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Fourier Analysis of QID (ProShares UltraShort QQQ)


QID (ProShares UltraShort QQQ) appears to have interesting cyclic behaviour every 56 weeks (48.9484*sine), 40 weeks (45.0477*sine), and 43 weeks (36.2169*cosine).

QID (ProShares UltraShort QQQ) has an average price of 345.95 (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 3/13/2017 for QID (ProShares UltraShort QQQ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0345.9507   0 
1154.1273 381.1385 (1*2π)/558558 weeks
2-56.61163 171.0451 (2*2π)/558279 weeks
3-6.27509 20.17827 (3*2π)/558186 weeks
475.12391 40.80847 (4*2π)/558140 weeks
550.43755 106.8575 (5*2π)/558112 weeks
6-19.22251 87.35052 (6*2π)/55893 weeks
7-22.96214 22.11599 (7*2π)/55880 weeks
835.19001 15.64022 (8*2π)/55870 weeks
924.06373 58.46897 (9*2π)/55862 weeks
10-7.51914 48.94836 (10*2π)/55856 weeks
11-15.30419 20.23117 (11*2π)/55851 weeks
1211.63407 -2.2227 (12*2π)/55847 weeks
1336.21685 21.35297 (13*2π)/55843 weeks
1419.9023 45.04774 (14*2π)/55840 weeks
15-2.08573 38.51552 (15*2π)/55837 weeks
16-5.87443 21.96152 (16*2π)/55835 weeks
17-.60555 12.01122 (17*2π)/55833 weeks
1815.26327 11.07013 (18*2π)/55831 weeks
1915.43253 23.45143 (19*2π)/55829 weeks
208.89793 26.83587 (20*2π)/55828 weeks
214.19624 24.26335 (21*2π)/55827 weeks
22.36723 23.14882 (22*2π)/55825 weeks
231.0698 15.07997 (23*2π)/55824 weeks
242.60272 20.34378 (24*2π)/55823 weeks
25-2.67119 16.7468 (25*2π)/55822 weeks
26-2.55106 8.4794 (26*2π)/55821 weeks
2710.50235 5.89187 (27*2π)/55821 weeks
2811.97574 17.22929 (28*2π)/55820 weeks
294.65236 23.81303 (29*2π)/55819 weeks
30-8.23801 15.97782 (30*2π)/55819 weeks
31-2.369 .85231 (31*2π)/55818 weeks
3213.65646 4.23205 (32*2π)/55817 weeks
3313.92479 21.25223 (33*2π)/55817 weeks
34-4.47077 24.66636 (34*2π)/55816 weeks
35-8.61618 6.67091 (35*2π)/55816 weeks
363.72823 2.38046 (36*2π)/55816 weeks
378.96197 9.46439 (37*2π)/55815 weeks
384.11691 13.50151 (38*2π)/55815 weeks
391.45657 12.25021 (39*2π)/55814 weeks
40.22765 9.2617 (40*2π)/55814 weeks
413.70309 7.07913 (41*2π)/55814 weeks
422.62346 12.06814 (42*2π)/55813 weeks
43-.17255 7.66695 (43*2π)/55813 weeks
443.39644 7.54464 (44*2π)/55813 weeks
451.85174 7.7774 (45*2π)/55812 weeks
461.37819 7.01572 (46*2π)/55812 weeks
473.82538 3.13879 (47*2π)/55812 weeks
489.54971 8.03671 (48*2π)/55812 weeks
496.02315 12.11782 (49*2π)/55811 weeks
501.03707 12.53042 (50*2π)/55811 weeks
51-1.03207 8.3384 (51*2π)/55811 weeks
522.2303 5.81539 (52*2π)/55811 weeks
532.83873 9.098 (53*2π)/55811 weeks
54.48271 8.77757 (54*2π)/55810 weeks
55-1.40649 5.72146 (55*2π)/55810 weeks
562.99994 1.7709 (56*2π)/55810 weeks
577.07289 7.90641 (57*2π)/55810 weeks
581.23813 9.28501 (58*2π)/55810 weeks
59.12921 6.00511 (59*2π)/5589 weeks
602.32832 4.44306 (60*2π)/5589 weeks
613.57261 6.16461 (61*2π)/5589 weeks
62.88098 6.25174 (62*2π)/5589 weeks
632.61416 2.79759 (63*2π)/5589 weeks
645.74426 5.38275 (64*2π)/5589 weeks
654.16045 9.2909 (65*2π)/5589 weeks
66-1.10158 7.6147 (66*2π)/5588 weeks
67.34132 2.1161 (67*2π)/5588 weeks
684.58096 4.15292 (68*2π)/5588 weeks
694.00794 5.97281 (69*2π)/5588 weeks
70.82099 6.29782 (70*2π)/5588 weeks
713.37786 1.2277 (71*2π)/5588 weeks
728.32267 6.3707 (72*2π)/5588 weeks
732.71819 12.0062 (73*2π)/5588 weeks
74-3.81091 6.66665 (74*2π)/5588 weeks
75.7142 -.62442 (75*2π)/5587 weeks
766.5594 3.60991 (76*2π)/5587 weeks
773.80189 6.64914 (77*2π)/5587 weeks
782.41653 7.697 (78*2π)/5587 weeks
79-1.20411 4.01788 (79*2π)/5587 weeks
804.99891 1.30104 (80*2π)/5587 weeks
816.33691 7.31701 (81*2π)/5587 weeks
821.62236 9.95686 (82*2π)/5587 weeks
83-2.78554 5.73466 (83*2π)/5587 weeks
84.28922 1.4527 (84*2π)/5587 weeks
854.36935 2.15764 (85*2π)/5587 weeks
865.30769 7.79153 (86*2π)/5586 weeks
87-2.03358 8.38451 (87*2π)/5586 weeks
88-2.78026 1.35164 (88*2π)/5586 weeks
892.97412 -.61393 (89*2π)/5586 weeks
905.62506 3.91853 (90*2π)/5586 weeks
912.04246 7.06066 (91*2π)/5586 weeks
92-1.23739 4.39121 (92*2π)/5586 weeks
93.89804 1.04234 (93*2π)/5586 weeks
943.55266 2.76198 (94*2π)/5586 weeks
951.43362 3.82825 (95*2π)/5586 weeks
962.66431 1.99426 (96*2π)/5586 weeks
972.66411 3.75069 (97*2π)/5586 weeks
981.69636 2.83016 (98*2π)/5586 weeks
992.51311 1.23783 (99*2π)/5586 weeks
1005.62069 2.35306 (100*2π)/5586 weeks
1014.69199 6.33824 (101*2π)/5586 weeks
102.34103 5.92079 (102*2π)/5585 weeks
103-.11612 1.74042 (103*2π)/5585 weeks
1044.2411 1.10152 (104*2π)/5585 weeks
1055.24098 5.77213 (105*2π)/5585 weeks
106.60575 7.7293 (106*2π)/5585 weeks
107-4.05063 3.09952 (107*2π)/5585 weeks
108.61446 -2.52149 (108*2π)/5585 weeks
1096.3638 -.26327 (109*2π)/5585 weeks
1105.58458 5.84076 (110*2π)/5585 weeks
111-.40967 5.72514 (111*2π)/5585 weeks
112-.86445 -.18405 (112*2π)/5585 weeks
1135.18146 -.87113 (113*2π)/5585 weeks
1146.46282 4.12231 (114*2π)/5585 weeks
1152.91356 6.71141 (115*2π)/5585 weeks
116-1.07566 3.74898 (116*2π)/5585 weeks
1171.76643 -.29819 (117*2π)/5585 weeks
1185.31927 1.88141 (118*2π)/5585 weeks
1193.92866 4.94984 (119*2π)/5585 weeks
1201.13853 4.84037 (120*2π)/5585 weeks
121.93556 2.11853 (121*2π)/5585 weeks
1222.8304 2.36466 (122*2π)/5585 weeks
1233.46539 4.13821 (123*2π)/5585 weeks
124.43199 5.29521 (124*2π)/5585 weeks
125-1.52169 1.70913 (125*2π)/5584 weeks
1262.16467 -.50568 (126*2π)/5584 weeks
1273.67879 1.70255 (127*2π)/5584 weeks
1282.41283 3.08079 (128*2π)/5584 weeks
1291.48745 2.19956 (129*2π)/5584 weeks
1301.70856 2.21061 (130*2π)/5584 weeks
1311.86756 1.17927 (131*2π)/5584 weeks
1322.85021 1.61933 (132*2π)/5584 weeks
1331.69119 2.198 (133*2π)/5584 weeks
1341.83693 .08863 (134*2π)/5584 weeks
1354.84252 .25734 (135*2π)/5584 weeks
1364.76102 3.28695 (136*2π)/5584 weeks
1372.80786 3.71518 (137*2π)/5584 weeks
138.86538 2.41212 (138*2π)/5584 weeks
1392.95865 .65503 (139*2π)/5584 weeks
1403.52065 2.80754 (140*2π)/5584 weeks
1412.3432 2.05447 (141*2π)/5584 weeks
1423.09662 1.91329 (142*2π)/5584 weeks
1433.58906 2.20143 (143*2π)/5584 weeks
1442.14721 3.03433 (144*2π)/5584 weeks
1452.71973 .83289 (145*2π)/5584 weeks
1464.31482 2.65611 (146*2π)/5584 weeks
1472.29503 3.77539 (147*2π)/5584 weeks
1481.15404 2.38382 (148*2π)/5584 weeks
1492.50215 .96727 (149*2π)/5584 weeks
1503.81856 2.39982 (150*2π)/5584 weeks
1512.49319 3.30645 (151*2π)/5584 weeks
152.9636 2.55957 (152*2π)/5584 weeks
1532.25248 .08886 (153*2π)/5584 weeks
1544.16943 2.54762 (154*2π)/5584 weeks
1552.22168 2.91556 (155*2π)/5584 weeks
1561.55182 2.45842 (156*2π)/5584 weeks
1571.80338 1.07032 (157*2π)/5584 weeks
1582.91889 1.27382 (158*2π)/5584 weeks
1593.17596 1.92062 (159*2π)/5584 weeks
1602.74659 2.92791 (160*2π)/5583 weeks
1611.10637 1.44005 (161*2π)/5583 weeks
1623.34863 .75946 (162*2π)/5583 weeks
1633.14787 1.83967 (163*2π)/5583 weeks
1643.25238 1.87466 (164*2π)/5583 weeks
1652.95565 2.41785 (165*2π)/5583 weeks
1662.17022 2.15826 (166*2π)/5583 weeks
1673.36018 .91652 (167*2π)/5583 weeks
1684.28448 2.34281 (168*2π)/5583 weeks
1693.86527 4.11506 (169*2π)/5583 weeks
1701.31161 4.41079 (170*2π)/5583 weeks
171.47662 1.79464 (171*2π)/5583 weeks
1722.65537 1.21532 (172*2π)/5583 weeks
1732.67567 2.59299 (173*2π)/5583 weeks
1741.97354 2.98651 (174*2π)/5583 weeks
175.87086 2.24024 (175*2π)/5583 weeks
1761.16268 .86873 (176*2π)/5583 weeks
1773.01248 .50714 (177*2π)/5583 weeks
1783.85008 2.78116 (178*2π)/5583 weeks
1791.26596 4.00586 (179*2π)/5583 weeks
180-.21645 1.69177 (180*2π)/5583 weeks
1811.01007 -.79779 (181*2π)/5583 weeks
1824.18597 .03387 (182*2π)/5583 weeks
1833.71095 3.0976 (183*2π)/5583 weeks
184.96524 2.93009 (184*2π)/5583 weeks
185.80213 .3966 (185*2π)/5583 weeks
1863.288 .03199 (186*2π)/5583 weeks
1874.33433 2.34 (187*2π)/5583 weeks
1882.01375 3.50939 (188*2π)/5583 weeks
1891.07327 2.21347 (189*2π)/5583 weeks
1901.46105 .81438 (190*2π)/5583 weeks
1912.76343 1.75278 (191*2π)/5583 weeks
1921.36709 2.6333 (192*2π)/5583 weeks
193.47808 1.24838 (193*2π)/5583 weeks
1941.44828 -.29528 (194*2π)/5583 weeks
1953.13611 .20239 (195*2π)/5583 weeks
1963.49624 .97793 (196*2π)/5583 weeks
1973.88305 3.23856 (197*2π)/5583 weeks
198-.00884 3.73699 (198*2π)/5583 weeks
199-.064 .09787 (199*2π)/5583 weeks
2001.96367 -.93895 (200*2π)/5583 weeks
2014.08424 .32188 (201*2π)/5583 weeks
2023.33853 2.25286 (202*2π)/5583 weeks
2032.08239 2.09952 (203*2π)/5583 weeks
2041.38246 1.35503 (204*2π)/5583 weeks
2053.3743 .7496 (205*2π)/5583 weeks
2062.45799 3.07864 (206*2π)/5583 weeks
2071.22029 2.37433 (207*2π)/5583 weeks
208-.02909 1.45811 (208*2π)/5583 weeks
2091.31778 -1.04701 (209*2π)/5583 weeks
2104.50148 .65777 (210*2π)/5583 weeks
2112.77041 3.58712 (211*2π)/5583 weeks
212-.38686 2.5454 (212*2π)/5583 weeks
213.60576 -.69715 (213*2π)/5583 weeks
2142.93782 .2855 (214*2π)/5583 weeks
2152.86384 1.75475 (215*2π)/5583 weeks
2161.05844 2.31804 (216*2π)/5583 weeks
217.19427 -.30677 (217*2π)/5583 weeks
2182.982 -.55977 (218*2π)/5583 weeks
2193.57382 1.65571 (219*2π)/5583 weeks
2201.4918 2.68374 (220*2π)/5583 weeks
221.49898 .66913 (221*2π)/5583 weeks
2221.90945 -.094 (222*2π)/5583 weeks
2232.19486 .60612 (223*2π)/5583 weeks
2242.38837 .53374 (224*2π)/5582 weeks
2252.67881 1.15095 (225*2π)/5582 weeks
2262.56354 1.28058 (226*2π)/5582 weeks
2272.47774 2.62352 (227*2π)/5582 weeks
228.01842 2.10422 (228*2π)/5582 weeks
229.69501 .0634 (229*2π)/5582 weeks
2302.15453 .16973 (230*2π)/5582 weeks
2311.692 2.21155 (231*2π)/5582 weeks
232-.53878 .8578 (232*2π)/5582 weeks
233.33505 -1.15322 (233*2π)/5582 weeks
2342.27552 -1.61131 (234*2π)/5582 weeks
2354.10724 .37442 (235*2π)/5582 weeks
2361.84827 2.58018 (236*2π)/5582 weeks
237-.40104 .3305 (237*2π)/5582 weeks
2381.53689 -2.3618 (238*2π)/5582 weeks
2394.8305 -.5273 (239*2π)/5582 weeks
2403.33028 2.8713 (240*2π)/5582 weeks
241.29269 2.34965 (241*2π)/5582 weeks
242-.58787 -.6026 (242*2π)/5582 weeks
2433.02539 -2.15507 (243*2π)/5582 weeks
2443.83413 .94031 (244*2π)/5582 weeks
2452.17847 2.12799 (245*2π)/5582 weeks
246.2398 .99503 (246*2π)/5582 weeks
2471.09066 -.46315 (247*2π)/5582 weeks
2481.86799 -.53978 (248*2π)/5582 weeks
2492.68353 .24698 (249*2π)/5582 weeks
2501.31046 1.14547 (250*2π)/5582 weeks
251.6792 -.79564 (251*2π)/5582 weeks
2522.15544 -1.46563 (252*2π)/5582 weeks
2533.95494 -.1963 (253*2π)/5582 weeks
2542.8735 2.31797 (254*2π)/5582 weeks
255-.2262 1.60776 (255*2π)/5582 weeks
256-.24544 -1.35671 (256*2π)/5582 weeks
2571.99219 -2.65402 (257*2π)/5582 weeks
2584.84111 -1.09965 (258*2π)/5582 weeks
2593.71928 2.39477 (259*2π)/5582 weeks
260-.10399 2.4794 (260*2π)/5582 weeks
261-.91741 -1.81289 (261*2π)/5582 weeks
2622.73876 -2.65804 (262*2π)/5582 weeks
2633.79466 -.35512 (263*2π)/5582 weeks
2642.26533 1.3591 (264*2π)/5582 weeks
265.20227 -.41187 (265*2π)/5582 weeks
2661.87786 -2.69145 (266*2π)/5582 weeks
2674.39975 -.87645 (267*2π)/5582 weeks
2682.96621 .93969 (268*2π)/5582 weeks
2691.29433 .13701 (269*2π)/5582 weeks
2701.8422 -1.89881 (270*2π)/5582 weeks
2713.85757 -2.14441 (271*2π)/5582 weeks
2725.56072 .5131 (272*2π)/5582 weeks
2732.39259 2.96858 (273*2π)/5582 weeks
274.4573 -.22748 (274*2π)/5582 weeks
2752.67475 -1.42419 (275*2π)/5582 weeks
2764.23825 -.56977 (276*2π)/5582 weeks
2773.87764 1.44085 (277*2π)/5582 weeks
2781.77251 2.54521 (278*2π)/5582 weeks
279-.66596   (279*2π)/5582 weeks
2801.77251 -2.54521 (280*2π)/5582 weeks
2813.87764 -1.44085 (281*2π)/5582 weeks
2824.23825 .56977 (282*2π)/5582 weeks
2832.67475 1.42419 (283*2π)/5582 weeks
284.4573 .22748 (284*2π)/5582 weeks
2852.39259 -2.96858 (285*2π)/5582 weeks
2865.56072 -.5131 (286*2π)/5582 weeks
2873.85757 2.14441 (287*2π)/5582 weeks
2881.8422 1.89881 (288*2π)/5582 weeks
2891.29433 -.13701 (289*2π)/5582 weeks
2902.96621 -.93969 (290*2π)/5582 weeks
2914.39975 .87645 (291*2π)/5582 weeks
2921.87786 2.69145 (292*2π)/5582 weeks
293.20227 .41187 (293*2π)/5582 weeks
2942.26533 -1.3591 (294*2π)/5582 weeks
2953.79466 .35512 (295*2π)/5582 weeks
2962.73876 2.65804 (296*2π)/5582 weeks
297-.91741 1.81289 (297*2π)/5582 weeks
298-.10399 -2.4794 (298*2π)/5582 weeks
2993.71928 -2.39477 (299*2π)/5582 weeks
3004.84111 1.09965 (300*2π)/5582 weeks
3011.99219 2.65402 (301*2π)/5582 weeks
302-.24544 1.35671 (302*2π)/5582 weeks
303-.2262 -1.60776 (303*2π)/5582 weeks
3042.8735 -2.31797 (304*2π)/5582 weeks
3053.95494 .1963 (305*2π)/5582 weeks
3062.15544 1.46563 (306*2π)/5582 weeks
307.6792 .79564 (307*2π)/5582 weeks
3081.31046 -1.14547 (308*2π)/5582 weeks
3092.68353 -.24698 (309*2π)/5582 weeks
3101.86799 .53978 (310*2π)/5582 weeks
3111.09066 .46315 (311*2π)/5582 weeks
312.2398 -.99503 (312*2π)/5582 weeks
3132.17847 -2.12799 (313*2π)/5582 weeks
3143.83413 -.94031 (314*2π)/5582 weeks
3153.02539 2.15507 (315*2π)/5582 weeks
316-.58787 .6026 (316*2π)/5582 weeks
317.29269 -2.34965 (317*2π)/5582 weeks
3183.33028 -2.8713 (318*2π)/5582 weeks
3194.8305 .5273 (319*2π)/5582 weeks
3201.53689 2.3618 (320*2π)/5582 weeks
321-.40104 -.3305 (321*2π)/5582 weeks
3221.84827 -2.58018 (322*2π)/5582 weeks
3234.10724 -.37442 (323*2π)/5582 weeks
3242.27552 1.61131 (324*2π)/5582 weeks
325.33505 1.15322 (325*2π)/5582 weeks
326-.53878 -.8578 (326*2π)/5582 weeks
3271.692 -2.21155 (327*2π)/5582 weeks
3282.15453 -.16973 (328*2π)/5582 weeks
329.69501 -.0634 (329*2π)/5582 weeks
330.01842 -2.10422 (330*2π)/5582 weeks
3312.47774 -2.62352 (331*2π)/5582 weeks
3322.56354 -1.28058 (332*2π)/5582 weeks
3332.67881 -1.15095 (333*2π)/5582 weeks
3342.38837 -.53374 (334*2π)/5582 weeks
3352.19486 -.60612 (335*2π)/5582 weeks
3361.90945 .094 (336*2π)/5582 weeks
337.49898 -.66913 (337*2π)/5582 weeks
3381.4918 -2.68374 (338*2π)/5582 weeks
3393.57382 -1.65571 (339*2π)/5582 weeks
3402.982 .55977 (340*2π)/5582 weeks
341.19427 .30677 (341*2π)/5582 weeks
3421.05844 -2.31804 (342*2π)/5582 weeks
3432.86384 -1.75475 (343*2π)/5582 weeks
3442.93782 -.2855 (344*2π)/5582 weeks
345.60576 .69715 (345*2π)/5582 weeks
346-.38686 -2.5454 (346*2π)/5582 weeks
3472.77041 -3.58712 (347*2π)/5582 weeks
3484.50148 -.65777 (348*2π)/5582 weeks
3491.31778 1.04701 (349*2π)/5582 weeks
350-.02909 -1.45811 (350*2π)/5582 weeks
3511.22029 -2.37433 (351*2π)/5582 weeks
3522.45799 -3.07864 (352*2π)/5582 weeks
3533.3743 -.7496 (353*2π)/5582 weeks
3541.38246 -1.35503 (354*2π)/5582 weeks
3552.08239 -2.09952 (355*2π)/5582 weeks
3563.33853 -2.25286 (356*2π)/5582 weeks
3574.08424 -.32188 (357*2π)/5582 weeks
3581.96367 .93895 (358*2π)/5582 weeks
359-.064 -.09787 (359*2π)/5582 weeks
360-.00884 -3.73699 (360*2π)/5582 weeks
3613.88305 -3.23856 (361*2π)/5582 weeks
3623.49624 -.97793 (362*2π)/5582 weeks
3633.13611 -.20239 (363*2π)/5582 weeks
3641.44828 .29528 (364*2π)/5582 weeks
365.47808 -1.24838 (365*2π)/5582 weeks
3661.36709 -2.6333 (366*2π)/5582 weeks
3672.76343 -1.75278 (367*2π)/5582 weeks
3681.46105 -.81438 (368*2π)/5582 weeks
3691.07327 -2.21347 (369*2π)/5582 weeks
3702.01375 -3.50939 (370*2π)/5582 weeks
3714.33433 -2.34 (371*2π)/5582 weeks
3723.288 -.03199 (372*2π)/5582 weeks
373.80213 -.3966 (373*2π)/5581 weeks
374.96524 -2.93009 (374*2π)/5581 weeks
3753.71095 -3.0976 (375*2π)/5581 weeks
3764.18597 -.03387 (376*2π)/5581 weeks
3771.01007 .79779 (377*2π)/5581 weeks
378-.21645 -1.69177 (378*2π)/5581 weeks
3791.26596 -4.00586 (379*2π)/5581 weeks
3803.85008 -2.78116 (380*2π)/5581 weeks
3813.01248 -.50714 (381*2π)/5581 weeks
3821.16268 -.86873 (382*2π)/5581 weeks
383.87086 -2.24024 (383*2π)/5581 weeks
3841.97354 -2.98651 (384*2π)/5581 weeks
3852.67567 -2.59299 (385*2π)/5581 weeks
3862.65537 -1.21532 (386*2π)/5581 weeks
387.47662 -1.79464 (387*2π)/5581 weeks
3881.31161 -4.41079 (388*2π)/5581 weeks
3893.86527 -4.11506 (389*2π)/5581 weeks
3904.28448 -2.34281 (390*2π)/5581 weeks
3913.36018 -.91652 (391*2π)/5581 weeks
3922.17022 -2.15826 (392*2π)/5581 weeks
3932.95565 -2.41785 (393*2π)/5581 weeks
3943.25238 -1.87466 (394*2π)/5581 weeks
3953.14787 -1.83967 (395*2π)/5581 weeks
3963.34863 -.75946 (396*2π)/5581 weeks
3971.10637 -1.44005 (397*2π)/5581 weeks
3982.74659 -2.92791 (398*2π)/5581 weeks
3993.17596 -1.92062 (399*2π)/5581 weeks
4002.91889 -1.27382 (400*2π)/5581 weeks
4011.80338 -1.07032 (401*2π)/5581 weeks
4021.55182 -2.45842 (402*2π)/5581 weeks
4032.22168 -2.91556 (403*2π)/5581 weeks
4044.16943 -2.54762 (404*2π)/5581 weeks
4052.25248 -.08886 (405*2π)/5581 weeks
406.9636 -2.55957 (406*2π)/5581 weeks
4072.49319 -3.30645 (407*2π)/5581 weeks
4083.81856 -2.39982 (408*2π)/5581 weeks
4092.50215 -.96727 (409*2π)/5581 weeks
4101.15404 -2.38382 (410*2π)/5581 weeks
4112.29503 -3.77539 (411*2π)/5581 weeks
4124.31482 -2.65611 (412*2π)/5581 weeks
4132.71973 -.83289 (413*2π)/5581 weeks
4142.14721 -3.03433 (414*2π)/5581 weeks
4153.58906 -2.20143 (415*2π)/5581 weeks
4163.09662 -1.91329 (416*2π)/5581 weeks
4172.3432 -2.05447 (417*2π)/5581 weeks
4183.52065 -2.80754 (418*2π)/5581 weeks
4192.95865 -.65503 (419*2π)/5581 weeks
420.86538 -2.41212 (420*2π)/5581 weeks
4212.80786 -3.71518 (421*2π)/5581 weeks
4224.76102 -3.28695 (422*2π)/5581 weeks
4234.84252 -.25734 (423*2π)/5581 weeks
4241.83693 -.08863 (424*2π)/5581 weeks
4251.69119 -2.198 (425*2π)/5581 weeks
4262.85021 -1.61933 (426*2π)/5581 weeks
4271.86756 -1.17927 (427*2π)/5581 weeks
4281.70856 -2.21061 (428*2π)/5581 weeks
4291.48745 -2.19956 (429*2π)/5581 weeks
4302.41283 -3.08079 (430*2π)/5581 weeks
4313.67879 -1.70255 (431*2π)/5581 weeks
4322.16467 .50568 (432*2π)/5581 weeks
433-1.52169 -1.70913 (433*2π)/5581 weeks
434.43199 -5.29521 (434*2π)/5581 weeks
4353.46539 -4.13821 (435*2π)/5581 weeks
4362.8304 -2.36466 (436*2π)/5581 weeks
437.93556 -2.11853 (437*2π)/5581 weeks
4381.13853 -4.84037 (438*2π)/5581 weeks
4393.92866 -4.94984 (439*2π)/5581 weeks
4405.31927 -1.88141 (440*2π)/5581 weeks
4411.76643 .29819 (441*2π)/5581 weeks
442-1.07566 -3.74898 (442*2π)/5581 weeks
4432.91356 -6.71141 (443*2π)/5581 weeks
4446.46282 -4.12231 (444*2π)/5581 weeks
4455.18146 .87113 (445*2π)/5581 weeks
446-.86445 .18405 (446*2π)/5581 weeks
447-.40967 -5.72514 (447*2π)/5581 weeks
4485.58458 -5.84076 (448*2π)/5581 weeks
4496.3638 .26327 (449*2π)/5581 weeks
450.61446 2.52149 (450*2π)/5581 weeks
451-4.05063 -3.09952 (451*2π)/5581 weeks
452.60575 -7.7293 (452*2π)/5581 weeks
4535.24098 -5.77213 (453*2π)/5581 weeks
4544.2411 -1.10152 (454*2π)/5581 weeks
455-.11612 -1.74042 (455*2π)/5581 weeks
456.34103 -5.92079 (456*2π)/5581 weeks
4574.69199 -6.33824 (457*2π)/5581 weeks
4585.62069 -2.35306 (458*2π)/5581 weeks
4592.51311 -1.23783 (459*2π)/5581 weeks
4601.69636 -2.83016 (460*2π)/5581 weeks
4612.66411 -3.75069 (461*2π)/5581 weeks
4622.66431 -1.99426 (462*2π)/5581 weeks
4631.43362 -3.82825 (463*2π)/5581 weeks
4643.55266 -2.76198 (464*2π)/5581 weeks
465.89804 -1.04234 (465*2π)/5581 weeks
466-1.23739 -4.39121 (466*2π)/5581 weeks
4672.04246 -7.06066 (467*2π)/5581 weeks
4685.62506 -3.91853 (468*2π)/5581 weeks
4692.97412 .61393 (469*2π)/5581 weeks
470-2.78026 -1.35164 (470*2π)/5581 weeks
471-2.03358 -8.38451 (471*2π)/5581 weeks
4725.30769 -7.79153 (472*2π)/5581 weeks
4734.36935 -2.15764 (473*2π)/5581 weeks
474.28922 -1.4527 (474*2π)/5581 weeks
475-2.78554 -5.73466 (475*2π)/5581 weeks
4761.62236 -9.95686 (476*2π)/5581 weeks
4776.33691 -7.31701 (477*2π)/5581 weeks
4784.99891 -1.30104 (478*2π)/5581 weeks
479-1.20411 -4.01788 (479*2π)/5581 weeks
4802.41653 -7.697 (480*2π)/5581 weeks
4813.80189 -6.64914 (481*2π)/5581 weeks
4826.5594 -3.60991 (482*2π)/5581 weeks
483.7142 .62442 (483*2π)/5581 weeks
484-3.81091 -6.66665 (484*2π)/5581 weeks
4852.71819 -12.0062 (485*2π)/5581 weeks
4868.32267 -6.3707 (486*2π)/5581 weeks
4873.37786 -1.2277 (487*2π)/5581 weeks
488.82099 -6.29782 (488*2π)/5581 weeks
4894.00794 -5.97281 (489*2π)/5581 weeks
4904.58096 -4.15292 (490*2π)/5581 weeks
491.34132 -2.1161 (491*2π)/5581 weeks
492-1.10158 -7.6147 (492*2π)/5581 weeks
4934.16045 -9.2909 (493*2π)/5581 weeks
4945.74426 -5.38275 (494*2π)/5581 weeks
4952.61416 -2.79759 (495*2π)/5581 weeks
496.88098 -6.25174 (496*2π)/5581 weeks
4973.57261 -6.16461 (497*2π)/5581 weeks
4982.32832 -4.44306 (498*2π)/5581 weeks
499.12921 -6.00511 (499*2π)/5581 weeks
5001.23813 -9.28501 (500*2π)/5581 weeks
5017.07289 -7.90641 (501*2π)/5581 weeks
5022.99994 -1.7709 (502*2π)/5581 weeks
503-1.40649 -5.72146 (503*2π)/5581 weeks
504.48271 -8.77757 (504*2π)/5581 weeks
5052.83873 -9.098 (505*2π)/5581 weeks
5062.2303 -5.81539 (506*2π)/5581 weeks
507-1.03207 -8.3384 (507*2π)/5581 weeks
5081.03707 -12.53042 (508*2π)/5581 weeks
5096.02315 -12.11782 (509*2π)/5581 weeks
5109.54971 -8.03671 (510*2π)/5581 weeks
5113.82538 -3.13879 (511*2π)/5581 weeks
5121.37819 -7.01572 (512*2π)/5581 weeks
5131.85174 -7.7774 (513*2π)/5581 weeks
5143.39644 -7.54464 (514*2π)/5581 weeks
515-.17255 -7.66695 (515*2π)/5581 weeks
5162.62346 -12.06814 (516*2π)/5581 weeks
5173.70309 -7.07913 (517*2π)/5581 weeks
518.22765 -9.2617 (518*2π)/5581 weeks
5191.45657 -12.25021 (519*2π)/5581 weeks
5204.11691 -13.50151 (520*2π)/5581 weeks
5218.96197 -9.46439 (521*2π)/5581 weeks
5223.72823 -2.38046 (522*2π)/5581 weeks
523-8.61618 -6.67091 (523*2π)/5581 weeks
524-4.47077 -24.66636 (524*2π)/5581 weeks
52513.92479 -21.25223 (525*2π)/5581 weeks
52613.65646 -4.23205 (526*2π)/5581 weeks
527-2.369 -.85231 (527*2π)/5581 weeks
528-8.23801 -15.97782 (528*2π)/5581 weeks
5294.65236 -23.81303 (529*2π)/5581 weeks
53011.97574 -17.22929 (530*2π)/5581 weeks
53110.50235 -5.89187 (531*2π)/5581 weeks
532-2.55106 -8.4794 (532*2π)/5581 weeks
533-2.67119 -16.7468 (533*2π)/5581 weeks
5342.60272 -20.34378 (534*2π)/5581 weeks
5351.0698 -15.07997 (535*2π)/5581 weeks
536.36723 -23.14882 (536*2π)/5581 weeks
5374.19624 -24.26335 (537*2π)/5581 weeks
5388.89793 -26.83587 (538*2π)/5581 weeks
53915.43253 -23.45143 (539*2π)/5581 weeks
54015.26327 -11.07013 (540*2π)/5581 weeks
541-.60555 -12.01122 (541*2π)/5581 weeks
542-5.87443 -21.96152 (542*2π)/5581 weeks
543-2.08573 -38.51552 (543*2π)/5581 weeks
54419.9023 -45.04774 (544*2π)/5581 weeks
54536.21685 -21.35297 (545*2π)/5581 weeks
54611.63407 2.2227 (546*2π)/5581 weeks
547-15.30419 -20.23117 (547*2π)/5581 weeks
548-7.51914 -48.94836 (548*2π)/5581 weeks
54924.06373 -58.46897 (549*2π)/5581 weeks
55035.19001 -15.64022 (550*2π)/5581 weeks
551-22.96214 -22.11599 (551*2π)/5581 weeks
552-19.22251 -87.35052 (552*2π)/5581 weeks
55350.43755 -106.8575 (553*2π)/5581 weeks
55475.12391 -40.80847 (554*2π)/5581 weeks
555-6.27509 -20.17827 (555*2π)/5581 weeks
556-56.61163 -171.0451 (556*2π)/5581 weeks

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