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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 33 weeks (15.8013*sine), 31 weeks (11.6109*sine), and 42 weeks (11.3114*sine).

VXZ (iPath S&P 500 VIX Mid-Term Futures ETN) has an average price of 144.28 (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 1/8/2018 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
0144.284   0 
153.92865 128.6374 (1*2π)/465465 weeks
2-6.39607 52.45478 (2*2π)/465233 weeks
39.88515 38.23629 (3*2π)/465155 weeks
4-1.98768 32.09563 (4*2π)/465116 weeks
54.89594 11.50314 (5*2π)/46593 weeks
617.71765 19.65979 (6*2π)/46578 weeks
77.20334 27.41891 (7*2π)/46566 weeks
8-3.10529 23.77772 (8*2π)/46558 weeks
9-4.12258 10.65058 (9*2π)/46552 weeks
103.53916 7.58956 (10*2π)/46547 weeks
112.75396 11.31141 (11*2π)/46542 weeks
124.58455 7.67761 (12*2π)/46539 weeks
137.40826 11.03665 (13*2π)/46536 weeks
143.84037 15.80129 (14*2π)/46533 weeks
15-1.75608 11.61091 (15*2π)/46531 weeks
16.86076 7.49468 (16*2π)/46529 weeks
171.17065 9.22721 (17*2π)/46527 weeks
18.02564 8.019 (18*2π)/46526 weeks
191.37246 6.32782 (19*2π)/46524 weeks
201.90595 5.68154 (20*2π)/46523 weeks
213.05356 8.47144 (21*2π)/46522 weeks
22.54075 9.0692 (22*2π)/46521 weeks
23-.25057 6.77598 (23*2π)/46520 weeks
24.3281 5.54644 (24*2π)/46519 weeks
25-.45888 6.28969 (25*2π)/46519 weeks
26-.57754 4.932 (26*2π)/46518 weeks
271.51852 3.95699 (27*2π)/46517 weeks
281.75962 4.69586 (28*2π)/46517 weeks
29.60198 6.15801 (29*2π)/46516 weeks
30-.12076 5.48255 (30*2π)/46516 weeks
31-.83148 4.56715 (31*2π)/46515 weeks
32-.40231 3.1396 (32*2π)/46515 weeks
33.40896 3.73041 (33*2π)/46514 weeks
34.34859 1.88664 (34*2π)/46514 weeks
353.33833 3.53019 (35*2π)/46513 weeks
36.07534 6.26587 (36*2π)/46513 weeks
37-1.27231 2.94371 (37*2π)/46513 weeks
381.70246 2.88934 (38*2π)/46512 weeks
39.35206 4.82736 (39*2π)/46512 weeks
40-2.22568 3.01288 (40*2π)/46512 weeks
41.64999 1.47552 (41*2π)/46511 weeks
42.70436 1.81567 (42*2π)/46511 weeks
431.11803 1.49578 (43*2π)/46511 weeks
441.39434 2.64375 (44*2π)/46511 weeks
451.55869 2.53329 (45*2π)/46510 weeks
461.41284 2.86186 (46*2π)/46510 weeks
47.74139 2.3285 (47*2π)/46510 weeks
48.85662 2.36082 (48*2π)/46510 weeks
491.22967 2.67325 (49*2π)/4659 weeks
50.79097 1.75414 (50*2π)/4659 weeks
512.04363 2.45061 (51*2π)/4659 weeks
521.13542 3.168 (52*2π)/4659 weeks
53.56568 2.44012 (53*2π)/4659 weeks
54.44888 2.1991 (54*2π)/4659 weeks
55.70021 1.52907 (55*2π)/4658 weeks
561.10114 1.90293 (56*2π)/4658 weeks
572.01669 1.65064 (57*2π)/4658 weeks
581.80841 2.73185 (58*2π)/4658 weeks
59.61997 3.18517 (59*2π)/4658 weeks
60.43213 2.2874 (60*2π)/4658 weeks
61.61723 1.70334 (61*2π)/4658 weeks
62.42073 2.24722 (62*2π)/4658 weeks
63-.06552 1.30704 (63*2π)/4657 weeks
641.22017 -.16794 (64*2π)/4657 weeks
653.25087 1.70091 (65*2π)/4657 weeks
661.28371 3.51066 (66*2π)/4657 weeks
67.37453 2.21131 (67*2π)/4657 weeks
68.66469 1.93094 (68*2π)/4657 weeks
69.12788 1.62682 (69*2π)/4657 weeks
70.556 .26869 (70*2π)/4657 weeks
712.42151 1.03421 (71*2π)/4657 weeks
721.79101 2.60009 (72*2π)/4656 weeks
73.55302 1.98497 (73*2π)/4656 weeks
741.1109 1.7659 (74*2π)/4656 weeks
75.8873 1.54294 (75*2π)/4656 weeks
761.01875 1.52707 (76*2π)/4656 weeks
771.03799 1.79706 (77*2π)/4656 weeks
781.17742 1.86726 (78*2π)/4656 weeks
791.03975 2.24658 (79*2π)/4656 weeks
80-.00808 1.53397 (80*2π)/4656 weeks
81.75335 .77352 (81*2π)/4656 weeks
821.18469 1.35661 (82*2π)/4656 weeks
831.00297 1.36139 (83*2π)/4656 weeks
84.91512 1.22166 (84*2π)/4656 weeks
851.30808 1.35867 (85*2π)/4655 weeks
86.81847 1.33868 (86*2π)/4655 weeks
87.71607 .98678 (87*2π)/4655 weeks
881.58296 .96026 (88*2π)/4655 weeks
891.2005 1.90618 (89*2π)/4655 weeks
90.99763 .98371 (90*2π)/4655 weeks
911.38943 1.26111 (91*2π)/4655 weeks
921.13308 1.85918 (92*2π)/4655 weeks
93.86434 1.72988 (93*2π)/4655 weeks
94.54032 1.2241 (94*2π)/4655 weeks
95.82221 .73322 (95*2π)/4655 weeks
961.53463 1.23452 (96*2π)/4655 weeks
97.89158 1.91422 (97*2π)/4655 weeks
98.74911 .90291 (98*2π)/4655 weeks
99.81229 .97583 (99*2π)/4655 weeks
100.89928 1.03841 (100*2π)/4655 weeks
1011.49958 1.07739 (101*2π)/4655 weeks
1021.34875 1.26435 (102*2π)/4655 weeks
1031.0235 1.11309 (103*2π)/4655 weeks
1041.3978 1.32131 (104*2π)/4654 weeks
105.92033 1.98141 (105*2π)/4654 weeks
106.73191 1.18206 (106*2π)/4654 weeks
107.93788 1.1292 (107*2π)/4654 weeks
108.64465 1.46327 (108*2π)/4654 weeks
109.35356 1.03066 (109*2π)/4654 weeks
110.86253 .59688 (110*2π)/4654 weeks
1111.23211 1.09866 (111*2π)/4654 weeks
112.94953 1.24736 (112*2π)/4654 weeks
113.71183 .97517 (113*2π)/4654 weeks
114.65511 1.18531 (114*2π)/4654 weeks
115.85627 .77838 (115*2π)/4654 weeks
1161.20222 .87583 (116*2π)/4654 weeks
117.89119 1.31279 (117*2π)/4654 weeks
118.66801 .89298 (118*2π)/4654 weeks
1191.43024 .84587 (119*2π)/4654 weeks
1201.19851 1.47716 (120*2π)/4654 weeks
121.50849 1.24357 (121*2π)/4654 weeks
122.35729 1.1771 (122*2π)/4654 weeks
123.54257 .92766 (123*2π)/4654 weeks
124.80643 .68288 (124*2π)/4654 weeks
125.59058 .65955 (125*2π)/4654 weeks
1261.02878 .95401 (126*2π)/4654 weeks
127.68724 1.1271 (127*2π)/4654 weeks
128.19563 .65437 (128*2π)/4654 weeks
129.71766 .18866 (129*2π)/4654 weeks
130.93773 .59703 (130*2π)/4654 weeks
131.83922 .58397 (131*2π)/4654 weeks
1321.13418 .36157 (132*2π)/4654 weeks
1331.38831 .64898 (133*2π)/4653 weeks
1341.03801 1.24906 (134*2π)/4653 weeks
135.49317 .92203 (135*2π)/4653 weeks
136.5441 .33736 (136*2π)/4653 weeks
1371.17466 .39931 (137*2π)/4653 weeks
1381.07766 .75403 (138*2π)/4653 weeks
1391.22508 .94899 (139*2π)/4653 weeks
140.68934 .90438 (140*2π)/4653 weeks
141.83593 .53866 (141*2π)/4653 weeks
142.99735 .55535 (142*2π)/4653 weeks
1431.06707 .54923 (143*2π)/4653 weeks
1441.16351 .80748 (144*2π)/4653 weeks
145.99971 .73481 (145*2π)/4653 weeks
1461.05771 1.12171 (146*2π)/4653 weeks
147.66814 .92607 (147*2π)/4653 weeks
148.63122 .61672 (148*2π)/4653 weeks
149.7479 .70602 (149*2π)/4653 weeks
150.8729 .6012 (150*2π)/4653 weeks
151.80062 .7242 (151*2π)/4653 weeks
152.65781 .52363 (152*2π)/4653 weeks
153.87312 .48852 (153*2π)/4653 weeks
154.58945 .63016 (154*2π)/4653 weeks
155.88429 .25874 (155*2π)/4653 weeks
1561.09597 .47616 (156*2π)/4653 weeks
1571.05268 .63496 (157*2π)/4653 weeks
158.90512 .9458 (158*2π)/4653 weeks
159.65717 .77582 (159*2π)/4653 weeks
160.616 .69435 (160*2π)/4653 weeks
161.71895 .48086 (161*2π)/4653 weeks
162.62368 .40232 (162*2π)/4653 weeks
163.75159 .03092 (163*2π)/4653 weeks
1641.4624 .27465 (164*2π)/4653 weeks
1651.4878 1.24997 (165*2π)/4653 weeks
166.40579 1.20574 (166*2π)/4653 weeks
167.41981 .53512 (167*2π)/4653 weeks
168.45158 .82557 (168*2π)/4653 weeks
169.2971 .5022 (169*2π)/4653 weeks
170.49014 -.04728 (170*2π)/4653 weeks
1711.24583 .40231 (171*2π)/4653 weeks
172.59739 1.15105 (172*2π)/4653 weeks
173-.08264 .37786 (173*2π)/4653 weeks
174.20119 .16029 (174*2π)/4653 weeks
175.48769 .09466 (175*2π)/4653 weeks
176.40584 -.12021 (176*2π)/4653 weeks
177.94792 -.24975 (177*2π)/4653 weeks
1781.21326 .35298 (178*2π)/4653 weeks
179.62301 .5024 (179*2π)/4653 weeks
180.37611 .33821 (180*2π)/4653 weeks
181.54208 .0076 (181*2π)/4653 weeks
182.37033 .01267 (182*2π)/4653 weeks
183.56274 -.39392 (183*2π)/4653 weeks
1841.25797 -.60558 (184*2π)/4653 weeks
1851.48057 .17669 (185*2π)/4653 weeks
1861.19218 .44937 (186*2π)/4653 weeks
1871.02937 .58618 (187*2π)/4652 weeks
188.3189 .59944 (188*2π)/4652 weeks
189.11238 -.17391 (189*2π)/4652 weeks
1901.04084 -.63038 (190*2π)/4652 weeks
1911.2277 .14592 (191*2π)/4652 weeks
192.97879 .06022 (192*2π)/4652 weeks
1931.1324 .093 (193*2π)/4652 weeks
1941.00934 .34409 (194*2π)/4652 weeks
195.68808 .38401 (195*2π)/4652 weeks
196.80381 -.02688 (196*2π)/4652 weeks
197.97754 .03453 (197*2π)/4652 weeks
198.90631 .18676 (198*2π)/4652 weeks
199.76528 .02365 (199*2π)/4652 weeks
200.96139 -.18588 (200*2π)/4652 weeks
2011.30451 .25473 (201*2π)/4652 weeks
202.37148 .35976 (202*2π)/4652 weeks
203.77355 -.36365 (203*2π)/4652 weeks
2041.11443 .09298 (204*2π)/4652 weeks
205.64545 -.23133 (205*2π)/4652 weeks
2061.2451 -.41078 (206*2π)/4652 weeks
2071.54059 .2623 (207*2π)/4652 weeks
208.84854 .38197 (208*2π)/4652 weeks
209.69096 .08304 (209*2π)/4652 weeks
2101.01796 .08445 (210*2π)/4652 weeks
211.72879 .16196 (211*2π)/4652 weeks
212.7495 -.08064 (212*2π)/4652 weeks
213.74129 -.14683 (213*2π)/4652 weeks
214.87171 -.47819 (214*2π)/4652 weeks
2151.28362 .07293 (215*2π)/4652 weeks
216.92132 -.21323 (216*2π)/4652 weeks
2171.33854 -.2231 (217*2π)/4652 weeks
2181.15345 .29944 (218*2π)/4652 weeks
219.57425 .08172 (219*2π)/4652 weeks
2201.16528 -.53005 (220*2π)/4652 weeks
2211.46733 -.25714 (221*2π)/4652 weeks
2221.46888 .00203 (222*2π)/4652 weeks
2231.29108 .4196 (223*2π)/4652 weeks
224.96309 .58504 (224*2π)/4652 weeks
225.61462 .32768 (225*2π)/4652 weeks
226.45071 -.25642 (226*2π)/4652 weeks
2271.06149 -.59422 (227*2π)/4652 weeks
2281.53864 -.09901 (228*2π)/4652 weeks
2291.24616 .27369 (229*2π)/4652 weeks
2301.08582 -.04953 (230*2π)/4652 weeks
2311.26053 .39533 (231*2π)/4652 weeks
232.4211 .55888 (232*2π)/4652 weeks
233.4211 -.55888 (233*2π)/4652 weeks
2341.26053 -.39533 (234*2π)/4652 weeks
2351.08582 .04953 (235*2π)/4652 weeks
2361.24616 -.27369 (236*2π)/4652 weeks
2371.53864 .09901 (237*2π)/4652 weeks
2381.06149 .59422 (238*2π)/4652 weeks
239.45071 .25642 (239*2π)/4652 weeks
240.61462 -.32768 (240*2π)/4652 weeks
241.96309 -.58504 (241*2π)/4652 weeks
2421.29108 -.4196 (242*2π)/4652 weeks
2431.46888 -.00203 (243*2π)/4652 weeks
2441.46733 .25714 (244*2π)/4652 weeks
2451.16528 .53005 (245*2π)/4652 weeks
246.57425 -.08172 (246*2π)/4652 weeks
2471.15345 -.29944 (247*2π)/4652 weeks
2481.33854 .2231 (248*2π)/4652 weeks
249.92132 .21323 (249*2π)/4652 weeks
2501.28362 -.07293 (250*2π)/4652 weeks
251.87171 .47819 (251*2π)/4652 weeks
252.74129 .14683 (252*2π)/4652 weeks
253.7495 .08064 (253*2π)/4652 weeks
254.72879 -.16196 (254*2π)/4652 weeks
2551.01796 -.08445 (255*2π)/4652 weeks
256.69096 -.08304 (256*2π)/4652 weeks
257.84854 -.38197 (257*2π)/4652 weeks
2581.54059 -.2623 (258*2π)/4652 weeks
2591.2451 .41078 (259*2π)/4652 weeks
260.64545 .23133 (260*2π)/4652 weeks
2611.11443 -.09298 (261*2π)/4652 weeks
262.77355 .36365 (262*2π)/4652 weeks
263.37148 -.35976 (263*2π)/4652 weeks
2641.30451 -.25473 (264*2π)/4652 weeks
265.96139 .18588 (265*2π)/4652 weeks
266.76528 -.02365 (266*2π)/4652 weeks
267.90631 -.18676 (267*2π)/4652 weeks
268.97754 -.03453 (268*2π)/4652 weeks
269.80381 .02688 (269*2π)/4652 weeks
270.68808 -.38401 (270*2π)/4652 weeks
2711.00934 -.34409 (271*2π)/4652 weeks
2721.1324 -.093 (272*2π)/4652 weeks
273.97879 -.06022 (273*2π)/4652 weeks
2741.2277 -.14592 (274*2π)/4652 weeks
2751.04084 .63038 (275*2π)/4652 weeks
276.11238 .17391 (276*2π)/4652 weeks
277.3189 -.59944 (277*2π)/4652 weeks
2781.02937 -.58618 (278*2π)/4652 weeks
2791.19218 -.44937 (279*2π)/4652 weeks
2801.48057 -.17669 (280*2π)/4652 weeks
2811.25797 .60558 (281*2π)/4652 weeks
282.56274 .39392 (282*2π)/4652 weeks
283.37033 -.01267 (283*2π)/4652 weeks
284.54208 -.0076 (284*2π)/4652 weeks
285.37611 -.33821 (285*2π)/4652 weeks
286.62301 -.5024 (286*2π)/4652 weeks
2871.21326 -.35298 (287*2π)/4652 weeks
288.94792 .24975 (288*2π)/4652 weeks
289.40584 .12021 (289*2π)/4652 weeks
290.48769 -.09466 (290*2π)/4652 weeks
291.20119 -.16029 (291*2π)/4652 weeks
292-.08264 -.37786 (292*2π)/4652 weeks
293.59739 -1.15105 (293*2π)/4652 weeks
2941.24583 -.40231 (294*2π)/4652 weeks
295.49014 .04728 (295*2π)/4652 weeks
296.2971 -.5022 (296*2π)/4652 weeks
297.45158 -.82557 (297*2π)/4652 weeks
298.41981 -.53512 (298*2π)/4652 weeks
299.40579 -1.20574 (299*2π)/4652 weeks
3001.4878 -1.24997 (300*2π)/4652 weeks
3011.4624 -.27465 (301*2π)/4652 weeks
302.75159 -.03092 (302*2π)/4652 weeks
303.62368 -.40232 (303*2π)/4652 weeks
304.71895 -.48086 (304*2π)/4652 weeks
305.616 -.69435 (305*2π)/4652 weeks
306.65717 -.77582 (306*2π)/4652 weeks
307.90512 -.9458 (307*2π)/4652 weeks
3081.05268 -.63496 (308*2π)/4652 weeks
3091.09597 -.47616 (309*2π)/4652 weeks
310.88429 -.25874 (310*2π)/4652 weeks
311.58945 -.63016 (311*2π)/4651 weeks
312.87312 -.48852 (312*2π)/4651 weeks
313.65781 -.52363 (313*2π)/4651 weeks
314.80062 -.7242 (314*2π)/4651 weeks
315.8729 -.6012 (315*2π)/4651 weeks
316.7479 -.70602 (316*2π)/4651 weeks
317.63122 -.61672 (317*2π)/4651 weeks
318.66814 -.92607 (318*2π)/4651 weeks
3191.05771 -1.12171 (319*2π)/4651 weeks
320.99971 -.73481 (320*2π)/4651 weeks
3211.16351 -.80748 (321*2π)/4651 weeks
3221.06707 -.54923 (322*2π)/4651 weeks
323.99735 -.55535 (323*2π)/4651 weeks
324.83593 -.53866 (324*2π)/4651 weeks
325.68934 -.90438 (325*2π)/4651 weeks
3261.22508 -.94899 (326*2π)/4651 weeks
3271.07766 -.75403 (327*2π)/4651 weeks
3281.17466 -.39931 (328*2π)/4651 weeks
329.5441 -.33736 (329*2π)/4651 weeks
330.49317 -.92203 (330*2π)/4651 weeks
3311.03801 -1.24906 (331*2π)/4651 weeks
3321.38831 -.64898 (332*2π)/4651 weeks
3331.13418 -.36157 (333*2π)/4651 weeks
334.83922 -.58397 (334*2π)/4651 weeks
335.93773 -.59703 (335*2π)/4651 weeks
336.71766 -.18866 (336*2π)/4651 weeks
337.19563 -.65437 (337*2π)/4651 weeks
338.68724 -1.1271 (338*2π)/4651 weeks
3391.02878 -.95401 (339*2π)/4651 weeks
340.59058 -.65955 (340*2π)/4651 weeks
341.80643 -.68288 (341*2π)/4651 weeks
342.54257 -.92766 (342*2π)/4651 weeks
343.35729 -1.1771 (343*2π)/4651 weeks
344.50849 -1.24357 (344*2π)/4651 weeks
3451.19851 -1.47716 (345*2π)/4651 weeks
3461.43024 -.84587 (346*2π)/4651 weeks
347.66801 -.89298 (347*2π)/4651 weeks
348.89119 -1.31279 (348*2π)/4651 weeks
3491.20222 -.87583 (349*2π)/4651 weeks
350.85627 -.77838 (350*2π)/4651 weeks
351.65511 -1.18531 (351*2π)/4651 weeks
352.71183 -.97517 (352*2π)/4651 weeks
353.94953 -1.24736 (353*2π)/4651 weeks
3541.23211 -1.09866 (354*2π)/4651 weeks
355.86253 -.59688 (355*2π)/4651 weeks
356.35356 -1.03066 (356*2π)/4651 weeks
357.64465 -1.46327 (357*2π)/4651 weeks
358.93788 -1.1292 (358*2π)/4651 weeks
359.73191 -1.18206 (359*2π)/4651 weeks
360.92033 -1.98141 (360*2π)/4651 weeks
3611.3978 -1.32131 (361*2π)/4651 weeks
3621.0235 -1.11309 (362*2π)/4651 weeks
3631.34875 -1.26435 (363*2π)/4651 weeks
3641.49958 -1.07739 (364*2π)/4651 weeks
365.89928 -1.03841 (365*2π)/4651 weeks
366.81229 -.97583 (366*2π)/4651 weeks
367.74911 -.90291 (367*2π)/4651 weeks
368.89158 -1.91422 (368*2π)/4651 weeks
3691.53463 -1.23452 (369*2π)/4651 weeks
370.82221 -.73322 (370*2π)/4651 weeks
371.54032 -1.2241 (371*2π)/4651 weeks
372.86434 -1.72988 (372*2π)/4651 weeks
3731.13308 -1.85918 (373*2π)/4651 weeks
3741.38943 -1.26111 (374*2π)/4651 weeks
375.99763 -.98371 (375*2π)/4651 weeks
3761.2005 -1.90618 (376*2π)/4651 weeks
3771.58296 -.96026 (377*2π)/4651 weeks
378.71607 -.98678 (378*2π)/4651 weeks
379.81847 -1.33868 (379*2π)/4651 weeks
3801.30808 -1.35867 (380*2π)/4651 weeks
381.91512 -1.22166 (381*2π)/4651 weeks
3821.00297 -1.36139 (382*2π)/4651 weeks
3831.18469 -1.35661 (383*2π)/4651 weeks
384.75335 -.77352 (384*2π)/4651 weeks
385-.00808 -1.53397 (385*2π)/4651 weeks
3861.03975 -2.24658 (386*2π)/4651 weeks
3871.17742 -1.86726 (387*2π)/4651 weeks
3881.03799 -1.79706 (388*2π)/4651 weeks
3891.01875 -1.52707 (389*2π)/4651 weeks
390.8873 -1.54294 (390*2π)/4651 weeks
3911.1109 -1.7659 (391*2π)/4651 weeks
392.55302 -1.98497 (392*2π)/4651 weeks
3931.79101 -2.60009 (393*2π)/4651 weeks
3942.42151 -1.03421 (394*2π)/4651 weeks
395.556 -.26869 (395*2π)/4651 weeks
396.12788 -1.62682 (396*2π)/4651 weeks
397.66469 -1.93094 (397*2π)/4651 weeks
398.37453 -2.21131 (398*2π)/4651 weeks
3991.28371 -3.51066 (399*2π)/4651 weeks
4003.25087 -1.70091 (400*2π)/4651 weeks
4011.22017 .16794 (401*2π)/4651 weeks
402-.06552 -1.30704 (402*2π)/4651 weeks
403.42073 -2.24722 (403*2π)/4651 weeks
404.61723 -1.70334 (404*2π)/4651 weeks
405.43213 -2.2874 (405*2π)/4651 weeks
406.61997 -3.18517 (406*2π)/4651 weeks
4071.80841 -2.73185 (407*2π)/4651 weeks
4082.01669 -1.65064 (408*2π)/4651 weeks
4091.10114 -1.90293 (409*2π)/4651 weeks
410.70021 -1.52907 (410*2π)/4651 weeks
411.44888 -2.1991 (411*2π)/4651 weeks
412.56568 -2.44012 (412*2π)/4651 weeks
4131.13542 -3.168 (413*2π)/4651 weeks
4142.04363 -2.45061 (414*2π)/4651 weeks
415.79097 -1.75414 (415*2π)/4651 weeks
4161.22967 -2.67325 (416*2π)/4651 weeks
417.85662 -2.36082 (417*2π)/4651 weeks
418.74139 -2.3285 (418*2π)/4651 weeks
4191.41284 -2.86186 (419*2π)/4651 weeks
4201.55869 -2.53329 (420*2π)/4651 weeks
4211.39434 -2.64375 (421*2π)/4651 weeks
4221.11803 -1.49578 (422*2π)/4651 weeks
423.70436 -1.81567 (423*2π)/4651 weeks
424.64999 -1.47552 (424*2π)/4651 weeks
425-2.22568 -3.01288 (425*2π)/4651 weeks
426.35206 -4.82736 (426*2π)/4651 weeks
4271.70246 -2.88934 (427*2π)/4651 weeks
428-1.27231 -2.94371 (428*2π)/4651 weeks
429.07534 -6.26587 (429*2π)/4651 weeks
4303.33833 -3.53019 (430*2π)/4651 weeks
431.34859 -1.88664 (431*2π)/4651 weeks
432.40896 -3.73041 (432*2π)/4651 weeks
433-.40231 -3.1396 (433*2π)/4651 weeks
434-.83148 -4.56715 (434*2π)/4651 weeks
435-.12076 -5.48255 (435*2π)/4651 weeks
436.60198 -6.15801 (436*2π)/4651 weeks
4371.75962 -4.69586 (437*2π)/4651 weeks
4381.51852 -3.95699 (438*2π)/4651 weeks
439-.57754 -4.932 (439*2π)/4651 weeks
440-.45888 -6.28969 (440*2π)/4651 weeks
441.3281 -5.54644 (441*2π)/4651 weeks
442-.25057 -6.77598 (442*2π)/4651 weeks
443.54075 -9.0692 (443*2π)/4651 weeks
4443.05356 -8.47144 (444*2π)/4651 weeks
4451.90595 -5.68154 (445*2π)/4651 weeks
4461.37246 -6.32782 (446*2π)/4651 weeks
447.02564 -8.019 (447*2π)/4651 weeks
4481.17065 -9.22721 (448*2π)/4651 weeks
449.86076 -7.49468 (449*2π)/4651 weeks
450-1.75608 -11.61091 (450*2π)/4651 weeks
4513.84037 -15.80129 (451*2π)/4651 weeks
4527.40826 -11.03665 (452*2π)/4651 weeks
4534.58455 -7.67761 (453*2π)/4651 weeks
4542.75396 -11.31141 (454*2π)/4651 weeks
4553.53916 -7.58956 (455*2π)/4651 weeks
456-4.12258 -10.65058 (456*2π)/4651 weeks
457-3.10529 -23.77772 (457*2π)/4651 weeks
4587.20334 -27.41891 (458*2π)/4651 weeks
45917.71765 -19.65979 (459*2π)/4651 weeks
4604.89594 -11.50314 (460*2π)/4651 weeks
461-1.98768 -32.09563 (461*2π)/4651 weeks
4629.88515 -38.23629 (462*2π)/4651 weeks
463-6.39607 -52.45478 (463*2π)/4651 weeks



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