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# Fourier Analysis of SZK (ProShares UltraShort Consumer Goods)

SZK (ProShares UltraShort Consumer Goods) appears to have interesting cyclic behaviour every 46 weeks (8.2305*sine), 49 weeks (8.1047*sine), and 54 weeks (6.125*sine).

SZK (ProShares UltraShort Consumer Goods) has an average price of 101.79 (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 2/1/2007 to 5/29/2018 for SZK (ProShares UltraShort Consumer Goods), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0101.7937   0
137.20368 103.1998 (1*2π)/592592 weeks
2-15.49612 51.90346 (2*2π)/592296 weeks
3-19.36138 17.29695 (3*2π)/592197 weeks
4-2.49083 .36625 (4*2π)/592148 weeks
59.06128 4.51425 (5*2π)/592118 weeks
610.69287 13.3373 (6*2π)/59299 weeks
71.26758 17.90822 (7*2π)/59285 weeks
8-6.25612 11.57973 (8*2π)/59274 weeks
9-3.81805 .96805 (9*2π)/59266 weeks
104.29757 2.32944 (10*2π)/59259 weeks
113.57618 6.12504 (11*2π)/59254 weeks
122.68785 8.10469 (12*2π)/59249 weeks
13-.94292 8.23049 (13*2π)/59246 weeks
14-2.43275 4.98841 (14*2π)/59242 weeks
15-1.14704 2.20326 (15*2π)/59239 weeks
161.31103 1.59154 (16*2π)/59237 weeks
172.29031 3.77226 (17*2π)/59235 weeks
18-.38379 4.21611 (18*2π)/59233 weeks
19.81083 2.04329 (19*2π)/59231 weeks
201.21802 3.13411 (20*2π)/59230 weeks
211.2413 3.05422 (21*2π)/59228 weeks
221.23414 2.8569 (22*2π)/59227 weeks
231.08838 3.84152 (23*2π)/59226 weeks
24-.03503 3.23163 (24*2π)/59225 weeks
25.69789 1.89038 (25*2π)/59224 weeks
261.44042 2.90404 (26*2π)/59223 weeks
271.61378 4.31174 (27*2π)/59222 weeks
28-1.17621 5.63561 (28*2π)/59221 weeks
29-3.00333 2.27104 (29*2π)/59220 weeks
30-1.50682 -.05995 (30*2π)/59220 weeks
31.64381 -.63108 (31*2π)/59219 weeks
322.78035 .86249 (32*2π)/59219 weeks
332.88968 3.40128 (33*2π)/59218 weeks
34.90718 5.09825 (34*2π)/59217 weeks
35-2.59635 3.98495 (35*2π)/59217 weeks
36-2.91509 .55552 (36*2π)/59216 weeks
37.15146 -1.12542 (37*2π)/59216 weeks
382.17335 .69125 (38*2π)/59216 weeks
391.69479 2.42874 (39*2π)/59215 weeks
40.16509 2.78304 (40*2π)/59215 weeks
41-.45129 2.03995 (41*2π)/59214 weeks
42-.40352 1.20138 (42*2π)/59214 weeks
43-.06877 .89373 (43*2π)/59214 weeks
44.9174 .60737 (44*2π)/59213 weeks
45.84415 1.84156 (45*2π)/59213 weeks
46.13969 1.42996 (46*2π)/59213 weeks
47.66276 1.40428 (47*2π)/59213 weeks
48.39878 1.77058 (48*2π)/59212 weeks
49.29372 1.9346 (49*2π)/59212 weeks
50-.18365 2.0295 (50*2π)/59212 weeks
51-.88658 1.12172 (51*2π)/59212 weeks
52-.43946 .84444 (52*2π)/59211 weeks
53.14789 .35714 (53*2π)/59211 weeks
54.52951 .62027 (54*2π)/59211 weeks
55.53444 1.19228 (55*2π)/59211 weeks
56-.02568 1.24024 (56*2π)/59211 weeks
57.20676 .97835 (57*2π)/59210 weeks
58-.18613 .75191 (58*2π)/59210 weeks
59.54241 .03653 (59*2π)/59210 weeks
601.35328 .79149 (60*2π)/59210 weeks
61.73663 1.87665 (61*2π)/59210 weeks
62-.07917 1.77953 (62*2π)/59210 weeks
63-.45001 .90204 (63*2π)/5929 weeks
64-.26016 .32858 (64*2π)/5929 weeks
65.84206 .20839 (65*2π)/5929 weeks
661.04805 1.45514 (66*2π)/5929 weeks
67-.12819 1.64048 (67*2π)/5929 weeks
68-.58493 1.00785 (68*2π)/5929 weeks
69-.5258 -.02065 (69*2π)/5929 weeks
70.59191 -.31771 (70*2π)/5928 weeks
711.34645 .77363 (71*2π)/5928 weeks
72.49781 1.02029 (72*2π)/5928 weeks
73.56572 1.13558 (73*2π)/5928 weeks
74.16635 .75696 (74*2π)/5928 weeks
75.83891 .85639 (75*2π)/5928 weeks
76.26938 1.58846 (76*2π)/5928 weeks
77-.6609 1.12463 (77*2π)/5928 weeks
78-.56242 .18053 (78*2π)/5928 weeks
79.19621 -.4771 (79*2π)/5927 weeks
801.42245 .10498 (80*2π)/5927 weeks
811.00979 1.40311 (81*2π)/5927 weeks
82.14778 1.03022 (82*2π)/5927 weeks
83.1574 1.20671 (83*2π)/5927 weeks
84-.728 .56273 (84*2π)/5927 weeks
85.19433 -.46209 (85*2π)/5927 weeks
861.19273 .09994 (86*2π)/5927 weeks
871.07725 .91424 (87*2π)/5927 weeks
88.48994 1.42324 (88*2π)/5927 weeks
89-.29002 .95646 (89*2π)/5927 weeks
90-.14052 .33353 (90*2π)/5927 weeks
91.01545 .00512 (91*2π)/5927 weeks
92.95499 -.27119 (92*2π)/5926 weeks
931.38453 .69774 (93*2π)/5926 weeks
94.92493 1.41613 (94*2π)/5926 weeks
95.15267 1.32119 (95*2π)/5926 weeks
96-.21858 .80982 (96*2π)/5926 weeks
97.04695 .39349 (97*2π)/5926 weeks
98.53309 .31393 (98*2π)/5926 weeks
99.67955 .70085 (99*2π)/5926 weeks
100.23349 .97814 (100*2π)/5926 weeks
101-.17794 .47304 (101*2π)/5926 weeks
102.64672 .2253 (102*2π)/5926 weeks
103.5706 .89002 (103*2π)/5926 weeks
104.0416 .9337 (104*2π)/5926 weeks
105-.25193 .52279 (105*2π)/5926 weeks
106.04758 -.06624 (106*2π)/5926 weeks
107.68079 -.06131 (107*2π)/5926 weeks
108.76275 .59749 (108*2π)/5925 weeks
109.56749 .94853 (109*2π)/5925 weeks
110-.03457 .87514 (110*2π)/5925 weeks
111-.4448 .17389 (111*2π)/5925 weeks
112.17715 -.44018 (112*2π)/5925 weeks
113.91272 -.39703 (113*2π)/5925 weeks
1141.42795 .44651 (114*2π)/5925 weeks
1151.01455 .97288 (115*2π)/5925 weeks
116.29657 1.30324 (116*2π)/5925 weeks
117-.26901 .78155 (117*2π)/5925 weeks
118-.09188 .0261 (118*2π)/5925 weeks
119.60423 -.31997 (119*2π)/5925 weeks
1201.04242 .33903 (120*2π)/5925 weeks
121.83875 .96339 (121*2π)/5925 weeks
122.38213 1.12134 (122*2π)/5925 weeks
123-.21551 .87247 (123*2π)/5925 weeks
124-.14917 .12618 (124*2π)/5925 weeks
125.29523 -.06033 (125*2π)/5925 weeks
126.59578 .28008 (126*2π)/5925 weeks
127.73642 .53908 (127*2π)/5925 weeks
128.46094 .81165 (128*2π)/5925 weeks
129.06827 .58425 (129*2π)/5925 weeks
130-.05535 .31034 (130*2π)/5925 weeks
131.27147 .05504 (131*2π)/5925 weeks
132.70218 .05036 (132*2π)/5924 weeks
133.86679 .63864 (133*2π)/5924 weeks
134.26996 .80728 (134*2π)/5924 weeks
135.0323 .45671 (135*2π)/5924 weeks
136.30086 .24852 (136*2π)/5924 weeks
137.38207 .42777 (137*2π)/5924 weeks
138.23305 .24794 (138*2π)/5924 weeks
139.53579 .14281 (139*2π)/5924 weeks
140.63515 .54004 (140*2π)/5924 weeks
141.28147 .70319 (141*2π)/5924 weeks
142.05929 .39875 (142*2π)/5924 weeks
143.25584 .03824 (143*2π)/5924 weeks
144.5741 .24049 (144*2π)/5924 weeks
145.63724 .34452 (145*2π)/5924 weeks
146.70859 .67627 (146*2π)/5924 weeks
147.28683 .87613 (147*2π)/5924 weeks
148-.00629 .54483 (148*2π)/5924 weeks
149.05754 .47754 (149*2π)/5924 weeks
150-.06878 .23357 (150*2π)/5924 weeks
151.29604 .0054 (151*2π)/5924 weeks
152.49322 -.10468 (152*2π)/5924 weeks
153.9345 .38531 (153*2π)/5924 weeks
154.44243 1.03199 (154*2π)/5924 weeks
155-.29791 .66626 (155*2π)/5924 weeks
156-.05843 -.03816 (156*2π)/5924 weeks
157.44648 -.05422 (157*2π)/5924 weeks
158.599 .25457 (158*2π)/5924 weeks
159.39589 .59553 (159*2π)/5924 weeks
160.11036 .44009 (160*2π)/5924 weeks
161.11596 .19959 (161*2π)/5924 weeks
162.29208 -.1053 (162*2π)/5924 weeks
163.70443 .17417 (163*2π)/5924 weeks
164.40309 .47119 (164*2π)/5924 weeks
165.47376 .26547 (165*2π)/5924 weeks
166.39042 .27362 (166*2π)/5924 weeks
167.494 .35297 (167*2π)/5924 weeks
168.29395 .51806 (168*2π)/5924 weeks
169.08632 .24027 (169*2π)/5924 weeks
170.56127 .00201 (170*2π)/5923 weeks
171.50705 .54915 (171*2π)/5923 weeks
172.29116 .31495 (172*2π)/5923 weeks
173.36491 .30674 (173*2π)/5923 weeks
174.29479 .35669 (174*2π)/5923 weeks
175.22981 .2401 (175*2π)/5923 weeks
176.37113 .06562 (176*2π)/5923 weeks
177.62042 .3607 (177*2π)/5923 weeks
178.37835 .48026 (178*2π)/5923 weeks
179.2241 .52573 (179*2π)/5923 weeks
180-.02621 .31897 (180*2π)/5923 weeks
181.14234 .05308 (181*2π)/5923 weeks
182.36663 .05079 (182*2π)/5923 weeks
183.39275 .26331 (183*2π)/5923 weeks
184.25143 .30657 (184*2π)/5923 weeks
185.22176 .32004 (185*2π)/5923 weeks
186.1338 .04188 (186*2π)/5923 weeks
187.31361 .01283 (187*2π)/5923 weeks
188.43216 -.0138 (188*2π)/5923 weeks
189.6399 .17458 (189*2π)/5923 weeks
190.60507 .42057 (190*2π)/5923 weeks
191.37668 .55754 (191*2π)/5923 weeks
192.0229 .501 (192*2π)/5923 weeks
193-.04357 .19423 (193*2π)/5923 weeks
194.22689 -.03496 (194*2π)/5923 weeks
195.45511 -.09234 (195*2π)/5923 weeks
196.70719 .21569 (196*2π)/5923 weeks
197.46725 .45504 (197*2π)/5923 weeks
198.3554 .57499 (198*2π)/5923 weeks
199-.01735 .35658 (199*2π)/5923 weeks
200.14307 .07287 (200*2π)/5923 weeks
201.25766 .1012 (201*2π)/5923 weeks
202.50608 .17325 (202*2π)/5923 weeks
203.36533 .44013 (203*2π)/5923 weeks
204.091 .36015 (204*2π)/5923 weeks
205-.03898 .1685 (205*2π)/5923 weeks
206.08243 -.07769 (206*2π)/5923 weeks
207.3539 -.17858 (207*2π)/5923 weeks
208.43278 -.03596 (208*2π)/5923 weeks
209.61417 -.17951 (209*2π)/5923 weeks
210.96503 .40017 (210*2π)/5923 weeks
211.33881 .52388 (211*2π)/5923 weeks
212.29705 .33825 (212*2π)/5923 weeks
213.18029 .27812 (213*2π)/5923 weeks
214.33402 .17204 (214*2π)/5923 weeks
215.39506 .38646 (215*2π)/5923 weeks
216.09897 .19696 (216*2π)/5923 weeks
217.3722 .24525 (217*2π)/5923 weeks
218-.02737 .37176 (218*2π)/5923 weeks
219.14011 -.09187 (219*2π)/5923 weeks
220.13598 .06254 (220*2π)/5923 weeks
221.17467 -.2526 (221*2π)/5923 weeks
222.6819 -.24335 (222*2π)/5923 weeks
223.77513 .29785 (223*2π)/5923 weeks
224.49305 .56724 (224*2π)/5923 weeks
225-.00773 .48131 (225*2π)/5923 weeks
226-.11052 .00543 (226*2π)/5923 weeks
227.33234 -.21236 (227*2π)/5923 weeks
228.61225 -.06144 (228*2π)/5923 weeks
229.75627 .27176 (229*2π)/5923 weeks
230.27796 .83872 (230*2π)/5923 weeks
231-.28164 .35427 (231*2π)/5923 weeks
232-.1779 -.26353 (232*2π)/5923 weeks
233.43195 -.47613 (233*2π)/5923 weeks
234.79165 .01327 (234*2π)/5923 weeks
235.52829 .40254 (235*2π)/5923 weeks
236.2823 .23655 (236*2π)/5923 weeks
237.38703 .28037 (237*2π)/5922 weeks
238.24042 .31236 (238*2π)/5922 weeks
239.17225 .20642 (239*2π)/5922 weeks
240.22491 .21864 (240*2π)/5922 weeks
241-.00144 .2408 (241*2π)/5922 weeks
242-.00722 -.1587 (242*2π)/5922 weeks
243.36066 -.24016 (243*2π)/5922 weeks
244.67617 -.0647 (244*2π)/5922 weeks
245.62084 .51747 (245*2π)/5922 weeks
246-.09512 .42206 (246*2π)/5922 weeks
247-.06681 .02149 (247*2π)/5922 weeks
248.04958 -.14646 (248*2π)/5922 weeks
249.32612 -.31289 (249*2π)/5922 weeks
250.659 -.12547 (250*2π)/5922 weeks
251.54882 .34467 (251*2π)/5922 weeks
252.12848 .47279 (252*2π)/5922 weeks
253-.15876 .07859 (253*2π)/5922 weeks
254-.05569 -.39617 (254*2π)/5922 weeks
255.49604 -.51944 (255*2π)/5922 weeks
256.80917 -.11313 (256*2π)/5922 weeks
257.75309 .26513 (257*2π)/5922 weeks
258.19401 .55874 (258*2π)/5922 weeks
259.05107 .10955 (259*2π)/5922 weeks
260.03218 -.04391 (260*2π)/5922 weeks
261.33008 -.25844 (261*2π)/5922 weeks
262.50163 .01235 (262*2π)/5922 weeks
263.40267 .02794 (263*2π)/5922 weeks
264.3864 .17219 (264*2π)/5922 weeks
265.12997 .24777 (265*2π)/5922 weeks
266-.02418 -.14368 (266*2π)/5922 weeks
267.23602 -.18253 (267*2π)/5922 weeks
268.36483 -.41722 (268*2π)/5922 weeks
269.79276 -.18722 (269*2π)/5922 weeks
270.71723 .28469 (270*2π)/5922 weeks
271.46353 .44783 (271*2π)/5922 weeks
272.00884 .35329 (272*2π)/5922 weeks
273-.06948 .02427 (273*2π)/5922 weeks
274.04344 -.29104 (274*2π)/5922 weeks
275.33905 -.40931 (275*2π)/5922 weeks
276.71249 -.26672 (276*2π)/5922 weeks
277.7411 .2961 (277*2π)/5922 weeks
278.28208 .4013 (278*2π)/5922 weeks
279.07557 .17717 (279*2π)/5922 weeks
280-.16592 -.04613 (280*2π)/5922 weeks
281.15273 -.47251 (281*2π)/5922 weeks
282.60329 -.3891 (282*2π)/5922 weeks
283.7322 .1693 (283*2π)/5922 weeks
284.2914 .23073 (284*2π)/5922 weeks
285.03224 .02733 (285*2π)/5922 weeks
286.09961 -.26514 (286*2π)/5922 weeks
287.29762 -.36735 (287*2π)/5922 weeks
288.68727 -.51457 (288*2π)/5922 weeks
289.96575 .07154 (289*2π)/5922 weeks
290.47082 .52322 (290*2π)/5922 weeks
291.03673 .19899 (291*2π)/5922 weeks
292.09532 -.14637 (292*2π)/5922 weeks
293.28993 -.34036 (293*2π)/5922 weeks
294.43066 -.28089 (294*2π)/5922 weeks
295.65191 -.34897 (295*2π)/5922 weeks
296.85837   (296*2π)/5922 weeks
297.65191 .34897 (297*2π)/5922 weeks
298.43066 .28089 (298*2π)/5922 weeks
299.28993 .34036 (299*2π)/5922 weeks
300.09532 .14637 (300*2π)/5922 weeks
301.03673 -.19899 (301*2π)/5922 weeks
302.47082 -.52322 (302*2π)/5922 weeks
303.96575 -.07154 (303*2π)/5922 weeks
304.68727 .51457 (304*2π)/5922 weeks
305.29762 .36735 (305*2π)/5922 weeks
306.09961 .26514 (306*2π)/5922 weeks
307.03224 -.02733 (307*2π)/5922 weeks
308.2914 -.23073 (308*2π)/5922 weeks
309.7322 -.1693 (309*2π)/5922 weeks
310.60329 .3891 (310*2π)/5922 weeks
311.15273 .47251 (311*2π)/5922 weeks
312-.16592 .04613 (312*2π)/5922 weeks
313.07557 -.17717 (313*2π)/5922 weeks
314.28208 -.4013 (314*2π)/5922 weeks
315.7411 -.2961 (315*2π)/5922 weeks
316.71249 .26672 (316*2π)/5922 weeks
317.33905 .40931 (317*2π)/5922 weeks
318.04344 .29104 (318*2π)/5922 weeks
319-.06948 -.02427 (319*2π)/5922 weeks
320.00884 -.35329 (320*2π)/5922 weeks
321.46353 -.44783 (321*2π)/5922 weeks
322.71723 -.28469 (322*2π)/5922 weeks
323.79276 .18722 (323*2π)/5922 weeks
324.36483 .41722 (324*2π)/5922 weeks
325.23602 .18253 (325*2π)/5922 weeks
326-.02418 .14368 (326*2π)/5922 weeks
327.12997 -.24777 (327*2π)/5922 weeks
328.3864 -.17219 (328*2π)/5922 weeks
329.40267 -.02794 (329*2π)/5922 weeks
330.50163 -.01235 (330*2π)/5922 weeks
331.33008 .25844 (331*2π)/5922 weeks
332.03218 .04391 (332*2π)/5922 weeks
333.05107 -.10955 (333*2π)/5922 weeks
334.19401 -.55874 (334*2π)/5922 weeks
335.75309 -.26513 (335*2π)/5922 weeks
336.80917 .11313 (336*2π)/5922 weeks
337.49604 .51944 (337*2π)/5922 weeks
338-.05569 .39617 (338*2π)/5922 weeks
339-.15876 -.07859 (339*2π)/5922 weeks
340.12848 -.47279 (340*2π)/5922 weeks
341.54882 -.34467 (341*2π)/5922 weeks
342.659 .12547 (342*2π)/5922 weeks
343.32612 .31289 (343*2π)/5922 weeks
344.04958 .14646 (344*2π)/5922 weeks
345-.06681 -.02149 (345*2π)/5922 weeks
346-.09512 -.42206 (346*2π)/5922 weeks
347.62084 -.51747 (347*2π)/5922 weeks
348.67617 .0647 (348*2π)/5922 weeks
349.36066 .24016 (349*2π)/5922 weeks
350-.00722 .1587 (350*2π)/5922 weeks
351-.00144 -.2408 (351*2π)/5922 weeks
352.22491 -.21864 (352*2π)/5922 weeks
353.17225 -.20642 (353*2π)/5922 weeks
354.24042 -.31236 (354*2π)/5922 weeks
355.38703 -.28037 (355*2π)/5922 weeks
356.2823 -.23655 (356*2π)/5922 weeks
357.52829 -.40254 (357*2π)/5922 weeks
358.79165 -.01327 (358*2π)/5922 weeks
359.43195 .47613 (359*2π)/5922 weeks
360-.1779 .26353 (360*2π)/5922 weeks
361-.28164 -.35427 (361*2π)/5922 weeks
362.27796 -.83872 (362*2π)/5922 weeks
363.75627 -.27176 (363*2π)/5922 weeks
364.61225 .06144 (364*2π)/5922 weeks
365.33234 .21236 (365*2π)/5922 weeks
366-.11052 -.00543 (366*2π)/5922 weeks
367-.00773 -.48131 (367*2π)/5922 weeks
368.49305 -.56724 (368*2π)/5922 weeks
369.77513 -.29785 (369*2π)/5922 weeks
370.6819 .24335 (370*2π)/5922 weeks
371.17467 .2526 (371*2π)/5922 weeks
372.13598 -.06254 (372*2π)/5922 weeks
373.14011 .09187 (373*2π)/5922 weeks
374-.02737 -.37176 (374*2π)/5922 weeks
375.3722 -.24525 (375*2π)/5922 weeks
376.09897 -.19696 (376*2π)/5922 weeks
377.39506 -.38646 (377*2π)/5922 weeks
378.33402 -.17204 (378*2π)/5922 weeks
379.18029 -.27812 (379*2π)/5922 weeks
380.29705 -.33825 (380*2π)/5922 weeks
381.33881 -.52388 (381*2π)/5922 weeks
382.96503 -.40017 (382*2π)/5922 weeks
383.61417 .17951 (383*2π)/5922 weeks
384.43278 .03596 (384*2π)/5922 weeks
385.3539 .17858 (385*2π)/5922 weeks
386.08243 .07769 (386*2π)/5922 weeks
387-.03898 -.1685 (387*2π)/5922 weeks
388.091 -.36015 (388*2π)/5922 weeks
389.36533 -.44013 (389*2π)/5922 weeks
390.50608 -.17325 (390*2π)/5922 weeks
391.25766 -.1012 (391*2π)/5922 weeks
392.14307 -.07287 (392*2π)/5922 weeks
393-.01735 -.35658 (393*2π)/5922 weeks
394.3554 -.57499 (394*2π)/5922 weeks
395.46725 -.45504 (395*2π)/5921 weeks
396.70719 -.21569 (396*2π)/5921 weeks
397.45511 .09234 (397*2π)/5921 weeks
398.22689 .03496 (398*2π)/5921 weeks
399-.04357 -.19423 (399*2π)/5921 weeks
400.0229 -.501 (400*2π)/5921 weeks
401.37668 -.55754 (401*2π)/5921 weeks
402.60507 -.42057 (402*2π)/5921 weeks
403.6399 -.17458 (403*2π)/5921 weeks
404.43216 .0138 (404*2π)/5921 weeks
405.31361 -.01283 (405*2π)/5921 weeks
406.1338 -.04188 (406*2π)/5921 weeks
407.22176 -.32004 (407*2π)/5921 weeks
408.25143 -.30657 (408*2π)/5921 weeks
409.39275 -.26331 (409*2π)/5921 weeks
410.36663 -.05079 (410*2π)/5921 weeks
411.14234 -.05308 (411*2π)/5921 weeks
412-.02621 -.31897 (412*2π)/5921 weeks
413.2241 -.52573 (413*2π)/5921 weeks
414.37835 -.48026 (414*2π)/5921 weeks
415.62042 -.3607 (415*2π)/5921 weeks
416.37113 -.06562 (416*2π)/5921 weeks
417.22981 -.2401 (417*2π)/5921 weeks
418.29479 -.35669 (418*2π)/5921 weeks
419.36491 -.30674 (419*2π)/5921 weeks
420.29116 -.31495 (420*2π)/5921 weeks
421.50705 -.54915 (421*2π)/5921 weeks
422.56127 -.00201 (422*2π)/5921 weeks
423.08632 -.24027 (423*2π)/5921 weeks
424.29395 -.51806 (424*2π)/5921 weeks
425.494 -.35297 (425*2π)/5921 weeks
426.39042 -.27362 (426*2π)/5921 weeks
427.47376 -.26547 (427*2π)/5921 weeks
428.40309 -.47119 (428*2π)/5921 weeks
429.70443 -.17417 (429*2π)/5921 weeks
430.29208 .1053 (430*2π)/5921 weeks
431.11596 -.19959 (431*2π)/5921 weeks
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