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Fourier Analysis of VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN)


VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN) appears to have interesting cyclic behaviour every 34 weeks (15.6664*sine), 31 weeks (13.5198*sine), and 44 weeks (11.4961*sine).

VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN) has an average price of 151.35 (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 2/20/2009 to 7/17/2017 for VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0151.3451   0 
149.71032 131.7931 (1*2π)/440440 weeks
2-3.57393 47.43174 (2*2π)/440220 weeks
39.15485 39.3967 (3*2π)/440147 weeks
4-4.73101 27.51052 (4*2π)/440110 weeks
510.52019 11.44489 (5*2π)/44088 weeks
616.25443 26.10823 (6*2π)/44073 weeks
73.51983 27.99517 (7*2π)/44063 weeks
8-6.79836 18.45826 (8*2π)/44055 weeks
9-.49828 8.22468 (9*2π)/44049 weeks
105.14651 11.49607 (10*2π)/44044 weeks
112.93533 8.75636 (11*2π)/44040 weeks
127.58844 10.09262 (12*2π)/44037 weeks
136.14506 15.66637 (13*2π)/44034 weeks
14-1.42967 13.51982 (14*2π)/44031 weeks
15.19588 7.88042 (15*2π)/44029 weeks
161.44465 9.65718 (16*2π)/44028 weeks
17.06289 8.44412 (17*2π)/44026 weeks
181.48632 6.61442 (18*2π)/44024 weeks
192.32357 5.84418 (19*2π)/44023 weeks
202.81719 9.06657 (20*2π)/44022 weeks
21-.14243 9.14204 (21*2π)/44021 weeks
22-.30404 6.96996 (22*2π)/44020 weeks
23.86811 6.27631 (23*2π)/44019 weeks
24-.5757 5.76056 (24*2π)/44018 weeks
25-.29476 3.96299 (25*2π)/44018 weeks
261.47872 4.95457 (26*2π)/44017 weeks
271.85969 6.24827 (27*2π)/44016 weeks
28.14153 5.87284 (28*2π)/44016 weeks
29-.67452 5.22831 (29*2π)/44015 weeks
30-.76047 3.68217 (30*2π)/44015 weeks
31.6542 3.59309 (31*2π)/44014 weeks
32-.11232 2.36664 (32*2π)/44014 weeks
333.35667 3.11231 (33*2π)/44013 weeks
34.44662 6.67309 (34*2π)/44013 weeks
35-1.33961 3.08428 (35*2π)/44013 weeks
361.86292 3.13582 (36*2π)/44012 weeks
37.1309 5.06302 (37*2π)/44012 weeks
38-2.25431 2.25365 (38*2π)/44012 weeks
39.71914 1.91725 (39*2π)/44011 weeks
40.83522 1.95035 (40*2π)/44011 weeks
411.79839 1.75551 (41*2π)/44011 weeks
421.25921 2.42461 (42*2π)/44010 weeks
431.42763 2.77121 (43*2π)/44010 weeks
44.83843 3.12924 (44*2π)/44010 weeks
451.13433 2.57605 (45*2π)/44010 weeks
461.39704 2.34465 (46*2π)/44010 weeks
47.59473 2.32003 (47*2π)/4409 weeks
482.05273 2.03444 (48*2π)/4409 weeks
491.41614 3.25937 (49*2π)/4409 weeks
50.50808 2.66034 (50*2π)/4409 weeks
51.47178 2.36764 (51*2π)/4409 weeks
52.68077 1.61958 (52*2π)/4408 weeks
531.13871 1.9743 (53*2π)/4408 weeks
542.17479 1.83048 (54*2π)/4408 weeks
551.84609 2.96608 (55*2π)/4408 weeks
56.40015 3.11304 (56*2π)/4408 weeks
57.38533 2.34121 (57*2π)/4408 weeks
58.91424 1.92857 (58*2π)/4408 weeks
59.11737 2.07308 (59*2π)/4407 weeks
60.04243 .64916 (60*2π)/4407 weeks
612.6726 .21182 (61*2π)/4407 weeks
622.73375 3.31175 (62*2π)/4407 weeks
63.38039 2.83941 (63*2π)/4407 weeks
64.5959 1.97245 (64*2π)/4407 weeks
65.27736 1.97426 (65*2π)/4407 weeks
66.19821 .66663 (66*2π)/4407 weeks
672.37141 .68289 (67*2π)/4407 weeks
682.10617 2.59523 (68*2π)/4406 weeks
69.59265 2.19541 (69*2π)/4406 weeks
701.17787 1.82798 (70*2π)/4406 weeks
71.95788 1.59548 (71*2π)/4406 weeks
721.11813 1.56012 (72*2π)/4406 weeks
731.04761 1.79369 (73*2π)/4406 weeks
741.14985 1.97074 (74*2π)/4406 weeks
75.69849 2.4999 (75*2π)/4406 weeks
76.13174 1.20297 (76*2π)/4406 weeks
771.16904 .93432 (77*2π)/4406 weeks
781.06525 1.45807 (78*2π)/4406 weeks
79.97082 1.4176 (79*2π)/4406 weeks
801.16937 1.16522 (80*2π)/4406 weeks
81.95011 1.64729 (81*2π)/4405 weeks
82.79965 1.31665 (82*2π)/4405 weeks
831.44912 .80797 (83*2π)/4405 weeks
841.59784 1.87167 (84*2π)/4405 weeks
85.85791 1.10659 (85*2π)/4405 weeks
861.42711 1.30069 (86*2π)/4405 weeks
871.25258 1.95192 (87*2π)/4405 weeks
88.91039 1.81049 (88*2π)/4405 weeks
89.58257 1.25004 (89*2π)/4405 weeks
90.98299 .70908 (90*2π)/4405 weeks
911.59461 1.43004 (91*2π)/4405 weeks
92.58389 1.8667 (92*2π)/4405 weeks
93.99918 1.0669 (93*2π)/4405 weeks
941.05987 .94472 (94*2π)/4405 weeks
951.07831 .74867 (95*2π)/4405 weeks
961.3269 1.29779 (96*2π)/4405 weeks
971.13742 1.50706 (97*2π)/4405 weeks
981.40593 1.22342 (98*2π)/4404 weeks
991.44603 1.87443 (99*2π)/4404 weeks
100.5409 1.36499 (100*2π)/4404 weeks
101.8439 1.20679 (101*2π)/4404 weeks
102.80996 1.5972 (102*2π)/4404 weeks
103.39584 1.20351 (103*2π)/4404 weeks
104.85063 .62961 (104*2π)/4404 weeks
1051.31793 1.13344 (105*2π)/4404 weeks
1061.00505 1.31434 (106*2π)/4404 weeks
107.80632 .99019 (107*2π)/4404 weeks
108.62144 1.14439 (108*2π)/4404 weeks
109.94616 .80845 (109*2π)/4404 weeks
1101.31338 1.06952 (110*2π)/4404 weeks
111.7748 1.25613 (111*2π)/4404 weeks
112.8398 .66202 (112*2π)/4404 weeks
1131.42368 1.29122 (113*2π)/4404 weeks
114.80265 1.75176 (114*2π)/4404 weeks
115.67316 1.33459 (115*2π)/4404 weeks
116.5476 .89481 (116*2π)/4404 weeks
117.59743 .66644 (117*2π)/4404 weeks
118.63001 .90611 (118*2π)/4404 weeks
1191.125 .81969 (119*2π)/4404 weeks
120.7867 1.14429 (120*2π)/4404 weeks
121.19247 .80536 (121*2π)/4404 weeks
122.69648 .19948 (122*2π)/4404 weeks
123.99039 .62633 (123*2π)/4404 weeks
124.87196 .60401 (124*2π)/4404 weeks
1251.23868 .41703 (125*2π)/4404 weeks
1261.51154 .7913 (126*2π)/4403 weeks
127.92547 1.31005 (127*2π)/4403 weeks
128.48909 .82032 (128*2π)/4403 weeks
129.83589 .20844 (129*2π)/4403 weeks
1301.31429 .59927 (130*2π)/4403 weeks
1311.18084 .67764 (131*2π)/4403 weeks
132.94105 1.11792 (132*2π)/4403 weeks
133.70032 .64638 (133*2π)/4403 weeks
134.95827 .56535 (134*2π)/4403 weeks
1351.03937 .61058 (135*2π)/4403 weeks
1361.24351 .76707 (136*2π)/4403 weeks
1371.008 .8442 (137*2π)/4403 weeks
1381.19828 1.10915 (138*2π)/4403 weeks
139.69784 1.00344 (139*2π)/4403 weeks
140.63549 .67201 (140*2π)/4403 weeks
141.77185 .75072 (141*2π)/4403 weeks
142.9136 .66152 (142*2π)/4403 weeks
143.80664 .78791 (143*2π)/4403 weeks
144.73156 .53046 (144*2π)/4403 weeks
145.96256 .61057 (145*2π)/4403 weeks
146.58977 .46559 (146*2π)/4403 weeks
1471.05589 .35199 (147*2π)/4403 weeks
1481.15937 .62454 (148*2π)/4403 weeks
1491.1789 .80079 (149*2π)/4403 weeks
150.76904 .89295 (150*2π)/4403 weeks
151.70136 .70584 (151*2π)/4403 weeks
152.62307 .48162 (152*2π)/4403 weeks
153.63304 .4999 (153*2π)/4403 weeks
154.65538 .1787 (154*2π)/4403 weeks
1551.43977 .1696 (155*2π)/4403 weeks
1561.66872 1.15164 (156*2π)/4403 weeks
157.46422 1.33287 (157*2π)/4403 weeks
158.4172 .57383 (158*2π)/4403 weeks
159.4441 .86612 (159*2π)/4403 weeks
160.28515 .51036 (160*2π)/4403 weeks
161.64925 -.08078 (161*2π)/4403 weeks
1621.30213 .67405 (162*2π)/4403 weeks
163.31077 1.18699 (163*2π)/4403 weeks
164.13131 .20705 (164*2π)/4403 weeks
165.31381 -.00347 (165*2π)/4403 weeks
166.4188 .08353 (166*2π)/4403 weeks
167.64394 -.32443 (167*2π)/4403 weeks
1681.23716 -.00633 (168*2π)/4403 weeks
169.84465 .64544 (169*2π)/4403 weeks
170.51875 .45215 (170*2π)/4403 weeks
171.45974 .01396 (171*2π)/4403 weeks
172.46528 .10142 (172*2π)/4403 weeks
173.5471 -.37793 (173*2π)/4403 weeks
1741.19878 -.69549 (174*2π)/4403 weeks
1751.5747 .14689 (175*2π)/4403 weeks
1761.25106 .46918 (176*2π)/4403 weeks
1771.06677 .64177 (177*2π)/4402 weeks
178.2715 .54377 (178*2π)/4402 weeks
179.18098 -.37752 (179*2π)/4402 weeks
1801.3058 -.51266 (180*2π)/4402 weeks
1811.12987 .19141 (181*2π)/4402 weeks
1821.06948 .03375 (182*2π)/4402 weeks
1831.21371 .22725 (183*2π)/4402 weeks
184.98071 .38786 (184*2π)/4402 weeks
185.63224 .06401 (185*2π)/4402 weeks
186.92984 -.02298 (186*2π)/4402 weeks
187.99232 .14768 (187*2π)/4402 weeks
188.78059 .10575 (188*2π)/4402 weeks
189.88022 -.15057 (189*2π)/4402 weeks
1901.34908 .09529 (190*2π)/4402 weeks
191.50411 .55059 (191*2π)/4402 weeks
192.73642 -.36828 (192*2π)/4402 weeks
1931.17868 .0818 (193*2π)/4402 weeks
194.67664 -.25348 (194*2π)/4402 weeks
1951.35334 -.40096 (195*2π)/4402 weeks
1961.5431 .41154 (196*2π)/4402 weeks
197.85999 .34186 (197*2π)/4402 weeks
198.78889 -.03505 (198*2π)/4402 weeks
1991.00271 .20052 (199*2π)/4402 weeks
200.70717 .05639 (200*2π)/4402 weeks
201.8065 -.08379 (201*2π)/4402 weeks
202.77375 -.26204 (202*2π)/4402 weeks
2031.39437 -.39883 (203*2π)/4402 weeks
204.91596 -.0105 (204*2π)/4402 weeks
2051.21549 -.32353 (205*2π)/4402 weeks
2061.37837 .22974 (206*2π)/4402 weeks
207.75291 .25072 (207*2π)/4402 weeks
2081.04415 -.62201 (208*2π)/4402 weeks
2091.48067 -.31879 (209*2π)/4402 weeks
2101.51499 -.00101 (210*2π)/4402 weeks
2111.35508 .44914 (211*2π)/4402 weeks
212.97216 .61754 (212*2π)/4402 weeks
213.59557 .32394 (213*2π)/4402 weeks
214.52807 -.37946 (214*2π)/4402 weeks
2151.26775 -.5892 (215*2π)/4402 weeks
2161.54663 .07423 (216*2π)/4402 weeks
2171.11304 .30066 (217*2π)/4402 weeks
2181.36205 .06357 (218*2π)/4402 weeks
2191.08432 .67545 (219*2π)/4402 weeks
220.16787   (220*2π)/4402 weeks
2211.08432 -.67545 (221*2π)/4402 weeks
2221.36205 -.06357 (222*2π)/4402 weeks
2231.11304 -.30066 (223*2π)/4402 weeks
2241.54663 -.07423 (224*2π)/4402 weeks
2251.26775 .5892 (225*2π)/4402 weeks
226.52807 .37946 (226*2π)/4402 weeks
227.59557 -.32394 (227*2π)/4402 weeks
228.97216 -.61754 (228*2π)/4402 weeks
2291.35508 -.44914 (229*2π)/4402 weeks
2301.51499 .00101 (230*2π)/4402 weeks
2311.48067 .31879 (231*2π)/4402 weeks
2321.04415 .62201 (232*2π)/4402 weeks
233.75291 -.25072 (233*2π)/4402 weeks
2341.37837 -.22974 (234*2π)/4402 weeks
2351.21549 .32353 (235*2π)/4402 weeks
236.91596 .0105 (236*2π)/4402 weeks
2371.39437 .39883 (237*2π)/4402 weeks
238.77375 .26204 (238*2π)/4402 weeks
239.8065 .08379 (239*2π)/4402 weeks
240.70717 -.05639 (240*2π)/4402 weeks
2411.00271 -.20052 (241*2π)/4402 weeks
242.78889 .03505 (242*2π)/4402 weeks
243.85999 -.34186 (243*2π)/4402 weeks
2441.5431 -.41154 (244*2π)/4402 weeks
2451.35334 .40096 (245*2π)/4402 weeks
246.67664 .25348 (246*2π)/4402 weeks
2471.17868 -.0818 (247*2π)/4402 weeks
248.73642 .36828 (248*2π)/4402 weeks
249.50411 -.55059 (249*2π)/4402 weeks
2501.34908 -.09529 (250*2π)/4402 weeks
251.88022 .15057 (251*2π)/4402 weeks
252.78059 -.10575 (252*2π)/4402 weeks
253.99232 -.14768 (253*2π)/4402 weeks
254.92984 .02298 (254*2π)/4402 weeks
255.63224 -.06401 (255*2π)/4402 weeks
256.98071 -.38786 (256*2π)/4402 weeks
2571.21371 -.22725 (257*2π)/4402 weeks
2581.06948 -.03375 (258*2π)/4402 weeks
2591.12987 -.19141 (259*2π)/4402 weeks
2601.3058 .51266 (260*2π)/4402 weeks
261.18098 .37752 (261*2π)/4402 weeks
262.2715 -.54377 (262*2π)/4402 weeks
2631.06677 -.64177 (263*2π)/4402 weeks
2641.25106 -.46918 (264*2π)/4402 weeks
2651.5747 -.14689 (265*2π)/4402 weeks
2661.19878 .69549 (266*2π)/4402 weeks
267.5471 .37793 (267*2π)/4402 weeks
268.46528 -.10142 (268*2π)/4402 weeks
269.45974 -.01396 (269*2π)/4402 weeks
270.51875 -.45215 (270*2π)/4402 weeks
271.84465 -.64544 (271*2π)/4402 weeks
2721.23716 .00633 (272*2π)/4402 weeks
273.64394 .32443 (273*2π)/4402 weeks
274.4188 -.08353 (274*2π)/4402 weeks
275.31381 .00347 (275*2π)/4402 weeks
276.13131 -.20705 (276*2π)/4402 weeks
277.31077 -1.18699 (277*2π)/4402 weeks
2781.30213 -.67405 (278*2π)/4402 weeks
279.64925 .08078 (279*2π)/4402 weeks
280.28515 -.51036 (280*2π)/4402 weeks
281.4441 -.86612 (281*2π)/4402 weeks
282.4172 -.57383 (282*2π)/4402 weeks
283.46422 -1.33287 (283*2π)/4402 weeks
2841.66872 -1.15164 (284*2π)/4402 weeks
2851.43977 -.1696 (285*2π)/4402 weeks
286.65538 -.1787 (286*2π)/4402 weeks
287.63304 -.4999 (287*2π)/4402 weeks
288.62307 -.48162 (288*2π)/4402 weeks
289.70136 -.70584 (289*2π)/4402 weeks
290.76904 -.89295 (290*2π)/4402 weeks
2911.1789 -.80079 (291*2π)/4402 weeks
2921.15937 -.62454 (292*2π)/4402 weeks
2931.05589 -.35199 (293*2π)/4402 weeks
294.58977 -.46559 (294*2π)/4401 weeks
295.96256 -.61057 (295*2π)/4401 weeks
296.73156 -.53046 (296*2π)/4401 weeks
297.80664 -.78791 (297*2π)/4401 weeks
298.9136 -.66152 (298*2π)/4401 weeks
299.77185 -.75072 (299*2π)/4401 weeks
300.63549 -.67201 (300*2π)/4401 weeks
301.69784 -1.00344 (301*2π)/4401 weeks
3021.19828 -1.10915 (302*2π)/4401 weeks
3031.008 -.8442 (303*2π)/4401 weeks
3041.24351 -.76707 (304*2π)/4401 weeks
3051.03937 -.61058 (305*2π)/4401 weeks
306.95827 -.56535 (306*2π)/4401 weeks
307.70032 -.64638 (307*2π)/4401 weeks
308.94105 -1.11792 (308*2π)/4401 weeks
3091.18084 -.67764 (309*2π)/4401 weeks
3101.31429 -.59927 (310*2π)/4401 weeks
311.83589 -.20844 (311*2π)/4401 weeks
312.48909 -.82032 (312*2π)/4401 weeks
313.92547 -1.31005 (313*2π)/4401 weeks
3141.51154 -.7913 (314*2π)/4401 weeks
3151.23868 -.41703 (315*2π)/4401 weeks
316.87196 -.60401 (316*2π)/4401 weeks
317.99039 -.62633 (317*2π)/4401 weeks
318.69648 -.19948 (318*2π)/4401 weeks
319.19247 -.80536 (319*2π)/4401 weeks
320.7867 -1.14429 (320*2π)/4401 weeks
3211.125 -.81969 (321*2π)/4401 weeks
322.63001 -.90611 (322*2π)/4401 weeks
323.59743 -.66644 (323*2π)/4401 weeks
324.5476 -.89481 (324*2π)/4401 weeks
325.67316 -1.33459 (325*2π)/4401 weeks
326.80265 -1.75176 (326*2π)/4401 weeks
3271.42368 -1.29122 (327*2π)/4401 weeks
328.8398 -.66202 (328*2π)/4401 weeks
329.7748 -1.25613 (329*2π)/4401 weeks
3301.31338 -1.06952 (330*2π)/4401 weeks
331.94616 -.80845 (331*2π)/4401 weeks
332.62144 -1.14439 (332*2π)/4401 weeks
333.80632 -.99019 (333*2π)/4401 weeks
3341.00505 -1.31434 (334*2π)/4401 weeks
3351.31793 -1.13344 (335*2π)/4401 weeks
336.85063 -.62961 (336*2π)/4401 weeks
337.39584 -1.20351 (337*2π)/4401 weeks
338.80996 -1.5972 (338*2π)/4401 weeks
339.8439 -1.20679 (339*2π)/4401 weeks
340.5409 -1.36499 (340*2π)/4401 weeks
3411.44603 -1.87443 (341*2π)/4401 weeks
3421.40593 -1.22342 (342*2π)/4401 weeks
3431.13742 -1.50706 (343*2π)/4401 weeks
3441.3269 -1.29779 (344*2π)/4401 weeks
3451.07831 -.74867 (345*2π)/4401 weeks
3461.05987 -.94472 (346*2π)/4401 weeks
347.99918 -1.0669 (347*2π)/4401 weeks
348.58389 -1.8667 (348*2π)/4401 weeks
3491.59461 -1.43004 (349*2π)/4401 weeks
350.98299 -.70908 (350*2π)/4401 weeks
351.58257 -1.25004 (351*2π)/4401 weeks
352.91039 -1.81049 (352*2π)/4401 weeks
3531.25258 -1.95192 (353*2π)/4401 weeks
3541.42711 -1.30069 (354*2π)/4401 weeks
355.85791 -1.10659 (355*2π)/4401 weeks
3561.59784 -1.87167 (356*2π)/4401 weeks
3571.44912 -.80797 (357*2π)/4401 weeks
358.79965 -1.31665 (358*2π)/4401 weeks
359.95011 -1.64729 (359*2π)/4401 weeks
3601.16937 -1.16522 (360*2π)/4401 weeks
361.97082 -1.4176 (361*2π)/4401 weeks
3621.06525 -1.45807 (362*2π)/4401 weeks
3631.16904 -.93432 (363*2π)/4401 weeks
364.13174 -1.20297 (364*2π)/4401 weeks
365.69849 -2.4999 (365*2π)/4401 weeks
3661.14985 -1.97074 (366*2π)/4401 weeks
3671.04761 -1.79369 (367*2π)/4401 weeks
3681.11813 -1.56012 (368*2π)/4401 weeks
369.95788 -1.59548 (369*2π)/4401 weeks
3701.17787 -1.82798 (370*2π)/4401 weeks
371.59265 -2.19541 (371*2π)/4401 weeks
3722.10617 -2.59523 (372*2π)/4401 weeks
3732.37141 -.68289 (373*2π)/4401 weeks
374.19821 -.66663 (374*2π)/4401 weeks
375.27736 -1.97426 (375*2π)/4401 weeks
376.5959 -1.97245 (376*2π)/4401 weeks
377.38039 -2.83941 (377*2π)/4401 weeks
3782.73375 -3.31175 (378*2π)/4401 weeks
3792.6726 -.21182 (379*2π)/4401 weeks
380.04243 -.64916 (380*2π)/4401 weeks
381.11737 -2.07308 (381*2π)/4401 weeks
382.91424 -1.92857 (382*2π)/4401 weeks
383.38533 -2.34121 (383*2π)/4401 weeks
384.40015 -3.11304 (384*2π)/4401 weeks
3851.84609 -2.96608 (385*2π)/4401 weeks
3862.17479 -1.83048 (386*2π)/4401 weeks
3871.13871 -1.9743 (387*2π)/4401 weeks
388.68077 -1.61958 (388*2π)/4401 weeks
389.47178 -2.36764 (389*2π)/4401 weeks
390.50808 -2.66034 (390*2π)/4401 weeks
3911.41614 -3.25937 (391*2π)/4401 weeks
3922.05273 -2.03444 (392*2π)/4401 weeks
393.59473 -2.32003 (393*2π)/4401 weeks
3941.39704 -2.34465 (394*2π)/4401 weeks
3951.13433 -2.57605 (395*2π)/4401 weeks
396.83843 -3.12924 (396*2π)/4401 weeks
3971.42763 -2.77121 (397*2π)/4401 weeks
3981.25921 -2.42461 (398*2π)/4401 weeks
3991.79839 -1.75551 (399*2π)/4401 weeks
400.83522 -1.95035 (400*2π)/4401 weeks
401.71914 -1.91725 (401*2π)/4401 weeks
402-2.25431 -2.25365 (402*2π)/4401 weeks
403.1309 -5.06302 (403*2π)/4401 weeks
4041.86292 -3.13582 (404*2π)/4401 weeks
405-1.33961 -3.08428 (405*2π)/4401 weeks
406.44662 -6.67309 (406*2π)/4401 weeks
4073.35667 -3.11231 (407*2π)/4401 weeks
408-.11232 -2.36664 (408*2π)/4401 weeks
409.6542 -3.59309 (409*2π)/4401 weeks
410-.76047 -3.68217 (410*2π)/4401 weeks
411-.67452 -5.22831 (411*2π)/4401 weeks
412.14153 -5.87284 (412*2π)/4401 weeks
4131.85969 -6.24827 (413*2π)/4401 weeks
4141.47872 -4.95457 (414*2π)/4401 weeks
415-.29476 -3.96299 (415*2π)/4401 weeks
416-.5757 -5.76056 (416*2π)/4401 weeks
417.86811 -6.27631 (417*2π)/4401 weeks
418-.30404 -6.96996 (418*2π)/4401 weeks
419-.14243 -9.14204 (419*2π)/4401 weeks
4202.81719 -9.06657 (420*2π)/4401 weeks
4212.32357 -5.84418 (421*2π)/4401 weeks
4221.48632 -6.61442 (422*2π)/4401 weeks
423.06289 -8.44412 (423*2π)/4401 weeks
4241.44465 -9.65718 (424*2π)/4401 weeks
425.19588 -7.88042 (425*2π)/4401 weeks
426-1.42967 -13.51982 (426*2π)/4401 weeks
4276.14506 -15.66637 (427*2π)/4401 weeks
4287.58844 -10.09262 (428*2π)/4401 weeks
4292.93533 -8.75636 (429*2π)/4401 weeks
4305.14651 -11.49607 (430*2π)/4401 weeks
431-.49828 -8.22468 (431*2π)/4401 weeks
432-6.79836 -18.45826 (432*2π)/4401 weeks
4333.51983 -27.99517 (433*2π)/4401 weeks
43416.25443 -26.10823 (434*2π)/4401 weeks
43510.52019 -11.44489 (435*2π)/4401 weeks
436-4.73101 -27.51052 (436*2π)/4401 weeks
4379.15485 -39.3967 (437*2π)/4401 weeks
438-3.57393 -47.43174 (438*2π)/4401 weeks



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