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Fourier Analysis of SDP (ProShares UltraShort Utilities ETF)


SDP (ProShares UltraShort Utilities ETF) appears to have interesting cyclic behaviour every 37 weeks (9.0154*sine), 25 weeks (8.2787*sine), and 50 weeks (7.2127*sine).

SDP (ProShares UltraShort Utilities ETF) has an average price of 161.32 (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 3/14/2007 to 10/16/2017 for SDP (ProShares UltraShort Utilities ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0161.3163   0 
131.55108 141.6405 (1*2π)/554554 weeks
2-23.44847 63.5379 (2*2π)/554277 weeks
3-18.88221 19.16253 (3*2π)/554185 weeks
4-2.12574 7.11478 (4*2π)/554139 weeks
512.64231 8.40237 (5*2π)/554111 weeks
612.65736 18.07575 (6*2π)/55492 weeks
7.99692 22.20111 (7*2π)/55479 weeks
8-7.56655 17.51813 (8*2π)/55469 weeks
9-4.82323 6.01724 (9*2π)/55462 weeks
101.47617 6.36253 (10*2π)/55455 weeks
112.97544 7.2127 (11*2π)/55450 weeks
12-.38174 7.17159 (12*2π)/55446 weeks
132.40185 7.0452 (13*2π)/55443 weeks
141.12092 6.33837 (14*2π)/55440 weeks
15-.36095 9.01539 (15*2π)/55437 weeks
16-2.85767 6.93305 (16*2π)/55435 weeks
17-3.9923 6.64248 (17*2π)/55433 weeks
18-5.93718 -1.68628 (18*2π)/55431 weeks
191.37906 -3.26461 (19*2π)/55429 weeks
206.82546 .17436 (20*2π)/55428 weeks
216.18649 5.31794 (21*2π)/55426 weeks
222.43844 8.27865 (22*2π)/55425 weeks
23-1.76041 5.62774 (23*2π)/55424 weeks
24-1.35914 1.96074 (24*2π)/55423 weeks
251.3529 .00266 (25*2π)/55422 weeks
263.89684 2.65517 (26*2π)/55421 weeks
272.44207 5.91362 (27*2π)/55421 weeks
28.20976 5.24291 (28*2π)/55420 weeks
29-.8124 4.2247 (29*2π)/55419 weeks
30-2.80251 1.73768 (30*2π)/55418 weeks
31.57909 -1.54382 (31*2π)/55418 weeks
324.36635 .00252 (32*2π)/55417 weeks
334.55543 4.61302 (33*2π)/55417 weeks
34.96526 6.09632 (34*2π)/55416 weeks
35-1.75663 3.61265 (35*2π)/55416 weeks
36.25874 1.68268 (36*2π)/55415 weeks
37.94348 1.49852 (37*2π)/55415 weeks
38-.0811 2.05869 (38*2π)/55415 weeks
391.77242 1.34254 (39*2π)/55414 weeks
401.4848 2.47983 (40*2π)/55414 weeks
411.12202 3.31005 (41*2π)/55414 weeks
42-.06953 1.40508 (42*2π)/55413 weeks
431.13034 2.9406 (43*2π)/55413 weeks
44.1547 2.39855 (44*2π)/55413 weeks
45-.32633 1.0211 (45*2π)/55412 weeks
461.05616 -.28343 (46*2π)/55412 weeks
472.69535 .08225 (47*2π)/55412 weeks
483.55657 3.14341 (48*2π)/55412 weeks
491.28143 4.84382 (49*2π)/55411 weeks
50-1.28425 3.32706 (50*2π)/55411 weeks
51-1.67075 1.11162 (51*2π)/55411 weeks
52.72927 -.9891 (52*2π)/55411 weeks
532.70894 .74239 (53*2π)/55410 weeks
543.44284 2.60164 (54*2π)/55410 weeks
551.83649 5.36334 (55*2π)/55410 weeks
56-1.26421 4.64108 (56*2π)/55410 weeks
57-3.66505 1.30323 (57*2π)/55410 weeks
58-.98305 -1.16904 (58*2π)/55410 weeks
592.18417 -.84177 (59*2π)/5549 weeks
603.30621 1.64859 (60*2π)/5549 weeks
61.91491 3.70967 (61*2π)/5549 weeks
62-.59958 2.16027 (62*2π)/5549 weeks
63.22321 1.341 (63*2π)/5549 weeks
64.17406 1.70009 (64*2π)/5549 weeks
65.65921 1.34125 (65*2π)/5549 weeks
66.08359 1.73297 (66*2π)/5548 weeks
67.00584 .63065 (67*2π)/5548 weeks
68.54696 1.73383 (68*2π)/5548 weeks
69.52109 1.06025 (69*2π)/5548 weeks
70.55637 2.00091 (70*2π)/5548 weeks
71-.95525 1.39208 (71*2π)/5548 weeks
72-.50183 -.52375 (72*2π)/5548 weeks
73.94807 -.48712 (73*2π)/5548 weeks
742.14554 -.01217 (74*2π)/5547 weeks
752.14354 2.2236 (75*2π)/5547 weeks
76.64416 2.42131 (76*2π)/5547 weeks
77-.22906 2.09024 (77*2π)/5547 weeks
78-1.5933 .83795 (78*2π)/5547 weeks
79.12256 -1.04046 (79*2π)/5547 weeks
802.17357 -.38335 (80*2π)/5547 weeks
812.17966 1.48831 (81*2π)/5547 weeks
821.06954 2.3208 (82*2π)/5547 weeks
83-.37823 1.95742 (83*2π)/5547 weeks
84-.39605 .74239 (84*2π)/5547 weeks
85-.0108 -.76748 (85*2π)/5547 weeks
862.24707 -.41172 (86*2π)/5546 weeks
872.53477 1.50506 (87*2π)/5546 weeks
881.12161 3.34994 (88*2π)/5546 weeks
89-.77727 2.0078 (89*2π)/5546 weeks
90-.13452 .63055 (90*2π)/5546 weeks
91.47281 .16056 (91*2π)/5546 weeks
921.26974 .72772 (92*2π)/5546 weeks
93.77202 1.56951 (93*2π)/5546 weeks
94.23972 1.2923 (94*2π)/5546 weeks
95.41068 .51575 (95*2π)/5546 weeks
961.23497 1.07626 (96*2π)/5546 weeks
97.43516 1.9135 (97*2π)/5546 weeks
98-.77554 1.6192 (98*2π)/5546 weeks
99-.74121 .01933 (99*2π)/5546 weeks
100.41232 -.73936 (100*2π)/5546 weeks
1011.82644 -.01498 (101*2π)/5545 weeks
1022.09018 1.58766 (102*2π)/5545 weeks
103.58649 2.67332 (103*2π)/5545 weeks
104-1.66364 1.66849 (104*2π)/5545 weeks
105-1.51143 -.86827 (105*2π)/5545 weeks
106.82382 -1.75176 (106*2π)/5545 weeks
1071.99473 -.26228 (107*2π)/5545 weeks
1082.24746 .62698 (108*2π)/5545 weeks
1091.63861 1.86385 (109*2π)/5545 weeks
110.12286 1.62038 (110*2π)/5545 weeks
111-.20821 .80787 (111*2π)/5545 weeks
112.39182 .03324 (112*2π)/5545 weeks
1131.36123 .10828 (113*2π)/5545 weeks
1141.75379 .45643 (114*2π)/5545 weeks
1151.36458 1.4301 (115*2π)/5545 weeks
116.79058 2.07558 (116*2π)/5545 weeks
117-.58785 1.94687 (117*2π)/5545 weeks
118-.62863 .61628 (118*2π)/5545 weeks
119-.17928 -.22543 (119*2π)/5545 weeks
120.92542 -.67052 (120*2π)/5545 weeks
1211.79364 .24374 (121*2π)/5545 weeks
1221.28853 1.59206 (122*2π)/5545 weeks
123.55066 1.5902 (123*2π)/5545 weeks
124-.31318 1.0854 (124*2π)/5544 weeks
125.25307 .40721 (125*2π)/5544 weeks
126.1793 .25606 (126*2π)/5544 weeks
127.48639 .15611 (127*2π)/5544 weeks
128.98628 .69833 (128*2π)/5544 weeks
1291.07226 1.20784 (129*2π)/5544 weeks
130-.1921 1.46386 (130*2π)/5544 weeks
131-.90975 .4075 (131*2π)/5544 weeks
132.1133 -.53761 (132*2π)/5544 weeks
1331.02155 .02781 (133*2π)/5544 weeks
134.70792 -.06884 (134*2π)/5544 weeks
1351.04954 .0666 (135*2π)/5544 weeks
1361.00549 .75789 (136*2π)/5544 weeks
137.6404 .80744 (137*2π)/5544 weeks
138.33376 .66195 (138*2π)/5544 weeks
139.0023 .17689 (139*2π)/5544 weeks
140.73764 -.40825 (140*2π)/5544 weeks
1411.59699 -.14345 (141*2π)/5544 weeks
1421.96477 .9879 (142*2π)/5544 weeks
143.32396 1.79102 (143*2π)/5544 weeks
144-.32933 .41867 (144*2π)/5544 weeks
145.85526 -.09307 (145*2π)/5544 weeks
146.64583 .65619 (146*2π)/5544 weeks
147.46983 .39658 (147*2π)/5544 weeks
148.74288 .24584 (148*2π)/5544 weeks
1491.13686 .37726 (149*2π)/5544 weeks
1501.0688 .89687 (150*2π)/5544 weeks
151.65305 1.28705 (151*2π)/5544 weeks
152-.19462 1.17929 (152*2π)/5544 weeks
153-.77825 -.19891 (153*2π)/5544 weeks
154.89996 -.63444 (154*2π)/5544 weeks
1551.46819 .11085 (155*2π)/5544 weeks
1561.13127 .97822 (156*2π)/5544 weeks
157.34977 1.0007 (157*2π)/5544 weeks
158.17583 .3527 (158*2π)/5544 weeks
159.24137 .53381 (159*2π)/5543 weeks
160.2083 -.28038 (160*2π)/5543 weeks
1611.42427 -.13527 (161*2π)/5543 weeks
1621.09397 1.19322 (162*2π)/5543 weeks
163.12246 .8869 (163*2π)/5543 weeks
164.3407 .22918 (164*2π)/5543 weeks
165.82425 .34624 (165*2π)/5543 weeks
166.36388 .60232 (166*2π)/5543 weeks
167.43465 .52707 (167*2π)/5543 weeks
168.08222 .50056 (168*2π)/5543 weeks
169.45663 -.11452 (169*2π)/5543 weeks
170.61474 -.023 (170*2π)/5543 weeks
171.77157 .06135 (171*2π)/5543 weeks
172.62385 .63359 (172*2π)/5543 weeks
173.22541 .11891 (173*2π)/5543 weeks
174.57978 -.45441 (174*2π)/5543 weeks
1751.17628 -.21948 (175*2π)/5543 weeks
1761.56311 .42086 (176*2π)/5543 weeks
1771.21544 1.31689 (177*2π)/5543 weeks
178.22076 1.15951 (178*2π)/5543 weeks
179-.14104 .64929 (179*2π)/5543 weeks
180-.00341 -.01854 (180*2π)/5543 weeks
181.84788 -.47384 (181*2π)/5543 weeks
1821.18758 .43278 (182*2π)/5543 weeks
1831.06389 .81611 (183*2π)/5543 weeks
184.05457 1.04386 (184*2π)/5543 weeks
185-.07144 .31102 (185*2π)/5543 weeks
186.20436 -.07697 (186*2π)/5543 weeks
187.83568 -.04535 (187*2π)/5543 weeks
188.83266 .42093 (188*2π)/5543 weeks
189.59003 .50581 (189*2π)/5543 weeks
190.61813 .378 (190*2π)/5543 weeks
191.2782 .66375 (191*2π)/5543 weeks
192.10276 .48971 (192*2π)/5543 weeks
193-.11707 -.10582 (193*2π)/5543 weeks
194.05523 -.44622 (194*2π)/5543 weeks
195.50893 -.70809 (195*2π)/5543 weeks
1961.47633 -.79962 (196*2π)/5543 weeks
1971.95963 .88607 (197*2π)/5543 weeks
198.79024 1.10678 (198*2π)/5543 weeks
199.14026 .66346 (199*2π)/5543 weeks
200.30448 .10005 (200*2π)/5543 weeks
201.83518 -.15225 (201*2π)/5543 weeks
202.8641 .29756 (202*2π)/5543 weeks
2031.03419 .30605 (203*2π)/5543 weeks
204.84462 1.36399 (204*2π)/5543 weeks
205-.23226 .95485 (205*2π)/5543 weeks
206-.54465 .26447 (206*2π)/5543 weeks
207-.30783 -.47081 (207*2π)/5543 weeks
208.36444 -.96343 (208*2π)/5543 weeks
2091.58044 -.53745 (209*2π)/5543 weeks
2101.73584 .64963 (210*2π)/5543 weeks
211.57072 1.48329 (211*2π)/5543 weeks
212-.56952 .57619 (212*2π)/5543 weeks
213-.27834 -.38847 (213*2π)/5543 weeks
214.59382 -.67576 (214*2π)/5543 weeks
2151.18598 -.54892 (215*2π)/5543 weeks
2161.30996 .57557 (216*2π)/5543 weeks
217.69268 1.01897 (217*2π)/5543 weeks
218-.29105 .44388 (218*2π)/5543 weeks
219-.10237 -.34616 (219*2π)/5543 weeks
220.62068 -.45013 (220*2π)/5543 weeks
221.45515 -.18499 (221*2π)/5543 weeks
222.75148 -.53889 (222*2π)/5542 weeks
2231.32458 -.2593 (223*2π)/5542 weeks
2241.00787 .52449 (224*2π)/5542 weeks
225.70264 .20534 (225*2π)/5542 weeks
226.65029 .36469 (226*2π)/5542 weeks
227.40142 .24449 (227*2π)/5542 weeks
228.14464 -.21798 (228*2π)/5542 weeks
229.70518 -.80726 (229*2π)/5542 weeks
2301.81725 -.02587 (230*2π)/5542 weeks
2311.28526 .85228 (231*2π)/5542 weeks
232.29226 .65159 (232*2π)/5542 weeks
233.32937 .34806 (233*2π)/5542 weeks
234.23275 -.05383 (234*2π)/5542 weeks
235.629 -.44257 (235*2π)/5542 weeks
2361.18018 -.32113 (236*2π)/5542 weeks
2371.50662 .36388 (237*2π)/5542 weeks
2381.16306 .9536 (238*2π)/5542 weeks
239.34299 1.09399 (239*2π)/5542 weeks
240-.07454 .55145 (240*2π)/5542 weeks
241-.10308 .00722 (241*2π)/5542 weeks
242.43388 -.17308 (242*2π)/5542 weeks
243.51056 -.23053 (243*2π)/5542 weeks
2441.1007 .20084 (244*2π)/5542 weeks
245.5404 .41204 (245*2π)/5542 weeks
246.47639 .39369 (246*2π)/5542 weeks
247-.06863 .31653 (247*2π)/5542 weeks
248.08067 -.3154 (248*2π)/5542 weeks
249.68625 -.62412 (249*2π)/5542 weeks
2501.00585 -.28674 (250*2π)/5542 weeks
2511.33246 .27602 (251*2π)/5542 weeks
252.67493 .97465 (252*2π)/5542 weeks
253-.05751 .58697 (253*2π)/5542 weeks
254-.23797 -.02094 (254*2π)/5542 weeks
255.09368 -.63917 (255*2π)/5542 weeks
256.80618 -.70567 (256*2π)/5542 weeks
2571.25234 -.29425 (257*2π)/5542 weeks
2581.20548 .61933 (258*2π)/5542 weeks
259.43711 .88158 (259*2π)/5542 weeks
260-.20141 .28203 (260*2π)/5542 weeks
261-.19701 -.05715 (261*2π)/5542 weeks
262.01735 -.96039 (262*2π)/5542 weeks
2631.13831 -.66004 (263*2π)/5542 weeks
2641.05407 -.06184 (264*2π)/5542 weeks
265.45001 .44115 (265*2π)/5542 weeks
266.23627 -.17349 (266*2π)/5542 weeks
267.40001 -.40621 (267*2π)/5542 weeks
268.57638 -.52316 (268*2π)/5542 weeks
269.88228 -.8904 (269*2π)/5542 weeks
2701.52938 -.27661 (270*2π)/5542 weeks
2711.28646 .64887 (271*2π)/5542 weeks
272.47801 .43515 (272*2π)/5542 weeks
273.42689 .07784 (273*2π)/5542 weeks
274.26985 -.18415 (274*2π)/5542 weeks
275.40757 -.64076 (275*2π)/5542 weeks
2761.24144 -.89002 (276*2π)/5542 weeks
2771.86981   (277*2π)/5542 weeks
2781.24144 .89002 (278*2π)/5542 weeks
279.40757 .64076 (279*2π)/5542 weeks
280.26985 .18415 (280*2π)/5542 weeks
281.42689 -.07784 (281*2π)/5542 weeks
282.47801 -.43515 (282*2π)/5542 weeks
2831.28646 -.64887 (283*2π)/5542 weeks
2841.52938 .27661 (284*2π)/5542 weeks
285.88228 .8904 (285*2π)/5542 weeks
286.57638 .52316 (286*2π)/5542 weeks
287.40001 .40621 (287*2π)/5542 weeks
288.23627 .17349 (288*2π)/5542 weeks
289.45001 -.44115 (289*2π)/5542 weeks
2901.05407 .06184 (290*2π)/5542 weeks
2911.13831 .66004 (291*2π)/5542 weeks
292.01735 .96039 (292*2π)/5542 weeks
293-.19701 .05715 (293*2π)/5542 weeks
294-.20141 -.28203 (294*2π)/5542 weeks
295.43711 -.88158 (295*2π)/5542 weeks
2961.20548 -.61933 (296*2π)/5542 weeks
2971.25234 .29425 (297*2π)/5542 weeks
298.80618 .70567 (298*2π)/5542 weeks
299.09368 .63917 (299*2π)/5542 weeks
300-.23797 .02094 (300*2π)/5542 weeks
301-.05751 -.58697 (301*2π)/5542 weeks
302.67493 -.97465 (302*2π)/5542 weeks
3031.33246 -.27602 (303*2π)/5542 weeks
3041.00585 .28674 (304*2π)/5542 weeks
305.68625 .62412 (305*2π)/5542 weeks
306.08067 .3154 (306*2π)/5542 weeks
307-.06863 -.31653 (307*2π)/5542 weeks
308.47639 -.39369 (308*2π)/5542 weeks
309.5404 -.41204 (309*2π)/5542 weeks
3101.1007 -.20084 (310*2π)/5542 weeks
311.51056 .23053 (311*2π)/5542 weeks
312.43388 .17308 (312*2π)/5542 weeks
313-.10308 -.00722 (313*2π)/5542 weeks
314-.07454 -.55145 (314*2π)/5542 weeks
315.34299 -1.09399 (315*2π)/5542 weeks
3161.16306 -.9536 (316*2π)/5542 weeks
3171.50662 -.36388 (317*2π)/5542 weeks
3181.18018 .32113 (318*2π)/5542 weeks
319.629 .44257 (319*2π)/5542 weeks
320.23275 .05383 (320*2π)/5542 weeks
321.32937 -.34806 (321*2π)/5542 weeks
322.29226 -.65159 (322*2π)/5542 weeks
3231.28526 -.85228 (323*2π)/5542 weeks
3241.81725 .02587 (324*2π)/5542 weeks
325.70518 .80726 (325*2π)/5542 weeks
326.14464 .21798 (326*2π)/5542 weeks
327.40142 -.24449 (327*2π)/5542 weeks
328.65029 -.36469 (328*2π)/5542 weeks
329.70264 -.20534 (329*2π)/5542 weeks
3301.00787 -.52449 (330*2π)/5542 weeks
3311.32458 .2593 (331*2π)/5542 weeks
332.75148 .53889 (332*2π)/5542 weeks
333.45515 .18499 (333*2π)/5542 weeks
334.62068 .45013 (334*2π)/5542 weeks
335-.10237 .34616 (335*2π)/5542 weeks
336-.29105 -.44388 (336*2π)/5542 weeks
337.69268 -1.01897 (337*2π)/5542 weeks
3381.30996 -.57557 (338*2π)/5542 weeks
3391.18598 .54892 (339*2π)/5542 weeks
340.59382 .67576 (340*2π)/5542 weeks
341-.27834 .38847 (341*2π)/5542 weeks
342-.56952 -.57619 (342*2π)/5542 weeks
343.57072 -1.48329 (343*2π)/5542 weeks
3441.73584 -.64963 (344*2π)/5542 weeks
3451.58044 .53745 (345*2π)/5542 weeks
346.36444 .96343 (346*2π)/5542 weeks
347-.30783 .47081 (347*2π)/5542 weeks
348-.54465 -.26447 (348*2π)/5542 weeks
349-.23226 -.95485 (349*2π)/5542 weeks
350.84462 -1.36399 (350*2π)/5542 weeks
3511.03419 -.30605 (351*2π)/5542 weeks
352.8641 -.29756 (352*2π)/5542 weeks
353.83518 .15225 (353*2π)/5542 weeks
354.30448 -.10005 (354*2π)/5542 weeks
355.14026 -.66346 (355*2π)/5542 weeks
356.79024 -1.10678 (356*2π)/5542 weeks
3571.95963 -.88607 (357*2π)/5542 weeks
3581.47633 .79962 (358*2π)/5542 weeks
359.50893 .70809 (359*2π)/5542 weeks
360.05523 .44622 (360*2π)/5542 weeks
361-.11707 .10582 (361*2π)/5542 weeks
362.10276 -.48971 (362*2π)/5542 weeks
363.2782 -.66375 (363*2π)/5542 weeks
364.61813 -.378 (364*2π)/5542 weeks
365.59003 -.50581 (365*2π)/5542 weeks
366.83266 -.42093 (366*2π)/5542 weeks
367.83568 .04535 (367*2π)/5542 weeks
368.20436 .07697 (368*2π)/5542 weeks
369-.07144 -.31102 (369*2π)/5542 weeks
370.05457 -1.04386 (370*2π)/5541 weeks
3711.06389 -.81611 (371*2π)/5541 weeks
3721.18758 -.43278 (372*2π)/5541 weeks
373.84788 .47384 (373*2π)/5541 weeks
374-.00341 .01854 (374*2π)/5541 weeks
375-.14104 -.64929 (375*2π)/5541 weeks
376.22076 -1.15951 (376*2π)/5541 weeks
3771.21544 -1.31689 (377*2π)/5541 weeks
3781.56311 -.42086 (378*2π)/5541 weeks
3791.17628 .21948 (379*2π)/5541 weeks
380.57978 .45441 (380*2π)/5541 weeks
381.22541 -.11891 (381*2π)/5541 weeks
382.62385 -.63359 (382*2π)/5541 weeks
383.77157 -.06135 (383*2π)/5541 weeks
384.61474 .023 (384*2π)/5541 weeks
385.45663 .11452 (385*2π)/5541 weeks
386.08222 -.50056 (386*2π)/5541 weeks
387.43465 -.52707 (387*2π)/5541 weeks
388.36388 -.60232 (388*2π)/5541 weeks
389.82425 -.34624 (389*2π)/5541 weeks
390.3407 -.22918 (390*2π)/5541 weeks
391.12246 -.8869 (391*2π)/5541 weeks
3921.09397 -1.19322 (392*2π)/5541 weeks
3931.42427 .13527 (393*2π)/5541 weeks
394.2083 .28038 (394*2π)/5541 weeks
395.24137 -.53381 (395*2π)/5541 weeks
396.17583 -.3527 (396*2π)/5541 weeks
397.34977 -1.0007 (397*2π)/5541 weeks
3981.13127 -.97822 (398*2π)/5541 weeks
3991.46819 -.11085 (399*2π)/5541 weeks
400.89996 .63444 (400*2π)/5541 weeks
401-.77825 .19891 (401*2π)/5541 weeks
402-.19462 -1.17929 (402*2π)/5541 weeks
403.65305 -1.28705 (403*2π)/5541 weeks
4041.0688 -.89687 (404*2π)/5541 weeks
4051.13686 -.37726 (405*2π)/5541 weeks
406.74288 -.24584 (406*2π)/5541 weeks
407.46983 -.39658 (407*2π)/5541 weeks
408.64583 -.65619 (408*2π)/5541 weeks
409.85526 .09307 (409*2π)/5541 weeks
410-.32933 -.41867 (410*2π)/5541 weeks
411.32396 -1.79102 (411*2π)/5541 weeks
4121.96477 -.9879 (412*2π)/5541 weeks
4131.59699 .14345 (413*2π)/5541 weeks
414.73764 .40825 (414*2π)/5541 weeks
415.0023 -.17689 (415*2π)/5541 weeks
416.33376 -.66195 (416*2π)/5541 weeks
417.6404 -.80744 (417*2π)/5541 weeks
4181.00549 -.75789 (418*2π)/5541 weeks
4191.04954 -.0666 (419*2π)/5541 weeks
420.70792 .06884 (420*2π)/5541 weeks
4211.02155 -.02781 (421*2π)/5541 weeks
422.1133 .53761 (422*2π)/5541 weeks
423-.90975 -.4075 (423*2π)/5541 weeks
424-.1921 -1.46386 (424*2π)/5541 weeks
4251.07226 -1.20784 (425*2π)/5541 weeks
426.98628 -.69833 (426*2π)/5541 weeks
427.48639 -.15611 (427*2π)/5541 weeks
428.1793 -.25606 (428*2π)/5541 weeks
429.25307 -.40721 (429*2π)/5541 weeks
430-.31318 -1.0854 (430*2π)/5541 weeks
431.55066 -1.5902 (431*2π)/5541 weeks
4321.28853 -1.59206 (432*2π)/5541 weeks
4331.79364 -.24374 (433*2π)/5541 weeks
434.92542 .67052 (434*2π)/5541 weeks
435-.17928 .22543 (435*2π)/5541 weeks
436-.62863 -.61628 (436*2π)/5541 weeks
437-.58785 -1.94687 (437*2π)/5541 weeks
438.79058 -2.07558 (438*2π)/5541 weeks
4391.36458 -1.4301 (439*2π)/5541 weeks
4401.75379 -.45643 (440*2π)/5541 weeks
4411.36123 -.10828 (441*2π)/5541 weeks
442.39182 -.03324 (442*2π)/5541 weeks
443-.20821 -.80787 (443*2π)/5541 weeks
444.12286 -1.62038 (444*2π)/5541 weeks
4451.63861 -1.86385 (445*2π)/5541 weeks
4462.24746 -.62698 (446*2π)/5541 weeks
4471.99473 .26228 (447*2π)/5541 weeks
448.82382 1.75176 (448*2π)/5541 weeks
449-1.51143 .86827 (449*2π)/5541 weeks
450-1.66364 -1.66849 (450*2π)/5541 weeks
451.58649 -2.67332 (451*2π)/5541 weeks
4522.09018 -1.58766 (452*2π)/5541 weeks
4531.82644 .01498 (453*2π)/5541 weeks
454.41232 .73936 (454*2π)/5541 weeks
455-.74121 -.01933 (455*2π)/5541 weeks
456-.77554 -1.6192 (456*2π)/5541 weeks
457.43516 -1.9135 (457*2π)/5541 weeks
4581.23497 -1.07626 (458*2π)/5541 weeks
459.41068 -.51575 (459*2π)/5541 weeks
460.23972 -1.2923 (460*2π)/5541 weeks
461.77202 -1.56951 (461*2π)/5541 weeks
4621.26974 -.72772 (462*2π)/5541 weeks
463.47281 -.16056 (463*2π)/5541 weeks
464-.13452 -.63055 (464*2π)/5541 weeks
465-.77727 -2.0078 (465*2π)/5541 weeks
4661.12161 -3.34994 (466*2π)/5541 weeks
4672.53477 -1.50506 (467*2π)/5541 weeks
4682.24707 .41172 (468*2π)/5541 weeks
469-.0108 .76748 (469*2π)/5541 weeks
470-.39605 -.74239 (470*2π)/5541 weeks
471-.37823 -1.95742 (471*2π)/5541 weeks
4721.06954 -2.3208 (472*2π)/5541 weeks
4732.17966 -1.48831 (473*2π)/5541 weeks
4742.17357 .38335 (474*2π)/5541 weeks
475.12256 1.04046 (475*2π)/5541 weeks
476-1.5933 -.83795 (476*2π)/5541 weeks
477-.22906 -2.09024 (477*2π)/5541 weeks
478.64416 -2.42131 (478*2π)/5541 weeks
4792.14354 -2.2236 (479*2π)/5541 weeks
4802.14554 .01217 (480*2π)/5541 weeks
481.94807 .48712 (481*2π)/5541 weeks
482-.50183 .52375 (482*2π)/5541 weeks
483-.95525 -1.39208 (483*2π)/5541 weeks
484.55637 -2.00091 (484*2π)/5541 weeks
485.52109 -1.06025 (485*2π)/5541 weeks
486.54696 -1.73383 (486*2π)/5541 weeks
487.00584 -.63065 (487*2π)/5541 weeks
488.08359 -1.73297 (488*2π)/5541 weeks
489.65921 -1.34125 (489*2π)/5541 weeks
490.17406 -1.70009 (490*2π)/5541 weeks
491.22321 -1.341 (491*2π)/5541 weeks
492-.59958 -2.16027 (492*2π)/5541 weeks
493.91491 -3.70967 (493*2π)/5541 weeks
4943.30621 -1.64859 (494*2π)/5541 weeks
4952.18417 .84177 (495*2π)/5541 weeks
496-.98305 1.16904 (496*2π)/5541 weeks
497-3.66505 -1.30323 (497*2π)/5541 weeks
498-1.26421 -4.64108 (498*2π)/5541 weeks
4991.83649 -5.36334 (499*2π)/5541 weeks
5003.44284 -2.60164 (500*2π)/5541 weeks
5012.70894 -.74239 (501*2π)/5541 weeks
502.72927 .9891 (502*2π)/5541 weeks
503-1.67075 -1.11162 (503*2π)/5541 weeks
504-1.28425 -3.32706 (504*2π)/5541 weeks
5051.28143 -4.84382 (505*2π)/5541 weeks
5063.55657 -3.14341 (506*2π)/5541 weeks
5072.69535 -.08225 (507*2π)/5541 weeks
5081.05616 .28343 (508*2π)/5541 weeks
509-.32633 -1.0211 (509*2π)/5541 weeks
510.1547 -2.39855 (510*2π)/5541 weeks
5111.13034 -2.9406 (511*2π)/5541 weeks
512-.06953 -1.40508 (512*2π)/5541 weeks
5131.12202 -3.31005 (513*2π)/5541 weeks
5141.4848 -2.47983 (514*2π)/5541 weeks
5151.77242 -1.34254 (515*2π)/5541 weeks
516-.0811 -2.05869 (516*2π)/5541 weeks
517.94348 -1.49852 (517*2π)/5541 weeks
518.25874 -1.68268 (518*2π)/5541 weeks
519-1.75663 -3.61265 (519*2π)/5541 weeks
520.96526 -6.09632 (520*2π)/5541 weeks
5214.55543 -4.61302 (521*2π)/5541 weeks
5224.36635 -.00252 (522*2π)/5541 weeks
523.57909 1.54382 (523*2π)/5541 weeks
524-2.80251 -1.73768 (524*2π)/5541 weeks
525-.8124 -4.2247 (525*2π)/5541 weeks
526.20976 -5.24291 (526*2π)/5541 weeks
5272.44207 -5.91362 (527*2π)/5541 weeks
5283.89684 -2.65517 (528*2π)/5541 weeks
5291.3529 -.00266 (529*2π)/5541 weeks
530-1.35914 -1.96074 (530*2π)/5541 weeks
531-1.76041 -5.62774 (531*2π)/5541 weeks
5322.43844 -8.27865 (532*2π)/5541 weeks
5336.18649 -5.31794 (533*2π)/5541 weeks
5346.82546 -.17436 (534*2π)/5541 weeks
5351.37906 3.26461 (535*2π)/5541 weeks
536-5.93718 1.68628 (536*2π)/5541 weeks
537-3.9923 -6.64248 (537*2π)/5541 weeks
538-2.85767 -6.93305 (538*2π)/5541 weeks
539-.36095 -9.01539 (539*2π)/5541 weeks
5401.12092 -6.33837 (540*2π)/5541 weeks
5412.40185 -7.0452 (541*2π)/5541 weeks
542-.38174 -7.17159 (542*2π)/5541 weeks
5432.97544 -7.2127 (543*2π)/5541 weeks
5441.47617 -6.36253 (544*2π)/5541 weeks
545-4.82323 -6.01724 (545*2π)/5541 weeks
546-7.56655 -17.51813 (546*2π)/5541 weeks
547.99692 -22.20111 (547*2π)/5541 weeks
54812.65736 -18.07575 (548*2π)/5541 weeks
54912.64231 -8.40237 (549*2π)/5541 weeks
550-2.12574 -7.11478 (550*2π)/5541 weeks
551-18.88221 -19.16253 (551*2π)/5541 weeks
552-23.44847 -63.5379 (552*2π)/5541 weeks



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