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Fourier Analysis of VXX (iPath S&P 500 VIX Short-Term Futures ETN)


VXX (iPath S&P 500 VIX Short-Term Futures ETN) appears to have interesting cyclic behaviour every 33 weeks (3648.125*sine), 47 weeks (3610.054*sine), and 43 weeks (3368.853*sine).

VXX (iPath S&P 500 VIX Short-Term Futures ETN) has an average price of 11,634.72 (topmost row, frequency = 0).



Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

Fourier Analysis

Using data from 1/30/2009 to 1/8/2018 for VXX (iPath S&P 500 VIX Short-Term Futures ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
011,634.72   0 
115,934.92 9,946.601 (1*2π)/468468 weeks
29,345.308 9,878.478 (2*2π)/468234 weeks
36,645.305 9,266.215 (3*2π)/468156 weeks
43,818.345 8,382.763 (4*2π)/468117 weeks
52,770.803 6,267.179 (5*2π)/46894 weeks
63,195.752 5,882.179 (6*2π)/46878 weeks
72,133.392 6,459.375 (7*2π)/46867 weeks
8574.8976 5,569.848 (8*2π)/46859 weeks
9400.3741 4,119.833 (9*2π)/46852 weeks
10745.0528 3,610.054 (10*2π)/46847 weeks
11686.0266 3,368.853 (11*2π)/46843 weeks
12941.7535 3,008.354 (12*2π)/46839 weeks
131,123.54 3,360.911 (13*2π)/46836 weeks
14437.7561 3,648.125 (14*2π)/46833 weeks
15-187.2216 2,954.79 (15*2π)/46831 weeks
1640.04511 2,367.254 (16*2π)/46829 weeks
17160.6539 2,285.48 (17*2π)/46828 weeks
18182.5109 2,109.075 (18*2π)/46826 weeks
19317.987 2,034.964 (19*2π)/46825 weeks
20300.8735 2,093.055 (20*2π)/46823 weeks
21152.7015 2,168.806 (21*2π)/46822 weeks
22-151.6055 2,002.599 (22*2π)/46821 weeks
23-188.8172 1,609.897 (23*2π)/46820 weeks
249.49042 1,428.352 (24*2π)/46820 weeks
2577.11597 1,421.604 (25*2π)/46819 weeks
26145.2704 1,371.753 (26*2π)/46818 weeks
27218.2552 1,458.655 (27*2π)/46817 weeks
2867.23907 1,533.119 (28*2π)/46817 weeks
29-130.9157 1,443.426 (29*2π)/46816 weeks
30-223.4721 1,225.292 (30*2π)/46816 weeks
31-171.1754 997.3081 (31*2π)/46815 weeks
32-30.91856 868.3625 (32*2π)/46815 weeks
33108.1104 852.3488 (33*2π)/46814 weeks
34249.4529 893.9896 (34*2π)/46814 weeks
35218.1387 1,128.223 (35*2π)/46813 weeks
36-80.88816 1,084.987 (36*2π)/46813 weeks
37-88.02485 816.7006 (37*2π)/46813 weeks
3822.16031 793.8718 (38*2π)/46812 weeks
39-51.06609 729.3512 (39*2π)/46812 weeks
4040.80937 521.4949 (40*2π)/46812 weeks
41275.5224 578.8223 (41*2π)/46811 weeks
42267.4194 689.6795 (42*2π)/46811 weeks
43239.8951 704.8802 (43*2π)/46811 weeks
44214.2629 717.5893 (44*2π)/46811 weeks
45208.0372 687.6786 (45*2π)/46810 weeks
46224.1574 683.9494 (46*2π)/46810 weeks
47218.7075 689.0676 (47*2π)/46810 weeks
48200.7548 707.597 (48*2π)/46810 weeks
49147.2054 710.8543 (49*2π)/46810 weeks
50118.8149 647.0012 (50*2π)/4689 weeks
51100.7889 629.6349 (51*2π)/4689 weeks
5270.17219 541.5463 (52*2π)/4689 weeks
53145.8869 464.0971 (53*2π)/4689 weeks
54207.5143 477.2028 (54*2π)/4689 weeks
55233.0171 507.4087 (55*2π)/4689 weeks
56217.5892 522.0405 (56*2π)/4688 weeks
57221.9484 540.6658 (57*2π)/4688 weeks
58139.426 523.6493 (58*2π)/4688 weeks
59145.1161 407.1226 (59*2π)/4688 weeks
60251.0747 373.6259 (60*2π)/4688 weeks
61320.9076 414.0826 (61*2π)/4688 weeks
62328.8478 467.1749 (62*2π)/4688 weeks
63359.5318 508.2811 (63*2π)/4687 weeks
64341.5615 635.0598 (64*2π)/4687 weeks
65125.2031 685.936 (65*2π)/4687 weeks
6624.10978 460.0025 (66*2π)/4687 weeks
67179.5451 361.5214 (67*2π)/4687 weeks
68226.9627 419.6454 (68*2π)/4687 weeks
69241.4028 407.5158 (69*2π)/4687 weeks
70308.9029 479.5858 (70*2π)/4687 weeks
71194.0866 602.7619 (71*2π)/4687 weeks
7235.29099 503.4626 (72*2π)/4687 weeks
7370.8699 359.1252 (73*2π)/4686 weeks
74129.6624 350.7467 (74*2π)/4686 weeks
75144.6246 326.9682 (75*2π)/4686 weeks
76169.7476 319.1398 (76*2π)/4686 weeks
77176.7269 319.0677 (77*2π)/4686 weeks
78182.0609 304.7826 (78*2π)/4686 weeks
79199.6401 267.2959 (79*2π)/4686 weeks
80288.1807 256.8881 (80*2π)/4686 weeks
81319.941 364.6487 (81*2π)/4686 weeks
82243.9373 405.7291 (82*2π)/4686 weeks
83213.0592 384.0393 (83*2π)/4686 weeks
84197.6588 387.4715 (84*2π)/4686 weeks
85155.5766 374.9818 (85*2π)/4686 weeks
86149.5697 323.5399 (86*2π)/4685 weeks
87166.1269 317.2151 (87*2π)/4685 weeks
88145.7118 323.4404 (88*2π)/4685 weeks
89126.6148 271.9495 (89*2π)/4685 weeks
90161.321 252.5238 (90*2π)/4685 weeks
91163.4623 235.6624 (91*2π)/4685 weeks
92188.2958 228.0725 (92*2π)/4685 weeks
93200.2262 233.6931 (93*2π)/4685 weeks
94219.9047 236.9934 (94*2π)/4685 weeks
95202.3869 275.3 (95*2π)/4685 weeks
96147.0513 249.1055 (96*2π)/4685 weeks
97172.8394 183.7304 (97*2π)/4685 weeks
98222.9654 212.1434 (98*2π)/4685 weeks
99181.4228 232.8286 (99*2π)/4685 weeks
100154.084 198.772 (100*2π)/4685 weeks
101155.2964 165.2188 (101*2π)/4685 weeks
102169.3785 114.7057 (102*2π)/4685 weeks
103221.7232 76.4487 (103*2π)/4685 weeks
104269.299 86.38036 (104*2π)/4685 weeks
105319.2126 86.59916 (105*2π)/4684 weeks
106373.4904 151.4346 (106*2π)/4684 weeks
107355.5843 210.7136 (107*2π)/4684 weeks
108321.6634 239.6017 (108*2π)/4684 weeks
109290.3065 260.3252 (109*2π)/4684 weeks
110237.2847 259.6641 (110*2π)/4684 weeks
111199.6868 206.5268 (111*2π)/4684 weeks
112225.622 164.2839 (112*2π)/4684 weeks
113242.1675 158.3643 (113*2π)/4684 weeks
114250.6203 143.4068 (114*2π)/4684 weeks
115267.898 153.6878 (115*2π)/4684 weeks
116255.0579 131.3783 (116*2π)/4684 weeks
117297.1225 94.61746 (117*2π)/4684 weeks
118354.5093 130.6422 (118*2π)/4684 weeks
119347.2836 170.943 (119*2π)/4684 weeks
120364.2054 160.1917 (120*2π)/4684 weeks
121402.3024 227.2575 (121*2π)/4684 weeks
122339.8754 295.0702 (122*2π)/4684 weeks
123278.0031 288.7098 (123*2π)/4684 weeks
124254.3176 272.0591 (124*2π)/4684 weeks
125224.5793 250.3769 (125*2π)/4684 weeks
126215.8256 214.1613 (126*2π)/4684 weeks
127251.5836 210.7273 (127*2π)/4684 weeks
128233.199 253.0142 (128*2π)/4684 weeks
129160.8352 242.2289 (129*2π)/4684 weeks
130137.6392 170.3195 (130*2π)/4684 weeks
131161.888 128.7145 (131*2π)/4684 weeks
132177.2607 99.54416 (132*2π)/4684 weeks
133215.21 69.52734 (133*2π)/4684 weeks
134265.875 77.8942 (134*2π)/4683 weeks
135277.3419 130.6918 (135*2π)/4683 weeks
136221.6606 138.9715 (136*2π)/4683 weeks
137206.9319 69.07565 (137*2π)/4683 weeks
138277.7053 34.81711 (138*2π)/4683 weeks
139318.5912 70.74644 (139*2π)/4683 weeks
140331.373 101.1165 (140*2π)/4683 weeks
141317.7731 125.1476 (141*2π)/4683 weeks
142304.902 124.4494 (142*2π)/4683 weeks
143304.9897 108.7744 (143*2π)/4683 weeks
144333.2977 103.8096 (144*2π)/4683 weeks
145358.7273 138.0716 (145*2π)/4683 weeks
146346.4926 163.8938 (146*2π)/4683 weeks
147348.3901 194.2323 (147*2π)/4683 weeks
148306.8188 227.783 (148*2π)/4683 weeks
149257.6942 213.9813 (149*2π)/4683 weeks
150239.3262 181.103 (150*2π)/4683 weeks
151250.8461 161.8441 (151*2π)/4683 weeks
152247.0293 162.9142 (152*2π)/4683 weeks
153239.9284 145.7448 (153*2π)/4683 weeks
154253.752 133.6098 (154*2π)/4683 weeks
155257.7531 134.0361 (155*2π)/4683 weeks
156270.2551 130.8792 (156*2π)/4683 weeks
157282.794 138.5987 (157*2π)/4683 weeks
158293.1356 167.1362 (158*2π)/4683 weeks
159259.4558 208.5901 (159*2π)/4683 weeks
160199.8334 193.4517 (160*2π)/4683 weeks
161178.7496 145.8657 (161*2π)/4683 weeks
162191.6238 109.2408 (162*2π)/4683 weeks
163206.9153 85.82358 (163*2π)/4683 weeks
164246.2668 59.78567 (164*2π)/4683 weeks
165315.8769 102.3228 (165*2π)/4683 weeks
166287.3315 200.896 (166*2π)/4683 weeks
167187.471 197.8765 (167*2π)/4683 weeks
168165.5467 144.2685 (168*2π)/4683 weeks
169151.6886 131.207 (169*2π)/4683 weeks
170125.9572 81.44955 (170*2π)/4683 weeks
171168.4104 17.46735 (171*2π)/4683 weeks
172227.4352 56.02098 (172*2π)/4683 weeks
173165.7717 92.55205 (173*2π)/4683 weeks
174125.7792 9.07145 (174*2π)/4683 weeks
175177.6146 -46.08707 (175*2π)/4683 weeks
176222.0744 -55.96957 (176*2π)/4683 weeks
177265.5976 -76.6075 (177*2π)/4683 weeks
178336.8326 -44.11407 (178*2π)/4683 weeks
179337.7817 28.70047 (179*2π)/4683 weeks
180288.2623 40.65619 (180*2π)/4683 weeks
181274.3577 7.40389 (181*2π)/4683 weeks
182302.6312 -17.91834 (182*2π)/4683 weeks
183329.3681 -24.02178 (183*2π)/4683 weeks
184386.7213 -21.03112 (184*2π)/4683 weeks
185441.1067 50.32579 (185*2π)/4683 weeks
186401.8535 146.6671 (186*2π)/4683 weeks
187317.865 164.6521 (187*2π)/4683 weeks
188263.6631 131.541 (188*2π)/4682 weeks
189240.2139 68.38705 (189*2π)/4682 weeks
190293.7398 15.64878 (190*2π)/4682 weeks
191355.9685 48.87416 (191*2π)/4682 weeks
192347.3413 94.783 (192*2π)/4682 weeks
193340.7944 112.5151 (193*2π)/4682 weeks
194315.8529 145.9813 (194*2π)/4682 weeks
195260.6329 140.93 (195*2π)/4682 weeks
196233.2765 93.6758 (196*2π)/4682 weeks
197263.3245 49.57219 (197*2π)/4682 weeks
198297.0535 54.79235 (198*2π)/4682 weeks
199306.2189 67.51914 (199*2π)/4682 weeks
200322.667 76.46371 (200*2π)/4682 weeks
201321.9781 113.3639 (201*2π)/4682 weeks
202273.2236 124.6828 (202*2π)/4682 weeks
203266.6004 65.81433 (203*2π)/4682 weeks
204327.7829 79.37821 (204*2π)/4682 weeks
205306.117 123.9118 (205*2π)/4682 weeks
206301.13 105.7562 (206*2π)/4682 weeks
207314.2081 150.9644 (207*2π)/4682 weeks
208241.5566 177.5148 (208*2π)/4682 weeks
209204.8947 105.254 (209*2π)/4682 weeks
210248.0633 77.10806 (210*2π)/4682 weeks
211257.3711 99.73178 (211*2π)/4682 weeks
212251.4399 81.50928 (212*2π)/4682 weeks
213279.5231 78.39046 (213*2π)/4682 weeks
214302.0023 101.3757 (214*2π)/4682 weeks
215308.9333 144.4418 (215*2π)/4682 weeks
216265.908 192.0499 (216*2π)/4682 weeks
217226.3252 184.8154 (217*2π)/4682 weeks
218188.2017 193.0069 (218*2π)/4682 weeks
219134.4229 150.239 (219*2π)/4682 weeks
220165.1886 102.3163 (220*2π)/4682 weeks
221177.6428 146.8659 (221*2π)/4682 weeks
222108.9377 147.9664 (222*2π)/4682 weeks
22371.39224 95.68824 (223*2π)/4682 weeks
22456.06679 31.16973 (224*2π)/4682 weeks
22593.36968 -41.70906 (225*2π)/4682 weeks
226173.9447 -64.05711 (226*2π)/4682 weeks
227240.9888 -23.92462 (227*2π)/4682 weeks
228237.0761 62.99973 (228*2π)/4682 weeks
229152.2729 82.60236 (229*2π)/4682 weeks
230118.5855 15.93343 (230*2π)/4682 weeks
231147.2042 -19.34009 (231*2π)/4682 weeks
232153.4656 -35.4071 (232*2π)/4682 weeks
233207.3509 -68.11628 (233*2π)/4682 weeks
234269.0486   (234*2π)/4682 weeks
235207.3509 68.11628 (235*2π)/4682 weeks
236153.4656 35.4071 (236*2π)/4682 weeks
237147.2042 19.34009 (237*2π)/4682 weeks
238118.5855 -15.93343 (238*2π)/4682 weeks
239152.2729 -82.60236 (239*2π)/4682 weeks
240237.0761 -62.99973 (240*2π)/4682 weeks
241240.9888 23.92462 (241*2π)/4682 weeks
242173.9447 64.05711 (242*2π)/4682 weeks
24393.36968 41.70906 (243*2π)/4682 weeks
24456.06679 -31.16973 (244*2π)/4682 weeks
24571.39224 -95.68824 (245*2π)/4682 weeks
246108.9377 -147.9664 (246*2π)/4682 weeks
247177.6428 -146.8659 (247*2π)/4682 weeks
248165.1886 -102.3163 (248*2π)/4682 weeks
249134.4229 -150.239 (249*2π)/4682 weeks
250188.2017 -193.0069 (250*2π)/4682 weeks
251226.3252 -184.8154 (251*2π)/4682 weeks
252265.908 -192.0499 (252*2π)/4682 weeks
253308.9333 -144.4418 (253*2π)/4682 weeks
254302.0023 -101.3757 (254*2π)/4682 weeks
255279.5231 -78.39046 (255*2π)/4682 weeks
256251.4399 -81.50928 (256*2π)/4682 weeks
257257.3711 -99.73178 (257*2π)/4682 weeks
258248.0633 -77.10806 (258*2π)/4682 weeks
259204.8947 -105.254 (259*2π)/4682 weeks
260241.5566 -177.5148 (260*2π)/4682 weeks
261314.2081 -150.9644 (261*2π)/4682 weeks
262301.13 -105.7562 (262*2π)/4682 weeks
263306.117 -123.9118 (263*2π)/4682 weeks
264327.7829 -79.37821 (264*2π)/4682 weeks
265266.6004 -65.81433 (265*2π)/4682 weeks
266273.2236 -124.6828 (266*2π)/4682 weeks
267321.9781 -113.3639 (267*2π)/4682 weeks
268322.667 -76.46371 (268*2π)/4682 weeks
269306.2189 -67.51914 (269*2π)/4682 weeks
270297.0535 -54.79235 (270*2π)/4682 weeks
271263.3245 -49.57219 (271*2π)/4682 weeks
272233.2765 -93.6758 (272*2π)/4682 weeks
273260.6329 -140.93 (273*2π)/4682 weeks
274315.8529 -145.9813 (274*2π)/4682 weeks
275340.7944 -112.5151 (275*2π)/4682 weeks
276347.3413 -94.783 (276*2π)/4682 weeks
277355.9685 -48.87416 (277*2π)/4682 weeks
278293.7398 -15.64878 (278*2π)/4682 weeks
279240.2139 -68.38705 (279*2π)/4682 weeks
280263.6631 -131.541 (280*2π)/4682 weeks
281317.865 -164.6521 (281*2π)/4682 weeks
282401.8535 -146.6671 (282*2π)/4682 weeks
283441.1067 -50.32579 (283*2π)/4682 weeks
284386.7213 21.03112 (284*2π)/4682 weeks
285329.3681 24.02178 (285*2π)/4682 weeks
286302.6312 17.91834 (286*2π)/4682 weeks
287274.3577 -7.40389 (287*2π)/4682 weeks
288288.2623 -40.65619 (288*2π)/4682 weeks
289337.7817 -28.70047 (289*2π)/4682 weeks
290336.8326 44.11407 (290*2π)/4682 weeks
291265.5976 76.6075 (291*2π)/4682 weeks
292222.0744 55.96957 (292*2π)/4682 weeks
293177.6146 46.08707 (293*2π)/4682 weeks
294125.7792 -9.07145 (294*2π)/4682 weeks
295165.7717 -92.55205 (295*2π)/4682 weeks
296227.4352 -56.02098 (296*2π)/4682 weeks
297168.4104 -17.46735 (297*2π)/4682 weeks
298125.9572 -81.44955 (298*2π)/4682 weeks
299151.6886 -131.207 (299*2π)/4682 weeks
300165.5467 -144.2685 (300*2π)/4682 weeks
301187.471 -197.8765 (301*2π)/4682 weeks
302287.3315 -200.896 (302*2π)/4682 weeks
303315.8769 -102.3228 (303*2π)/4682 weeks
304246.2668 -59.78567 (304*2π)/4682 weeks
305206.9153 -85.82358 (305*2π)/4682 weeks
306191.6238 -109.2408 (306*2π)/4682 weeks
307178.7496 -145.8657 (307*2π)/4682 weeks
308199.8334 -193.4517 (308*2π)/4682 weeks
309259.4558 -208.5901 (309*2π)/4682 weeks
310293.1356 -167.1362 (310*2π)/4682 weeks
311282.794 -138.5987 (311*2π)/4682 weeks
312270.2551 -130.8792 (312*2π)/4682 weeks
313257.7531 -134.0361 (313*2π)/4681 weeks
314253.752 -133.6098 (314*2π)/4681 weeks
315239.9284 -145.7448 (315*2π)/4681 weeks
316247.0293 -162.9142 (316*2π)/4681 weeks
317250.8461 -161.8441 (317*2π)/4681 weeks
318239.3262 -181.103 (318*2π)/4681 weeks
319257.6942 -213.9813 (319*2π)/4681 weeks
320306.8188 -227.783 (320*2π)/4681 weeks
321348.3901 -194.2323 (321*2π)/4681 weeks
322346.4926 -163.8938 (322*2π)/4681 weeks
323358.7273 -138.0716 (323*2π)/4681 weeks
324333.2977 -103.8096 (324*2π)/4681 weeks
325304.9897 -108.7744 (325*2π)/4681 weeks
326304.902 -124.4494 (326*2π)/4681 weeks
327317.7731 -125.1476 (327*2π)/4681 weeks
328331.373 -101.1165 (328*2π)/4681 weeks
329318.5912 -70.74644 (329*2π)/4681 weeks
330277.7053 -34.81711 (330*2π)/4681 weeks
331206.9319 -69.07565 (331*2π)/4681 weeks
332221.6606 -138.9715 (332*2π)/4681 weeks
333277.3419 -130.6918 (333*2π)/4681 weeks
334265.875 -77.8942 (334*2π)/4681 weeks
335215.21 -69.52734 (335*2π)/4681 weeks
336177.2607 -99.54416 (336*2π)/4681 weeks
337161.888 -128.7145 (337*2π)/4681 weeks
338137.6392 -170.3195 (338*2π)/4681 weeks
339160.8352 -242.2289 (339*2π)/4681 weeks
340233.199 -253.0142 (340*2π)/4681 weeks
341251.5836 -210.7273 (341*2π)/4681 weeks
342215.8256 -214.1613 (342*2π)/4681 weeks
343224.5793 -250.3769 (343*2π)/4681 weeks
344254.3176 -272.0591 (344*2π)/4681 weeks
345278.0031 -288.7098 (345*2π)/4681 weeks
346339.8754 -295.0702 (346*2π)/4681 weeks
347402.3024 -227.2575 (347*2π)/4681 weeks
348364.2054 -160.1917 (348*2π)/4681 weeks
349347.2836 -170.943 (349*2π)/4681 weeks
350354.5093 -130.6422 (350*2π)/4681 weeks
351297.1225 -94.61746 (351*2π)/4681 weeks
352255.0579 -131.3783 (352*2π)/4681 weeks
353267.898 -153.6878 (353*2π)/4681 weeks
354250.6203 -143.4068 (354*2π)/4681 weeks
355242.1675 -158.3643 (355*2π)/4681 weeks
356225.622 -164.2839 (356*2π)/4681 weeks
357199.6868 -206.5268 (357*2π)/4681 weeks
358237.2847 -259.6641 (358*2π)/4681 weeks
359290.3065 -260.3252 (359*2π)/4681 weeks
360321.6634 -239.6017 (360*2π)/4681 weeks
361355.5843 -210.7136 (361*2π)/4681 weeks
362373.4904 -151.4346 (362*2π)/4681 weeks
363319.2126 -86.59916 (363*2π)/4681 weeks
364269.299 -86.38036 (364*2π)/4681 weeks
365221.7232 -76.4487 (365*2π)/4681 weeks
366169.3785 -114.7057 (366*2π)/4681 weeks
367155.2964 -165.2188 (367*2π)/4681 weeks
368154.084 -198.772 (368*2π)/4681 weeks
369181.4228 -232.8286 (369*2π)/4681 weeks
370222.9654 -212.1434 (370*2π)/4681 weeks
371172.8394 -183.7304 (371*2π)/4681 weeks
372147.0513 -249.1055 (372*2π)/4681 weeks
373202.3869 -275.3 (373*2π)/4681 weeks
374219.9047 -236.9934 (374*2π)/4681 weeks
375200.2262 -233.6931 (375*2π)/4681 weeks
376188.2958 -228.0725 (376*2π)/4681 weeks
377163.4623 -235.6624 (377*2π)/4681 weeks
378161.321 -252.5238 (378*2π)/4681 weeks
379126.6148 -271.9495 (379*2π)/4681 weeks
380145.7118 -323.4404 (380*2π)/4681 weeks
381166.1269 -317.2151 (381*2π)/4681 weeks
382149.5697 -323.5399 (382*2π)/4681 weeks
383155.5766 -374.9818 (383*2π)/4681 weeks
384197.6588 -387.4715 (384*2π)/4681 weeks
385213.0592 -384.0393 (385*2π)/4681 weeks
386243.9373 -405.7291 (386*2π)/4681 weeks
387319.941 -364.6487 (387*2π)/4681 weeks
388288.1807 -256.8881 (388*2π)/4681 weeks
389199.6401 -267.2959 (389*2π)/4681 weeks
390182.0609 -304.7826 (390*2π)/4681 weeks
391176.7269 -319.0677 (391*2π)/4681 weeks
392169.7476 -319.1398 (392*2π)/4681 weeks
393144.6246 -326.9682 (393*2π)/4681 weeks
394129.6624 -350.7467 (394*2π)/4681 weeks
39570.8699 -359.1252 (395*2π)/4681 weeks
39635.29099 -503.4626 (396*2π)/4681 weeks
397194.0866 -602.7619 (397*2π)/4681 weeks
398308.9029 -479.5858 (398*2π)/4681 weeks
399241.4028 -407.5158 (399*2π)/4681 weeks
400226.9627 -419.6454 (400*2π)/4681 weeks
401179.5451 -361.5214 (401*2π)/4681 weeks
40224.10978 -460.0025 (402*2π)/4681 weeks
403125.2031 -685.936 (403*2π)/4681 weeks
404341.5615 -635.0598 (404*2π)/4681 weeks
405359.5318 -508.2811 (405*2π)/4681 weeks
406328.8478 -467.1749 (406*2π)/4681 weeks
407320.9076 -414.0826 (407*2π)/4681 weeks
408251.0747 -373.6259 (408*2π)/4681 weeks
409145.1161 -407.1226 (409*2π)/4681 weeks
410139.426 -523.6493 (410*2π)/4681 weeks
411221.9484 -540.6658 (411*2π)/4681 weeks
412217.5892 -522.0405 (412*2π)/4681 weeks
413233.0171 -507.4087 (413*2π)/4681 weeks
414207.5143 -477.2028 (414*2π)/4681 weeks
415145.8869 -464.0971 (415*2π)/4681 weeks
41670.17219 -541.5463 (416*2π)/4681 weeks
417100.7889 -629.6349 (417*2π)/4681 weeks
418118.8149 -647.0012 (418*2π)/4681 weeks
419147.2054 -710.8543 (419*2π)/4681 weeks
420200.7548 -707.597 (420*2π)/4681 weeks
421218.7075 -689.0676 (421*2π)/4681 weeks
422224.1574 -683.9494 (422*2π)/4681 weeks
423208.0372 -687.6786 (423*2π)/4681 weeks
424214.2629 -717.5893 (424*2π)/4681 weeks
425239.8951 -704.8802 (425*2π)/4681 weeks
426267.4194 -689.6795 (426*2π)/4681 weeks
427275.5224 -578.8223 (427*2π)/4681 weeks
42840.80937 -521.4949 (428*2π)/4681 weeks
429-51.06609 -729.3512 (429*2π)/4681 weeks
43022.16031 -793.8718 (430*2π)/4681 weeks
431-88.02485 -816.7006 (431*2π)/4681 weeks
432-80.88816 -1,084.987 (432*2π)/4681 weeks
433218.1387 -1,128.223 (433*2π)/4681 weeks
434249.4529 -893.9896 (434*2π)/4681 weeks
435108.1104 -852.3488 (435*2π)/4681 weeks
436-30.91856 -868.3625 (436*2π)/4681 weeks
437-171.1754 -997.3081 (437*2π)/4681 weeks
438-223.4721 -1,225.292 (438*2π)/4681 weeks
439-130.9157 -1,443.426 (439*2π)/4681 weeks
44067.23907 -1,533.119 (440*2π)/4681 weeks
441218.2552 -1,458.655 (441*2π)/4681 weeks
442145.2704 -1,371.753 (442*2π)/4681 weeks
44377.11597 -1,421.604 (443*2π)/4681 weeks
4449.49042 -1,428.352 (444*2π)/4681 weeks
445-188.8172 -1,609.897 (445*2π)/4681 weeks
446-151.6055 -2,002.599 (446*2π)/4681 weeks
447152.7015 -2,168.806 (447*2π)/4681 weeks
448300.8735 -2,093.055 (448*2π)/4681 weeks
449317.987 -2,034.964 (449*2π)/4681 weeks
450182.5109 -2,109.075 (450*2π)/4681 weeks
451160.6539 -2,285.48 (451*2π)/4681 weeks
45240.04511 -2,367.254 (452*2π)/4681 weeks
453-187.2216 -2,954.79 (453*2π)/4681 weeks
454437.7561 -3,648.125 (454*2π)/4681 weeks
4551,123.54 -3,360.911 (455*2π)/4681 weeks
456941.7535 -3,008.354 (456*2π)/4681 weeks
457686.0266 -3,368.853 (457*2π)/4681 weeks
458745.0528 -3,610.054 (458*2π)/4681 weeks
459400.3741 -4,119.833 (459*2π)/4681 weeks
460574.8976 -5,569.848 (460*2π)/4681 weeks
4612,133.392 -6,459.375 (461*2π)/4681 weeks
4623,195.752 -5,882.179 (462*2π)/4681 weeks
4632,770.803 -6,267.179 (463*2π)/4681 weeks
4643,818.345 -8,382.763 (464*2π)/4681 weeks
4656,645.305 -9,266.215 (465*2π)/4681 weeks
4669,345.308 -9,878.478 (466*2π)/4681 weeks



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