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Fourier Analysis of UNG (United States Natural Gas Fund )


UNG (United States Natural Gas Fund ) appears to have interesting cyclic behaviour every 51 weeks (20.1404*sine), 46 weeks (18.4005*sine), and 51 weeks (7.4011*cosine).

UNG (United States Natural Gas Fund ) has an average price of 88.55 (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 1/17/2017 for UNG (United States Natural Gas Fund ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
088.55402   0 
184.80926 80.37122 (1*2π)/510510 weeks
226.19156 79.08044 (2*2π)/510255 weeks
3-1.65213 61.53573 (3*2π)/510170 weeks
4-14.99303 32.01501 (4*2π)/510128 weeks
5-10.58202 13.30098 (5*2π)/510102 weeks
6-1.83815 2.6975 (6*2π)/51085 weeks
711.78493 3.94729 (7*2π)/51073 weeks
814.45511 8.94537 (8*2π)/51064 weeks
913.87555 16.20134 (9*2π)/51057 weeks
107.40114 20.14036 (10*2π)/51051 weeks
112.16319 18.4005 (11*2π)/51046 weeks
12-2.06238 15.1395 (12*2π)/51043 weeks
13-2.56219 10.80805 (13*2π)/51039 weeks
14-1.36454 5.94666 (14*2π)/51036 weeks
151.3352 4.86021 (15*2π)/51034 weeks
163.66843 4.87446 (16*2π)/51032 weeks
175.90239 6.19936 (17*2π)/51030 weeks
186.54782 9.397 (18*2π)/51028 weeks
193.03219 11.5744 (19*2π)/51027 weeks
20-.50619 9.94617 (20*2π)/51026 weeks
21-.18648 7.44777 (21*2π)/51024 weeks
22-.43875 6.22636 (22*2π)/51023 weeks
23.90034 4.5234 (23*2π)/51022 weeks
242.71862 5.00188 (24*2π)/51021 weeks
252.44139 7.36716 (25*2π)/51020 weeks
261.4557 7.68722 (26*2π)/51020 weeks
27-.02355 7.5017 (27*2π)/51019 weeks
28-1.23767 6.89209 (28*2π)/51018 weeks
29-2.59062 5.4141 (29*2π)/51018 weeks
30-2.19329 2.71919 (30*2π)/51017 weeks
31-.08829 1.22383 (31*2π)/51016 weeks
321.98003 2.02321 (32*2π)/51016 weeks
332.25881 3.16134 (33*2π)/51015 weeks
342.49533 4.00863 (34*2π)/51015 weeks
351.89784 5.05528 (35*2π)/51015 weeks
36.88459 5.34329 (36*2π)/51014 weeks
37-.29254 4.60212 (37*2π)/51014 weeks
38-.54971 3.17289 (38*2π)/51013 weeks
39.57062 2.53503 (39*2π)/51013 weeks
401.36689 3.03797 (40*2π)/51013 weeks
411.45879 3.60127 (41*2π)/51012 weeks
42.9742 3.89602 (42*2π)/51012 weeks
43.26914 4.64032 (43*2π)/51012 weeks
44-.62467 4.1393 (44*2π)/51012 weeks
45-1.31708 3.1658 (45*2π)/51011 weeks
46-.58832 1.71332 (46*2π)/51011 weeks
47.33183 1.79318 (47*2π)/51011 weeks
48.59372 2.17884 (48*2π)/51011 weeks
49.63274 2.39381 (49*2π)/51010 weeks
50.75827 2.3184 (50*2π)/51010 weeks
51.40687 2.54204 (51*2π)/51010 weeks
52.06294 2.76366 (52*2π)/51010 weeks
53-.70663 1.91711 (53*2π)/51010 weeks
54.06507 .49766 (54*2π)/5109 weeks
551.22577 .7251 (55*2π)/5109 weeks
562.13785 1.60979 (56*2π)/5109 weeks
571.91382 2.38044 (57*2π)/5109 weeks
581.23835 2.91827 (58*2π)/5109 weeks
59.74416 2.86361 (59*2π)/5109 weeks
60-.02862 2.81626 (60*2π)/5109 weeks
61-.64253 1.65451 (61*2π)/5108 weeks
62.25175 .89167 (62*2π)/5108 weeks
63.93222 1.06911 (63*2π)/5108 weeks
641.07616 .72915 (64*2π)/5108 weeks
651.63729 1.04203 (65*2π)/5108 weeks
661.9135 1.53784 (66*2π)/5108 weeks
672.13015 1.70042 (67*2π)/5108 weeks
682.22354 2.42946 (68*2π)/5108 weeks
691.5094 3.07383 (69*2π)/5107 weeks
70.55571 2.81911 (70*2π)/5107 weeks
71.65782 2.30126 (71*2π)/5107 weeks
72.59029 2.30432 (72*2π)/5107 weeks
73.60416 1.97504 (73*2π)/5107 weeks
74.60821 2.1068 (74*2π)/5107 weeks
75.84452 2.09052 (75*2π)/5107 weeks
76.38378 2.35492 (76*2π)/5107 weeks
77-.05829 2.20267 (77*2π)/5107 weeks
78-.33946 1.59933 (78*2π)/5107 weeks
79-.16213 .80782 (79*2π)/5106 weeks
801.07709 .69938 (80*2π)/5106 weeks
811.2946 1.74544 (81*2π)/5106 weeks
82.40871 2.01593 (82*2π)/5106 weeks
83-.05047 1.70053 (83*2π)/5106 weeks
84-.21467 .93594 (84*2π)/5106 weeks
85.53251 .50345 (85*2π)/5106 weeks
86.89391 .7798 (86*2π)/5106 weeks
87.91688 1.10301 (87*2π)/5106 weeks
88.73619 1.00857 (88*2π)/5106 weeks
891.10486 .83586 (89*2π)/5106 weeks
901.24851 1.27636 (90*2π)/5106 weeks
911.19771 1.50692 (91*2π)/5106 weeks
921.00145 1.54169 (92*2π)/5106 weeks
93.67808 1.55936 (93*2π)/5105 weeks
94.61258 1.03936 (94*2π)/5105 weeks
95.98036 1.2104 (95*2π)/5105 weeks
961.10106 1.24822 (96*2π)/5105 weeks
971.35666 1.57092 (97*2π)/5105 weeks
981.04175 2.03332 (98*2π)/5105 weeks
99.47547 2.0091 (99*2π)/5105 weeks
100.14979 2.04964 (100*2π)/5105 weeks
101-.08261 1.30661 (101*2π)/5105 weeks
102.17979 1.08933 (102*2π)/5105 weeks
103.25533 .93889 (103*2π)/5105 weeks
104.60554 1.07142 (104*2π)/5105 weeks
105.30837 1.36764 (105*2π)/5105 weeks
106-.00566 1.12347 (106*2π)/5105 weeks
107.09164 .67174 (107*2π)/5105 weeks
108.51839 .55452 (108*2π)/5105 weeks
109.57044 1.00279 (109*2π)/5105 weeks
110.21591 1.16609 (110*2π)/5105 weeks
111-.15918 .5587 (111*2π)/5105 weeks
112.08221 -.01798 (112*2π)/5105 weeks
113.70127 -.04935 (113*2π)/5105 weeks
1141.17916 .39529 (114*2π)/5104 weeks
115.79065 .62863 (115*2π)/5104 weeks
116.59916 .43899 (116*2π)/5104 weeks
117.92953 .20696 (117*2π)/5104 weeks
118.91061 .24658 (118*2π)/5104 weeks
1191.29602 .32282 (119*2π)/5104 weeks
1201.46552 .34555 (120*2π)/5104 weeks
1211.6885 .73256 (121*2π)/5104 weeks
1221.46461 1.11121 (122*2π)/5104 weeks
1231.0317 1.12151 (123*2π)/5104 weeks
1241.05168 .97619 (124*2π)/5104 weeks
125.99308 1.21855 (125*2π)/5104 weeks
126.73046 .95611 (126*2π)/5104 weeks
127.96827 .72014 (127*2π)/5104 weeks
1281.17095 .74132 (128*2π)/5104 weeks
1291.34839 1.20544 (129*2π)/5104 weeks
130.92689 1.45669 (130*2π)/5104 weeks
131.73727 1.20266 (131*2π)/5104 weeks
132.58263 1.27918 (132*2π)/5104 weeks
133.45588 1.2446 (133*2π)/5104 weeks
134.32208 .96663 (134*2π)/5104 weeks
135.3859 .7539 (135*2π)/5104 weeks
136.53973 .66571 (136*2π)/5104 weeks
137.81751 .64066 (137*2π)/5104 weeks
138.80512 .95079 (138*2π)/5104 weeks
139.48859 1.1287 (139*2π)/5104 weeks
140.05443 .92082 (140*2π)/5104 weeks
141-.01186 .24208 (141*2π)/5104 weeks
142.42952 -.01713 (142*2π)/5104 weeks
143.90451 .1465 (143*2π)/5104 weeks
144.91325 .38666 (144*2π)/5104 weeks
145.85979 .38096 (145*2π)/5104 weeks
1461.11112 .36904 (146*2π)/5103 weeks
1471.16175 .70262 (147*2π)/5103 weeks
148.73923 .90801 (148*2π)/5103 weeks
149.64981 .66981 (149*2π)/5103 weeks
150.63877 .52814 (150*2π)/5103 weeks
151.77657 .30655 (151*2π)/5103 weeks
1521.11801 .50879 (152*2π)/5103 weeks
1531.14399 .90373 (153*2π)/5103 weeks
154.67156 1.04491 (154*2π)/5103 weeks
155.3965 .60066 (155*2π)/5103 weeks
156.77014 .3699 (156*2π)/5103 weeks
1571.06848 .57933 (157*2π)/5103 weeks
158.86733 .99827 (158*2π)/5103 weeks
159.39494 .94353 (159*2π)/5103 weeks
160.22021 .51902 (160*2π)/5103 weeks
161.52401 .20773 (161*2π)/5103 weeks
162.74034 .36848 (162*2π)/5103 weeks
163.77769 .33595 (163*2π)/5103 weeks
164.6923 .38696 (164*2π)/5103 weeks
165.96501 .30659 (165*2π)/5103 weeks
1661.19032 .68197 (166*2π)/5103 weeks
167.82416 .83343 (167*2π)/5103 weeks
168.5854 .79026 (168*2π)/5103 weeks
169.51425 .65458 (169*2π)/5103 weeks
170.46686 .63739 (170*2π)/5103 weeks
171.3208 .37577 (171*2π)/5103 weeks
172.52705 .2994 (172*2π)/5103 weeks
173.49365 .25396 (173*2π)/5103 weeks
174.5734 .14446 (174*2π)/5103 weeks
175.8137 .18094 (175*2π)/5103 weeks
176.87589 .21659 (176*2π)/5103 weeks
177.90321 .38633 (177*2π)/5103 weeks
178.79313 .51114 (178*2π)/5103 weeks
179.70351 .52302 (179*2π)/5103 weeks
180.60418 .43227 (180*2π)/5103 weeks
181.4556 .21678 (181*2π)/5103 weeks
182.79232 .02902 (182*2π)/5103 weeks
183.85441 .21336 (183*2π)/5103 weeks
184.99028 .17945 (184*2π)/5103 weeks
1851.06935 .50238 (185*2π)/5103 weeks
186.78587 .47657 (186*2π)/5103 weeks
187.82407 .22484 (187*2π)/5103 weeks
1881.08411 .39509 (188*2π)/5103 weeks
189.9943 .69882 (189*2π)/5103 weeks
190.84671 .61432 (190*2π)/5103 weeks
191.6655 .89304 (191*2π)/5103 weeks
192.16506 .6986 (192*2π)/5103 weeks
193.17107 .01421 (193*2π)/5103 weeks
194.81093 -.29512 (194*2π)/5103 weeks
1951.18834 .12656 (195*2π)/5103 weeks
1961.06218 .60589 (196*2π)/5103 weeks
197.74584 .63653 (197*2π)/5103 weeks
198.69674 .44299 (198*2π)/5103 weeks
199.67875 .53401 (199*2π)/5103 weeks
200.48506 .49291 (200*2π)/5103 weeks
201.47224 .41699 (201*2π)/5103 weeks
202.46227 .16934 (202*2π)/5103 weeks
203.64956 .11225 (203*2π)/5103 weeks
204.71864 .07375 (204*2π)/5103 weeks
205.86981 .22209 (205*2π)/5102 weeks
206.82895 .37463 (206*2π)/5102 weeks
207.6742 .35021 (207*2π)/5102 weeks
208.62638 .21545 (208*2π)/5102 weeks
209.65563 .34257 (209*2π)/5102 weeks
210.58434 .30949 (210*2π)/5102 weeks
211.53365 .17203 (211*2π)/5102 weeks
212.47522 .04163 (212*2π)/5102 weeks
213.70912 -.16826 (213*2π)/5102 weeks
214.97832 -.04569 (214*2π)/5102 weeks
2151.06093 .12481 (215*2π)/5102 weeks
216.98804 .32719 (216*2π)/5102 weeks
217.89404 .39695 (217*2π)/5102 weeks
218.72626 .29807 (218*2π)/5102 weeks
219.83204 .23449 (219*2π)/5102 weeks
2201.01798 .31814 (220*2π)/5102 weeks
221.95002 .62267 (221*2π)/5102 weeks
222.61521 .76384 (222*2π)/5102 weeks
223.37272 .61413 (223*2π)/5102 weeks
224.2718 .51306 (224*2π)/5102 weeks
225.07923 .23788 (225*2π)/5102 weeks
226.22455 -.02517 (226*2π)/5102 weeks
227.32651 -.12226 (227*2π)/5102 weeks
228.51365 -.24717 (228*2π)/5102 weeks
229.71879 -.06161 (229*2π)/5102 weeks
230.59335 .11931 (230*2π)/5102 weeks
231.51486 .00506 (231*2π)/5102 weeks
232.4387 -.0842 (232*2π)/5102 weeks
233.58186 -.21521 (233*2π)/5102 weeks
234.64429 -.21054 (234*2π)/5102 weeks
235.76366 -.22919 (235*2π)/5102 weeks
236.82846 .00371 (236*2π)/5102 weeks
237.62483 -.01013 (237*2π)/5102 weeks
238.47738 -.12828 (238*2π)/5102 weeks
239.45892 -.45398 (239*2π)/5102 weeks
240.93291 -.64079 (240*2π)/5102 weeks
2411.31867 -.34805 (241*2π)/5102 weeks
2421.33551 -.03594 (242*2π)/5102 weeks
2431.20199 .20477 (243*2π)/5102 weeks
2441.07055 .38638 (244*2π)/5102 weeks
245.55206 .63703 (245*2π)/5102 weeks
246.1584 .20118 (246*2π)/5102 weeks
247.25166 -.42248 (247*2π)/5102 weeks
248.65134 -.70603 (248*2π)/5102 weeks
2491.15356 -.64794 (249*2π)/5102 weeks
2501.50457 -.21523 (250*2π)/5102 weeks
2511.39292 .2363 (251*2π)/5102 weeks
2521.09548 .49698 (252*2π)/5102 weeks
253.73185 .45122 (253*2π)/5102 weeks
254.4918 .1944 (254*2π)/5102 weeks
255.57769   (255*2π)/5102 weeks
256.4918 -.1944 (256*2π)/5102 weeks
257.73185 -.45122 (257*2π)/5102 weeks
2581.09548 -.49698 (258*2π)/5102 weeks
2591.39292 -.2363 (259*2π)/5102 weeks
2601.50457 .21523 (260*2π)/5102 weeks
2611.15356 .64794 (261*2π)/5102 weeks
262.65134 .70603 (262*2π)/5102 weeks
263.25166 .42248 (263*2π)/5102 weeks
264.1584 -.20118 (264*2π)/5102 weeks
265.55206 -.63703 (265*2π)/5102 weeks
2661.07055 -.38638 (266*2π)/5102 weeks
2671.20199 -.20477 (267*2π)/5102 weeks
2681.33551 .03594 (268*2π)/5102 weeks
2691.31867 .34805 (269*2π)/5102 weeks
270.93291 .64079 (270*2π)/5102 weeks
271.45892 .45398 (271*2π)/5102 weeks
272.47738 .12828 (272*2π)/5102 weeks
273.62483 .01013 (273*2π)/5102 weeks
274.82846 -.00371 (274*2π)/5102 weeks
275.76366 .22919 (275*2π)/5102 weeks
276.64429 .21054 (276*2π)/5102 weeks
277.58186 .21521 (277*2π)/5102 weeks
278.4387 .0842 (278*2π)/5102 weeks
279.51486 -.00506 (279*2π)/5102 weeks
280.59335 -.11931 (280*2π)/5102 weeks
281.71879 .06161 (281*2π)/5102 weeks
282.51365 .24717 (282*2π)/5102 weeks
283.32651 .12226 (283*2π)/5102 weeks
284.22455 .02517 (284*2π)/5102 weeks
285.07923 -.23788 (285*2π)/5102 weeks
286.2718 -.51306 (286*2π)/5102 weeks
287.37272 -.61413 (287*2π)/5102 weeks
288.61521 -.76384 (288*2π)/5102 weeks
289.95002 -.62267 (289*2π)/5102 weeks
2901.01798 -.31814 (290*2π)/5102 weeks
291.83204 -.23449 (291*2π)/5102 weeks
292.72626 -.29807 (292*2π)/5102 weeks
293.89404 -.39695 (293*2π)/5102 weeks
294.98804 -.32719 (294*2π)/5102 weeks
2951.06093 -.12481 (295*2π)/5102 weeks
296.97832 .04569 (296*2π)/5102 weeks
297.70912 .16826 (297*2π)/5102 weeks
298.47522 -.04163 (298*2π)/5102 weeks
299.53365 -.17203 (299*2π)/5102 weeks
300.58434 -.30949 (300*2π)/5102 weeks
301.65563 -.34257 (301*2π)/5102 weeks
302.62638 -.21545 (302*2π)/5102 weeks
303.6742 -.35021 (303*2π)/5102 weeks
304.82895 -.37463 (304*2π)/5102 weeks
305.86981 -.22209 (305*2π)/5102 weeks
306.71864 -.07375 (306*2π)/5102 weeks
307.64956 -.11225 (307*2π)/5102 weeks
308.46227 -.16934 (308*2π)/5102 weeks
309.47224 -.41699 (309*2π)/5102 weeks
310.48506 -.49291 (310*2π)/5102 weeks
311.67875 -.53401 (311*2π)/5102 weeks
312.69674 -.44299 (312*2π)/5102 weeks
313.74584 -.63653 (313*2π)/5102 weeks
3141.06218 -.60589 (314*2π)/5102 weeks
3151.18834 -.12656 (315*2π)/5102 weeks
316.81093 .29512 (316*2π)/5102 weeks
317.17107 -.01421 (317*2π)/5102 weeks
318.16506 -.6986 (318*2π)/5102 weeks
319.6655 -.89304 (319*2π)/5102 weeks
320.84671 -.61432 (320*2π)/5102 weeks
321.9943 -.69882 (321*2π)/5102 weeks
3221.08411 -.39509 (322*2π)/5102 weeks
323.82407 -.22484 (323*2π)/5102 weeks
324.78587 -.47657 (324*2π)/5102 weeks
3251.06935 -.50238 (325*2π)/5102 weeks
326.99028 -.17945 (326*2π)/5102 weeks
327.85441 -.21336 (327*2π)/5102 weeks
328.79232 -.02902 (328*2π)/5102 weeks
329.4556 -.21678 (329*2π)/5102 weeks
330.60418 -.43227 (330*2π)/5102 weeks
331.70351 -.52302 (331*2π)/5102 weeks
332.79313 -.51114 (332*2π)/5102 weeks
333.90321 -.38633 (333*2π)/5102 weeks
334.87589 -.21659 (334*2π)/5102 weeks
335.8137 -.18094 (335*2π)/5102 weeks
336.5734 -.14446 (336*2π)/5102 weeks
337.49365 -.25396 (337*2π)/5102 weeks
338.52705 -.2994 (338*2π)/5102 weeks
339.3208 -.37577 (339*2π)/5102 weeks
340.46686 -.63739 (340*2π)/5102 weeks
341.51425 -.65458 (341*2π)/5101 weeks
342.5854 -.79026 (342*2π)/5101 weeks
343.82416 -.83343 (343*2π)/5101 weeks
3441.19032 -.68197 (344*2π)/5101 weeks
345.96501 -.30659 (345*2π)/5101 weeks
346.6923 -.38696 (346*2π)/5101 weeks
347.77769 -.33595 (347*2π)/5101 weeks
348.74034 -.36848 (348*2π)/5101 weeks
349.52401 -.20773 (349*2π)/5101 weeks
350.22021 -.51902 (350*2π)/5101 weeks
351.39494 -.94353 (351*2π)/5101 weeks
352.86733 -.99827 (352*2π)/5101 weeks
3531.06848 -.57933 (353*2π)/5101 weeks
354.77014 -.3699 (354*2π)/5101 weeks
355.3965 -.60066 (355*2π)/5101 weeks
356.67156 -1.04491 (356*2π)/5101 weeks
3571.14399 -.90373 (357*2π)/5101 weeks
3581.11801 -.50879 (358*2π)/5101 weeks
359.77657 -.30655 (359*2π)/5101 weeks
360.63877 -.52814 (360*2π)/5101 weeks
361.64981 -.66981 (361*2π)/5101 weeks
362.73923 -.90801 (362*2π)/5101 weeks
3631.16175 -.70262 (363*2π)/5101 weeks
3641.11112 -.36904 (364*2π)/5101 weeks
365.85979 -.38096 (365*2π)/5101 weeks
366.91325 -.38666 (366*2π)/5101 weeks
367.90451 -.1465 (367*2π)/5101 weeks
368.42952 .01713 (368*2π)/5101 weeks
369-.01186 -.24208 (369*2π)/5101 weeks
370.05443 -.92082 (370*2π)/5101 weeks
371.48859 -1.1287 (371*2π)/5101 weeks
372.80512 -.95079 (372*2π)/5101 weeks
373.81751 -.64066 (373*2π)/5101 weeks
374.53973 -.66571 (374*2π)/5101 weeks
375.3859 -.7539 (375*2π)/5101 weeks
376.32208 -.96663 (376*2π)/5101 weeks
377.45588 -1.2446 (377*2π)/5101 weeks
378.58263 -1.27918 (378*2π)/5101 weeks
379.73727 -1.20266 (379*2π)/5101 weeks
380.92689 -1.45669 (380*2π)/5101 weeks
3811.34839 -1.20544 (381*2π)/5101 weeks
3821.17095 -.74132 (382*2π)/5101 weeks
383.96827 -.72014 (383*2π)/5101 weeks
384.73046 -.95611 (384*2π)/5101 weeks
385.99308 -1.21855 (385*2π)/5101 weeks
3861.05168 -.97619 (386*2π)/5101 weeks
3871.0317 -1.12151 (387*2π)/5101 weeks
3881.46461 -1.11121 (388*2π)/5101 weeks
3891.6885 -.73256 (389*2π)/5101 weeks
3901.46552 -.34555 (390*2π)/5101 weeks
3911.29602 -.32282 (391*2π)/5101 weeks
392.91061 -.24658 (392*2π)/5101 weeks
393.92953 -.20696 (393*2π)/5101 weeks
394.59916 -.43899 (394*2π)/5101 weeks
395.79065 -.62863 (395*2π)/5101 weeks
3961.17916 -.39529 (396*2π)/5101 weeks
397.70127 .04935 (397*2π)/5101 weeks
398.08221 .01798 (398*2π)/5101 weeks
399-.15918 -.5587 (399*2π)/5101 weeks
400.21591 -1.16609 (400*2π)/5101 weeks
401.57044 -1.00279 (401*2π)/5101 weeks
402.51839 -.55452 (402*2π)/5101 weeks
403.09164 -.67174 (403*2π)/5101 weeks
404-.00566 -1.12347 (404*2π)/5101 weeks
405.30837 -1.36764 (405*2π)/5101 weeks
406.60554 -1.07142 (406*2π)/5101 weeks
407.25533 -.93889 (407*2π)/5101 weeks
408.17979 -1.08933 (408*2π)/5101 weeks
409-.08261 -1.30661 (409*2π)/5101 weeks
410.14979 -2.04964 (410*2π)/5101 weeks
411.47547 -2.0091 (411*2π)/5101 weeks
4121.04175 -2.03332 (412*2π)/5101 weeks
4131.35666 -1.57092 (413*2π)/5101 weeks
4141.10106 -1.24822 (414*2π)/5101 weeks
415.98036 -1.2104 (415*2π)/5101 weeks
416.61258 -1.03936 (416*2π)/5101 weeks
417.67808 -1.55936 (417*2π)/5101 weeks
4181.00145 -1.54169 (418*2π)/5101 weeks
4191.19771 -1.50692 (419*2π)/5101 weeks
4201.24851 -1.27636 (420*2π)/5101 weeks
4211.10486 -.83586 (421*2π)/5101 weeks
422.73619 -1.00857 (422*2π)/5101 weeks
423.91688 -1.10301 (423*2π)/5101 weeks
424.89391 -.7798 (424*2π)/5101 weeks
425.53251 -.50345 (425*2π)/5101 weeks
426-.21467 -.93594 (426*2π)/5101 weeks
427-.05047 -1.70053 (427*2π)/5101 weeks
428.40871 -2.01593 (428*2π)/5101 weeks
4291.2946 -1.74544 (429*2π)/5101 weeks
4301.07709 -.69938 (430*2π)/5101 weeks
431-.16213 -.80782 (431*2π)/5101 weeks
432-.33946 -1.59933 (432*2π)/5101 weeks
433-.05829 -2.20267 (433*2π)/5101 weeks
434.38378 -2.35492 (434*2π)/5101 weeks
435.84452 -2.09052 (435*2π)/5101 weeks
436.60821 -2.1068 (436*2π)/5101 weeks
437.60416 -1.97504 (437*2π)/5101 weeks
438.59029 -2.30432 (438*2π)/5101 weeks
439.65782 -2.30126 (439*2π)/5101 weeks
440.55571 -2.81911 (440*2π)/5101 weeks
4411.5094 -3.07383 (441*2π)/5101 weeks
4422.22354 -2.42946 (442*2π)/5101 weeks
4432.13015 -1.70042 (443*2π)/5101 weeks
4441.9135 -1.53784 (444*2π)/5101 weeks
4451.63729 -1.04203 (445*2π)/5101 weeks
4461.07616 -.72915 (446*2π)/5101 weeks
447.93222 -1.06911 (447*2π)/5101 weeks
448.25175 -.89167 (448*2π)/5101 weeks
449-.64253 -1.65451 (449*2π)/5101 weeks
450-.02862 -2.81626 (450*2π)/5101 weeks
451.74416 -2.86361 (451*2π)/5101 weeks
4521.23835 -2.91827 (452*2π)/5101 weeks
4531.91382 -2.38044 (453*2π)/5101 weeks
4542.13785 -1.60979 (454*2π)/5101 weeks
4551.22577 -.7251 (455*2π)/5101 weeks
456.06507 -.49766 (456*2π)/5101 weeks
457-.70663 -1.91711 (457*2π)/5101 weeks
458.06294 -2.76366 (458*2π)/5101 weeks
459.40687 -2.54204 (459*2π)/5101 weeks
460.75827 -2.3184 (460*2π)/5101 weeks
461.63274 -2.39381 (461*2π)/5101 weeks
462.59372 -2.17884 (462*2π)/5101 weeks
463.33183 -1.79318 (463*2π)/5101 weeks
464-.58832 -1.71332 (464*2π)/5101 weeks
465-1.31708 -3.1658 (465*2π)/5101 weeks
466-.62467 -4.1393 (466*2π)/5101 weeks
467.26914 -4.64032 (467*2π)/5101 weeks
468.9742 -3.89602 (468*2π)/5101 weeks
4691.45879 -3.60127 (469*2π)/5101 weeks
4701.36689 -3.03797 (470*2π)/5101 weeks
471.57062 -2.53503 (471*2π)/5101 weeks
472-.54971 -3.17289 (472*2π)/5101 weeks
473-.29254 -4.60212 (473*2π)/5101 weeks
474.88459 -5.34329 (474*2π)/5101 weeks
4751.89784 -5.05528 (475*2π)/5101 weeks
4762.49533 -4.00863 (476*2π)/5101 weeks
4772.25881 -3.16134 (477*2π)/5101 weeks
4781.98003 -2.02321 (478*2π)/5101 weeks
479-.08829 -1.22383 (479*2π)/5101 weeks
480-2.19329 -2.71919 (480*2π)/5101 weeks
481-2.59062 -5.4141 (481*2π)/5101 weeks
482-1.23767 -6.89209 (482*2π)/5101 weeks
483-.02355 -7.5017 (483*2π)/5101 weeks
4841.4557 -7.68722 (484*2π)/5101 weeks
4852.44139 -7.36716 (485*2π)/5101 weeks
4862.71862 -5.00188 (486*2π)/5101 weeks
487.90034 -4.5234 (487*2π)/5101 weeks
488-.43875 -6.22636 (488*2π)/5101 weeks
489-.18648 -7.44777 (489*2π)/5101 weeks
490-.50619 -9.94617 (490*2π)/5101 weeks
4913.03219 -11.5744 (491*2π)/5101 weeks
4926.54782 -9.397 (492*2π)/5101 weeks
4935.90239 -6.19936 (493*2π)/5101 weeks
4943.66843 -4.87446 (494*2π)/5101 weeks
4951.3352 -4.86021 (495*2π)/5101 weeks
496-1.36454 -5.94666 (496*2π)/5101 weeks
497-2.56219 -10.80805 (497*2π)/5101 weeks
498-2.06238 -15.1395 (498*2π)/5101 weeks
4992.16319 -18.4005 (499*2π)/5101 weeks
5007.40114 -20.14036 (500*2π)/5101 weeks
50113.87555 -16.20134 (501*2π)/5101 weeks
50214.45511 -8.94537 (502*2π)/5101 weeks
50311.78493 -3.94729 (503*2π)/5101 weeks
504-1.83815 -2.6975 (504*2π)/5101 weeks
505-10.58202 -13.30098 (505*2π)/5101 weeks
506-14.99303 -32.01501 (506*2π)/5101 weeks
507-1.65213 -61.53573 (507*2π)/5101 weeks
50826.19156 -79.08044 (508*2π)/5101 weeks

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