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Fourier Analysis of SIJ (ProShares UltraShort Industrial)


SIJ (ProShares UltraShort Industrial) appears to have interesting cyclic behaviour every 44 weeks (34.3908*sine), 48 weeks (31.474*sine), and 48 weeks (23.6635*cosine).

SIJ (ProShares UltraShort Industrial) has an average price of 267.04 (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 2/1/2007 to 3/13/2017 for SIJ (ProShares UltraShort Industrial), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0267.0397   0 
199.02737 297.8927 (1*2π)/529529 weeks
2-75.40618 143.5598 (2*2π)/529265 weeks
3-71.04514 .4258 (3*2π)/529176 weeks
422.89653 -26.31869 (4*2π)/529132 weeks
558.48999 25.44929 (5*2π)/529106 weeks
626.22712 69.64338 (6*2π)/52988 weeks
7-28.37311 55.98922 (7*2π)/52976 weeks
8-28.61172 -4.07294 (8*2π)/52966 weeks
915.06448 -8.17914 (9*2π)/52959 weeks
1022.50551 9.40993 (10*2π)/52953 weeks
1123.66353 31.47396 (11*2π)/52948 weeks
12-6.23331 34.39075 (12*2π)/52944 weeks
13-9.01603 13.78808 (13*2π)/52941 weeks
14-2.14614 7.78641 (14*2π)/52938 weeks
154.706 9.96119 (15*2π)/52935 weeks
16-.85243 13.58461 (16*2π)/52933 weeks
172.3572 6.00734 (17*2π)/52931 weeks
184.32748 9.77205 (18*2π)/52929 weeks
196.25398 9.03425 (19*2π)/52928 weeks
205.78756 14.97093 (20*2π)/52926 weeks
21-3.21879 15.28808 (21*2π)/52925 weeks
22-6.25802 3.93592 (22*2π)/52924 weeks
235.83376 .94869 (23*2π)/52923 weeks
2413.77603 12.13459 (24*2π)/52922 weeks
25-.52704 25.47683 (25*2π)/52921 weeks
26-15.12662 11.983 (26*2π)/52920 weeks
27-12.36483 -3.92669 (27*2π)/52920 weeks
285.44761 -12.55432 (28*2π)/52919 weeks
2920.66726 4.37193 (29*2π)/52918 weeks
308.5912 24.01477 (30*2π)/52918 weeks
31-13.54424 21.11437 (31*2π)/52917 weeks
32-18.80127 -2.56525 (32*2π)/52917 weeks
333.15728 -12.93904 (33*2π)/52916 weeks
3414.27034 1.94745 (34*2π)/52916 weeks
357.35761 13.46827 (35*2π)/52915 weeks
36-4.20576 11.87531 (36*2π)/52915 weeks
37-4.92026 2.41538 (37*2π)/52914 weeks
38.39492 .38876 (38*2π)/52914 weeks
394.40851 1.38879 (39*2π)/52914 weeks
404.13565 8.37313 (40*2π)/52913 weeks
41-2.19718 6.34486 (41*2π)/52913 weeks
42.81899 2.43933 (42*2π)/52913 weeks
432.29912 3.6351 (43*2π)/52912 weeks
442.76663 6.85031 (44*2π)/52912 weeks
45-2.3428 8.10881 (45*2π)/52912 weeks
46-3.80714 3.2486 (46*2π)/52912 weeks
47-1.86387 -.87119 (47*2π)/52911 weeks
482.78503 .14398 (48*2π)/52911 weeks
493.77273 4.26729 (49*2π)/52911 weeks
50-.70736 5.66759 (50*2π)/52911 weeks
51-2.40627 1.86261 (51*2π)/52910 weeks
52.15479 -1.56386 (52*2π)/52910 weeks
535.82784 -1.24309 (53*2π)/52910 weeks
547.52767 6.94069 (54*2π)/52910 weeks
55-1.21091 8.3733 (55*2π)/52910 weeks
56-3.41758 2.36499 (56*2π)/5299 weeks
57.50142 -.53649 (57*2π)/5299 weeks
584.66464 1.28162 (58*2π)/5299 weeks
592.98307 7.31656 (59*2π)/5299 weeks
60-3.47257 5.16497 (60*2π)/5299 weeks
61-2.92955 -.22122 (61*2π)/5299 weeks
622.55704 -2.67306 (62*2π)/5299 weeks
635.99398 2.59462 (63*2π)/5298 weeks
641.001 6.07389 (64*2π)/5298 weeks
65-.27142 3.17201 (65*2π)/5298 weeks
66-.12671 .41277 (66*2π)/5298 weeks
675.22985 1.90604 (67*2π)/5298 weeks
681.67367 8.02436 (68*2π)/5298 weeks
69-4.82094 4.87443 (69*2π)/5298 weeks
70-3.69931 -1.48287 (70*2π)/5298 weeks
712.52673 -3.88555 (71*2π)/5297 weeks
725.85173 1.90764 (72*2π)/5297 weeks
732.26665 4.30315 (73*2π)/5297 weeks
741.25389 5.14893 (74*2π)/5297 weeks
75-3.71071 2.74698 (75*2π)/5297 weeks
76-.05335 -3.29914 (76*2π)/5297 weeks
775.08339 -.39034 (77*2π)/5297 weeks
785.52579 4.04689 (78*2π)/5297 weeks
79.7143 6.92235 (79*2π)/5297 weeks
80-2.47879 3.85336 (80*2π)/5297 weeks
81-3.61062 -.21836 (81*2π)/5297 weeks
821.8568 -4.12244 (82*2π)/5296 weeks
836.42444 .95195 (83*2π)/5296 weeks
843.4259 5.52591 (84*2π)/5296 weeks
85-1.18284 4.50415 (85*2π)/5296 weeks
86-1.47806 .41392 (86*2π)/5296 weeks
872.06767 -.49729 (87*2π)/5296 weeks
883.44905 2.76244 (88*2π)/5296 weeks
89.32931 4.79043 (89*2π)/5296 weeks
90-2.93574 1.34494 (90*2π)/5296 weeks
911.4333 -2.0319 (91*2π)/5296 weeks
923.53707 2.0401 (92*2π)/5296 weeks
93.71958 3.84636 (93*2π)/5296 weeks
94-1.79396 1.42204 (94*2π)/5296 weeks
95-.14694 -1.90774 (95*2π)/5296 weeks
964.19686 -1.55524 (96*2π)/5296 weeks
975.15665 2.68288 (97*2π)/5295 weeks
981.08512 5.70292 (98*2π)/5295 weeks
99-3.38802 2.2002 (99*2π)/5295 weeks
100-.94532 -2.93415 (100*2π)/5295 weeks
1014.4802 -2.88413 (101*2π)/5295 weeks
1026.83902 2.63897 (102*2π)/5295 weeks
1032.98334 6.41168 (103*2π)/5295 weeks
104-2.54711 4.97327 (104*2π)/5295 weeks
105-3.22329 -1.14665 (105*2π)/5295 weeks
1062.16447 -3.33691 (106*2π)/5295 weeks
1075.94007 .78787 (107*2π)/5295 weeks
1083.59958 4.96987 (108*2π)/5295 weeks
109-.10797 5.00798 (109*2π)/5295 weeks
110-2.95709 2.12785 (110*2π)/5295 weeks
111-.43294 -2.0793 (111*2π)/5295 weeks
1123.19114 -.92439 (112*2π)/5295 weeks
1133.21252 1.38948 (113*2π)/5295 weeks
1142.20041 3.06388 (114*2π)/5295 weeks
115.00497 2.79462 (115*2π)/5295 weeks
116-.84558 .84952 (116*2π)/5295 weeks
1171.26138 -1.49813 (117*2π)/5295 weeks
1184.39109 .20274 (118*2π)/5294 weeks
1193.30985 4.01842 (119*2π)/5294 weeks
120.05749 3.57037 (120*2π)/5294 weeks
121-.65475 1.25311 (121*2π)/5294 weeks
122.76555 .43923 (122*2π)/5294 weeks
1231.02727 1.07098 (123*2π)/5294 weeks
1241.28041 .60512 (124*2π)/5294 weeks
1251.78546 1.30685 (125*2π)/5294 weeks
126.80602 1.83242 (126*2π)/5294 weeks
127.56635 .54908 (127*2π)/5294 weeks
1282.26881 .00766 (128*2π)/5294 weeks
1292.93577 1.50643 (129*2π)/5294 weeks
1302.28706 2.4327 (130*2π)/5294 weeks
131.70756 3.47553 (131*2π)/5294 weeks
132-.64026 1.76919 (132*2π)/5294 weeks
133.26602 1.26384 (133*2π)/5294 weeks
134-.23881 .62936 (134*2π)/5294 weeks
135.92443 -.39278 (135*2π)/5294 weeks
1362.49996 -.33197 (136*2π)/5294 weeks
1373.39231 2.70323 (137*2π)/5294 weeks
138-.6006 3.47399 (138*2π)/5294 weeks
139-1.35799 -.43682 (139*2π)/5294 weeks
1401.80288 -1.24915 (140*2π)/5294 weeks
1413.55211 .97055 (141*2π)/5294 weeks
1421.93627 3.7689 (142*2π)/5294 weeks
143-1.065 2.44174 (143*2π)/5294 weeks
144-1.1448 -.02661 (144*2π)/5294 weeks
1451.38095 -1.70311 (145*2π)/5294 weeks
1463.14254 .92974 (146*2π)/5294 weeks
1471.71784 2.00089 (147*2π)/5294 weeks
148.74114 1.82525 (148*2π)/5294 weeks
149.40478 1.01306 (149*2π)/5294 weeks
150.73892 .69342 (150*2π)/5294 weeks
1511.03104 .12789 (151*2π)/5294 weeks
1522.65304 .69963 (152*2π)/5293 weeks
1531.32568 2.42923 (153*2π)/5293 weeks
154.69083 1.42024 (154*2π)/5293 weeks
155.60147 1.56728 (155*2π)/5293 weeks
156-.0695 .77193 (156*2π)/5293 weeks
157.66525 -.22653 (157*2π)/5293 weeks
1582.53777 .02483 (158*2π)/5293 weeks
1592.31515 1.89795 (159*2π)/5293 weeks
160.8389 3.19516 (160*2π)/5293 weeks
161-1.41231 1.72831 (161*2π)/5293 weeks
162-.78636 -.71723 (162*2π)/5293 weeks
1631.51445 -1.27903 (163*2π)/5293 weeks
1642.60053 .51874 (164*2π)/5293 weeks
1651.77117 1.92312 (165*2π)/5293 weeks
166.07794 1.78971 (166*2π)/5293 weeks
167-.50781 .56737 (167*2π)/5293 weeks
168-.0384 -.88715 (168*2π)/5293 weeks
1692.13741 -1.53424 (169*2π)/5293 weeks
1703.83612 .50048 (170*2π)/5293 weeks
1712.92522 3.17046 (171*2π)/5293 weeks
172-.47617 3.49757 (172*2π)/5293 weeks
173-1.85 .42882 (173*2π)/5293 weeks
174.3203 -1.85535 (174*2π)/5293 weeks
1753.17001 -.66091 (175*2π)/5293 weeks
1762.72036 2.09786 (176*2π)/5293 weeks
177.75999 2.87755 (177*2π)/5293 weeks
178-.96493 .91165 (178*2π)/5293 weeks
179.3835 -.4195 (179*2π)/5293 weeks
1801.48886 -.56426 (180*2π)/5293 weeks
1812.32722 1.33801 (181*2π)/5293 weeks
182.35062 2.14644 (182*2π)/5293 weeks
183-.4078 .66918 (183*2π)/5293 weeks
184-.00056 -.48925 (184*2π)/5293 weeks
1851.38647 -.7216 (185*2π)/5293 weeks
1861.21625 -.05932 (186*2π)/5293 weeks
1872.62908 -.59918 (187*2π)/5293 weeks
1882.35099 2.28766 (188*2π)/5293 weeks
189.73433 1.34211 (189*2π)/5293 weeks
190.65082 1.27102 (190*2π)/5293 weeks
191.48934 .55255 (191*2π)/5293 weeks
192.82501 1.00529 (192*2π)/5293 weeks
193.10394 -.08115 (193*2π)/5293 weeks
1941.75644 .45293 (194*2π)/5293 weeks
195.43945 .81249 (195*2π)/5293 weeks
196.96647 .68428 (196*2π)/5293 weeks
197-.51651 .41341 (197*2π)/5293 weeks
198.98587 -1.4991 (198*2π)/5293 weeks
1993.00422 .02481 (199*2π)/5293 weeks
2001.90501 2.11056 (200*2π)/5293 weeks
201-.48254 1.85383 (201*2π)/5293 weeks
202-.60497 -.93576 (202*2π)/5293 weeks
2032.09413 -1.09204 (203*2π)/5293 weeks
2042.68949 .52525 (204*2π)/5293 weeks
2052.04796 2.51382 (205*2π)/5293 weeks
206-1.27861 2.10348 (206*2π)/5293 weeks
207-.94441 -1.25597 (207*2π)/5293 weeks
2081.92157 -1.72946 (208*2π)/5293 weeks
2093.12683 .75833 (209*2π)/5293 weeks
210.87497 2.19061 (210*2π)/5293 weeks
211-.20148 .18431 (211*2π)/5293 weeks
2121.49746 -.52122 (212*2π)/5292 weeks
2132.06992 .7302 (213*2π)/5292 weeks
2141.76965 1.74663 (214*2π)/5292 weeks
215-.26159 2.57031 (215*2π)/5292 weeks
216-1.79981 -.09869 (216*2π)/5292 weeks
217.4861 -1.84113 (217*2π)/5292 weeks
2182.63767 -1.02622 (218*2π)/5292 weeks
2192.57361 2.11029 (219*2π)/5292 weeks
220-.52753 1.89387 (220*2π)/5292 weeks
221-1.02106 .26183 (221*2π)/5292 weeks
222-.30169 -1.58481 (222*2π)/5292 weeks
2232.23323 -1.53439 (223*2π)/5292 weeks
2242.82472 .83241 (224*2π)/5292 weeks
2251.17602 2.26379 (225*2π)/5292 weeks
226-1.34184 1.37952 (226*2π)/5292 weeks
227-1.01916 -1.61384 (227*2π)/5292 weeks
2281.47765 -2.19943 (228*2π)/5292 weeks
2292.82878 -.85962 (229*2π)/5292 weeks
2302.83908 1.63973 (230*2π)/5292 weeks
231.20208 1.43599 (231*2π)/5292 weeks
232.23669 .40356 (232*2π)/5292 weeks
233.40555 -.62682 (233*2π)/5292 weeks
2341.2618 -.00356 (234*2π)/5292 weeks
235.888 -.17023 (235*2π)/5292 weeks
2361.67046 .05865 (236*2π)/5292 weeks
237.96119 .92794 (237*2π)/5292 weeks
238.30932 .05003 (238*2π)/5292 weeks
239.00001 -.43365 (239*2π)/5292 weeks
2401.30298 -1.50171 (240*2π)/5292 weeks
2412.93381 -.32891 (241*2π)/5292 weeks
2422.20678 1.33077 (242*2π)/5292 weeks
243.88667 2.00068 (243*2π)/5292 weeks
244-1.03571 1.40577 (244*2π)/5292 weeks
245-1.62202 -1.25888 (245*2π)/5292 weeks
246.56961 -3.50838 (246*2π)/5292 weeks
2474.52765 -1.77724 (247*2π)/5292 weeks
2483.49495 2.34721 (248*2π)/5292 weeks
249.39649 2.66083 (249*2π)/5292 weeks
250-1.97876 .9191 (250*2π)/5292 weeks
251-.7554 -2.76443 (251*2π)/5292 weeks
2523.18364 -2.50057 (252*2π)/5292 weeks
2533.7562 1.63268 (253*2π)/5292 weeks
254.44306 2.37771 (254*2π)/5292 weeks
255-1.1071 .35931 (255*2π)/5292 weeks
256-.25291 -1.89805 (256*2π)/5292 weeks
2571.95753 -2.50724 (257*2π)/5292 weeks
2584.15083 -.18315 (258*2π)/5292 weeks
2591.83585 3.04648 (259*2π)/5292 weeks
260-1.12106 1.06358 (260*2π)/5292 weeks
261.02869 -1.33394 (261*2π)/5292 weeks
2621.57604 -1.33713 (262*2π)/5292 weeks
2631.66281 -.39631 (263*2π)/5292 weeks
2641.98905 -.52923 (264*2π)/5292 weeks
2651.98905 .52923 (265*2π)/5292 weeks
2661.66281 .39631 (266*2π)/5292 weeks
2671.57604 1.33713 (267*2π)/5292 weeks
268.02869 1.33394 (268*2π)/5292 weeks
269-1.12106 -1.06358 (269*2π)/5292 weeks
2701.83585 -3.04648 (270*2π)/5292 weeks
2714.15083 .18315 (271*2π)/5292 weeks
2721.95753 2.50724 (272*2π)/5292 weeks
273-.25291 1.89805 (273*2π)/5292 weeks
274-1.1071 -.35931 (274*2π)/5292 weeks
275.44306 -2.37771 (275*2π)/5292 weeks
2763.7562 -1.63268 (276*2π)/5292 weeks
2773.18364 2.50057 (277*2π)/5292 weeks
278-.7554 2.76443 (278*2π)/5292 weeks
279-1.97876 -.9191 (279*2π)/5292 weeks
280.39649 -2.66083 (280*2π)/5292 weeks
2813.49495 -2.34721 (281*2π)/5292 weeks
2824.52765 1.77724 (282*2π)/5292 weeks
283.56961 3.50838 (283*2π)/5292 weeks
284-1.62202 1.25888 (284*2π)/5292 weeks
285-1.03571 -1.40577 (285*2π)/5292 weeks
286.88667 -2.00068 (286*2π)/5292 weeks
2872.20678 -1.33077 (287*2π)/5292 weeks
2882.93381 .32891 (288*2π)/5292 weeks
2891.30298 1.50171 (289*2π)/5292 weeks
290.00001 .43365 (290*2π)/5292 weeks
291.30932 -.05003 (291*2π)/5292 weeks
292.96119 -.92794 (292*2π)/5292 weeks
2931.67046 -.05865 (293*2π)/5292 weeks
294.888 .17023 (294*2π)/5292 weeks
2951.2618 .00356 (295*2π)/5292 weeks
296.40555 .62682 (296*2π)/5292 weeks
297.23669 -.40356 (297*2π)/5292 weeks
298.20208 -1.43599 (298*2π)/5292 weeks
2992.83908 -1.63973 (299*2π)/5292 weeks
3002.82878 .85962 (300*2π)/5292 weeks
3011.47765 2.19943 (301*2π)/5292 weeks
302-1.01916 1.61384 (302*2π)/5292 weeks
303-1.34184 -1.37952 (303*2π)/5292 weeks
3041.17602 -2.26379 (304*2π)/5292 weeks
3052.82472 -.83241 (305*2π)/5292 weeks
3062.23323 1.53439 (306*2π)/5292 weeks
307-.30169 1.58481 (307*2π)/5292 weeks
308-1.02106 -.26183 (308*2π)/5292 weeks
309-.52753 -1.89387 (309*2π)/5292 weeks
3102.57361 -2.11029 (310*2π)/5292 weeks
3112.63767 1.02622 (311*2π)/5292 weeks
312.4861 1.84113 (312*2π)/5292 weeks
313-1.79981 .09869 (313*2π)/5292 weeks
314-.26159 -2.57031 (314*2π)/5292 weeks
3151.76965 -1.74663 (315*2π)/5292 weeks
3162.06992 -.7302 (316*2π)/5292 weeks
3171.49746 .52122 (317*2π)/5292 weeks
318-.20148 -.18431 (318*2π)/5292 weeks
319.87497 -2.19061 (319*2π)/5292 weeks
3203.12683 -.75833 (320*2π)/5292 weeks
3211.92157 1.72946 (321*2π)/5292 weeks
322-.94441 1.25597 (322*2π)/5292 weeks
323-1.27861 -2.10348 (323*2π)/5292 weeks
3242.04796 -2.51382 (324*2π)/5292 weeks
3252.68949 -.52525 (325*2π)/5292 weeks
3262.09413 1.09204 (326*2π)/5292 weeks
327-.60497 .93576 (327*2π)/5292 weeks
328-.48254 -1.85383 (328*2π)/5292 weeks
3291.90501 -2.11056 (329*2π)/5292 weeks
3303.00422 -.02481 (330*2π)/5292 weeks
331.98587 1.4991 (331*2π)/5292 weeks
332-.51651 -.41341 (332*2π)/5292 weeks
333.96647 -.68428 (333*2π)/5292 weeks
334.43945 -.81249 (334*2π)/5292 weeks
3351.75644 -.45293 (335*2π)/5292 weeks
336.10394 .08115 (336*2π)/5292 weeks
337.82501 -1.00529 (337*2π)/5292 weeks
338.48934 -.55255 (338*2π)/5292 weeks
339.65082 -1.27102 (339*2π)/5292 weeks
340.73433 -1.34211 (340*2π)/5292 weeks
3412.35099 -2.28766 (341*2π)/5292 weeks
3422.62908 .59918 (342*2π)/5292 weeks
3431.21625 .05932 (343*2π)/5292 weeks
3441.38647 .7216 (344*2π)/5292 weeks
345-.00056 .48925 (345*2π)/5292 weeks
346-.4078 -.66918 (346*2π)/5292 weeks
347.35062 -2.14644 (347*2π)/5292 weeks
3482.32722 -1.33801 (348*2π)/5292 weeks
3491.48886 .56426 (349*2π)/5292 weeks
350.3835 .4195 (350*2π)/5292 weeks
351-.96493 -.91165 (351*2π)/5292 weeks
352.75999 -2.87755 (352*2π)/5292 weeks
3532.72036 -2.09786 (353*2π)/5291 weeks
3543.17001 .66091 (354*2π)/5291 weeks
355.3203 1.85535 (355*2π)/5291 weeks
356-1.85 -.42882 (356*2π)/5291 weeks
357-.47617 -3.49757 (357*2π)/5291 weeks
3582.92522 -3.17046 (358*2π)/5291 weeks
3593.83612 -.50048 (359*2π)/5291 weeks
3602.13741 1.53424 (360*2π)/5291 weeks
361-.0384 .88715 (361*2π)/5291 weeks
362-.50781 -.56737 (362*2π)/5291 weeks
363.07794 -1.78971 (363*2π)/5291 weeks
3641.77117 -1.92312 (364*2π)/5291 weeks
3652.60053 -.51874 (365*2π)/5291 weeks
3661.51445 1.27903 (366*2π)/5291 weeks
367-.78636 .71723 (367*2π)/5291 weeks
368-1.41231 -1.72831 (368*2π)/5291 weeks
369.8389 -3.19516 (369*2π)/5291 weeks
3702.31515 -1.89795 (370*2π)/5291 weeks
3712.53777 -.02483 (371*2π)/5291 weeks
372.66525 .22653 (372*2π)/5291 weeks
373-.0695 -.77193 (373*2π)/5291 weeks
374.60147 -1.56728 (374*2π)/5291 weeks
375.69083 -1.42024 (375*2π)/5291 weeks
3761.32568 -2.42923 (376*2π)/5291 weeks
3772.65304 -.69963 (377*2π)/5291 weeks
3781.03104 -.12789 (378*2π)/5291 weeks
379.73892 -.69342 (379*2π)/5291 weeks
380.40478 -1.01306 (380*2π)/5291 weeks
381.74114 -1.82525 (381*2π)/5291 weeks
3821.71784 -2.00089 (382*2π)/5291 weeks
3833.14254 -.92974 (383*2π)/5291 weeks
3841.38095 1.70311 (384*2π)/5291 weeks
385-1.1448 .02661 (385*2π)/5291 weeks
386-1.065 -2.44174 (386*2π)/5291 weeks
3871.93627 -3.7689 (387*2π)/5291 weeks
3883.55211 -.97055 (388*2π)/5291 weeks
3891.80288 1.24915 (389*2π)/5291 weeks
390-1.35799 .43682 (390*2π)/5291 weeks
391-.6006 -3.47399 (391*2π)/5291 weeks
3923.39231 -2.70323 (392*2π)/5291 weeks
3932.49996 .33197 (393*2π)/5291 weeks
394.92443 .39278 (394*2π)/5291 weeks
395-.23881 -.62936 (395*2π)/5291 weeks
396.26602 -1.26384 (396*2π)/5291 weeks
397-.64026 -1.76919 (397*2π)/5291 weeks
398.70756 -3.47553 (398*2π)/5291 weeks
3992.28706 -2.4327 (399*2π)/5291 weeks
4002.93577 -1.50643 (400*2π)/5291 weeks
4012.26881 -.00766 (401*2π)/5291 weeks
402.56635 -.54908 (402*2π)/5291 weeks
403.80602 -1.83242 (403*2π)/5291 weeks
4041.78546 -1.30685 (404*2π)/5291 weeks
4051.28041 -.60512 (405*2π)/5291 weeks
4061.02727 -1.07098 (406*2π)/5291 weeks
407.76555 -.43923 (407*2π)/5291 weeks
408-.65475 -1.25311 (408*2π)/5291 weeks
409.05749 -3.57037 (409*2π)/5291 weeks
4103.30985 -4.01842 (410*2π)/5291 weeks
4114.39109 -.20274 (411*2π)/5291 weeks
4121.26138 1.49813 (412*2π)/5291 weeks
413-.84558 -.84952 (413*2π)/5291 weeks
414.00497 -2.79462 (414*2π)/5291 weeks
4152.20041 -3.06388 (415*2π)/5291 weeks
4163.21252 -1.38948 (416*2π)/5291 weeks
4173.19114 .92439 (417*2π)/5291 weeks
418-.43294 2.0793 (418*2π)/5291 weeks
419-2.95709 -2.12785 (419*2π)/5291 weeks
420-.10797 -5.00798 (420*2π)/5291 weeks
4213.59958 -4.96987 (421*2π)/5291 weeks
4225.94007 -.78787 (422*2π)/5291 weeks
4232.16447 3.33691 (423*2π)/5291 weeks
424-3.22329 1.14665 (424*2π)/5291 weeks
425-2.54711 -4.97327 (425*2π)/5291 weeks
4262.98334 -6.41168 (426*2π)/5291 weeks
4276.83902 -2.63897 (427*2π)/5291 weeks
4284.4802 2.88413 (428*2π)/5291 weeks
429-.94532 2.93415 (429*2π)/5291 weeks
430-3.38802 -2.2002 (430*2π)/5291 weeks
4311.08512 -5.70292 (431*2π)/5291 weeks
4325.15665 -2.68288 (432*2π)/5291 weeks
4334.19686 1.55524 (433*2π)/5291 weeks
434-.14694 1.90774 (434*2π)/5291 weeks
435-1.79396 -1.42204 (435*2π)/5291 weeks
436.71958 -3.84636 (436*2π)/5291 weeks
4373.53707 -2.0401 (437*2π)/5291 weeks
4381.4333 2.0319 (438*2π)/5291 weeks
439-2.93574 -1.34494 (439*2π)/5291 weeks
440.32931 -4.79043 (440*2π)/5291 weeks
4413.44905 -2.76244 (441*2π)/5291 weeks
4422.06767 .49729 (442*2π)/5291 weeks
443-1.47806 -.41392 (443*2π)/5291 weeks
444-1.18284 -4.50415 (444*2π)/5291 weeks
4453.4259 -5.52591 (445*2π)/5291 weeks
4466.42444 -.95195 (446*2π)/5291 weeks
4471.8568 4.12244 (447*2π)/5291 weeks
448-3.61062 .21836 (448*2π)/5291 weeks
449-2.47879 -3.85336 (449*2π)/5291 weeks
450.7143 -6.92235 (450*2π)/5291 weeks
4515.52579 -4.04689 (451*2π)/5291 weeks
4525.08339 .39034 (452*2π)/5291 weeks
453-.05335 3.29914 (453*2π)/5291 weeks
454-3.71071 -2.74698 (454*2π)/5291 weeks
4551.25389 -5.14893 (455*2π)/5291 weeks
4562.26665 -4.30315 (456*2π)/5291 weeks
4575.85173 -1.90764 (457*2π)/5291 weeks
4582.52673 3.88555 (458*2π)/5291 weeks
459-3.69931 1.48287 (459*2π)/5291 weeks
460-4.82094 -4.87443 (460*2π)/5291 weeks
4611.67367 -8.02436 (461*2π)/5291 weeks
4625.22985 -1.90604 (462*2π)/5291 weeks
463-.12671 -.41277 (463*2π)/5291 weeks
464-.27142 -3.17201 (464*2π)/5291 weeks
4651.001 -6.07389 (465*2π)/5291 weeks
4665.99398 -2.59462 (466*2π)/5291 weeks
4672.55704 2.67306 (467*2π)/5291 weeks
468-2.92955 .22122 (468*2π)/5291 weeks
469-3.47257 -5.16497 (469*2π)/5291 weeks
4702.98307 -7.31656 (470*2π)/5291 weeks
4714.66464 -1.28162 (471*2π)/5291 weeks
472.50142 .53649 (472*2π)/5291 weeks
473-3.41758 -2.36499 (473*2π)/5291 weeks
474-1.21091 -8.3733 (474*2π)/5291 weeks
4757.52767 -6.94069 (475*2π)/5291 weeks
4765.82784 1.24309 (476*2π)/5291 weeks
477.15479 1.56386 (477*2π)/5291 weeks
478-2.40627 -1.86261 (478*2π)/5291 weeks
479-.70736 -5.66759 (479*2π)/5291 weeks
4803.77273 -4.26729 (480*2π)/5291 weeks
4812.78503 -.14398 (481*2π)/5291 weeks
482-1.86387 .87119 (482*2π)/5291 weeks
483-3.80714 -3.2486 (483*2π)/5291 weeks
484-2.3428 -8.10881 (484*2π)/5291 weeks
4852.76663 -6.85031 (485*2π)/5291 weeks
4862.29912 -3.6351 (486*2π)/5291 weeks
487.81899 -2.43933 (487*2π)/5291 weeks
488-2.19718 -6.34486 (488*2π)/5291 weeks
4894.13565 -8.37313 (489*2π)/5291 weeks
4904.40851 -1.38879 (490*2π)/5291 weeks
491.39492 -.38876 (491*2π)/5291 weeks
492-4.92026 -2.41538 (492*2π)/5291 weeks
493-4.20576 -11.87531 (493*2π)/5291 weeks
4947.35761 -13.46827 (494*2π)/5291 weeks
49514.27034 -1.94745 (495*2π)/5291 weeks
4963.15728 12.93904 (496*2π)/5291 weeks
497-18.80127 2.56525 (497*2π)/5291 weeks
498-13.54424 -21.11437 (498*2π)/5291 weeks
4998.5912 -24.01477 (499*2π)/5291 weeks
50020.66726 -4.37193 (500*2π)/5291 weeks
5015.44761 12.55432 (501*2π)/5291 weeks
502-12.36483 3.92669 (502*2π)/5291 weeks
503-15.12662 -11.983 (503*2π)/5291 weeks
504-.52704 -25.47683 (504*2π)/5291 weeks
50513.77603 -12.13459 (505*2π)/5291 weeks
5065.83376 -.94869 (506*2π)/5291 weeks
507-6.25802 -3.93592 (507*2π)/5291 weeks
508-3.21879 -15.28808 (508*2π)/5291 weeks
5095.78756 -14.97093 (509*2π)/5291 weeks
5106.25398 -9.03425 (510*2π)/5291 weeks
5114.32748 -9.77205 (511*2π)/5291 weeks
5122.3572 -6.00734 (512*2π)/5291 weeks
513-.85243 -13.58461 (513*2π)/5291 weeks
5144.706 -9.96119 (514*2π)/5291 weeks
515-2.14614 -7.78641 (515*2π)/5291 weeks
516-9.01603 -13.78808 (516*2π)/5291 weeks
517-6.23331 -34.39075 (517*2π)/5291 weeks
51823.66353 -31.47396 (518*2π)/5291 weeks
51922.50551 -9.40993 (519*2π)/5291 weeks
52015.06448 8.17914 (520*2π)/5291 weeks
521-28.61172 4.07294 (521*2π)/5291 weeks
522-28.37311 -55.98922 (522*2π)/5291 weeks
52326.22712 -69.64338 (523*2π)/5291 weeks
52458.48999 -25.44929 (524*2π)/5291 weeks
52522.89653 26.31869 (525*2π)/5291 weeks
526-71.04514 -.4258 (526*2π)/5291 weeks
527-75.40618 -143.5598 (527*2π)/5291 weeks

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