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Fourier Analysis of SMK (ProShares UltraShort MSCI Mexico Capped IMI ETF)


SMK (ProShares UltraShort MSCI Mexico Capped IMI ETF) appears to have interesting cyclic behaviour every 38 weeks (5.8926*sine), 42 weeks (5.8115*sine), and 30 weeks (2.8859*cosine).

SMK (ProShares UltraShort MSCI Mexico Capped IMI ETF) has an average price of 44.84 (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 6/18/2009 to 7/10/2017 for SMK (ProShares UltraShort MSCI Mexico Capped IMI ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
044.84381   0 
125.85155 21.59722 (1*2π)/422422 weeks
28.916 15.16136 (2*2π)/422211 weeks
37.59583 12.96049 (3*2π)/422141 weeks
44.93658 13.15652 (4*2π)/422106 weeks
52.37151 7.7063 (5*2π)/42284 weeks
63.50541 6.29532 (6*2π)/42270 weeks
74.64909 6.13412 (7*2π)/42260 weeks
83.32346 8.07249 (8*2π)/42253 weeks
91.42292 7.75781 (9*2π)/42247 weeks
102.64188 5.81153 (10*2π)/42242 weeks
111.57634 5.8926 (11*2π)/42238 weeks
121.50015 5.13794 (12*2π)/42235 weeks
132.1056 3.37465 (13*2π)/42232 weeks
142.88592 4.62207 (14*2π)/42230 weeks
151.67292 5.06288 (15*2π)/42228 weeks
161.83924 4.16498 (16*2π)/42226 weeks
171.60793 3.67521 (17*2π)/42225 weeks
18.7328 2.92521 (18*2π)/42223 weeks
19.99966 3.28281 (19*2π)/42222 weeks
20.61476 3.32433 (20*2π)/42221 weeks
211.13194 2.80324 (21*2π)/42220 weeks
221.91837 2.46978 (22*2π)/42219 weeks
23.92546 2.31745 (23*2π)/42218 weeks
241.50619 1.77367 (24*2π)/42218 weeks
251.99252 2.89053 (25*2π)/42217 weeks
262.08174 3.42866 (26*2π)/42216 weeks
271.45878 3.26866 (27*2π)/42216 weeks
281.61011 3.22367 (28*2π)/42215 weeks
29.9517 3.43674 (29*2π)/42215 weeks
30.40811 2.99469 (30*2π)/42214 weeks
31-.01362 2.67383 (31*2π)/42214 weeks
32.51492 1.57142 (32*2π)/42213 weeks
331.22339 2.39798 (33*2π)/42213 weeks
34.61895 2.18948 (34*2π)/42212 weeks
351.12012 1.96435 (35*2π)/42212 weeks
36.9609 2.39879 (36*2π)/42212 weeks
37.71194 2.46212 (37*2π)/42211 weeks
381.38649 1.98432 (38*2π)/42211 weeks
39.89414 2.52054 (39*2π)/42211 weeks
40.45562 2.11196 (40*2π)/42211 weeks
41.56106 2.06243 (41*2π)/42210 weeks
42.56033 2.04865 (42*2π)/42210 weeks
43.36153 2.37941 (43*2π)/42210 weeks
44.36534 1.90706 (44*2π)/42210 weeks
45.28727 1.83101 (45*2π)/4229 weeks
46.63931 2.05544 (46*2π)/4229 weeks
47.19927 2.29038 (47*2π)/4229 weeks
48.03818 1.79746 (48*2π)/4229 weeks
49.18132 1.47266 (49*2π)/4229 weeks
50.48527 1.36004 (50*2π)/4228 weeks
51-.1098 1.16043 (51*2π)/4228 weeks
52.40746 .95942 (52*2π)/4228 weeks
53.55213 1.31699 (53*2π)/4228 weeks
54.23371 1.71712 (54*2π)/4228 weeks
55-.04936 1.70994 (55*2π)/4228 weeks
56.12173 1.37364 (56*2π)/4228 weeks
57.08796 1.69319 (57*2π)/4227 weeks
58-.26277 1.4734 (58*2π)/4227 weeks
59-.04183 .43066 (59*2π)/4227 weeks
60.81469 .59575 (60*2π)/4227 weeks
61.53725 1.16321 (61*2π)/4227 weeks
62.39035 1.1032 (62*2π)/4227 weeks
63.57284 .86154 (63*2π)/4227 weeks
64.54835 1.35681 (64*2π)/4227 weeks
65.27858 1.18788 (65*2π)/4226 weeks
66.18044 1.01548 (66*2π)/4226 weeks
67.16899 1.15788 (67*2π)/4226 weeks
68.27658 1.15226 (68*2π)/4226 weeks
69.29695 1.1087 (69*2π)/4226 weeks
70.06433 .98762 (70*2π)/4226 weeks
71.03564 .98809 (71*2π)/4226 weeks
72-.23657 .90343 (72*2π)/4226 weeks
73-.19147 .57265 (73*2π)/4226 weeks
74-.01226 .61988 (74*2π)/4226 weeks
75.32242 .44309 (75*2π)/4226 weeks
76.29669 .40609 (76*2π)/4226 weeks
77.45619 .27696 (77*2π)/4225 weeks
78.20765 .37626 (78*2π)/4225 weeks
79.4706 .59787 (79*2π)/4225 weeks
80.42977 .53308 (80*2π)/4225 weeks
81.53177 .60037 (81*2π)/4225 weeks
82.37038 .4088 (82*2π)/4225 weeks
83.60391 .57113 (83*2π)/4225 weeks
84.59895 .533 (84*2π)/4225 weeks
85.75086 .47521 (85*2π)/4225 weeks
86.63782 .50451 (86*2π)/4225 weeks
87.41655 .76418 (87*2π)/4225 weeks
88.2848 .52038 (88*2π)/4225 weeks
89.55823 .67033 (89*2π)/4225 weeks
90.62257 .6287 (90*2π)/4225 weeks
91.50334 .71546 (91*2π)/4225 weeks
92.43629 .61967 (92*2π)/4225 weeks
93.60169 .84222 (93*2π)/4225 weeks
94.50033 .92934 (94*2π)/4224 weeks
95.25431 1.05044 (95*2π)/4224 weeks
96.2191 .55578 (96*2π)/4224 weeks
97.22878 .64304 (97*2π)/4224 weeks
98-.11701 .58358 (98*2π)/4224 weeks
99-.11162 .29855 (99*2π)/4224 weeks
100.0661 .17395 (100*2π)/4224 weeks
101.146 .22942 (101*2π)/4224 weeks
102.24367 .1214 (102*2π)/4224 weeks
103.37529 .04697 (103*2π)/4224 weeks
104.04043 .28098 (104*2π)/4224 weeks
105.21723 -.01065 (105*2π)/4224 weeks
106.50377 -.05179 (106*2π)/4224 weeks
107.62061 -.08463 (107*2π)/4224 weeks
108.56582 .01551 (108*2π)/4224 weeks
109.6733 -.07548 (109*2π)/4224 weeks
110.86134 .11522 (110*2π)/4224 weeks
111.87387 .36183 (111*2π)/4224 weeks
112.60962 .33227 (112*2π)/4224 weeks
113.76255 .13535 (113*2π)/4224 weeks
114.72711 .38582 (114*2π)/4224 weeks
115.70383 .20088 (115*2π)/4224 weeks
116.84373 .12371 (116*2π)/4224 weeks
117.9705 .40428 (117*2π)/4224 weeks
118.70043 .45527 (118*2π)/4224 weeks
119.67482 .31369 (119*2π)/4224 weeks
120.65824 .48525 (120*2π)/4224 weeks
121.63573 .48715 (121*2π)/4223 weeks
122.34893 .52445 (122*2π)/4223 weeks
123.40493 .26432 (123*2π)/4223 weeks
124.47735 .32861 (124*2π)/4223 weeks
125.57235 .25394 (125*2π)/4223 weeks
126.66103 .28854 (126*2π)/4223 weeks
127.62527 .23754 (127*2π)/4223 weeks
128.53636 .13027 (128*2π)/4223 weeks
129.73678 .20832 (129*2π)/4223 weeks
130.68452 .32492 (130*2π)/4223 weeks
131.5983 .1564 (131*2π)/4223 weeks
132.60763 .20568 (132*2π)/4223 weeks
133.7223 .29343 (133*2π)/4223 weeks
134.63975 .34876 (134*2π)/4223 weeks
135.64805 .18294 (135*2π)/4223 weeks
136.80259 .25762 (136*2π)/4223 weeks
137.64584 .37762 (137*2π)/4223 weeks
138.62553 .32615 (138*2π)/4223 weeks
139.66009 .27734 (139*2π)/4223 weeks
140.66156 .37506 (140*2π)/4223 weeks
141.48793 .3279 (141*2π)/4223 weeks
142.57003 .26314 (142*2π)/4223 weeks
143.65848 .22928 (143*2π)/4223 weeks
144.54965 .17111 (144*2π)/4223 weeks
145.49833 -.09247 (145*2π)/4223 weeks
146.67409 .12183 (146*2π)/4223 weeks
147.73342 .13506 (147*2π)/4223 weeks
148.77756 -.03584 (148*2π)/4223 weeks
1491.00066 .16684 (149*2π)/4223 weeks
150.91376 .54442 (150*2π)/4223 weeks
151.81629 .43074 (151*2π)/4223 weeks
152.89471 .40903 (152*2π)/4223 weeks
153.80895 .4479 (153*2π)/4223 weeks
154.54998 .5357 (154*2π)/4223 weeks
155.59575 .18142 (155*2π)/4223 weeks
156.84932 .36886 (156*2π)/4223 weeks
157.74666 .56449 (157*2π)/4223 weeks
158.53822 .45954 (158*2π)/4223 weeks
159.57582 .4424 (159*2π)/4223 weeks
160.51792 .47203 (160*2π)/4223 weeks
161.33216 .32122 (161*2π)/4223 weeks
162.39027 .21921 (162*2π)/4223 weeks
163.48341 .25432 (163*2π)/4223 weeks
164.82127 .38935 (164*2π)/4223 weeks
165.54444 .20319 (165*2π)/4223 weeks
166.68942 .22476 (166*2π)/4223 weeks
167.65244 .40925 (167*2π)/4223 weeks
168.50753 .42697 (168*2π)/4223 weeks
169.43961 .344 (169*2π)/4222 weeks
170.4339 .42883 (170*2π)/4222 weeks
171.3202 .25032 (171*2π)/4222 weeks
172.4146 .2108 (172*2π)/4222 weeks
173.49457 .41563 (173*2π)/4222 weeks
174.51477 .23327 (174*2π)/4222 weeks
175.54383 .1239 (175*2π)/4222 weeks
176.58344 .36661 (176*2π)/4222 weeks
177.4811 .3842 (177*2π)/4222 weeks
178.4475 .39399 (178*2π)/4222 weeks
179.4558 .36114 (179*2π)/4222 weeks
180.38967 .2359 (180*2π)/4222 weeks
181.39694 .12731 (181*2π)/4222 weeks
182.29051 .0987 (182*2π)/4222 weeks
183.45048 .18876 (183*2π)/4222 weeks
184.29604 .27057 (184*2π)/4222 weeks
185.40353 -.02304 (185*2π)/4222 weeks
186.61572 .16108 (186*2π)/4222 weeks
187.28003 .29925 (187*2π)/4222 weeks
188.1816 .12671 (188*2π)/4222 weeks
189.36481 -.01486 (189*2π)/4222 weeks
190.53325 .19774 (190*2π)/4222 weeks
191.29589 .04959 (191*2π)/4222 weeks
192.40782 -.05377 (192*2π)/4222 weeks
193.47117 -.15563 (193*2π)/4222 weeks
194.47818 .00342 (194*2π)/4222 weeks
195.49573 -.00956 (195*2π)/4222 weeks
196.7102 -.06058 (196*2π)/4222 weeks
197.66075 .06292 (197*2π)/4222 weeks
198.42374 .24012 (198*2π)/4222 weeks
199.22702 .01915 (199*2π)/4222 weeks
200.42006 -.12549 (200*2π)/4222 weeks
201.5293 -.05821 (201*2π)/4222 weeks
202.69638 .02657 (202*2π)/4222 weeks
203.61931 .03549 (203*2π)/4222 weeks
204.58083 .10947 (204*2π)/4222 weeks
205.31626 .31564 (205*2π)/4222 weeks
206.20874 .09489 (206*2π)/4222 weeks
207.25262 -.10579 (207*2π)/4222 weeks
208.45256 -.11188 (208*2π)/4222 weeks
209.38162 -.18195 (209*2π)/4222 weeks
210.70803 -.32494 (210*2π)/4222 weeks
211.78393   (211*2π)/4222 weeks
212.70803 .32494 (212*2π)/4222 weeks
213.38162 .18195 (213*2π)/4222 weeks
214.45256 .11188 (214*2π)/4222 weeks
215.25262 .10579 (215*2π)/4222 weeks
216.20874 -.09489 (216*2π)/4222 weeks
217.31626 -.31564 (217*2π)/4222 weeks
218.58083 -.10947 (218*2π)/4222 weeks
219.61931 -.03549 (219*2π)/4222 weeks
220.69638 -.02657 (220*2π)/4222 weeks
221.5293 .05821 (221*2π)/4222 weeks
222.42006 .12549 (222*2π)/4222 weeks
223.22702 -.01915 (223*2π)/4222 weeks
224.42374 -.24012 (224*2π)/4222 weeks
225.66075 -.06292 (225*2π)/4222 weeks
226.7102 .06058 (226*2π)/4222 weeks
227.49573 .00956 (227*2π)/4222 weeks
228.47818 -.00342 (228*2π)/4222 weeks
229.47117 .15563 (229*2π)/4222 weeks
230.40782 .05377 (230*2π)/4222 weeks
231.29589 -.04959 (231*2π)/4222 weeks
232.53325 -.19774 (232*2π)/4222 weeks
233.36481 .01486 (233*2π)/4222 weeks
234.1816 -.12671 (234*2π)/4222 weeks
235.28003 -.29925 (235*2π)/4222 weeks
236.61572 -.16108 (236*2π)/4222 weeks
237.40353 .02304 (237*2π)/4222 weeks
238.29604 -.27057 (238*2π)/4222 weeks
239.45048 -.18876 (239*2π)/4222 weeks
240.29051 -.0987 (240*2π)/4222 weeks
241.39694 -.12731 (241*2π)/4222 weeks
242.38967 -.2359 (242*2π)/4222 weeks
243.4558 -.36114 (243*2π)/4222 weeks
244.4475 -.39399 (244*2π)/4222 weeks
245.4811 -.3842 (245*2π)/4222 weeks
246.58344 -.36661 (246*2π)/4222 weeks
247.54383 -.1239 (247*2π)/4222 weeks
248.51477 -.23327 (248*2π)/4222 weeks
249.49457 -.41563 (249*2π)/4222 weeks
250.4146 -.2108 (250*2π)/4222 weeks
251.3202 -.25032 (251*2π)/4222 weeks
252.4339 -.42883 (252*2π)/4222 weeks
253.43961 -.344 (253*2π)/4222 weeks
254.50753 -.42697 (254*2π)/4222 weeks
255.65244 -.40925 (255*2π)/4222 weeks
256.68942 -.22476 (256*2π)/4222 weeks
257.54444 -.20319 (257*2π)/4222 weeks
258.82127 -.38935 (258*2π)/4222 weeks
259.48341 -.25432 (259*2π)/4222 weeks
260.39027 -.21921 (260*2π)/4222 weeks
261.33216 -.32122 (261*2π)/4222 weeks
262.51792 -.47203 (262*2π)/4222 weeks
263.57582 -.4424 (263*2π)/4222 weeks
264.53822 -.45954 (264*2π)/4222 weeks
265.74666 -.56449 (265*2π)/4222 weeks
266.84932 -.36886 (266*2π)/4222 weeks
267.59575 -.18142 (267*2π)/4222 weeks
268.54998 -.5357 (268*2π)/4222 weeks
269.80895 -.4479 (269*2π)/4222 weeks
270.89471 -.40903 (270*2π)/4222 weeks
271.81629 -.43074 (271*2π)/4222 weeks
272.91376 -.54442 (272*2π)/4222 weeks
2731.00066 -.16684 (273*2π)/4222 weeks
274.77756 .03584 (274*2π)/4222 weeks
275.73342 -.13506 (275*2π)/4222 weeks
276.67409 -.12183 (276*2π)/4222 weeks
277.49833 .09247 (277*2π)/4222 weeks
278.54965 -.17111 (278*2π)/4222 weeks
279.65848 -.22928 (279*2π)/4222 weeks
280.57003 -.26314 (280*2π)/4222 weeks
281.48793 -.3279 (281*2π)/4222 weeks
282.66156 -.37506 (282*2π)/4221 weeks
283.66009 -.27734 (283*2π)/4221 weeks
284.62553 -.32615 (284*2π)/4221 weeks
285.64584 -.37762 (285*2π)/4221 weeks
286.80259 -.25762 (286*2π)/4221 weeks
287.64805 -.18294 (287*2π)/4221 weeks
288.63975 -.34876 (288*2π)/4221 weeks
289.7223 -.29343 (289*2π)/4221 weeks
290.60763 -.20568 (290*2π)/4221 weeks
291.5983 -.1564 (291*2π)/4221 weeks
292.68452 -.32492 (292*2π)/4221 weeks
293.73678 -.20832 (293*2π)/4221 weeks
294.53636 -.13027 (294*2π)/4221 weeks
295.62527 -.23754 (295*2π)/4221 weeks
296.66103 -.28854 (296*2π)/4221 weeks
297.57235 -.25394 (297*2π)/4221 weeks
298.47735 -.32861 (298*2π)/4221 weeks
299.40493 -.26432 (299*2π)/4221 weeks
300.34893 -.52445 (300*2π)/4221 weeks
301.63573 -.48715 (301*2π)/4221 weeks
302.65824 -.48525 (302*2π)/4221 weeks
303.67482 -.31369 (303*2π)/4221 weeks
304.70043 -.45527 (304*2π)/4221 weeks
305.9705 -.40428 (305*2π)/4221 weeks
306.84373 -.12371 (306*2π)/4221 weeks
307.70383 -.20088 (307*2π)/4221 weeks
308.72711 -.38582 (308*2π)/4221 weeks
309.76255 -.13535 (309*2π)/4221 weeks
310.60962 -.33227 (310*2π)/4221 weeks
311.87387 -.36183 (311*2π)/4221 weeks
312.86134 -.11522 (312*2π)/4221 weeks
313.6733 .07548 (313*2π)/4221 weeks
314.56582 -.01551 (314*2π)/4221 weeks
315.62061 .08463 (315*2π)/4221 weeks
316.50377 .05179 (316*2π)/4221 weeks
317.21723 .01065 (317*2π)/4221 weeks
318.04043 -.28098 (318*2π)/4221 weeks
319.37529 -.04697 (319*2π)/4221 weeks
320.24367 -.1214 (320*2π)/4221 weeks
321.146 -.22942 (321*2π)/4221 weeks
322.0661 -.17395 (322*2π)/4221 weeks
323-.11162 -.29855 (323*2π)/4221 weeks
324-.11701 -.58358 (324*2π)/4221 weeks
325.22878 -.64304 (325*2π)/4221 weeks
326.2191 -.55578 (326*2π)/4221 weeks
327.25431 -1.05044 (327*2π)/4221 weeks
328.50033 -.92934 (328*2π)/4221 weeks
329.60169 -.84222 (329*2π)/4221 weeks
330.43629 -.61967 (330*2π)/4221 weeks
331.50334 -.71546 (331*2π)/4221 weeks
332.62257 -.6287 (332*2π)/4221 weeks
333.55823 -.67033 (333*2π)/4221 weeks
334.2848 -.52038 (334*2π)/4221 weeks
335.41655 -.76418 (335*2π)/4221 weeks
336.63782 -.50451 (336*2π)/4221 weeks
337.75086 -.47521 (337*2π)/4221 weeks
338.59895 -.533 (338*2π)/4221 weeks
339.60391 -.57113 (339*2π)/4221 weeks
340.37038 -.4088 (340*2π)/4221 weeks
341.53177 -.60037 (341*2π)/4221 weeks
342.42977 -.53308 (342*2π)/4221 weeks
343.4706 -.59787 (343*2π)/4221 weeks
344.20765 -.37626 (344*2π)/4221 weeks
345.45619 -.27696 (345*2π)/4221 weeks
346.29669 -.40609 (346*2π)/4221 weeks
347.32242 -.44309 (347*2π)/4221 weeks
348-.01226 -.61988 (348*2π)/4221 weeks
349-.19147 -.57265 (349*2π)/4221 weeks
350-.23657 -.90343 (350*2π)/4221 weeks
351.03564 -.98809 (351*2π)/4221 weeks
352.06433 -.98762 (352*2π)/4221 weeks
353.29695 -1.1087 (353*2π)/4221 weeks
354.27658 -1.15226 (354*2π)/4221 weeks
355.16899 -1.15788 (355*2π)/4221 weeks
356.18044 -1.01548 (356*2π)/4221 weeks
357.27858 -1.18788 (357*2π)/4221 weeks
358.54835 -1.35681 (358*2π)/4221 weeks
359.57284 -.86154 (359*2π)/4221 weeks
360.39035 -1.1032 (360*2π)/4221 weeks
361.53725 -1.16321 (361*2π)/4221 weeks
362.81469 -.59575 (362*2π)/4221 weeks
363-.04183 -.43066 (363*2π)/4221 weeks
364-.26277 -1.4734 (364*2π)/4221 weeks
365.08796 -1.69319 (365*2π)/4221 weeks
366.12173 -1.37364 (366*2π)/4221 weeks
367-.04936 -1.70994 (367*2π)/4221 weeks
368.23371 -1.71712 (368*2π)/4221 weeks
369.55213 -1.31699 (369*2π)/4221 weeks
370.40746 -.95942 (370*2π)/4221 weeks
371-.1098 -1.16043 (371*2π)/4221 weeks
372.48527 -1.36004 (372*2π)/4221 weeks
373.18132 -1.47266 (373*2π)/4221 weeks
374.03818 -1.79746 (374*2π)/4221 weeks
375.19927 -2.29038 (375*2π)/4221 weeks
376.63931 -2.05544 (376*2π)/4221 weeks
377.28727 -1.83101 (377*2π)/4221 weeks
378.36534 -1.90706 (378*2π)/4221 weeks
379.36153 -2.37941 (379*2π)/4221 weeks
380.56033 -2.04865 (380*2π)/4221 weeks
381.56106 -2.06243 (381*2π)/4221 weeks
382.45562 -2.11196 (382*2π)/4221 weeks
383.89414 -2.52054 (383*2π)/4221 weeks
3841.38649 -1.98432 (384*2π)/4221 weeks
385.71194 -2.46212 (385*2π)/4221 weeks
386.9609 -2.39879 (386*2π)/4221 weeks
3871.12012 -1.96435 (387*2π)/4221 weeks
388.61895 -2.18948 (388*2π)/4221 weeks
3891.22339 -2.39798 (389*2π)/4221 weeks
390.51492 -1.57142 (390*2π)/4221 weeks
391-.01362 -2.67383 (391*2π)/4221 weeks
392.40811 -2.99469 (392*2π)/4221 weeks
393.9517 -3.43674 (393*2π)/4221 weeks
3941.61011 -3.22367 (394*2π)/4221 weeks
3951.45878 -3.26866 (395*2π)/4221 weeks
3962.08174 -3.42866 (396*2π)/4221 weeks
3971.99252 -2.89053 (397*2π)/4221 weeks
3981.50619 -1.77367 (398*2π)/4221 weeks
399.92546 -2.31745 (399*2π)/4221 weeks
4001.91837 -2.46978 (400*2π)/4221 weeks
4011.13194 -2.80324 (401*2π)/4221 weeks
402.61476 -3.32433 (402*2π)/4221 weeks
403.99966 -3.28281 (403*2π)/4221 weeks
404.7328 -2.92521 (404*2π)/4221 weeks
4051.60793 -3.67521 (405*2π)/4221 weeks
4061.83924 -4.16498 (406*2π)/4221 weeks
4071.67292 -5.06288 (407*2π)/4221 weeks
4082.88592 -4.62207 (408*2π)/4221 weeks
4092.1056 -3.37465 (409*2π)/4221 weeks
4101.50015 -5.13794 (410*2π)/4221 weeks
4111.57634 -5.8926 (411*2π)/4221 weeks
4122.64188 -5.81153 (412*2π)/4221 weeks
4131.42292 -7.75781 (413*2π)/4221 weeks
4143.32346 -8.07249 (414*2π)/4221 weeks
4154.64909 -6.13412 (415*2π)/4221 weeks
4163.50541 -6.29532 (416*2π)/4221 weeks
4172.37151 -7.7063 (417*2π)/4221 weeks
4184.93658 -13.15652 (418*2π)/4221 weeks
4197.59583 -12.96049 (419*2π)/4221 weeks
4208.916 -15.16136 (420*2π)/4221 weeks



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