Movies of the Periodic Planar Collisionless Three-Body Orbits in Real Space or on Shape Sphere

Xiaoming LI and Shijun LIAO

Shanghai Jiaotong University, China


Parameters:

Body mass: m1 = m2 = m3 = 1

Newton's gravitational constant: G = 1

Initial positions: (-1, 0), (1, 0), (0, 0)

Initial velocities: (v1, v2), (v1, v2), (-2v1, -2v2)

T is the period, T* = T|E|3/2 is the scale-invariant period and Lf is the length of the free group element.

Periodic orbits
Class and number v1 v2 T T* Lf Real Space Shape Sphere
I.Ai.c.1 0.3471168881 0.5327249454 6.3259139829 9.238 4

movie

movie

I.Ai.c.2 0.3068934205 0.1255065670 6.2346748391 19.932 8

movie

movie

I.Ai.c.3 0.6150407229 0.5226158545 37.3205235945 15.048 8

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movie

I.Ai.c.4 0.5379557207 0.3414578545 26.9186696160 39.075 16

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movie

I.Ai.c.5 0.4112926910 0.2607551013 20.7490650080 49.630 20

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I.Ai.c.6 0.4425908552 0.4235138348 35.8334644158 57.728 24

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I.Ai.c.7 0.1214534165 0.1012023800 15.7440944954 59.455 24

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movie

I.Ai.c.8 0.4094945913 0.3628231655 33.8677507235 68.673 28

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movie

I.Ai.c.9 0.5255769251 0.2501253528 43.8698538026 79.277 32

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I.Ai.c.10 0.4121028725 0.2833837497 34.2470499687 79.255 32

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I.Ai.c.11 0.4364192674 0.4457095477 49.5954033190 76.298 32

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movie

I.Ai.c.12 0.1182009612 0.5847367662 48.2723717545 82.749 36

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I.Ai.c.13 0.4763527642 0.3789434497 53.4714914343 87.484 36

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I.Ai.c.14 0.4027121690 0.2100155085 34.7120153702 89.560 36

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I.Ai.c.15 0.3960494651 0.3529413931 46.1340735475 98.289 40

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I.Ai.c.16 0.4340543928 0.4606927255 64.1162217970 94.824 40

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I.Ai.c.17 0.1842784887 0.5871881740 63.5343529785 101.184 44

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I.Ai.c.18 0.4580378828 0.4093753024 66.3519736810 106.147 44

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I.Ai.c.19 0.4152505707 0.2913461808 47.9254977196 108.869 44

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I.Ai.c.20 0.0969422653 0.5615968396 53.6899444096 101.174 44

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I.Ai.c.21 0.4082108156 0.2436851904 48.4868513719 119.241 48

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I.Ai.c.22 0.4289870678 0.4723797648 78.3984979261 113.331 48

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I.Ai.c.23 0.4138807521 0.3477955684 61.8447789156 127.900 52

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I.Ai.c.24 0.4905050535 0.4044215155 85.3859524958 124.747 52

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I.Ai.c.25 0.1982770999 0.5760625510 73.2768117405 119.634 52

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I.Ai.c.26 0.3991287659 0.1847081193 48.6673769352 129.450 52

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I.Ai.c.27 0.4151691260 0.2953409098 61.3228288140 138.477 56

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I.Ai.c.28 0.0490506729 0.5901941115 79.1518362736 137.886 60

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I.Ai.c.29 0.3447503346 0.3930446386 67.3877746400 146.737 60

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I.Ai.c.30 0.2203123981 0.5718227262 85.7935924161 138.093 60

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I.Ai.c.31 0.4441311511 0.3823106072 82.3618800834 146.756 60

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movie

I.Ai.c.32 0.4041322114 0.2191641945 62.4468134238 159.167 64

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I.Ai.c.33 0.4089912496 0.3457125084 75.0210999574 157.507 64

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I.Ai.c.34 0.4572423635 0.4074171858 95.8806923191 154.561 64

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I.Ai.c.35 0.3972193787 0.1691985386 62.6275833821 169.327 68

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I.Ai.c.36 0.4160674674 0.2971499303 74.7892110946 168.084 68

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I.Ai.c.37 0.1038901209 0.5907210858 92.2887207815 156.291 68

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I.Ai.c.38 0.4135366646 0.2710056059 76.0285224477 178.523 72

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I.Ai.c.39 0.3967429300 0.3708809839 85.9343829011 176.391 72

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I.Ai.c.40 0.4073762182 0.2388431491 76.2219729678 188.847 76

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I.Ai.c.41 0.1334658448 0.5838277552 102.8155095976 174.712 76

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I.Ai.c.42 0.4015585101 0.2022664462 76.4010838847 199.069 80

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I.Ai.c.43 0.4157753114 0.2981866614 88.0489003051 197.691 80

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I.Ai.c.44 0.4188475683 0.2770588072 90.4212103693 208.148 84

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I.Ai.c.45 0.3960577146 0.1586009694 76.5926988984 209.198 84

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I.Ai.c.46 0.4096220179 0.2516961122 89.9866883856 218.506 88

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movie

I.Ai.c.47 0.4046803380 0.2225972157 90.1813477230 228.773 92

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I.Ai.c.48 0.2744365569 0.3448729405 37.0281899697 98.299 40

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I.Ai.c.49 0.5196830772 0.2059463323 61.0651489089 119.273 48

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I.Ai.c.50 0.0481112024 0.5584284134 61.5066511920 119.557 52

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I.Ai.c.51 0.3240593189 0.3665712251 61.6980804867 146.748 60

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I.Ai.c.52 0.4392326535 0.4490130778 107.1704322355 161.864 68

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I.Ai.c.53 0.4157392818 0.3443683086 90.2692922120 187.114 76

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I.Ai.c.54 0.2591633491 0.5655538324 112.9677142326 175.025 76

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I.Ai.c.55 0.4372549674 0.4568896400 121.6765447969 180.390 76

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I.Ai.c.56 0.4713347232 0.3856148608 112.7807985048 184.312 76

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I.Ai.c.57 0.1538860573 0.5805527776 114.4056830978 193.146 84

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I.Ai.c.58 0.4162411626 0.4666456940 130.1232036082 198.902 84

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I.Ai.c.59 0.4602603277 0.4047836526 126.1735921874 202.975 84

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I.Ai.c.60 0.4260682804 0.4689275280 134.8572983004 198.903 84

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I.Ai.c.61 0.4115604103 0.3439515057 103.4777852547 216.720 88

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I.Ai.c.62 0.4538585041 0.4151335211 138.9526711783 221.605 92

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I.Ai.c.63 0.1807391308 0.5804273075 128.9311229083 211.590 92

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I.Ai.c.64 0.0616295799 0.5887684684 121.2588070481 211.428 92

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I.Ai.c.65 0.4164511851 0.2985460701 101.4417348354 227.296 92

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I.Ai.c.66 0.4755802612 0.3834289883 143.4920831622 232.725 96

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I.Ai.c.67 0.4189618506 0.3575723235 117.5497551541 235.641 96

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I.Ai.c.68 0.3998065241 0.1898070007 90.3562840799 238.958 96

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I.Ai.c.69 0.1938115742 0.5776286093 140.9274473884 230.040 100

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I.Ai.c.70 0.4311833725 0.4733759409 164.8353415245 235.912 100

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I.Ai.c.71 0.0960540551 0.5889671026 134.1667723286 229.832 100

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I.Ai.c.72 0.3952890968 0.1508523182 90.5619718006 249.067 100

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I.Ai.c.73 0.4395870869 0.4502293684 164.6132228870 247.429 104

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I.Ai.c.74 0.3674149486 0.3838228297 119.7236640531 254.456 104

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I.Ai.c.75 0.3939961214 0.3865732823 127.4002458975 254.459 104

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I.Ai.c.76 0.3430511121 0.3718832371 111.6289843304 254.460 104

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I.Ai.c.77 0.4159559963 0.2988672319 114.5882843578 256.902 104

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I.Ai.c.78 0.4069867693 0.2365548555 103.9566166835 258.453 104

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I.Ai.c.79 0.4589974678 0.4050034288 155.7660607190 251.388 104

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I.Ai.c.80 0.4139140441 0.2867091579 116.5535148563 267.382 108

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I.Ai.c.81 0.4379684294 0.4556963530 179.1036444528 265.955 112

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I.Ai.c.82 0.4126145620 0.3435200139 131.9570363471 275.931 112

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I.Ai.c.83 0.4561844518 0.4117892184 168.9508799790 270.024 112

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I.Ai.c.84 0.3985475384 0.1801838327 104.3138748764 278.839 112

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I.Ai.c.85 0.4126594494 0.2674571676 117.5120633437 277.786 112

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I.Ai.c.86 0.3921967782 0.3732670713 137.7155574878 284.106 116

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I.Ai.c.87 0.4180525186 0.2985930530 128.3273660780 286.508 116

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I.Ai.c.88 0.1382080826 0.5834341742 157.3466528910 266.675 116

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I.Ai.c.89 0.3974576989 0.2491169363 115.4448017793 288.116 116

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I.Ai.c.90 0.0188646524 0.5900765061 151.9903843649 266.578 116

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I.Ai.c.91 0.3947500473 0.1449169673 104.5346721644 288.934 116

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I.Ai.c.92 0.4146876683 0.2893277049 130.1851727452 296.995 120

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I.Ai.c.93 0.4049707755 0.2243966352 117.9157508493 298.378 120

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I.Ai.c.94 0.4948547469 0.3816681253 195.8237684806 299.800 124

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I.Ai.c.95 0.4098282065 0.4859736518 199.4325323563 291.389 124

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I.Ai.c.96 0.3557656112 0.2101434426 110.1033827881 308.577 124

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I.Ai.c.97 0.1458080611 0.5760627737 164.8777227366 285.109 124

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I.Ai.c.98 0.4373040972 0.1890148898 125.7688001626 308.577 124

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I.Ai.c.99 0.3693848766 0.2787954099 121.4331832032 307.415 124

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I.Ai.c.100 0.0670760777 0.5889627892 163.9101889958 284.971 124

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I.Ai.c.101 0.4024084539 0.3670928188 153.5887772816 313.740 128

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I.Ai.c.102 0.4101448519 0.2545904027 131.4852184733 317.767 128

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I.Ai.c.103 0.3976053675 0.1724965035 118.2740940483 318.716 128

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I.Ai.c.104 0.4070387234 0.3507052842 155.3531711573 324.480 132

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I.Ai.c.105 0.3654211421 0.1497581124 113.5033068728 328.800 132

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I.Ai.c.106 0.3288064734 0.2480300294 116.7651488382 328.060 132

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I.Ai.c.107 0.0921822548 0.5888237645 176.5993385200 303.375 132

movie

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I.Ai.c.108 0.3943552252 0.1402131694 118.5101674005 328.800 132

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I.Ai.c.109 0.4164334853 0.2763211125 145.5011286545 337.039 136

movie

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I.Ai.c.110 0.4033838433 0.2143907433 131.8709942386 338.289 136

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I.Ai.c.111 0.1818464802 0.5795638348 195.8266870843 321.997 140

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I.Ai.c.112 0.4109222799 0.3490743143 170.4845107382 354.091 144

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I.Ai.c.113 0.4159829843 0.2928634271 157.4236701613 356.215 144

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I.Ai.c.114 0.3968779003 0.1661961334 132.2368607224 358.590 144

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movie

I.Ai.c.115 0.3369172422 0.2901238678 139.2379425543 366.661 148

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I.Ai.c.116 0.4786094582 0.2027583452 167.5764021354 367.991 148

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I.Ai.c.117 0.1262212709 0.5844212753 199.4597414280 340.210 148

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I.Ai.c.118 0.3596345346 0.3768544947 165.4459242130 362.173 148

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I.Ai.c.119 0.3735693647 0.3814544097 171.6871768580 362.171 148

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I.Ai.c.120 0.3940559464 0.1363870337 132.4879124177 368.666 148

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I.Ai.c.121 0.0398375597 0.5900216545 194.6214443391 340.118 148

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I.Ai.c.122 0.3366050958 0.1545246545 122.1507473925 368.667 148

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movie

I.Ai.c.123 0.4148912516 0.3594943116 185.0089900186 372.989 152

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I.Ai.c.124 0.4021066869 0.2059880758 145.8250755871 378.190 152

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I.Ai.c.125 0.2984912721 0.2642719294 134.6157747992 387.392 156

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I.Ai.c.126 0.3151887676 0.2026092096 129.5701866405 388.355 156

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I.Ai.c.127 0.3682819786 0.0540125357 129.1627539603 388.682 156

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I.Ai.c.128 0.4094064944 0.2504917575 159.2238172130 387.380 156

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I.Ai.c.129 0.3963021063 0.1609272065 146.2019999818 398.462 160

movie

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I.Ai.c.130 0.4858230168 0.1897852046 186.6816128151 407.911 164

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I.Ai.c.131 0.3938225013 0.1332100629 146.4674258412 408.531 164

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I.Ai.c.132 0.2844202818 0.2576751665 144.7361096869 427.351 172

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I.Ai.c.133 0.3613650149 0.0662137880 141.3166709722 428.547 172

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I.Ai.c.134 0.4052729644 0.2262551267 173.3843818847 437.587 176

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I.Ai.c.135 0.2792503345 0.2309398618 146.5213559661 447.823 180

movie

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I.Ai.c.136 0.4088863339 0.2475714173 186.9603460122 456.990 184

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movie

I.Ai.c.137 0.2755037979 0.2512907499 155.4548586490 467.296 188

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movie

I.Ai.c.138 0.3000356874 0.1954805934 152.1599660045 468.121 188

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movie

I.Ai.c.139 0.2759217512 0.2671023857 164.8956499133 486.678 196

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I.Ai.c.140 0.3060236507 0.1574877923 155.4631165813 488.269 196

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I.Ai.c.141 0.2738106556 0.2266665399 157.9002511121 487.729 196

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I.Ai.c.142 0.2716635736 0.2803602873 173.2990630202 505.979 204

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I.Ai.c.143 0.2690738475 0.2460748830 166.5414191753 507.230 204

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I.Ai.c.144 0.2813047676 0.2931043691 185.0094674080 525.199 212

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I.Ai.c.145 0.2844033114 0.2864772055 184.1463025888 525.201 212

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I.Ai.c.146 0.3406159593 0.0878815592 176.4815564147 548.142 220

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I.Ai.c.147 0.2745076841 0.2185259293 182.4778598891 567.527 228

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I.Ai.c.148 0.5236560165 0.2615293843 77.5451687834 138.512 56

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I.Ai.c.149 0.5252433392 0.2395323622 97.1790201428 178.571 72

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I.Ai.c.150 0.2485711669 0.2285602706 62.8143378441 199.118 80

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I.Ai.c.151 0.4717436769 0.4159399383 127.4097749092 191.768 80

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I.Ai.c.152 0.4244996083 0.4906100936 136.0765222404 187.283 80

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I.Ai.c.153 0.3303010815 0.4704859697 107.3481952603 198.916 84

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I.Ai.c.154 0.2538439618 0.5599410925 121.1861154175 193.495 84

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I.Ai.c.155 0.4824594978 0.3739325421 131.7096541850 214.035 88

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I.Ai.c.156 0.4299480127 0.4772693278 179.4317919632 254.406 108

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I.Ai.c.157 0.2242029652 0.5716643145 178.2257295831 285.417 124

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I.Ai.c.158 0.4721688158 0.3825825184 189.2718322389 310.866 128

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I.Ai.c.159 0.2338958736 0.5689557210 190.6014315264 303.881 132

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I.Ai.c.160 0.4067612870 0.2352215102 131.6910976773 328.058 132

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I.Ai.c.161 0.4664129400 0.2183545493 147.4412391934 328.060 132

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I.Ai.c.162 0.1082811863 0.5839631505 185.8736775605 321.788 140

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I.Ai.c.163 0.3733531828 0.0372160210 116.4750673801 348.816 140

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I.Ai.c.164 0.3289795673 0.2068164036 118.9835822292 348.468 140

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I.Ai.c.165 0.4000579116 0.1916547891 132.0453999094 348.465 140

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I.Ai.c.166 0.4122855598 0.2657302751 159.0067612686 377.047 152

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I.Ai.c.167 0.3897682267 0.3744628158 189.3994398298 391.821 160

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I.Ai.c.168 0.3218496119 0.1559752782 132.7019091118 408.535 164

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I.Ai.c.169 0.2959833070 0.2812516245 143.8012840531 406.693 164

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I.Ai.c.170 0.4132174699 0.2698100668 172.7929755123 406.678 164

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I.Ai.c.171 0.4010600790 0.1988153634 159.7793954306 418.084 168

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I.Ai.c.172 0.3983719278 0.1787862095 159.9605934536 428.228 172

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I.Ai.c.173 0.4134354098 0.2854601690 185.1176308487 425.893 172

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I.Ai.c.174 0.4920112032 0.1412368522 190.8552755255 428.247 172

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I.Ai.c.175 0.3958370784 0.1564483425 160.1693147940 438.332 176

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I.Ai.c.176 0.2816607693 0.2752504513 153.9063858244 446.695 180

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I.Ai.c.177 0.4155517978 0.2960847052 197.4708451315 445.039 180

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I.Ai.c.178 0.3124918736 0.1567548343 143.9064578456 448.402 180

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I.Ai.c.179 0.3936357530 0.1305277271 160.4482656408 448.395 180

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I.Ai.c.180 0.3977453372 0.1736695550 173.9208149453 468.105 188

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I.Ai.c.181 0.4065107464 0.2337325768 187.1598824391 467.267 188

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I.Ai.c.182 0.3934827897 0.1282315783 174.4300043958 488.259 196

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I.Ai.c.183 0.4514746238 0.0973655800 192.4707838219 488.269 196

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I.Ai.c.184 0.3994542144 0.1871787471 187.6908780809 497.857 200

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I.Ai.c.185 0.3466891157 0.0826041253 164.7857262001 508.277 204

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I.Ai.c.186 0.3951370317 0.1492265626 188.1097039559 518.068 208

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I.Ai.c.187 0.2704861637 0.2617400496 176.1949991668 526.644 212

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I.Ai.c.188 0.2701991673 0.2977922273 183.6255697046 525.201 212

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I.Ai.c.189 0.2719181145 0.2227169845 169.8054736884 527.630 212

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I.Ai.c.190 0.3933545122 0.1262431781 188.4122024989 528.123 212

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I.Bi.c.1 0.4644451728 0.3960600146 14.8943051743 24.206 10

movie

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I.Bi.c.2 0.4059155671 0.2301631260 13.8671234361 34.802 14

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I.Bi.c.3 0.0833000718 0.1278892555 10.4648495256 39.644 16

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I.Bi.c.4 0.0805842255 0.5888360898 21.2723373956 36.771 16

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I.Bi.c.5 0.4391659182 0.4529676431 28.6692709402 42.782 18

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I.Bi.c.6 0.3834435199 0.3773636946 25.8392363356 53.857 22

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I.Bi.c.7 0.1862378160 0.5787138661 33.6414187604 55.204 24

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I.Bi.c.8 0.4290898149 0.4753132903 42.8299661050 61.290 26

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I.Bi.c.9 0.4149129608 0.2746187551 27.6646471048 64.445 26

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I.Bi.c.10 0.3980444335 0.1761383334 27.8234143343 74.695 30

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I.Bi.c.11 0.2302567240 0.5696545030 46.0668997027 73.662 32

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I.Bi.c.12 0.4281877764 0.3550351874 42.3641397966 83.484 34

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I.Bi.c.13 0.3580870041 0.4976954491 49.6315066172 79.780 34

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I.Bi.c.14 0.4097171234 0.4392219554 54.0572550607 91.244 38

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I.Bi.c.15 0.4143481483 0.2881031095 41.1260553556 94.063 38

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I.Bi.c.16 0.2590629830 0.5643154612 59.1751946306 92.130 40

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II.Ci.c.277 0.2507351786 0.2255040571 149.0890582528 472.908 190

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II.Ci.c.279 0.3489312300 0.1929567624 167.8515325534 482.985 194

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II.Ci.c.280 0.3367192080 0.2245212441 169.5289089831 482.607 194

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II.Ci.c.282 0.2661161012 0.2372575353 161.3204581667 497.491 200

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II.Ci.c.283 0.3263451304 0.2232000030 173.6238700114 502.560 202

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II.Ci.c.284 0.2691801071 0.2735720090 174.8747847822 516.330 208

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II.Ci.c.286 0.3160793968 0.2637288074 185.5272060127 521.457 210

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II.Ci.c.287 0.2760184543 0.3032382309 185.9955024470 524.332 212

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II.Ci.c.288 0.2727528907 0.2677183168 181.1571379148 536.321 216

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II.Ci.c.289 0.2622757577 0.2330074672 172.7824864667 537.404 216

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II.Ci.c.290 0.3183530021 0.1922865149 180.2913171422 542.805 218

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II.Ci.c.293 0.3065816346 0.2427199104 185.8437676373 542.005 218

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II.Ci.c.294 0.3498808794 0.1024629340 184.8631924652 563.078 226

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II.Ci.c.295 0.2992239248 0.2591926454 194.1284833538 561.418 226

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II.Ci.c.297 0.3397933101 0.1078662760 189.0456502718 583.010 234

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II.Ci.c.298 0.2461251004 0.2456980192 191.0226619103 596.818 240

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movie