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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 32 weeks (15.4827*sine), 35 weeks (13.1831*sine), and 41 weeks (10.0655*sine).

VXZ (iPath® S&P 500 VIX Mid-Term Futures™ ETN) has an average price of 147.9 (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 10/9/2017 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
0147.8964   0 
151.86584 130.2882 (1*2π)/452452 weeks
2-5.15256 49.73827 (2*2π)/452226 weeks
39.54274 38.86892 (3*2π)/452151 weeks
4-3.65875 30.07787 (4*2π)/452113 weeks
57.73016 11.20322 (5*2π)/45290 weeks
617.50195 23.1374 (6*2π)/45275 weeks
75.35346 27.76807 (7*2π)/45265 weeks
8-5.46833 21.57423 (8*2π)/45257 weeks
9-2.28435 9.19955 (9*2π)/45250 weeks
105.26676 9.39987 (10*2π)/45245 weeks
112.2008 10.06553 (11*2π)/45241 weeks
126.48047 8.47619 (12*2π)/45238 weeks
137.44216 13.18311 (13*2π)/45235 weeks
14.58489 15.48271 (14*2π)/45232 weeks
15-1.48214 9.23909 (15*2π)/45230 weeks
162.08215 8.65938 (16*2π)/45228 weeks
17.54103 8.90245 (17*2π)/45227 weeks
18.21759 6.74652 (18*2π)/45225 weeks
191.37131 6.70719 (19*2π)/45224 weeks
203.84347 7.07188 (20*2π)/45223 weeks
211.75268 9.1448 (21*2π)/45222 weeks
22-.64187 7.45488 (22*2π)/45221 weeks
23-.36921 6.08013 (23*2π)/45220 weeks
24.26059 6.79548 (24*2π)/45219 weeks
25-.41868 5.34826 (25*2π)/45218 weeks
26.86224 3.55208 (26*2π)/45217 weeks
271.46262 4.71724 (27*2π)/45217 weeks
281.08651 6.4125 (28*2π)/45216 weeks
29.00423 5.66587 (29*2π)/45216 weeks
30-.79393 4.8534 (30*2π)/45215 weeks
31-.5597 3.33303 (31*2π)/45215 weeks
32.53095 3.73462 (32*2π)/45214 weeks
33.21127 2.00569 (33*2π)/45214 weeks
343.42041 3.4944 (34*2π)/45213 weeks
35.05745 6.39396 (35*2π)/45213 weeks
36-1.237 2.86204 (36*2π)/45213 weeks
371.81194 3.13937 (37*2π)/45212 weeks
38.13757 4.95169 (38*2π)/45212 weeks
39-2.25727 2.41353 (39*2π)/45212 weeks
40.71555 1.79082 (40*2π)/45211 weeks
41.79749 1.89027 (41*2π)/45211 weeks
421.5402 1.56901 (42*2π)/45211 weeks
431.2061 2.52364 (43*2π)/45211 weeks
441.46043 2.7237 (44*2π)/45210 weeks
451.13658 3.14043 (45*2π)/45210 weeks
461.08334 2.3616 (46*2π)/45210 weeks
471.10058 2.16352 (47*2π)/45210 weeks
48.7547 2.67448 (48*2π)/4529 weeks
491.51443 1.61645 (49*2π)/4529 weeks
501.7209 3.04088 (50*2π)/4529 weeks
51.59693 3.0387 (51*2π)/4529 weeks
52.63173 2.48795 (52*2π)/4529 weeks
53.50816 1.93406 (53*2π)/4529 weeks
541.32229 1.68315 (54*2π)/4528 weeks
551.37444 1.37214 (55*2π)/4528 weeks
562.0079 2.53015 (56*2π)/4528 weeks
571.25772 3.35307 (57*2π)/4528 weeks
58.33862 2.44249 (58*2π)/4528 weeks
59.34368 1.91528 (59*2π)/4528 weeks
60.74117 2.29041 (60*2π)/4528 weeks
61-.029 1.62835 (61*2π)/4527 weeks
62.66098 .00286 (62*2π)/4527 weeks
633.23372 1.13634 (63*2π)/4527 weeks
641.77025 3.62404 (64*2π)/4527 weeks
65.3507 2.38928 (65*2π)/4527 weeks
66.66864 1.94774 (66*2π)/4527 weeks
67.15004 1.73563 (67*2π)/4527 weeks
68.48216 .32815 (68*2π)/4527 weeks
692.47718 1.02482 (69*2π)/4527 weeks
701.81769 2.67598 (70*2π)/4526 weeks
71.57148 1.97248 (71*2π)/4526 weeks
721.12337 1.84513 (72*2π)/4526 weeks
73.96488 1.55581 (73*2π)/4526 weeks
741.10472 1.52542 (74*2π)/4526 weeks
751.0145 1.75373 (75*2π)/4526 weeks
761.12117 1.93328 (76*2π)/4526 weeks
77.75736 2.4419 (77*2π)/4526 weeks
78.08 1.26327 (78*2π)/4526 weeks
791.04987 .86057 (79*2π)/4526 weeks
801.07531 1.44716 (80*2π)/4526 weeks
81.9763 1.4117 (81*2π)/4526 weeks
821.03638 1.15899 (82*2π)/4526 weeks
831.11665 1.65298 (83*2π)/4525 weeks
84.87343 1.33956 (84*2π)/4525 weeks
851.12353 .72995 (85*2π)/4525 weeks
861.76109 1.47815 (86*2π)/4525 weeks
87.67285 1.50028 (87*2π)/4525 weeks
881.35627 1.20555 (88*2π)/4525 weeks
891.54784 1.68728 (89*2π)/4525 weeks
90.96891 1.68941 (90*2π)/4525 weeks
91.51189 1.5143 (91*2π)/4525 weeks
92.64955 .97865 (92*2π)/4525 weeks
931.51422 .95006 (93*2π)/4525 weeks
941.30541 1.83652 (94*2π)/4525 weeks
95.46221 1.07387 (95*2π)/4525 weeks
96.83142 1.13529 (96*2π)/4525 weeks
971.03314 1.11761 (97*2π)/4525 weeks
981.50544 .89384 (98*2π)/4525 weeks
991.34423 1.22264 (99*2π)/4525 weeks
100.99334 1.22025 (100*2π)/4525 weeks
1011.41576 1.32143 (101*2π)/4524 weeks
1021.04189 2.03288 (102*2π)/4524 weeks
103.72506 1.21024 (103*2π)/4524 weeks
104.95499 1.1559 (104*2π)/4524 weeks
105.65092 1.49445 (105*2π)/4524 weeks
106.36358 1.01533 (106*2π)/4524 weeks
107.94171 .61145 (107*2π)/4524 weeks
1081.22782 1.17909 (108*2π)/4524 weeks
109.94302 1.29759 (109*2π)/4524 weeks
110.83453 .95064 (110*2π)/4524 weeks
111.58232 1.06562 (111*2π)/4524 weeks
112.91894 .7842 (112*2π)/4524 weeks
1131.27072 1.04081 (113*2π)/4524 weeks
114.756 1.23666 (114*2π)/4524 weeks
115.76776 .68382 (115*2π)/4524 weeks
1161.41864 1.20653 (116*2π)/4524 weeks
117.91481 1.71418 (117*2π)/4524 weeks
118.67127 1.24101 (118*2π)/4524 weeks
119.43371 .89258 (119*2π)/4524 weeks
120.4759 .75236 (120*2π)/4524 weeks
121.73659 .93945 (121*2π)/4524 weeks
122.9846 .61033 (122*2π)/4524 weeks
123.82127 1.08771 (123*2π)/4524 weeks
124.29221 1.05914 (124*2π)/4524 weeks
125.4406 .29903 (125*2π)/4524 weeks
1261.05011 .48158 (126*2π)/4524 weeks
127.91376 .59572 (127*2π)/4524 weeks
128.96412 .33372 (128*2π)/4524 weeks
1291.31405 .56531 (129*2π)/4524 weeks
1301.26734 1.21308 (130*2π)/4523 weeks
131.56638 1.07885 (131*2π)/4523 weeks
132.47452 .49103 (132*2π)/4523 weeks
1331.14422 .33336 (133*2π)/4523 weeks
1341.16123 .77876 (134*2π)/4523 weeks
1351.28636 .88179 (135*2π)/4523 weeks
136.72849 .9606 (136*2π)/4523 weeks
137.83165 .54642 (137*2π)/4523 weeks
1381.01044 .5615 (138*2π)/4523 weeks
1391.08594 .56071 (139*2π)/4523 weeks
1401.18065 .8347 (140*2π)/4523 weeks
1411.03572 .74307 (141*2π)/4523 weeks
1421.01689 1.1749 (142*2π)/4523 weeks
143.66469 .93408 (143*2π)/4523 weeks
144.69536 .60385 (144*2π)/4523 weeks
145.72304 .69553 (145*2π)/4523 weeks
146.8929 .67393 (146*2π)/4523 weeks
147.76173 .76903 (147*2π)/4523 weeks
148.73626 .5073 (148*2π)/4523 weeks
149.94425 .61261 (149*2π)/4523 weeks
150.58513 .43626 (150*2π)/4523 weeks
1511.03227 .3352 (151*2π)/4523 weeks
1521.13836 .59248 (152*2π)/4523 weeks
1531.1521 .74091 (153*2π)/4523 weeks
154.76827 .88199 (154*2π)/4523 weeks
155.67347 .68521 (155*2π)/4523 weeks
156.56095 .51772 (156*2π)/4523 weeks
157.64463 .53122 (157*2π)/4523 weeks
158.61931 .2842 (158*2π)/4523 weeks
1591.2576 .0367 (159*2π)/4523 weeks
1601.69328 .78799 (160*2π)/4523 weeks
161.70851 1.47991 (161*2π)/4523 weeks
162.27027 .75263 (162*2π)/4523 weeks
163.64951 .78808 (163*2π)/4523 weeks
164.31267 .55842 (164*2π)/4523 weeks
165.30717 .08415 (165*2π)/4523 weeks
1661.17859 .17707 (166*2π)/4523 weeks
167.82013 1.13488 (167*2π)/4523 weeks
168-.13569 .58976 (168*2π)/4523 weeks
169.21861 .21252 (169*2π)/4523 weeks
170.50473 .0657 (170*2π)/4523 weeks
171.4015 -.09099 (171*2π)/4523 weeks
172.94215 -.27858 (172*2π)/4523 weeks
1731.25184 .33725 (173*2π)/4523 weeks
174.63687 .51076 (174*2π)/4523 weeks
175.37431 .32729 (175*2π)/4523 weeks
176.57057 .01114 (176*2π)/4523 weeks
177.36088 -.04505 (177*2π)/4523 weeks
178.60067 -.45288 (178*2π)/4523 weeks
1791.42233 -.52913 (179*2π)/4523 weeks
1801.45557 .25972 (180*2π)/4523 weeks
1811.16072 .48727 (181*2π)/4522 weeks
182.96868 .71627 (182*2π)/4522 weeks
183.21601 .42237 (183*2π)/4522 weeks
184.26538 -.4889 (184*2π)/4522 weeks
1851.33468 -.41685 (185*2π)/4522 weeks
1861.074 .17855 (186*2π)/4522 weeks
1871.049 .03005 (187*2π)/4522 weeks
1881.18258 .22199 (188*2π)/4522 weeks
189.95991 .37108 (189*2π)/4522 weeks
190.6027 .08718 (190*2π)/4522 weeks
191.89165 -.02483 (191*2π)/4522 weeks
192.9753 .12832 (192*2π)/4522 weeks
193.77373 .13806 (193*2π)/4522 weeks
194.81535 -.10417 (194*2π)/4522 weeks
1951.25909 -.02969 (195*2π)/4522 weeks
196.76144 .65928 (196*2π)/4522 weeks
197.54176 -.29106 (197*2π)/4522 weeks
1981.17511 -.13441 (198*2π)/4522 weeks
199.63648 .00102 (199*2π)/4522 weeks
2001.11228 -.45859 (200*2π)/4522 weeks
2011.61131 .0644 (201*2π)/4522 weeks
202.936 .48897 (202*2π)/4522 weeks
203.7147 .17867 (203*2π)/4522 weeks
2041.03757 .03532 (204*2π)/4522 weeks
205.7745 .19683 (205*2π)/4522 weeks
206.75523 -.07293 (206*2π)/4522 weeks
207.75901 -.13794 (207*2π)/4522 weeks
208.88063 -.48029 (208*2π)/4522 weeks
2091.30691 .08582 (209*2π)/4522 weeks
210.95477 -.22825 (210*2π)/4522 weeks
2111.40052 -.19028 (211*2π)/4522 weeks
2121.12578 .32044 (212*2π)/4522 weeks
213.53483 -.04245 (213*2π)/4522 weeks
2141.27412 -.45703 (214*2π)/4522 weeks
2151.54943 -.15336 (215*2π)/4522 weeks
2161.58221 .08922 (216*2π)/4522 weeks
2171.27818 .42856 (217*2π)/4522 weeks
218.82647 .53559 (218*2π)/4522 weeks
219.50951 .23617 (219*2π)/4522 weeks
220.6156 -.46832 (220*2π)/4522 weeks
2211.34243 -.53034 (221*2π)/4522 weeks
2221.47795 .11804 (222*2π)/4522 weeks
2231.04771 .26343 (223*2π)/4522 weeks
2241.35133 .09585 (224*2π)/4522 weeks
2251.04105 .6702 (225*2π)/4522 weeks
226.1747   (226*2π)/4522 weeks
2271.04105 -.6702 (227*2π)/4522 weeks
2281.35133 -.09585 (228*2π)/4522 weeks
2291.04771 -.26343 (229*2π)/4522 weeks
2301.47795 -.11804 (230*2π)/4522 weeks
2311.34243 .53034 (231*2π)/4522 weeks
232.6156 .46832 (232*2π)/4522 weeks
233.50951 -.23617 (233*2π)/4522 weeks
234.82647 -.53559 (234*2π)/4522 weeks
2351.27818 -.42856 (235*2π)/4522 weeks
2361.58221 -.08922 (236*2π)/4522 weeks
2371.54943 .15336 (237*2π)/4522 weeks
2381.27412 .45703 (238*2π)/4522 weeks
239.53483 .04245 (239*2π)/4522 weeks
2401.12578 -.32044 (240*2π)/4522 weeks
2411.40052 .19028 (241*2π)/4522 weeks
242.95477 .22825 (242*2π)/4522 weeks
2431.30691 -.08582 (243*2π)/4522 weeks
244.88063 .48029 (244*2π)/4522 weeks
245.75901 .13794 (245*2π)/4522 weeks
246.75523 .07293 (246*2π)/4522 weeks
247.7745 -.19683 (247*2π)/4522 weeks
2481.03757 -.03532 (248*2π)/4522 weeks
249.7147 -.17867 (249*2π)/4522 weeks
250.936 -.48897 (250*2π)/4522 weeks
2511.61131 -.0644 (251*2π)/4522 weeks
2521.11228 .45859 (252*2π)/4522 weeks
253.63648 -.00102 (253*2π)/4522 weeks
2541.17511 .13441 (254*2π)/4522 weeks
255.54176 .29106 (255*2π)/4522 weeks
256.76144 -.65928 (256*2π)/4522 weeks
2571.25909 .02969 (257*2π)/4522 weeks
258.81535 .10417 (258*2π)/4522 weeks
259.77373 -.13806 (259*2π)/4522 weeks
260.9753 -.12832 (260*2π)/4522 weeks
261.89165 .02483 (261*2π)/4522 weeks
262.6027 -.08718 (262*2π)/4522 weeks
263.95991 -.37108 (263*2π)/4522 weeks
2641.18258 -.22199 (264*2π)/4522 weeks
2651.049 -.03005 (265*2π)/4522 weeks
2661.074 -.17855 (266*2π)/4522 weeks
2671.33468 .41685 (267*2π)/4522 weeks
268.26538 .4889 (268*2π)/4522 weeks
269.21601 -.42237 (269*2π)/4522 weeks
270.96868 -.71627 (270*2π)/4522 weeks
2711.16072 -.48727 (271*2π)/4522 weeks
2721.45557 -.25972 (272*2π)/4522 weeks
2731.42233 .52913 (273*2π)/4522 weeks
274.60067 .45288 (274*2π)/4522 weeks
275.36088 .04505 (275*2π)/4522 weeks
276.57057 -.01114 (276*2π)/4522 weeks
277.37431 -.32729 (277*2π)/4522 weeks
278.63687 -.51076 (278*2π)/4522 weeks
2791.25184 -.33725 (279*2π)/4522 weeks
280.94215 .27858 (280*2π)/4522 weeks
281.4015 .09099 (281*2π)/4522 weeks
282.50473 -.0657 (282*2π)/4522 weeks
283.21861 -.21252 (283*2π)/4522 weeks
284-.13569 -.58976 (284*2π)/4522 weeks
285.82013 -1.13488 (285*2π)/4522 weeks
2861.17859 -.17707 (286*2π)/4522 weeks
287.30717 -.08415 (287*2π)/4522 weeks
288.31267 -.55842 (288*2π)/4522 weeks
289.64951 -.78808 (289*2π)/4522 weeks
290.27027 -.75263 (290*2π)/4522 weeks
291.70851 -1.47991 (291*2π)/4522 weeks
2921.69328 -.78799 (292*2π)/4522 weeks
2931.2576 -.0367 (293*2π)/4522 weeks
294.61931 -.2842 (294*2π)/4522 weeks
295.64463 -.53122 (295*2π)/4522 weeks
296.56095 -.51772 (296*2π)/4522 weeks
297.67347 -.68521 (297*2π)/4522 weeks
298.76827 -.88199 (298*2π)/4522 weeks
2991.1521 -.74091 (299*2π)/4522 weeks
3001.13836 -.59248 (300*2π)/4522 weeks
3011.03227 -.3352 (301*2π)/4522 weeks
302.58513 -.43626 (302*2π)/4521 weeks
303.94425 -.61261 (303*2π)/4521 weeks
304.73626 -.5073 (304*2π)/4521 weeks
305.76173 -.76903 (305*2π)/4521 weeks
306.8929 -.67393 (306*2π)/4521 weeks
307.72304 -.69553 (307*2π)/4521 weeks
308.69536 -.60385 (308*2π)/4521 weeks
309.66469 -.93408 (309*2π)/4521 weeks
3101.01689 -1.1749 (310*2π)/4521 weeks
3111.03572 -.74307 (311*2π)/4521 weeks
3121.18065 -.8347 (312*2π)/4521 weeks
3131.08594 -.56071 (313*2π)/4521 weeks
3141.01044 -.5615 (314*2π)/4521 weeks
315.83165 -.54642 (315*2π)/4521 weeks
316.72849 -.9606 (316*2π)/4521 weeks
3171.28636 -.88179 (317*2π)/4521 weeks
3181.16123 -.77876 (318*2π)/4521 weeks
3191.14422 -.33336 (319*2π)/4521 weeks
320.47452 -.49103 (320*2π)/4521 weeks
321.56638 -1.07885 (321*2π)/4521 weeks
3221.26734 -1.21308 (322*2π)/4521 weeks
3231.31405 -.56531 (323*2π)/4521 weeks
324.96412 -.33372 (324*2π)/4521 weeks
325.91376 -.59572 (325*2π)/4521 weeks
3261.05011 -.48158 (326*2π)/4521 weeks
327.4406 -.29903 (327*2π)/4521 weeks
328.29221 -1.05914 (328*2π)/4521 weeks
329.82127 -1.08771 (329*2π)/4521 weeks
330.9846 -.61033 (330*2π)/4521 weeks
331.73659 -.93945 (331*2π)/4521 weeks
332.4759 -.75236 (332*2π)/4521 weeks
333.43371 -.89258 (333*2π)/4521 weeks
334.67127 -1.24101 (334*2π)/4521 weeks
335.91481 -1.71418 (335*2π)/4521 weeks
3361.41864 -1.20653 (336*2π)/4521 weeks
337.76776 -.68382 (337*2π)/4521 weeks
338.756 -1.23666 (338*2π)/4521 weeks
3391.27072 -1.04081 (339*2π)/4521 weeks
340.91894 -.7842 (340*2π)/4521 weeks
341.58232 -1.06562 (341*2π)/4521 weeks
342.83453 -.95064 (342*2π)/4521 weeks
343.94302 -1.29759 (343*2π)/4521 weeks
3441.22782 -1.17909 (344*2π)/4521 weeks
345.94171 -.61145 (345*2π)/4521 weeks
346.36358 -1.01533 (346*2π)/4521 weeks
347.65092 -1.49445 (347*2π)/4521 weeks
348.95499 -1.1559 (348*2π)/4521 weeks
349.72506 -1.21024 (349*2π)/4521 weeks
3501.04189 -2.03288 (350*2π)/4521 weeks
3511.41576 -1.32143 (351*2π)/4521 weeks
352.99334 -1.22025 (352*2π)/4521 weeks
3531.34423 -1.22264 (353*2π)/4521 weeks
3541.50544 -.89384 (354*2π)/4521 weeks
3551.03314 -1.11761 (355*2π)/4521 weeks
356.83142 -1.13529 (356*2π)/4521 weeks
357.46221 -1.07387 (357*2π)/4521 weeks
3581.30541 -1.83652 (358*2π)/4521 weeks
3591.51422 -.95006 (359*2π)/4521 weeks
360.64955 -.97865 (360*2π)/4521 weeks
361.51189 -1.5143 (361*2π)/4521 weeks
362.96891 -1.68941 (362*2π)/4521 weeks
3631.54784 -1.68728 (363*2π)/4521 weeks
3641.35627 -1.20555 (364*2π)/4521 weeks
365.67285 -1.50028 (365*2π)/4521 weeks
3661.76109 -1.47815 (366*2π)/4521 weeks
3671.12353 -.72995 (367*2π)/4521 weeks
368.87343 -1.33956 (368*2π)/4521 weeks
3691.11665 -1.65298 (369*2π)/4521 weeks
3701.03638 -1.15899 (370*2π)/4521 weeks
371.9763 -1.4117 (371*2π)/4521 weeks
3721.07531 -1.44716 (372*2π)/4521 weeks
3731.04987 -.86057 (373*2π)/4521 weeks
374.08 -1.26327 (374*2π)/4521 weeks
375.75736 -2.4419 (375*2π)/4521 weeks
3761.12117 -1.93328 (376*2π)/4521 weeks
3771.0145 -1.75373 (377*2π)/4521 weeks
3781.10472 -1.52542 (378*2π)/4521 weeks
379.96488 -1.55581 (379*2π)/4521 weeks
3801.12337 -1.84513 (380*2π)/4521 weeks
381.57148 -1.97248 (381*2π)/4521 weeks
3821.81769 -2.67598 (382*2π)/4521 weeks
3832.47718 -1.02482 (383*2π)/4521 weeks
384.48216 -.32815 (384*2π)/4521 weeks
385.15004 -1.73563 (385*2π)/4521 weeks
386.66864 -1.94774 (386*2π)/4521 weeks
387.3507 -2.38928 (387*2π)/4521 weeks
3881.77025 -3.62404 (388*2π)/4521 weeks
3893.23372 -1.13634 (389*2π)/4521 weeks
390.66098 -.00286 (390*2π)/4521 weeks
391-.029 -1.62835 (391*2π)/4521 weeks
392.74117 -2.29041 (392*2π)/4521 weeks
393.34368 -1.91528 (393*2π)/4521 weeks
394.33862 -2.44249 (394*2π)/4521 weeks
3951.25772 -3.35307 (395*2π)/4521 weeks
3962.0079 -2.53015 (396*2π)/4521 weeks
3971.37444 -1.37214 (397*2π)/4521 weeks
3981.32229 -1.68315 (398*2π)/4521 weeks
399.50816 -1.93406 (399*2π)/4521 weeks
400.63173 -2.48795 (400*2π)/4521 weeks
401.59693 -3.0387 (401*2π)/4521 weeks
4021.7209 -3.04088 (402*2π)/4521 weeks
4031.51443 -1.61645 (403*2π)/4521 weeks
404.7547 -2.67448 (404*2π)/4521 weeks
4051.10058 -2.16352 (405*2π)/4521 weeks
4061.08334 -2.3616 (406*2π)/4521 weeks
4071.13658 -3.14043 (407*2π)/4521 weeks
4081.46043 -2.7237 (408*2π)/4521 weeks
4091.2061 -2.52364 (409*2π)/4521 weeks
4101.5402 -1.56901 (410*2π)/4521 weeks
411.79749 -1.89027 (411*2π)/4521 weeks
412.71555 -1.79082 (412*2π)/4521 weeks
413-2.25727 -2.41353 (413*2π)/4521 weeks
414.13757 -4.95169 (414*2π)/4521 weeks
4151.81194 -3.13937 (415*2π)/4521 weeks
416-1.237 -2.86204 (416*2π)/4521 weeks
417.05745 -6.39396 (417*2π)/4521 weeks
4183.42041 -3.4944 (418*2π)/4521 weeks
419.21127 -2.00569 (419*2π)/4521 weeks
420.53095 -3.73462 (420*2π)/4521 weeks
421-.5597 -3.33303 (421*2π)/4521 weeks
422-.79393 -4.8534 (422*2π)/4521 weeks
423.00423 -5.66587 (423*2π)/4521 weeks
4241.08651 -6.4125 (424*2π)/4521 weeks
4251.46262 -4.71724 (425*2π)/4521 weeks
426.86224 -3.55208 (426*2π)/4521 weeks
427-.41868 -5.34826 (427*2π)/4521 weeks
428.26059 -6.79548 (428*2π)/4521 weeks
429-.36921 -6.08013 (429*2π)/4521 weeks
430-.64187 -7.45488 (430*2π)/4521 weeks
4311.75268 -9.1448 (431*2π)/4521 weeks
4323.84347 -7.07188 (432*2π)/4521 weeks
4331.37131 -6.70719 (433*2π)/4521 weeks
434.21759 -6.74652 (434*2π)/4521 weeks
435.54103 -8.90245 (435*2π)/4521 weeks
4362.08215 -8.65938 (436*2π)/4521 weeks
437-1.48214 -9.23909 (437*2π)/4521 weeks
438.58489 -15.48271 (438*2π)/4521 weeks
4397.44216 -13.18311 (439*2π)/4521 weeks
4406.48047 -8.47619 (440*2π)/4521 weeks
4412.2008 -10.06553 (441*2π)/4521 weeks
4425.26676 -9.39987 (442*2π)/4521 weeks
443-2.28435 -9.19955 (443*2π)/4521 weeks
444-5.46833 -21.57423 (444*2π)/4521 weeks
4455.35346 -27.76807 (445*2π)/4521 weeks
44617.50195 -23.1374 (446*2π)/4521 weeks
4477.73016 -11.20322 (447*2π)/4521 weeks
448-3.65875 -30.07787 (448*2π)/4521 weeks
4499.54274 -38.86892 (449*2π)/4521 weeks
450-5.15256 -49.73827 (450*2π)/4521 weeks



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