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Fourier Analysis of VXZ (iPath S&P 500 VIX Mid-Term Futu)


VXZ (iPath S&P 500 VIX Mid-Term Futu) appears to have interesting cyclic behaviour every 33 weeks (16.8694*sine), 35 weeks (12.8767*sine), and 42 weeks (12.2014*sine).

VXZ (iPath S&P 500 VIX Mid-Term Futu) has an average price of 156.45 (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 3/20/2017 for VXZ (iPath S&P 500 VIX Mid-Term Futu), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0156.451   0 
146.22377 133.8525 (1*2π)/423423 weeks
2-.64914 44.72227 (2*2π)/423212 weeks
38.50205 40.17098 (3*2π)/423141 weeks
4-4.8707 23.06321 (4*2π)/423106 weeks
514.7379 12.95408 (5*2π)/42385 weeks
613.27075 29.23409 (6*2π)/42371 weeks
7.32066 27.98521 (7*2π)/42360 weeks
8-6.14578 13.64386 (8*2π)/42353 weeks
92.89371 7.7751 (9*2π)/42347 weeks
103.02931 12.20138 (10*2π)/42342 weeks
115.55495 8.25635 (11*2π)/42338 weeks
128.10223 12.87667 (12*2π)/42335 weeks
131.48827 16.86942 (13*2π)/42333 weeks
14-1.7376 9.98631 (14*2π)/42330 weeks
152.17852 9.22093 (15*2π)/42328 weeks
16.44365 9.27433 (16*2π)/42326 weeks
17.64396 6.75517 (17*2π)/42325 weeks
181.48296 6.52687 (18*2π)/42324 weeks
193.66359 8.83718 (19*2π)/42322 weeks
20.61653 9.81901 (20*2π)/42321 weeks
21-.28002 7.2624 (21*2π)/42320 weeks
22.75787 6.16888 (22*2π)/42319 weeks
23-.66354 6.07218 (23*2π)/42318 weeks
24-.417 4.16378 (24*2π)/42318 weeks
251.52676 5.09256 (25*2π)/42317 weeks
261.81343 6.5456 (26*2π)/42316 weeks
27.10498 6.02457 (27*2π)/42316 weeks
28-.7921 5.22886 (28*2π)/42315 weeks
29-.60407 3.51686 (29*2π)/42315 weeks
30.50125 3.9947 (30*2π)/42314 weeks
31.6856 1.86567 (31*2π)/42314 weeks
323.72664 4.73108 (32*2π)/42313 weeks
33-.98924 5.96186 (33*2π)/42313 weeks
34-.22296 2.08586 (34*2π)/42312 weeks
351.58902 4.557 (35*2π)/42312 weeks
36-1.39735 4.91831 (36*2π)/42312 weeks
37-.27429 .86654 (37*2π)/42311 weeks
38.55476 1.91559 (38*2π)/42311 weeks
39.96737 1.62093 (39*2π)/42311 weeks
401.52873 2.80577 (40*2π)/42311 weeks
411.64296 2.7466 (41*2π)/42310 weeks
421.36675 3.21961 (42*2π)/42310 weeks
431.08804 2.42453 (43*2π)/42310 weeks
441.17048 2.24659 (44*2π)/42310 weeks
45.6897 2.68898 (45*2π)/4239 weeks
461.89238 1.81623 (46*2π)/4239 weeks
471.57147 3.30781 (47*2π)/4239 weeks
48.48969 2.81104 (48*2π)/4239 weeks
49.47981 2.44987 (49*2π)/4239 weeks
50.69928 1.64012 (50*2π)/4238 weeks
511.12526 1.9867 (51*2π)/4238 weeks
522.2914 2.04666 (52*2π)/4238 weeks
531.81758 3.19791 (53*2π)/4238 weeks
54.28304 2.9305 (54*2π)/4238 weeks
55.30565 2.25326 (55*2π)/4238 weeks
56.91989 2.27501 (56*2π)/4238 weeks
57-.02533 1.80654 (57*2π)/4237 weeks
58.62324 .0002 (58*2π)/4237 weeks
593.47682 1.33263 (59*2π)/4237 weeks
601.50356 3.8344 (60*2π)/4237 weeks
61.39141 2.33752 (61*2π)/4237 weeks
62.6613 2.13474 (62*2π)/4237 weeks
63.04479 1.4584 (63*2π)/4237 weeks
641.48223 .06463 (64*2π)/4237 weeks
652.61936 2.02466 (65*2π)/4237 weeks
66.94091 2.76353 (66*2π)/4236 weeks
671.08289 1.67731 (67*2π)/4236 weeks
68.86375 1.7759 (68*2π)/4236 weeks
691.07422 1.67166 (69*2π)/4236 weeks
701.15535 1.92264 (70*2π)/4236 weeks
711.25534 1.99951 (71*2π)/4236 weeks
72.92163 2.52896 (72*2π)/4236 weeks
73.08744 1.29278 (73*2π)/4236 weeks
741.19076 .91826 (74*2π)/4236 weeks
751.10322 1.48294 (75*2π)/4236 weeks
76.99891 1.43448 (76*2π)/4236 weeks
771.2822 1.20696 (77*2π)/4235 weeks
78.90211 1.6002 (78*2π)/4235 weeks
79.76469 1.21299 (79*2π)/4235 weeks
801.69296 .97721 (80*2π)/4235 weeks
811.23719 2.06422 (81*2π)/4235 weeks
821.24248 1.06462 (82*2π)/4235 weeks
831.62813 1.46582 (83*2π)/4235 weeks
841.01658 1.85746 (84*2π)/4235 weeks
85.59993 1.74696 (85*2π)/4235 weeks
86.65771 1.09101 (86*2π)/4235 weeks
871.57596 .95477 (87*2π)/4235 weeks
881.33684 1.96526 (88*2π)/4235 weeks
89.59075 1.01574 (89*2π)/4235 weeks
90.84932 1.0776 (90*2π)/4235 weeks
91.94845 1.07732 (91*2π)/4235 weeks
921.56193 1.27399 (92*2π)/4235 weeks
931.39624 1.50844 (93*2π)/4235 weeks
941.34469 1.14873 (94*2π)/4235 weeks
951.58137 1.71562 (95*2π)/4234 weeks
96.49192 1.5749 (96*2π)/4234 weeks
97.8454 1.27238 (97*2π)/4234 weeks
98.89367 1.64374 (98*2π)/4234 weeks
99.41763 1.25124 (99*2π)/4234 weeks
100.89975 .63899 (100*2π)/4234 weeks
1011.34998 1.20745 (101*2π)/4234 weeks
1021.01593 1.37776 (102*2π)/4234 weeks
103.94198 1.01643 (103*2π)/4234 weeks
104.62789 1.01212 (104*2π)/4234 weeks
1051.04392 .8129 (105*2π)/4234 weeks
1061.29566 1.29738 (106*2π)/4234 weeks
107.74146 1.14558 (107*2π)/4234 weeks
1081.30026 .63393 (108*2π)/4234 weeks
1091.34043 1.49293 (109*2π)/4234 weeks
110.51253 1.41652 (110*2π)/4234 weeks
111.35932 1.25653 (111*2π)/4234 weeks
112.52617 .98255 (112*2π)/4234 weeks
113.89733 .88056 (113*2π)/4234 weeks
114.87088 .57301 (114*2π)/4234 weeks
115.9038 1.14475 (115*2π)/4234 weeks
116.33634 1.15047 (116*2π)/4234 weeks
117.47367 .29286 (117*2π)/4234 weeks
1181.09991 .55372 (118*2π)/4234 weeks
119.9491 .6342 (119*2π)/4234 weeks
1201.18184 .35365 (120*2π)/4234 weeks
1211.51564 .70573 (121*2π)/4233 weeks
1221.03119 1.36093 (122*2π)/4233 weeks
123.49972 .87626 (123*2π)/4233 weeks
124.83859 .21089 (124*2π)/4233 weeks
1251.3527 .63043 (125*2π)/4233 weeks
1261.24826 .7051 (126*2π)/4233 weeks
127.89337 1.12725 (127*2π)/4233 weeks
128.76924 .60386 (128*2π)/4233 weeks
1291.0204 .57393 (129*2π)/4233 weeks
1301.10727 .59049 (130*2π)/4233 weeks
1311.24091 .87397 (131*2π)/4233 weeks
1321.10405 .77392 (132*2π)/4233 weeks
133.96803 1.24845 (133*2π)/4233 weeks
134.65471 .94544 (134*2π)/4233 weeks
135.83168 .64317 (135*2π)/4233 weeks
136.77926 .61693 (136*2π)/4233 weeks
137.88855 .7508 (137*2π)/4233 weeks
138.66275 .68346 (138*2π)/4233 weeks
139.87942 .50991 (139*2π)/4233 weeks
140.68216 .74375 (140*2π)/4233 weeks
141.9591 .27999 (141*2π)/4233 weeks
1421.20208 .54718 (142*2π)/4233 weeks
1431.18249 .71567 (143*2π)/4233 weeks
144.83853 .97908 (144*2π)/4233 weeks
145.69712 .74415 (145*2π)/4233 weeks
146.58681 .55292 (146*2π)/4233 weeks
147.65695 .55037 (147*2π)/4233 weeks
148.65563 .22124 (148*2π)/4233 weeks
1491.47591 .16794 (149*2π)/4233 weeks
1501.6999 1.23649 (150*2π)/4233 weeks
151.42194 1.32787 (151*2π)/4233 weeks
152.50301 .56463 (152*2π)/4233 weeks
153.35337 .83356 (153*2π)/4233 weeks
154.2302 .43664 (154*2π)/4233 weeks
155.90437 -.06302 (155*2π)/4233 weeks
1561.16892 1.00553 (156*2π)/4233 weeks
157-.06022 .95673 (157*2π)/4233 weeks
158.24131 .237 (158*2π)/4233 weeks
159.51159 .02777 (159*2π)/4233 weeks
160.40973 -.09113 (160*2π)/4233 weeks
1611.01615 -.29186 (161*2π)/4233 weeks
1621.2821 .45389 (162*2π)/4233 weeks
163.6402 .49514 (163*2π)/4233 weeks
164.35505 .20039 (164*2π)/4233 weeks
165.61544 .08681 (165*2π)/4233 weeks
166.43763 -.28983 (166*2π)/4233 weeks
167.89731 -.7159 (167*2π)/4233 weeks
1681.68859 -.05402 (168*2π)/4233 weeks
1691.35235 .43856 (169*2π)/4233 weeks
1701.12563 .58744 (170*2π)/4232 weeks
171.3439 .66945 (171*2π)/4232 weeks
172.12901 -.28645 (172*2π)/4232 weeks
1731.30486 -.57513 (173*2π)/4232 weeks
1741.16646 .20212 (174*2π)/4232 weeks
1751.10407 .038 (175*2π)/4232 weeks
1761.23663 .27098 (176*2π)/4232 weeks
177.96949 .43159 (177*2π)/4232 weeks
178.71195 -.00698 (178*2π)/4232 weeks
179.99722 -.01007 (179*2π)/4232 weeks
180.98352 .18658 (180*2π)/4232 weeks
181.80028 .02974 (181*2π)/4232 weeks
1821.05725 -.20632 (182*2π)/4232 weeks
1831.33523 .45226 (183*2π)/4232 weeks
184.32045 .03312 (184*2π)/4232 weeks
1851.07877 -.34978 (185*2π)/4232 weeks
186.80903 .17745 (186*2π)/4232 weeks
1871.04229 -.50097 (187*2π)/4232 weeks
1881.69157 -.05249 (188*2π)/4232 weeks
1891.01559 .53364 (189*2π)/4232 weeks
190.74863 .16825 (190*2π)/4232 weeks
1911.10423 .0761 (191*2π)/4232 weeks
192.76904 .159 (192*2π)/4232 weeks
193.82771 -.09198 (193*2π)/4232 weeks
194.7986 -.21662 (194*2π)/4232 weeks
1951.29038 -.54322 (195*2π)/4232 weeks
196.99496 .073 (196*2π)/4232 weeks
1971.21083 -.33537 (197*2π)/4232 weeks
1981.44816 .21631 (198*2π)/4232 weeks
199.77496 .26337 (199*2π)/4232 weeks
2001.12099 -.63763 (200*2π)/4232 weeks
2011.56807 -.29868 (201*2π)/4232 weeks
2021.61064 .02071 (202*2π)/4232 weeks
2031.35218 .45494 (203*2π)/4232 weeks
204.8671 .57564 (204*2π)/4232 weeks
205.49938 .21703 (205*2π)/4232 weeks
206.72303 -.56671 (206*2π)/4232 weeks
2071.54677 -.46718 (207*2π)/4232 weeks
2081.47248 .20262 (208*2π)/4232 weeks
2091.04198 .05726 (209*2π)/4232 weeks
2101.40452 .35204 (210*2π)/4232 weeks
211.50281 .65586 (211*2π)/4232 weeks
212.50281 -.65586 (212*2π)/4232 weeks
2131.40452 -.35204 (213*2π)/4232 weeks
2141.04198 -.05726 (214*2π)/4232 weeks
2151.47248 -.20262 (215*2π)/4232 weeks
2161.54677 .46718 (216*2π)/4232 weeks
217.72303 .56671 (217*2π)/4232 weeks
218.49938 -.21703 (218*2π)/4232 weeks
219.8671 -.57564 (219*2π)/4232 weeks
2201.35218 -.45494 (220*2π)/4232 weeks
2211.61064 -.02071 (221*2π)/4232 weeks
2221.56807 .29868 (222*2π)/4232 weeks
2231.12099 .63763 (223*2π)/4232 weeks
224.77496 -.26337 (224*2π)/4232 weeks
2251.44816 -.21631 (225*2π)/4232 weeks
2261.21083 .33537 (226*2π)/4232 weeks
227.99496 -.073 (227*2π)/4232 weeks
2281.29038 .54322 (228*2π)/4232 weeks
229.7986 .21662 (229*2π)/4232 weeks
230.82771 .09198 (230*2π)/4232 weeks
231.76904 -.159 (231*2π)/4232 weeks
2321.10423 -.0761 (232*2π)/4232 weeks
233.74863 -.16825 (233*2π)/4232 weeks
2341.01559 -.53364 (234*2π)/4232 weeks
2351.69157 .05249 (235*2π)/4232 weeks
2361.04229 .50097 (236*2π)/4232 weeks
237.80903 -.17745 (237*2π)/4232 weeks
2381.07877 .34978 (238*2π)/4232 weeks
239.32045 -.03312 (239*2π)/4232 weeks
2401.33523 -.45226 (240*2π)/4232 weeks
2411.05725 .20632 (241*2π)/4232 weeks
242.80028 -.02974 (242*2π)/4232 weeks
243.98352 -.18658 (243*2π)/4232 weeks
244.99722 .01007 (244*2π)/4232 weeks
245.71195 .00698 (245*2π)/4232 weeks
246.96949 -.43159 (246*2π)/4232 weeks
2471.23663 -.27098 (247*2π)/4232 weeks
2481.10407 -.038 (248*2π)/4232 weeks
2491.16646 -.20212 (249*2π)/4232 weeks
2501.30486 .57513 (250*2π)/4232 weeks
251.12901 .28645 (251*2π)/4232 weeks
252.3439 -.66945 (252*2π)/4232 weeks
2531.12563 -.58744 (253*2π)/4232 weeks
2541.35235 -.43856 (254*2π)/4232 weeks
2551.68859 .05402 (255*2π)/4232 weeks
256.89731 .7159 (256*2π)/4232 weeks
257.43763 .28983 (257*2π)/4232 weeks
258.61544 -.08681 (258*2π)/4232 weeks
259.35505 -.20039 (259*2π)/4232 weeks
260.6402 -.49514 (260*2π)/4232 weeks
2611.2821 -.45389 (261*2π)/4232 weeks
2621.01615 .29186 (262*2π)/4232 weeks
263.40973 .09113 (263*2π)/4232 weeks
264.51159 -.02777 (264*2π)/4232 weeks
265.24131 -.237 (265*2π)/4232 weeks
266-.06022 -.95673 (266*2π)/4232 weeks
2671.16892 -1.00553 (267*2π)/4232 weeks
268.90437 .06302 (268*2π)/4232 weeks
269.2302 -.43664 (269*2π)/4232 weeks
270.35337 -.83356 (270*2π)/4232 weeks
271.50301 -.56463 (271*2π)/4232 weeks
272.42194 -1.32787 (272*2π)/4232 weeks
2731.6999 -1.23649 (273*2π)/4232 weeks
2741.47591 -.16794 (274*2π)/4232 weeks
275.65563 -.22124 (275*2π)/4232 weeks
276.65695 -.55037 (276*2π)/4232 weeks
277.58681 -.55292 (277*2π)/4232 weeks
278.69712 -.74415 (278*2π)/4232 weeks
279.83853 -.97908 (279*2π)/4232 weeks
2801.18249 -.71567 (280*2π)/4232 weeks
2811.20208 -.54718 (281*2π)/4232 weeks
282.9591 -.27999 (282*2π)/4232 weeks
283.68216 -.74375 (283*2π)/4231 weeks
284.87942 -.50991 (284*2π)/4231 weeks
285.66275 -.68346 (285*2π)/4231 weeks
286.88855 -.7508 (286*2π)/4231 weeks
287.77926 -.61693 (287*2π)/4231 weeks
288.83168 -.64317 (288*2π)/4231 weeks
289.65471 -.94544 (289*2π)/4231 weeks
290.96803 -1.24845 (290*2π)/4231 weeks
2911.10405 -.77392 (291*2π)/4231 weeks
2921.24091 -.87397 (292*2π)/4231 weeks
2931.10727 -.59049 (293*2π)/4231 weeks
2941.0204 -.57393 (294*2π)/4231 weeks
295.76924 -.60386 (295*2π)/4231 weeks
296.89337 -1.12725 (296*2π)/4231 weeks
2971.24826 -.7051 (297*2π)/4231 weeks
2981.3527 -.63043 (298*2π)/4231 weeks
299.83859 -.21089 (299*2π)/4231 weeks
300.49972 -.87626 (300*2π)/4231 weeks
3011.03119 -1.36093 (301*2π)/4231 weeks
3021.51564 -.70573 (302*2π)/4231 weeks
3031.18184 -.35365 (303*2π)/4231 weeks
304.9491 -.6342 (304*2π)/4231 weeks
3051.09991 -.55372 (305*2π)/4231 weeks
306.47367 -.29286 (306*2π)/4231 weeks
307.33634 -1.15047 (307*2π)/4231 weeks
308.9038 -1.14475 (308*2π)/4231 weeks
309.87088 -.57301 (309*2π)/4231 weeks
310.89733 -.88056 (310*2π)/4231 weeks
311.52617 -.98255 (311*2π)/4231 weeks
312.35932 -1.25653 (312*2π)/4231 weeks
313.51253 -1.41652 (313*2π)/4231 weeks
3141.34043 -1.49293 (314*2π)/4231 weeks
3151.30026 -.63393 (315*2π)/4231 weeks
316.74146 -1.14558 (316*2π)/4231 weeks
3171.29566 -1.29738 (317*2π)/4231 weeks
3181.04392 -.8129 (318*2π)/4231 weeks
319.62789 -1.01212 (319*2π)/4231 weeks
320.94198 -1.01643 (320*2π)/4231 weeks
3211.01593 -1.37776 (321*2π)/4231 weeks
3221.34998 -1.20745 (322*2π)/4231 weeks
323.89975 -.63899 (323*2π)/4231 weeks
324.41763 -1.25124 (324*2π)/4231 weeks
325.89367 -1.64374 (325*2π)/4231 weeks
326.8454 -1.27238 (326*2π)/4231 weeks
327.49192 -1.5749 (327*2π)/4231 weeks
3281.58137 -1.71562 (328*2π)/4231 weeks
3291.34469 -1.14873 (329*2π)/4231 weeks
3301.39624 -1.50844 (330*2π)/4231 weeks
3311.56193 -1.27399 (331*2π)/4231 weeks
332.94845 -1.07732 (332*2π)/4231 weeks
333.84932 -1.0776 (333*2π)/4231 weeks
334.59075 -1.01574 (334*2π)/4231 weeks
3351.33684 -1.96526 (335*2π)/4231 weeks
3361.57596 -.95477 (336*2π)/4231 weeks
337.65771 -1.09101 (337*2π)/4231 weeks
338.59993 -1.74696 (338*2π)/4231 weeks
3391.01658 -1.85746 (339*2π)/4231 weeks
3401.62813 -1.46582 (340*2π)/4231 weeks
3411.24248 -1.06462 (341*2π)/4231 weeks
3421.23719 -2.06422 (342*2π)/4231 weeks
3431.69296 -.97721 (343*2π)/4231 weeks
344.76469 -1.21299 (344*2π)/4231 weeks
345.90211 -1.6002 (345*2π)/4231 weeks
3461.2822 -1.20696 (346*2π)/4231 weeks
347.99891 -1.43448 (347*2π)/4231 weeks
3481.10322 -1.48294 (348*2π)/4231 weeks
3491.19076 -.91826 (349*2π)/4231 weeks
350.08744 -1.29278 (350*2π)/4231 weeks
351.92163 -2.52896 (351*2π)/4231 weeks
3521.25534 -1.99951 (352*2π)/4231 weeks
3531.15535 -1.92264 (353*2π)/4231 weeks
3541.07422 -1.67166 (354*2π)/4231 weeks
355.86375 -1.7759 (355*2π)/4231 weeks
3561.08289 -1.67731 (356*2π)/4231 weeks
357.94091 -2.76353 (357*2π)/4231 weeks
3582.61936 -2.02466 (358*2π)/4231 weeks
3591.48223 -.06463 (359*2π)/4231 weeks
360.04479 -1.4584 (360*2π)/4231 weeks
361.6613 -2.13474 (361*2π)/4231 weeks
362.39141 -2.33752 (362*2π)/4231 weeks
3631.50356 -3.8344 (363*2π)/4231 weeks
3643.47682 -1.33263 (364*2π)/4231 weeks
365.62324 -.0002 (365*2π)/4231 weeks
366-.02533 -1.80654 (366*2π)/4231 weeks
367.91989 -2.27501 (367*2π)/4231 weeks
368.30565 -2.25326 (368*2π)/4231 weeks
369.28304 -2.9305 (369*2π)/4231 weeks
3701.81758 -3.19791 (370*2π)/4231 weeks
3712.2914 -2.04666 (371*2π)/4231 weeks
3721.12526 -1.9867 (372*2π)/4231 weeks
373.69928 -1.64012 (373*2π)/4231 weeks
374.47981 -2.44987 (374*2π)/4231 weeks
375.48969 -2.81104 (375*2π)/4231 weeks
3761.57147 -3.30781 (376*2π)/4231 weeks
3771.89238 -1.81623 (377*2π)/4231 weeks
378.6897 -2.68898 (378*2π)/4231 weeks
3791.17048 -2.24659 (379*2π)/4231 weeks
3801.08804 -2.42453 (380*2π)/4231 weeks
3811.36675 -3.21961 (381*2π)/4231 weeks
3821.64296 -2.7466 (382*2π)/4231 weeks
3831.52873 -2.80577 (383*2π)/4231 weeks
384.96737 -1.62093 (384*2π)/4231 weeks
385.55476 -1.91559 (385*2π)/4231 weeks
386-.27429 -.86654 (386*2π)/4231 weeks
387-1.39735 -4.91831 (387*2π)/4231 weeks
3881.58902 -4.557 (388*2π)/4231 weeks
389-.22296 -2.08586 (389*2π)/4231 weeks
390-.98924 -5.96186 (390*2π)/4231 weeks
3913.72664 -4.73108 (391*2π)/4231 weeks
392.6856 -1.86567 (392*2π)/4231 weeks
393.50125 -3.9947 (393*2π)/4231 weeks
394-.60407 -3.51686 (394*2π)/4231 weeks
395-.7921 -5.22886 (395*2π)/4231 weeks
396.10498 -6.02457 (396*2π)/4231 weeks
3971.81343 -6.5456 (397*2π)/4231 weeks
3981.52676 -5.09256 (398*2π)/4231 weeks
399-.417 -4.16378 (399*2π)/4231 weeks
400-.66354 -6.07218 (400*2π)/4231 weeks
401.75787 -6.16888 (401*2π)/4231 weeks
402-.28002 -7.2624 (402*2π)/4231 weeks
403.61653 -9.81901 (403*2π)/4231 weeks
4043.66359 -8.83718 (404*2π)/4231 weeks
4051.48296 -6.52687 (405*2π)/4231 weeks
406.64396 -6.75517 (406*2π)/4231 weeks
407.44365 -9.27433 (407*2π)/4231 weeks
4082.17852 -9.22093 (408*2π)/4231 weeks
409-1.7376 -9.98631 (409*2π)/4231 weeks
4101.48827 -16.86942 (410*2π)/4231 weeks
4118.10223 -12.87667 (411*2π)/4231 weeks
4125.55495 -8.25635 (412*2π)/4231 weeks
4133.02931 -12.20138 (413*2π)/4231 weeks
4142.89371 -7.7751 (414*2π)/4231 weeks
415-6.14578 -13.64386 (415*2π)/4231 weeks
416.32066 -27.98521 (416*2π)/4231 weeks
41713.27075 -29.23409 (417*2π)/4231 weeks
41814.7379 -12.95408 (418*2π)/4231 weeks
419-4.8707 -23.06321 (419*2π)/4231 weeks
4208.50205 -40.17098 (420*2π)/4231 weeks
421-.64914 -44.72227 (421*2π)/4231 weeks

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