880964261540920936792832966790748621 : 81018532637538309434613698615216374266465448118531] [-34784137627122219753381401084661393332964185964127 : -34967119177273998009312636078671843870636672603138 : 34922325492899525629912088944210910779172223426053] - - 523
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42955770
 1 [11956 : 14271012 : 226981] 9.41202187735616 [-4496347 : -4364208 : 4488563] [-1014881 : -1152449 : 1150545] ???,
 ...
 ?,
 ...
 524
525 [0, 1108797, 0, 16896, 0]
[4224, 4456320]
72902610
 0 - - - - - - 525
526 [0, 1113013, 0, 16928, 0]
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51004478
 1 [155743940772524436579929831303781100850693468053118765119573394656123391379322021228 : -164549786345329841062088977060637747415982469335054807112198647244549335595062342652716 : 47778512065501930930278775641704574559137481049176276234578246332135949901090147] 122.486172116606 [36775116028851039278822604706007531649946189366619648798337281008223120426444160 : -36795886158980306105217620894426404775317767607166956617442768121688252487169083 : 36811883357249046593710228156539564362944170040197747746881050422546221838330803] [104965322395489352077368817734589174037184662356987423384221977787604428832222009 : -104939544795183952611506022927146747415428420083279132952785928940033338260451689 : 13611457486973947498908560441599294857997727820608093238727400057005772510847769] ???,
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14648166
 0 - - - - - - 528
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298309690
 1 [241395616 : 275981094368 : 1331] 9.11784722203651 [-1158049 : 1160029 : 1076669] [-826633 : 787330 : 828063] - - 529
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1200001530
 1 [7365796 : -8218880835 : 64] 10.1098413180704 [7723919 : -7710599 : 7359136] [-2433101 : 2437245 : 2255261] ???,
 ...
 ?,
 ...
 530
531 [0, 1134213, 0, 17088, 0]
[4272, 4558224]
603394902
 1 [4643668496870900 : 16947685512721285252 : 381078125] 25.0606474642029 [-21833818907461552 : 21845782929448977 : 6379062172203775] [-20896570864905673 : 20864228783639273 : 20914280049720823] - - 531
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50851794
 0 - - - - - - 533
534 [0, 1147029, 0, 17184, 0]
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1227308130
 1 [342116 : 372016988 : 704969] 10.7908739368738 [-14656128 : -11449085 : 14634893] [-9077947 : -9214757 : 9199877] ???,
 ...
 ?,
 ...
 534
535 [0, 1151317, 0, 17216, 0]
[4304, 4626800]
123419890
 0 - - - - - - 535
536 [0, 1155613, 0, 17248, 0]
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177302202
 1 [-30649740490765435621708917795225433212 : 31603218416901718144286408420829336567396 : 164243674699938779562521233826805030619] 59.8538396451529 [-1201059404973260553658278697402285477321 : -1098451552970332897345660488243748670284 : 1096168189185182481728299942716754425151] [4349865315224267104152795489367585829181 : -4164336492676258470511082406603794070755 : 4172799311126227595014722159657975913559] ???,
 ...
 ?,
 ...
 536
537 [0, 1159917, 0, 17280, 0]
[4320, 4661280]
11556090
 1 [21070404812916 : 23679923524780716 : 204336469] 21.6200513204622 [-328607442409915 : 329168211056216 : 315483043359299] [-293708510230277 : 269618189584987 : 294198962981653] - - 537
538 [0, 1164229, 0, 17312, 0]
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1255025866
 1 [126857334604 : -297271412762324 : 31707522387451] 24.24199938299869 [-17116594827848875 : -17190912681039456 : 17170895351782531] [1083011596748081 : -2348882702264431 : 2350886271432031] ???,
 ...
 ?,
 ...
 538
539 [0, 1168549, 0, 17344, 0]
[4336, 4695888]
6642210
 1 [6650235947785096601484196 : 13599789823811688601324598412 : 1155475137541775440144528801] 41.8839947958476 [-11016959070107460991165350867 : -10957310869125830778001646488 : 11002929279992635489012023643] [-831997107875334003740696431 : -1573262284571318623202744399 : 1571726611962351089379192095] - - 539
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1269039870
 1 [65820430154365725836753359610916 : 73652612164654015148721605947619668 : 830347785751085373440327841] 51.6205727612239 [-9198799845660119017218384671518757 : 9214353195503384769962016815386160 : 8919119164764218690237858325296781] [-2443149724741753334810916003157601 : 2185523171104197163483469510193215 : 2447123214678302507543199004246097] ???,
 ...
 ?,
 ...
 540
541 [0, 1177213, 0, 17408, 0]
[4352, 4730624]
39877682
 1 [167608722703027915531193434112 : -432653048014188998912361119125504 : 30551859508144975055873] 41.9261587798138 [1555386541855448796073485185 : -1554182857970541593993507679 : 654119731116249194003735599] [-2823776614702381589915146808 : 2826850824292988524850312653 : 2816229938061360402467224427] - - 541
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38883570
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33954102
 1 [271663 : 327978602 : 1] 7.08579197218725 [-42911 : 42981 : 38774] [-49841 : 48181 : 49925] - - 543
544 [0, 1190269, 0, 17504, 0]
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1297380070
 1 [2617972 : -2882082469 : 3241792] 15.5746930795631 [-11301381351 : -17065546289 : 17044907216] [12727350013 : -12819217165 : 12837817747] ???,
 ...
 ?,
 ...
 544
545 [0, 1194637, 0, 17536, 0]
[4384, 4800480]
326132610
 1 [1698427266226397681255947546524124117492 : 1862398342118210671296271677060037095447444 : 752267952629573184312013963121259995317] 60.5679770683857 [-2944430718710064562579272228217532414840 : -818405214008910828222797711025709246521 : 2942935007750986246186002186199198404113] [-2824730241917972747139770118163476875117 : -2830960072028862811379453762261100539651 : 2828711959664949351150043719673451090675] - - 545
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131890990
 1 [74303450122116864691479942647767560000 : 81524550009735352657532029322954972672000 : 202095515638891697966188859187739989] 55.1834251138000 [-1311138006822043937323117521667727087 : 1285185241895642453044144558681157393 : 1313286759600245874240385477829217147] [-734242604957665816260795692138027270 : -620921501636919644733656753932594303 : 733121979976027248878945296552195073] - - 547
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 141682527.053437,
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 548
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166674330
 1 [58265319510167376007659261432717470870373928466988637141448015536999902242800357666863835009050551036 : 81061502706437088279353669478151533889376460142945387104516395014386510653988456710622919386122358278852 : 80545751485803076626718808218684343212252367342461637668024184976158993945037114406534722939551] 153.231061486095 [-9179917619783032888682274910128729615657945548609766860603681889579597174735144791121178015463486943 : 9193043102437522025042491517376151138960472434832070651752708639519793272678376675475131908861616928 : 7276602197443677432777299375465973097145477615262427747106488567154889731378428766181002429432253887] [-5650238336044772506188201308736329036671930517813900755374120600356293883584508490851921296495227889 : 5572781368529619405793689925811648936800783082914354398101446252095837400717438729026205684022291599 : 5659189654555578126312176954361715097014011168115248674868766001621370003646624880130551184214769585] - - 549
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 12.5087418449363,
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340670374
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 1 [562192376997986900 : 763745153589473449548 : 919747953125] 25.7510948961779 [-85712832390987712 : 85838190427851787 : 70211368106316325] [-49722934678923187 : 48924545808128787 : 49802244077053837] ???,
 ...
 ?,
 ...
 554
555 [0, 1238757, 0, 17856, 0]
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25508970
 1 [9537718641924955408 : 10618476502066697716880 : 13919778751592377] 26.4304174726927 [-598154522184522485 : 592257641724300129 : 599055855350420891] [-52502185540789273 : -38520568290489997 : 52433318842744642] - - 555
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[19]Q1+[4]Q2+TC,
[57]Q1+[12]Q2+TC,
[95]Q1+[20]Q2+TC,
...
 6573.30433383557,
59159.7390045201,
164332.608345889,
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1430138170
 1 [108401765460697239717195409237430469214758799214615974498390788680434826737640 : -124003864904499393248562589855804873914775729473622344156795297085864646720361640 : 2818935576851265566005030284848514659752233970156640317119681445448091937] 117.440151880321 [27455647141847947515026867815963448915426638976834480556871749317347711542377 : -27413319630054438878142419730852866976067046630963016857639444083477353378137 : 27055294917803950026848399193962186849670355223812373285048272254792900428233] [-44160617602373597465666220154686033360421263020547731167823138701144702203437 : 44221990499366553804290028880333102421605651465167805927311839420905821297045 : 34816306113407491417874594859162601405390693644432055178647861542213697954592] ???,
 ...
 ?,
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718883958
 0 - - - - - - 563
564 [0, 1279149, 0, 18144, 0]
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 1 [-3756414399257184 : -3613675588482567168 : 73228222264137409] 23.4215259887567 [-12082719072375845 : -12348508686121253 : 12059096612612833] [-1691227275624316 : -1438775820788779 : 1435749432883349] ???,
 ...
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25948370
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1476323926
 1 [9322012 : 10728366412 : 343] 13.3715524151654 [-1340076403 : 1342015200 : 1328582563] [-224331253 : 159533387 : 224610133] ???,
 ...
 ?,
 ...
 568
569 [0, 1301869, 0, 18304, 0]
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123676410
 0 - - - - - - 569
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1491937290
 0 - - - - - - 570
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749892542
 1 [23231428362302193759701980942928 : 26616750349793943342640912444951856 : 2091923301727643353023122377037] 46.2152385176487 [-1972516931286234711528083501491 : 928175129502120055542634942815 : 1974135173535944437974098088271] [-872756127450631319950136870867 : -869085885987514261513644154802 : 871784927942599908722887131497] - - 571
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301532070
 1 [11687090337179633232743344966868478161700335989187592 : 56684110185289256196686362276735905597167046157130835663 : 526247995105532106147522798807583561636561408] 85.5710416222998 [-56672425515692854048901307210373911633889729349324124871 : 56695794854885658344471417343097899560444362964937546455 : 13416782127822996436637048300569887444516369243769832416] [-55087639566406479607744642422264097534467995766349885329 : 55028128470514800388482550291594813864122365348802840241 : 55124354673057696505001604122511820408166646639180627569] ???,
 ...
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 572
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45042690
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386862610
 1 [2394344259410257279980 : 2772803976970662453810540 : 318358890466915771871] 32.8509722992944 [-1740817575605631712300 : 531972569452288331807 : 1741736026296543898237] [-3712103690917253330871 : -3703474040122152791953 : 3709108213614963829369] - - 577
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[183]Q+TC,
...
 81626.3515254973,
734637.163729476,
 ...
 578
579 [0, 1347909, 0, 18624, 0]
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781780230
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 26.8997649602361,
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 5.96431678956932,
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 1 [386397047470505608457762704174475475688338830428615644539325185944191473133840550760470705212353707094574894576332212802138646989528434939788 : 49803643997469527998484907180290882775281120399002168539048108868259000577278949163384132030684585666881890782414057145335245021858238572747964916 : 23260889050478195701967446423183391115027458537339933056333275219115814051246012360918511285770249844066643675169132422319653525203] 222.267240528765 [-6225407200068411764940528002905762628918481429741880970021075967831044342448191858210660011316319822242172904084991952833694186521627257361589760 : 6225503799298970234680698792166958064901798670008661164740951249233705801871545432635372996354826594478299791518522333500117068942932385825401469 : 64914703990699520551875960008735971358443345732420907878236406185536461708950155384247644794573580887211960433880662944148118814461903892346003] [-6225119568247476033004809635149668717004138207274205119793224386582819352543791298244201615309733880178804738167824278872037571263549493883151797 : 6224924343087782476576730380272855980192366946104633024411833201776742844469277460251761835659057870817474576883831973311617060609582863350936789 : 6225310761111783672637518747411942863994124914307007133151598928198430799101626328664527540155060335434840934385780020701424249963577369347126795] ???,
 ...
 ?,
 ...
 670
671 [0, 1809013, 0, 21568, 0]
[5392, 7263024]
1215648642
 2 [68268273100275712 : -309931354631199396864 : 3630961153],
[755998176914140240 : -48955574094447562511856 : 180362125]
 24.5500683019715,
27.9468312394489
 [14383797481725925 : -14377464083901339 : 4263600369854939],
[2271544640481252973 : -2271474484838676733 : 47214808235845645]
 [-6869487631220768 : 6874152596712493 : 6860886618793907],
[-1135511231850443761 : 1135579943089779721 : 1135439601349239576]
 - - 671
672 [0, 1814397, 0, 21600, 0]
[5400, 7284600]
18090090
 0 - - - - - - 672
673 [0, 1819789, 0, 21632, 0]
[5408, 7306208]
47174218
 1 [2758928346309393808202704460 : 3759368728145754831995431841836 : 4711488814926692300937912875] 41.9268702267190 [-2705064888131291395416308472 : -2009400800761610634499315163 : 2702098887735125240983149875] [-1801543731783671773547789183 : -1819325588736297205726951537 : 1817047599978328312938646753] - - 673
674 [0, 1825189, 0, 21664, 0]
[5416, 7327848]
2463988890
 0 - - - - - - 674
675 [0, 1830597, 0, 21696, 0]
[5424, 7349520]
1237475430
 1 [5560600862540504145337374215365276053175580067624631692208 : -10352839611017839184445255282971774540724539648878061143292080 : 3399361884644511345450416531967331903543594263591787] 90.3374074111364 [129479772171768967209513186676598380324618380106130000664145 : -129341218103677012401618195397695983193495111115821527918157 : 94113400075233811557704280133298164585099752900237962913779] [-44596364754289255133638418390744534358436680845853539140895 : 44651452319660625459909584004778034169146266450516608175018 : 44246720519077076231333501749293894037379337791068028127761] - - 675
676 [0, 1836013, 0, 21728, 0]
[5432, 7371224]
2485945294
 2 [-181944 : -246510712 : 729],
[332532534236 : 474175906628948 : 1685159]
 9.65552613989806,
15.8669495224151
 [-4328015 : 4475939 : 4334931],
[-43648906400 : 43708482441 : 41536778759]
 [-995429 : -1091356 : 993791],
[-13980968191 : 13213370591 : 13999987009]
 [9]Q1+[18]Q2,
[89]Q1+TC,
[39]Q1+[97]Q2+TC,
[59]Q1+[-79]Q2,
...
 4912.08426293349,
76481.4225541326,
140371.679526814,
161721.877742740,
 ...
 676
677 [0, 1841437, 0, 21760, 0]
[5440, 7392960]
104040510
 1 [2827697843776 : 4405466813805504 : 4826809] 19.2853659014386 [-7643516273963 : 7653243496195 : 6666735989043] [-3792322905087 : 3717485978468 : 3797427607547] - - 677
678 [0, 1846869, 0, 21792, 0]
[5448, 7414728]
2508031746
 0 - - - - - - 678
679 [0, 1852309, 0, 21824, 0]
[5456, 7436528]
1259561930
 1 [5376 : 7390592 : 9261] 7.40743335951342 [-124813 : -92957 : 124677] [-41428 : -41837 : 41785] - - 679
680 [0, 1857757, 0, 21856, 0]
[5464, 7458360]
2530248630
 3 [830028 : -1140646780 : 27],
[454276 : -690743508 : 1],
[5734124 : 7824653340 : 1331]
 7.76170968260294,
8.09569314092889,
9.95832459745620
 [313552 : -313177 : 311073],
[316480 : -316069 : 283717],
[-9316895 : 9313232 : 9319783]
 [-47077 : 47125 : 32827],
[-141877 : 142069 : 138315],
[-1015493 : -120037 : 1015317]
 ???,
 ...
 ??,
 ...
 680
681 [0, 1863213, 0, 21888, 0]
[5472, 7480224]
70594614
 1 [2652080256 : 3620411937792 : 10218313] 15.2272044629546 [-12755814119 : 12385935449 : 12773111939] [-6940033498 : -6311212335 : 6930922753] - - 681
682 [0, 1868677, 0, 21920, 0]
[5480, 7502120]
68989090
 0 - - - - - - 682
683 [0, 1874149, 0, 21952, 0]
[5488, 7524048]
26161422
 0 - - - - - - 683
684 [0, 1879629, 0, 21984, 0]
[5496, 7546008]
2575075230
 1 [1419544132892212718586700 : -1947192503447652976211360420 : 736330716842507310763] 34.9714403893629 [177036159319080368604333 : -177514551432495191521552 : 177682212668234001281947] [21827903930760463957105 : -21812629864737224036719 : 10487209395916966510399] ???,
 ...
 ?,
 ...
 684
685 [0, 1885117, 0, 22016, 0]
[5504, 7568000]
6465910
 0 - - - - - - 685
686 [0, 1890613, 0, 22048, 0]
[5512, 7590024]
2600286
 1 [-552290648 : -292472274744 : 343] 11.8877099638694 [-34653145 : 34784717 : 90212493] [-105688011 : 106190296 : 105911269] [2669]Q,
...
 84682827.0779319,
 ...
 686
687 [0, 1896117, 0, 22080, 0]
[5520, 7612080]
1304520210
 0 - - - - - - 687
688 [0, 1901629, 0, 22112, 0]
[5528, 7634168]
2620428166
 1 [-14872143994079438431223473178338202740569928210996938261674232251459634767199635666520865911039673170630248174006052652824 : 6446959942253457096582536689868714632523795023016314223766128450743025500077258071093796569201337253023821490572488797374104 : 1152613631073572491454857542903582854933651976299947845063872651211202839322454977123003942784462645826022005346417107050577] 184.096054074212 [-835468905670003105681911408988386563527091948976933570059647078578638010181250343356699264824617677139466160201575373063 : -833779930540754323864015199030767419009307222462396212688479420635888250024000134015984259189635230524976193124462978157 : 831934088149865068168183370366606983536548006810294967665366753179719780832147735852311214628139537556781551450644708777] [879830567403425553939589013598473554189590900398531424501799478144815917658653038265315038680798526885432160671329429859 : -275737680584833137475763933465132614486071227573923161076376945149705792295812993079725421482074135873287118631858909889 : 277016913539078862147568003782841277102279258143608569663372812481214434468813947397784499031068436070753209888160112300] ???,
 ...
 ?,
 ...
 688
689 [0, 1907149, 0, 22144, 0]
[5536, 7656288]
26318490
 1 [785163931972236668205616736397321224374706241645508812707663961448113619362214480797159273944402762271847575334588438079543988061664 : 24217642800036913804216355919091701012614195423344140782630541970724242977956359880386344587087033070316353142999441052794073829071670048 : 826968131128402438455504955090798148617718995949229626977547788745593272633027917439846919192802245715584597412398914912371] 199.532894364876 [-3163002442003623314780607286670117310473754287697927198584061822349224509688324423428427715723348078364533116793096445122105474355 : 3163207543837273423747607931746875627256434394688143122341833852088373182027650701955137946144918389750656161091810980720306365187 : 141726194020356424599884203544951987630102547958199265850099527299521332067731094984686661152004360613269325996341510755730477283] [-29389246119492016576270289085525213076207698657909988787068560114152020806274814110034179219880320381314218239987508137559633639591 : 29385255916244768876344429578784698411436513150818025738821392107050156653281796095271899125055587533308734581398857610277694030936 : 29392893849598505781330999305537595476149278021724014415458728706803800216188305233102600250217202580379877124538982870163923822319] - - 689
690 [0, 1912677, 0, 22176, 0]
[5544, 7678440]
32633370
 1 [-41676907800 : -57601159593912 : 4699421875] 16.7552369838924 [-119340484133 : 317031937033 : 119800172425] [-595083360881 : -596600325344 : 593829325231] ???,
 ...
 ?,
 ...
 690
691 [0, 1918213, 0, 22208, 0]
[5552, 7700624]
1327395062
 0 - - - - - - 691
692 [0, 1923757, 0, 22240, 0]
[5560, 7722840]
2666310510
 1 [-5027122271726500601932167796141593700864645016 : -6971782642940542864858586022314815678302253716072 : 88744780277788432792327043135427132447965257] 65.6937403613776 [-4191032406682200251417429012310043473767877 : 4836453133534278226524087349954117998310081 : 4198083046399950762385670647852057792463291] [-9905630071035844910466991255362398500719047 : -10108648690073991684841455776136045869065255 : 9890010733645993558491708061282817189011348] [??]Q+[?]TC= (where ?? > 1000)
???,
 ...
 ?,
 ...
 692
693 [0, 1929309, 0, 22272, 0]
[5568, 7745088]
334733022
 1 [41419840 : -57987705152 : 57066625] 13.1352391787302 [-312160869 : -451554391 : 451106425] [324940211 : -327043466 : 327426119] - - 693
694 [0, 1934869, 0, 22304, 0]
[5576, 7767368]
2689451170
 0 - - - - - - 694
695 [0, 1940437, 0, 22336, 0]
[5584, 7789680]
450178590
 1 [6141905872 : 8818912212720 : 50653] 12.9744021497017 [-1184550155 : 1186125171 : 1150819843] [-150340175 : 136917796 : 150533907] - - 695
696 [0, 1946013, 0, 22368, 0]
[5592, 7812024]
2712725334
 0 - - - - - - 696
697 [0, 1951597, 0, 22400, 0]
[5600, 7834400]
136220630
 0 - - - - - - 697
698 [0, 1957189, 0, 22432, 0]
[5608, 7856808]
2736133386
 1 [56871449246347937526889853392685508083055473041302475400839413256366109448382209498738883775122908893670640476865153097399259760659070502317308766260945863770785016679805452980604061703543178207389685162068243896334203853367090199420181593996678497330025482320161207267100649997493295076952 : 164534219358677469733504285216306645209380154695549240001356023801569506875861972481229018481111433297975315433522522971798716548701469846638686601421862440660813351913192876245335616523958428542820993222510590738030208228140848963679845144539572085099438988590592567659695573297303770447824863 : 8868453964452334226355330221777957051134652364261676593379872811115208160741769569493853802294456240989550101753876801542510587097845248423790033926106264548670088646214831326503116530402285907940678015459218279039194659413316162305096669170605744613420845624826543707141496546846208] 445.210464796708 [-117399998318144863986201096904786469259157917191747606213731277703525956816917170386562473461005305964591180772621433586325781826795277102678459995196368131620966563767573303900877295854198706538638811754939923761191993487573969923881130028499426206537562280636955510692138174373175525957375 : 117481114256698062114447418750183759448022888940371223195770540714132154354905773912122777761138067765566300217417856880196297471850647018147645074642122147694969698778026804943284897613265145770884376285760419904804021113626385484655408364847571773618667538907073850706427954530898379035951 : 56830891277071338462766692469986862988622987166990666909819781751063010679387907735958731625056527993183080754466941450464001938131385544582716226538068855733783449174578702459400260824009958591266902896657995824528190040340882419033042425822605713789472853185102037259955759918631868537664] [-102886509741419249701930191014274883988286529597881291840559702362016221712692924128247637892902437279367500797024359171778627775385941887949788893784330427661866952230821256127621508545600960453195540887875939029138343805231603990808626037752144783587060460402548779521577094975117143279799 : 102611173042497208369145338154170331355525630195186015403180190251093122053852760939152155069655203804368790086052166557200868311367694408542826704602237258869140581933323201259521905348011200558137529231144373364157806298267792335994135496596856744668035972732649848359026468486716310501719 : 102982182428669205906321050962402883482869031979812515147063152408449248533720426812945260989030689098250235358472822716045281026956583680332330714504104771959045784719658234158620420256288773919143061783604297776066201482758742723404227507728549771703008038511058471759831448200287903205911] ???,
 ...
 ?,
 ...
 698
699 [0, 1962789, 0, 22464, 0]
[5616, 7879248]
50886810
 2 [1455552 : -2041428096 : 343],
[114660 : 162825012 : 274625]
 9.82008645384253,
10.8987931644736
 [14173315 : -14179853 : 14184793],
[-23680616 : -19157699 : 23653435]
 [2292958 : -2292503 : 318973],
[-41467237 : -42025003 : 41972027]
 - - 699
700 [0, 1968397, 0, 22496, 0]
[5624, 7901720]
2759675710
 0 - - - - - - 700
701 [0, 1974013, 0, 22528, 0]
[5632, 7924224]
43304646
 1 [562842136132063357560003460368884834228773105092 : 791064616800459625274276897990782332570004372388356 : 416734969124929514806256042957347827744869673] 71.9459042781812 [-211313652987856920294271249617363867457791765800 : 210362581980405140086473365516315414295941908181 : 211541336553249649188900239688856039416714843219] [-28469492958730610487709761965504001298216984681 : -17451389080353327917018242860541012675407392519 : 28444711415612983482161378461096113083552009719] - - 701
702 [0, 1979637, 0, 22560, 0]
[5640, 7946760]
2783352690
 0 - - - - - - 702
703 [0, 1985269, 0, 22592, 0]
[5648, 7969328]
1397620898
 0 - - - - - - 703
704 [0, 1990909, 0, 22624, 0]
[5656, 7991928]
935721570
 0 - - - - - - 704
705 [0, 1996557, 0, 22656, 0]
[5664, 8014560]
704780370
 1 [10103621744531633555521427587362198342946260 : 14372839339136597290905677484602194230076327604 : 12072784959541453299940155046718367496189125] 70.5057861874131 [-10342873716029357143526399280203458191268573168 : -6749663881245207820799979909052909633749491267 : 10333346894701315167296042099142872744417651955] [-7809548773520133480227895885436748691934952987 : -7859938014683708088748914691554718596065304133 : 7851204355326004798170166160279402109561992357] - - 705
706 [0, 2002213, 0, 22688, 0]
[5672, 8037224]
2831112154
 2 [-1976836 : -314913068 : 1],
[679447598748 : -967261984330564 : 27818127]
 13.1118885173075,
16.0795511924808
 [-39116320 : 39611947 : 349899263],
[85372587113 : -85280550560 : 84884931567]
 [-346433479 : 347541619 : 347317641],
[-11539435813 : 11549561467 : 7181786773]
 [71]Q1+[-21]Q2+TC,
[37]Q1+[74]Q2,
...
 102681.282157005,
51841.9723319532,
 ...
 706
707 [0, 2007877, 0, 22720, 0]
[5680, 8059920]
1421568390
 0 - - - - - - 707
708 [0, 2013549, 0, 22752, 0]
[5688, 8082648]
45320562
 0 - - - - - - 708
709 [0, 2019229, 0, 22784, 0]
[5696, 8105408]
358411010
 1 [472752681062570689982806598528244228036756341298164424728570888086021886868102055293347763290334731440007601680213850179469529996755064 : 718510195428719782969166865932169035151747648270112442410485524670797249389924825165885780319283546179806142938326613291809078292097541073 : 1626279330238723966855784409217411203042255116003805739686794155092390737469052624920253680125952048695978692005335677447126982144] 208.946556018085 [-8067940517244070247762913144737479699976667647347809389474721458002456559108958953194876160909609088440848400351416425097172444914506497 : 8078356009244014762780162494187667157365976134003032013008099321116582753024183185364354857501257117846930092644687244381683247042741617 : 7553523323124051246373777456799530276881798269787983928556416391436298082967210633156090619818179612702923391953862442103645061692988688] [-27546988592939368198319682838724847871323570792836175303368942191997188233817762807050255923896806048073690263950906415122095531689341597 : 26452914436672634349224437857157061828969976938466568802084860540256399414810719701429076349511456348233949134127230994252013031957778237 : 27582992616874006678196229305651614059007268299354222444607115348376452566385947290224759329139723653036793587185470633367318126576775165] - - 709
710 [0, 2024917, 0, 22816, 0]
[5704, 8128200]
575882970
 1 [363757628 : 517685834055 : 6644672] 13.6925923351512 [-1948151879 : 1684731167 : 1950498496] [-992023643 : -973247893 : 990755019] ???,
 ...
 ?,
 ...
 710
711 [0, 2030613, 0, 22848, 0]
[5712, 8151024]
1445787882
 0 - - - - - - 711
712 [0, 2036317, 0, 22880, 0]
[5720, 8173880]
414824410
 0 - - - - - - 712
713 [0, 2042029, 0, 22912, 0]
[5728, 8196768]
81000006
 0 - - - - - - 713
714 [0, 2047749, 0, 22944, 0]
[5736, 8219688]
585652770
 1 [-4291083580495771239337504 : -5938666814436289620332059520 : 24765228691284681455928857] 37.0028446793598 [-11873602236771906750010049 : -12909657159039228735413409 : 11855244250343596337794541] [-1821014312267431422943216 : -1761297594275721223780231 : 1758644027514707963930209] ???,
 ...
 ?,
 ...
 714
715 [0, 2053477, 0, 22976, 0]
[5744, 8242640]
1470280910
 0 - - - - - - 715
716 [0, 2059213, 0, 23008, 0]
[5752, 8265624]
2952894174
 0 - - - - - - 716
717 [0, 2064957, 0, 23040, 0]
[5760, 8288640]
6864030
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 ...
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 ...
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 ...
 ?,
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 ...
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 820
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 ...
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 824
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 ...
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 832
833 [0, 2785549, 0, 26752, 0]
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1161568914
 1 [4031882893402769233329952 : 8019481867453461947168887392 : 176430727860762444614543179] 36.9480818025023 [-2019721719978067176636201 : -1992453474685871900443499 : 2017541810097318314770901] [-710364495895068753609677 : -846483964259704609030750 : 845638091590526635616227] - - 833
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 ...
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 1 [20781194911359762072560558675376598964665883759053873245444916082355131366534441220947612 : -35268057646390940135596850118378516925156628168842552761556078522025354639078017851627973703 : 66640680136065288645214518269033937014195006660384586846943533625947248922207562409408] 135.007403852291 [20503638738303152404286022338331055180944536790648023216152034967305043247659529645947585 : -21012615112657342163809151432567728721535308022586294337180606023896080518176865706174809 : 21035683098536856952322123222494935734961269375023008805959201610650650001793109251061224] [4920448932135685171052407208984511049603085707293647461351243788932352352373971457512091 : -4915223717666528405349405447934530877685766851352788873284896057608982118608173930338571 : 4488775897222563035463686033927556854754267597824363244396825929445253959363265583420501] - - 847
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 1 [140 : -475308 : 42875] 9.22146978491364 [-4133216 : -4146419 : 4143195] [236289 : -461969 : 462241] ???,
 ...
 ?,
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[39]Q1+[19]Q2,
[77]Q1+[46]Q2+TC,
45483.5827818219,
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 ...
 ??,
 ...
 874
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 ...
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 ...
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 892
893 [0, 3200509, 0, 28672, 0]
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 894
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2880483170
 1 [360009320731038082173605495017852578917253809864721945793536 : 980088983166653189504793758544183839761572869824506141920174848 : 52575928960482076361437952449872557020794894609712859178670821] 93.9317970802457 [-65927089593654101450555861865065044502885302662289662562594979 : -65585832983916408835825780472814284112996175618478901371118595 : 65868964201513704543870072886132743238852380955967007574917267] [-2717620234404037017708009573148678506142735828824089197157144 : -4125502940869408797286162156344534827548593750537434413369345 : 4122478453159517048693514700576515461297409456867370220283113] - - 895
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 ...
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 896
897 [0, 3229197, 0, 28800, 0]
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 1 [12623617068878183317608900 : -22688444430681912639314022500 : 11816470963867869061209] 34.8294272566878 [62857113554227187785967 : -63259864937612237668808 : 63319461036083441529465] [44334399338143608225377 : -44297932356803303247551 : 32873319106575405388399] - - 897
898 [0, 3236389, 0, 28832, 0]
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 1 [15666868834181736158628 : 28574327706307167194884277 : 48965183126087747499072] 35.5192909108502 [-211826596785293431111625 : -180094972458467037780271 : 211627653456061970604576] [-110731932157639110427621 : -112251952119645741071339 : 112138763257933731543349] ???,
 ...
 ?,
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 898
899 [0, 3243589, 0, 28864, 0]
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2919219270
 1 [56462879767806373020822224030080596749894898617945546719325695179837857379243975123209209373113967301958347814194179544231788592 : 138923626175702630647466659920339693253661510118390600414755448317134764280090483450368825329604829254768473122223496505621650960336 : 5497197626675070051156122425683542356032710398879389799076019536604452831827023538449693875471600411359373365518096453376006471307] 198.025900471328 [-4139626168613065756386961861629445845859915750159468536293738882982496522554753857417661878278213423841171455943530918249515403091 : -4110731903601480350678254153659325277379536900301234218403814704879931055774368981492044402128129224744921773513783934783287938249 : 4135765826063736748474012174650025673510331618721216167358650361777433387423169664790454866960630193162163804943818835180945131031] [-208806076978444992547462053316004643519149533668332962801993284392246041962503000251415483669958371551737614099855896615593888801 : -285217938408037396133714330621231135105753140616743380661673980381604860203939973235699033795032564857028825306491253256876021570 : 284986784570798559101720641806904005327509007167197142787456637794580258252138636252589056404223875093543785537949046567320698231] - - 899
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 1 [16956065884733436006308 : -32112182080731341116987220 : 50486028902970857] 33.7571536992422 [42274701888872736173056 : -42231040428841319397963 : 40248825746226202127435] [-13207499162544716400821 : 13221180663280257445045 : 12637911158812694605643] ???,
 ...
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655221810
 1 [42097548 : 92465282548 : 27] 12.3881420172923 [-172431680 : 172588031 : 142001049] [-98525419 : 97517659 : 98622901] ???,
 ...
 ?,
 ...
 902
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2958301098
 0 - - - - - - 903
904 [0, 3279709, 0, 29024, 0]
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44633470
 1 [35920499794422032773977724 : -65620337103130848313765801717 : 71245534451916963729543616] 39.9792539866737 [-1742476217684108951641037445 : -2249196967515235193446178771 : 2247280091160626301961452176] [1415789344035628765539703121 : -1426587801714027794067741761 : 1427953420343288356240414751] ???,
 ...
 ?,
 ...
 904
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135362370
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906 [0, 3294213, 0, 29088, 0]
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 ...
 ?,
 ...
 906
907 [0, 3301477, 0, 29120, 0]
[7280, 13242320]
2997730190
 1 [2254585445 : 4097383656940 : 99252847] 17.5336407344511 [-137648279933 : 96487929035 : 137754201862] [-583282809359 : -579763910269 : 582756891363] - - 907
908 [0, 3308749, 0, 29152, 0]
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 ...
 ?,
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 908
909 [0, 3316029, 0, 29184, 0]
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34290630
 1 [497207675317406838413750402399134996164096 : -925486782628711689621645738086780804931422208 : 3344504454679883192342393956133903549] 58.5556990197120 [1322738944504719430015039538739480462275 : -1321388131482411700052288063675211451613 : 1294136247961259776721099268715612880513] [-703693765034124238217254053524504100442 : 704386279927456068192916206416119649617 : 637194690085168644267034303107580321833] - - 909
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 1 [-2889816 : -1934452824 : 1] 7.59995342615432 [-44003 : 44135 : 120343] [-68359 : 68596 : 68469] ???,
 ...
 ?,
 ...
 912
913 [0, 3345229, 0, 29312, 0]
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1528764154
 1 [1786648724909025247997403500519415729694870211565567351049365938553654716215089387010219756313016868825185152462932502943827272709483317129684206960716030536671123412510820105690315500270188148436119531721248562770387469679757456540101592372446905500502751632495595543034582185354849694752493259350269008746 : 3268034061924311690756826574166134227838201489949538594876284406688369769465604083154540778425491123951811386504774065733544479736696558618618246748873159166033233715088492576441942830001140853745992986095991175442685984627318675391158377841897641950421413210719448229656917515627972566302980213887592074424889 : 28560809169189328140563676961330968151288152085746673062320472267825140073179196234211502203568780230367316012180299746214833498462279408877874265911493833981688556744552137330489728718262491463310800713006217707006026528549347091718953741382865803606821774934827532596024014092050023142952736730118679944] 472.118633063924 [-15177035034022803764728732731171389286991904795730675317580434329818509786924218968435949549418908858563833594277591134370580577907068379081858625163807292362071512382096331086000354788420516170483399188599037075270112487156543814073077595049689238662671180898730868091605008334974499066374608626142146253475 : 13364747166189525412186783200410569034739112583741277476098905466586466365613807958677943711939092223984737466899474941904917061714735626320920822424604578083633585566274783118732770364427875565289465318789532142569939780330955534321318717979984490161969982513666059678324402281863689285616484944928526885607 : 15191531773691421836023139872153555108970533037770043111882201259090876668689391826344995817469750617808823234691806624137407025917406348714319481915763155884392880300082440418214437107169746065856944500763294468239079615350068825137565096325028286789304914647115091714484495085004006598203582180651973679628] [-110203109005576726003579880333059604873451838092952637591082428295972358651162531471021928740940654231447706066830149295500483437785362546139816171192865347976627705322233190102179734484306536021567629255096881994321675850236478648978857834137814110927862866228024027239795643221124595719171944305001762581189 : -108343974323001782892940988177163436389789961948038723716100550035774737820004133339789103042581191766589384742627409719611585983007404880961796861096721708820231607016183304250580479901702515443130873295177277362234910048312272110757551548564198383758454587567820200510373609222533889044606486752224194354771 : 110092162471575563465670146126769431520127294221345979945984402351128426742142696203350619257637943319575462295497623168155067993964410110820430456209894852088835229234008905825199821424493514772241158215255312705040545931884526847334694130270010542459994499342564488127060079494324065172973659137940794557181] - - 913
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 ...
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 920
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 0 - - - - - - 933
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[29]Q1+[4]Q2+TC,
[43]Q1+[-2]Q2+TC,
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[79]Q1+[-1]Q2+TC,
[101]Q1+[6]Q2+TC,
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 47235.8601782365,
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 1 [8409113315633026776836 : 15996774280124550859445948 : 1680613164407889089] 36.5108141151080 [-2000145589583631039496367 : 1999047980447506675365120 : 2000866634524268426605487] [-187408432492936248647633 : -38779530875996480220113 : 187367658700913342072273] - - 949
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 [-5885 : -7267 : 7261],
[-207211 : 207376 : 206459],
[-16669123 : -1104997 : 16667992]
 - - 975
976 [0, 3822013, 0, 31328, 0]
[7832, 15327224]
7468189894
 1 [-25152988636105242769809909136384179942960664 : 49171142242243731954461509244523725406783262952 : 288640462598947241029427534130297037525273] 65.2968346202918 [5677066122457501322702316372569350836785543 : -5172700479979332736093250539284957505399643 : 5178576088829093122904424737804387640173557] [2696928462846647763070667242566974717747503 : -2693976247555567326308831813663605502382900 : 2757517833721492044798870007616162551386947] ???,
 ...
 ?,
 ...
 976
977 [0, 3829837, 0, 31360, 0]
[7840, 15358560]
267540630
 1 [3709188204443361430070463271310022325145723113360579961320068334250683635848172 : -7259338019086372153119001585440934885627217059444864337861561394390683598506871684 : 8850131606062771883280441774867472684172067967322225922277832702785646403541] 122.202887066197 [128458253133915774696145596164237212894793817315971761903432558113126693113195686 : -130803818976311802200961603315796175877606791949916250163051777400826292547764017 : 130928134573064889493622959798928298187129194086139675276702714408083536192758611] =[70629759300929507133477837649811782926594899128284825195291783127146679729769907 : -70565494959717558089549471606754606077240156823967074872063431062705353012211943 : 63458768291022383965159199541526042457956126183196531284242160126402183780951075] - - 977
978 [0, 3837669, 0, 31392, 0]
[7848, 15389928]
834903594
 1 [89908 : 194066132 : 2352637] 13.7730586820680 [-2332183925 : -2283667392 : 2329964357] [-450717917 : -496589213 : 496133693] ???,
 ...
 ?,
 ...
 978
979 [0, 3845509, 0, 31424, 0]
[7856, 15421328]
3768587030
 1 [11564 : 24266788 : 205379] 10.4884436649878 [-15747237 : -15280568 : 15732173] [-3677569 : -3935201 : 3931505] - - 979
980 [0, 3853357, 0, 31456, 0]
[7864, 15452760]
7560262830
 0 - - - - - - 980
981 [0, 3861213, 0, 31488, 0]
[7872, 15484224]
947924838
 1 [5712895612830139025939980013714627543232 : 15345131740363191884218262546333785481766464 : 1703481077622768228118482539869323] 58.2851648624180 [-121849836795829664397113420778903666001 : 121940385312126485263191970463054034205 : 89218719692322511847272912872215871261] [-83300695529282390936859723230645921951 : 82839473208782069979101312979653383214 : 83371969744764030632286810916783782881] - - 981
982 [0, 3869077, 0, 31520, 0]
[7880, 15515720]
7606581730
 2 [177608 : -349374157 : 512],
[-545061560 : -1072002943000 : 15813251]
 10.9281808342054,
14.1772433583917
 [31410655 : -32111919 : 32142464],
[-2151930599 : 2720810051 : 2154710755]
 [7125031 : -7118471 : 6523961],
[-1307374417 : -1318710824 : 1305876951]
 [11]Q1+[-23]Q2+TC,
[33]Q1+[-69]Q2+TC,
[55]Q1+[-115]Q2+TC,
[102]Q1+[-81]Q2+TC,
[200]Q1+[27]Q2,
...
 9241.74384607159,
83175.6946146443,
231043.596151789,
220418.556449871,
438505.012811525,
 ...
 982
983 [0, 3876949, 0, 31552, 0]
[7888, 15547248]
423878442
 1 [330492940837646080 : -3350660370435983578752 : 3341362375] 25.8959089259403 [106259222381410287 : -106238264328126977 : 20645329775711225] [-52117009547054884 : 52134222231508849 : 52091489122694219] - - 983
984 [0, 3884829, 0, 31584, 0]
[7896, 15578808]
7653089430
 1 [4571391353842389562500 : 10057239879100272049831500 : 138274046021947988058733] 32.9208221209213 [-3324235922685563872312 : -3263552168919844083437 : 3321104708623194391937] [-2741804843273317208375 : -3060229110433759425121 : 3057471369891172316121] ???,
 ...
 ?,
 ...
 984
985 [0, 3892717, 0, 31616, 0]
[7904, 15610400]
383820710
 0 - - - - - - 985
986 [0, 3900613, 0, 31648, 0]
[7912, 15642024]
7699786314
 0 - - - - - - 986
987 [0, 3908517, 0, 31680, 0]
[7920, 15673680]
143022330
 0 - - - - - - 987
988 [0, 3916429, 0, 31712, 0]
[7928, 15705368]
7746672766
 0 - - - - - - 988
989 [0, 3924349, 0, 31744, 0]
[7936, 15737088]
48563670
 1 [18542402697060692666870456012392705617932364946455016110558076759078564 : 64803411503649316026616418730315106381815784277037955928545541674746868428 : 2236769374347196129065169419304257861621097132204851924693404911] 105.047227917167 [-131734433922116234268089300456068569279985200285325146995713276488965 : 131809770458869385543114068219264936412822147155982239696596931548494 : 74730084542352023825674938749017564892986223929409421837292352950391] [-605006446182903057265066986610469394361186204402290720574122674095079 : 603408830535038092531726226445006863031749940555611627722112101803849 : 605447383069224267450819929424735713925238061685210018672950716361531] - - 989
990 [0, 3932277, 0, 31776, 0]
[7944, 15768840]
7793749170
 0 - - - - - - 990
991 [0, 3940213, 0, 31808, 0]
[7952, 15800624]
3908679362
 1 [2124915276916535881040534200334659417136928017338634423090386091657120927306731960849813686320789657553769950434978201873615774121898257919737159249220106015771221075172748032942504243616219901227524565709382452395100733032392168026259454938686400 : 4549196786155063208197859227206239418688478930309893735081270376052939787791673036216223215936083150192266486203988417226679824090262004835616998346225723193210153948658429776869319947062423283493076843291863868871585171112077641633858710565240004480 : 3303812907580730996721446406593784361667559079796587032747678922088036945324283034515016515450258100546760657117181950555085672999137068568021308550582883488649782285110645481767179273160874556225946606514764397406868535709459427593444052017] 374.704742879627 [-20432355591695969131001979931823504534135209139416733963253398876195588786640644200490976461558582666740636746415535062080653813885846375169254233286101163465579321260748383369981884280988870690139120477090236051413105946678594844557483797259881 : 20451216071930668371674877024160385561203051432064804384949836223855994610725027632640657875346327375248960692329058521450511475587354473522393246279519326803402578486343695291939533030306183622653647184961887293827252554220801604089603615253959 : 18963027589494577888954035385391018568045793294199486423887371430251233938910772220084210063827463873904498298784115072758069152380480396535369415371327579186188559558387594333150677800486164080417063125612231989463468955446683834754113795812661] [-10255080875513247177450056703981228707503778050434275971105510980588883744596908676803380243157708641396623883013103992136938808858032297266090899612738144443859365029353594437095232026925421639857817173467759297827618852280872629616664631667730 : 9995023529477069956402610203768020283973527859571533269434838723025129470389412318518844970039314972255480014430655134175360285582227859581996546902277486306374846020260548549520772579176642205194750919049465322893011901603292114119956015006269 : 10264775582431677863963402528510259311767861026692106335488304276169148866399715351089662451607095095128724265924472976758928368758789073092476232843623144507945108739717606831233108729961761553683934801798530211797855224927586014496904368685121] - - 991
992 [0, 3948157, 0, 31840, 0]
[7960, 15832440]
2613671970
 1 [922073252504455604 : -1836790407617844924804 : 46117651982381] 25.9551241066463 [346407500822128512 : -346198233573740615 : 345672836064976903] [-34358279394266713 : 34373142134324697 : 14780321800598183] ???,
 ...
 ?,
 ...
 992
993 [0, 3956109, 0, 31872, 0]
[7968, 15864288]
1966180194
 0 - - - - - - 993
994 [0, 3964069, 0, 31904, 0]
[7976, 15896168]
7888473370
 2 [-3929642005294644516 : -7822185239462294784588 : 212392551286602721],
[138276786103552439666304430940672671721387292 : 275342773593249683690893440435202601530805995844 : 4111731690663761644156736763896644080962367]
27.1596436092918,
66.2237408225501
[-384107664851671904 : 597099715913794075 : 384709225130769479],
[-19317590866274479059522156825959706601156576 : 15221141395798988538432364051511768753937001 : 19332822998181800218832950254808052888783199]
[-455500192560270597 : -457519450552961447 : 454940779900259147],
[-11966528843061737148129907532731294912251917 : -11867398873032403721889227343347769506718883 : 11956022334265763954841921592943868432005075]
[27]Q1+[2]Q2,
[47]Q1+[59]Q2,
[65]Q1+[-86]Q2+TC,
[9]Q1+[147]Q2+TC,
[139]Q1+[-25]Q2+TC,
[101]Q1+[63]Q2,
[193]Q1+[-21]Q2+TC,
...
 22606.6825068074,
421077.820240826,
341354.038787648,
1495517.72669925,
402532.690904152,
839477.884800899,
850052.438226584,
 ...
 994
995 [0, 3972037, 0, 31936, 0]
[7984, 15928080]
3956136870
 1 [4176 : 8515920 : 24389] 7.90860617536574 [-362917 : -332503 : 362587] [-71871 : -73535 : 73466] - - 995
996 [0, 3980013, 0, 31968, 0]
[7992, 15960024]
293930442
 1 [-3944196 : -746453988 : 1] 12.1543372876907 [-10312525 : 10422308 : 109341767] [-325721543 : 326445193 : 326319907] ???,
 ...
 ?,
 ...
 996
997 [0, 3987997, 0, 32000, 0]
[8000, 15992000]
39800090
 1 [66397484517026000222605208613392706750828666303246710700057950878527256597683563157743482557262203044079544790874113550078643123168321379518827959046752396252300432075439786415990286328465988877143344772316286864384 : 181974898460399579686941275110987241051376159885446438431732367955633834810272732064222628250923522794025319922835191347232799968753870608315208818189749823312532341422309016852166261560876020164764815539761684963887616 : 7310742209939706552916327663118020337960313638670218096238556573816091188528942999486893010700272791102249312991203262022612433395436434248763035296774529650623840661512556891272349869865650722090065167754408744385971] 330.320907043802 [-458571834202206845430663300203590361993708842238157265833146924247541620933788918243467116139089455582548897451129239724663755225183858931630189879036603772791919438884213112081388735228549847821538964906126964449137 : -455727054023673835493086054156957870106337404020838505852660862967594868888855940315999903966582522072137045901560155317659740718418697122470684988807274267049790056358226540407236561304699234699903697029379814546625 : 458186904808518871715352883564858377093004821040486115697592299090045233295661234954073251967793210749906714563702105545381726770600783048605419120782044526112296941872398572907062496490506822336926695729820831480137] [-43523092765996653017186973225446801973083278526615656760200852765786263813501310086240856548467963940472325796952670358978200032173923109578932077929471623005276781314514174220359702831161113266702982401225332738988 : -59723012239664174467464342543784018244292995291366725158901395555249224284816134824330765710079915857700185136425990538700648675737639622229231499402119943147849838896258269406321713526993060706977146770081998128613 : 59679544549708222799573671710040551983147515815376639038578061473236501500973333082855146689493749071819788859657378339811992213119078990523142069953445948167339737481813773592847358719158654549398238058007565504113] - - 997
998 [0, 3995989, 0, 32032, 0]
[8008, 16024008]
7983961986
 1 [113868799103162443648 : 370314827842231241737152 : 23391896612148467598187] 30.5976783895497 [-152271679930430934375 : -151670819925624520631 : 152156101874623770431] [-32862296342213613472 : -53452419528110232353 : 53419597244117160053] ???,
 ...
 ?,
 ...
 998
999 [0, 4003989, 0, 32064, 0]
[8016, 16056048]
4003976970
 0 - - - - - - 999
1000 [0, 4011997, 0, 32096, 0]
[8024, 16088120]
8031993910
 1 [-23182099885022478631772397678025333938442036 : -35075067236803873721978275279585362686941928140 : 13456402151627221527291793678590075181] 68.9803448692204 [-876294429068699664663024197313871508656005844 : 877458932771494021435889566665396625691090563 : 1161420504885354563031158748935257305146864695] [-757145240717116528774330352328825111229528069 : 763358788319132803345669045355191618727017017 : 758014171175652577464878095147963681791546475] ???,
 ...
 ?,
 ...
 1000


[2020.08.02追記]
Twitter上で、Christopher D. Long氏は、n=424(rank 3)の場合の自然数解を報告している(11:04 AM ・ Nov 21, 2018)。
a/(b+c) + b/(a+c) + c/(a+b) = 424

a = 6383088000457968550863626020707964592827
b = 86901761472912010754925122912564100123
c = 2743260400516683056616306684496286550899825
a→b→cの順序をずらした解を同一視すると、こちらで求めた最小の自然数解[c:a:b]と一致している。

[参考文献]

Last Update: 2022.12.12
H.Nakao

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