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Fourier Analysis of UNG (United States Natural Gas Fund ETF)


UNG (United States Natural Gas Fund ETF) appears to have interesting cyclic behaviour every 49 weeks (18.575*sine), 54 weeks (18.4572*sine), and 54 weeks (10.832*cosine).

UNG (United States Natural Gas Fund ETF) has an average price of 84.61 (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 4/18/2007 to 7/17/2017 for UNG (United States Natural Gas Fund ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
084.60695   0 
183.69171 75.97186 (1*2π)/536536 weeks
229.20042 77.67482 (2*2π)/536268 weeks
32.92632 60.92214 (3*2π)/536179 weeks
4-14.33671 34.97829 (4*2π)/536134 weeks
5-12.02241 16.02801 (5*2π)/536107 weeks
6-4.85725 5.27054 (6*2π)/53689 weeks
77.63296 1.04676 (7*2π)/53677 weeks
812.10232 7.38685 (8*2π)/53667 weeks
914.40272 13.00228 (9*2π)/53660 weeks
1010.83195 18.45718 (10*2π)/53654 weeks
114.49844 18.57504 (11*2π)/53649 weeks
12.48818 16.59943 (12*2π)/53645 weeks
13-2.46333 12.30489 (13*2π)/53641 weeks
14-2.89134 8.96539 (14*2π)/53638 weeks
15-.29164 5.2943 (15*2π)/53636 weeks
161.87368 4.47642 (16*2π)/53634 weeks
173.8537 4.6848 (17*2π)/53632 weeks
185.75083 6.21705 (18*2π)/53630 weeks
196.08051 9.29795 (19*2π)/53628 weeks
202.75855 11.0239 (20*2π)/53627 weeks
21-.46488 9.52837 (21*2π)/53626 weeks
22-.2219 7.11957 (22*2π)/53624 weeks
23-.43795 6.13401 (23*2π)/53623 weeks
24.44916 4.45406 (24*2π)/53622 weeks
252.16047 4.63515 (25*2π)/53621 weeks
262.85474 6.70523 (26*2π)/53621 weeks
271.62738 7.07447 (27*2π)/53620 weeks
28.33456 7.34057 (28*2π)/53619 weeks
29-.70762 6.89174 (29*2π)/53618 weeks
30-1.87619 6.03163 (30*2π)/53618 weeks
31-2.63041 3.8513 (31*2π)/53617 weeks
32-1.40144 1.85247 (32*2π)/53617 weeks
33.86548 1.3441 (33*2π)/53616 weeks
342.13397 2.51311 (34*2π)/53616 weeks
352.26966 3.2183 (35*2π)/53615 weeks
362.38229 4.1028 (36*2π)/53615 weeks
371.62618 4.91222 (37*2π)/53614 weeks
38.65475 5.12911 (38*2π)/53614 weeks
39-.30904 4.31627 (39*2π)/53614 weeks
40-.45454 2.95578 (40*2π)/53613 weeks
41.55843 2.41684 (41*2π)/53613 weeks
421.29293 2.85733 (42*2π)/53613 weeks
431.37874 3.35848 (43*2π)/53612 weeks
44.90646 3.76061 (44*2π)/53612 weeks
45.57275 4.47355 (45*2π)/53612 weeks
46-.36653 4.10261 (46*2π)/53612 weeks
47-1.04782 3.38883 (47*2π)/53611 weeks
48-.97814 1.91702 (48*2π)/53611 weeks
49.1046 1.64068 (49*2π)/53611 weeks
50.60867 1.93336 (50*2π)/53611 weeks
51.66878 2.11306 (51*2π)/53611 weeks
52.52785 2.18821 (52*2π)/53610 weeks
53.67806 2.48669 (53*2π)/53610 weeks
54.4412 2.43535 (54*2π)/53610 weeks
55-.24701 2.49227 (55*2π)/53610 weeks
56-.67718 1.39524 (56*2π)/53610 weeks
57.46996 .40768 (57*2π)/5369 weeks
581.34892 .68468 (58*2π)/5369 weeks
592.00691 1.69366 (59*2π)/5369 weeks
601.80882 2.3449 (60*2π)/5369 weeks
611.15997 2.78795 (61*2π)/5369 weeks
62.71985 2.7319 (62*2π)/5369 weeks
63.0346 2.70903 (63*2π)/5369 weeks
64-.60885 1.73924 (64*2π)/5368 weeks
65.16215 .861 (65*2π)/5368 weeks
66.87251 .86566 (66*2π)/5368 weeks
67.82585 .78077 (67*2π)/5368 weeks
681.48915 .90445 (68*2π)/5368 weeks
691.83958 1.22937 (69*2π)/5368 weeks
701.80688 1.45256 (70*2π)/5368 weeks
712.07324 1.95883 (71*2π)/5368 weeks
721.80863 2.74098 (72*2π)/5367 weeks
73.99474 2.99018 (73*2π)/5367 weeks
74.48142 2.35074 (74*2π)/5367 weeks
75.63612 2.19447 (75*2π)/5367 weeks
76.46196 2.13503 (76*2π)/5367 weeks
77.64383 1.92186 (77*2π)/5367 weeks
78.53382 1.96368 (78*2π)/5367 weeks
79.78755 2.11972 (79*2π)/5367 weeks
80.32919 2.23833 (80*2π)/5367 weeks
81-.08118 2.07873 (81*2π)/5367 weeks
82-.31487 1.51969 (82*2π)/5367 weeks
83-.16594 .80611 (83*2π)/5366 weeks
84.95236 .61239 (84*2π)/5366 weeks
851.26771 1.53973 (85*2π)/5366 weeks
86.48613 1.98635 (86*2π)/5366 weeks
87.04744 1.72603 (87*2π)/5366 weeks
88-.24097 1.14739 (88*2π)/5366 weeks
89.25341 .50167 (89*2π)/5366 weeks
90.78278 .70196 (90*2π)/5366 weeks
91.96267 .96659 (91*2π)/5366 weeks
92.79327 1.07798 (92*2π)/5366 weeks
93.83908 .80578 (93*2π)/5366 weeks
941.25619 .95201 (94*2π)/5366 weeks
951.1628 1.23195 (95*2π)/5366 weeks
961.00977 1.47711 (96*2π)/5366 weeks
97.89763 1.53381 (97*2π)/5366 weeks
98.57776 1.4282 (98*2π)/5365 weeks
99.73448 .93368 (99*2π)/5365 weeks
100.93418 1.15242 (100*2π)/5365 weeks
1011.06797 1.19862 (101*2π)/5365 weeks
1021.29118 1.53462 (102*2π)/5365 weeks
103.99392 1.93977 (103*2π)/5365 weeks
104.47231 1.92834 (104*2π)/5365 weeks
105.2389 1.9532 (105*2π)/5365 weeks
106-.11071 1.3017 (106*2π)/5365 weeks
107.1349 1.04178 (107*2π)/5365 weeks
108.19798 .96511 (108*2π)/5365 weeks
109.51452 .91781 (109*2π)/5365 weeks
110.44888 1.28194 (110*2π)/5365 weeks
111.09718 1.17522 (111*2π)/5365 weeks
112-.01793 .77969 (112*2π)/5365 weeks
113.26769 .51672 (113*2π)/5365 weeks
114.65488 .72913 (114*2π)/5365 weeks
115.43313 1.00473 (115*2π)/5365 weeks
116-.0826 .99802 (116*2π)/5365 weeks
117-.11723 .38881 (117*2π)/5365 weeks
118.28286 -.11643 (118*2π)/5365 weeks
119.77786 -.05173 (119*2π)/5365 weeks
1201.08066 .5038 (120*2π)/5364 weeks
121.73631 .59493 (121*2π)/5364 weeks
122.56992 .39547 (122*2π)/5364 weeks
123.88927 .21534 (123*2π)/5364 weeks
124.85595 .24216 (124*2π)/5364 weeks
1251.23134 .27822 (125*2π)/5364 weeks
1261.3544 .29429 (126*2π)/5364 weeks
1271.59544 .60552 (127*2π)/5364 weeks
1281.43511 1.01208 (128*2π)/5364 weeks
1291.05123 1.17322 (129*2π)/5364 weeks
130.97997 .9783 (130*2π)/5364 weeks
1311.07663 1.06747 (131*2π)/5364 weeks
132.73197 1.0271 (132*2π)/5364 weeks
133.76757 .70992 (133*2π)/5364 weeks
1341.00024 .72534 (134*2π)/5364 weeks
1351.29502 .85055 (135*2π)/5364 weeks
1361.14881 1.31587 (136*2π)/5364 weeks
137.72414 1.33901 (137*2π)/5364 weeks
138.73935 1.1816 (138*2π)/5364 weeks
139.53551 1.15146 (139*2π)/5364 weeks
140.36577 1.13298 (140*2π)/5364 weeks
141.30997 .88336 (141*2π)/5364 weeks
142.38107 .70436 (142*2π)/5364 weeks
143.51475 .63853 (143*2π)/5364 weeks
144.77883 .61882 (144*2π)/5364 weeks
145.76623 .89062 (145*2π)/5364 weeks
146.494 1.06189 (146*2π)/5364 weeks
147.09391 .91884 (147*2π)/5364 weeks
148-.08948 .35545 (148*2π)/5364 weeks
149.3123 .04709 (149*2π)/5364 weeks
150.77971 .05231 (150*2π)/5364 weeks
151.87704 .32794 (151*2π)/5364 weeks
152.81774 .39954 (152*2π)/5364 weeks
153.91164 .30685 (153*2π)/5364 weeks
1541.11356 .55281 (154*2π)/5363 weeks
155.99873 .897 (155*2π)/5363 weeks
156.63856 .74463 (156*2π)/5363 weeks
157.62179 .59909 (157*2π)/5363 weeks
158.63457 .44632 (158*2π)/5363 weeks
159.8877 .2688 (159*2π)/5363 weeks
1601.09725 .53563 (160*2π)/5363 weeks
1611.02518 .93982 (161*2π)/5363 weeks
162.57692 .97725 (162*2π)/5363 weeks
163.39631 .52788 (163*2π)/5363 weeks
164.74703 .35491 (164*2π)/5363 weeks
1651.01913 .54265 (165*2π)/5363 weeks
166.85274 .93225 (166*2π)/5363 weeks
167.41964 .92673 (167*2π)/5363 weeks
168.21152 .57234 (168*2π)/5363 weeks
169.4227 .22856 (169*2π)/5363 weeks
170.70289 .30886 (170*2π)/5363 weeks
171.67867 .32608 (171*2π)/5363 weeks
172.72616 .43123 (172*2π)/5363 weeks
173.82255 .24064 (173*2π)/5363 weeks
1741.08991 .38841 (174*2π)/5363 weeks
175.90459 .83141 (175*2π)/5363 weeks
176.68517 .83747 (176*2π)/5363 weeks
177.52001 .71034 (177*2π)/5363 weeks
178.49482 .60941 (178*2π)/5363 weeks
179.38305 .59026 (179*2π)/5363 weeks
180.38811 .28757 (180*2π)/5363 weeks
181.52969 .30006 (181*2π)/5363 weeks
182.50406 .21618 (182*2π)/5363 weeks
183.57453 .11522 (183*2π)/5363 weeks
184.77669 .1861 (184*2π)/5363 weeks
185.83837 .20682 (185*2π)/5363 weeks
186.86194 .36115 (186*2π)/5363 weeks
187.77575 .48449 (187*2π)/5363 weeks
188.70331 .4921 (188*2π)/5363 weeks
189.5928 .41703 (189*2π)/5363 weeks
190.44716 .30232 (190*2π)/5363 weeks
191.66301 .01941 (191*2π)/5363 weeks
192.85742 .18599 (192*2π)/5363 weeks
193.88032 .14348 (193*2π)/5363 weeks
1941.07238 .29108 (194*2π)/5363 weeks
195.83308 .50307 (195*2π)/5363 weeks
196.70442 .34601 (196*2π)/5363 weeks
197.95347 .22651 (197*2π)/5363 weeks
1981.04824 .47421 (198*2π)/5363 weeks
199.81655 .67044 (199*2π)/5363 weeks
200.83709 .64187 (200*2π)/5363 weeks
201.50557 .83693 (201*2π)/5363 weeks
202.07515 .53705 (202*2π)/5363 weeks
203.21778 -.0633 (203*2π)/5363 weeks
204.85193 -.24647 (204*2π)/5363 weeks
2051.145 .15105 (205*2π)/5363 weeks
2061.00878 .58476 (206*2π)/5363 weeks
207.72073 .61319 (207*2π)/5363 weeks
208.64896 .42336 (208*2π)/5363 weeks
209.66704 .4974 (209*2π)/5363 weeks
210.50947 .50654 (210*2π)/5363 weeks
211.5068 .38722 (211*2π)/5363 weeks
212.41081 .20718 (212*2π)/5363 weeks
213.56092 .07937 (213*2π)/5363 weeks
214.62131 .0985 (214*2π)/5363 weeks
215.79762 .10961 (215*2π)/5362 weeks
216.80545 .26077 (216*2π)/5362 weeks
217.67651 .37342 (217*2π)/5362 weeks
218.59591 .32716 (218*2π)/5362 weeks
219.68807 .22604 (219*2π)/5362 weeks
220.57975 .29751 (220*2π)/5362 weeks
221.49796 .27413 (221*2π)/5362 weeks
222.50067 .15683 (222*2π)/5362 weeks
223.4612 -.01727 (223*2π)/5362 weeks
224.71727 -.16117 (224*2π)/5362 weeks
225.94324 -.01958 (225*2π)/5362 weeks
2261.01434 .13638 (226*2π)/5362 weeks
227.94151 .31734 (227*2π)/5362 weeks
228.85834 .37303 (228*2π)/5362 weeks
229.69044 .30565 (229*2π)/5362 weeks
230.78634 .22181 (230*2π)/5362 weeks
231.93918 .24865 (231*2π)/5362 weeks
232.94755 .52954 (232*2π)/5362 weeks
233.6984 .73034 (233*2π)/5362 weeks
234.41072 .63909 (234*2π)/5362 weeks
235.30132 .49172 (235*2π)/5362 weeks
236.11262 .38439 (236*2π)/5362 weeks
237.119 .06784 (237*2π)/5362 weeks
238.26694 -.04394 (238*2π)/5362 weeks
239.35906 -.14979 (239*2π)/5362 weeks
240.60127 -.19754 (240*2π)/5362 weeks
241.67966 .00677 (241*2π)/5362 weeks
242.50583 .08818 (242*2π)/5362 weeks
243.49403 .00462 (243*2π)/5362 weeks
244.43583 -.11074 (244*2π)/5362 weeks
245.57955 -.18777 (245*2π)/5362 weeks
246.62304 -.19227 (246*2π)/5362 weeks
247.72937 -.21517 (247*2π)/5362 weeks
248.79353 -.01309 (248*2π)/5362 weeks
249.60549 -.02061 (249*2π)/5362 weeks
250.4794 -.10281 (250*2π)/5362 weeks
251.43215 -.35065 (251*2π)/5362 weeks
252.79659 -.61882 (252*2π)/5362 weeks
2531.18876 -.45368 (253*2π)/5362 weeks
2541.23586 -.12959 (254*2π)/5362 weeks
2551.16881 .1338 (255*2π)/5362 weeks
2561.06186 .29648 (256*2π)/5362 weeks
257.89129 .57748 (257*2π)/5362 weeks
258.31395 .40645 (258*2π)/5362 weeks
259.08976 -.07046 (259*2π)/5362 weeks
260.36785 -.50162 (260*2π)/5362 weeks
261.78834 -.691 (261*2π)/5362 weeks
2621.22533 -.56141 (262*2π)/5362 weeks
2631.43796 -.10252 (263*2π)/5362 weeks
2641.29362 .27263 (264*2π)/5362 weeks
265.99526 .4968 (265*2π)/5362 weeks
266.67437 .43831 (266*2π)/5362 weeks
267.46004 .18358 (267*2π)/5362 weeks
268.53885   (268*2π)/5362 weeks
269.46004 -.18358 (269*2π)/5362 weeks
270.67437 -.43831 (270*2π)/5362 weeks
271.99526 -.4968 (271*2π)/5362 weeks
2721.29362 -.27263 (272*2π)/5362 weeks
2731.43796 .10252 (273*2π)/5362 weeks
2741.22533 .56141 (274*2π)/5362 weeks
275.78834 .691 (275*2π)/5362 weeks
276.36785 .50162 (276*2π)/5362 weeks
277.08976 .07046 (277*2π)/5362 weeks
278.31395 -.40645 (278*2π)/5362 weeks
279.89129 -.57748 (279*2π)/5362 weeks
2801.06186 -.29648 (280*2π)/5362 weeks
2811.16881 -.1338 (281*2π)/5362 weeks
2821.23586 .12959 (282*2π)/5362 weeks
2831.18876 .45368 (283*2π)/5362 weeks
284.79659 .61882 (284*2π)/5362 weeks
285.43215 .35065 (285*2π)/5362 weeks
286.4794 .10281 (286*2π)/5362 weeks
287.60549 .02061 (287*2π)/5362 weeks
288.79353 .01309 (288*2π)/5362 weeks
289.72937 .21517 (289*2π)/5362 weeks
290.62304 .19227 (290*2π)/5362 weeks
291.57955 .18777 (291*2π)/5362 weeks
292.43583 .11074 (292*2π)/5362 weeks
293.49403 -.00462 (293*2π)/5362 weeks
294.50583 -.08818 (294*2π)/5362 weeks
295.67966 -.00677 (295*2π)/5362 weeks
296.60127 .19754 (296*2π)/5362 weeks
297.35906 .14979 (297*2π)/5362 weeks
298.26694 .04394 (298*2π)/5362 weeks
299.119 -.06784 (299*2π)/5362 weeks
300.11262 -.38439 (300*2π)/5362 weeks
301.30132 -.49172 (301*2π)/5362 weeks
302.41072 -.63909 (302*2π)/5362 weeks
303.6984 -.73034 (303*2π)/5362 weeks
304.94755 -.52954 (304*2π)/5362 weeks
305.93918 -.24865 (305*2π)/5362 weeks
306.78634 -.22181 (306*2π)/5362 weeks
307.69044 -.30565 (307*2π)/5362 weeks
308.85834 -.37303 (308*2π)/5362 weeks
309.94151 -.31734 (309*2π)/5362 weeks
3101.01434 -.13638 (310*2π)/5362 weeks
311.94324 .01958 (311*2π)/5362 weeks
312.71727 .16117 (312*2π)/5362 weeks
313.4612 .01727 (313*2π)/5362 weeks
314.50067 -.15683 (314*2π)/5362 weeks
315.49796 -.27413 (315*2π)/5362 weeks
316.57975 -.29751 (316*2π)/5362 weeks
317.68807 -.22604 (317*2π)/5362 weeks
318.59591 -.32716 (318*2π)/5362 weeks
319.67651 -.37342 (319*2π)/5362 weeks
320.80545 -.26077 (320*2π)/5362 weeks
321.79762 -.10961 (321*2π)/5362 weeks
322.62131 -.0985 (322*2π)/5362 weeks
323.56092 -.07937 (323*2π)/5362 weeks
324.41081 -.20718 (324*2π)/5362 weeks
325.5068 -.38722 (325*2π)/5362 weeks
326.50947 -.50654 (326*2π)/5362 weeks
327.66704 -.4974 (327*2π)/5362 weeks
328.64896 -.42336 (328*2π)/5362 weeks
329.72073 -.61319 (329*2π)/5362 weeks
3301.00878 -.58476 (330*2π)/5362 weeks
3311.145 -.15105 (331*2π)/5362 weeks
332.85193 .24647 (332*2π)/5362 weeks
333.21778 .0633 (333*2π)/5362 weeks
334.07515 -.53705 (334*2π)/5362 weeks
335.50557 -.83693 (335*2π)/5362 weeks
336.83709 -.64187 (336*2π)/5362 weeks
337.81655 -.67044 (337*2π)/5362 weeks
3381.04824 -.47421 (338*2π)/5362 weeks
339.95347 -.22651 (339*2π)/5362 weeks
340.70442 -.34601 (340*2π)/5362 weeks
341.83308 -.50307 (341*2π)/5362 weeks
3421.07238 -.29108 (342*2π)/5362 weeks
343.88032 -.14348 (343*2π)/5362 weeks
344.85742 -.18599 (344*2π)/5362 weeks
345.66301 -.01941 (345*2π)/5362 weeks
346.44716 -.30232 (346*2π)/5362 weeks
347.5928 -.41703 (347*2π)/5362 weeks
348.70331 -.4921 (348*2π)/5362 weeks
349.77575 -.48449 (349*2π)/5362 weeks
350.86194 -.36115 (350*2π)/5362 weeks
351.83837 -.20682 (351*2π)/5362 weeks
352.77669 -.1861 (352*2π)/5362 weeks
353.57453 -.11522 (353*2π)/5362 weeks
354.50406 -.21618 (354*2π)/5362 weeks
355.52969 -.30006 (355*2π)/5362 weeks
356.38811 -.28757 (356*2π)/5362 weeks
357.38305 -.59026 (357*2π)/5362 weeks
358.49482 -.60941 (358*2π)/5361 weeks
359.52001 -.71034 (359*2π)/5361 weeks
360.68517 -.83747 (360*2π)/5361 weeks
361.90459 -.83141 (361*2π)/5361 weeks
3621.08991 -.38841 (362*2π)/5361 weeks
363.82255 -.24064 (363*2π)/5361 weeks
364.72616 -.43123 (364*2π)/5361 weeks
365.67867 -.32608 (365*2π)/5361 weeks
366.70289 -.30886 (366*2π)/5361 weeks
367.4227 -.22856 (367*2π)/5361 weeks
368.21152 -.57234 (368*2π)/5361 weeks
369.41964 -.92673 (369*2π)/5361 weeks
370.85274 -.93225 (370*2π)/5361 weeks
3711.01913 -.54265 (371*2π)/5361 weeks
372.74703 -.35491 (372*2π)/5361 weeks
373.39631 -.52788 (373*2π)/5361 weeks
374.57692 -.97725 (374*2π)/5361 weeks
3751.02518 -.93982 (375*2π)/5361 weeks
3761.09725 -.53563 (376*2π)/5361 weeks
377.8877 -.2688 (377*2π)/5361 weeks
378.63457 -.44632 (378*2π)/5361 weeks
379.62179 -.59909 (379*2π)/5361 weeks
380.63856 -.74463 (380*2π)/5361 weeks
381.99873 -.897 (381*2π)/5361 weeks
3821.11356 -.55281 (382*2π)/5361 weeks
383.91164 -.30685 (383*2π)/5361 weeks
384.81774 -.39954 (384*2π)/5361 weeks
385.87704 -.32794 (385*2π)/5361 weeks
386.77971 -.05231 (386*2π)/5361 weeks
387.3123 -.04709 (387*2π)/5361 weeks
388-.08948 -.35545 (388*2π)/5361 weeks
389.09391 -.91884 (389*2π)/5361 weeks
390.494 -1.06189 (390*2π)/5361 weeks
391.76623 -.89062 (391*2π)/5361 weeks
392.77883 -.61882 (392*2π)/5361 weeks
393.51475 -.63853 (393*2π)/5361 weeks
394.38107 -.70436 (394*2π)/5361 weeks
395.30997 -.88336 (395*2π)/5361 weeks
396.36577 -1.13298 (396*2π)/5361 weeks
397.53551 -1.15146 (397*2π)/5361 weeks
398.73935 -1.1816 (398*2π)/5361 weeks
399.72414 -1.33901 (399*2π)/5361 weeks
4001.14881 -1.31587 (400*2π)/5361 weeks
4011.29502 -.85055 (401*2π)/5361 weeks
4021.00024 -.72534 (402*2π)/5361 weeks
403.76757 -.70992 (403*2π)/5361 weeks
404.73197 -1.0271 (404*2π)/5361 weeks
4051.07663 -1.06747 (405*2π)/5361 weeks
406.97997 -.9783 (406*2π)/5361 weeks
4071.05123 -1.17322 (407*2π)/5361 weeks
4081.43511 -1.01208 (408*2π)/5361 weeks
4091.59544 -.60552 (409*2π)/5361 weeks
4101.3544 -.29429 (410*2π)/5361 weeks
4111.23134 -.27822 (411*2π)/5361 weeks
412.85595 -.24216 (412*2π)/5361 weeks
413.88927 -.21534 (413*2π)/5361 weeks
414.56992 -.39547 (414*2π)/5361 weeks
415.73631 -.59493 (415*2π)/5361 weeks
4161.08066 -.5038 (416*2π)/5361 weeks
417.77786 .05173 (417*2π)/5361 weeks
418.28286 .11643 (418*2π)/5361 weeks
419-.11723 -.38881 (419*2π)/5361 weeks
420-.0826 -.99802 (420*2π)/5361 weeks
421.43313 -1.00473 (421*2π)/5361 weeks
422.65488 -.72913 (422*2π)/5361 weeks
423.26769 -.51672 (423*2π)/5361 weeks
424-.01793 -.77969 (424*2π)/5361 weeks
425.09718 -1.17522 (425*2π)/5361 weeks
426.44888 -1.28194 (426*2π)/5361 weeks
427.51452 -.91781 (427*2π)/5361 weeks
428.19798 -.96511 (428*2π)/5361 weeks
429.1349 -1.04178 (429*2π)/5361 weeks
430-.11071 -1.3017 (430*2π)/5361 weeks
431.2389 -1.9532 (431*2π)/5361 weeks
432.47231 -1.92834 (432*2π)/5361 weeks
433.99392 -1.93977 (433*2π)/5361 weeks
4341.29118 -1.53462 (434*2π)/5361 weeks
4351.06797 -1.19862 (435*2π)/5361 weeks
436.93418 -1.15242 (436*2π)/5361 weeks
437.73448 -.93368 (437*2π)/5361 weeks
438.57776 -1.4282 (438*2π)/5361 weeks
439.89763 -1.53381 (439*2π)/5361 weeks
4401.00977 -1.47711 (440*2π)/5361 weeks
4411.1628 -1.23195 (441*2π)/5361 weeks
4421.25619 -.95201 (442*2π)/5361 weeks
443.83908 -.80578 (443*2π)/5361 weeks
444.79327 -1.07798 (444*2π)/5361 weeks
445.96267 -.96659 (445*2π)/5361 weeks
446.78278 -.70196 (446*2π)/5361 weeks
447.25341 -.50167 (447*2π)/5361 weeks
448-.24097 -1.14739 (448*2π)/5361 weeks
449.04744 -1.72603 (449*2π)/5361 weeks
450.48613 -1.98635 (450*2π)/5361 weeks
4511.26771 -1.53973 (451*2π)/5361 weeks
452.95236 -.61239 (452*2π)/5361 weeks
453-.16594 -.80611 (453*2π)/5361 weeks
454-.31487 -1.51969 (454*2π)/5361 weeks
455-.08118 -2.07873 (455*2π)/5361 weeks
456.32919 -2.23833 (456*2π)/5361 weeks
457.78755 -2.11972 (457*2π)/5361 weeks
458.53382 -1.96368 (458*2π)/5361 weeks
459.64383 -1.92186 (459*2π)/5361 weeks
460.46196 -2.13503 (460*2π)/5361 weeks
461.63612 -2.19447 (461*2π)/5361 weeks
462.48142 -2.35074 (462*2π)/5361 weeks
463.99474 -2.99018 (463*2π)/5361 weeks
4641.80863 -2.74098 (464*2π)/5361 weeks
4652.07324 -1.95883 (465*2π)/5361 weeks
4661.80688 -1.45256 (466*2π)/5361 weeks
4671.83958 -1.22937 (467*2π)/5361 weeks
4681.48915 -.90445 (468*2π)/5361 weeks
469.82585 -.78077 (469*2π)/5361 weeks
470.87251 -.86566 (470*2π)/5361 weeks
471.16215 -.861 (471*2π)/5361 weeks
472-.60885 -1.73924 (472*2π)/5361 weeks
473.0346 -2.70903 (473*2π)/5361 weeks
474.71985 -2.7319 (474*2π)/5361 weeks
4751.15997 -2.78795 (475*2π)/5361 weeks
4761.80882 -2.3449 (476*2π)/5361 weeks
4772.00691 -1.69366 (477*2π)/5361 weeks
4781.34892 -.68468 (478*2π)/5361 weeks
479.46996 -.40768 (479*2π)/5361 weeks
480-.67718 -1.39524 (480*2π)/5361 weeks
481-.24701 -2.49227 (481*2π)/5361 weeks
482.4412 -2.43535 (482*2π)/5361 weeks
483.67806 -2.48669 (483*2π)/5361 weeks
484.52785 -2.18821 (484*2π)/5361 weeks
485.66878 -2.11306 (485*2π)/5361 weeks
486.60867 -1.93336 (486*2π)/5361 weeks
487.1046 -1.64068 (487*2π)/5361 weeks
488-.97814 -1.91702 (488*2π)/5361 weeks
489-1.04782 -3.38883 (489*2π)/5361 weeks
490-.36653 -4.10261 (490*2π)/5361 weeks
491.57275 -4.47355 (491*2π)/5361 weeks
492.90646 -3.76061 (492*2π)/5361 weeks
4931.37874 -3.35848 (493*2π)/5361 weeks
4941.29293 -2.85733 (494*2π)/5361 weeks
495.55843 -2.41684 (495*2π)/5361 weeks
496-.45454 -2.95578 (496*2π)/5361 weeks
497-.30904 -4.31627 (497*2π)/5361 weeks
498.65475 -5.12911 (498*2π)/5361 weeks
4991.62618 -4.91222 (499*2π)/5361 weeks
5002.38229 -4.1028 (500*2π)/5361 weeks
5012.26966 -3.2183 (501*2π)/5361 weeks
5022.13397 -2.51311 (502*2π)/5361 weeks
503.86548 -1.3441 (503*2π)/5361 weeks
504-1.40144 -1.85247 (504*2π)/5361 weeks
505-2.63041 -3.8513 (505*2π)/5361 weeks
506-1.87619 -6.03163 (506*2π)/5361 weeks
507-.70762 -6.89174 (507*2π)/5361 weeks
508.33456 -7.34057 (508*2π)/5361 weeks
5091.62738 -7.07447 (509*2π)/5361 weeks
5102.85474 -6.70523 (510*2π)/5361 weeks
5112.16047 -4.63515 (511*2π)/5361 weeks
512.44916 -4.45406 (512*2π)/5361 weeks
513-.43795 -6.13401 (513*2π)/5361 weeks
514-.2219 -7.11957 (514*2π)/5361 weeks
515-.46488 -9.52837 (515*2π)/5361 weeks
5162.75855 -11.0239 (516*2π)/5361 weeks
5176.08051 -9.29795 (517*2π)/5361 weeks
5185.75083 -6.21705 (518*2π)/5361 weeks
5193.8537 -4.6848 (519*2π)/5361 weeks
5201.87368 -4.47642 (520*2π)/5361 weeks
521-.29164 -5.2943 (521*2π)/5361 weeks
522-2.89134 -8.96539 (522*2π)/5361 weeks
523-2.46333 -12.30489 (523*2π)/5361 weeks
524.48818 -16.59943 (524*2π)/5361 weeks
5254.49844 -18.57504 (525*2π)/5361 weeks
52610.83195 -18.45718 (526*2π)/5361 weeks
52714.40272 -13.00228 (527*2π)/5361 weeks
52812.10232 -7.38685 (528*2π)/5361 weeks
5297.63296 -1.04676 (529*2π)/5361 weeks
530-4.85725 -5.27054 (530*2π)/5361 weeks
531-12.02241 -16.02801 (531*2π)/5361 weeks
532-14.33671 -34.97829 (532*2π)/5361 weeks
5332.92632 -60.92214 (533*2π)/5361 weeks
53429.20042 -77.67482 (534*2π)/5361 weeks



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