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# Fourier Analysis of DTO (DB Crude Oil Double Short ETN)

DTO (DB Crude Oil Double Short ETN) appears to have interesting cyclic behaviour every 51 weeks (9.0924*sine), 47 weeks (7.0317*cosine), and 40 weeks (7.0124*cosine).

DTO (DB Crude Oil Double Short ETN) has an average price of 79.05 (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.

## Fourier Analysis

Using data from 6/17/2008 to 4/16/2018 for DTO (DB Crude Oil Double Short ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
079.04972   0
137.65131 -23.68433 (1*2π)/514514 weeks
2-13.71994 -10.12536 (2*2π)/514257 weeks
3-10.67574 14.1304 (3*2π)/514171 weeks
4-.0807 6.07178 (4*2π)/514129 weeks
5-7.4159 .62647 (5*2π)/514103 weeks
6-13.62878 -2.15279 (6*2π)/51486 weeks
7-18.7366 .03963 (7*2π)/51473 weeks
8-12.65569 2.20828 (8*2π)/51464 weeks
91.46867 -3.67861 (9*2π)/51457 weeks
10-4.06381 -9.09236 (10*2π)/51451 weeks
11-7.03175 -4.12284 (11*2π)/51447 weeks
124.93467 -2.66002 (12*2π)/51443 weeks
137.01237 -4.25243 (13*2π)/51440 weeks
143.81733 -6.26563 (14*2π)/51437 weeks
152.7759 -3.27799 (15*2π)/51434 weeks
16-.87169 .53498 (16*2π)/51432 weeks
17-.60911 3.39237 (17*2π)/51430 weeks
184.77108 1.08472 (18*2π)/51429 weeks
19-.08817 -3.09483 (19*2π)/51427 weeks
20-4.43099 .45782 (20*2π)/51426 weeks
21-2.1985 2.76546 (21*2π)/51424 weeks
222.75553 -1.26971 (22*2π)/51423 weeks
23-.89007 -3.38959 (23*2π)/51422 weeks
24-1.27305 -2.19862 (24*2π)/51421 weeks
25.63723 .94963 (25*2π)/51421 weeks
26.77868 -.25192 (26*2π)/51420 weeks
27.62375 -.79852 (27*2π)/51419 weeks
28-1.8325 -.00843 (28*2π)/51418 weeks
29-.97471 -1.60938 (29*2π)/51418 weeks
30-.05784 -1.19158 (30*2π)/51417 weeks
31-.88635 .24288 (31*2π)/51417 weeks
32-.28346 .35456 (32*2π)/51416 weeks
33.2901 -.48258 (33*2π)/51416 weeks
34.25606 .57177 (34*2π)/51415 weeks
351.01895 -.13835 (35*2π)/51415 weeks
36.7757 -1.40547 (36*2π)/51414 weeks
37-1.15183 -.50832 (37*2π)/51414 weeks
38-2.06048 .18476 (38*2π)/51414 weeks
39-.9682 -.72693 (39*2π)/51413 weeks
40-.45755 -1.01172 (40*2π)/51413 weeks
41-.49353 -1.28832 (41*2π)/51413 weeks
42-.92295 -1.24206 (42*2π)/51412 weeks
43-1.33124 -.4743 (43*2π)/51412 weeks
441.29487 -.30255 (44*2π)/51412 weeks
451.61162 -1.29643 (45*2π)/51411 weeks
46.05995 .12579 (46*2π)/51411 weeks
47.6715 1.94086 (47*2π)/51411 weeks
481.63766 1.38938 (48*2π)/51411 weeks
49-.10711 .2786 (49*2π)/51410 weeks
50-1.5036 .56087 (50*2π)/51410 weeks
51-1.90434 -.58406 (51*2π)/51410 weeks
52-2.24233 -.79858 (52*2π)/51410 weeks
53-.58332 -.4541 (53*2π)/51410 weeks
54.91949 -1.50717 (54*2π)/51410 weeks
55.42067 -1.8768 (55*2π)/5149 weeks
56.09682 -.76385 (56*2π)/5149 weeks
571.50877 .39517 (57*2π)/5149 weeks
58.50108 -.24269 (58*2π)/5149 weeks
59-.13835 -.17782 (59*2π)/5149 weeks
60.46888 .78902 (60*2π)/5149 weeks
61.86117 .3464 (61*2π)/5148 weeks
621.11287 -.23206 (62*2π)/5148 weeks
63.5013 -1.01211 (63*2π)/5148 weeks
64-1.77145 -1.57622 (64*2π)/5148 weeks
65-2.28064 -.97235 (65*2π)/5148 weeks
66-.88065 1.03316 (66*2π)/5148 weeks
67.79405 .30535 (67*2π)/5148 weeks
68.43348 -.47371 (68*2π)/5148 weeks
69-.27917 -.406 (69*2π)/5147 weeks
70-1.2151 -.43152 (70*2π)/5147 weeks
71-.38669 -.06853 (71*2π)/5147 weeks
721.06071 .53997 (72*2π)/5147 weeks
73.90287 -.35797 (73*2π)/5147 weeks
74-.45092 -.79621 (74*2π)/5147 weeks
75-.52726 .03629 (75*2π)/5147 weeks
76-.26021 .21986 (76*2π)/5147 weeks
77-.41959 -.38685 (77*2π)/5147 weeks
78-.05268 -.08735 (78*2π)/5147 weeks
79-.10551 .58938 (79*2π)/5147 weeks
80-.18625 .14617 (80*2π)/5146 weeks
81.64689 -.772 (81*2π)/5146 weeks
82.0266 -1.19495 (82*2π)/5146 weeks
83-1.18074 -1.11536 (83*2π)/5146 weeks
84-.66225 -.20309 (84*2π)/5146 weeks
85.19955 .24657 (85*2π)/5146 weeks
86.70042 .4235 (86*2π)/5146 weeks
87.35439 -.021 (87*2π)/5146 weeks
88-.27608 .02507 (88*2π)/5146 weeks
89-.72792 .58441 (89*2π)/5146 weeks
90.8248 .39706 (90*2π)/5146 weeks
911.13192 -.87183 (91*2π)/5146 weeks
92.17007 -1.51444 (92*2π)/5146 weeks
93-.88448 -.02646 (93*2π)/5146 weeks
94-.28569 .83209 (94*2π)/5145 weeks
95.31032 .09971 (95*2π)/5145 weeks
96.36071 -.95673 (96*2π)/5145 weeks
97-.86482 -.53022 (97*2π)/5145 weeks
98-.79398 .62869 (98*2π)/5145 weeks
99.30427 .42576 (99*2π)/5145 weeks
100.50592 -.53196 (100*2π)/5145 weeks
101-.09077 -.36643 (101*2π)/5145 weeks
102-.25599 .15335 (102*2π)/5145 weeks
103-.02166 -.15254 (103*2π)/5145 weeks
104-.03706 -.58371 (104*2π)/5145 weeks
105-.12161 -.33176 (105*2π)/5145 weeks
106-.05357 .02309 (106*2π)/5145 weeks
107-.48086 .44777 (107*2π)/5145 weeks
108.32524 .44542 (108*2π)/5145 weeks
109.2313 -.14027 (109*2π)/5145 weeks
110-.42545 -.37871 (110*2π)/5145 weeks
111-.87143 .15738 (111*2π)/5145 weeks
112-.36329 .0081 (112*2π)/5145 weeks
113-.36095 -.4298 (113*2π)/5145 weeks
114-.10277 -.70323 (114*2π)/5145 weeks
115-.26694 -.42623 (115*2π)/5144 weeks
116-.24556 -.21623 (116*2π)/5144 weeks
117.04782 -.79514 (117*2π)/5144 weeks
118-.01737 -.74615 (118*2π)/5144 weeks
119-.1373 -.01499 (119*2π)/5144 weeks
120.32996 .5267 (120*2π)/5144 weeks
121.50485 -.16471 (121*2π)/5144 weeks
122.06716 -.21135 (122*2π)/5144 weeks
123-.66449 .77176 (123*2π)/5144 weeks
124-.08973 1.07473 (124*2π)/5144 weeks
125.09019 .02597 (125*2π)/5144 weeks
126-.26846 -.60933 (126*2π)/5144 weeks
127-.6939 -.02663 (127*2π)/5144 weeks
128-.62782 .22585 (128*2π)/5144 weeks
129.31854 -.38464 (129*2π)/5144 weeks
130.52954 -.31437 (130*2π)/5144 weeks
131-.04489 -.19808 (131*2π)/5144 weeks
132-.14175 .3295 (132*2π)/5144 weeks
133.19144 .29449 (133*2π)/5144 weeks
134-.02927 -.42256 (134*2π)/5144 weeks
135-.34818 -.27437 (135*2π)/5144 weeks
136.01461 .57413 (136*2π)/5144 weeks
137.40957 .25163 (137*2π)/5144 weeks
138.47202 -.2204 (138*2π)/5144 weeks
139.11524 -.03485 (139*2π)/5144 weeks
140-.1429 .33589 (140*2π)/5144 weeks
141.14707 .81441 (141*2π)/5144 weeks
142.15426 .42216 (142*2π)/5144 weeks
143-.29189 -.62078 (143*2π)/5144 weeks
144-.82057 -.50041 (144*2π)/5144 weeks
145-.54828 .00454 (145*2π)/5144 weeks
146-.12171 -.06801 (146*2π)/5144 weeks
147.06583 -.33223 (147*2π)/5143 weeks
148-.03845 -.11267 (148*2π)/5143 weeks
149.05209 -.45481 (149*2π)/5143 weeks
150.19095 -.38252 (150*2π)/5143 weeks
151.42686 .11772 (151*2π)/5143 weeks
152.29224 .35517 (152*2π)/5143 weeks
153.0956 .19005 (153*2π)/5143 weeks
154.30572 .20817 (154*2π)/5143 weeks
155.3357 .02365 (155*2π)/5143 weeks
156-.24511 -.09161 (156*2π)/5143 weeks
157-.52141 -.04093 (157*2π)/5143 weeks
158-.53358 -.05316 (158*2π)/5143 weeks
159-.55583 -.19643 (159*2π)/5143 weeks
160.05834 .15368 (160*2π)/5143 weeks
161.38938 -.48209 (161*2π)/5143 weeks
162-.13517 -.64123 (162*2π)/5143 weeks
163-.36319 .16062 (163*2π)/5143 weeks
164-.06069 .59445 (164*2π)/5143 weeks
165.13213 .08096 (165*2π)/5143 weeks
166-.27887 -.08693 (166*2π)/5143 weeks
167-.14697 -.19819 (167*2π)/5143 weeks
168-.45712 -.25362 (168*2π)/5143 weeks
169-.6049 -.46273 (169*2π)/5143 weeks
170-.28088 -.32253 (170*2π)/5143 weeks
171-.10209 -.17172 (171*2π)/5143 weeks
172.2143 -.10639 (172*2π)/5143 weeks
173.44491 -.30035 (173*2π)/5143 weeks
174.62136 -.36871 (174*2π)/5143 weeks
175.47514 .29968 (175*2π)/5143 weeks
176.31645 .46227 (176*2π)/5143 weeks
177.14208 -.10229 (177*2π)/5143 weeks
178-.26956 .3184 (178*2π)/5143 weeks
179-.17508 .8176 (179*2π)/5143 weeks
180.04492 .57326 (180*2π)/5143 weeks
181-.24043 .22027 (181*2π)/5143 weeks
182-.78466 .02918 (182*2π)/5143 weeks
183-.70879 -.18574 (183*2π)/5143 weeks
184-.34859 -.30511 (184*2π)/5143 weeks
185-.13473 -.53662 (185*2π)/5143 weeks
186-.1287 -.75593 (186*2π)/5143 weeks
187.16872 -.69763 (187*2π)/5143 weeks
188-.20907 -.47976 (188*2π)/5143 weeks
189-.09198 -.07675 (189*2π)/5143 weeks
190.2072 .20199 (190*2π)/5143 weeks
191.26222 -.29893 (191*2π)/5143 weeks
192.35728 -.38059 (192*2π)/5143 weeks
193.20609 .02845 (193*2π)/5143 weeks
194.31792 .19389 (194*2π)/5143 weeks
195.59233 .22456 (195*2π)/5143 weeks
196.35691 .15158 (196*2π)/5143 weeks
197-.21387 .02467 (197*2π)/5143 weeks
198-.71225 .24391 (198*2π)/5143 weeks
199-.40625 .3206 (199*2π)/5143 weeks
200-.58393 -.13533 (200*2π)/5143 weeks
201-.63945 -.49016 (201*2π)/5143 weeks
202-.5315 -.2687 (202*2π)/5143 weeks
203-.26022 -.55049 (203*2π)/5143 weeks
204-.05064 -.73179 (204*2π)/5143 weeks
205.02041 -.44295 (205*2π)/5143 weeks
206.07623 -.08889 (206*2π)/5142 weeks
207.03755 .25723 (207*2π)/5142 weeks
208.15512 .0757 (208*2π)/5142 weeks
209.38898 -.2592 (209*2π)/5142 weeks
210.00023 -.27602 (210*2π)/5142 weeks
211-.55757 -.17581 (211*2π)/5142 weeks
212-.40918 .22519 (212*2π)/5142 weeks
213-.05114 .28403 (213*2π)/5142 weeks
214.13406 -.01978 (214*2π)/5142 weeks
215-.03675 -.18481 (215*2π)/5142 weeks
216-.17736 -.13332 (216*2π)/5142 weeks
217-.27345 .17112 (217*2π)/5142 weeks
218-.03851 .37926 (218*2π)/5142 weeks
219.12228 .35359 (219*2π)/5142 weeks
220-.17823 .08665 (220*2π)/5142 weeks
221-.35776 .143 (221*2π)/5142 weeks
222-.40371 .0226 (222*2π)/5142 weeks
223-.37806 -.18663 (223*2π)/5142 weeks
224-.11656 -.40126 (224*2π)/5142 weeks
225-.37699 -.42714 (225*2π)/5142 weeks
226-.35285 -.42161 (226*2π)/5142 weeks
227-.04807 .09439 (227*2π)/5142 weeks
228.13593 .00696 (228*2π)/5142 weeks
229.04625 -.01371 (229*2π)/5142 weeks
230.08505 .13586 (230*2π)/5142 weeks
231.14643 .00647 (231*2π)/5142 weeks
232.2276 .12545 (232*2π)/5142 weeks
233.22695 .05073 (233*2π)/5142 weeks
234.19423 .1241 (234*2π)/5142 weeks
235-.17057 -.0777 (235*2π)/5142 weeks
236-.12035 -.38266 (236*2π)/5142 weeks
237-.33862 -.37046 (237*2π)/5142 weeks
238-.49116 -.14771 (238*2π)/5142 weeks
239-.22297 .01461 (239*2π)/5142 weeks
240-.26099 .11193 (240*2π)/5142 weeks
241-.23321 .52095 (241*2π)/5142 weeks
242.30254 .52316 (242*2π)/5142 weeks
243.17942 .40756 (243*2π)/5142 weeks
244-.29833 .37624 (244*2π)/5142 weeks
245.00487 .11963 (245*2π)/5142 weeks
246.05811 -.35128 (246*2π)/5142 weeks
247-.27758 -.27897 (247*2π)/5142 weeks
248-.30785 .12688 (248*2π)/5142 weeks
249-.36287 -.0823 (249*2π)/5142 weeks
250-.33648 -.28325 (250*2π)/5142 weeks
251.05971 -.18579 (251*2π)/5142 weeks
252-.00223 -.1215 (252*2π)/5142 weeks
253-.12391 -.02976 (253*2π)/5142 weeks
254-.16358 -.13613 (254*2π)/5142 weeks
255-.06946 -.09781 (255*2π)/5142 weeks
256.07642 -.06367 (256*2π)/5142 weeks
257.51686   (257*2π)/5142 weeks
258.07642 .06367 (258*2π)/5142 weeks
259-.06946 .09781 (259*2π)/5142 weeks
260-.16358 .13613 (260*2π)/5142 weeks
261-.12391 .02976 (261*2π)/5142 weeks
262-.00223 .1215 (262*2π)/5142 weeks
263.05971 .18579 (263*2π)/5142 weeks
264-.33648 .28325 (264*2π)/5142 weeks
265-.36287 .0823 (265*2π)/5142 weeks
266-.30785 -.12688 (266*2π)/5142 weeks
267-.27758 .27897 (267*2π)/5142 weeks
268.05811 .35128 (268*2π)/5142 weeks
269.00487 -.11963 (269*2π)/5142 weeks
270-.29833 -.37624 (270*2π)/5142 weeks
271.17942 -.40756 (271*2π)/5142 weeks
272.30254 -.52316 (272*2π)/5142 weeks
273-.23321 -.52095 (273*2π)/5142 weeks
274-.26099 -.11193 (274*2π)/5142 weeks
275-.22297 -.01461 (275*2π)/5142 weeks
276-.49116 .14771 (276*2π)/5142 weeks
277-.33862 .37046 (277*2π)/5142 weeks
278-.12035 .38266 (278*2π)/5142 weeks
279-.17057 .0777 (279*2π)/5142 weeks
280.19423 -.1241 (280*2π)/5142 weeks
281.22695 -.05073 (281*2π)/5142 weeks
282.2276 -.12545 (282*2π)/5142 weeks
283.14643 -.00647 (283*2π)/5142 weeks
284.08505 -.13586 (284*2π)/5142 weeks
285.04625 .01371 (285*2π)/5142 weeks
286.13593 -.00696 (286*2π)/5142 weeks
287-.04807 -.09439 (287*2π)/5142 weeks
288-.35285 .42161 (288*2π)/5142 weeks
289-.37699 .42714 (289*2π)/5142 weeks
290-.11656 .40126 (290*2π)/5142 weeks
291-.37806 .18663 (291*2π)/5142 weeks
292-.40371 -.0226 (292*2π)/5142 weeks
293-.35776 -.143 (293*2π)/5142 weeks
294-.17823 -.08665 (294*2π)/5142 weeks
295.12228 -.35359 (295*2π)/5142 weeks
296-.03851 -.37926 (296*2π)/5142 weeks
297-.27345 -.17112 (297*2π)/5142 weeks
298-.17736 .13332 (298*2π)/5142 weeks
299-.03675 .18481 (299*2π)/5142 weeks
300.13406 .01978 (300*2π)/5142 weeks
301-.05114 -.28403 (301*2π)/5142 weeks
302-.40918 -.22519 (302*2π)/5142 weeks
303-.55757 .17581 (303*2π)/5142 weeks
304.00023 .27602 (304*2π)/5142 weeks
305.38898 .2592 (305*2π)/5142 weeks
306.15512 -.0757 (306*2π)/5142 weeks
307.03755 -.25723 (307*2π)/5142 weeks
308.07623 .08889 (308*2π)/5142 weeks
309.02041 .44295 (309*2π)/5142 weeks
310-.05064 .73179 (310*2π)/5142 weeks
311-.26022 .55049 (311*2π)/5142 weeks
312-.5315 .2687 (312*2π)/5142 weeks
313-.63945 .49016 (313*2π)/5142 weeks
314-.58393 .13533 (314*2π)/5142 weeks
315-.40625 -.3206 (315*2π)/5142 weeks
316-.71225 -.24391 (316*2π)/5142 weeks
317-.21387 -.02467 (317*2π)/5142 weeks
318.35691 -.15158 (318*2π)/5142 weeks
319.59233 -.22456 (319*2π)/5142 weeks
320.31792 -.19389 (320*2π)/5142 weeks
321.20609 -.02845 (321*2π)/5142 weeks
322.35728 .38059 (322*2π)/5142 weeks
323.26222 .29893 (323*2π)/5142 weeks
324.2072 -.20199 (324*2π)/5142 weeks
325-.09198 .07675 (325*2π)/5142 weeks
326-.20907 .47976 (326*2π)/5142 weeks
327.16872 .69763 (327*2π)/5142 weeks
328-.1287 .75593 (328*2π)/5142 weeks
329-.13473 .53662 (329*2π)/5142 weeks
330-.34859 .30511 (330*2π)/5142 weeks
331-.70879 .18574 (331*2π)/5142 weeks
332-.78466 -.02918 (332*2π)/5142 weeks
333-.24043 -.22027 (333*2π)/5142 weeks
334.04492 -.57326 (334*2π)/5142 weeks
335-.17508 -.8176 (335*2π)/5142 weeks
336-.26956 -.3184 (336*2π)/5142 weeks
337.14208 .10229 (337*2π)/5142 weeks
338.31645 -.46227 (338*2π)/5142 weeks
339.47514 -.29968 (339*2π)/5142 weeks
340.62136 .36871 (340*2π)/5142 weeks
341.44491 .30035 (341*2π)/5142 weeks
342.2143 .10639 (342*2π)/5142 weeks
343-.10209 .17172 (343*2π)/5141 weeks
344-.28088 .32253 (344*2π)/5141 weeks
345-.6049 .46273 (345*2π)/5141 weeks
346-.45712 .25362 (346*2π)/5141 weeks
347-.14697 .19819 (347*2π)/5141 weeks
348-.27887 .08693 (348*2π)/5141 weeks
349.13213 -.08096 (349*2π)/5141 weeks
350-.06069 -.59445 (350*2π)/5141 weeks
351-.36319 -.16062 (351*2π)/5141 weeks
352-.13517 .64123 (352*2π)/5141 weeks
353.38938 .48209 (353*2π)/5141 weeks
354.05834 -.15368 (354*2π)/5141 weeks
355-.55583 .19643 (355*2π)/5141 weeks
356-.53358 .05316 (356*2π)/5141 weeks
357-.52141 .04093 (357*2π)/5141 weeks
358-.24511 .09161 (358*2π)/5141 weeks
359.3357 -.02365 (359*2π)/5141 weeks
360.30572 -.20817 (360*2π)/5141 weeks
361.0956 -.19005 (361*2π)/5141 weeks
362.29224 -.35517 (362*2π)/5141 weeks
363.42686 -.11772 (363*2π)/5141 weeks
364.19095 .38252 (364*2π)/5141 weeks
365.05209 .45481 (365*2π)/5141 weeks
366-.03845 .11267 (366*2π)/5141 weeks
367.06583 .33223 (367*2π)/5141 weeks
368-.12171 .06801 (368*2π)/5141 weeks
369-.54828 -.00454 (369*2π)/5141 weeks
370-.82057 .50041 (370*2π)/5141 weeks
371-.29189 .62078 (371*2π)/5141 weeks
372.15426 -.42216 (372*2π)/5141 weeks
373.14707 -.81441 (373*2π)/5141 weeks
374-.1429 -.33589 (374*2π)/5141 weeks
375.11524 .03485 (375*2π)/5141 weeks
376.47202 .2204 (376*2π)/5141 weeks
377.40957 -.25163 (377*2π)/5141 weeks
378.01461 -.57413 (378*2π)/5141 weeks
379-.34818 .27437 (379*2π)/5141 weeks
380-.02927 .42256 (380*2π)/5141 weeks
381.19144 -.29449 (381*2π)/5141 weeks
382-.14175 -.3295 (382*2π)/5141 weeks
383-.04489 .19808 (383*2π)/5141 weeks
384.52954 .31437 (384*2π)/5141 weeks
385.31854 .38464 (385*2π)/5141 weeks
386-.62782 -.22585 (386*2π)/5141 weeks
387-.6939 .02663 (387*2π)/5141 weeks
388-.26846 .60933 (388*2π)/5141 weeks
389.09019 -.02597 (389*2π)/5141 weeks
390-.08973 -1.07473 (390*2π)/5141 weeks
391-.66449 -.77176 (391*2π)/5141 weeks
392.06716 .21135 (392*2π)/5141 weeks
393.50485 .16471 (393*2π)/5141 weeks
394.32996 -.5267 (394*2π)/5141 weeks
395-.1373 .01499 (395*2π)/5141 weeks
396-.01737 .74615 (396*2π)/5141 weeks
397.04782 .79514 (397*2π)/5141 weeks
398-.24556 .21623 (398*2π)/5141 weeks
399-.26694 .42623 (399*2π)/5141 weeks
400-.10277 .70323 (400*2π)/5141 weeks
401-.36095 .4298 (401*2π)/5141 weeks
402-.36329 -.0081 (402*2π)/5141 weeks
403-.87143 -.15738 (403*2π)/5141 weeks
404-.42545 .37871 (404*2π)/5141 weeks
405.2313 .14027 (405*2π)/5141 weeks
406.32524 -.44542 (406*2π)/5141 weeks
407-.48086 -.44777 (407*2π)/5141 weeks
408-.05357 -.02309 (408*2π)/5141 weeks
409-.12161 .33176 (409*2π)/5141 weeks
410-.03706 .58371 (410*2π)/5141 weeks
411-.02166 .15254 (411*2π)/5141 weeks
412-.25599 -.15335 (412*2π)/5141 weeks
413-.09077 .36643 (413*2π)/5141 weeks
414.50592 .53196 (414*2π)/5141 weeks
415.30427 -.42576 (415*2π)/5141 weeks
416-.79398 -.62869 (416*2π)/5141 weeks
417-.86482 .53022 (417*2π)/5141 weeks
418.36071 .95673 (418*2π)/5141 weeks
419.31032 -.09971 (419*2π)/5141 weeks
420-.28569 -.83209 (420*2π)/5141 weeks
421-.88448 .02646 (421*2π)/5141 weeks
422.17007 1.51444 (422*2π)/5141 weeks
4231.13192 .87183 (423*2π)/5141 weeks
424.8248 -.39706 (424*2π)/5141 weeks
425-.72792 -.58441 (425*2π)/5141 weeks
426-.27608 -.02507 (426*2π)/5141 weeks
427.35439 .021 (427*2π)/5141 weeks
428.70042 -.4235 (428*2π)/5141 weeks
429.19955 -.24657 (429*2π)/5141 weeks
430-.66225 .20309 (430*2π)/5141 weeks
431-1.18074 1.11536 (431*2π)/5141 weeks
432.0266 1.19495 (432*2π)/5141 weeks
433.64689 .772 (433*2π)/5141 weeks
434-.18625 -.14617 (434*2π)/5141 weeks
435-.10551 -.58938 (435*2π)/5141 weeks
436-.05268 .08735 (436*2π)/5141 weeks
437-.41959 .38685 (437*2π)/5141 weeks
438-.26021 -.21986 (438*2π)/5141 weeks
439-.52726 -.03629 (439*2π)/5141 weeks
440-.45092 .79621 (440*2π)/5141 weeks
441.90287 .35797 (441*2π)/5141 weeks
4421.06071 -.53997 (442*2π)/5141 weeks
443-.38669 .06853 (443*2π)/5141 weeks
444-1.2151 .43152 (444*2π)/5141 weeks
445-.27917 .406 (445*2π)/5141 weeks
446.43348 .47371 (446*2π)/5141 weeks
447.79405 -.30535 (447*2π)/5141 weeks
448-.88065 -1.03316 (448*2π)/5141 weeks
449-2.28064 .97235 (449*2π)/5141 weeks
450-1.77145 1.57622 (450*2π)/5141 weeks
451.5013 1.01211 (451*2π)/5141 weeks
4521.11287 .23206 (452*2π)/5141 weeks
453.86117 -.3464 (453*2π)/5141 weeks
454.46888 -.78902 (454*2π)/5141 weeks
455-.13835 .17782 (455*2π)/5141 weeks
456.50108 .24269 (456*2π)/5141 weeks
4571.50877 -.39517 (457*2π)/5141 weeks
458.09682 .76385 (458*2π)/5141 weeks
459.42067 1.8768 (459*2π)/5141 weeks
460.91949 1.50717 (460*2π)/5141 weeks
461-.58332 .4541 (461*2π)/5141 weeks
462-2.24233 .79858 (462*2π)/5141 weeks
463-1.90434 .58406 (463*2π)/5141 weeks
464-1.5036 -.56087 (464*2π)/5141 weeks
465-.10711 -.2786 (465*2π)/5141 weeks
4661.63766 -1.38938 (466*2π)/5141 weeks
467.6715 -1.94086 (467*2π)/5141 weeks
468.05995 -.12579 (468*2π)/5141 weeks
4691.61162 1.29643 (469*2π)/5141 weeks
4701.29487 .30255 (470*2π)/5141 weeks
471-1.33124 .4743 (471*2π)/5141 weeks
472-.92295 1.24206 (472*2π)/5141 weeks
473-.49353 1.28832 (473*2π)/5141 weeks
474-.45755 1.01172 (474*2π)/5141 weeks
475-.9682 .72693 (475*2π)/5141 weeks
476-2.06048 -.18476 (476*2π)/5141 weeks
477-1.15183 .50832 (477*2π)/5141 weeks
478.7757 1.40547 (478*2π)/5141 weeks
4791.01895 .13835 (479*2π)/5141 weeks
480.25606 -.57177 (480*2π)/5141 weeks
481.2901 .48258 (481*2π)/5141 weeks
482-.28346 -.35456 (482*2π)/5141 weeks
483-.88635 -.24288 (483*2π)/5141 weeks
484-.05784 1.19158 (484*2π)/5141 weeks
485-.97471 1.60938 (485*2π)/5141 weeks
486-1.8325 .00843 (486*2π)/5141 weeks
487.62375 .79852 (487*2π)/5141 weeks
488.77868 .25192 (488*2π)/5141 weeks
489.63723 -.94963 (489*2π)/5141 weeks
490-1.27305 2.19862 (490*2π)/5141 weeks
491-.89007 3.38959 (491*2π)/5141 weeks
4922.75553 1.26971 (492*2π)/5141 weeks
493-2.1985 -2.76546 (493*2π)/5141 weeks
494-4.43099 -.45782 (494*2π)/5141 weeks
495-.08817 3.09483 (495*2π)/5141 weeks
4964.77108 -1.08472 (496*2π)/5141 weeks
497-.60911 -3.39237 (497*2π)/5141 weeks
498-.87169 -.53498 (498*2π)/5141 weeks
4992.7759 3.27799 (499*2π)/5141 weeks
5003.81733 6.26563 (500*2π)/5141 weeks
5017.01237 4.25243 (501*2π)/5141 weeks
5024.93467 2.66002 (502*2π)/5141 weeks
503-7.03175 4.12284 (503*2π)/5141 weeks
504-4.06381 9.09236 (504*2π)/5141 weeks
5051.46867 3.67861 (505*2π)/5141 weeks
506-12.65569 -2.20828 (506*2π)/5141 weeks
507-18.7366 -.03963 (507*2π)/5141 weeks
508-13.62878 2.15279 (508*2π)/5141 weeks
509-7.4159 -.62647 (509*2π)/5141 weeks
510-.0807 -6.07178 (510*2π)/5141 weeks
511-10.67574 -14.1304 (511*2π)/5141 weeks
512-13.71994 10.12536 (512*2π)/5141 weeks