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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 50 weeks (18.4857*sine), 46 weeks (16.801*sine), and 55 weeks (16.7943*sine).

UNG (United States Natural Gas Fund ETF) has an average price of 82.76 (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 10/16/2017 for UNG (United States Natural Gas Fund ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
082.75795   0 
183.0977 73.94446 (1*2π)/549549 weeks
230.6531 76.831 (2*2π)/549275 weeks
34.76322 60.28868 (3*2π)/549183 weeks
4-13.91492 36.53141 (4*2π)/549137 weeks
5-12.51471 17.52287 (5*2π)/549110 weeks
6-5.8581 6.54398 (6*2π)/54992 weeks
75.18396 .59857 (7*2π)/54978 weeks
811.67551 6.827 (8*2π)/54969 weeks
914.38563 11.15112 (9*2π)/54961 weeks
1011.93226 16.79433 (10*2π)/54955 weeks
115.60484 18.48569 (11*2π)/54950 weeks
121.4614 16.80096 (12*2π)/54946 weeks
13-2.13149 13.6712 (13*2π)/54942 weeks
14-2.39492 10.05529 (14*2π)/54939 weeks
15-1.53245 5.72163 (15*2π)/54937 weeks
16.94205 4.70147 (16*2π)/54934 weeks
173.06736 4.53067 (17*2π)/54932 weeks
185.05137 5.19324 (18*2π)/54931 weeks
196.12633 7.40794 (19*2π)/54929 weeks
204.31353 10.53929 (20*2π)/54927 weeks
211.0162 10.5479 (21*2π)/54926 weeks
22-.67021 7.76545 (22*2π)/54925 weeks
23-.21139 6.73333 (23*2π)/54924 weeks
24-.26655 5.29296 (24*2π)/54923 weeks
251.35104 4.25133 (25*2π)/54922 weeks
262.83341 4.90988 (26*2π)/54921 weeks
272.10379 6.86545 (27*2π)/54920 weeks
281.32528 7.13447 (28*2π)/54920 weeks
29.02689 6.97196 (29*2π)/54919 weeks
30-1.00659 6.49289 (30*2π)/54918 weeks
31-2.1792 5.45319 (31*2π)/54918 weeks
32-2.40218 3.13104 (32*2π)/54917 weeks
33-.97825 1.46505 (33*2π)/54917 weeks
341.16493 1.44258 (34*2π)/54916 weeks
352.06515 2.6548 (35*2π)/54916 weeks
362.2404 3.25761 (36*2π)/54915 weeks
372.27788 4.14875 (37*2π)/54915 weeks
381.48624 4.82863 (38*2π)/54914 weeks
39.5231 5.00601 (39*2π)/54914 weeks
40-.33226 4.1803 (40*2π)/54914 weeks
41-.41678 2.85487 (41*2π)/54913 weeks
42.5494 2.36109 (42*2π)/54913 weeks
431.25227 2.77855 (43*2π)/54913 weeks
441.3299 3.25783 (44*2π)/54912 weeks
45.88815 3.70864 (45*2π)/54912 weeks
46.70442 4.34065 (46*2π)/54912 weeks
47-.26104 4.04502 (47*2π)/54912 weeks
48-.92835 3.41921 (48*2π)/54911 weeks
49-1.11139 2.07597 (49*2π)/54911 weeks
50-.03164 1.56188 (50*2π)/54911 weeks
51.53163 1.7801 (51*2π)/54911 weeks
52.59357 2.02191 (52*2π)/54911 weeks
53.52539 2.21484 (53*2π)/54910 weeks
54.74381 2.26794 (54*2π)/54910 weeks
55.38896 2.35214 (55*2π)/54910 weeks
56.03878 2.57425 (56*2π)/54910 weeks
57-.63815 1.85222 (57*2π)/54910 weeks
58-.12402 .55658 (58*2π)/5499 weeks
591.04045 .65144 (59*2π)/5499 weeks
601.95278 1.11759 (60*2π)/5499 weeks
611.82877 1.97979 (61*2π)/5499 weeks
621.47068 2.61587 (62*2π)/5499 weeks
63.85653 2.66769 (63*2π)/5499 weeks
64.44709 2.71877 (64*2π)/5499 weeks
65-.35376 2.34193 (65*2π)/5498 weeks
66-.39342 1.09589 (66*2π)/5498 weeks
67.37885 .76817 (67*2π)/5498 weeks
68.82116 1.06822 (68*2π)/5498 weeks
691.10469 .69151 (69*2π)/5498 weeks
701.54432 .98901 (70*2π)/5498 weeks
711.8035 1.41988 (71*2π)/5498 weeks
721.94056 1.51175 (72*2π)/5498 weeks
732.07616 2.08418 (73*2π)/5498 weeks
741.59839 2.76917 (74*2π)/5497 weeks
75.76497 2.84547 (75*2π)/5497 weeks
76.52666 2.19435 (76*2π)/5497 weeks
77.62134 2.13459 (77*2π)/5497 weeks
78.43058 2.01373 (78*2π)/5497 weeks
79.64357 1.89696 (79*2π)/5497 weeks
80.52155 1.87871 (80*2π)/5497 weeks
81.74083 2.119 (81*2π)/5497 weeks
82.30328 2.18232 (82*2π)/5497 weeks
83-.09372 2.01735 (83*2π)/5497 weeks
84-.30668 1.47782 (84*2π)/5497 weeks
85-.16831 .79816 (85*2π)/5496 weeks
86.89356 .5711 (86*2π)/5496 weeks
871.24683 1.44557 (87*2π)/5496 weeks
88.53507 1.96537 (88*2π)/5496 weeks
89.09639 1.72329 (89*2π)/5496 weeks
90-.21886 1.22535 (90*2π)/5496 weeks
91.13508 .53382 (91*2π)/5496 weeks
92.73889 .63415 (92*2π)/5496 weeks
93.94237 .85616 (93*2π)/5496 weeks
94.81414 1.04362 (94*2π)/5496 weeks
95.73087 .83995 (95*2π)/5496 weeks
961.11974 .81267 (96*2π)/5496 weeks
971.14043 1.19712 (97*2π)/5496 weeks
981.10362 1.41422 (98*2π)/5496 weeks
99.93732 1.42764 (99*2π)/5496 weeks
100.66533 1.469 (100*2π)/5495 weeks
101.49502 1.07327 (101*2π)/5495 weeks
102.9435 1.08232 (102*2π)/5495 weeks
103.99634 1.1286 (103*2π)/5495 weeks
1041.19925 1.24338 (104*2π)/5495 weeks
1051.13591 1.7264 (105*2π)/5495 weeks
106.70516 1.97508 (106*2π)/5495 weeks
107.41446 1.78787 (107*2π)/5495 weeks
108-.12879 1.71422 (108*2π)/5495 weeks
109-.01219 1.14919 (109*2π)/5495 weeks
110.19408 1.03491 (110*2π)/5495 weeks
111.27915 .86565 (111*2π)/5495 weeks
112.56731 1.02632 (112*2π)/5495 weeks
113.29944 1.27798 (113*2π)/5495 weeks
114.02565 1.07857 (114*2π)/5495 weeks
115.05278 .6691 (115*2π)/5495 weeks
116.37923 .48976 (116*2π)/5495 weeks
117.63403 .8297 (117*2π)/5495 weeks
118.38883 1.01443 (118*2π)/5495 weeks
119-.15678 .84295 (119*2π)/5495 weeks
120-.10051 .30476 (120*2π)/5495 weeks
121.37524 -.12094 (121*2π)/5495 weeks
122.82595 -.04191 (122*2π)/5495 weeks
1231.02055 .53418 (123*2π)/5494 weeks
124.70883 .57509 (124*2π)/5494 weeks
125.55759 .36825 (125*2π)/5494 weeks
126.87308 .21284 (126*2π)/5494 weeks
127.8353 .23802 (127*2π)/5494 weeks
1281.20124 .25901 (128*2π)/5494 weeks
1291.29979 .278 (129*2π)/5494 weeks
1301.54089 .55596 (130*2π)/5494 weeks
1311.41935 .97011 (131*2π)/5494 weeks
1321.08716 1.1737 (132*2π)/5494 weeks
133.96263 .96727 (133*2π)/5494 weeks
1341.06213 .97652 (134*2π)/5494 weeks
135.75123 1.06012 (135*2π)/5494 weeks
136.69643 .76043 (136*2π)/5494 weeks
137.95705 .69866 (137*2π)/5494 weeks
1381.17822 .7283 (138*2π)/5494 weeks
1391.22257 1.18735 (139*2π)/5494 weeks
140.83333 1.3594 (140*2π)/5494 weeks
141.67616 1.12079 (141*2π)/5494 weeks
142.55995 1.20544 (142*2π)/5494 weeks
143.48395 1.15507 (143*2π)/5494 weeks
144.31187 .94188 (144*2π)/5494 weeks
145.34024 .7447 (145*2π)/5494 weeks
146.45868 .61418 (146*2π)/5494 weeks
147.57027 .53273 (147*2π)/5494 weeks
148.76076 .7677 (148*2π)/5494 weeks
149.64169 1.003 (149*2π)/5494 weeks
150.30662 1.05211 (150*2π)/5494 weeks
151-.02992 .75253 (151*2π)/5494 weeks
152.10833 .15118 (152*2π)/5494 weeks
153.47367 -.0309 (153*2π)/5494 weeks
154.85127 .1583 (154*2π)/5494 weeks
155.84931 .35493 (155*2π)/5494 weeks
156.79706 .35797 (156*2π)/5494 weeks
157.98301 .30492 (157*2π)/5493 weeks
1581.07652 .59239 (158*2π)/5493 weeks
159.83686 .90967 (159*2π)/5493 weeks
160.61081 .68775 (160*2π)/5493 weeks
161.59815 .56592 (161*2π)/5493 weeks
162.62763 .41005 (162*2π)/5493 weeks
163.93003 .28681 (163*2π)/5493 weeks
1641.08649 .55108 (164*2π)/5493 weeks
165.96032 .94234 (165*2π)/5493 weeks
166.53179 .93853 (166*2π)/5493 weeks
167.39587 .49455 (167*2π)/5493 weeks
168.73472 .34767 (168*2π)/5493 weeks
169.9933 .52803 (169*2π)/5493 weeks
170.83897 .90366 (170*2π)/5493 weeks
171.42428 .91716 (171*2π)/5493 weeks
172.20671 .59237 (172*2π)/5493 weeks
173.37773 .24191 (173*2π)/5493 weeks
174.67366 .27791 (174*2π)/5493 weeks
175.64865 .33752 (175*2π)/5493 weeks
176.74339 .40919 (176*2π)/5493 weeks
177.7346 .24047 (177*2π)/5493 weeks
178.99196 .32587 (178*2π)/5493 weeks
179.99917 .78322 (179*2π)/5493 weeks
180.73786 .80282 (180*2π)/5493 weeks
181.53146 .72215 (181*2π)/5493 weeks
182.47706 .60484 (182*2π)/5493 weeks
183.43277 .58973 (183*2π)/5493 weeks
184.28977 .3738 (184*2π)/5493 weeks
185.48145 .27579 (185*2π)/5493 weeks
186.46468 .28844 (186*2π)/5493 weeks
187.52799 .19709 (187*2π)/5493 weeks
188.71488 .11306 (188*2π)/5493 weeks
189.7597 .20784 (189*2π)/5493 weeks
190.87284 .29964 (190*2π)/5493 weeks
191.84843 .41496 (191*2π)/5493 weeks
192.7212 .44743 (192*2π)/5493 weeks
193.61197 .46696 (193*2π)/5493 weeks
194.54844 .40363 (194*2π)/5493 weeks
195.45297 .14641 (195*2π)/5493 weeks
196.76582 .04234 (196*2π)/5493 weeks
197.79841 .20002 (197*2π)/5493 weeks
198.91569 .16118 (198*2π)/5493 weeks
1991.04165 .41144 (199*2π)/5493 weeks
200.77397 .46445 (200*2π)/5493 weeks
201.71088 .27263 (201*2π)/5493 weeks
202.98815 .2735 (202*2π)/5493 weeks
2031.02697 .51985 (203*2π)/5493 weeks
204.76778 .62337 (204*2π)/5493 weeks
205.81828 .67058 (205*2π)/5493 weeks
206.4463 .79926 (206*2π)/5493 weeks
207.05297 .45362 (207*2π)/5493 weeks
208.24064 -.09886 (208*2π)/5493 weeks
209.863 -.22493 (209*2π)/5493 weeks
2101.12347 .1569 (210*2π)/5493 weeks
211.98513 .57005 (211*2π)/5493 weeks
212.71102 .59836 (212*2π)/5493 weeks
213.62926 .41471 (213*2π)/5493 weeks
214.66004 .47939 (214*2π)/5493 weeks
215.52013 .50216 (215*2π)/5493 weeks
216.49917 .36301 (216*2π)/5493 weeks
217.38312 .23055 (217*2π)/5493 weeks
218.50778 .08296 (218*2π)/5493 weeks
219.5972 .115 (219*2π)/5493 weeks
220.73899 .0798 (220*2π)/5492 weeks
221.78718 .24007 (221*2π)/5492 weeks
222.71998 .37572 (222*2π)/5492 weeks
223.62345 .32937 (223*2π)/5492 weeks
224.61007 .19708 (224*2π)/5492 weeks
225.6096 .32446 (225*2π)/5492 weeks
226.55214 .29113 (226*2π)/5492 weeks
227.48949 .16405 (227*2π)/5492 weeks
228.45192 .08127 (228*2π)/5492 weeks
229.58639 -.14757 (229*2π)/5492 weeks
230.85696 -.12259 (230*2π)/5492 weeks
231.951 .04219 (231*2π)/5492 weeks
232.97393 .22949 (232*2π)/5492 weeks
233.86007 .31826 (233*2π)/5492 weeks
234.74128 .38308 (234*2π)/5492 weeks
235.69884 .22618 (235*2π)/5492 weeks
236.79389 .20845 (236*2π)/5492 weeks
237.95894 .35028 (237*2π)/5492 weeks
238.86281 .608 (238*2π)/5492 weeks
239.55968 .71342 (239*2π)/5492 weeks
240.34798 .57982 (240*2π)/5492 weeks
241.27091 .47431 (241*2π)/5492 weeks
242.07804 .28504 (242*2π)/5492 weeks
243.15731 .01172 (243*2π)/5492 weeks
244.26964 -.06508 (244*2π)/5492 weeks
245.37109 -.17153 (245*2π)/5492 weeks
246.61997 -.15634 (246*2π)/5492 weeks
247.65194 .03963 (247*2π)/5492 weeks
248.47446 .06974 (248*2π)/5492 weeks
249.47326 .00942 (249*2π)/5492 weeks
250.42959 -.11809 (250*2π)/5492 weeks
251.571 -.17484 (251*2π)/5492 weeks
252.61254 -.18417 (252*2π)/5492 weeks
253.71648 -.20679 (253*2π)/5492 weeks
254.77965 -.01467 (254*2π)/5492 weeks
255.59431 -.01668 (255*2π)/5492 weeks
256.47518 -.08671 (256*2π)/5492 weeks
257.42129 -.3086 (257*2π)/5492 weeks
258.72778 -.60452 (258*2π)/5492 weeks
2591.11351 -.48712 (259*2π)/5492 weeks
2601.20157 -.14983 (260*2π)/5492 weeks
2611.17385 .10894 (261*2π)/5492 weeks
2621.07423 .26303 (262*2π)/5492 weeks
263.96903 .46932 (263*2π)/5492 weeks
264.39369 .49915 (264*2π)/5492 weeks
265.11765 .10511 (265*2π)/5492 weeks
266.27365 -.41064 (266*2π)/5492 weeks
267.61481 -.65525 (267*2π)/5492 weeks
2681.04912 -.61599 (268*2π)/5492 weeks
2691.3949 -.2736 (269*2π)/5492 weeks
2701.35356 .14347 (270*2π)/5492 weeks
2711.13393 .40407 (271*2π)/5492 weeks
272.77901 .45081 (272*2π)/5492 weeks
273.50409 .31259 (273*2π)/5492 weeks
274.46533 .03155 (274*2π)/5492 weeks
275.46533 -.03155 (275*2π)/5492 weeks
276.50409 -.31259 (276*2π)/5492 weeks
277.77901 -.45081 (277*2π)/5492 weeks
2781.13393 -.40407 (278*2π)/5492 weeks
2791.35356 -.14347 (279*2π)/5492 weeks
2801.3949 .2736 (280*2π)/5492 weeks
2811.04912 .61599 (281*2π)/5492 weeks
282.61481 .65525 (282*2π)/5492 weeks
283.27365 .41064 (283*2π)/5492 weeks
284.11765 -.10511 (284*2π)/5492 weeks
285.39369 -.49915 (285*2π)/5492 weeks
286.96903 -.46932 (286*2π)/5492 weeks
2871.07423 -.26303 (287*2π)/5492 weeks
2881.17385 -.10894 (288*2π)/5492 weeks
2891.20157 .14983 (289*2π)/5492 weeks
2901.11351 .48712 (290*2π)/5492 weeks
291.72778 .60452 (291*2π)/5492 weeks
292.42129 .3086 (292*2π)/5492 weeks
293.47518 .08671 (293*2π)/5492 weeks
294.59431 .01668 (294*2π)/5492 weeks
295.77965 .01467 (295*2π)/5492 weeks
296.71648 .20679 (296*2π)/5492 weeks
297.61254 .18417 (297*2π)/5492 weeks
298.571 .17484 (298*2π)/5492 weeks
299.42959 .11809 (299*2π)/5492 weeks
300.47326 -.00942 (300*2π)/5492 weeks
301.47446 -.06974 (301*2π)/5492 weeks
302.65194 -.03963 (302*2π)/5492 weeks
303.61997 .15634 (303*2π)/5492 weeks
304.37109 .17153 (304*2π)/5492 weeks
305.26964 .06508 (305*2π)/5492 weeks
306.15731 -.01172 (306*2π)/5492 weeks
307.07804 -.28504 (307*2π)/5492 weeks
308.27091 -.47431 (308*2π)/5492 weeks
309.34798 -.57982 (309*2π)/5492 weeks
310.55968 -.71342 (310*2π)/5492 weeks
311.86281 -.608 (311*2π)/5492 weeks
312.95894 -.35028 (312*2π)/5492 weeks
313.79389 -.20845 (313*2π)/5492 weeks
314.69884 -.22618 (314*2π)/5492 weeks
315.74128 -.38308 (315*2π)/5492 weeks
316.86007 -.31826 (316*2π)/5492 weeks
317.97393 -.22949 (317*2π)/5492 weeks
318.951 -.04219 (318*2π)/5492 weeks
319.85696 .12259 (319*2π)/5492 weeks
320.58639 .14757 (320*2π)/5492 weeks
321.45192 -.08127 (321*2π)/5492 weeks
322.48949 -.16405 (322*2π)/5492 weeks
323.55214 -.29113 (323*2π)/5492 weeks
324.6096 -.32446 (324*2π)/5492 weeks
325.61007 -.19708 (325*2π)/5492 weeks
326.62345 -.32937 (326*2π)/5492 weeks
327.71998 -.37572 (327*2π)/5492 weeks
328.78718 -.24007 (328*2π)/5492 weeks
329.73899 -.0798 (329*2π)/5492 weeks
330.5972 -.115 (330*2π)/5492 weeks
331.50778 -.08296 (331*2π)/5492 weeks
332.38312 -.23055 (332*2π)/5492 weeks
333.49917 -.36301 (333*2π)/5492 weeks
334.52013 -.50216 (334*2π)/5492 weeks
335.66004 -.47939 (335*2π)/5492 weeks
336.62926 -.41471 (336*2π)/5492 weeks
337.71102 -.59836 (337*2π)/5492 weeks
338.98513 -.57005 (338*2π)/5492 weeks
3391.12347 -.1569 (339*2π)/5492 weeks
340.863 .22493 (340*2π)/5492 weeks
341.24064 .09886 (341*2π)/5492 weeks
342.05297 -.45362 (342*2π)/5492 weeks
343.4463 -.79926 (343*2π)/5492 weeks
344.81828 -.67058 (344*2π)/5492 weeks
345.76778 -.62337 (345*2π)/5492 weeks
3461.02697 -.51985 (346*2π)/5492 weeks
347.98815 -.2735 (347*2π)/5492 weeks
348.71088 -.27263 (348*2π)/5492 weeks
349.77397 -.46445 (349*2π)/5492 weeks
3501.04165 -.41144 (350*2π)/5492 weeks
351.91569 -.16118 (351*2π)/5492 weeks
352.79841 -.20002 (352*2π)/5492 weeks
353.76582 -.04234 (353*2π)/5492 weeks
354.45297 -.14641 (354*2π)/5492 weeks
355.54844 -.40363 (355*2π)/5492 weeks
356.61197 -.46696 (356*2π)/5492 weeks
357.7212 -.44743 (357*2π)/5492 weeks
358.84843 -.41496 (358*2π)/5492 weeks
359.87284 -.29964 (359*2π)/5492 weeks
360.7597 -.20784 (360*2π)/5492 weeks
361.71488 -.11306 (361*2π)/5492 weeks
362.52799 -.19709 (362*2π)/5492 weeks
363.46468 -.28844 (363*2π)/5492 weeks
364.48145 -.27579 (364*2π)/5492 weeks
365.28977 -.3738 (365*2π)/5492 weeks
366.43277 -.58973 (366*2π)/5492 weeks
367.47706 -.60484 (367*2π)/5491 weeks
368.53146 -.72215 (368*2π)/5491 weeks
369.73786 -.80282 (369*2π)/5491 weeks
370.99917 -.78322 (370*2π)/5491 weeks
371.99196 -.32587 (371*2π)/5491 weeks
372.7346 -.24047 (372*2π)/5491 weeks
373.74339 -.40919 (373*2π)/5491 weeks
374.64865 -.33752 (374*2π)/5491 weeks
375.67366 -.27791 (375*2π)/5491 weeks
376.37773 -.24191 (376*2π)/5491 weeks
377.20671 -.59237 (377*2π)/5491 weeks
378.42428 -.91716 (378*2π)/5491 weeks
379.83897 -.90366 (379*2π)/5491 weeks
380.9933 -.52803 (380*2π)/5491 weeks
381.73472 -.34767 (381*2π)/5491 weeks
382.39587 -.49455 (382*2π)/5491 weeks
383.53179 -.93853 (383*2π)/5491 weeks
384.96032 -.94234 (384*2π)/5491 weeks
3851.08649 -.55108 (385*2π)/5491 weeks
386.93003 -.28681 (386*2π)/5491 weeks
387.62763 -.41005 (387*2π)/5491 weeks
388.59815 -.56592 (388*2π)/5491 weeks
389.61081 -.68775 (389*2π)/5491 weeks
390.83686 -.90967 (390*2π)/5491 weeks
3911.07652 -.59239 (391*2π)/5491 weeks
392.98301 -.30492 (392*2π)/5491 weeks
393.79706 -.35797 (393*2π)/5491 weeks
394.84931 -.35493 (394*2π)/5491 weeks
395.85127 -.1583 (395*2π)/5491 weeks
396.47367 .0309 (396*2π)/5491 weeks
397.10833 -.15118 (397*2π)/5491 weeks
398-.02992 -.75253 (398*2π)/5491 weeks
399.30662 -1.05211 (399*2π)/5491 weeks
400.64169 -1.003 (400*2π)/5491 weeks
401.76076 -.7677 (401*2π)/5491 weeks
402.57027 -.53273 (402*2π)/5491 weeks
403.45868 -.61418 (403*2π)/5491 weeks
404.34024 -.7447 (404*2π)/5491 weeks
405.31187 -.94188 (405*2π)/5491 weeks
406.48395 -1.15507 (406*2π)/5491 weeks
407.55995 -1.20544 (407*2π)/5491 weeks
408.67616 -1.12079 (408*2π)/5491 weeks
409.83333 -1.3594 (409*2π)/5491 weeks
4101.22257 -1.18735 (410*2π)/5491 weeks
4111.17822 -.7283 (411*2π)/5491 weeks
412.95705 -.69866 (412*2π)/5491 weeks
413.69643 -.76043 (413*2π)/5491 weeks
414.75123 -1.06012 (414*2π)/5491 weeks
4151.06213 -.97652 (415*2π)/5491 weeks
416.96263 -.96727 (416*2π)/5491 weeks
4171.08716 -1.1737 (417*2π)/5491 weeks
4181.41935 -.97011 (418*2π)/5491 weeks
4191.54089 -.55596 (419*2π)/5491 weeks
4201.29979 -.278 (420*2π)/5491 weeks
4211.20124 -.25901 (421*2π)/5491 weeks
422.8353 -.23802 (422*2π)/5491 weeks
423.87308 -.21284 (423*2π)/5491 weeks
424.55759 -.36825 (424*2π)/5491 weeks
425.70883 -.57509 (425*2π)/5491 weeks
4261.02055 -.53418 (426*2π)/5491 weeks
427.82595 .04191 (427*2π)/5491 weeks
428.37524 .12094 (428*2π)/5491 weeks
429-.10051 -.30476 (429*2π)/5491 weeks
430-.15678 -.84295 (430*2π)/5491 weeks
431.38883 -1.01443 (431*2π)/5491 weeks
432.63403 -.8297 (432*2π)/5491 weeks
433.37923 -.48976 (433*2π)/5491 weeks
434.05278 -.6691 (434*2π)/5491 weeks
435.02565 -1.07857 (435*2π)/5491 weeks
436.29944 -1.27798 (436*2π)/5491 weeks
437.56731 -1.02632 (437*2π)/5491 weeks
438.27915 -.86565 (438*2π)/5491 weeks
439.19408 -1.03491 (439*2π)/5491 weeks
440-.01219 -1.14919 (440*2π)/5491 weeks
441-.12879 -1.71422 (441*2π)/5491 weeks
442.41446 -1.78787 (442*2π)/5491 weeks
443.70516 -1.97508 (443*2π)/5491 weeks
4441.13591 -1.7264 (444*2π)/5491 weeks
4451.19925 -1.24338 (445*2π)/5491 weeks
446.99634 -1.1286 (446*2π)/5491 weeks
447.9435 -1.08232 (447*2π)/5491 weeks
448.49502 -1.07327 (448*2π)/5491 weeks
449.66533 -1.469 (449*2π)/5491 weeks
450.93732 -1.42764 (450*2π)/5491 weeks
4511.10362 -1.41422 (451*2π)/5491 weeks
4521.14043 -1.19712 (452*2π)/5491 weeks
4531.11974 -.81267 (453*2π)/5491 weeks
454.73087 -.83995 (454*2π)/5491 weeks
455.81414 -1.04362 (455*2π)/5491 weeks
456.94237 -.85616 (456*2π)/5491 weeks
457.73889 -.63415 (457*2π)/5491 weeks
458.13508 -.53382 (458*2π)/5491 weeks
459-.21886 -1.22535 (459*2π)/5491 weeks
460.09639 -1.72329 (460*2π)/5491 weeks
461.53507 -1.96537 (461*2π)/5491 weeks
4621.24683 -1.44557 (462*2π)/5491 weeks
463.89356 -.5711 (463*2π)/5491 weeks
464-.16831 -.79816 (464*2π)/5491 weeks
465-.30668 -1.47782 (465*2π)/5491 weeks
466-.09372 -2.01735 (466*2π)/5491 weeks
467.30328 -2.18232 (467*2π)/5491 weeks
468.74083 -2.119 (468*2π)/5491 weeks
469.52155 -1.87871 (469*2π)/5491 weeks
470.64357 -1.89696 (470*2π)/5491 weeks
471.43058 -2.01373 (471*2π)/5491 weeks
472.62134 -2.13459 (472*2π)/5491 weeks
473.52666 -2.19435 (473*2π)/5491 weeks
474.76497 -2.84547 (474*2π)/5491 weeks
4751.59839 -2.76917 (475*2π)/5491 weeks
4762.07616 -2.08418 (476*2π)/5491 weeks
4771.94056 -1.51175 (477*2π)/5491 weeks
4781.8035 -1.41988 (478*2π)/5491 weeks
4791.54432 -.98901 (479*2π)/5491 weeks
4801.10469 -.69151 (480*2π)/5491 weeks
481.82116 -1.06822 (481*2π)/5491 weeks
482.37885 -.76817 (482*2π)/5491 weeks
483-.39342 -1.09589 (483*2π)/5491 weeks
484-.35376 -2.34193 (484*2π)/5491 weeks
485.44709 -2.71877 (485*2π)/5491 weeks
486.85653 -2.66769 (486*2π)/5491 weeks
4871.47068 -2.61587 (487*2π)/5491 weeks
4881.82877 -1.97979 (488*2π)/5491 weeks
4891.95278 -1.11759 (489*2π)/5491 weeks
4901.04045 -.65144 (490*2π)/5491 weeks
491-.12402 -.55658 (491*2π)/5491 weeks
492-.63815 -1.85222 (492*2π)/5491 weeks
493.03878 -2.57425 (493*2π)/5491 weeks
494.38896 -2.35214 (494*2π)/5491 weeks
495.74381 -2.26794 (495*2π)/5491 weeks
496.52539 -2.21484 (496*2π)/5491 weeks
497.59357 -2.02191 (497*2π)/5491 weeks
498.53163 -1.7801 (498*2π)/5491 weeks
499-.03164 -1.56188 (499*2π)/5491 weeks
500-1.11139 -2.07597 (500*2π)/5491 weeks
501-.92835 -3.41921 (501*2π)/5491 weeks
502-.26104 -4.04502 (502*2π)/5491 weeks
503.70442 -4.34065 (503*2π)/5491 weeks
504.88815 -3.70864 (504*2π)/5491 weeks
5051.3299 -3.25783 (505*2π)/5491 weeks
5061.25227 -2.77855 (506*2π)/5491 weeks
507.5494 -2.36109 (507*2π)/5491 weeks
508-.41678 -2.85487 (508*2π)/5491 weeks
509-.33226 -4.1803 (509*2π)/5491 weeks
510.5231 -5.00601 (510*2π)/5491 weeks
5111.48624 -4.82863 (511*2π)/5491 weeks
5122.27788 -4.14875 (512*2π)/5491 weeks
5132.2404 -3.25761 (513*2π)/5491 weeks
5142.06515 -2.6548 (514*2π)/5491 weeks
5151.16493 -1.44258 (515*2π)/5491 weeks
516-.97825 -1.46505 (516*2π)/5491 weeks
517-2.40218 -3.13104 (517*2π)/5491 weeks
518-2.1792 -5.45319 (518*2π)/5491 weeks
519-1.00659 -6.49289 (519*2π)/5491 weeks
520.02689 -6.97196 (520*2π)/5491 weeks
5211.32528 -7.13447 (521*2π)/5491 weeks
5222.10379 -6.86545 (522*2π)/5491 weeks
5232.83341 -4.90988 (523*2π)/5491 weeks
5241.35104 -4.25133 (524*2π)/5491 weeks
525-.26655 -5.29296 (525*2π)/5491 weeks
526-.21139 -6.73333 (526*2π)/5491 weeks
527-.67021 -7.76545 (527*2π)/5491 weeks
5281.0162 -10.5479 (528*2π)/5491 weeks
5294.31353 -10.53929 (529*2π)/5491 weeks
5306.12633 -7.40794 (530*2π)/5491 weeks
5315.05137 -5.19324 (531*2π)/5491 weeks
5323.06736 -4.53067 (532*2π)/5491 weeks
533.94205 -4.70147 (533*2π)/5491 weeks
534-1.53245 -5.72163 (534*2π)/5491 weeks
535-2.39492 -10.05529 (535*2π)/5491 weeks
536-2.13149 -13.6712 (536*2π)/5491 weeks
5371.4614 -16.80096 (537*2π)/5491 weeks
5385.60484 -18.48569 (538*2π)/5491 weeks
53911.93226 -16.79433 (539*2π)/5491 weeks
54014.38563 -11.15112 (540*2π)/5491 weeks
54111.67551 -6.827 (541*2π)/5491 weeks
5425.18396 -.59857 (542*2π)/5491 weeks
543-5.8581 -6.54398 (543*2π)/5491 weeks
544-12.51471 -17.52287 (544*2π)/5491 weeks
545-13.91492 -36.53141 (545*2π)/5491 weeks
5464.76322 -60.28868 (546*2π)/5491 weeks
54730.6531 -76.831 (547*2π)/5491 weeks



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