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Fourier Analysis of REW (ProShares UltraShort Technology ETF)


REW (ProShares UltraShort Technology ETF) appears to have interesting cyclic behaviour every 43 weeks (49.9733*sine), 47 weeks (46.4892*sine), and 51 weeks (32.2034*cosine).

REW (ProShares UltraShort Technology ETF) has an average price of 310.58 (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 2/2/2007 to 10/9/2017 for REW (ProShares UltraShort Technology ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0310.5786   0 
1158.6915 326.8404 (1*2π)/559559 weeks
2-37.52622 210.9808 (2*2π)/559280 weeks
3-83.18035 64.89616 (3*2π)/559186 weeks
4-22.53846 -12.221 (4*2π)/559140 weeks
554.88078 .9386 (5*2π)/559112 weeks
655.83397 57.79128 (6*2π)/55993 weeks
710.34075 83.06939 (7*2π)/55980 weeks
8-37.55857 42.99302 (8*2π)/55970 weeks
9-11.45581 -2.00787 (9*2π)/55962 weeks
1017.19955 2.75404 (10*2π)/55956 weeks
1132.20343 17.25873 (11*2π)/55951 weeks
1226.25393 46.48917 (12*2π)/55947 weeks
13-5.83575 49.97326 (13*2π)/55943 weeks
14-20.49848 27.90565 (14*2π)/55940 weeks
15-15.51206 8.71042 (15*2π)/55937 weeks
16-2.22104 1.20003 (16*2π)/55935 weeks
175.71677 2.98637 (17*2π)/55933 weeks
1814.72912 11.03113 (18*2π)/55931 weeks
198.46388 19.11864 (19*2π)/55929 weeks
204.0393 18.0446 (20*2π)/55928 weeks
211.6066 15.4511 (21*2π)/55927 weeks
222.09792 15.51769 (22*2π)/55925 weeks
23-1.19332 12.33592 (23*2π)/55924 weeks
245.93756 13.27116 (24*2π)/55923 weeks
252.12779 16.43774 (25*2π)/55922 weeks
26-1.94812 18.24701 (26*2π)/55922 weeks
27-11.66542 11.07285 (27*2π)/55921 weeks
28-5.91313 2.69038 (28*2π)/55920 weeks
29-.79944 -1.34023 (29*2π)/55919 weeks
3011.10343 1.75875 (30*2π)/55919 weeks
3112.59312 13.82669 (31*2π)/55918 weeks
322.32571 20.62937 (32*2π)/55917 weeks
33-10.05854 16.53443 (33*2π)/55917 weeks
34-13.42783 1.42208 (34*2π)/55916 weeks
351.44595 -5.94365 (35*2π)/55916 weeks
369.73312 2.50012 (36*2π)/55916 weeks
377.98684 10.90098 (37*2π)/55915 weeks
38.54664 12.09662 (38*2π)/55915 weeks
39-1.81825 8.60821 (39*2π)/55914 weeks
40-2.72275 5.25349 (40*2π)/55914 weeks
411.26975 1.12521 (41*2π)/55914 weeks
426.33427 7.13044 (42*2π)/55913 weeks
43.63962 9.89858 (43*2π)/55913 weeks
44-.94445 5.44455 (44*2π)/55913 weeks
45.81004 6.07054 (45*2π)/55912 weeks
461.95146 5.46444 (46*2π)/55912 weeks
47.84169 9.51355 (47*2π)/55912 weeks
48-4.6623 6.53091 (48*2π)/55912 weeks
49-3.76157 3.53829 (49*2π)/55911 weeks
50-1.06933 .03535 (50*2π)/55911 weeks
512.65136 .22046 (51*2π)/55911 weeks
523.95561 4.23494 (52*2π)/55911 weeks
53.79343 5.03762 (53*2π)/55911 weeks
54.29028 4.25033 (54*2π)/55910 weeks
55-.00821 2.1857 (55*2π)/55910 weeks
563.8165 .70954 (56*2π)/55910 weeks
575.70326 6.67867 (57*2π)/55910 weeks
58-.0799 6.97737 (58*2π)/55910 weeks
59-1.09182 4.17606 (59*2π)/5599 weeks
60.42686 1.7458 (60*2π)/5599 weeks
612.74386 2.71337 (61*2π)/5599 weeks
621.99644 5.58048 (62*2π)/5599 weeks
63-1.65068 4.48657 (63*2π)/5599 weeks
64-.67385 .65032 (64*2π)/5599 weeks
652.93651 -1.03406 (65*2π)/5599 weeks
666.62432 2.7348 (66*2π)/5598 weeks
674.72132 7.42717 (67*2π)/5598 weeks
68-.28349 6.33315 (68*2π)/5598 weeks
69-.91568 4.24128 (69*2π)/5598 weeks
70.01467 .76803 (70*2π)/5598 weeks
714.90622 3.21102 (71*2π)/5598 weeks
721.68755 7.69521 (72*2π)/5598 weeks
73-3.67588 6.14139 (73*2π)/5598 weeks
74-4.04634 -.11983 (74*2π)/5598 weeks
751.95095 -3.27389 (75*2π)/5597 weeks
765.49127 1.73731 (76*2π)/5597 weeks
772.38406 4.44662 (77*2π)/5597 weeks
782.06737 4.61112 (78*2π)/5597 weeks
79-1.90899 4.43529 (79*2π)/5597 weeks
80-1.41854 -1.38347 (80*2π)/5597 weeks
814.037 -1.37338 (81*2π)/5597 weeks
826.33549 2.10337 (82*2π)/5597 weeks
834.54208 6.84733 (83*2π)/5597 weeks
84-.07984 6.33505 (84*2π)/5597 weeks
85-2.35363 4.46161 (85*2π)/5597 weeks
86-2.89783 -.39533 (86*2π)/5597 weeks
872.59729 -2.47961 (87*2π)/5596 weeks
885.99999 1.59969 (88*2π)/5596 weeks
894.13365 5.76439 (89*2π)/5596 weeks
90-.02835 5.81375 (90*2π)/5596 weeks
91-2.20401 2.46206 (91*2π)/5596 weeks
92-.2873 -.36102 (92*2π)/5596 weeks
933.03696 .13316 (93*2π)/5596 weeks
943.57422 3.22847 (94*2π)/5596 weeks
95.71562 3.85944 (95*2π)/5596 weeks
96.82451 1.62811 (96*2π)/5596 weeks
971.48935 2.80636 (97*2π)/5596 weeks
98.12957 2.47183 (98*2π)/5596 weeks
99-.80861 1.17057 (99*2π)/5596 weeks
100.59777 -1.6132 (100*2π)/5596 weeks
1014.27765 -1.06886 (101*2π)/5596 weeks
1025.5596 2.60799 (102*2π)/5595 weeks
1033.06099 5.49993 (103*2π)/5595 weeks
104-.93635 4.52333 (104*2π)/5595 weeks
105-2.05348 .06086 (105*2π)/5595 weeks
1061.46215 -2.54589 (106*2π)/5595 weeks
1076.5476 -1.3839 (107*2π)/5595 weeks
1086.56497 4.87748 (108*2π)/5595 weeks
1092.56572 7.22857 (109*2π)/5595 weeks
110-2.23442 5.34968 (110*2π)/5595 weeks
111-2.99827 -.03098 (111*2π)/5595 weeks
1121.29075 -3.14862 (112*2π)/5595 weeks
1136.12786 -.16989 (113*2π)/5595 weeks
1145.31426 4.48133 (114*2π)/5595 weeks
1152.08951 6.14842 (115*2π)/5595 weeks
116-2.10187 4.93615 (116*2π)/5595 weeks
117-2.54176 -.22224 (117*2π)/5595 weeks
1181.42019 -2.02786 (118*2π)/5595 weeks
1194.20632 .24667 (119*2π)/5595 weeks
1203.91557 2.96513 (120*2π)/5595 weeks
1211.44316 4.09371 (121*2π)/5595 weeks
122.10641 2.03546 (122*2π)/5595 weeks
123-.09665 .44827 (123*2π)/5595 weeks
1242.59848 -.94311 (124*2π)/5595 weeks
1254.88731 1.45255 (125*2π)/5594 weeks
1262.89176 4.68699 (126*2π)/5594 weeks
127.70504 3.47053 (127*2π)/5594 weeks
128.24095 1.93035 (128*2π)/5594 weeks
1291.04779 1.24507 (129*2π)/5594 weeks
130.87184 1.78473 (130*2π)/5594 weeks
1311.51796 .973 (131*2π)/5594 weeks
1321.94851 1.77604 (132*2π)/5594 weeks
133.75897 2.21795 (133*2π)/5594 weeks
134.52073 .29741 (134*2π)/5594 weeks
1352.59632 -.50766 (135*2π)/5594 weeks
1363.80808 1.44859 (136*2π)/5594 weeks
1372.7975 2.65643 (137*2π)/5594 weeks
1382.00949 3.7087 (138*2π)/5594 weeks
139.28877 2.27886 (139*2π)/5594 weeks
1401.71024 1.0282 (140*2π)/5594 weeks
1411.74775 2.58624 (141*2π)/5594 weeks
142.60003 2.22782 (142*2π)/5594 weeks
143.30984 1.84659 (143*2π)/5594 weeks
1441.14715 .20147 (144*2π)/5594 weeks
1452.69963 1.82447 (145*2π)/5594 weeks
1461.01247 2.34892 (146*2π)/5594 weeks
147.51987 1.10719 (147*2π)/5594 weeks
1481.20273 .55004 (148*2π)/5594 weeks
1492.10983 .89871 (149*2π)/5594 weeks
1502.12575 2.09931 (150*2π)/5594 weeks
1511.19333 1.68709 (151*2π)/5594 weeks
152.62725 1.71734 (152*2π)/5594 weeks
153.88879 -.18926 (153*2π)/5594 weeks
1543.18387 .89906 (154*2π)/5594 weeks
1551.86085 2.03408 (155*2π)/5594 weeks
1561.83014 2.02166 (156*2π)/5594 weeks
1571.09828 1.90771 (157*2π)/5594 weeks
1581.23274 1.49285 (158*2π)/5594 weeks
1591.15941 1.22567 (159*2π)/5594 weeks
1601.58239 .6242 (160*2π)/5593 weeks
1612.5958 2.13257 (161*2π)/5593 weeks
162.60729 2.44461 (162*2π)/5593 weeks
163.81606 1.33711 (163*2π)/5593 weeks
164.91192 1.37623 (164*2π)/5593 weeks
165.84177 .80789 (165*2π)/5593 weeks
1661.3926 .41971 (166*2π)/5593 weeks
1672.76311 1.47678 (167*2π)/5593 weeks
1681.48954 2.56593 (168*2π)/5593 weeks
169.6276 2.716 (169*2π)/5593 weeks
170-.61404 1.61638 (170*2π)/5593 weeks
171-.31371 -.38254 (171*2π)/5593 weeks
1721.98708 -.5592 (172*2π)/5593 weeks
1732.34737 1.11932 (173*2π)/5593 weeks
1741.7655 1.58939 (174*2π)/5593 weeks
175.95417 2.01122 (175*2π)/5593 weeks
176.09098 1.49184 (176*2π)/5593 weeks
177-.24853 -.09062 (177*2π)/5593 weeks
1781.47435 -1.39563 (178*2π)/5593 weeks
1793.69884 -.28223 (179*2π)/5593 weeks
1803.36985 2.26093 (180*2π)/5593 weeks
1812.12905 3.39055 (181*2π)/5593 weeks
182-.50973 2.91742 (182*2π)/5593 weeks
183-1.06149 .24426 (183*2π)/5593 weeks
1841.14692 -1.26589 (184*2π)/5593 weeks
1853.0662 -.16286 (185*2π)/5593 weeks
1862.9507 2.06277 (186*2π)/5593 weeks
1871.35705 3.2227 (187*2π)/5593 weeks
188-.57232 1.88922 (188*2π)/5593 weeks
189-.13648 .5236 (189*2π)/5593 weeks
190.36168 -.56386 (190*2π)/5593 weeks
1912.09937 .19279 (191*2π)/5593 weeks
1921.41102 1.32936 (192*2π)/5593 weeks
193.98572 1.02603 (193*2π)/5593 weeks
194.28896 .8564 (194*2π)/5593 weeks
195.4551 -.13288 (195*2π)/5593 weeks
196.93515 -.41295 (196*2π)/5593 weeks
1972.23714 -1.61031 (197*2π)/5593 weeks
1984.72211 .81434 (198*2π)/5593 weeks
1992.18376 3.70191 (199*2π)/5593 weeks
200.06053 2.92697 (200*2π)/5593 weeks
201-1.35028 1.33337 (201*2π)/5593 weeks
202-.24805 -1.06565 (202*2π)/5593 weeks
2031.74806 -1.00935 (203*2π)/5593 weeks
2042.45917 -.11923 (204*2π)/5593 weeks
2052.59177 2.19479 (205*2π)/5593 weeks
206-.6352 1.87621 (206*2π)/5593 weeks
207-.23861 -.43356 (207*2π)/5593 weeks
208.34138 -1.28382 (208*2π)/5593 weeks
2092.79945 -2.02621 (209*2π)/5593 weeks
2104.72193 .54215 (210*2π)/5593 weeks
2112.6105 3.341 (211*2π)/5593 weeks
212-.19807 2.88112 (212*2π)/5593 weeks
213-1.25985 -.07871 (213*2π)/5593 weeks
2141.33792 -1.67951 (214*2π)/5593 weeks
2152.81175 -.45526 (215*2π)/5593 weeks
2163.149 1.4415 (216*2π)/5593 weeks
2171.44794 3.12498 (217*2π)/5593 weeks
218-1.18415 1.19868 (218*2π)/5593 weeks
219-.28882 -1.10282 (219*2π)/5593 weeks
2201.7792 -1.6261 (220*2π)/5593 weeks
2213.22609 .14404 (221*2π)/5593 weeks
2222.17631 1.44643 (222*2π)/5593 weeks
2231.24922 .80822 (223*2π)/5593 weeks
2241.91888 .79573 (224*2π)/5592 weeks
2251.53806 1.64375 (225*2π)/5592 weeks
2261.111 1.47019 (226*2π)/5592 weeks
227.29846 1.9104 (227*2π)/5592 weeks
228-1.29726 .25146 (228*2π)/5592 weeks
229.65022 -1.57523 (229*2π)/5592 weeks
2302.08737 -.75342 (230*2π)/5592 weeks
2312.71736 1.03019 (231*2π)/5592 weeks
232.56377 2.11917 (232*2π)/5592 weeks
233-.48935 .44272 (233*2π)/5592 weeks
234-.18129 -.85981 (234*2π)/5592 weeks
235.84074 -2.12352 (235*2π)/5592 weeks
2363.48318 -1.21268 (236*2π)/5592 weeks
2373.23911 1.76691 (237*2π)/5592 weeks
238.9081 2.7132 (238*2π)/5592 weeks
239-1.55293 .79585 (239*2π)/5592 weeks
240-.33721 -2.09271 (240*2π)/5592 weeks
2412.1456 -2.10363 (241*2π)/5592 weeks
2423.37634 -.78239 (242*2π)/5592 weeks
2433.54213 1.76088 (243*2π)/5592 weeks
244.58533 2.01526 (244*2π)/5592 weeks
245.1215 .61274 (245*2π)/5592 weeks
246.17534 -.55221 (246*2π)/5592 weeks
2471.47569 -.71348 (247*2π)/5592 weeks
2481.44531 -.19313 (248*2π)/5592 weeks
2491.79027 -.45257 (249*2π)/5592 weeks
2501.98801 .70002 (250*2π)/5592 weeks
251.54418 .59067 (251*2π)/5592 weeks
252.83116 -.20323 (252*2π)/5592 weeks
253.92281 -1.12457 (253*2π)/5592 weeks
2542.34669 -1.41729 (254*2π)/5592 weeks
2553.67297 .36003 (255*2π)/5592 weeks
2562.38493 2.19585 (256*2π)/5592 weeks
257.35822 2.35685 (257*2π)/5592 weeks
258-1.55402 .9962 (258*2π)/5592 weeks
259-1.25436 -2.10986 (259*2π)/5592 weeks
2601.30319 -3.53909 (260*2π)/5592 weeks
2614.51291 -1.90337 (261*2π)/5592 weeks
2623.78509 1.64865 (262*2π)/5592 weeks
2631.07044 2.00131 (263*2π)/5592 weeks
264-.25887 .75869 (264*2π)/5592 weeks
265-.15992 -1.47554 (265*2π)/5592 weeks
2662.02995 -2.14963 (266*2π)/5592 weeks
2673.79953 -.37998 (267*2π)/5592 weeks
2682.37281 1.3856 (268*2π)/5592 weeks
269.66674 1.17939 (269*2π)/5592 weeks
270-.145 -.28876 (270*2π)/5592 weeks
271.74431 -1.49022 (271*2π)/5592 weeks
2722.56269 -2.43458 (272*2π)/5592 weeks
2734.68885 -.4271 (273*2π)/5592 weeks
2742.60683 2.71831 (274*2π)/5592 weeks
275-.11611 1.45498 (275*2π)/5592 weeks
276-.09438 -.17918 (276*2π)/5592 weeks
277.81318 -1.78282 (277*2π)/5592 weeks
2782.00881 -2.02688 (278*2π)/5592 weeks
2794.0664 -1.46786 (279*2π)/5592 weeks
2804.0664 1.46786 (280*2π)/5592 weeks
2812.00881 2.02688 (281*2π)/5592 weeks
282.81318 1.78282 (282*2π)/5592 weeks
283-.09438 .17918 (283*2π)/5592 weeks
284-.11611 -1.45498 (284*2π)/5592 weeks
2852.60683 -2.71831 (285*2π)/5592 weeks
2864.68885 .4271 (286*2π)/5592 weeks
2872.56269 2.43458 (287*2π)/5592 weeks
288.74431 1.49022 (288*2π)/5592 weeks
289-.145 .28876 (289*2π)/5592 weeks
290.66674 -1.17939 (290*2π)/5592 weeks
2912.37281 -1.3856 (291*2π)/5592 weeks
2923.79953 .37998 (292*2π)/5592 weeks
2932.02995 2.14963 (293*2π)/5592 weeks
294-.15992 1.47554 (294*2π)/5592 weeks
295-.25887 -.75869 (295*2π)/5592 weeks
2961.07044 -2.00131 (296*2π)/5592 weeks
2973.78509 -1.64865 (297*2π)/5592 weeks
2984.51291 1.90337 (298*2π)/5592 weeks
2991.30319 3.53909 (299*2π)/5592 weeks
300-1.25436 2.10986 (300*2π)/5592 weeks
301-1.55402 -.9962 (301*2π)/5592 weeks
302.35822 -2.35685 (302*2π)/5592 weeks
3032.38493 -2.19585 (303*2π)/5592 weeks
3043.67297 -.36003 (304*2π)/5592 weeks
3052.34669 1.41729 (305*2π)/5592 weeks
306.92281 1.12457 (306*2π)/5592 weeks
307.83116 .20323 (307*2π)/5592 weeks
308.54418 -.59067 (308*2π)/5592 weeks
3091.98801 -.70002 (309*2π)/5592 weeks
3101.79027 .45257 (310*2π)/5592 weeks
3111.44531 .19313 (311*2π)/5592 weeks
3121.47569 .71348 (312*2π)/5592 weeks
313.17534 .55221 (313*2π)/5592 weeks
314.1215 -.61274 (314*2π)/5592 weeks
315.58533 -2.01526 (315*2π)/5592 weeks
3163.54213 -1.76088 (316*2π)/5592 weeks
3173.37634 .78239 (317*2π)/5592 weeks
3182.1456 2.10363 (318*2π)/5592 weeks
319-.33721 2.09271 (319*2π)/5592 weeks
320-1.55293 -.79585 (320*2π)/5592 weeks
321.9081 -2.7132 (321*2π)/5592 weeks
3223.23911 -1.76691 (322*2π)/5592 weeks
3233.48318 1.21268 (323*2π)/5592 weeks
324.84074 2.12352 (324*2π)/5592 weeks
325-.18129 .85981 (325*2π)/5592 weeks
326-.48935 -.44272 (326*2π)/5592 weeks
327.56377 -2.11917 (327*2π)/5592 weeks
3282.71736 -1.03019 (328*2π)/5592 weeks
3292.08737 .75342 (329*2π)/5592 weeks
330.65022 1.57523 (330*2π)/5592 weeks
331-1.29726 -.25146 (331*2π)/5592 weeks
332.29846 -1.9104 (332*2π)/5592 weeks
3331.111 -1.47019 (333*2π)/5592 weeks
3341.53806 -1.64375 (334*2π)/5592 weeks
3351.91888 -.79573 (335*2π)/5592 weeks
3361.24922 -.80822 (336*2π)/5592 weeks
3372.17631 -1.44643 (337*2π)/5592 weeks
3383.22609 -.14404 (338*2π)/5592 weeks
3391.7792 1.6261 (339*2π)/5592 weeks
340-.28882 1.10282 (340*2π)/5592 weeks
341-1.18415 -1.19868 (341*2π)/5592 weeks
3421.44794 -3.12498 (342*2π)/5592 weeks
3433.149 -1.4415 (343*2π)/5592 weeks
3442.81175 .45526 (344*2π)/5592 weeks
3451.33792 1.67951 (345*2π)/5592 weeks
346-1.25985 .07871 (346*2π)/5592 weeks
347-.19807 -2.88112 (347*2π)/5592 weeks
3482.6105 -3.341 (348*2π)/5592 weeks
3494.72193 -.54215 (349*2π)/5592 weeks
3502.79945 2.02621 (350*2π)/5592 weeks
351.34138 1.28382 (351*2π)/5592 weeks
352-.23861 .43356 (352*2π)/5592 weeks
353-.6352 -1.87621 (353*2π)/5592 weeks
3542.59177 -2.19479 (354*2π)/5592 weeks
3552.45917 .11923 (355*2π)/5592 weeks
3561.74806 1.00935 (356*2π)/5592 weeks
357-.24805 1.06565 (357*2π)/5592 weeks
358-1.35028 -1.33337 (358*2π)/5592 weeks
359.06053 -2.92697 (359*2π)/5592 weeks
3602.18376 -3.70191 (360*2π)/5592 weeks
3614.72211 -.81434 (361*2π)/5592 weeks
3622.23714 1.61031 (362*2π)/5592 weeks
363.93515 .41295 (363*2π)/5592 weeks
364.4551 .13288 (364*2π)/5592 weeks
365.28896 -.8564 (365*2π)/5592 weeks
366.98572 -1.02603 (366*2π)/5592 weeks
3671.41102 -1.32936 (367*2π)/5592 weeks
3682.09937 -.19279 (368*2π)/5592 weeks
369.36168 .56386 (369*2π)/5592 weeks
370-.13648 -.5236 (370*2π)/5592 weeks
371-.57232 -1.88922 (371*2π)/5592 weeks
3721.35705 -3.2227 (372*2π)/5592 weeks
3732.9507 -2.06277 (373*2π)/5591 weeks
3743.0662 .16286 (374*2π)/5591 weeks
3751.14692 1.26589 (375*2π)/5591 weeks
376-1.06149 -.24426 (376*2π)/5591 weeks
377-.50973 -2.91742 (377*2π)/5591 weeks
3782.12905 -3.39055 (378*2π)/5591 weeks
3793.36985 -2.26093 (379*2π)/5591 weeks
3803.69884 .28223 (380*2π)/5591 weeks
3811.47435 1.39563 (381*2π)/5591 weeks
382-.24853 .09062 (382*2π)/5591 weeks
383.09098 -1.49184 (383*2π)/5591 weeks
384.95417 -2.01122 (384*2π)/5591 weeks
3851.7655 -1.58939 (385*2π)/5591 weeks
3862.34737 -1.11932 (386*2π)/5591 weeks
3871.98708 .5592 (387*2π)/5591 weeks
388-.31371 .38254 (388*2π)/5591 weeks
389-.61404 -1.61638 (389*2π)/5591 weeks
390.6276 -2.716 (390*2π)/5591 weeks
3911.48954 -2.56593 (391*2π)/5591 weeks
3922.76311 -1.47678 (392*2π)/5591 weeks
3931.3926 -.41971 (393*2π)/5591 weeks
394.84177 -.80789 (394*2π)/5591 weeks
395.91192 -1.37623 (395*2π)/5591 weeks
396.81606 -1.33711 (396*2π)/5591 weeks
397.60729 -2.44461 (397*2π)/5591 weeks
3982.5958 -2.13257 (398*2π)/5591 weeks
3991.58239 -.6242 (399*2π)/5591 weeks
4001.15941 -1.22567 (400*2π)/5591 weeks
4011.23274 -1.49285 (401*2π)/5591 weeks
4021.09828 -1.90771 (402*2π)/5591 weeks
4031.83014 -2.02166 (403*2π)/5591 weeks
4041.86085 -2.03408 (404*2π)/5591 weeks
4053.18387 -.89906 (405*2π)/5591 weeks
406.88879 .18926 (406*2π)/5591 weeks
407.62725 -1.71734 (407*2π)/5591 weeks
4081.19333 -1.68709 (408*2π)/5591 weeks
4092.12575 -2.09931 (409*2π)/5591 weeks
4102.10983 -.89871 (410*2π)/5591 weeks
4111.20273 -.55004 (411*2π)/5591 weeks
412.51987 -1.10719 (412*2π)/5591 weeks
4131.01247 -2.34892 (413*2π)/5591 weeks
4142.69963 -1.82447 (414*2π)/5591 weeks
4151.14715 -.20147 (415*2π)/5591 weeks
416.30984 -1.84659 (416*2π)/5591 weeks
417.60003 -2.22782 (417*2π)/5591 weeks
4181.74775 -2.58624 (418*2π)/5591 weeks
4191.71024 -1.0282 (419*2π)/5591 weeks
420.28877 -2.27886 (420*2π)/5591 weeks
4212.00949 -3.7087 (421*2π)/5591 weeks
4222.7975 -2.65643 (422*2π)/5591 weeks
4233.80808 -1.44859 (423*2π)/5591 weeks
4242.59632 .50766 (424*2π)/5591 weeks
425.52073 -.29741 (425*2π)/5591 weeks
426.75897 -2.21795 (426*2π)/5591 weeks
4271.94851 -1.77604 (427*2π)/5591 weeks
4281.51796 -.973 (428*2π)/5591 weeks
429.87184 -1.78473 (429*2π)/5591 weeks
4301.04779 -1.24507 (430*2π)/5591 weeks
431.24095 -1.93035 (431*2π)/5591 weeks
432.70504 -3.47053 (432*2π)/5591 weeks
4332.89176 -4.68699 (433*2π)/5591 weeks
4344.88731 -1.45255 (434*2π)/5591 weeks
4352.59848 .94311 (435*2π)/5591 weeks
436-.09665 -.44827 (436*2π)/5591 weeks
437.10641 -2.03546 (437*2π)/5591 weeks
4381.44316 -4.09371 (438*2π)/5591 weeks
4393.91557 -2.96513 (439*2π)/5591 weeks
4404.20632 -.24667 (440*2π)/5591 weeks
4411.42019 2.02786 (441*2π)/5591 weeks
442-2.54176 .22224 (442*2π)/5591 weeks
443-2.10187 -4.93615 (443*2π)/5591 weeks
4442.08951 -6.14842 (444*2π)/5591 weeks
4455.31426 -4.48133 (445*2π)/5591 weeks
4466.12786 .16989 (446*2π)/5591 weeks
4471.29075 3.14862 (447*2π)/5591 weeks
448-2.99827 .03098 (448*2π)/5591 weeks
449-2.23442 -5.34968 (449*2π)/5591 weeks
4502.56572 -7.22857 (450*2π)/5591 weeks
4516.56497 -4.87748 (451*2π)/5591 weeks
4526.5476 1.3839 (452*2π)/5591 weeks
4531.46215 2.54589 (453*2π)/5591 weeks
454-2.05348 -.06086 (454*2π)/5591 weeks
455-.93635 -4.52333 (455*2π)/5591 weeks
4563.06099 -5.49993 (456*2π)/5591 weeks
4575.5596 -2.60799 (457*2π)/5591 weeks
4584.27765 1.06886 (458*2π)/5591 weeks
459.59777 1.6132 (459*2π)/5591 weeks
460-.80861 -1.17057 (460*2π)/5591 weeks
461.12957 -2.47183 (461*2π)/5591 weeks
4621.48935 -2.80636 (462*2π)/5591 weeks
463.82451 -1.62811 (463*2π)/5591 weeks
464.71562 -3.85944 (464*2π)/5591 weeks
4653.57422 -3.22847 (465*2π)/5591 weeks
4663.03696 -.13316 (466*2π)/5591 weeks
467-.2873 .36102 (467*2π)/5591 weeks
468-2.20401 -2.46206 (468*2π)/5591 weeks
469-.02835 -5.81375 (469*2π)/5591 weeks
4704.13365 -5.76439 (470*2π)/5591 weeks
4715.99999 -1.59969 (471*2π)/5591 weeks
4722.59729 2.47961 (472*2π)/5591 weeks
473-2.89783 .39533 (473*2π)/5591 weeks
474-2.35363 -4.46161 (474*2π)/5591 weeks
475-.07984 -6.33505 (475*2π)/5591 weeks
4764.54208 -6.84733 (476*2π)/5591 weeks
4776.33549 -2.10337 (477*2π)/5591 weeks
4784.037 1.37338 (478*2π)/5591 weeks
479-1.41854 1.38347 (479*2π)/5591 weeks
480-1.90899 -4.43529 (480*2π)/5591 weeks
4812.06737 -4.61112 (481*2π)/5591 weeks
4822.38406 -4.44662 (482*2π)/5591 weeks
4835.49127 -1.73731 (483*2π)/5591 weeks
4841.95095 3.27389 (484*2π)/5591 weeks
485-4.04634 .11983 (485*2π)/5591 weeks
486-3.67588 -6.14139 (486*2π)/5591 weeks
4871.68755 -7.69521 (487*2π)/5591 weeks
4884.90622 -3.21102 (488*2π)/5591 weeks
489.01467 -.76803 (489*2π)/5591 weeks
490-.91568 -4.24128 (490*2π)/5591 weeks
491-.28349 -6.33315 (491*2π)/5591 weeks
4924.72132 -7.42717 (492*2π)/5591 weeks
4936.62432 -2.7348 (493*2π)/5591 weeks
4942.93651 1.03406 (494*2π)/5591 weeks
495-.67385 -.65032 (495*2π)/5591 weeks
496-1.65068 -4.48657 (496*2π)/5591 weeks
4971.99644 -5.58048 (497*2π)/5591 weeks
4982.74386 -2.71337 (498*2π)/5591 weeks
499.42686 -1.7458 (499*2π)/5591 weeks
500-1.09182 -4.17606 (500*2π)/5591 weeks
501-.0799 -6.97737 (501*2π)/5591 weeks
5025.70326 -6.67867 (502*2π)/5591 weeks
5033.8165 -.70954 (503*2π)/5591 weeks
504-.00821 -2.1857 (504*2π)/5591 weeks
505.29028 -4.25033 (505*2π)/5591 weeks
506.79343 -5.03762 (506*2π)/5591 weeks
5073.95561 -4.23494 (507*2π)/5591 weeks
5082.65136 -.22046 (508*2π)/5591 weeks
509-1.06933 -.03535 (509*2π)/5591 weeks
510-3.76157 -3.53829 (510*2π)/5591 weeks
511-4.6623 -6.53091 (511*2π)/5591 weeks
512.84169 -9.51355 (512*2π)/5591 weeks
5131.95146 -5.46444 (513*2π)/5591 weeks
514.81004 -6.07054 (514*2π)/5591 weeks
515-.94445 -5.44455 (515*2π)/5591 weeks
516.63962 -9.89858 (516*2π)/5591 weeks
5176.33427 -7.13044 (517*2π)/5591 weeks
5181.26975 -1.12521 (518*2π)/5591 weeks
519-2.72275 -5.25349 (519*2π)/5591 weeks
520-1.81825 -8.60821 (520*2π)/5591 weeks
521.54664 -12.09662 (521*2π)/5591 weeks
5227.98684 -10.90098 (522*2π)/5591 weeks
5239.73312 -2.50012 (523*2π)/5591 weeks
5241.44595 5.94365 (524*2π)/5591 weeks
525-13.42783 -1.42208 (525*2π)/5591 weeks
526-10.05854 -16.53443 (526*2π)/5591 weeks
5272.32571 -20.62937 (527*2π)/5591 weeks
52812.59312 -13.82669 (528*2π)/5591 weeks
52911.10343 -1.75875 (529*2π)/5591 weeks
530-.79944 1.34023 (530*2π)/5591 weeks
531-5.91313 -2.69038 (531*2π)/5591 weeks
532-11.66542 -11.07285 (532*2π)/5591 weeks
533-1.94812 -18.24701 (533*2π)/5591 weeks
5342.12779 -16.43774 (534*2π)/5591 weeks
5355.93756 -13.27116 (535*2π)/5591 weeks
536-1.19332 -12.33592 (536*2π)/5591 weeks
5372.09792 -15.51769 (537*2π)/5591 weeks
5381.6066 -15.4511 (538*2π)/5591 weeks
5394.0393 -18.0446 (539*2π)/5591 weeks
5408.46388 -19.11864 (540*2π)/5591 weeks
54114.72912 -11.03113 (541*2π)/5591 weeks
5425.71677 -2.98637 (542*2π)/5591 weeks
543-2.22104 -1.20003 (543*2π)/5591 weeks
544-15.51206 -8.71042 (544*2π)/5591 weeks
545-20.49848 -27.90565 (545*2π)/5591 weeks
546-5.83575 -49.97326 (546*2π)/5591 weeks
54726.25393 -46.48917 (547*2π)/5591 weeks
54832.20343 -17.25873 (548*2π)/5591 weeks
54917.19955 -2.75404 (549*2π)/5591 weeks
550-11.45581 2.00787 (550*2π)/5591 weeks
551-37.55857 -42.99302 (551*2π)/5591 weeks
55210.34075 -83.06939 (552*2π)/5591 weeks
55355.83397 -57.79128 (553*2π)/5591 weeks
55454.88078 -.9386 (554*2π)/5591 weeks
555-22.53846 12.221 (555*2π)/5591 weeks
556-83.18035 -64.89616 (556*2π)/5591 weeks
557-37.52622 -210.9808 (557*2π)/5591 weeks



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