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Fourier Analysis of AGQ (ProShares Ultra Silver ETF)


AGQ (ProShares Ultra Silver ETF) appears to have interesting cyclic behaviour every 25 weeks (11.6055*cosine), 24 weeks (9.6106*sine), and 17 weeks (8.0786*cosine).

AGQ (ProShares Ultra Silver ETF) has an average price of 123.55 (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 12/4/2008 to 6/12/2017 for AGQ (ProShares Ultra Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0123.5461   0 
1-50.57663 112.4501 (1*2π)/447447 weeks
2-38.23424 -35.11967 (2*2π)/447224 weeks
324.74264 -18.00166 (3*2π)/447149 weeks
417.38615 22.56275 (4*2π)/447112 weeks
5-30.22436 19.0255 (5*2π)/44789 weeks
6-5.39226 -24.42163 (6*2π)/44775 weeks
712.57778 4.79164 (7*2π)/44764 weeks
81.71607 8.15694 (8*2π)/44756 weeks
9-4.94822 3.00049 (9*2π)/44750 weeks
102.28626 -6.68552 (10*2π)/44745 weeks
113.16455 7.98782 (11*2π)/44741 weeks
12-4.47466 -1.94328 (12*2π)/44737 weeks
13.51165 .3961 (13*2π)/44734 weeks
14-3.58757 2.59624 (14*2π)/44732 weeks
15-.80418 -3.3598 (15*2π)/44730 weeks
16.33431 4.88361 (16*2π)/44728 weeks
17-8.02266 -5.58556 (17*2π)/44726 weeks
1811.60551 -2.31455 (18*2π)/44725 weeks
19-.66654 9.61059 (19*2π)/44724 weeks
20-7.64587 2.46334 (20*2π)/44722 weeks
21.30247 -8.74261 (21*2π)/44721 weeks
227.70449 2.74742 (22*2π)/44720 weeks
23-5.79472 8.45263 (23*2π)/44719 weeks
24-6.15622 -6.37638 (24*2π)/44719 weeks
256.06654 -3.01655 (25*2π)/44718 weeks
262.23741 6.51966 (26*2π)/44717 weeks
27-8.07863 .93931 (27*2π)/44717 weeks
28.1681 -7.60549 (28*2π)/44716 weeks
296.4999 1.88159 (29*2π)/44715 weeks
30-4.60868 2.93533 (30*2π)/44715 weeks
31-1.12053 -5.991 (31*2π)/44714 weeks
325.99086 -.21097 (32*2π)/44714 weeks
33-2.07048 3.34611 (33*2π)/44714 weeks
34.59523 -2.17969 (34*2π)/44713 weeks
35.75696 2.30052 (35*2π)/44713 weeks
36.42152 -.26757 (36*2π)/44712 weeks
37.43783 .50386 (37*2π)/44712 weeks
381.38908 1.17401 (38*2π)/44712 weeks
39-1.76865 .44265 (39*2π)/44711 weeks
401.78156 -.74449 (40*2π)/44711 weeks
41-.74134 3.75708 (41*2π)/44711 weeks
42-3.80368 -2.48512 (42*2π)/44711 weeks
434.90466 -.42381 (43*2π)/44710 weeks
44-2.19036 4.31088 (44*2π)/44710 weeks
45-1.91203 -2.23793 (45*2π)/44710 weeks
461.85127 -2.43171 (46*2π)/44710 weeks
473.73955 2.23631 (47*2π)/44710 weeks
48-5.97876 1.96626 (48*2π)/4479 weeks
491.20164 -5.10697 (49*2π)/4479 weeks
502.92753 2.00146 (50*2π)/4479 weeks
51-1.12667 2.29845 (51*2π)/4479 weeks
52-2.49885 -1.3814 (52*2π)/4479 weeks
532.99492 -2.73866 (53*2π)/4478 weeks
541.80917 3.89964 (54*2π)/4478 weeks
55-1.99808 .10785 (55*2π)/4478 weeks
56-.83699 .72727 (56*2π)/4478 weeks
57-.08915 -1.71389 (57*2π)/4478 weeks
581.0935 1.61906 (58*2π)/4478 weeks
59-2.40381 .28274 (59*2π)/4478 weeks
60-1.33971 -1.11961 (60*2π)/4477 weeks
612.97543 -2.38604 (61*2π)/4477 weeks
62.99242 4.43915 (62*2π)/4477 weeks
63-4.91164 -.01465 (63*2π)/4477 weeks
64.37534 -3.48291 (64*2π)/4477 weeks
653.23666 1.34789 (65*2π)/4477 weeks
66-3.10288 3.43402 (66*2π)/4477 weeks
67-2.44417 -4.82894 (67*2π)/4477 weeks
685.85204 -.09598 (68*2π)/4477 weeks
69-2.22009 4.61253 (69*2π)/4476 weeks
70-2.49346 -2.65441 (70*2π)/4476 weeks
712.16085 -1.5002 (71*2π)/4476 weeks
72.37471 3.10438 (72*2π)/4476 weeks
73-3.57681 -.09617 (73*2π)/4476 weeks
74.42274 -2.96047 (74*2π)/4476 weeks
751.96095 -.0779 (75*2π)/4476 weeks
76-.12438 1.45082 (76*2π)/4476 weeks
77-1.03245 -.56886 (77*2π)/4476 weeks
782.10912 -1.20626 (78*2π)/4476 weeks
79.89161 2.53494 (79*2π)/4476 weeks
80-1.99628 1.11625 (80*2π)/4476 weeks
81-.42994 -2.06121 (81*2π)/4476 weeks
822.06641 -.31265 (82*2π)/4475 weeks
83-.01153 1.61642 (83*2π)/4475 weeks
84-1.82303 -1.0234 (84*2π)/4475 weeks
851.06482 -.59648 (85*2π)/4475 weeks
86.26325 -.03838 (86*2π)/4475 weeks
87-.09771 1.50599 (87*2π)/4475 weeks
88-.78134 -1.39891 (88*2π)/4475 weeks
892.2697 .4564 (89*2π)/4475 weeks
90-.34274 1.78768 (90*2π)/4475 weeks
91-1.80441 .78117 (91*2π)/4475 weeks
92.0619 -1.70561 (92*2π)/4475 weeks
931.5475 1.21022 (93*2π)/4475 weeks
94-2.00964 .88632 (94*2π)/4475 weeks
95.00945 -1.23843 (95*2π)/4475 weeks
96.45237 -.41408 (96*2π)/4475 weeks
97.53795 .51285 (97*2π)/4475 weeks
98-.678 .07761 (98*2π)/4475 weeks
99.36999 -.81205 (99*2π)/4475 weeks
100.78057 .52561 (100*2π)/4474 weeks
101-.72351 .49691 (101*2π)/4474 weeks
102-.46936 -.00917 (102*2π)/4474 weeks
103.64426 -.93274 (103*2π)/4474 weeks
104-.13665 1.18539 (104*2π)/4474 weeks
105-.69738 -.03682 (105*2π)/4474 weeks
106.09848 -1.23306 (106*2π)/4474 weeks
1072.05622 -.23414 (107*2π)/4474 weeks
108.13339 2.4402 (108*2π)/4474 weeks
109-2.67151 -1.1558 (109*2π)/4474 weeks
1102.42618 -1.8496 (110*2π)/4474 weeks
111.95913 2.3128 (111*2π)/4474 weeks
112-2.49595 1.34185 (112*2π)/4474 weeks
113-.4169 -3.17854 (113*2π)/4474 weeks
1142.85202 1.19862 (114*2π)/4474 weeks
115-1.69134 1.61105 (115*2π)/4474 weeks
116-.32107 -1.60839 (116*2π)/4474 weeks
117.79311 -.01298 (117*2π)/4474 weeks
118.47411 .77454 (118*2π)/4474 weeks
119-1.48106 -.1755 (119*2π)/4474 weeks
1201.41277 -.89853 (120*2π)/4474 weeks
121-.06446 1.01675 (121*2π)/4474 weeks
122.1916 .6487 (122*2π)/4474 weeks
123-1.02758 .01991 (123*2π)/4474 weeks
124.47449 -.15616 (124*2π)/4474 weeks
125-.03295 1.03169 (125*2π)/4474 weeks
126-.62831 -.13377 (126*2π)/4474 weeks
127-.70327 -.43176 (127*2π)/4474 weeks
1281.44852 -.97911 (128*2π)/4473 weeks
129-.1307 2.24504 (129*2π)/4473 weeks
130-1.90642 -.62421 (130*2π)/4473 weeks
131.61565 -1.21918 (131*2π)/4473 weeks
1321.26946 .36394 (132*2π)/4473 weeks
133-.77473 1.58572 (133*2π)/4473 weeks
134-1.31989 -1.52611 (134*2π)/4473 weeks
1351.75086 -.3064 (135*2π)/4473 weeks
136-.36203 1.15657 (136*2π)/4473 weeks
137-.77757 -.21273 (137*2π)/4473 weeks
138.64398 -.84191 (138*2π)/4473 weeks
139.83644 1.40177 (139*2π)/4473 weeks
140-1.70382 .14748 (140*2π)/4473 weeks
141.41407 -1.05331 (141*2π)/4473 weeks
142.37972 .19724 (142*2π)/4473 weeks
143-.0772 .15378 (143*2π)/4473 weeks
144-1.0305 -.2543 (144*2π)/4473 weeks
1451.04352 -.76023 (145*2π)/4473 weeks
146-.6734 .29906 (146*2π)/4473 weeks
147.81246 -.21653 (147*2π)/4473 weeks
148-.64079 .62447 (148*2π)/4473 weeks
149.54602 -.30987 (149*2π)/4473 weeks
150-.205 .10281 (150*2π)/4473 weeks
151.09345 -.06184 (151*2π)/4473 weeks
152-.02458 -.27031 (152*2π)/4473 weeks
153.79866 -.54323 (153*2π)/4473 weeks
154-.2422 1.38223 (154*2π)/4473 weeks
155-.77268 -1.00158 (155*2π)/4473 weeks
156.77844 .2514 (156*2π)/4473 weeks
157-.12722 .32449 (157*2π)/4473 weeks
158-.73237 .3507 (158*2π)/4473 weeks
159.16769 -1.0926 (159*2π)/4473 weeks
1601.27147 .48528 (160*2π)/4473 weeks
161-.51815 .58864 (161*2π)/4473 weeks
162.18644 .38004 (162*2π)/4473 weeks
163-.65752 -.42057 (163*2π)/4473 weeks
164.69331 .03209 (164*2π)/4473 weeks
165-.55934 .41249 (165*2π)/4473 weeks
166-.38294 -.36206 (166*2π)/4473 weeks
167.23948 -.62528 (167*2π)/4473 weeks
168.2047 .5187 (168*2π)/4473 weeks
169-1.04675 -.29737 (169*2π)/4473 weeks
1701.18741 -.95858 (170*2π)/4473 weeks
171.50308 1.38763 (171*2π)/4473 weeks
172-.60167 .21512 (172*2π)/4473 weeks
173-.88681 -.84051 (173*2π)/4473 weeks
1741.74231 -.20077 (174*2π)/4473 weeks
175-.94939 1.48692 (175*2π)/4473 weeks
176-.60277 -1.38983 (176*2π)/4473 weeks
1771.03154 -.17488 (177*2π)/4473 weeks
178.57072 .66802 (178*2π)/4473 weeks
179-.95762 1.09392 (179*2π)/4472 weeks
180-.81092 -1.32778 (180*2π)/4472 weeks
181.69693 .04291 (181*2π)/4472 weeks
182.28 -.04695 (182*2π)/4472 weeks
183-.33292 .69833 (183*2π)/4472 weeks
184-.42024 -1.183 (184*2π)/4472 weeks
1851.18381 .47051 (185*2π)/4472 weeks
186-.96837 .41634 (186*2π)/4472 weeks
187-.2871 -.54431 (187*2π)/4472 weeks
188.15607 -1.10745 (188*2π)/4472 weeks
1891.50414 .77877 (189*2π)/4472 weeks
190-1.20459 .07406 (190*2π)/4472 weeks
191.56433 -.68893 (191*2π)/4472 weeks
192.89614 -.45525 (192*2π)/4472 weeks
193.85803 1.45764 (193*2π)/4472 weeks
194-1.707 .23997 (194*2π)/4472 weeks
195.70978 -1.71948 (195*2π)/4472 weeks
1961.15164 1.5875 (196*2π)/4472 weeks
197-1.11482 .50744 (197*2π)/4472 weeks
198-1.07008 -.51832 (198*2π)/4472 weeks
1991.28729 -.90608 (199*2π)/4472 weeks
200.14579 1.42579 (200*2π)/4472 weeks
201-.66571 -.63148 (201*2π)/4472 weeks
202.65602 .32095 (202*2π)/4472 weeks
203-.39347 .34369 (203*2π)/4472 weeks
204-.259 .34611 (204*2π)/4472 weeks
205-.76051 -1.16669 (205*2π)/4472 weeks
2061.15329 .88624 (206*2π)/4472 weeks
207-1.65008 -.24469 (207*2π)/4472 weeks
208.56827 -.75104 (208*2π)/4472 weeks
209.47192 -.08453 (209*2π)/4472 weeks
210.27167 .56188 (210*2π)/4472 weeks
211-.61659 -.17897 (211*2π)/4472 weeks
212.61782 -.5325 (212*2π)/4472 weeks
213-.06487 .24795 (213*2π)/4472 weeks
214.6118 .41979 (214*2π)/4472 weeks
215-1.35637 .69716 (215*2π)/4472 weeks
216-.23722 -1.5054 (216*2π)/4472 weeks
2171.43341 -.53482 (217*2π)/4472 weeks
218.35007 1.55344 (218*2π)/4472 weeks
219-1.19554 -.44979 (219*2π)/4472 weeks
2201.1712 -1.03096 (220*2π)/4472 weeks
221.27565 1.76203 (221*2π)/4472 weeks
222-1.24162 -.71511 (222*2π)/4472 weeks
223.75618 -.44849 (223*2π)/4472 weeks
224.75618 .44849 (224*2π)/4472 weeks
225-1.24162 .71511 (225*2π)/4472 weeks
226.27565 -1.76203 (226*2π)/4472 weeks
2271.1712 1.03096 (227*2π)/4472 weeks
228-1.19554 .44979 (228*2π)/4472 weeks
229.35007 -1.55344 (229*2π)/4472 weeks
2301.43341 .53482 (230*2π)/4472 weeks
231-.23722 1.5054 (231*2π)/4472 weeks
232-1.35637 -.69716 (232*2π)/4472 weeks
233.6118 -.41979 (233*2π)/4472 weeks
234-.06487 -.24795 (234*2π)/4472 weeks
235.61782 .5325 (235*2π)/4472 weeks
236-.61659 .17897 (236*2π)/4472 weeks
237.27167 -.56188 (237*2π)/4472 weeks
238.47192 .08453 (238*2π)/4472 weeks
239.56827 .75104 (239*2π)/4472 weeks
240-1.65008 .24469 (240*2π)/4472 weeks
2411.15329 -.88624 (241*2π)/4472 weeks
242-.76051 1.16669 (242*2π)/4472 weeks
243-.259 -.34611 (243*2π)/4472 weeks
244-.39347 -.34369 (244*2π)/4472 weeks
245.65602 -.32095 (245*2π)/4472 weeks
246-.66571 .63148 (246*2π)/4472 weeks
247.14579 -1.42579 (247*2π)/4472 weeks
2481.28729 .90608 (248*2π)/4472 weeks
249-1.07008 .51832 (249*2π)/4472 weeks
250-1.11482 -.50744 (250*2π)/4472 weeks
2511.15164 -1.5875 (251*2π)/4472 weeks
252.70978 1.71948 (252*2π)/4472 weeks
253-1.707 -.23997 (253*2π)/4472 weeks
254.85803 -1.45764 (254*2π)/4472 weeks
255.89614 .45525 (255*2π)/4472 weeks
256.56433 .68893 (256*2π)/4472 weeks
257-1.20459 -.07406 (257*2π)/4472 weeks
2581.50414 -.77877 (258*2π)/4472 weeks
259.15607 1.10745 (259*2π)/4472 weeks
260-.2871 .54431 (260*2π)/4472 weeks
261-.96837 -.41634 (261*2π)/4472 weeks
2621.18381 -.47051 (262*2π)/4472 weeks
263-.42024 1.183 (263*2π)/4472 weeks
264-.33292 -.69833 (264*2π)/4472 weeks
265.28 .04695 (265*2π)/4472 weeks
266.69693 -.04291 (266*2π)/4472 weeks
267-.81092 1.32778 (267*2π)/4472 weeks
268-.95762 -1.09392 (268*2π)/4472 weeks
269.57072 -.66802 (269*2π)/4472 weeks
2701.03154 .17488 (270*2π)/4472 weeks
271-.60277 1.38983 (271*2π)/4472 weeks
272-.94939 -1.48692 (272*2π)/4472 weeks
2731.74231 .20077 (273*2π)/4472 weeks
274-.88681 .84051 (274*2π)/4472 weeks
275-.60167 -.21512 (275*2π)/4472 weeks
276.50308 -1.38763 (276*2π)/4472 weeks
2771.18741 .95858 (277*2π)/4472 weeks
278-1.04675 .29737 (278*2π)/4472 weeks
279.2047 -.5187 (279*2π)/4472 weeks
280.23948 .62528 (280*2π)/4472 weeks
281-.38294 .36206 (281*2π)/4472 weeks
282-.55934 -.41249 (282*2π)/4472 weeks
283.69331 -.03209 (283*2π)/4472 weeks
284-.65752 .42057 (284*2π)/4472 weeks
285.18644 -.38004 (285*2π)/4472 weeks
286-.51815 -.58864 (286*2π)/4472 weeks
2871.27147 -.48528 (287*2π)/4472 weeks
288.16769 1.0926 (288*2π)/4472 weeks
289-.73237 -.3507 (289*2π)/4472 weeks
290-.12722 -.32449 (290*2π)/4472 weeks
291.77844 -.2514 (291*2π)/4472 weeks
292-.77268 1.00158 (292*2π)/4472 weeks
293-.2422 -1.38223 (293*2π)/4472 weeks
294.79866 .54323 (294*2π)/4472 weeks
295-.02458 .27031 (295*2π)/4472 weeks
296.09345 .06184 (296*2π)/4472 weeks
297-.205 -.10281 (297*2π)/4472 weeks
298.54602 .30987 (298*2π)/4472 weeks
299-.64079 -.62447 (299*2π)/4471 weeks
300.81246 .21653 (300*2π)/4471 weeks
301-.6734 -.29906 (301*2π)/4471 weeks
3021.04352 .76023 (302*2π)/4471 weeks
303-1.0305 .2543 (303*2π)/4471 weeks
304-.0772 -.15378 (304*2π)/4471 weeks
305.37972 -.19724 (305*2π)/4471 weeks
306.41407 1.05331 (306*2π)/4471 weeks
307-1.70382 -.14748 (307*2π)/4471 weeks
308.83644 -1.40177 (308*2π)/4471 weeks
309.64398 .84191 (309*2π)/4471 weeks
310-.77757 .21273 (310*2π)/4471 weeks
311-.36203 -1.15657 (311*2π)/4471 weeks
3121.75086 .3064 (312*2π)/4471 weeks
313-1.31989 1.52611 (313*2π)/4471 weeks
314-.77473 -1.58572 (314*2π)/4471 weeks
3151.26946 -.36394 (315*2π)/4471 weeks
316.61565 1.21918 (316*2π)/4471 weeks
317-1.90642 .62421 (317*2π)/4471 weeks
318-.1307 -2.24504 (318*2π)/4471 weeks
3191.44852 .97911 (319*2π)/4471 weeks
320-.70327 .43176 (320*2π)/4471 weeks
321-.62831 .13377 (321*2π)/4471 weeks
322-.03295 -1.03169 (322*2π)/4471 weeks
323.47449 .15616 (323*2π)/4471 weeks
324-1.02758 -.01991 (324*2π)/4471 weeks
325.1916 -.6487 (325*2π)/4471 weeks
326-.06446 -1.01675 (326*2π)/4471 weeks
3271.41277 .89853 (327*2π)/4471 weeks
328-1.48106 .1755 (328*2π)/4471 weeks
329.47411 -.77454 (329*2π)/4471 weeks
330.79311 .01298 (330*2π)/4471 weeks
331-.32107 1.60839 (331*2π)/4471 weeks
332-1.69134 -1.61105 (332*2π)/4471 weeks
3332.85202 -1.19862 (333*2π)/4471 weeks
334-.4169 3.17854 (334*2π)/4471 weeks
335-2.49595 -1.34185 (335*2π)/4471 weeks
336.95913 -2.3128 (336*2π)/4471 weeks
3372.42618 1.8496 (337*2π)/4471 weeks
338-2.67151 1.1558 (338*2π)/4471 weeks
339.13339 -2.4402 (339*2π)/4471 weeks
3402.05622 .23414 (340*2π)/4471 weeks
341.09848 1.23306 (341*2π)/4471 weeks
342-.69738 .03682 (342*2π)/4471 weeks
343-.13665 -1.18539 (343*2π)/4471 weeks
344.64426 .93274 (344*2π)/4471 weeks
345-.46936 .00917 (345*2π)/4471 weeks
346-.72351 -.49691 (346*2π)/4471 weeks
347.78057 -.52561 (347*2π)/4471 weeks
348.36999 .81205 (348*2π)/4471 weeks
349-.678 -.07761 (349*2π)/4471 weeks
350.53795 -.51285 (350*2π)/4471 weeks
351.45237 .41408 (351*2π)/4471 weeks
352.00945 1.23843 (352*2π)/4471 weeks
353-2.00964 -.88632 (353*2π)/4471 weeks
3541.5475 -1.21022 (354*2π)/4471 weeks
355.0619 1.70561 (355*2π)/4471 weeks
356-1.80441 -.78117 (356*2π)/4471 weeks
357-.34274 -1.78768 (357*2π)/4471 weeks
3582.2697 -.4564 (358*2π)/4471 weeks
359-.78134 1.39891 (359*2π)/4471 weeks
360-.09771 -1.50599 (360*2π)/4471 weeks
361.26325 .03838 (361*2π)/4471 weeks
3621.06482 .59648 (362*2π)/4471 weeks
363-1.82303 1.0234 (363*2π)/4471 weeks
364-.01153 -1.61642 (364*2π)/4471 weeks
3652.06641 .31265 (365*2π)/4471 weeks
366-.42994 2.06121 (366*2π)/4471 weeks
367-1.99628 -1.11625 (367*2π)/4471 weeks
368.89161 -2.53494 (368*2π)/4471 weeks
3692.10912 1.20626 (369*2π)/4471 weeks
370-1.03245 .56886 (370*2π)/4471 weeks
371-.12438 -1.45082 (371*2π)/4471 weeks
3721.96095 .0779 (372*2π)/4471 weeks
373.42274 2.96047 (373*2π)/4471 weeks
374-3.57681 .09617 (374*2π)/4471 weeks
375.37471 -3.10438 (375*2π)/4471 weeks
3762.16085 1.5002 (376*2π)/4471 weeks
377-2.49346 2.65441 (377*2π)/4471 weeks
378-2.22009 -4.61253 (378*2π)/4471 weeks
3795.85204 .09598 (379*2π)/4471 weeks
380-2.44417 4.82894 (380*2π)/4471 weeks
381-3.10288 -3.43402 (381*2π)/4471 weeks
3823.23666 -1.34789 (382*2π)/4471 weeks
383.37534 3.48291 (383*2π)/4471 weeks
384-4.91164 .01465 (384*2π)/4471 weeks
385.99242 -4.43915 (385*2π)/4471 weeks
3862.97543 2.38604 (386*2π)/4471 weeks
387-1.33971 1.11961 (387*2π)/4471 weeks
388-2.40381 -.28274 (388*2π)/4471 weeks
3891.0935 -1.61906 (389*2π)/4471 weeks
390-.08915 1.71389 (390*2π)/4471 weeks
391-.83699 -.72727 (391*2π)/4471 weeks
392-1.99808 -.10785 (392*2π)/4471 weeks
3931.80917 -3.89964 (393*2π)/4471 weeks
3942.99492 2.73866 (394*2π)/4471 weeks
395-2.49885 1.3814 (395*2π)/4471 weeks
396-1.12667 -2.29845 (396*2π)/4471 weeks
3972.92753 -2.00146 (397*2π)/4471 weeks
3981.20164 5.10697 (398*2π)/4471 weeks
399-5.97876 -1.96626 (399*2π)/4471 weeks
4003.73955 -2.23631 (400*2π)/4471 weeks
4011.85127 2.43171 (401*2π)/4471 weeks
402-1.91203 2.23793 (402*2π)/4471 weeks
403-2.19036 -4.31088 (403*2π)/4471 weeks
4044.90466 .42381 (404*2π)/4471 weeks
405-3.80368 2.48512 (405*2π)/4471 weeks
406-.74134 -3.75708 (406*2π)/4471 weeks
4071.78156 .74449 (407*2π)/4471 weeks
408-1.76865 -.44265 (408*2π)/4471 weeks
4091.38908 -1.17401 (409*2π)/4471 weeks
410.43783 -.50386 (410*2π)/4471 weeks
411.42152 .26757 (411*2π)/4471 weeks
412.75696 -2.30052 (412*2π)/4471 weeks
413.59523 2.17969 (413*2π)/4471 weeks
414-2.07048 -3.34611 (414*2π)/4471 weeks
4155.99086 .21097 (415*2π)/4471 weeks
416-1.12053 5.991 (416*2π)/4471 weeks
417-4.60868 -2.93533 (417*2π)/4471 weeks
4186.4999 -1.88159 (418*2π)/4471 weeks
419.1681 7.60549 (419*2π)/4471 weeks
420-8.07863 -.93931 (420*2π)/4471 weeks
4212.23741 -6.51966 (421*2π)/4471 weeks
4226.06654 3.01655 (422*2π)/4471 weeks
423-6.15622 6.37638 (423*2π)/4471 weeks
424-5.79472 -8.45263 (424*2π)/4471 weeks
4257.70449 -2.74742 (425*2π)/4471 weeks
426.30247 8.74261 (426*2π)/4471 weeks
427-7.64587 -2.46334 (427*2π)/4471 weeks
428-.66654 -9.61059 (428*2π)/4471 weeks
42911.60551 2.31455 (429*2π)/4471 weeks
430-8.02266 5.58556 (430*2π)/4471 weeks
431.33431 -4.88361 (431*2π)/4471 weeks
432-.80418 3.3598 (432*2π)/4471 weeks
433-3.58757 -2.59624 (433*2π)/4471 weeks
434.51165 -.3961 (434*2π)/4471 weeks
435-4.47466 1.94328 (435*2π)/4471 weeks
4363.16455 -7.98782 (436*2π)/4471 weeks
4372.28626 6.68552 (437*2π)/4471 weeks
438-4.94822 -3.00049 (438*2π)/4471 weeks
4391.71607 -8.15694 (439*2π)/4471 weeks
44012.57778 -4.79164 (440*2π)/4471 weeks
441-5.39226 24.42163 (441*2π)/4471 weeks
442-30.22436 -19.0255 (442*2π)/4471 weeks
44317.38615 -22.56275 (443*2π)/4471 weeks
44424.74264 18.00166 (444*2π)/4471 weeks
445-38.23424 35.11967 (445*2π)/4471 weeks



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