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Fourier Analysis of SCO (ProShares UltraShort Bloomberg Crude Oil ETF)


SCO (ProShares UltraShort Bloomberg Crude Oil ETF) appears to have interesting cyclic behaviour every 45 weeks (13.4869*sine), 41 weeks (6.8526*sine), and 30 weeks (4.0728*cosine).

SCO (ProShares UltraShort Bloomberg Crude Oil ETF) has an average price of 65.65 (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 11/25/2008 to 7/10/2017 for SCO (ProShares UltraShort Bloomberg Crude Oil ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
065.65368   0 
134.24743 -6.68754 (1*2π)/451451 weeks
2-.87318 -5.08217 (2*2π)/451226 weeks
3-6.50693 12.99657 (3*2π)/451150 weeks
44.55444 14.66994 (4*2π)/451113 weeks
56.21962 13.76111 (5*2π)/45190 weeks
68.05813 12.75525 (6*2π)/45175 weeks
75.99203 8.92683 (7*2π)/45164 weeks
8-2.81757 3.66849 (8*2π)/45156 weeks
9-2.5296 9.42106 (9*2π)/45150 weeks
103.87861 13.48694 (10*2π)/45145 weeks
112.88751 6.85257 (11*2π)/45141 weeks
122.7105 3.49231 (12*2π)/45138 weeks
13.3819 3.40044 (13*2π)/45135 weeks
14-1.66384 .09903 (14*2π)/45132 weeks
15-4.07278 .572 (15*2π)/45130 weeks
16-4.05668 6.41473 (16*2π)/45128 weeks
171.06133 5.56905 (17*2π)/45127 weeks
18.90968 .90853 (18*2π)/45125 weeks
19-1.5563 -2.75807 (19*2π)/45124 weeks
20-3.87397 .86866 (20*2π)/45123 weeks
21-2.45465 1.37197 (21*2π)/45121 weeks
22.78183 2.48234 (22*2π)/45121 weeks
23.75764 1.72825 (23*2π)/45120 weeks
241.31044 .54875 (24*2π)/45119 weeks
25-.87041 2.41303 (25*2π)/45118 weeks
26-.69931 1.77707 (26*2π)/45117 weeks
271.62805 .56772 (27*2π)/45117 weeks
281.30408 -.24831 (28*2π)/45116 weeks
29.37498 .38823 (29*2π)/45116 weeks
30.88069 .26009 (30*2π)/45115 weeks
31.58871 -.23037 (31*2π)/45115 weeks
32-.6883 .14415 (32*2π)/45114 weeks
33-.58084 .50059 (33*2π)/45114 weeks
341.40641 .83425 (34*2π)/45113 weeks
351.51521 .95111 (35*2π)/45113 weeks
361.0602 .71416 (36*2π)/45113 weeks
37.80857 .56017 (37*2π)/45112 weeks
38.32688 -.23848 (38*2π)/45112 weeks
39.70258 1.25903 (39*2π)/45112 weeks
402.10203 2.26083 (40*2π)/45111 weeks
412.74496 1.30156 (41*2π)/45111 weeks
421.77892 .98168 (42*2π)/45111 weeks
43.74077 2.30087 (43*2π)/45110 weeks
441.40747 3.13716 (44*2π)/45110 weeks
45.55563 2.51328 (45*2π)/45110 weeks
46-.751 2.77109 (46*2π)/45110 weeks
47-.60038 3.26866 (47*2π)/45110 weeks
48-.10559 2.38876 (48*2π)/4519 weeks
49-.36577 1.34992 (49*2π)/4519 weeks
50-1.71252 .99297 (50*2π)/4519 weeks
51-.60796 1.21228 (51*2π)/4519 weeks
52-.06927 1.29044 (52*2π)/4519 weeks
53-.43755 .51649 (53*2π)/4519 weeks
54-.56185 .6807 (54*2π)/4518 weeks
55-1.02892 .47085 (55*2π)/4518 weeks
56-1.87436 -.19453 (56*2π)/4518 weeks
57-1.41105 -.01304 (57*2π)/4518 weeks
58-1.10897 1.37581 (58*2π)/4518 weeks
59-.04577 1.39227 (59*2π)/4518 weeks
60-.14009 1.13717 (60*2π)/4518 weeks
61-.18123 1.38858 (61*2π)/4517 weeks
62-.19819 .26749 (62*2π)/4517 weeks
63.17181 -1.18087 (63*2π)/4517 weeks
64-.32128 -.82948 (64*2π)/4517 weeks
65-.51196 .23359 (65*2π)/4517 weeks
66.00666 .1595 (66*2π)/4517 weeks
67.20406 -.02292 (67*2π)/4517 weeks
68-.48684 .28433 (68*2π)/4517 weeks
69-.62754 .01719 (69*2π)/4517 weeks
70.03453 .14366 (70*2π)/4516 weeks
71.1827 1.2187 (71*2π)/4516 weeks
72.33645 1.01678 (72*2π)/4516 weeks
731.14307 .35656 (73*2π)/4516 weeks
74.86509 .30089 (74*2π)/4516 weeks
75.54763 .52299 (75*2π)/4516 weeks
76.01188 .37879 (76*2π)/4516 weeks
77-.21984 .56643 (77*2π)/4516 weeks
78-.54272 .94547 (78*2π)/4516 weeks
79.65753 .67066 (79*2π)/4516 weeks
801.17589 -.09513 (80*2π)/4516 weeks
811.15311 -.92643 (81*2π)/4516 weeks
82.16581 -.5048 (82*2π)/4516 weeks
83-.31423 .53617 (83*2π)/4515 weeks
84-.43619 1.13617 (84*2π)/4515 weeks
85.68626 1.11631 (85*2π)/4515 weeks
861.02874 .43886 (86*2π)/4515 weeks
87.25256 .00815 (87*2π)/4515 weeks
88-.46556 .43512 (88*2π)/4515 weeks
89-.33934 .88699 (89*2π)/4515 weeks
90.26549 .8579 (90*2π)/4515 weeks
91.51052 .59887 (91*2π)/4515 weeks
92.222 .41124 (92*2π)/4515 weeks
93-.09432 .40589 (93*2π)/4515 weeks
94-.4164 -.1512 (94*2π)/4515 weeks
95-.53008 .49579 (95*2π)/4515 weeks
96-.27662 .6921 (96*2π)/4515 weeks
97.226 .54453 (97*2π)/4515 weeks
98.21815 -.22024 (98*2π)/4515 weeks
99-.14672 -.37388 (99*2π)/4515 weeks
100-.26826 -.4936 (100*2π)/4515 weeks
101-.25329 .08059 (101*2π)/4514 weeks
102.01818 .52037 (102*2π)/4514 weeks
103.20512 -.17419 (103*2π)/4514 weeks
104.11307 -.78599 (104*2π)/4514 weeks
105-.32002 -.56755 (105*2π)/4514 weeks
106-.19612 .36956 (106*2π)/4514 weeks
107.34575 .49371 (107*2π)/4514 weeks
1081.21923 -.29183 (108*2π)/4514 weeks
109.99153 -.99913 (109*2π)/4514 weeks
110.52314 -.64496 (110*2π)/4514 weeks
111.18114 .07224 (111*2π)/4514 weeks
112.56662 .25427 (112*2π)/4514 weeks
1131.48004 .36022 (113*2π)/4514 weeks
1141.32937 .36748 (114*2π)/4514 weeks
115.81171 -.10599 (115*2π)/4514 weeks
116.21426 .03115 (116*2π)/4514 weeks
117.07019 .55692 (117*2π)/4514 weeks
118.60727 .49159 (118*2π)/4514 weeks
119.98866 .13695 (119*2π)/4514 weeks
120.52195 .09855 (120*2π)/4514 weeks
121.38371 .06343 (121*2π)/4514 weeks
122.46964 .23424 (122*2π)/4514 weeks
123.44235 .54624 (123*2π)/4514 weeks
1241.14814 .84658 (124*2π)/4514 weeks
1251.68585 .89737 (125*2π)/4514 weeks
1261.19633 .34893 (126*2π)/4514 weeks
127.41787 .33221 (127*2π)/4514 weeks
128.30861 .67822 (128*2π)/4514 weeks
129.38345 .92401 (129*2π)/4513 weeks
130.49322 .52172 (130*2π)/4513 weeks
131.59751 .74643 (131*2π)/4513 weeks
132.50748 .85018 (132*2π)/4513 weeks
133.10084 .71701 (133*2π)/4513 weeks
134.03684 .5865 (134*2π)/4513 weeks
135.41267 .75841 (135*2π)/4513 weeks
136.55021 .71861 (136*2π)/4513 weeks
137.1088 .54804 (137*2π)/4513 weeks
138-.02513 .61876 (138*2π)/4513 weeks
139.04574 .65991 (139*2π)/4513 weeks
140.07693 .1418 (140*2π)/4513 weeks
141-.28391 .46843 (141*2π)/4513 weeks
142.02654 .90499 (142*2π)/4513 weeks
143.58408 .69732 (143*2π)/4513 weeks
144.78138 .30845 (144*2π)/4513 weeks
145.44297 .12812 (145*2π)/4513 weeks
146.36404 .48944 (146*2π)/4513 weeks
147.3322 .32079 (147*2π)/4513 weeks
148.54327 .46804 (148*2π)/4513 weeks
149.35454 .58086 (149*2π)/4513 weeks
150.18682 .37958 (150*2π)/4513 weeks
151-.03484 .53004 (151*2π)/4513 weeks
152.18819 .87098 (152*2π)/4513 weeks
153.39521 1.26014 (153*2π)/4513 weeks
154.07067 .9245 (154*2π)/4513 weeks
155-.18284 .5551 (155*2π)/4513 weeks
156-.05924 1.10206 (156*2π)/4513 weeks
157.23091 1.33041 (157*2π)/4513 weeks
158.34584 1.17345 (158*2π)/4513 weeks
159.23021 1.08269 (159*2π)/4513 weeks
160-.19035 .96862 (160*2π)/4513 weeks
161-.52012 .73277 (161*2π)/4513 weeks
162-.57818 .68603 (162*2π)/4513 weeks
163-.54229 .72197 (163*2π)/4513 weeks
164-.78178 .45801 (164*2π)/4513 weeks
165-.44912 .64558 (165*2π)/4513 weeks
166-.28644 .58393 (166*2π)/4513 weeks
167-.05696 .14778 (167*2π)/4513 weeks
168-.36198 .33876 (168*2π)/4513 weeks
169-.75116 .44046 (169*2π)/4513 weeks
170-.56209 .653 (170*2π)/4513 weeks
171-.45431 .82053 (171*2π)/4513 weeks
172-.50768 .65934 (172*2π)/4513 weeks
173-.4964 .35881 (173*2π)/4513 weeks
174-.5598 -.02489 (174*2π)/4513 weeks
175-.73696 .21686 (175*2π)/4513 weeks
176-.60224 .07445 (176*2π)/4513 weeks
177-.22514 -.02046 (177*2π)/4513 weeks
178-.44741 -.31098 (178*2π)/4513 weeks
179-.48746 -.52609 (179*2π)/4513 weeks
180-.33388 -.45854 (180*2π)/4513 weeks
181-.21915 -.34687 (181*2π)/4512 weeks
182-.21921 .1196 (182*2π)/4512 weeks
183-.24526 .28034 (183*2π)/4512 weeks
184.07985 .01936 (184*2π)/4512 weeks
185.27529 -.0125 (185*2π)/4512 weeks
186.05159 -.22309 (186*2π)/4512 weeks
187-.01363 -.17319 (187*2π)/4512 weeks
188-.14933 -.00903 (188*2π)/4512 weeks
189-.07396 .05753 (189*2π)/4512 weeks
190-.12364 .17461 (190*2π)/4512 weeks
191-.06845 .2166 (191*2π)/4512 weeks
192-.02172 .26546 (192*2π)/4512 weeks
193.01317 .09571 (193*2π)/4512 weeks
194-.01672 .02754 (194*2π)/4512 weeks
195-.07157 -.19777 (195*2π)/4512 weeks
196-.23642 -.31069 (196*2π)/4512 weeks
197-.15281 .08489 (197*2π)/4512 weeks
198-.06148 .01301 (198*2π)/4512 weeks
199.39293 -.22488 (199*2π)/4512 weeks
200.07165 -.24631 (200*2π)/4512 weeks
201-.10076 -.07607 (201*2π)/4512 weeks
202-.01852 .06385 (202*2π)/4512 weeks
203-.20213 .01579 (203*2π)/4512 weeks
204-.07539 .02402 (204*2π)/4512 weeks
205.01084 -.00685 (205*2π)/4512 weeks
206.36711 -.0663 (206*2π)/4512 weeks
207.32619 .16575 (207*2π)/4512 weeks
208.2986 .04393 (208*2π)/4512 weeks
209.36487 -.04468 (209*2π)/4512 weeks
210.19621 .14763 (210*2π)/4512 weeks
211.37346 .3442 (211*2π)/4512 weeks
212.58157 .06916 (212*2π)/4512 weeks
213.09869 -.00933 (213*2π)/4512 weeks
214-.40265 .07731 (214*2π)/4512 weeks
215-.02525 .07292 (215*2π)/4512 weeks
216.32086 -.15172 (216*2π)/4512 weeks
217.19136 -.13021 (217*2π)/4512 weeks
218-.05656 .15603 (218*2π)/4512 weeks
219-.2468 .08829 (219*2π)/4512 weeks
220-.34183 -.1213 (220*2π)/4512 weeks
221-.00494 .08702 (221*2π)/4512 weeks
222.28198 .07573 (222*2π)/4512 weeks
223.09618 .16022 (223*2π)/4512 weeks
224.0248 .30156 (224*2π)/4512 weeks
225.13372 .352 (225*2π)/4512 weeks
226.13372 -.352 (226*2π)/4512 weeks
227.0248 -.30156 (227*2π)/4512 weeks
228.09618 -.16022 (228*2π)/4512 weeks
229.28198 -.07573 (229*2π)/4512 weeks
230-.00494 -.08702 (230*2π)/4512 weeks
231-.34183 .1213 (231*2π)/4512 weeks
232-.2468 -.08829 (232*2π)/4512 weeks
233-.05656 -.15603 (233*2π)/4512 weeks
234.19136 .13021 (234*2π)/4512 weeks
235.32086 .15172 (235*2π)/4512 weeks
236-.02525 -.07292 (236*2π)/4512 weeks
237-.40265 -.07731 (237*2π)/4512 weeks
238.09869 .00933 (238*2π)/4512 weeks
239.58157 -.06916 (239*2π)/4512 weeks
240.37346 -.3442 (240*2π)/4512 weeks
241.19621 -.14763 (241*2π)/4512 weeks
242.36487 .04468 (242*2π)/4512 weeks
243.2986 -.04393 (243*2π)/4512 weeks
244.32619 -.16575 (244*2π)/4512 weeks
245.36711 .0663 (245*2π)/4512 weeks
246.01084 .00685 (246*2π)/4512 weeks
247-.07539 -.02402 (247*2π)/4512 weeks
248-.20213 -.01579 (248*2π)/4512 weeks
249-.01852 -.06385 (249*2π)/4512 weeks
250-.10076 .07607 (250*2π)/4512 weeks
251.07165 .24631 (251*2π)/4512 weeks
252.39293 .22488 (252*2π)/4512 weeks
253-.06148 -.01301 (253*2π)/4512 weeks
254-.15281 -.08489 (254*2π)/4512 weeks
255-.23642 .31069 (255*2π)/4512 weeks
256-.07157 .19777 (256*2π)/4512 weeks
257-.01672 -.02754 (257*2π)/4512 weeks
258.01317 -.09571 (258*2π)/4512 weeks
259-.02172 -.26546 (259*2π)/4512 weeks
260-.06845 -.2166 (260*2π)/4512 weeks
261-.12364 -.17461 (261*2π)/4512 weeks
262-.07396 -.05753 (262*2π)/4512 weeks
263-.14933 .00903 (263*2π)/4512 weeks
264-.01363 .17319 (264*2π)/4512 weeks
265.05159 .22309 (265*2π)/4512 weeks
266.27529 .0125 (266*2π)/4512 weeks
267.07985 -.01936 (267*2π)/4512 weeks
268-.24526 -.28034 (268*2π)/4512 weeks
269-.21921 -.1196 (269*2π)/4512 weeks
270-.21915 .34687 (270*2π)/4512 weeks
271-.33388 .45854 (271*2π)/4512 weeks
272-.48746 .52609 (272*2π)/4512 weeks
273-.44741 .31098 (273*2π)/4512 weeks
274-.22514 .02046 (274*2π)/4512 weeks
275-.60224 -.07445 (275*2π)/4512 weeks
276-.73696 -.21686 (276*2π)/4512 weeks
277-.5598 .02489 (277*2π)/4512 weeks
278-.4964 -.35881 (278*2π)/4512 weeks
279-.50768 -.65934 (279*2π)/4512 weeks
280-.45431 -.82053 (280*2π)/4512 weeks
281-.56209 -.653 (281*2π)/4512 weeks
282-.75116 -.44046 (282*2π)/4512 weeks
283-.36198 -.33876 (283*2π)/4512 weeks
284-.05696 -.14778 (284*2π)/4512 weeks
285-.28644 -.58393 (285*2π)/4512 weeks
286-.44912 -.64558 (286*2π)/4512 weeks
287-.78178 -.45801 (287*2π)/4512 weeks
288-.54229 -.72197 (288*2π)/4512 weeks
289-.57818 -.68603 (289*2π)/4512 weeks
290-.52012 -.73277 (290*2π)/4512 weeks
291-.19035 -.96862 (291*2π)/4512 weeks
292.23021 -1.08269 (292*2π)/4512 weeks
293.34584 -1.17345 (293*2π)/4512 weeks
294.23091 -1.33041 (294*2π)/4512 weeks
295-.05924 -1.10206 (295*2π)/4512 weeks
296-.18284 -.5551 (296*2π)/4512 weeks
297.07067 -.9245 (297*2π)/4512 weeks
298.39521 -1.26014 (298*2π)/4512 weeks
299.18819 -.87098 (299*2π)/4512 weeks
300-.03484 -.53004 (300*2π)/4512 weeks
301.18682 -.37958 (301*2π)/4511 weeks
302.35454 -.58086 (302*2π)/4511 weeks
303.54327 -.46804 (303*2π)/4511 weeks
304.3322 -.32079 (304*2π)/4511 weeks
305.36404 -.48944 (305*2π)/4511 weeks
306.44297 -.12812 (306*2π)/4511 weeks
307.78138 -.30845 (307*2π)/4511 weeks
308.58408 -.69732 (308*2π)/4511 weeks
309.02654 -.90499 (309*2π)/4511 weeks
310-.28391 -.46843 (310*2π)/4511 weeks
311.07693 -.1418 (311*2π)/4511 weeks
312.04574 -.65991 (312*2π)/4511 weeks
313-.02513 -.61876 (313*2π)/4511 weeks
314.1088 -.54804 (314*2π)/4511 weeks
315.55021 -.71861 (315*2π)/4511 weeks
316.41267 -.75841 (316*2π)/4511 weeks
317.03684 -.5865 (317*2π)/4511 weeks
318.10084 -.71701 (318*2π)/4511 weeks
319.50748 -.85018 (319*2π)/4511 weeks
320.59751 -.74643 (320*2π)/4511 weeks
321.49322 -.52172 (321*2π)/4511 weeks
322.38345 -.92401 (322*2π)/4511 weeks
323.30861 -.67822 (323*2π)/4511 weeks
324.41787 -.33221 (324*2π)/4511 weeks
3251.19633 -.34893 (325*2π)/4511 weeks
3261.68585 -.89737 (326*2π)/4511 weeks
3271.14814 -.84658 (327*2π)/4511 weeks
328.44235 -.54624 (328*2π)/4511 weeks
329.46964 -.23424 (329*2π)/4511 weeks
330.38371 -.06343 (330*2π)/4511 weeks
331.52195 -.09855 (331*2π)/4511 weeks
332.98866 -.13695 (332*2π)/4511 weeks
333.60727 -.49159 (333*2π)/4511 weeks
334.07019 -.55692 (334*2π)/4511 weeks
335.21426 -.03115 (335*2π)/4511 weeks
336.81171 .10599 (336*2π)/4511 weeks
3371.32937 -.36748 (337*2π)/4511 weeks
3381.48004 -.36022 (338*2π)/4511 weeks
339.56662 -.25427 (339*2π)/4511 weeks
340.18114 -.07224 (340*2π)/4511 weeks
341.52314 .64496 (341*2π)/4511 weeks
342.99153 .99913 (342*2π)/4511 weeks
3431.21923 .29183 (343*2π)/4511 weeks
344.34575 -.49371 (344*2π)/4511 weeks
345-.19612 -.36956 (345*2π)/4511 weeks
346-.32002 .56755 (346*2π)/4511 weeks
347.11307 .78599 (347*2π)/4511 weeks
348.20512 .17419 (348*2π)/4511 weeks
349.01818 -.52037 (349*2π)/4511 weeks
350-.25329 -.08059 (350*2π)/4511 weeks
351-.26826 .4936 (351*2π)/4511 weeks
352-.14672 .37388 (352*2π)/4511 weeks
353.21815 .22024 (353*2π)/4511 weeks
354.226 -.54453 (354*2π)/4511 weeks
355-.27662 -.6921 (355*2π)/4511 weeks
356-.53008 -.49579 (356*2π)/4511 weeks
357-.4164 .1512 (357*2π)/4511 weeks
358-.09432 -.40589 (358*2π)/4511 weeks
359.222 -.41124 (359*2π)/4511 weeks
360.51052 -.59887 (360*2π)/4511 weeks
361.26549 -.8579 (361*2π)/4511 weeks
362-.33934 -.88699 (362*2π)/4511 weeks
363-.46556 -.43512 (363*2π)/4511 weeks
364.25256 -.00815 (364*2π)/4511 weeks
3651.02874 -.43886 (365*2π)/4511 weeks
366.68626 -1.11631 (366*2π)/4511 weeks
367-.43619 -1.13617 (367*2π)/4511 weeks
368-.31423 -.53617 (368*2π)/4511 weeks
369.16581 .5048 (369*2π)/4511 weeks
3701.15311 .92643 (370*2π)/4511 weeks
3711.17589 .09513 (371*2π)/4511 weeks
372.65753 -.67066 (372*2π)/4511 weeks
373-.54272 -.94547 (373*2π)/4511 weeks
374-.21984 -.56643 (374*2π)/4511 weeks
375.01188 -.37879 (375*2π)/4511 weeks
376.54763 -.52299 (376*2π)/4511 weeks
377.86509 -.30089 (377*2π)/4511 weeks
3781.14307 -.35656 (378*2π)/4511 weeks
379.33645 -1.01678 (379*2π)/4511 weeks
380.1827 -1.2187 (380*2π)/4511 weeks
381.03453 -.14366 (381*2π)/4511 weeks
382-.62754 -.01719 (382*2π)/4511 weeks
383-.48684 -.28433 (383*2π)/4511 weeks
384.20406 .02292 (384*2π)/4511 weeks
385.00666 -.1595 (385*2π)/4511 weeks
386-.51196 -.23359 (386*2π)/4511 weeks
387-.32128 .82948 (387*2π)/4511 weeks
388.17181 1.18087 (388*2π)/4511 weeks
389-.19819 -.26749 (389*2π)/4511 weeks
390-.18123 -1.38858 (390*2π)/4511 weeks
391-.14009 -1.13717 (391*2π)/4511 weeks
392-.04577 -1.39227 (392*2π)/4511 weeks
393-1.10897 -1.37581 (393*2π)/4511 weeks
394-1.41105 .01304 (394*2π)/4511 weeks
395-1.87436 .19453 (395*2π)/4511 weeks
396-1.02892 -.47085 (396*2π)/4511 weeks
397-.56185 -.6807 (397*2π)/4511 weeks
398-.43755 -.51649 (398*2π)/4511 weeks
399-.06927 -1.29044 (399*2π)/4511 weeks
400-.60796 -1.21228 (400*2π)/4511 weeks
401-1.71252 -.99297 (401*2π)/4511 weeks
402-.36577 -1.34992 (402*2π)/4511 weeks
403-.10559 -2.38876 (403*2π)/4511 weeks
404-.60038 -3.26866 (404*2π)/4511 weeks
405-.751 -2.77109 (405*2π)/4511 weeks
406.55563 -2.51328 (406*2π)/4511 weeks
4071.40747 -3.13716 (407*2π)/4511 weeks
408.74077 -2.30087 (408*2π)/4511 weeks
4091.77892 -.98168 (409*2π)/4511 weeks
4102.74496 -1.30156 (410*2π)/4511 weeks
4112.10203 -2.26083 (411*2π)/4511 weeks
412.70258 -1.25903 (412*2π)/4511 weeks
413.32688 .23848 (413*2π)/4511 weeks
414.80857 -.56017 (414*2π)/4511 weeks
4151.0602 -.71416 (415*2π)/4511 weeks
4161.51521 -.95111 (416*2π)/4511 weeks
4171.40641 -.83425 (417*2π)/4511 weeks
418-.58084 -.50059 (418*2π)/4511 weeks
419-.6883 -.14415 (419*2π)/4511 weeks
420.58871 .23037 (420*2π)/4511 weeks
421.88069 -.26009 (421*2π)/4511 weeks
422.37498 -.38823 (422*2π)/4511 weeks
4231.30408 .24831 (423*2π)/4511 weeks
4241.62805 -.56772 (424*2π)/4511 weeks
425-.69931 -1.77707 (425*2π)/4511 weeks
426-.87041 -2.41303 (426*2π)/4511 weeks
4271.31044 -.54875 (427*2π)/4511 weeks
428.75764 -1.72825 (428*2π)/4511 weeks
429.78183 -2.48234 (429*2π)/4511 weeks
430-2.45465 -1.37197 (430*2π)/4511 weeks
431-3.87397 -.86866 (431*2π)/4511 weeks
432-1.5563 2.75807 (432*2π)/4511 weeks
433.90968 -.90853 (433*2π)/4511 weeks
4341.06133 -5.56905 (434*2π)/4511 weeks
435-4.05668 -6.41473 (435*2π)/4511 weeks
436-4.07278 -.572 (436*2π)/4511 weeks
437-1.66384 -.09903 (437*2π)/4511 weeks
438.3819 -3.40044 (438*2π)/4511 weeks
4392.7105 -3.49231 (439*2π)/4511 weeks
4402.88751 -6.85257 (440*2π)/4511 weeks
4413.87861 -13.48694 (441*2π)/4511 weeks
442-2.5296 -9.42106 (442*2π)/4511 weeks
443-2.81757 -3.66849 (443*2π)/4511 weeks
4445.99203 -8.92683 (444*2π)/4511 weeks
4458.05813 -12.75525 (445*2π)/4511 weeks
4466.21962 -13.76111 (446*2π)/4511 weeks
4474.55444 -14.66994 (447*2π)/4511 weeks
448-6.50693 -12.99657 (448*2π)/4511 weeks
449-.87318 5.08217 (449*2π)/4511 weeks



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