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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 46 weeks (3672.005*sine), 35 weeks (3649.421*sine), and 41 weeks (3302.536*sine).

VXX (iPath® S&P 500 VIX Short-Term Futures™ ETN) has an average price of 11,966.26 (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 10/9/2017 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
011,966.26   0 
116,125.12 10,315.73 (1*2π)/455455 weeks
29,399.832 10,071.82 (2*2π)/455228 weeks
36,587.907 9,512.706 (3*2π)/455152 weeks
43,652.374 8,392.696 (4*2π)/455114 weeks
52,902.96 6,241.204 (5*2π)/45591 weeks
63,251.792 6,183.384 (6*2π)/45576 weeks
71,831.705 6,589.429 (7*2π)/45565 weeks
8399.1817 5,345.01 (8*2π)/45557 weeks
9517.2573 4,021.877 (9*2π)/45551 weeks
10793.9463 3,672.005 (10*2π)/45546 weeks
11719.0699 3,302.536 (11*2π)/45541 weeks
121,110.917 3,143.327 (12*2π)/45538 weeks
13992.3272 3,649.421 (13*2π)/45535 weeks
1479.28503 3,562.962 (14*2π)/45533 weeks
15-153.5123 2,691.906 (15*2π)/45530 weeks
16153.2577 2,388.585 (16*2π)/45528 weeks
17160.9307 2,265.984 (17*2π)/45527 weeks
18253.8245 2,093.577 (18*2π)/45525 weeks
19333.4492 2,137.534 (19*2π)/45524 weeks
20262.0706 2,200.014 (20*2π)/45523 weeks
21-37.45683 2,169.333 (21*2π)/45522 weeks
22-231.9941 1,795.891 (22*2π)/45521 weeks
23-66.99731 1,497.789 (23*2π)/45520 weeks
2473.84364 1,478.085 (24*2π)/45519 weeks
25124.7817 1,419.983 (25*2π)/45518 weeks
26225.7705 1,455.844 (26*2π)/45518 weeks
27110.615 1,575.297 (27*2π)/45517 weeks
28-97.67188 1,520.259 (28*2π)/45516 weeks
29-222.3563 1,302.085 (29*2π)/45516 weeks
30-192.7102 1,053.588 (30*2π)/45515 weeks
31-50.72513 903.0534 (31*2π)/45515 weeks
32102.108 876.3532 (32*2π)/45514 weeks
33247.6909 910.6432 (33*2π)/45514 weeks
34231.4257 1,154.592 (34*2π)/45513 weeks
35-83.2013 1,115.872 (35*2π)/45513 weeks
36-86.07687 834.9713 (36*2π)/45513 weeks
3721.44553 818.9333 (37*2π)/45512 weeks
38-55.69661 733.5979 (38*2π)/45512 weeks
3973.20595 521.3419 (39*2π)/45512 weeks
40292.1806 621.471 (40*2π)/45511 weeks
41268.5367 716.9667 (41*2π)/45511 weeks
42246.735 727.3355 (42*2π)/45511 weeks
43212.2521 729.934 (43*2π)/45511 weeks
44216.2053 702.6033 (44*2π)/45510 weeks
45228.5116 708.8939 (45*2π)/45510 weeks
46225.2732 715.2203 (46*2π)/45510 weeks
47194.8271 731.6152 (47*2π)/45510 weeks
48126.4201 708.4546 (48*2π)/4559 weeks
49125.2045 656.946 (49*2π)/4559 weeks
5079.8465 619.5887 (50*2π)/4559 weeks
5196.33183 507.1355 (51*2π)/4559 weeks
52189.0943 481.7137 (52*2π)/4559 weeks
53232.8369 504.5183 (53*2π)/4559 weeks
54233.8666 537.1769 (54*2π)/4558 weeks
55230.8731 535.1608 (55*2π)/4558 weeks
56178.0288 566.4485 (56*2π)/4558 weeks
57128.8259 463.9004 (57*2π)/4558 weeks
58222.8508 380.2684 (58*2π)/4558 weeks
59310.6835 407.0424 (59*2π)/4558 weeks
60339.3552 472.4081 (60*2π)/4558 weeks
61360.0001 504.0439 (61*2π)/4557 weeks
62369.8796 616.6719 (62*2π)/4557 weeks
63181.9782 722.0358 (63*2π)/4557 weeks
6416.5472 517.3702 (64*2π)/4557 weeks
65162.6883 367.9188 (65*2π)/4557 weeks
66234.6547 427.6119 (66*2π)/4557 weeks
67242.6724 420.2185 (67*2π)/4557 weeks
68316.6859 484.5336 (68*2π)/4557 weeks
69205.614 619.2185 (69*2π)/4557 weeks
7036.28885 517.819 (70*2π)/4557 weeks
7175.75429 367.4167 (71*2π)/4556 weeks
72133.6032 360.6308 (72*2π)/4556 weeks
73151.6614 334.9305 (73*2π)/4556 weeks
74177.2701 328.2158 (74*2π)/4556 weeks
75182.1877 325.5895 (75*2π)/4556 weeks
76187.1738 308.83 (76*2π)/4556 weeks
77216.0741 265.7038 (77*2π)/4556 weeks
78318.2937 283.6084 (78*2π)/4556 weeks
79312.2287 398.696 (79*2π)/4556 weeks
80235.1932 410.9214 (80*2π)/4556 weeks
81216.6819 393.2182 (81*2π)/4556 weeks
82189.9642 399.0396 (82*2π)/4556 weeks
83147.2754 366.4409 (83*2π)/4555 weeks
84164.3493 326.6858 (84*2π)/4555 weeks
85169.9609 331.2353 (85*2π)/4555 weeks
86131.7602 314.2106 (86*2π)/4555 weeks
87149.3661 258.8199 (87*2π)/4555 weeks
88163.4911 257.3889 (88*2π)/4555 weeks
89183.8365 235.1575 (89*2π)/4555 weeks
90204.0079 237.7541 (90*2π)/4555 weeks
91214.3603 236.787 (91*2π)/4555 weeks
92224.5347 271.5647 (92*2π)/4555 weeks
93167.7805 276.5117 (93*2π)/4555 weeks
94158.5225 203.2571 (94*2π)/4555 weeks
95223.917 199.87 (95*2π)/4555 weeks
96198.2229 243.2854 (96*2π)/4555 weeks
97161.8297 215.7921 (97*2π)/4555 weeks
98161.6848 176.4811 (98*2π)/4555 weeks
99168.7201 125.7927 (99*2π)/4555 weeks
100217.1635 80.89115 (100*2π)/4555 weeks
101273.3062 88.45325 (101*2π)/4555 weeks
102322.0481 87.84476 (102*2π)/4554 weeks
103383.8073 150.5399 (103*2π)/4554 weeks
104366.4425 215.3146 (104*2π)/4554 weeks
105330.8434 246.4252 (105*2π)/4554 weeks
106297.2786 268.1712 (106*2π)/4554 weeks
107240.5876 265.4881 (107*2π)/4554 weeks
108205.5849 206.4461 (108*2π)/4554 weeks
109235.2396 167.8139 (109*2π)/4554 weeks
110250.0556 162.1775 (110*2π)/4554 weeks
111263.2791 145.0527 (111*2π)/4554 weeks
112271.0965 158.9706 (112*2π)/4554 weeks
113266.1783 124.9379 (113*2π)/4554 weeks
114326.2248 98.29263 (114*2π)/4554 weeks
115367.6846 149.6347 (115*2π)/4554 weeks
116350.7475 173.5291 (116*2π)/4554 weeks
117394.8325 178.3662 (117*2π)/4554 weeks
118400.5659 271.7833 (118*2π)/4554 weeks
119321.5546 305.7118 (119*2π)/4554 weeks
120272.9928 284.2338 (120*2π)/4554 weeks
121244.5728 273.6045 (121*2π)/4554 weeks
122222.7662 242.7018 (122*2π)/4554 weeks
123240.7112 206.142 (123*2π)/4554 weeks
124257.6935 241.3993 (124*2π)/4554 weeks
125197.7546 266.5219 (125*2π)/4554 weeks
126141.4046 205.5999 (126*2π)/4554 weeks
127157.9493 142.9299 (127*2π)/4554 weeks
128176.4381 113.9801 (128*2π)/4554 weeks
129205.2742 77.90673 (129*2π)/4554 weeks
130258.9762 72.90874 (130*2π)/4554 weeks
131290.9167 119.663 (131*2π)/4553 weeks
132241.9993 149.7504 (132*2π)/4553 weeks
133207.2695 87.51125 (133*2π)/4553 weeks
134271.6607 34.42229 (134*2π)/4553 weeks
135325.4727 68.02251 (135*2π)/4553 weeks
136340.4732 99.69478 (136*2π)/4553 weeks
137328.5446 127.856 (137*2π)/4553 weeks
138314.1577 128.2714 (138*2π)/4553 weeks
139313.16 112.373 (139*2π)/4553 weeks
140342.7835 106.7599 (140*2π)/4553 weeks
141368.8951 143.3436 (141*2π)/4553 weeks
142356.2724 169.167 (142*2π)/4553 weeks
143356.5165 204.0493 (143*2π)/4553 weeks
144308.889 235.3168 (144*2π)/4553 weeks
145260.6663 215.6536 (145*2π)/4553 weeks
146246.4612 180.2176 (146*2π)/4553 weeks
147259.4518 166.969 (147*2π)/4553 weeks
148250.9881 165.3436 (148*2π)/4553 weeks
149248.9122 144.4888 (149*2π)/4553 weeks
150264.1953 138.6436 (150*2π)/4553 weeks
151267.5634 134.9427 (151*2π)/4553 weeks
152282.0244 137.0373 (152*2π)/4553 weeks
153297.0708 149.989 (153*2π)/4553 weeks
154296.1346 190.9594 (154*2π)/4553 weeks
155237.8906 215.7506 (155*2π)/4553 weeks
156190.1432 177.2063 (156*2π)/4553 weeks
157187.6145 128.008 (157*2π)/4553 weeks
158204.6404 100.8237 (158*2π)/4553 weeks
159228.3311 72.46788 (159*2π)/4553 weeks
160298.8608 71.98705 (160*2π)/4553 weeks
161324.2157 169.4124 (161*2π)/4553 weeks
162225.2499 220.7057 (162*2π)/4553 weeks
163169.8657 163.0899 (163*2π)/4553 weeks
164166.3062 139.8705 (164*2π)/4553 weeks
165133.4329 103.0713 (165*2π)/4553 weeks
166152.8593 28.53014 (166*2π)/4553 weeks
167229.6112 39.80874 (167*2π)/4553 weeks
168188.8581 98.45721 (168*2π)/4553 weeks
169126.4574 27.13879 (169*2π)/4553 weeks
170174.7402 -43.23017 (170*2π)/4553 weeks
171225.0233 -56.96122 (171*2π)/4553 weeks
172266.9227 -77.6311 (172*2π)/4553 weeks
173343.544 -49.41895 (173*2π)/4553 weeks
174348.6137 27.871 (174*2π)/4553 weeks
175296.4902 41.80444 (175*2π)/4553 weeks
176282.4393 6.44759 (176*2π)/4553 weeks
177313.2343 -18.65707 (177*2π)/4553 weeks
178342.0838 -26.08153 (178*2π)/4553 weeks
179405.7882 -17.41869 (179*2π)/4553 weeks
180455.04 67.87859 (180*2π)/4553 weeks
181398.3995 160.1692 (181*2π)/4553 weeks
182312.5113 164.7318 (182*2π)/4553 weeks
183261.7537 124.7042 (183*2π)/4552 weeks
184254.1264 50.38955 (184*2π)/4552 weeks
185325.4176 16.57488 (185*2π)/4552 weeks
186369.4507 70.15528 (186*2π)/4552 weeks
187352.1018 102.4591 (187*2π)/4552 weeks
188346.3577 128.7912 (188*2π)/4552 weeks
189302.2436 156.0759 (189*2π)/4552 weeks
190251.4418 127.6301 (190*2π)/4552 weeks
191247.2123 68.6526 (191*2π)/4552 weeks
192290.8319 49.80806 (192*2π)/4552 weeks
193312.4236 64.84212 (193*2π)/4552 weeks
194321.6921 71.12673 (194*2π)/4552 weeks
195337.1279 99.02657 (195*2π)/4552 weeks
196304.813 133.2654 (196*2π)/4552 weeks
197262.4848 92.11044 (197*2π)/4552 weeks
198321.2496 62.81033 (198*2π)/4552 weeks
199329.0383 121.0839 (199*2π)/4552 weeks
200301.2961 112.2678 (200*2π)/4552 weeks
201328.0424 138.265 (201*2π)/4552 weeks
202269.7696 186.2861 (202*2π)/4552 weeks
203207.4068 124.4503 (203*2π)/4552 weeks
204247.6181 78.94454 (204*2π)/4552 weeks
205267.8734 100.5906 (205*2π)/4552 weeks
206256.5309 86.43856 (206*2π)/4552 weeks
207284.9599 79.56026 (207*2π)/4552 weeks
208309.5816 102.4002 (208*2π)/4552 weeks
209317.9409 146.9639 (209*2π)/4552 weeks
210273.491 197.5442 (210*2π)/4552 weeks
211232.1591 190.2115 (211*2π)/4552 weeks
212190.038 198.314 (212*2π)/4552 weeks
213137.3052 147.7632 (213*2π)/4552 weeks
214176.0203 106.1627 (214*2π)/4552 weeks
215174.2214 157.5553 (215*2π)/4552 weeks
216101.9153 144.5872 (216*2π)/4552 weeks
21769.21674 87.76818 (217*2π)/4552 weeks
21861.10114 13.00408 (218*2π)/4552 weeks
219115.1768 -56.43098 (219*2π)/4552 weeks
220200.7474 -59.84151 (220*2π)/4552 weeks
221259.202 2.37586 (221*2π)/4552 weeks
222217.8692 85.10527 (222*2π)/4552 weeks
223131.2638 62.83618 (223*2π)/4552 weeks
224131.325 -5.36011 (224*2π)/4552 weeks
225157.5428 -21.4271 (225*2π)/4552 weeks
226172.5684 -57.94876 (226*2π)/4552 weeks
227255.8547 -50.51598 (227*2π)/4552 weeks
228255.8547 50.51598 (228*2π)/4552 weeks
229172.5684 57.94876 (229*2π)/4552 weeks
230157.5428 21.4271 (230*2π)/4552 weeks
231131.325 5.36011 (231*2π)/4552 weeks
232131.2638 -62.83618 (232*2π)/4552 weeks
233217.8692 -85.10527 (233*2π)/4552 weeks
234259.202 -2.37586 (234*2π)/4552 weeks
235200.7474 59.84151 (235*2π)/4552 weeks
236115.1768 56.43098 (236*2π)/4552 weeks
23761.10114 -13.00408 (237*2π)/4552 weeks
23869.21674 -87.76818 (238*2π)/4552 weeks
239101.9153 -144.5872 (239*2π)/4552 weeks
240174.2214 -157.5553 (240*2π)/4552 weeks
241176.0203 -106.1627 (241*2π)/4552 weeks
242137.3052 -147.7632 (242*2π)/4552 weeks
243190.038 -198.314 (243*2π)/4552 weeks
244232.1591 -190.2115 (244*2π)/4552 weeks
245273.491 -197.5442 (245*2π)/4552 weeks
246317.9409 -146.9639 (246*2π)/4552 weeks
247309.5816 -102.4002 (247*2π)/4552 weeks
248284.9599 -79.56026 (248*2π)/4552 weeks
249256.5309 -86.43856 (249*2π)/4552 weeks
250267.8734 -100.5906 (250*2π)/4552 weeks
251247.6181 -78.94454 (251*2π)/4552 weeks
252207.4068 -124.4503 (252*2π)/4552 weeks
253269.7696 -186.2861 (253*2π)/4552 weeks
254328.0424 -138.265 (254*2π)/4552 weeks
255301.2961 -112.2678 (255*2π)/4552 weeks
256329.0383 -121.0839 (256*2π)/4552 weeks
257321.2496 -62.81033 (257*2π)/4552 weeks
258262.4848 -92.11044 (258*2π)/4552 weeks
259304.813 -133.2654 (259*2π)/4552 weeks
260337.1279 -99.02657 (260*2π)/4552 weeks
261321.6921 -71.12673 (261*2π)/4552 weeks
262312.4236 -64.84212 (262*2π)/4552 weeks
263290.8319 -49.80806 (263*2π)/4552 weeks
264247.2123 -68.6526 (264*2π)/4552 weeks
265251.4418 -127.6301 (265*2π)/4552 weeks
266302.2436 -156.0759 (266*2π)/4552 weeks
267346.3577 -128.7912 (267*2π)/4552 weeks
268352.1018 -102.4591 (268*2π)/4552 weeks
269369.4507 -70.15528 (269*2π)/4552 weeks
270325.4176 -16.57488 (270*2π)/4552 weeks
271254.1264 -50.38955 (271*2π)/4552 weeks
272261.7537 -124.7042 (272*2π)/4552 weeks
273312.5113 -164.7318 (273*2π)/4552 weeks
274398.3995 -160.1692 (274*2π)/4552 weeks
275455.04 -67.87859 (275*2π)/4552 weeks
276405.7882 17.41869 (276*2π)/4552 weeks
277342.0838 26.08153 (277*2π)/4552 weeks
278313.2343 18.65707 (278*2π)/4552 weeks
279282.4393 -6.44759 (279*2π)/4552 weeks
280296.4902 -41.80444 (280*2π)/4552 weeks
281348.6137 -27.871 (281*2π)/4552 weeks
282343.544 49.41895 (282*2π)/4552 weeks
283266.9227 77.6311 (283*2π)/4552 weeks
284225.0233 56.96122 (284*2π)/4552 weeks
285174.7402 43.23017 (285*2π)/4552 weeks
286126.4574 -27.13879 (286*2π)/4552 weeks
287188.8581 -98.45721 (287*2π)/4552 weeks
288229.6112 -39.80874 (288*2π)/4552 weeks
289152.8593 -28.53014 (289*2π)/4552 weeks
290133.4329 -103.0713 (290*2π)/4552 weeks
291166.3062 -139.8705 (291*2π)/4552 weeks
292169.8657 -163.0899 (292*2π)/4552 weeks
293225.2499 -220.7057 (293*2π)/4552 weeks
294324.2157 -169.4124 (294*2π)/4552 weeks
295298.8608 -71.98705 (295*2π)/4552 weeks
296228.3311 -72.46788 (296*2π)/4552 weeks
297204.6404 -100.8237 (297*2π)/4552 weeks
298187.6145 -128.008 (298*2π)/4552 weeks
299190.1432 -177.2063 (299*2π)/4552 weeks
300237.8906 -215.7506 (300*2π)/4552 weeks
301296.1346 -190.9594 (301*2π)/4552 weeks
302297.0708 -149.989 (302*2π)/4552 weeks
303282.0244 -137.0373 (303*2π)/4552 weeks
304267.5634 -134.9427 (304*2π)/4551 weeks
305264.1953 -138.6436 (305*2π)/4551 weeks
306248.9122 -144.4888 (306*2π)/4551 weeks
307250.9881 -165.3436 (307*2π)/4551 weeks
308259.4518 -166.969 (308*2π)/4551 weeks
309246.4612 -180.2176 (309*2π)/4551 weeks
310260.6663 -215.6536 (310*2π)/4551 weeks
311308.889 -235.3168 (311*2π)/4551 weeks
312356.5165 -204.0493 (312*2π)/4551 weeks
313356.2724 -169.167 (313*2π)/4551 weeks
314368.8951 -143.3436 (314*2π)/4551 weeks
315342.7835 -106.7599 (315*2π)/4551 weeks
316313.16 -112.373 (316*2π)/4551 weeks
317314.1577 -128.2714 (317*2π)/4551 weeks
318328.5446 -127.856 (318*2π)/4551 weeks
319340.4732 -99.69478 (319*2π)/4551 weeks
320325.4727 -68.02251 (320*2π)/4551 weeks
321271.6607 -34.42229 (321*2π)/4551 weeks
322207.2695 -87.51125 (322*2π)/4551 weeks
323241.9993 -149.7504 (323*2π)/4551 weeks
324290.9167 -119.663 (324*2π)/4551 weeks
325258.9762 -72.90874 (325*2π)/4551 weeks
326205.2742 -77.90673 (326*2π)/4551 weeks
327176.4381 -113.9801 (327*2π)/4551 weeks
328157.9493 -142.9299 (328*2π)/4551 weeks
329141.4046 -205.5999 (329*2π)/4551 weeks
330197.7546 -266.5219 (330*2π)/4551 weeks
331257.6935 -241.3993 (331*2π)/4551 weeks
332240.7112 -206.142 (332*2π)/4551 weeks
333222.7662 -242.7018 (333*2π)/4551 weeks
334244.5728 -273.6045 (334*2π)/4551 weeks
335272.9928 -284.2338 (335*2π)/4551 weeks
336321.5546 -305.7118 (336*2π)/4551 weeks
337400.5659 -271.7833 (337*2π)/4551 weeks
338394.8325 -178.3662 (338*2π)/4551 weeks
339350.7475 -173.5291 (339*2π)/4551 weeks
340367.6846 -149.6347 (340*2π)/4551 weeks
341326.2248 -98.29263 (341*2π)/4551 weeks
342266.1783 -124.9379 (342*2π)/4551 weeks
343271.0965 -158.9706 (343*2π)/4551 weeks
344263.2791 -145.0527 (344*2π)/4551 weeks
345250.0556 -162.1775 (345*2π)/4551 weeks
346235.2396 -167.8139 (346*2π)/4551 weeks
347205.5849 -206.4461 (347*2π)/4551 weeks
348240.5876 -265.4881 (348*2π)/4551 weeks
349297.2786 -268.1712 (349*2π)/4551 weeks
350330.8434 -246.4252 (350*2π)/4551 weeks
351366.4425 -215.3146 (351*2π)/4551 weeks
352383.8073 -150.5399 (352*2π)/4551 weeks
353322.0481 -87.84476 (353*2π)/4551 weeks
354273.3062 -88.45325 (354*2π)/4551 weeks
355217.1635 -80.89115 (355*2π)/4551 weeks
356168.7201 -125.7927 (356*2π)/4551 weeks
357161.6848 -176.4811 (357*2π)/4551 weeks
358161.8297 -215.7921 (358*2π)/4551 weeks
359198.2229 -243.2854 (359*2π)/4551 weeks
360223.917 -199.87 (360*2π)/4551 weeks
361158.5225 -203.2571 (361*2π)/4551 weeks
362167.7805 -276.5117 (362*2π)/4551 weeks
363224.5347 -271.5647 (363*2π)/4551 weeks
364214.3603 -236.787 (364*2π)/4551 weeks
365204.0079 -237.7541 (365*2π)/4551 weeks
366183.8365 -235.1575 (366*2π)/4551 weeks
367163.4911 -257.3889 (367*2π)/4551 weeks
368149.3661 -258.8199 (368*2π)/4551 weeks
369131.7602 -314.2106 (369*2π)/4551 weeks
370169.9609 -331.2353 (370*2π)/4551 weeks
371164.3493 -326.6858 (371*2π)/4551 weeks
372147.2754 -366.4409 (372*2π)/4551 weeks
373189.9642 -399.0396 (373*2π)/4551 weeks
374216.6819 -393.2182 (374*2π)/4551 weeks
375235.1932 -410.9214 (375*2π)/4551 weeks
376312.2287 -398.696 (376*2π)/4551 weeks
377318.2937 -283.6084 (377*2π)/4551 weeks
378216.0741 -265.7038 (378*2π)/4551 weeks
379187.1738 -308.83 (379*2π)/4551 weeks
380182.1877 -325.5895 (380*2π)/4551 weeks
381177.2701 -328.2158 (381*2π)/4551 weeks
382151.6614 -334.9305 (382*2π)/4551 weeks
383133.6032 -360.6308 (383*2π)/4551 weeks
38475.75429 -367.4167 (384*2π)/4551 weeks
38536.28885 -517.819 (385*2π)/4551 weeks
386205.614 -619.2185 (386*2π)/4551 weeks
387316.6859 -484.5336 (387*2π)/4551 weeks
388242.6724 -420.2185 (388*2π)/4551 weeks
389234.6547 -427.6119 (389*2π)/4551 weeks
390162.6883 -367.9188 (390*2π)/4551 weeks
39116.5472 -517.3702 (391*2π)/4551 weeks
392181.9782 -722.0358 (392*2π)/4551 weeks
393369.8796 -616.6719 (393*2π)/4551 weeks
394360.0001 -504.0439 (394*2π)/4551 weeks
395339.3552 -472.4081 (395*2π)/4551 weeks
396310.6835 -407.0424 (396*2π)/4551 weeks
397222.8508 -380.2684 (397*2π)/4551 weeks
398128.8259 -463.9004 (398*2π)/4551 weeks
399178.0288 -566.4485 (399*2π)/4551 weeks
400230.8731 -535.1608 (400*2π)/4551 weeks
401233.8666 -537.1769 (401*2π)/4551 weeks
402232.8369 -504.5183 (402*2π)/4551 weeks
403189.0943 -481.7137 (403*2π)/4551 weeks
40496.33183 -507.1355 (404*2π)/4551 weeks
40579.8465 -619.5887 (405*2π)/4551 weeks
406125.2045 -656.946 (406*2π)/4551 weeks
407126.4201 -708.4546 (407*2π)/4551 weeks
408194.8271 -731.6152 (408*2π)/4551 weeks
409225.2732 -715.2203 (409*2π)/4551 weeks
410228.5116 -708.8939 (410*2π)/4551 weeks
411216.2053 -702.6033 (411*2π)/4551 weeks
412212.2521 -729.934 (412*2π)/4551 weeks
413246.735 -727.3355 (413*2π)/4551 weeks
414268.5367 -716.9667 (414*2π)/4551 weeks
415292.1806 -621.471 (415*2π)/4551 weeks
41673.20595 -521.3419 (416*2π)/4551 weeks
417-55.69661 -733.5979 (417*2π)/4551 weeks
41821.44553 -818.9333 (418*2π)/4551 weeks
419-86.07687 -834.9713 (419*2π)/4551 weeks
420-83.2013 -1,115.872 (420*2π)/4551 weeks
421231.4257 -1,154.592 (421*2π)/4551 weeks
422247.6909 -910.6432 (422*2π)/4551 weeks
423102.108 -876.3532 (423*2π)/4551 weeks
424-50.72513 -903.0534 (424*2π)/4551 weeks
425-192.7102 -1,053.588 (425*2π)/4551 weeks
426-222.3563 -1,302.085 (426*2π)/4551 weeks
427-97.67188 -1,520.259 (427*2π)/4551 weeks
428110.615 -1,575.297 (428*2π)/4551 weeks
429225.7705 -1,455.844 (429*2π)/4551 weeks
430124.7817 -1,419.983 (430*2π)/4551 weeks
43173.84364 -1,478.085 (431*2π)/4551 weeks
432-66.99731 -1,497.789 (432*2π)/4551 weeks
433-231.9941 -1,795.891 (433*2π)/4551 weeks
434-37.45683 -2,169.333 (434*2π)/4551 weeks
435262.0706 -2,200.014 (435*2π)/4551 weeks
436333.4492 -2,137.534 (436*2π)/4551 weeks
437253.8245 -2,093.577 (437*2π)/4551 weeks
438160.9307 -2,265.984 (438*2π)/4551 weeks
439153.2577 -2,388.585 (439*2π)/4551 weeks
440-153.5123 -2,691.906 (440*2π)/4551 weeks
44179.28503 -3,562.962 (441*2π)/4551 weeks
442992.3272 -3,649.421 (442*2π)/4551 weeks
4431,110.917 -3,143.327 (443*2π)/4551 weeks
444719.0699 -3,302.536 (444*2π)/4551 weeks
445793.9463 -3,672.005 (445*2π)/4551 weeks
446517.2573 -4,021.877 (446*2π)/4551 weeks
447399.1817 -5,345.01 (447*2π)/4551 weeks
4481,831.705 -6,589.429 (448*2π)/4551 weeks
4493,251.792 -6,183.384 (449*2π)/4551 weeks
4502,902.96 -6,241.204 (450*2π)/4551 weeks
4513,652.374 -8,392.696 (451*2π)/4551 weeks
4526,587.907 -9,512.706 (452*2π)/4551 weeks
4539,399.832 -10,071.82 (453*2π)/4551 weeks



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