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Fourier Analysis of AGQ (ProShares Ultra Silver)


AGQ (ProShares Ultra Silver) appears to have interesting cyclic behaviour every 25 weeks (12.2099*cosine), 19 weeks (9.9104*cosine), and 15 weeks (7.1412*cosine).

AGQ (ProShares Ultra Silver) has an average price of 130.05 (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.

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 11/21/2016 for AGQ (ProShares Ultra Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0130.049   0 
1-66.32978 107.4296 (1*2π)/417417 weeks
2-27.22653 -39.89177 (2*2π)/417209 weeks
330.22565 -8.88189 (3*2π)/417139 weeks
411.24126 32.05492 (4*2π)/417104 weeks
5-35.00662 -2.16186 (5*2π)/41783 weeks
613.43302 -18.41216 (6*2π)/41770 weeks
74.99728 5.84573 (7*2π)/41760 weeks
8-3.10928 6.43626 (8*2π)/41752 weeks
9-6.24237 -5.25292 (9*2π)/41746 weeks
108.00585 4.20317 (10*2π)/41742 weeks
11-7.09934 1.65787 (11*2π)/41738 weeks
12.65891 .47764 (12*2π)/41735 weeks
13-2.97784 3.5805 (13*2π)/41732 weeks
14-1.02008 -3.01745 (14*2π)/41730 weeks
15.19853 5.03584 (15*2π)/41728 weeks
16-8.04928 -6.90053 (16*2π)/41726 weeks
1712.20991 -.61276 (17*2π)/41725 weeks
18-1.93286 9.37543 (18*2π)/41723 weeks
19-9.67877 -.51719 (19*2π)/41722 weeks
204.94602 -6.57473 (20*2π)/41721 weeks
215.78131 7.85412 (21*2π)/41720 weeks
22-9.9104 3.10654 (22*2π)/41719 weeks
23.64929 -8.69863 (23*2π)/41718 weeks
246.14549 3.42664 (24*2π)/41717 weeks
25-5.70496 5.82077 (25*2π)/41717 weeks
26-4.99628 -6.39659 (26*2π)/41716 weeks
277.14124 -2.14189 (27*2π)/41715 weeks
28-3.63014 5.18859 (28*2π)/41715 weeks
29-2.98774 -6.26756 (29*2π)/41714 weeks
305.9851 -.69982 (30*2π)/41714 weeks
31-2.04696 1.98997 (31*2π)/41713 weeks
321.00336 -1.74913 (32*2π)/41713 weeks
33.03346 1.02049 (33*2π)/41713 weeks
34.20371 .26454 (34*2π)/41712 weeks
35.94286 -.4102 (35*2π)/41712 weeks
36.01015 2.72011 (36*2π)/41712 weeks
37-.38198 -1.64738 (37*2π)/41711 weeks
382.4447 2.79349 (38*2π)/41711 weeks
39-3.90083 1.6351 (39*2π)/41711 weeks
402.14311 -4.05151 (40*2π)/41710 weeks
411.76422 4.95572 (41*2π)/41710 weeks
42-3.73608 -.67709 (42*2π)/41710 weeks
43.80616 -3.14872 (43*2π)/41710 weeks
444.66025 1.23687 (44*2π)/4179 weeks
45-5.59604 2.83266 (45*2π)/4179 weeks
46.22099 -4.96161 (46*2π)/4179 weeks
473.29054 1.35455 (47*2π)/4179 weeks
48-1.96118 2.45728 (48*2π)/4179 weeks
49-2.23489 -2.29069 (49*2π)/4179 weeks
503.81805 -1.92749 (50*2π)/4178 weeks
51-.02676 3.56485 (51*2π)/4178 weeks
52-.25786 .46902 (52*2π)/4178 weeks
53-1.42719 -.30703 (53*2π)/4178 weeks
541.46873 -.32482 (54*2π)/4178 weeks
55-.76896 2.51356 (55*2π)/4178 weeks
56-2.44617 -.17582 (56*2π)/4177 weeks
571.5242 -3.62375 (57*2π)/4177 weeks
583.26337 2.99579 (58*2π)/4177 weeks
59-4.28328 2.4583 (59*2π)/4177 weeks
60-1.20508 -3.87264 (60*2π)/4177 weeks
614.19737 1.14552 (61*2π)/4177 weeks
62-3.98474 3.77607 (62*2π)/4177 weeks
63-1.94506 -5.2179 (63*2π)/4177 weeks
645.3355 .95406 (64*2π)/4177 weeks
65-3.18896 3.84678 (65*2π)/4176 weeks
66-1.37211 -3.08175 (66*2π)/4176 weeks
673.15261 .70251 (67*2π)/4176 weeks
68-1.5638 3.09205 (68*2π)/4176 weeks
69-2.67799 -1.505 (69*2π)/4176 weeks
70.79682 -2.34357 (70*2π)/4176 weeks
71.90898 1.67949 (71*2π)/4176 weeks
72-1.48418 -.37858 (72*2π)/4176 weeks
73.78187 -1.92293 (73*2π)/4176 weeks
742.31724 1.07401 (74*2π)/4176 weeks
75-1.88224 2.51215 (75*2π)/4176 weeks
76-1.11835 -1.92172 (76*2π)/4175 weeks
771.72141 -.05801 (77*2π)/4175 weeks
78.20458 1.71129 (78*2π)/4175 weeks
79-1.38324 -.64631 (79*2π)/4175 weeks
80.76763 -.73187 (80*2π)/4175 weeks
81.9619 .34695 (81*2π)/4175 weeks
82-1.07891 .40337 (82*2π)/4175 weeks
83.60897 -2.04296 (83*2π)/4175 weeks
841.88599 .77697 (84*2π)/4175 weeks
85-.5776 2.42759 (85*2π)/4175 weeks
86-1.0263 -1.48368 (86*2π)/4175 weeks
871.6252 .15698 (87*2π)/4175 weeks
88-.4892 1.71868 (88*2π)/4175 weeks
89-1.30676 -.39554 (89*2π)/4175 weeks
90.56937 -.64324 (90*2π)/4175 weeks
91.14009 .44502 (91*2π)/4175 weeks
92-.48421 .22008 (92*2π)/4175 weeks
93-.15964 -.81517 (93*2π)/4174 weeks
941.35533 .58755 (94*2π)/4174 weeks
95-.71192 .44527 (95*2π)/4174 weeks
96-.40651 -.36813 (96*2π)/4174 weeks
97.61089 .00986 (97*2π)/4174 weeks
98.2699 1.14887 (98*2π)/4174 weeks
99-1.71134 -.63603 (99*2π)/4174 weeks
100.93498 -1.97578 (100*2π)/4174 weeks
1012.08396 1.19693 (101*2π)/4174 weeks
102-2.44 1.49014 (102*2π)/4174 weeks
103.0278 -3.39361 (103*2π)/4174 weeks
1043.03247 1.14261 (104*2π)/4174 weeks
105-2.14196 2.32498 (105*2π)/4174 weeks
106-1.22158 -2.63193 (106*2π)/4174 weeks
1072.47286 .09025 (107*2π)/4174 weeks
108-1.29719 1.73431 (108*2π)/4174 weeks
109-.54684 -1.21567 (109*2π)/4174 weeks
110.93453 -.20512 (110*2π)/4174 weeks
111-.30638 1.05588 (111*2π)/4174 weeks
112-.77748 -.87597 (112*2π)/4174 weeks
113.76198 -.52259 (113*2π)/4174 weeks
114.80212 .45241 (114*2π)/4174 weeks
115-.41547 .37663 (115*2π)/4174 weeks
116.05383 -.19326 (116*2π)/4174 weeks
117.81069 .3638 (117*2π)/4174 weeks
118.04706 1.07252 (118*2π)/4174 weeks
119-1.40286 -.27131 (119*2π)/4174 weeks
1201.15126 -1.21412 (120*2π)/4173 weeks
1211.2394 1.46495 (121*2π)/4173 weeks
122-2.01639 .75183 (122*2π)/4173 weeks
123-.05831 -1.6172 (123*2π)/4173 weeks
1241.57624 .3777 (124*2π)/4173 weeks
125-.96709 1.54829 (125*2π)/4173 weeks
126-.93715 -1.2385 (126*2π)/4173 weeks
1271.45316 -.21722 (127*2π)/4173 weeks
128-.76446 1.41687 (128*2π)/4173 weeks
129-.34163 -1.22744 (129*2π)/4173 weeks
1301.28865 -.0942 (130*2π)/4173 weeks
131-.14284 1.47823 (131*2π)/4173 weeks
132-.8176 -.35977 (132*2π)/4173 weeks
133.64536 -.2799 (133*2π)/4173 weeks
134.21918 .69095 (134*2π)/4173 weeks
135-.85758 .01852 (135*2π)/4173 weeks
136.17569 -.0256 (136*2π)/4173 weeks
137-.16097 -.42309 (137*2π)/4173 weeks
138.35877 -.02771 (138*2π)/4173 weeks
139-.14542 -.22969 (139*2π)/4173 weeks
140-.23145 .10167 (140*2π)/4173 weeks
141.36033 -.07111 (141*2π)/4173 weeks
142-.7913 .16028 (142*2π)/4173 weeks
143-.05058 -1.12562 (143*2π)/4173 weeks
144.6723 .30751 (144*2π)/4173 weeks
145-.63519 .47107 (145*2π)/4173 weeks
146-.10776 -.86784 (146*2π)/4173 weeks
147.76562 .17731 (147*2π)/4173 weeks
148-.75035 .8242 (148*2π)/4173 weeks
149-.72801 -.73055 (149*2π)/4173 weeks
150.51308 -.61303 (150*2π)/4173 weeks
151.49459 .08157 (151*2π)/4173 weeks
152-.19436 .31246 (152*2π)/4173 weeks
153-.11701 -.00854 (153*2π)/4173 weeks
154.50121 -.32806 (154*2π)/4173 weeks
155.04623 .98744 (155*2π)/4173 weeks
156-.85701 -.43746 (156*2π)/4173 weeks
157.74451 .02198 (157*2π)/4173 weeks
158-.71845 .94117 (158*2π)/4173 weeks
159-.81323 -.7187 (159*2π)/4173 weeks
1601.01945 -.88139 (160*2π)/4173 weeks
161.70226 1.24977 (161*2π)/4173 weeks
162-1.58719 -.21591 (162*2π)/4173 weeks
1631.03057 -1.08438 (163*2π)/4173 weeks
164.37874 1.29531 (164*2π)/4173 weeks
165-1.13538 .05423 (165*2π)/4173 weeks
166-.08228 -1.42367 (166*2π)/4173 weeks
1671.47385 .28397 (167*2π)/4172 weeks
168-.14115 .93578 (168*2π)/4172 weeks
169-.6264 .10512 (169*2π)/4172 weeks
170.15111 -.77354 (170*2π)/4172 weeks
171.67525 .46066 (171*2π)/4172 weeks
172-.92092 .39177 (172*2π)/4172 weeks
173.32325 -.86363 (173*2π)/4172 weeks
174.6947 .35084 (174*2π)/4172 weeks
175-.50987 1.24985 (175*2π)/4172 weeks
176-1.15764 -.85551 (176*2π)/4172 weeks
177.80016 -.1685 (177*2π)/4172 weeks
178-.14584 .55196 (178*2π)/4172 weeks
179-1.33713 .18989 (179*2π)/4172 weeks
180.10767 -1.8945 (180*2π)/4172 weeks
1811.4526 .70552 (181*2π)/4172 weeks
182-1.20718 .83884 (182*2π)/4172 weeks
183-.35368 -1.84913 (183*2π)/4172 weeks
1841.77093 .0788 (184*2π)/4172 weeks
185-.34018 1.43607 (185*2π)/4172 weeks
186-.78679 -.68642 (186*2π)/4172 weeks
187.88442 -.60777 (187*2π)/4172 weeks
188-.22821 .50358 (188*2π)/4172 weeks
189.01301 -.69831 (189*2π)/4172 weeks
190.80705 -.07546 (190*2π)/4172 weeks
191.53541 .64081 (191*2π)/4172 weeks
192-.76098 -.30258 (192*2π)/4172 weeks
1931.28475 -.20355 (193*2π)/4172 weeks
194-.27459 1.16179 (194*2π)/4172 weeks
195-.74414 -.40789 (195*2π)/4172 weeks
196.29888 -.38962 (196*2π)/4172 weeks
197.23703 .27449 (197*2π)/4172 weeks
198-.36957 .25841 (198*2π)/4172 weeks
199-.42114 -.299 (199*2π)/4172 weeks
200.42912 -.60304 (200*2π)/4172 weeks
2011.27118 .36645 (201*2π)/4172 weeks
202-.7393 1.81969 (202*2π)/4172 weeks
203-1.30015 -1.57754 (203*2π)/4172 weeks
2041.57792 -.01082 (204*2π)/4172 weeks
205-.61245 1.05642 (205*2π)/4172 weeks
206-.63658 -1.23501 (206*2π)/4172 weeks
2071.44172 -.10729 (207*2π)/4172 weeks
208-.6249 1.20703 (208*2π)/4172 weeks
209-.6249 -1.20703 (209*2π)/4172 weeks
2101.44172 .10729 (210*2π)/4172 weeks
211-.63658 1.23501 (211*2π)/4172 weeks
212-.61245 -1.05642 (212*2π)/4172 weeks
2131.57792 .01082 (213*2π)/4172 weeks
214-1.30015 1.57754 (214*2π)/4172 weeks
215-.7393 -1.81969 (215*2π)/4172 weeks
2161.27118 -.36645 (216*2π)/4172 weeks
217.42912 .60304 (217*2π)/4172 weeks
218-.42114 .299 (218*2π)/4172 weeks
219-.36957 -.25841 (219*2π)/4172 weeks
220.23703 -.27449 (220*2π)/4172 weeks
221.29888 .38962 (221*2π)/4172 weeks
222-.74414 .40789 (222*2π)/4172 weeks
223-.27459 -1.16179 (223*2π)/4172 weeks
2241.28475 .20355 (224*2π)/4172 weeks
225-.76098 .30258 (225*2π)/4172 weeks
226.53541 -.64081 (226*2π)/4172 weeks
227.80705 .07546 (227*2π)/4172 weeks
228.01301 .69831 (228*2π)/4172 weeks
229-.22821 -.50358 (229*2π)/4172 weeks
230.88442 .60777 (230*2π)/4172 weeks
231-.78679 .68642 (231*2π)/4172 weeks
232-.34018 -1.43607 (232*2π)/4172 weeks
2331.77093 -.0788 (233*2π)/4172 weeks
234-.35368 1.84913 (234*2π)/4172 weeks
235-1.20718 -.83884 (235*2π)/4172 weeks
2361.4526 -.70552 (236*2π)/4172 weeks
237.10767 1.8945 (237*2π)/4172 weeks
238-1.33713 -.18989 (238*2π)/4172 weeks
239-.14584 -.55196 (239*2π)/4172 weeks
240.80016 .1685 (240*2π)/4172 weeks
241-1.15764 .85551 (241*2π)/4172 weeks
242-.50987 -1.24985 (242*2π)/4172 weeks
243.6947 -.35084 (243*2π)/4172 weeks
244.32325 .86363 (244*2π)/4172 weeks
245-.92092 -.39177 (245*2π)/4172 weeks
246.67525 -.46066 (246*2π)/4172 weeks
247.15111 .77354 (247*2π)/4172 weeks
248-.6264 -.10512 (248*2π)/4172 weeks
249-.14115 -.93578 (249*2π)/4172 weeks
2501.47385 -.28397 (250*2π)/4172 weeks
251-.08228 1.42367 (251*2π)/4172 weeks
252-1.13538 -.05423 (252*2π)/4172 weeks
253.37874 -1.29531 (253*2π)/4172 weeks
2541.03057 1.08438 (254*2π)/4172 weeks
255-1.58719 .21591 (255*2π)/4172 weeks
256.70226 -1.24977 (256*2π)/4172 weeks
2571.01945 .88139 (257*2π)/4172 weeks
258-.81323 .7187 (258*2π)/4172 weeks
259-.71845 -.94117 (259*2π)/4172 weeks
260.74451 -.02198 (260*2π)/4172 weeks
261-.85701 .43746 (261*2π)/4172 weeks
262.04623 -.98744 (262*2π)/4172 weeks
263.50121 .32806 (263*2π)/4172 weeks
264-.11701 .00854 (264*2π)/4172 weeks
265-.19436 -.31246 (265*2π)/4172 weeks
266.49459 -.08157 (266*2π)/4172 weeks
267.51308 .61303 (267*2π)/4172 weeks
268-.72801 .73055 (268*2π)/4172 weeks
269-.75035 -.8242 (269*2π)/4172 weeks
270.76562 -.17731 (270*2π)/4172 weeks
271-.10776 .86784 (271*2π)/4172 weeks
272-.63519 -.47107 (272*2π)/4172 weeks
273.6723 -.30751 (273*2π)/4172 weeks
274-.05058 1.12562 (274*2π)/4172 weeks
275-.7913 -.16028 (275*2π)/4172 weeks
276.36033 .07111 (276*2π)/4172 weeks
277-.23145 -.10167 (277*2π)/4172 weeks
278-.14542 .22969 (278*2π)/4172 weeks
279.35877 .02771 (279*2π)/4171 weeks
280-.16097 .42309 (280*2π)/4171 weeks
281.17569 .0256 (281*2π)/4171 weeks
282-.85758 -.01852 (282*2π)/4171 weeks
283.21918 -.69095 (283*2π)/4171 weeks
284.64536 .2799 (284*2π)/4171 weeks
285-.8176 .35977 (285*2π)/4171 weeks
286-.14284 -1.47823 (286*2π)/4171 weeks
2871.28865 .0942 (287*2π)/4171 weeks
288-.34163 1.22744 (288*2π)/4171 weeks
289-.76446 -1.41687 (289*2π)/4171 weeks
2901.45316 .21722 (290*2π)/4171 weeks
291-.93715 1.2385 (291*2π)/4171 weeks
292-.96709 -1.54829 (292*2π)/4171 weeks
2931.57624 -.3777 (293*2π)/4171 weeks
294-.05831 1.6172 (294*2π)/4171 weeks
295-2.01639 -.75183 (295*2π)/4171 weeks
2961.2394 -1.46495 (296*2π)/4171 weeks
2971.15126 1.21412 (297*2π)/4171 weeks
298-1.40286 .27131 (298*2π)/4171 weeks
299.04706 -1.07252 (299*2π)/4171 weeks
300.81069 -.3638 (300*2π)/4171 weeks
301.05383 .19326 (301*2π)/4171 weeks
302-.41547 -.37663 (302*2π)/4171 weeks
303.80212 -.45241 (303*2π)/4171 weeks
304.76198 .52259 (304*2π)/4171 weeks
305-.77748 .87597 (305*2π)/4171 weeks
306-.30638 -1.05588 (306*2π)/4171 weeks
307.93453 .20512 (307*2π)/4171 weeks
308-.54684 1.21567 (308*2π)/4171 weeks
309-1.29719 -1.73431 (309*2π)/4171 weeks
3102.47286 -.09025 (310*2π)/4171 weeks
311-1.22158 2.63193 (311*2π)/4171 weeks
312-2.14196 -2.32498 (312*2π)/4171 weeks
3133.03247 -1.14261 (313*2π)/4171 weeks
314.0278 3.39361 (314*2π)/4171 weeks
315-2.44 -1.49014 (315*2π)/4171 weeks
3162.08396 -1.19693 (316*2π)/4171 weeks
317.93498 1.97578 (317*2π)/4171 weeks
318-1.71134 .63603 (318*2π)/4171 weeks
319.2699 -1.14887 (319*2π)/4171 weeks
320.61089 -.00986 (320*2π)/4171 weeks
321-.40651 .36813 (321*2π)/4171 weeks
322-.71192 -.44527 (322*2π)/4171 weeks
3231.35533 -.58755 (323*2π)/4171 weeks
324-.15964 .81517 (324*2π)/4171 weeks
325-.48421 -.22008 (325*2π)/4171 weeks
326.14009 -.44502 (326*2π)/4171 weeks
327.56937 .64324 (327*2π)/4171 weeks
328-1.30676 .39554 (328*2π)/4171 weeks
329-.4892 -1.71868 (329*2π)/4171 weeks
3301.6252 -.15698 (330*2π)/4171 weeks
331-1.0263 1.48368 (331*2π)/4171 weeks
332-.5776 -2.42759 (332*2π)/4171 weeks
3331.88599 -.77697 (333*2π)/4171 weeks
334.60897 2.04296 (334*2π)/4171 weeks
335-1.07891 -.40337 (335*2π)/4171 weeks
336.9619 -.34695 (336*2π)/4171 weeks
337.76763 .73187 (337*2π)/4171 weeks
338-1.38324 .64631 (338*2π)/4171 weeks
339.20458 -1.71129 (339*2π)/4171 weeks
3401.72141 .05801 (340*2π)/4171 weeks
341-1.11835 1.92172 (341*2π)/4171 weeks
342-1.88224 -2.51215 (342*2π)/4171 weeks
3432.31724 -1.07401 (343*2π)/4171 weeks
344.78187 1.92293 (344*2π)/4171 weeks
345-1.48418 .37858 (345*2π)/4171 weeks
346.90898 -1.67949 (346*2π)/4171 weeks
347.79682 2.34357 (347*2π)/4171 weeks
348-2.67799 1.505 (348*2π)/4171 weeks
349-1.5638 -3.09205 (349*2π)/4171 weeks
3503.15261 -.70251 (350*2π)/4171 weeks
351-1.37211 3.08175 (351*2π)/4171 weeks
352-3.18896 -3.84678 (352*2π)/4171 weeks
3535.3355 -.95406 (353*2π)/4171 weeks
354-1.94506 5.2179 (354*2π)/4171 weeks
355-3.98474 -3.77607 (355*2π)/4171 weeks
3564.19737 -1.14552 (356*2π)/4171 weeks
357-1.20508 3.87264 (357*2π)/4171 weeks
358-4.28328 -2.4583 (358*2π)/4171 weeks
3593.26337 -2.99579 (359*2π)/4171 weeks
3601.5242 3.62375 (360*2π)/4171 weeks
361-2.44617 .17582 (361*2π)/4171 weeks
362-.76896 -2.51356 (362*2π)/4171 weeks
3631.46873 .32482 (363*2π)/4171 weeks
364-1.42719 .30703 (364*2π)/4171 weeks
365-.25786 -.46902 (365*2π)/4171 weeks
366-.02676 -3.56485 (366*2π)/4171 weeks
3673.81805 1.92749 (367*2π)/4171 weeks
368-2.23489 2.29069 (368*2π)/4171 weeks
369-1.96118 -2.45728 (369*2π)/4171 weeks
3703.29054 -1.35455 (370*2π)/4171 weeks
371.22099 4.96161 (371*2π)/4171 weeks
372-5.59604 -2.83266 (372*2π)/4171 weeks
3734.66025 -1.23687 (373*2π)/4171 weeks
374.80616 3.14872 (374*2π)/4171 weeks
375-3.73608 .67709 (375*2π)/4171 weeks
3761.76422 -4.95572 (376*2π)/4171 weeks
3772.14311 4.05151 (377*2π)/4171 weeks
378-3.90083 -1.6351 (378*2π)/4171 weeks
3792.4447 -2.79349 (379*2π)/4171 weeks
380-.38198 1.64738 (380*2π)/4171 weeks
381.01015 -2.72011 (381*2π)/4171 weeks
382.94286 .4102 (382*2π)/4171 weeks
383.20371 -.26454 (383*2π)/4171 weeks
384.03346 -1.02049 (384*2π)/4171 weeks
3851.00336 1.74913 (385*2π)/4171 weeks
386-2.04696 -1.98997 (386*2π)/4171 weeks
3875.9851 .69982 (387*2π)/4171 weeks
388-2.98774 6.26756 (388*2π)/4171 weeks
389-3.63014 -5.18859 (389*2π)/4171 weeks
3907.14124 2.14189 (390*2π)/4171 weeks
391-4.99628 6.39659 (391*2π)/4171 weeks
392-5.70496 -5.82077 (392*2π)/4171 weeks
3936.14549 -3.42664 (393*2π)/4171 weeks
394.64929 8.69863 (394*2π)/4171 weeks
395-9.9104 -3.10654 (395*2π)/4171 weeks
3965.78131 -7.85412 (396*2π)/4171 weeks
3974.94602 6.57473 (397*2π)/4171 weeks
398-9.67877 .51719 (398*2π)/4171 weeks
399-1.93286 -9.37543 (399*2π)/4171 weeks
40012.20991 .61276 (400*2π)/4171 weeks
401-8.04928 6.90053 (401*2π)/4171 weeks
402.19853 -5.03584 (402*2π)/4171 weeks
403-1.02008 3.01745 (403*2π)/4171 weeks
404-2.97784 -3.5805 (404*2π)/4171 weeks
405.65891 -.47764 (405*2π)/4171 weeks
406-7.09934 -1.65787 (406*2π)/4171 weeks
4078.00585 -4.20317 (407*2π)/4171 weeks
408-6.24237 5.25292 (408*2π)/4171 weeks
409-3.10928 -6.43626 (409*2π)/4171 weeks
4104.99728 -5.84573 (410*2π)/4171 weeks
41113.43302 18.41216 (411*2π)/4171 weeks
412-35.00662 2.16186 (412*2π)/4171 weeks
41311.24126 -32.05492 (413*2π)/4171 weeks
41430.22565 8.88189 (414*2π)/4171 weeks
415-27.22653 39.89177 (415*2π)/4171 weeks

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