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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 48 weeks (3575.215*sine), 35 weeks (3506.829*sine), and 44 weeks (3391.356*sine).

VXX (iPath® S&P 500 VIX Short-Term Futures™ ETN) has an average price of 11,274.68 (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.

## Fourier Analysis

Using data from 1/30/2009 to 4/23/2018 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
011,274.68   0
115,715.75 9,541.752 (1*2π)/483483 weeks
29,292.562 9,665.364 (2*2π)/483242 weeks
36,686.631 8,990.84 (3*2π)/483161 weeks
44,010.46 8,327.898 (4*2π)/483121 weeks
52,666.78 6,333.435 (5*2π)/48397 weeks
63,068.157 5,607.045 (6*2π)/48381 weeks
72,424.549 6,235.203 (7*2π)/48369 weeks
8854.3419 5,741.853 (8*2π)/48360 weeks
9304.5209 4,298.355 (9*2π)/48354 weeks
10643.4623 3,575.215 (10*2π)/48348 weeks
11711.3466 3,391.356 (11*2π)/48344 weeks
12760.3271 2,980.464 (12*2π)/48340 weeks
131,106.847 3,053.263 (13*2π)/48337 weeks
14804.9688 3,506.829 (14*2π)/48335 weeks
15-16.40574 3,258.593 (15*2π)/48332 weeks
16-125.0975 2,489.566 (16*2π)/48330 weeks
17146.3012 2,249.154 (17*2π)/48328 weeks
18150.9359 2,142.233 (18*2π)/48327 weeks
19223.2566 1,981.92 (19*2π)/48325 weeks
20320.3616 2,002.642 (20*2π)/48324 weeks
21273.087 2,049.164 (21*2π)/48323 weeks
2251.4305 2,085.156 (22*2π)/48322 weeks
23-202.2305 1,833.527 (23*2π)/48321 weeks
24-142.7438 1,489.649 (24*2π)/48320 weeks
2544.07284 1,385.21 (25*2π)/48319 weeks
2682.54861 1,363.902 (26*2π)/48319 weeks
27156.6236 1,327.125 (27*2π)/48318 weeks
28201.312 1,433.667 (28*2π)/48317 weeks
2947.27209 1,484.456 (29*2π)/48317 weeks
30-137.4426 1,385.656 (30*2π)/48316 weeks
31-217.6996 1,178.337 (31*2π)/48316 weeks
32-165.296 965.1429 (32*2π)/48315 weeks
33-34.0113 843.2098 (33*2π)/48315 weeks
3499.07865 825.7086 (34*2π)/48314 weeks
35228.7146 853.9991 (35*2π)/48314 weeks
36236.7268 1,069.149 (36*2π)/48313 weeks
37-43.91481 1,085.691 (37*2π)/48313 weeks
38-108.415 826.6168 (38*2π)/48313 weeks
3917.78943 758.7136 (39*2π)/48312 weeks
40-34.19459 743.3703 (40*2π)/48312 weeks
41-15.58278 554.8001 (41*2π)/48312 weeks
42223.3829 508.8018 (42*2π)/48312 weeks
43270.0188 647.5813 (43*2π)/48311 weeks
44236.9269 683.2015 (44*2π)/48311 weeks
45225.6184 695.0695 (45*2π)/48311 weeks
46198.1495 674.767 (46*2π)/48311 weeks
47208.7803 657.8857 (47*2π)/48310 weeks
48211.9046 668.4293 (48*2π)/48310 weeks
49209.6804 677.8354 (49*2π)/48310 weeks
50179.1456 690.5521 (50*2π)/48310 weeks
51117.2461 663.8739 (51*2π)/4839 weeks
52117.9669 618.8143 (52*2π)/4839 weeks
5378.50684 589.5904 (53*2π)/4839 weeks
5481.34367 490.1058 (54*2π)/4839 weeks
55165.8424 450.2885 (55*2π)/4839 weeks
56211.1892 467.6335 (56*2π)/4839 weeks
57224.9684 498.5341 (57*2π)/4838 weeks
58210.4477 502.6323 (58*2π)/4838 weeks
59205.689 531.6724 (59*2π)/4838 weeks
60127.4691 493.928 (60*2π)/4838 weeks
61149.5423 384.2936 (61*2π)/4838 weeks
62249.2066 363.7155 (62*2π)/4838 weeks
63312.687 404.1107 (63*2π)/4838 weeks
64318.5047 452.8696 (64*2π)/4838 weeks
65347.5916 491.0091 (65*2π)/4837 weeks
66335.6473 607.8254 (66*2π)/4837 weeks
67140.9786 672.7539 (67*2π)/4837 weeks
6816.98654 472.5666 (68*2π)/4837 weeks
69153.1334 346.6779 (69*2π)/4837 weeks
70221.2087 400.4049 (70*2π)/4837 weeks
71222.5113 398.4207 (71*2π)/4837 weeks
72291.1792 433.6 (72*2π)/4837 weeks
73238.047 568.8979 (73*2π)/4837 weeks
7463.3354 535.5529 (74*2π)/4837 weeks
7540.38589 379.9841 (75*2π)/4836 weeks
76117.7097 336.4985 (76*2π)/4836 weeks
77129.1681 327.1658 (77*2π)/4836 weeks
78155.3732 311.8545 (78*2π)/4836 weeks
79172.3788 311.8244 (79*2π)/4836 weeks
80175.1517 301.4217 (80*2π)/4836 weeks
81179.0257 280.0188 (81*2π)/4836 weeks
82222.4058 241.1243 (82*2π)/4836 weeks
83311.7305 287.5807 (83*2π)/4836 weeks
84283.7575 383.9348 (84*2π)/4836 weeks
85218.7787 385.2002 (85*2π)/4836 weeks
86204.0748 370.4155 (86*2π)/4836 weeks
87180.8125 376.0437 (87*2π)/4836 weeks
88141.2413 351.0209 (88*2π)/4835 weeks
89151.4277 308.8808 (89*2π)/4835 weeks
90161.7036 308.8951 (90*2π)/4835 weeks
91133.7516 308.6262 (91*2π)/4835 weeks
92126.6154 255.6701 (92*2π)/4835 weeks
93156.8148 245.5353 (93*2π)/4835 weeks
94160.4583 226.3183 (94*2π)/4835 weeks
95183.3922 220.905 (95*2π)/4835 weeks
96194.0175 226.3156 (96*2π)/4835 weeks
97212.758 229.1655 (97*2π)/4835 weeks
98198.2523 265.8496 (98*2π)/4835 weeks
99145.024 246.305 (99*2π)/4835 weeks
100160.7463 181.3847 (100*2π)/4835 weeks
101215.0401 196.91 (101*2π)/4835 weeks
102182.5469 228.2865 (102*2π)/4835 weeks
103151.8043 201.9419 (103*2π)/4835 weeks
104152.4489 166.989 (104*2π)/4835 weeks
105156.3224 122.6265 (105*2π)/4835 weeks
106194.3972 80.50986 (106*2π)/4835 weeks
107250.9581 81.45337 (107*2π)/4835 weeks
108287.1566 81.83137 (108*2π)/4834 weeks
109351.7112 113.5647 (109*2π)/4834 weeks
110352.9839 184.8526 (110*2π)/4834 weeks
111325.9604 224.9958 (111*2π)/4834 weeks
112299.1766 242.5186 (112*2π)/4834 weeks
113258.3127 256.4286 (113*2π)/4834 weeks
114206.1433 233.7405 (114*2π)/4834 weeks
115200.0802 174.8537 (115*2π)/4834 weeks
116227.2894 156.3401 (116*2π)/4834 weeks
117236.2566 151.061 (117*2π)/4834 weeks
118253.5117 136.4952 (118*2π)/4834 weeks
119252.992 148.8515 (119*2π)/4834 weeks
120251.827 115.7529 (120*2π)/4834 weeks
121306.2126 92.28308 (121*2π)/4834 weeks
122346.0183 137.3207 (122*2π)/4834 weeks
123332.2111 165.4836 (123*2π)/4834 weeks
124361.5313 159.1971 (124*2π)/4834 weeks
125388.0568 231.9218 (125*2π)/4834 weeks
126323.0701 286.7909 (126*2π)/4834 weeks
127267.0029 278.0337 (127*2π)/4834 weeks
128245.6212 263.4438 (128*2π)/4834 weeks
129217.6681 242.6788 (129*2π)/4834 weeks
130208.5011 209.0166 (130*2π)/4834 weeks
131242.2048 201.6161 (131*2π)/4834 weeks
132230.8031 241.6914 (132*2π)/4834 weeks
133164.1202 241.3257 (133*2π)/4834 weeks
134131.8297 176.0794 (134*2π)/4834 weeks
135153.019 129.4726 (135*2π)/4834 weeks
136167.8807 103.7037 (136*2π)/4834 weeks
137196.0257 71.86087 (137*2π)/4834 weeks
138243.8887 68.65196 (138*2π)/4834 weeks
139274.3496 109.2414 (139*2π)/4833 weeks
140235.2098 142.4124 (140*2π)/4833 weeks
141194.3289 96.57083 (141*2π)/4833 weeks
142236.934 35.60533 (142*2π)/4833 weeks
143299.6449 52.53844 (143*2π)/4833 weeks
144316.5509 82.23213 (144*2π)/4833 weeks
145316.8137 113.1531 (145*2π)/4833 weeks
146300.4948 122.2062 (146*2π)/4833 weeks
147291.7413 116.0318 (147*2π)/4833 weeks
148304.3042 100.6137 (148*2π)/4833 weeks
149336.2298 108.0758 (149*2π)/4833 weeks
150344.3992 147.2565 (150*2π)/4833 weeks
151336.8107 163.0067 (151*2π)/4833 weeks
152330.3812 200.9427 (152*2π)/4833 weeks
153283.569 221.9765 (153*2π)/4833 weeks
154243.6918 201.0248 (154*2π)/4833 weeks
155232.324 169.3669 (155*2π)/4833 weeks
156244.2885 157.1848 (156*2π)/4833 weeks
157237.8355 156.9145 (157*2π)/4833 weeks
158233.0877 139.3009 (158*2π)/4833 weeks
159246.7826 129.6087 (159*2π)/4833 weeks
160249.9293 129.595 (160*2π)/4833 weeks
161261.9273 126.7904 (161*2π)/4833 weeks
162273.5728 133.8656 (162*2π)/4833 weeks
163284.1715 159.4188 (163*2π)/4833 weeks
164257.0793 199.9554 (164*2π)/4833 weeks
165199.2815 192.0683 (165*2π)/4833 weeks
166173.862 148.495 (166*2π)/4833 weeks
167182.4659 110.195 (167*2π)/4833 weeks
168196.6541 88.55696 (168*2π)/4833 weeks
169224.1792 62.57225 (169*2π)/4833 weeks
170291.8269 76.57475 (170*2π)/4833 weeks
171301.2055 168.3405 (171*2π)/4833 weeks
172209.2545 206.9953 (172*2π)/4833 weeks
173160.2286 155.073 (173*2π)/4833 weeks
174158.5849 132.2422 (174*2π)/4833 weeks
175128.9827 105.1761 (175*2π)/4833 weeks
176132.1324 39.68467 (176*2π)/4833 weeks
177202.4498 22.19448 (177*2π)/4833 weeks
178203.5311 85.13782 (178*2π)/4833 weeks
179128.6795 63.18173 (179*2π)/4833 weeks
180140.094 -22.31051 (180*2π)/4833 weeks
181191.4165 -51.61116 (181*2π)/4833 weeks
182224.2252 -59.48406 (182*2π)/4833 weeks
183281.129 -73.35042 (183*2π)/4833 weeks
184335.7316 -21.94093 (184*2π)/4833 weeks
185315.3251 38.69944 (185*2π)/4833 weeks
186272.6656 33.54345 (186*2π)/4833 weeks
187268.1631 -.06237 (187*2π)/4833 weeks
188298.1489 -17.73514 (188*2π)/4833 weeks
189323.9576 -25.18978 (189*2π)/4833 weeks
190381.1975 -16.94706 (190*2π)/4833 weeks
191428.233 55.99401 (191*2π)/4833 weeks
192386.3162 144.287 (192*2π)/4833 weeks
193307.4803 159.4658 (193*2π)/4833 weeks
194256.4034 128.4779 (194*2π)/4832 weeks
195232.0884 70.57428 (195*2π)/4832 weeks
196278.0102 16.66411 (196*2π)/4832 weeks
197341.4091 40.28114 (197*2π)/4832 weeks
198339.6141 88.55437 (198*2π)/4832 weeks
199330.5358 104.2568 (199*2π)/4832 weeks
200314.8221 135.5593 (200*2π)/4832 weeks
201264.3602 143.2847 (201*2π)/4832 weeks
202229.3209 106.1468 (202*2π)/4832 weeks
203241.8881 54.88409 (203*2π)/4832 weeks
204279.5905 48.47149 (204*2π)/4832 weeks
205295.0157 62.56329 (205*2π)/4832 weeks
206304.2084 67.43291 (206*2π)/4832 weeks
207317.571 93.28355 (207*2π)/4832 weeks
208290.3781 124.9689 (208*2π)/4832 weeks
209247.4585 94.76231 (209*2π)/4832 weeks
210290.6333 54.45918 (210*2π)/4832 weeks
211317.3748 103.6462 (211*2π)/4832 weeks
212283.3334 113.9471 (212*2π)/4832 weeks
213304.7323 111.2183 (213*2π)/4832 weeks
214287.0835 165.6116 (214*2π)/4832 weeks
215209.5562 155.7203 (215*2π)/4832 weeks
216209.173 85.6843 (216*2π)/4832 weeks
217249.3372 78.67311 (217*2π)/4832 weeks
218243.987 96.18887 (218*2π)/4832 weeks
219248.0195 75.68912 (219*2π)/4832 weeks
220275.205 78.46793 (220*2π)/4832 weeks
221294.7054 102.756 (221*2π)/4832 weeks
222298.2473 145.7774 (222*2π)/4832 weeks
223252.781 186.6737 (223*2π)/4832 weeks
224218.3577 179.2661 (224*2π)/4832 weeks
225181.5995 187.0107 (225*2π)/4832 weeks
226130.517 146.9879 (226*2π)/4832 weeks
227157.4489 99.26741 (227*2π)/4832 weeks
228175.653 138.1238 (228*2π)/4832 weeks
229112.3643 147.2844 (229*2π)/4832 weeks
23072.00882 100.0733 (230*2π)/4832 weeks
23154.29676 43.71867 (231*2π)/4832 weeks
23278.68996 -27.95632 (232*2π)/4832 weeks
233149.9939 -63.6693 (233*2π)/4832 weeks
234218.6592 -39.56031 (234*2π)/4832 weeks
235242.5203 37.18232 (235*2π)/4832 weeks
236176.2901 86.72073 (236*2π)/4832 weeks
237115.3025 39.9459 (237*2π)/4832 weeks
238130.3853 -12.25112 (238*2π)/4832 weeks
239148.308 -21.8119 (239*2π)/4832 weeks
240167.4765 -58.01874 (240*2π)/4832 weeks
241243.1156 -45.44554 (241*2π)/4832 weeks
242243.1156 45.44554 (242*2π)/4832 weeks
243167.4765 58.01874 (243*2π)/4832 weeks
244148.308 21.8119 (244*2π)/4832 weeks
245130.3853 12.25112 (245*2π)/4832 weeks
246115.3025 -39.9459 (246*2π)/4832 weeks
247176.2901 -86.72073 (247*2π)/4832 weeks
248242.5203 -37.18232 (248*2π)/4832 weeks
249218.6592 39.56031 (249*2π)/4832 weeks
250149.9939 63.6693 (250*2π)/4832 weeks
25178.68996 27.95632 (251*2π)/4832 weeks
25254.29676 -43.71867 (252*2π)/4832 weeks
25372.00882 -100.0733 (253*2π)/4832 weeks
254112.3643 -147.2844 (254*2π)/4832 weeks
255175.653 -138.1238 (255*2π)/4832 weeks
256157.4489 -99.26741 (256*2π)/4832 weeks
257130.517 -146.9879 (257*2π)/4832 weeks
258181.5995 -187.0107 (258*2π)/4832 weeks
259218.3577 -179.2661 (259*2π)/4832 weeks
260252.781 -186.6737 (260*2π)/4832 weeks
261298.2473 -145.7774 (261*2π)/4832 weeks
262294.7054 -102.756 (262*2π)/4832 weeks
263275.205 -78.46793 (263*2π)/4832 weeks
264248.0195 -75.68912 (264*2π)/4832 weeks
265243.987 -96.18887 (265*2π)/4832 weeks
266249.3372 -78.67311 (266*2π)/4832 weeks
267209.173 -85.6843 (267*2π)/4832 weeks
268209.5562 -155.7203 (268*2π)/4832 weeks
269287.0835 -165.6116 (269*2π)/4832 weeks
270304.7323 -111.2183 (270*2π)/4832 weeks
271283.3334 -113.9471 (271*2π)/4832 weeks
272317.3748 -103.6462 (272*2π)/4832 weeks
273290.6333 -54.45918 (273*2π)/4832 weeks
274247.4585 -94.76231 (274*2π)/4832 weeks
275290.3781 -124.9689 (275*2π)/4832 weeks
276317.571 -93.28355 (276*2π)/4832 weeks
277304.2084 -67.43291 (277*2π)/4832 weeks
278295.0157 -62.56329 (278*2π)/4832 weeks
279279.5905 -48.47149 (279*2π)/4832 weeks
280241.8881 -54.88409 (280*2π)/4832 weeks
281229.3209 -106.1468 (281*2π)/4832 weeks
282264.3602 -143.2847 (282*2π)/4832 weeks
283314.8221 -135.5593 (283*2π)/4832 weeks
284330.5358 -104.2568 (284*2π)/4832 weeks
285339.6141 -88.55437 (285*2π)/4832 weeks
286341.4091 -40.28114 (286*2π)/4832 weeks
287278.0102 -16.66411 (287*2π)/4832 weeks
288232.0884 -70.57428 (288*2π)/4832 weeks
289256.4034 -128.4779 (289*2π)/4832 weeks
290307.4803 -159.4658 (290*2π)/4832 weeks
291386.3162 -144.287 (291*2π)/4832 weeks
292428.233 -55.99401 (292*2π)/4832 weeks
293381.1975 16.94706 (293*2π)/4832 weeks
294323.9576 25.18978 (294*2π)/4832 weeks
295298.1489 17.73514 (295*2π)/4832 weeks
296268.1631 .06237 (296*2π)/4832 weeks
297272.6656 -33.54345 (297*2π)/4832 weeks
298315.3251 -38.69944 (298*2π)/4832 weeks
299335.7316 21.94093 (299*2π)/4832 weeks
300281.129 73.35042 (300*2π)/4832 weeks
301224.2252 59.48406 (301*2π)/4832 weeks
302191.4165 51.61116 (302*2π)/4832 weeks
303140.094 22.31051 (303*2π)/4832 weeks
304128.6795 -63.18173 (304*2π)/4832 weeks
305203.5311 -85.13782 (305*2π)/4832 weeks
306202.4498 -22.19448 (306*2π)/4832 weeks
307132.1324 -39.68467 (307*2π)/4832 weeks
308128.9827 -105.1761 (308*2π)/4832 weeks
309158.5849 -132.2422 (309*2π)/4832 weeks
310160.2286 -155.073 (310*2π)/4832 weeks
311209.2545 -206.9953 (311*2π)/4832 weeks
312301.2055 -168.3405 (312*2π)/4832 weeks
313291.8269 -76.57475 (313*2π)/4832 weeks
314224.1792 -62.57225 (314*2π)/4832 weeks
315196.6541 -88.55696 (315*2π)/4832 weeks
316182.4659 -110.195 (316*2π)/4832 weeks
317173.862 -148.495 (317*2π)/4832 weeks
318199.2815 -192.0683 (318*2π)/4832 weeks
319257.0793 -199.9554 (319*2π)/4832 weeks
320284.1715 -159.4188 (320*2π)/4832 weeks
321273.5728 -133.8656 (321*2π)/4832 weeks
322261.9273 -126.7904 (322*2π)/4832 weeks
323249.9293 -129.595 (323*2π)/4831 weeks
324246.7826 -129.6087 (324*2π)/4831 weeks
325233.0877 -139.3009 (325*2π)/4831 weeks
326237.8355 -156.9145 (326*2π)/4831 weeks
327244.2885 -157.1848 (327*2π)/4831 weeks
328232.324 -169.3669 (328*2π)/4831 weeks
329243.6918 -201.0248 (329*2π)/4831 weeks
330283.569 -221.9765 (330*2π)/4831 weeks
331330.3812 -200.9427 (331*2π)/4831 weeks
332336.8107 -163.0067 (332*2π)/4831 weeks
333344.3992 -147.2565 (333*2π)/4831 weeks
334336.2298 -108.0758 (334*2π)/4831 weeks
335304.3042 -100.6137 (335*2π)/4831 weeks
336291.7413 -116.0318 (336*2π)/4831 weeks
337300.4948 -122.2062 (337*2π)/4831 weeks
338316.8137 -113.1531 (338*2π)/4831 weeks
339316.5509 -82.23213 (339*2π)/4831 weeks
340299.6449 -52.53844 (340*2π)/4831 weeks
341236.934 -35.60533 (341*2π)/4831 weeks
342194.3289 -96.57083 (342*2π)/4831 weeks
343235.2098 -142.4124 (343*2π)/4831 weeks
344274.3496 -109.2414 (344*2π)/4831 weeks
345243.8887 -68.65196 (345*2π)/4831 weeks
346196.0257 -71.86087 (346*2π)/4831 weeks
347167.8807 -103.7037 (347*2π)/4831 weeks
348153.019 -129.4726 (348*2π)/4831 weeks
349131.8297 -176.0794 (349*2π)/4831 weeks
350164.1202 -241.3257 (350*2π)/4831 weeks
351230.8031 -241.6914 (351*2π)/4831 weeks
352242.2048 -201.6161 (352*2π)/4831 weeks
353208.5011 -209.0166 (353*2π)/4831 weeks
354217.6681 -242.6788 (354*2π)/4831 weeks
355245.6212 -263.4438 (355*2π)/4831 weeks
356267.0029 -278.0337 (356*2π)/4831 weeks
357323.0701 -286.7909 (357*2π)/4831 weeks
358388.0568 -231.9218 (358*2π)/4831 weeks
359361.5313 -159.1971 (359*2π)/4831 weeks
360332.2111 -165.4836 (360*2π)/4831 weeks
361346.0183 -137.3207 (361*2π)/4831 weeks
362306.2126 -92.28308 (362*2π)/4831 weeks
363251.827 -115.7529 (363*2π)/4831 weeks
364252.992 -148.8515 (364*2π)/4831 weeks
365253.5117 -136.4952 (365*2π)/4831 weeks
366236.2566 -151.061 (366*2π)/4831 weeks
367227.2894 -156.3401 (367*2π)/4831 weeks
368200.0802 -174.8537 (368*2π)/4831 weeks
369206.1433 -233.7405 (369*2π)/4831 weeks
370258.3127 -256.4286 (370*2π)/4831 weeks
371299.1766 -242.5186 (371*2π)/4831 weeks
372325.9604 -224.9958 (372*2π)/4831 weeks
373352.9839 -184.8526 (373*2π)/4831 weeks
374351.7112 -113.5647 (374*2π)/4831 weeks
375287.1566 -81.83137 (375*2π)/4831 weeks
376250.9581 -81.45337 (376*2π)/4831 weeks
377194.3972 -80.50986 (377*2π)/4831 weeks
378156.3224 -122.6265 (378*2π)/4831 weeks
379152.4489 -166.989 (379*2π)/4831 weeks
380151.8043 -201.9419 (380*2π)/4831 weeks
381182.5469 -228.2865 (381*2π)/4831 weeks
382215.0401 -196.91 (382*2π)/4831 weeks
383160.7463 -181.3847 (383*2π)/4831 weeks
384145.024 -246.305 (384*2π)/4831 weeks
385198.2523 -265.8496 (385*2π)/4831 weeks
386212.758 -229.1655 (386*2π)/4831 weeks
387194.0175 -226.3156 (387*2π)/4831 weeks
388183.3922 -220.905 (388*2π)/4831 weeks
389160.4583 -226.3183 (389*2π)/4831 weeks
390156.8148 -245.5353 (390*2π)/4831 weeks
391126.6154 -255.6701 (391*2π)/4831 weeks
392133.7516 -308.6262 (392*2π)/4831 weeks
393161.7036 -308.8951 (393*2π)/4831 weeks
394151.4277 -308.8808 (394*2π)/4831 weeks
395141.2413 -351.0209 (395*2π)/4831 weeks
396180.8125 -376.0437 (396*2π)/4831 weeks
397204.0748 -370.4155 (397*2π)/4831 weeks
398218.7787 -385.2002 (398*2π)/4831 weeks
399283.7575 -383.9348 (399*2π)/4831 weeks
400311.7305 -287.5807 (400*2π)/4831 weeks
401222.4058 -241.1243 (401*2π)/4831 weeks
402179.0257 -280.0188 (402*2π)/4831 weeks
403175.1517 -301.4217 (403*2π)/4831 weeks
404172.3788 -311.8244 (404*2π)/4831 weeks
405155.3732 -311.8545 (405*2π)/4831 weeks
406129.1681 -327.1658 (406*2π)/4831 weeks
407117.7097 -336.4985 (407*2π)/4831 weeks
40840.38589 -379.9841 (408*2π)/4831 weeks
40963.3354 -535.5529 (409*2π)/4831 weeks
410238.047 -568.8979 (410*2π)/4831 weeks
411291.1792 -433.6 (411*2π)/4831 weeks
412222.5113 -398.4207 (412*2π)/4831 weeks
413221.2087 -400.4049 (413*2π)/4831 weeks
414153.1334 -346.6779 (414*2π)/4831 weeks
41516.98654 -472.5666 (415*2π)/4831 weeks
416140.9786 -672.7539 (416*2π)/4831 weeks
417335.6473 -607.8254 (417*2π)/4831 weeks
418347.5916 -491.0091 (418*2π)/4831 weeks
419318.5047 -452.8696 (419*2π)/4831 weeks
420312.687 -404.1107 (420*2π)/4831 weeks
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422149.5423 -384.2936 (422*2π)/4831 weeks
423127.4691 -493.928 (423*2π)/4831 weeks
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425210.4477 -502.6323 (425*2π)/4831 weeks
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428165.8424 -450.2885 (428*2π)/4831 weeks
42981.34367 -490.1058 (429*2π)/4831 weeks
43078.50684 -589.5904 (430*2π)/4831 weeks
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432117.2461 -663.8739 (432*2π)/4831 weeks
433179.1456 -690.5521 (433*2π)/4831 weeks
434209.6804 -677.8354 (434*2π)/4831 weeks
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436208.7803 -657.8857 (436*2π)/4831 weeks
437198.1495 -674.767 (437*2π)/4831 weeks
438225.6184 -695.0695 (438*2π)/4831 weeks
439236.9269 -683.2015 (439*2π)/4831 weeks
440270.0188 -647.5813 (440*2π)/4831 weeks
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442-15.58278 -554.8001 (442*2π)/4831 weeks
443-34.19459 -743.3703 (443*2π)/4831 weeks
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445-108.415 -826.6168 (445*2π)/4831 weeks
446-43.91481 -1,085.691 (446*2π)/4831 weeks
447236.7268 -1,069.149 (447*2π)/4831 weeks
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450-34.0113 -843.2098 (450*2π)/4831 weeks
451-165.296 -965.1429 (451*2π)/4831 weeks
452-217.6996 -1,178.337 (452*2π)/4831 weeks
453-137.4426 -1,385.656 (453*2π)/4831 weeks
45447.27209 -1,484.456 (454*2π)/4831 weeks
455201.312 -1,433.667 (455*2π)/4831 weeks
456156.6236 -1,327.125 (456*2π)/4831 weeks
45782.54861 -1,363.902 (457*2π)/4831 weeks
45844.07284 -1,385.21 (458*2π)/4831 weeks
459-142.7438 -1,489.649 (459*2π)/4831 weeks
460-202.2305 -1,833.527 (460*2π)/4831 weeks
46151.4305 -2,085.156 (461*2π)/4831 weeks
462273.087 -2,049.164 (462*2π)/4831 weeks
463320.3616 -2,002.642 (463*2π)/4831 weeks
464223.2566 -1,981.92 (464*2π)/4831 weeks
465150.9359 -2,142.233 (465*2π)/4831 weeks
466146.3012 -2,249.154 (466*2π)/4831 weeks
467-125.0975 -2,489.566 (467*2π)/4831 weeks
468-16.40574 -3,258.593 (468*2π)/4831 weeks
469804.9688 -3,506.829 (469*2π)/4831 weeks
4701,106.847 -3,053.263 (470*2π)/4831 weeks
471760.3271 -2,980.464 (471*2π)/4831 weeks
472711.3466 -3,391.356 (472*2π)/4831 weeks
473643.4623 -3,575.215 (473*2π)/4831 weeks
474304.5209 -4,298.355 (474*2π)/4831 weeks
475854.3419 -5,741.853 (475*2π)/4831 weeks
4762,424.549 -6,235.203 (476*2π)/4831 weeks
4773,068.157 -5,607.045 (477*2π)/4831 weeks
4782,666.78 -6,333.435 (478*2π)/4831 weeks
4794,010.46 -8,327.898 (479*2π)/4831 weeks
4806,686.631 -8,990.84 (480*2π)/4831 weeks
4819,292.562 -9,665.364 (481*2π)/4831 weeks