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Fourier Analysis of QID (ProShares UltraShort QQQ ETF)


QID (ProShares UltraShort QQQ ETF) appears to have interesting cyclic behaviour every 59 weeks (55.5045*sine), 39 weeks (43.658*sine), and 54 weeks (36.3996*sine).

QID (ProShares UltraShort QQQ ETF) has an average price of 328.84 (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 7/13/2006 to 10/16/2017 for QID (ProShares UltraShort QQQ ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0328.8422   0 
1169.0174 368.4969 (1*2π)/589589 weeks
2-47.54852 183.8657 (2*2π)/589295 weeks
3-23.30719 30.74349 (3*2π)/589196 weeks
461.57214 27.29483 (4*2π)/589147 weeks
564.43089 90.36258 (5*2π)/589118 weeks
6-1.31797 98.26009 (6*2π)/58998 weeks
7-29.26584 43.88763 (7*2π)/58984 weeks
810.74939 3.84159 (8*2π)/58974 weeks
937.57515 41.47192 (9*2π)/58965 weeks
105.90263 55.5045 (10*2π)/58959 weeks
11-13.16621 36.39958 (11*2π)/58954 weeks
12-9.54237 8.17246 (12*2π)/58949 weeks
1322.41079 1.28271 (13*2π)/58945 weeks
1433.50924 28.58505 (14*2π)/58942 weeks
1513.71225 43.65798 (15*2π)/58939 weeks
16-3.61418 34.21588 (16*2π)/58937 weeks
17-5.00623 19.60305 (17*2π)/58935 weeks
18-.10319 10.79973 (18*2π)/58933 weeks
1914.52704 10.5408 (19*2π)/58931 weeks
2015.00101 21.97138 (20*2π)/58929 weeks
219.16073 25.435 (21*2π)/58928 weeks
224.18585 23.43387 (22*2π)/58927 weeks
231.62775 22.60627 (23*2π)/58926 weeks
24-.94063 16.03874 (24*2π)/58925 weeks
254.58455 17.91339 (25*2π)/58924 weeks
26-1.12651 17.65437 (26*2π)/58923 weeks
27-3.26814 11.62265 (27*2π)/58922 weeks
282.94057 3.54228 (28*2π)/58921 weeks
2912.51013 11.22376 (29*2π)/58920 weeks
309.10234 19.25911 (30*2π)/58920 weeks
31-1.17909 22.76256 (31*2π)/58919 weeks
32-8.19551 10.3599 (32*2π)/58918 weeks
332.32724 -.46714 (33*2π)/58918 weeks
3414.99175 6.93673 (34*2π)/58917 weeks
3511.18429 22.19646 (35*2π)/58917 weeks
36-6.05261 22.09852 (36*2π)/58916 weeks
37-7.66371 5.63978 (37*2π)/58916 weeks
383.58247 2.28275 (38*2π)/58916 weeks
398.56712 8.57737 (39*2π)/58915 weeks
404.39502 12.9372 (40*2π)/58915 weeks
411.72799 11.84303 (41*2π)/58914 weeks
42.15144 9.47733 (42*2π)/58914 weeks
432.09253 6.61979 (43*2π)/58914 weeks
444.41606 10.53117 (44*2π)/58913 weeks
45-.39608 9.2599 (45*2π)/58913 weeks
462.12743 6.09966 (46*2π)/58913 weeks
472.31542 8.13194 (47*2π)/58913 weeks
482.00305 7.09747 (48*2π)/58912 weeks
491.25776 5.06969 (49*2π)/58912 weeks
506.3629 3.14671 (50*2π)/58912 weeks
518.03739 9.80634 (51*2π)/58912 weeks
524.77658 12.20094 (52*2π)/58911 weeks
53.23054 11.23022 (53*2π)/58911 weeks
54-.76421 7.22142 (54*2π)/58911 weeks
552.55044 5.69321 (55*2π)/58911 weeks
562.51781 8.74221 (56*2π)/58911 weeks
57.4456 8.37614 (57*2π)/58910 weeks
58-1.32888 5.70978 (58*2π)/58910 weeks
592.10857 1.73431 (59*2π)/58910 weeks
607.0672 6.19335 (60*2π)/58910 weeks
612.03269 9.39509 (61*2π)/58910 weeks
62.02166 6.53422 (62*2π)/58910 weeks
631.3644 4.27574 (63*2π)/5899 weeks
643.25573 4.99496 (64*2π)/5899 weeks
652.03701 6.765 (65*2π)/5899 weeks
66.79576 4.01357 (66*2π)/5899 weeks
674.5699 3.38094 (67*2π)/5899 weeks
685.45533 6.64901 (68*2π)/5899 weeks
691.94957 9.26447 (69*2π)/5899 weeks
70-1.42847 5.49132 (70*2π)/5898 weeks
711.9878 1.64482 (71*2π)/5898 weeks
724.21614 4.53631 (72*2π)/5898 weeks
733.61726 5.96377 (73*2π)/5898 weeks
74.4466 5.46051 (74*2π)/5898 weeks
753.62534 1.13942 (75*2π)/5898 weeks
767.9132 6.07321 (76*2π)/5898 weeks
773.03802 11.37035 (77*2π)/5898 weeks
78-3.40231 7.17026 (78*2π)/5898 weeks
79-.72347 -.16454 (79*2π)/5897 weeks
805.89594 2.08035 (80*2π)/5897 weeks
814.33014 6.39496 (81*2π)/5897 weeks
823.14568 6.74357 (82*2π)/5897 weeks
83-.60162 6.18036 (83*2π)/5897 weeks
841.63838 .72921 (84*2π)/5897 weeks
856.62356 4.23794 (85*2π)/5897 weeks
864.29975 8.70386 (86*2π)/5897 weeks
87-.88651 8.63304 (87*2π)/5897 weeks
88-2.18276 3.27865 (88*2π)/5897 weeks
891.50839 1.19999 (89*2π)/5897 weeks
905.00565 2.94757 (90*2π)/5897 weeks
913.8683 8.55385 (91*2π)/5896 weeks
92-2.72541 7.0854 (92*2π)/5896 weeks
93-2.19641 .8081 (93*2π)/5896 weeks
943.10877 -.43414 (94*2π)/5896 weeks
955.33236 3.72321 (95*2π)/5896 weeks
962.19617 6.72819 (96*2π)/5896 weeks
97-1.00799 4.6618 (97*2π)/5896 weeks
98.32126 1.22517 (98*2π)/5896 weeks
993.22233 1.98165 (99*2π)/5896 weeks
1002.03874 3.94613 (100*2π)/5896 weeks
1011.69725 1.91182 (101*2π)/5896 weeks
1023.0762 3.13052 (102*2π)/5896 weeks
1031.72832 3.22638 (103*2π)/5896 weeks
1041.68495 1.99657 (104*2π)/5896 weeks
1053.81518 1.01576 (105*2π)/5896 weeks
1065.63359 3.90101 (106*2π)/5896 weeks
1072.89788 6.68811 (107*2π)/5896 weeks
108-.31903 4.59201 (108*2π)/5895 weeks
109.85627 .84809 (109*2π)/5895 weeks
1104.75758 1.68588 (110*2π)/5895 weeks
1114.48389 6.10095 (111*2π)/5895 weeks
112.04755 7.24691 (112*2π)/5895 weeks
113-3.84223 2.5385 (113*2π)/5895 weeks
114.57785 -2.36777 (114*2π)/5895 weeks
1155.82972 -.52769 (115*2π)/5895 weeks
1165.75463 5.05762 (116*2π)/5895 weeks
117.38579 6.05166 (117*2π)/5895 weeks
118-1.42495 1.06767 (118*2π)/5895 weeks
1193.5263 -1.5406 (119*2π)/5895 weeks
1206.46787 2.39955 (120*2π)/5895 weeks
1214.28757 5.84135 (121*2π)/5895 weeks
122.05632 5.51842 (122*2π)/5895 weeks
123-.37389 .92517 (123*2π)/5895 weeks
1243.69236 .18224 (124*2π)/5895 weeks
1254.96579 3.45355 (125*2π)/5895 weeks
1262.85076 5.05356 (126*2π)/5895 weeks
127.60218 3.85554 (127*2π)/5895 weeks
1281.57251 1.69012 (128*2π)/5895 weeks
1292.85632 2.38473 (129*2π)/5895 weeks
1303.04987 4.33466 (130*2π)/5895 weeks
131.03989 4.84557 (131*2π)/5894 weeks
132-1.37802 1.38241 (132*2π)/5894 weeks
1332.05933 -.47394 (133*2π)/5894 weeks
1343.47188 1.50703 (134*2π)/5894 weeks
1352.43642 2.93041 (135*2π)/5894 weeks
1361.39481 2.31964 (136*2π)/5894 weeks
1371.82253 2.07816 (137*2π)/5894 weeks
1381.53777 1.30983 (138*2π)/5894 weeks
1392.53244 1.21503 (139*2π)/5894 weeks
1402.26293 2.21542 (140*2π)/5894 weeks
1411.24808 .9156 (141*2π)/5894 weeks
1423.14471 -.49408 (142*2π)/5894 weeks
1435.0803 1.69634 (143*2π)/5894 weeks
1443.55024 3.61705 (144*2π)/5894 weeks
1452.03793 3.57859 (145*2π)/5894 weeks
1461.06967 1.27143 (146*2π)/5894 weeks
1473.42508 .94282 (147*2π)/5894 weeks
1482.8981 2.788 (148*2π)/5894 weeks
1492.31588 1.81623 (149*2π)/5894 weeks
1502.93114 1.88694 (150*2π)/5894 weeks
1513.43082 2.17147 (151*2π)/5894 weeks
1522.05773 2.85779 (152*2π)/5894 weeks
1532.45191 .81609 (153*2π)/5894 weeks
1544.1188 2.27324 (154*2π)/5894 weeks
1552.48889 3.71331 (155*2π)/5894 weeks
1561.21318 2.66693 (156*2π)/5894 weeks
1571.89979 .99911 (157*2π)/5894 weeks
1583.56976 1.58421 (158*2π)/5894 weeks
1592.84647 3.10376 (159*2π)/5894 weeks
1601.53843 3.04509 (160*2π)/5894 weeks
161.87439 1.0193 (161*2π)/5894 weeks
1623.74073 .65185 (162*2π)/5894 weeks
1633.04199 3.12946 (163*2π)/5894 weeks
1642.0031 2.6247 (164*2π)/5894 weeks
1651.29273 1.94673 (165*2π)/5894 weeks
1662.06949 .88205 (166*2π)/5894 weeks
1672.87251 1.29854 (167*2π)/5894 weeks
1683.03929 1.91114 (168*2π)/5894 weeks
1692.4137 2.88471 (169*2π)/5893 weeks
1701.08293 1.25153 (170*2π)/5893 weeks
1713.16175 .72855 (171*2π)/5893 weeks
1723.01766 1.73414 (172*2π)/5893 weeks
1733.08343 1.74864 (173*2π)/5893 weeks
1742.93326 2.30424 (174*2π)/5893 weeks
1752.27677 2.27611 (175*2π)/5893 weeks
1762.60074 .87567 (176*2π)/5893 weeks
1774.0238 1.77248 (177*2π)/5893 weeks
1784.09558 3.15873 (178*2π)/5893 weeks
1792.35199 4.45103 (179*2π)/5893 weeks
180.30533 3.03987 (180*2π)/5893 weeks
1811.35391 .94346 (181*2π)/5893 weeks
1822.83152 1.83172 (182*2π)/5893 weeks
1832.32421 2.58886 (183*2π)/5893 weeks
1841.50546 2.84722 (184*2π)/5893 weeks
185.81193 1.80675 (185*2π)/5893 weeks
1861.3564 .58773 (186*2π)/5893 weeks
1873.14573 .65712 (187*2π)/5893 weeks
1883.53087 2.87942 (188*2π)/5893 weeks
1891.07273 3.73947 (189*2π)/5893 weeks
190-.18553 1.62577 (190*2π)/5893 weeks
191.7888 -.65094 (191*2π)/5893 weeks
1923.71804 -.26045 (192*2π)/5893 weeks
1933.84976 2.57646 (193*2π)/5893 weeks
1941.38468 3.13266 (194*2π)/5893 weeks
195.48658 1.04771 (195*2π)/5893 weeks
1962.41977 -.21972 (196*2π)/5893 weeks
1974.05064 1.15588 (197*2π)/5893 weeks
1982.93295 3.33714 (198*2π)/5893 weeks
1991.18238 2.63533 (199*2π)/5893 weeks
200.91235 1.58409 (200*2π)/5893 weeks
2012.1754 .85141 (201*2π)/5893 weeks
2022.35146 2.24081 (202*2π)/5893 weeks
203.82252 2.15304 (203*2π)/5893 weeks
204.51089 .73233 (204*2π)/5893 weeks
2051.80862 -.34181 (205*2π)/5893 weeks
2063.07527 .43175 (206*2π)/5893 weeks
2073.40518 1.0038 (207*2π)/5893 weeks
2083.57118 3.20557 (208*2π)/5893 weeks
209.02103 3.52244 (209*2π)/5893 weeks
210-.11853 .20357 (210*2π)/5893 weeks
2111.6429 -.82953 (211*2π)/5893 weeks
2123.67294 -.07074 (212*2π)/5893 weeks
2133.43215 1.8882 (213*2π)/5893 weeks
2142.14533 2.13766 (214*2π)/5893 weeks
2151.56421 1.76526 (215*2π)/5893 weeks
2162.26417 .34995 (216*2π)/5893 weeks
2173.28546 2.37917 (217*2π)/5893 weeks
2181.40022 2.57544 (218*2π)/5893 weeks
219.76006 2.15255 (219*2π)/5893 weeks
220.07614 .23054 (220*2π)/5893 weeks
2212.60092 -1.09841 (221*2π)/5893 weeks
2224.18162 1.83581 (222*2π)/5893 weeks
2231.78957 3.55522 (223*2π)/5893 weeks
224-.62763 1.65007 (224*2π)/5893 weeks
2251.1011 -.80921 (225*2π)/5893 weeks
2262.83266 .46984 (226*2π)/5893 weeks
2272.66399 1.77688 (227*2π)/5893 weeks
228.98771 2.20304 (228*2π)/5893 weeks
229.08718 -.14564 (229*2π)/5893 weeks
2302.65515 -.68214 (230*2π)/5893 weeks
2313.53602 1.2392 (231*2π)/5893 weeks
2321.95037 2.62306 (232*2π)/5893 weeks
233.33781 1.18428 (233*2π)/5893 weeks
2341.3268 -.12918 (234*2π)/5893 weeks
2352.2046 .44469 (235*2π)/5893 weeks
2362.14588 .54147 (236*2π)/5892 weeks
2372.56608 .74931 (237*2π)/5892 weeks
2382.33495 1.22004 (238*2π)/5892 weeks
2392.63697 1.49445 (239*2π)/5892 weeks
2401.50633 2.83957 (240*2π)/5892 weeks
241-.10634 1.19259 (241*2π)/5892 weeks
2421.04182 .00244 (242*2π)/5892 weeks
2432.29588 .49893 (243*2π)/5892 weeks
2441.1702 2.17393 (244*2π)/5892 weeks
245-.50365 .51626 (245*2π)/5892 weeks
246.43458 -1.1474 (246*2π)/5892 weeks
2472.17074 -1.49348 (247*2π)/5892 weeks
2483.87442 .19596 (248*2π)/5892 weeks
2492.10177 2.38982 (249*2π)/5892 weeks
250-.27943 .77523 (250*2π)/5892 weeks
251.785 -1.92563 (251*2π)/5892 weeks
2524.07565 -1.38233 (252*2π)/5892 weeks
2534.07666 2.05609 (253*2π)/5892 weeks
2541.18251 2.73849 (254*2π)/5892 weeks
255-.55319 .75502 (255*2π)/5892 weeks
256.81552 -2.17531 (256*2π)/5892 weeks
2573.89405 -.53025 (257*2π)/5892 weeks
2583.01362 1.58051 (258*2π)/5892 weeks
2591.25204 2.01317 (259*2π)/5892 weeks
260.30171 .22984 (260*2π)/5892 weeks
2611.30609 -.47526 (261*2π)/5892 weeks
2621.96847 -.46982 (262*2π)/5892 weeks
2632.49348 .51157 (263*2π)/5892 weeks
2641.02718 .99982 (264*2π)/5892 weeks
265.73203 -.8625 (265*2π)/5892 weeks
2662.07685 -1.39641 (266*2π)/5892 weeks
2673.73519 -.29345 (267*2π)/5892 weeks
2682.99173 2.03637 (268*2π)/5892 weeks
269.11914 1.90283 (269*2π)/5892 weeks
270-.49985 -.80188 (270*2π)/5892 weeks
2711.2682 -2.38281 (271*2π)/5892 weeks
2723.90124 -1.96881 (272*2π)/5892 weeks
2734.40858 1.33003 (273*2π)/5892 weeks
2741.50994 2.89917 (274*2π)/5892 weeks
275-1.34356 .37099 (275*2π)/5892 weeks
276.81667 -2.82695 (276*2π)/5892 weeks
2773.45928 -1.60694 (277*2π)/5892 weeks
2783.39455 .41836 (278*2π)/5892 weeks
2791.26112 1.17204 (279*2π)/5892 weeks
280.29758 -1.16279 (280*2π)/5892 weeks
2812.50304 -2.66089 (281*2π)/5892 weeks
2824.14377 -.38158 (282*2π)/5892 weeks
2832.60935 .94389 (283*2π)/5892 weeks
2841.15495 .04938 (284*2π)/5892 weeks
2851.73349 -1.83041 (285*2π)/5892 weeks
2863.55214 -2.08732 (286*2π)/5892 weeks
2875.33251 .10338 (287*2π)/5892 weeks
2883.02067 2.86685 (288*2π)/5892 weeks
289.31135 .50657 (289*2π)/5892 weeks
2902.02008 -1.49511 (290*2π)/5892 weeks
2913.5337 -1.08472 (291*2π)/5892 weeks
2924.03298 .8029 (292*2π)/5892 weeks
2932.79761 2.21069 (293*2π)/5892 weeks
294.04511 1.73348 (294*2π)/5892 weeks
295.04511 -1.73348 (295*2π)/5892 weeks
2962.79761 -2.21069 (296*2π)/5892 weeks
2974.03298 -.8029 (297*2π)/5892 weeks
2983.5337 1.08472 (298*2π)/5892 weeks
2992.02008 1.49511 (299*2π)/5892 weeks
300.31135 -.50657 (300*2π)/5892 weeks
3013.02067 -2.86685 (301*2π)/5892 weeks
3025.33251 -.10338 (302*2π)/5892 weeks
3033.55214 2.08732 (303*2π)/5892 weeks
3041.73349 1.83041 (304*2π)/5892 weeks
3051.15495 -.04938 (305*2π)/5892 weeks
3062.60935 -.94389 (306*2π)/5892 weeks
3074.14377 .38158 (307*2π)/5892 weeks
3082.50304 2.66089 (308*2π)/5892 weeks
309.29758 1.16279 (309*2π)/5892 weeks
3101.26112 -1.17204 (310*2π)/5892 weeks
3113.39455 -.41836 (311*2π)/5892 weeks
3123.45928 1.60694 (312*2π)/5892 weeks
313.81667 2.82695 (313*2π)/5892 weeks
314-1.34356 -.37099 (314*2π)/5892 weeks
3151.50994 -2.89917 (315*2π)/5892 weeks
3164.40858 -1.33003 (316*2π)/5892 weeks
3173.90124 1.96881 (317*2π)/5892 weeks
3181.2682 2.38281 (318*2π)/5892 weeks
319-.49985 .80188 (319*2π)/5892 weeks
320.11914 -1.90283 (320*2π)/5892 weeks
3212.99173 -2.03637 (321*2π)/5892 weeks
3223.73519 .29345 (322*2π)/5892 weeks
3232.07685 1.39641 (323*2π)/5892 weeks
324.73203 .8625 (324*2π)/5892 weeks
3251.02718 -.99982 (325*2π)/5892 weeks
3262.49348 -.51157 (326*2π)/5892 weeks
3271.96847 .46982 (327*2π)/5892 weeks
3281.30609 .47526 (328*2π)/5892 weeks
329.30171 -.22984 (329*2π)/5892 weeks
3301.25204 -2.01317 (330*2π)/5892 weeks
3313.01362 -1.58051 (331*2π)/5892 weeks
3323.89405 .53025 (332*2π)/5892 weeks
333.81552 2.17531 (333*2π)/5892 weeks
334-.55319 -.75502 (334*2π)/5892 weeks
3351.18251 -2.73849 (335*2π)/5892 weeks
3364.07666 -2.05609 (336*2π)/5892 weeks
3374.07565 1.38233 (337*2π)/5892 weeks
338.785 1.92563 (338*2π)/5892 weeks
339-.27943 -.77523 (339*2π)/5892 weeks
3402.10177 -2.38982 (340*2π)/5892 weeks
3413.87442 -.19596 (341*2π)/5892 weeks
3422.17074 1.49348 (342*2π)/5892 weeks
343.43458 1.1474 (343*2π)/5892 weeks
344-.50365 -.51626 (344*2π)/5892 weeks
3451.1702 -2.17393 (345*2π)/5892 weeks
3462.29588 -.49893 (346*2π)/5892 weeks
3471.04182 -.00244 (347*2π)/5892 weeks
348-.10634 -1.19259 (348*2π)/5892 weeks
3491.50633 -2.83957 (349*2π)/5892 weeks
3502.63697 -1.49445 (350*2π)/5892 weeks
3512.33495 -1.22004 (351*2π)/5892 weeks
3522.56608 -.74931 (352*2π)/5892 weeks
3532.14588 -.54147 (353*2π)/5892 weeks
3542.2046 -.44469 (354*2π)/5892 weeks
3551.3268 .12918 (355*2π)/5892 weeks
356.33781 -1.18428 (356*2π)/5892 weeks
3571.95037 -2.62306 (357*2π)/5892 weeks
3583.53602 -1.2392 (358*2π)/5892 weeks
3592.65515 .68214 (359*2π)/5892 weeks
360.08718 .14564 (360*2π)/5892 weeks
361.98771 -2.20304 (361*2π)/5892 weeks
3622.66399 -1.77688 (362*2π)/5892 weeks
3632.83266 -.46984 (363*2π)/5892 weeks
3641.1011 .80921 (364*2π)/5892 weeks
365-.62763 -1.65007 (365*2π)/5892 weeks
3661.78957 -3.55522 (366*2π)/5892 weeks
3674.18162 -1.83581 (367*2π)/5892 weeks
3682.60092 1.09841 (368*2π)/5892 weeks
369.07614 -.23054 (369*2π)/5892 weeks
370.76006 -2.15255 (370*2π)/5892 weeks
3711.40022 -2.57544 (371*2π)/5892 weeks
3723.28546 -2.37917 (372*2π)/5892 weeks
3732.26417 -.34995 (373*2π)/5892 weeks
3741.56421 -1.76526 (374*2π)/5892 weeks
3752.14533 -2.13766 (375*2π)/5892 weeks
3763.43215 -1.8882 (376*2π)/5892 weeks
3773.67294 .07074 (377*2π)/5892 weeks
3781.6429 .82953 (378*2π)/5892 weeks
379-.11853 -.20357 (379*2π)/5892 weeks
380.02103 -3.52244 (380*2π)/5892 weeks
3813.57118 -3.20557 (381*2π)/5892 weeks
3823.40518 -1.0038 (382*2π)/5892 weeks
3833.07527 -.43175 (383*2π)/5892 weeks
3841.80862 .34181 (384*2π)/5892 weeks
385.51089 -.73233 (385*2π)/5892 weeks
386.82252 -2.15304 (386*2π)/5892 weeks
3872.35146 -2.24081 (387*2π)/5892 weeks
3882.1754 -.85141 (388*2π)/5892 weeks
389.91235 -1.58409 (389*2π)/5892 weeks
3901.18238 -2.63533 (390*2π)/5892 weeks
3912.93295 -3.33714 (391*2π)/5892 weeks
3924.05064 -1.15588 (392*2π)/5892 weeks
3932.41977 .21972 (393*2π)/5891 weeks
394.48658 -1.04771 (394*2π)/5891 weeks
3951.38468 -3.13266 (395*2π)/5891 weeks
3963.84976 -2.57646 (396*2π)/5891 weeks
3973.71804 .26045 (397*2π)/5891 weeks
398.7888 .65094 (398*2π)/5891 weeks
399-.18553 -1.62577 (399*2π)/5891 weeks
4001.07273 -3.73947 (400*2π)/5891 weeks
4013.53087 -2.87942 (401*2π)/5891 weeks
4023.14573 -.65712 (402*2π)/5891 weeks
4031.3564 -.58773 (403*2π)/5891 weeks
404.81193 -1.80675 (404*2π)/5891 weeks
4051.50546 -2.84722 (405*2π)/5891 weeks
4062.32421 -2.58886 (406*2π)/5891 weeks
4072.83152 -1.83172 (407*2π)/5891 weeks
4081.35391 -.94346 (408*2π)/5891 weeks
409.30533 -3.03987 (409*2π)/5891 weeks
4102.35199 -4.45103 (410*2π)/5891 weeks
4114.09558 -3.15873 (411*2π)/5891 weeks
4124.0238 -1.77248 (412*2π)/5891 weeks
4132.60074 -.87567 (413*2π)/5891 weeks
4142.27677 -2.27611 (414*2π)/5891 weeks
4152.93326 -2.30424 (415*2π)/5891 weeks
4163.08343 -1.74864 (416*2π)/5891 weeks
4173.01766 -1.73414 (417*2π)/5891 weeks
4183.16175 -.72855 (418*2π)/5891 weeks
4191.08293 -1.25153 (419*2π)/5891 weeks
4202.4137 -2.88471 (420*2π)/5891 weeks
4213.03929 -1.91114 (421*2π)/5891 weeks
4222.87251 -1.29854 (422*2π)/5891 weeks
4232.06949 -.88205 (423*2π)/5891 weeks
4241.29273 -1.94673 (424*2π)/5891 weeks
4252.0031 -2.6247 (425*2π)/5891 weeks
4263.04199 -3.12946 (426*2π)/5891 weeks
4273.74073 -.65185 (427*2π)/5891 weeks
428.87439 -1.0193 (428*2π)/5891 weeks
4291.53843 -3.04509 (429*2π)/5891 weeks
4302.84647 -3.10376 (430*2π)/5891 weeks
4313.56976 -1.58421 (431*2π)/5891 weeks
4321.89979 -.99911 (432*2π)/5891 weeks
4331.21318 -2.66693 (433*2π)/5891 weeks
4342.48889 -3.71331 (434*2π)/5891 weeks
4354.1188 -2.27324 (435*2π)/5891 weeks
4362.45191 -.81609 (436*2π)/5891 weeks
4372.05773 -2.85779 (437*2π)/5891 weeks
4383.43082 -2.17147 (438*2π)/5891 weeks
4392.93114 -1.88694 (439*2π)/5891 weeks
4402.31588 -1.81623 (440*2π)/5891 weeks
4412.8981 -2.788 (441*2π)/5891 weeks
4423.42508 -.94282 (442*2π)/5891 weeks
4431.06967 -1.27143 (443*2π)/5891 weeks
4442.03793 -3.57859 (444*2π)/5891 weeks
4453.55024 -3.61705 (445*2π)/5891 weeks
4465.0803 -1.69634 (446*2π)/5891 weeks
4473.14471 .49408 (447*2π)/5891 weeks
4481.24808 -.9156 (448*2π)/5891 weeks
4492.26293 -2.21542 (449*2π)/5891 weeks
4502.53244 -1.21503 (450*2π)/5891 weeks
4511.53777 -1.30983 (451*2π)/5891 weeks
4521.82253 -2.07816 (452*2π)/5891 weeks
4531.39481 -2.31964 (453*2π)/5891 weeks
4542.43642 -2.93041 (454*2π)/5891 weeks
4553.47188 -1.50703 (455*2π)/5891 weeks
4562.05933 .47394 (456*2π)/5891 weeks
457-1.37802 -1.38241 (457*2π)/5891 weeks
458.03989 -4.84557 (458*2π)/5891 weeks
4593.04987 -4.33466 (459*2π)/5891 weeks
4602.85632 -2.38473 (460*2π)/5891 weeks
4611.57251 -1.69012 (461*2π)/5891 weeks
462.60218 -3.85554 (462*2π)/5891 weeks
4632.85076 -5.05356 (463*2π)/5891 weeks
4644.96579 -3.45355 (464*2π)/5891 weeks
4653.69236 -.18224 (465*2π)/5891 weeks
466-.37389 -.92517 (466*2π)/5891 weeks
467.05632 -5.51842 (467*2π)/5891 weeks
4684.28757 -5.84135 (468*2π)/5891 weeks
4696.46787 -2.39955 (469*2π)/5891 weeks
4703.5263 1.5406 (470*2π)/5891 weeks
471-1.42495 -1.06767 (471*2π)/5891 weeks
472.38579 -6.05166 (472*2π)/5891 weeks
4735.75463 -5.05762 (473*2π)/5891 weeks
4745.82972 .52769 (474*2π)/5891 weeks
475.57785 2.36777 (475*2π)/5891 weeks
476-3.84223 -2.5385 (476*2π)/5891 weeks
477.04755 -7.24691 (477*2π)/5891 weeks
4784.48389 -6.10095 (478*2π)/5891 weeks
4794.75758 -1.68588 (479*2π)/5891 weeks
480.85627 -.84809 (480*2π)/5891 weeks
481-.31903 -4.59201 (481*2π)/5891 weeks
4822.89788 -6.68811 (482*2π)/5891 weeks
4835.63359 -3.90101 (483*2π)/5891 weeks
4843.81518 -1.01576 (484*2π)/5891 weeks
4851.68495 -1.99657 (485*2π)/5891 weeks
4861.72832 -3.22638 (486*2π)/5891 weeks
4873.0762 -3.13052 (487*2π)/5891 weeks
4881.69725 -1.91182 (488*2π)/5891 weeks
4892.03874 -3.94613 (489*2π)/5891 weeks
4903.22233 -1.98165 (490*2π)/5891 weeks
491.32126 -1.22517 (491*2π)/5891 weeks
492-1.00799 -4.6618 (492*2π)/5891 weeks
4932.19617 -6.72819 (493*2π)/5891 weeks
4945.33236 -3.72321 (494*2π)/5891 weeks
4953.10877 .43414 (495*2π)/5891 weeks
496-2.19641 -.8081 (496*2π)/5891 weeks
497-2.72541 -7.0854 (497*2π)/5891 weeks
4983.8683 -8.55385 (498*2π)/5891 weeks
4995.00565 -2.94757 (499*2π)/5891 weeks
5001.50839 -1.19999 (500*2π)/5891 weeks
501-2.18276 -3.27865 (501*2π)/5891 weeks
502-.88651 -8.63304 (502*2π)/5891 weeks
5034.29975 -8.70386 (503*2π)/5891 weeks
5046.62356 -4.23794 (504*2π)/5891 weeks
5051.63838 -.72921 (505*2π)/5891 weeks
506-.60162 -6.18036 (506*2π)/5891 weeks
5073.14568 -6.74357 (507*2π)/5891 weeks
5084.33014 -6.39496 (508*2π)/5891 weeks
5095.89594 -2.08035 (509*2π)/5891 weeks
510-.72347 .16454 (510*2π)/5891 weeks
511-3.40231 -7.17026 (511*2π)/5891 weeks
5123.03802 -11.37035 (512*2π)/5891 weeks
5137.9132 -6.07321 (513*2π)/5891 weeks
5143.62534 -1.13942 (514*2π)/5891 weeks
515.4466 -5.46051 (515*2π)/5891 weeks
5163.61726 -5.96377 (516*2π)/5891 weeks
5174.21614 -4.53631 (517*2π)/5891 weeks
5181.9878 -1.64482 (518*2π)/5891 weeks
519-1.42847 -5.49132 (519*2π)/5891 weeks
5201.94957 -9.26447 (520*2π)/5891 weeks
5215.45533 -6.64901 (521*2π)/5891 weeks
5224.5699 -3.38094 (522*2π)/5891 weeks
523.79576 -4.01357 (523*2π)/5891 weeks
5242.03701 -6.765 (524*2π)/5891 weeks
5253.25573 -4.99496 (525*2π)/5891 weeks
5261.3644 -4.27574 (526*2π)/5891 weeks
527.02166 -6.53422 (527*2π)/5891 weeks
5282.03269 -9.39509 (528*2π)/5891 weeks
5297.0672 -6.19335 (529*2π)/5891 weeks
5302.10857 -1.73431 (530*2π)/5891 weeks
531-1.32888 -5.70978 (531*2π)/5891 weeks
532.4456 -8.37614 (532*2π)/5891 weeks
5332.51781 -8.74221 (533*2π)/5891 weeks
5342.55044 -5.69321 (534*2π)/5891 weeks
535-.76421 -7.22142 (535*2π)/5891 weeks
536.23054 -11.23022 (536*2π)/5891 weeks
5374.77658 -12.20094 (537*2π)/5891 weeks
5388.03739 -9.80634 (538*2π)/5891 weeks
5396.3629 -3.14671 (539*2π)/5891 weeks
5401.25776 -5.06969 (540*2π)/5891 weeks
5412.00305 -7.09747 (541*2π)/5891 weeks
5422.31542 -8.13194 (542*2π)/5891 weeks
5432.12743 -6.09966 (543*2π)/5891 weeks
544-.39608 -9.2599 (544*2π)/5891 weeks
5454.41606 -10.53117 (545*2π)/5891 weeks
5462.09253 -6.61979 (546*2π)/5891 weeks
547.15144 -9.47733 (547*2π)/5891 weeks
5481.72799 -11.84303 (548*2π)/5891 weeks
5494.39502 -12.9372 (549*2π)/5891 weeks
5508.56712 -8.57737 (550*2π)/5891 weeks
5513.58247 -2.28275 (551*2π)/5891 weeks
552-7.66371 -5.63978 (552*2π)/5891 weeks
553-6.05261 -22.09852 (553*2π)/5891 weeks
55411.18429 -22.19646 (554*2π)/5891 weeks
55514.99175 -6.93673 (555*2π)/5891 weeks
5562.32724 .46714 (556*2π)/5891 weeks
557-8.19551 -10.3599 (557*2π)/5891 weeks
558-1.17909 -22.76256 (558*2π)/5891 weeks
5599.10234 -19.25911 (559*2π)/5891 weeks
56012.51013 -11.22376 (560*2π)/5891 weeks
5612.94057 -3.54228 (561*2π)/5891 weeks
562-3.26814 -11.62265 (562*2π)/5891 weeks
563-1.12651 -17.65437 (563*2π)/5891 weeks
5644.58455 -17.91339 (564*2π)/5891 weeks
565-.94063 -16.03874 (565*2π)/5891 weeks
5661.62775 -22.60627 (566*2π)/5891 weeks
5674.18585 -23.43387 (567*2π)/5891 weeks
5689.16073 -25.435 (568*2π)/5891 weeks
56915.00101 -21.97138 (569*2π)/5891 weeks
57014.52704 -10.5408 (570*2π)/5891 weeks
571-.10319 -10.79973 (571*2π)/5891 weeks
572-5.00623 -19.60305 (572*2π)/5891 weeks
573-3.61418 -34.21588 (573*2π)/5891 weeks
57413.71225 -43.65798 (574*2π)/5891 weeks
57533.50924 -28.58505 (575*2π)/5891 weeks
57622.41079 -1.28271 (576*2π)/5891 weeks
577-9.54237 -8.17246 (577*2π)/5891 weeks
578-13.16621 -36.39958 (578*2π)/5891 weeks
5795.90263 -55.5045 (579*2π)/5891 weeks
58037.57515 -41.47192 (580*2π)/5891 weeks
58110.74939 -3.84159 (581*2π)/5891 weeks
582-29.26584 -43.88763 (582*2π)/5891 weeks
583-1.31797 -98.26009 (583*2π)/5891 weeks
58464.43089 -90.36258 (584*2π)/5891 weeks
58561.57214 -27.29483 (585*2π)/5891 weeks
586-23.30719 -30.74349 (586*2π)/5891 weeks
587-47.54852 -183.8657 (587*2π)/5891 weeks



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