Movies of the Collisionless Periodic Orbits in the Free-fall Three-body Problem in Real Space or on Shape Sphere

Xiaoming LI and Shijun LIAO

Shanghai Jiaotong University, China


Parameters:

Body mass: m1, m2, m3

Newton's gravitational constant: G = 1

Initial positions: (-0.5, 0), (0.5, 0), (x, y)

Initial velocities: (0,0), (0,0), (0,0)

T is the period

Periodic orbits
Fi(m1,m2,m3) x y T Real Space Shape Sphere
F1(1,1,1) 0.0207067154 0.3133550361 2.1740969264

movie

movie

F2(1,1,1) 0.2053886532 0.1952668419 1.6896364928

movie

movie

F3(1,1,1) 0.0562664280 0.4691503375 4.5419125588

movie

movie

F4(1,1,1) 0.1846729355 0.5753740774 5.1586391029

movie

movie

F5(1,1,1) 0.0880412663 0.5488924176 4.9647695145

movie

movie

F6(1,1,1) 0.3142334050 0.5384825297 4.8672002993

movie

movie

F7(1,1,1) 0.0741834378 0.5324424488 5.4455591108

movie

movie

F8(1,1,1) 0.2871136862 0.5252098584 5.1183291764

movie

movie

F9(1,1,1) 0.0623175679 0.4902842102 5.1999756815

movie

movie

F10(1,1,1) 0.3089693008 0.4236727692 4.8914942162

movie

movie

F11(1,1,1) 0.4006912162 0.3484015305 4.2747107264

movie

movie

F12(1,1,1) 0.3895924236 0.3466357955 4.2763269534

movie

movie

F13(1,1,1) 0.1887216677 0.5103459122 5.9705993269

movie

movie

F14(1,1,1) 0.1938233757 0.6063751102 7.6482262218

movie

movie

F15(1,1,1) 0.2574316821 0.3631991970 6.4040019625

movie

movie

F16(1,1,1) 0.1472358808 0.3114646878 6.5387455881

movie

movie

F17(1,1,1) 0.1403948993 0.5079077887 8.1068148513

movie

movie

F18(1,1,1) 0.2104156341 0.1080829305 5.3952449725

movie

movie

F19(1,1,1) 0.0410117513 0.1882022887 8.1010474180

movie

movie

F20(1,1,1) 0.0548189646 0.2383162534 8.8215019091

movie

movie

F21(1,1,1) 0.2760396991 0.0985020359 5.4225040686

movie

movie

F22(1,1,1) 0.2662035004 0.0764101615 5.4473716994

movie

movie

F23(1,1,1) 0.0135939022 0.1210361097 8.4973950159

movie

movie

F24(1,1,1) 0.0616197629 0.2644961757 9.4244325344

movie

movie

F25(1,1,1) 0.2927953055 0.1170062116 5.7810404779

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movie

F26(1,1,1) 0.0327160645 0.2313291840 10.0217304818

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movie

F27(1,1,1) 0.1523536847 0.1611243738 10.3340878156

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movie

F28(1,1,1) 0.0726030609 0.3037940331 11.8427589787

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movie

F29(1,1,1) 0.3085035769 0.1499949186 7.2938821180

movie

movie

F30(1,1,1) 0.3401651301 0.1168579357 6.1839976588

movie

movie

F1(1,0.8,0.8) 0.0009114239 0.3019805958 1.8286248401

movie

movie

F2(1,0.8,0.8) 0.0554096945 0.4358787847 2.6796265060

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movie

F3(1,0.8,0.8) 0.3147083050 0.3171002382 2.5504611351

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movie

F4(1,0.8,0.8) 0.0470065136 0.4047349033 3.1695717646

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movie

F5(1,0.8,0.8) 0.0428491303 0.3894443945 3.6573170641

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movie

F6(1,0.8,0.8) 0.1080771428 0.5456908479 5.5072190289

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movie

F7(1,0.8,0.8) 0.1942960822 0.2920607463 3.9686010634

movie

movie

F8(1,0.8,0.8) 0.0403354335 0.3800701110 4.1385691346

movie

movie

F9(1,0.8,0.8) 0.2016807138 0.3445130538 4.4274165052

movie

movie

F10(1,0.8,0.8) 0.1885308478 0.3499578547 4.9200108461

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movie

F11(1,0.8,0.8) 0.0386388457 0.3736416400 4.6139352019

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F12(1,0.8,0.8) 0.2604939376 0.4347691928 5.5847931336

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F13(1,0.8,0.8) 0.1947764043 0.3822990161 5.7130074726

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F14(1,0.8,0.8) 0.1181940386 0.5724230518 8.1600955849

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F15(1,0.8,0.8) 0.3253474955 0.1256079633 3.2110917765

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F16(1,0.8,0.8) 0.4292485918 0.2660046008 4.2565848643

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movie

F17(1,0.8,0.8) 0.0075986006 0.1288965886 5.1331657257

movie

movie

F18(1,0.8,0.8) 0.3701389869 0.1898186752 3.5781033123

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movie

F19(1,0.8,0.8) 0.1691814162 0.1508888822 5.9395400603

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movie

F20(1,0.8,0.8) 0.2150366646 0.4048515918 8.5571805321

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F21(1,0.8,0.8) 0.2470665630 0.0780584462 5.1791534733

movie

movie

F22(1,0.8,0.8) 0.1505569937 0.1515667886 7.5382540932

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movie

F23(1,0.8,0.8) 0.1674779976 0.1427324464 7.7585512519

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movie

F24(1,0.8,0.8) 0.1527845023 0.0684942940 7.5001089956

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F25(1,0.8,0.8) 0.1500221997 0.0630122343 9.2986382763

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F26(1,0.8,0.8) 0.1830123116 0.6092070111 18.8535978723

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F27(1,0.8,0.8) 0.1464997313 0.0473029499 11.0720042333

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F28(1,0.8,0.8) 0.1624065612 0.1384893670 13.3138834463

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F29(1,0.8,0.8) 0.1547961371 0.1653004219 17.5487952899

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F1(1,0.8,0.6) 0.0445314006 0.7402164268 2.8030997992

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F2(1,0.8,0.6) 0.0596000878 0.7375612563 3.4959622385

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F3(1,0.8,0.6) 0.1174556037 0.7167529190 2.7369656923

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F4(1,0.8,0.6) 0.0651532615 0.7533349173 4.1668179824

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F5(1,0.8,0.6) 0.1290881090 0.4010761427 2.5007648710

movie

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F6(1,0.8,0.6) 0.3133248745 0.3258575422 2.6081696286

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F7(1,0.8,0.6) 0.0078965470 0.2369793668 2.5608925720

movie

movie

F8(1,0.8,0.6) 0.0666851373 0.7642377831 4.7961908510

movie

movie

F9(1,0.8,0.6) 0.1288237799 0.2575989050 2.5632081060

movie

movie

F10(1,0.8,0.6) 0.1156599683 0.4136953992 3.1416626327

movie

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F11(1,0.8,0.6) 0.0119593475 0.2408362224 2.9430485048

movie

movie

F12(1,0.8,0.6) 0.1023506488 0.4088669490 3.6750954828

movie

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F13(1,0.8,0.6) 0.1694637420 0.0159900098 2.4177885604

movie

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F14(1,0.8,0.6) 0.2707648383 0.1015364734 2.0709517775

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F15(1,0.8,0.6) 0.3612643450 0.2943015410 2.7889383936

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F16(1,0.8,0.6) 0.4108603284 0.2242851684 2.1055583251

movie

movie

F17(1,0.8,0.6) 0.0932368548 0.4030127578 4.1731767189

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F18(1,0.8,0.6) 0.1352566765 0.6807175103 6.7293787182

movie

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F19(1,0.8,0.6) 0.2725304223 0.1732922849 2.6175552797

movie

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F20(1,0.8,0.6) 0.3125456686 0.0866160290 1.9950219564

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movie

F21(1,0.8,0.6) 0.1882144839 0.3345735824 3.5219440458

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F22(1,0.8,0.6) 0.0716145199 0.0915187956 3.8642156146

movie

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F23(1,0.8,0.6) 0.0869005363 0.3979937240 4.6539481356

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F24(1,0.8,0.6) 0.3563440713 0.2981031724 3.6559375422

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F25(1,0.8,0.6) 0.2880532139 0.4825865222 4.6073152572

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F26(1,0.8,0.6) 0.4160772504 0.2310953494 2.8622355529

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movie

F27(1,0.8,0.6) 0.3987945492 0.3025049316 3.3736146266

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F28(1,0.8,0.6) 0.0776425870 0.1746563917 4.4628708319

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movie

F29(1,0.8,0.6) 0.0599809897 0.0926220002 4.3653925159

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F30(1,0.8,0.6) 0.0579903544 0.0443882673 4.3050365191

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F31(1,0.8,0.6) 0.0934614700 0.0471665194 4.1680025233

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F32(1,0.8,0.6) 0.1325902103 0.4123819959 5.6679076918

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F33(1,0.8,0.6) 0.1041449120 0.1482283553 4.3424138584

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F34(1,0.8,0.6) 0.1993569698 0.0777479367 3.8425401785

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F35(1,0.8,0.6) 0.1341720545 0.4004224629 5.4787823377

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movie

F36(1,0.8,0.6) 0.2974062043 0.5279669906 6.3977820308

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F37(1,0.8,0.6) 0.2979333584 0.4813611322 5.0215788607

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F38(1,0.8,0.6) 0.2660209853 0.5078995460 6.1326779990

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F39(1,0.8,0.6) 0.3523683160 0.2982025789 4.0622574955

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F40(1,0.8,0.6) 0.4161870623 0.2320188370 3.1969547246

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F41(1,0.8,0.6) 0.4020135877 0.3030079422 3.6862253065

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F42(1,0.8,0.6) 0.1226012128 0.3700294495 5.7506652807

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F43(1,0.8,0.6) 0.1005984521 0.1891151438 4.8651314925

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F44(1,0.8,0.6) 0.2712808805 0.1853534625 4.0744291974

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F45(1,0.8,0.6) 0.1681172791 0.3751181431 5.7460113210

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F46(1,0.8,0.6) 0.2156072166 0.0352712952 3.9293028391

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F47(1,0.8,0.6) 0.2256928469 0.0765660306 3.8667808099

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F48(1,0.8,0.6) 0.1370635146 0.4370979031 6.4419369834

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F49(1,0.8,0.6) 0.2751838416 0.5445094738 7.2105813537

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F50(1,0.8,0.6) 0.1171739128 0.2424690464 5.0831185087

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F51(1,0.8,0.6) 0.1845105186 0.4501096494 6.2787672531

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F52(1,0.8,0.6) 0.4158959655 0.2325668494 3.5206991506

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F53(1,0.8,0.6) 0.1631890832 0.2103797105 5.2589880358

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F54(1,0.8,0.6) 0.1983940001 0.4025046079 6.3528167889

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F55(1,0.8,0.6) 0.2278308853 0.5414697914 7.8346766349

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F56(1,0.8,0.6) 0.1400273104 0.0081786581 4.6831272984

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F57(1,0.8,0.6) 0.2396969281 0.6174793436 8.4831505812

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F58(1,0.8,0.6) 0.3162910832 0.1332526561 3.5796429232

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F59(1,0.8,0.6) 0.2092641475 0.4289510221 6.9927421590

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F60(1,0.8,0.6) 0.2451298945 0.5563343875 8.6490881257

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F61(1,0.8,0.6) 0.2033682605 0.5895584432 8.8821315833

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F62(1,0.8,0.6) 0.0792440005 0.0978998982 6.2066610525

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F63(1,0.8,0.6) 0.1798006367 0.5682045433 9.3055595206

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F64(1,0.8,0.6) 0.1635781743 0.5519695391 9.7486824006

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F65(1,0.8,0.6) 0.1496991995 0.1853063639 7.1021694436

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F66(1,0.8,0.6) 0.1517569566 0.5393156268 10.2043588748

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F67(1,0.8,0.6) 0.2762432619 0.1953715885 6.2775182238

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F68(1,0.8,0.6) 0.1707850755 0.0856593151 6.9891771436

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F69(1,0.8,0.6) 0.1843011931 0.2329050114 10.3627717531

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F1(1,0.8,0.4) 0.0907814512 0.4017862494 2.6296980224

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F2(1,0.8,0.4) 0.0731681909 0.6154884228 3.9909158705

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F3(1,0.8,0.4) 0.1643021746 0.3586184694 2.8687541956

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F4(1,0.8,0.4) 0.0820569602 0.4346030503 3.2699876372

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F5(1,0.8,0.4) 0.3039731933 0.2570037825 2.4050767593

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F6(1,0.8,0.4) 0.0038230030 0.5336567474 3.7553714566

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F7(1,0.8,0.4) 0.2215676344 0.3878099512 3.3450631915

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F8(1,0.8,0.4) 0.3334492443 0.2914625638 2.9491668861

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F9(1,0.8,0.4) 0.0734875559 0.4307592210 3.7612586546

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F10(1,0.8,0.4) 0.0041432429 0.3565873877 3.3430163241

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F11(1,0.8,0.4) 0.3647347270 0.2936105654 2.8392914831

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F12(1,0.8,0.4) 0.3400677332 0.3044773669 3.4135118241

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F13(1,0.8,0.4) 0.0654701140 0.3237298022 4.9143582571

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F14(1,0.8,0.4) 0.0683822051 0.4258256814 4.2186879217

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F15(1,0.8,0.4) 0.3051209633 0.1717154384 2.6362825973

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F16(1,0.8,0.4) 0.3818190460 0.2165579773 2.6549491894

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F17(1,0.8,0.4) 0.3406869343 0.2557425196 2.9271614571

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F18(1,0.8,0.4) 0.3519249675 0.1805278285 2.3962764398

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F19(1,0.8,0.4) 0.0067573659 0.3551234191 3.7006572503

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F20(1,0.8,0.4) 0.3966555518 0.2200475447 2.5793846625

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F21(1,0.8,0.4) 0.3377184031 0.3084466213 3.8289301499

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F22(1,0.8,0.4) 0.2559808544 0.3985035719 4.1088019361

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F23(1,0.8,0.4) 0.3919889126 0.2253938155 3.0196263432

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F24(1,0.8,0.4) 0.0650272018 0.4217643778 4.6597662391

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F25(1,0.8,0.4) 0.3507035957 0.1514721792 2.5093279573

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F26(1,0.8,0.4) 0.0083551748 0.3537463108 4.0436510812

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F27(1,0.8,0.4) 0.0839240210 0.3307729197 5.3174336486

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F28(1,0.8,0.4) 0.1534813802 0.3445489508 5.3109746054

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F29(1,0.8,0.4) 0.2639061633 0.4003107771 4.4615936588

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F30(1,0.8,0.4) 0.3968538929 0.2304351014 3.3613134500

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F31(1,0.8,0.4) 0.3332373486 0.3087120049 4.2145144195

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F32(1,0.8,0.4) 0.4200988856 0.2278457172 3.1002444220

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F33(1,0.8,0.4) 0.4130847007 0.1836206658 2.7777999782

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F34(1,0.8,0.4) 0.0626424176 0.4185140509 5.0903858286

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F35(1,0.8,0.4) 0.2968561297 0.1524320976 3.0849296562

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F36(1,0.8,0.4) 0.1204686367 0.3718569619 5.9520762241

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F37(1,0.8,0.4) 0.3388963416 0.4809266124 6.4469817763

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F38(1,0.8,0.4) 0.3987797585 0.2334398833 3.6879026872

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F39(1,0.8,0.4) 0.3289050765 0.3077086141 4.5828783734

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F40(1,0.8,0.4) 0.4211234979 0.1897019745 3.3348881047

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F41(1,0.8,0.4) 0.1740093467 0.4061799018 6.9459548660

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F42(1,0.8,0.4) 0.4229990097 0.1914129869 3.6005720033

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F43(1,0.8,0.4) 0.1491465141 0.1587305525 5.9110461898

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F44(1,0.8,0.4) 0.1071012257 0.1862114119 7.0200258193

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F1(1,0.8,0.2) 0.0247367455 0.5956711592 2.9388503785

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F2(1,0.8,0.2) 0.0788881323 0.7268131374 3.0188278709

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F3(1,0.8,0.2) 0.0213288594 0.6061184155 3.4342304620

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F4(1,0.8,0.2) 0.0726486463 0.3079938956 2.7012372544

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F5(1,0.8,0.2) 0.0191076293 0.6201117694 3.8749764277

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F6(1,0.8,0.2) 0.1310631652 0.3036588095 2.9464698551

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F7(1,0.8,0.2) 0.0071275432 0.4202963121 3.2293710330

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F8(1,0.8,0.2) 0.0578321783 0.4378406225 3.3345102032

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F9(1,0.8,0.2) 0.3280512200 0.4258152565 4.5412446489

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F10(1,0.8,0.2) 0.0107850066 0.4129517340 3.5152661840

movie

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F11(1,0.8,0.2) 0.0518431819 0.4240660566 3.6691833705

movie

movie

F12(1,0.8,0.2) 0.2677953092 0.1910152983 2.7646135824

movie

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F13(1,0.8,0.2) 0.3185180627 0.2611918166 3.0178876890

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F14(1,0.8,0.2) 0.0161474528 0.6441659117 4.6837208272

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F15(1,0.8,0.2) 0.0957979866 0.7922510102 4.8571260165

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F16(1,0.8,0.2) 0.2973457769 0.2160446151 3.0341335482

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movie

F17(1,0.8,0.2) 0.3192685287 0.1435620243 2.6213636288

movie

movie

F18(1,0.8,0.2) 0.0151043114 0.6535617498 5.0657847438

movie

movie

F19(1,0.8,0.2) 0.2809348051 0.4215890462 5.6828932918

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movie

F20(1,0.8,0.2) 0.3505735652 0.1838631164 2.7916720023

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movie

F21(1,0.8,0.2) 0.0835830692 0.3734731952 5.6217700487

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F22(1,0.8,0.2) 0.2271206540 0.3551247364 3.8574172516

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F23(1,0.8,0.2) 0.3402615147 0.1637450999 2.8506619375

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F24(1,0.8,0.2) 0.3793454984 0.2079457559 3.1028333360

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F25(1,0.8,0.2) 0.3188392408 0.2307237833 3.4919940375

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F26(1,0.8,0.2) 0.2365256725 0.3585230897 4.1103828594

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F27(1,0.8,0.2) 0.4062681391 0.1740808481 3.1511604419

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F28(1,0.8,0.2) 0.2121623131 0.6190535787 9.7560815483

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F29(1,0.8,0.2) 0.4109560735 0.1434385455 2.9753651036

movie

movie

F30(1,0.8,0.2) 0.2875973419 0.5233120555 10.9328732255

movie

movie

F31(1,0.8,0.2) 0.2145732729 0.5784826450 9.5431888036

movie

movie

F32(1,0.8,0.2) 0.4217142944 0.1509680324 3.1849044537

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