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Fourier Analysis of QID (ProShares UltraShort QQQ ETF)


QID (ProShares UltraShort QQQ ETF) appears to have interesting cyclic behaviour every 58 weeks (53.6294*sine), 38 weeks (43.3576*sine), and 41 weeks (37.2922*sine).

QID (ProShares UltraShort QQQ ETF) has an average price of 335.68 (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 7/17/2017 for QID (ProShares UltraShort QQQ ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0335.6844   0 
1162.9284 373.6923 (1*2π)/576576 weeks
2-51.42603 178.6714 (2*2π)/576288 weeks
3-16.65701 25.83205 (3*2π)/576192 weeks
467.40705 32.29792 (4*2π)/576144 weeks
559.40418 97.77399 (5*2π)/576115 weeks
6-9.32969 94.73006 (6*2π)/57696 weeks
7-28.24873 34.92375 (7*2π)/57682 weeks
821.84259 6.18516 (8*2π)/57672 weeks
933.48111 50.09638 (9*2π)/57664 weeks
10-.25219 53.62944 (10*2π)/57658 weeks
11-15.19366 30.32836 (11*2π)/57652 weeks
12-2.74624 1.78006 (12*2π)/57648 weeks
1330.33896 8.05475 (13*2π)/57644 weeks
1429.63008 37.29216 (14*2π)/57641 weeks
156.18997 43.35762 (15*2π)/57638 weeks
16-5.9926 29.31636 (16*2π)/57636 weeks
17-2.97184 16.76566 (17*2π)/57634 weeks
185.52413 7.70255 (18*2π)/57632 weeks
1917.26528 16.47844 (19*2π)/57630 weeks
2012.63442 24.55701 (20*2π)/57629 weeks
216.27064 25.63629 (21*2π)/57627 weeks
223.64627 23.26454 (22*2π)/57626 weeks
23-1.08016 20.68761 (23*2π)/57625 weeks
243.49784 14.82286 (24*2π)/57624 weeks
25.87599 19.51093 (25*2π)/57623 weeks
26-3.13969 14.95174 (26*2π)/57622 weeks
27-1.54072 6.60551 (27*2π)/57621 weeks
2811.39397 7.19943 (28*2π)/57621 weeks
2911.16295 17.49213 (29*2π)/57620 weeks
303.67291 23.37225 (30*2π)/57619 weeks
31-8.08259 15.01148 (31*2π)/57619 weeks
32-2.26085 .83774 (32*2π)/57618 weeks
3312.91934 3.7611 (33*2π)/57617 weeks
3414.21995 19.72977 (34*2π)/57617 weeks
35-2.51425 24.8476 (35*2π)/57616 weeks
36-9.34745 8.37619 (36*2π)/57616 weeks
372.03829 1.80035 (37*2π)/57616 weeks
388.59748 7.51986 (38*2π)/57615 weeks
395.09266 13.16634 (39*2π)/57615 weeks
401.97609 12.17868 (40*2π)/57614 weeks
41.16252 9.92129 (41*2π)/57614 weeks
421.8777 6.82688 (42*2π)/57614 weeks
434.62987 10.58044 (43*2π)/57613 weeks
44-.39092 9.48195 (44*2π)/57613 weeks
452.24098 6.23803 (45*2π)/57613 weeks
462.27165 8.27424 (46*2π)/57613 weeks
472.02863 7.23908 (47*2π)/57612 weeks
481.4593 4.8006 (48*2π)/57612 weeks
497.30045 3.60475 (49*2π)/57612 weeks
507.66241 10.50831 (50*2π)/57612 weeks
514.16674 12.73758 (51*2π)/57611 weeks
52-.23337 10.84815 (52*2π)/57611 weeks
53-.31619 6.61247 (53*2π)/57611 weeks
543.33433 6.35156 (54*2π)/57611 weeks
551.86572 8.92044 (55*2π)/57610 weeks
56-.2017 8.15608 (56*2π)/57610 weeks
57-1.2077 4.3698 (57*2π)/57610 weeks
584.2954 1.99249 (58*2π)/57610 weeks
596.09885 8.80564 (59*2π)/57610 weeks
60.80524 8.65907 (60*2π)/57610 weeks
61.18211 5.57091 (61*2π)/5769 weeks
622.38638 4.34448 (62*2π)/5769 weeks
633.44823 6.0621 (63*2π)/5769 weeks
64.86425 6.08689 (64*2π)/5769 weeks
652.36249 2.78174 (65*2π)/5769 weeks
665.48818 5.01992 (66*2π)/5769 weeks
674.4262 8.7092 (67*2π)/5769 weeks
68-.66502 8.01848 (68*2π)/5768 weeks
69-.45411 2.7094 (69*2π)/5768 weeks
704.33998 3.35635 (70*2π)/5768 weeks
713.96721 5.45377 (71*2π)/5768 weeks
721.86393 6.75655 (72*2π)/5768 weeks
731.3907 1.95919 (73*2π)/5768 weeks
747.64049 3.77499 (74*2π)/5768 weeks
755.51729 10.6684 (75*2π)/5768 weeks
76-2.3658 9.35395 (76*2π)/5768 weeks
77-2.60984 1.33754 (77*2π)/5767 weeks
785.07936 .77637 (78*2π)/5767 weeks
795.2206 6.19776 (79*2π)/5767 weeks
803.40189 6.54256 (80*2π)/5767 weeks
81.08315 7.03704 (81*2π)/5767 weeks
82.62821 1.17974 (82*2π)/5767 weeks
836.59522 3.53365 (83*2π)/5767 weeks
844.82451 8.58371 (84*2π)/5767 weeks
85-.47329 9.08889 (85*2π)/5767 weeks
86-2.37531 3.65181 (86*2π)/5767 weeks
871.40062 1.22654 (87*2π)/5767 weeks
885.07464 2.94376 (88*2π)/5767 weeks
893.90154 8.76556 (89*2π)/5766 weeks
90-2.91178 7.04118 (90*2π)/5766 weeks
91-2.01072 .59253 (91*2π)/5766 weeks
923.57398 -.24012 (92*2π)/5766 weeks
935.38643 4.24479 (93*2π)/5766 weeks
941.71714 6.80223 (94*2π)/5766 weeks
95-1.21375 4.13481 (95*2π)/5766 weeks
96.86229 1.03773 (96*2π)/5766 weeks
973.42395 2.58476 (97*2π)/5766 weeks
981.53223 3.82293 (98*2π)/5766 weeks
992.35516 1.86382 (99*2π)/5766 weeks
1002.81643 3.56458 (100*2π)/5766 weeks
1011.6522 2.95136 (101*2π)/5766 weeks
1022.03272 1.50628 (102*2π)/5766 weeks
1034.90759 1.5752 (103*2π)/5766 weeks
1045.29362 5.29831 (104*2π)/5766 weeks
1051.3076 6.5205 (105*2π)/5765 weeks
106-.62585 3.12357 (106*2π)/5765 weeks
1072.65455 .5599 (107*2π)/5765 weeks
1085.61171 3.68086 (108*2π)/5765 weeks
1092.67828 7.33351 (109*2π)/5765 weeks
110-2.4756 6.05375 (110*2π)/5765 weeks
111-2.41225 -.98009 (111*2π)/5765 weeks
1123.63071 -2.14948 (112*2π)/5765 weeks
1136.88517 2.70523 (113*2π)/5765 weeks
1142.89025 6.7975 (114*2π)/5765 weeks
115-1.52939 3.43335 (115*2π)/5765 weeks
1161.24733 -1.59624 (116*2π)/5765 weeks
1176.21164 .68918 (117*2π)/5765 weeks
1185.43898 5.1545 (118*2π)/5765 weeks
1191.43507 6.40444 (119*2π)/5765 weeks
120-1.00243 2.29309 (120*2π)/5765 weeks
1212.7485 -.21828 (121*2π)/5765 weeks
1225.26515 2.61586 (122*2π)/5765 weeks
1233.44202 4.97222 (123*2π)/5765 weeks
124.86965 4.40703 (124*2π)/5765 weeks
1251.14553 1.88923 (125*2π)/5765 weeks
1262.78538 2.34883 (126*2π)/5765 weeks
1273.30756 4.10126 (127*2π)/5765 weeks
128.41244 5.12208 (128*2π)/5765 weeks
129-1.48975 1.79449 (129*2π)/5764 weeks
1301.86227 -.57396 (130*2π)/5764 weeks
1313.52674 1.45847 (131*2π)/5764 weeks
1322.51206 2.99539 (132*2π)/5764 weeks
1331.42021 2.36189 (133*2π)/5764 weeks
1341.84774 2.13088 (134*2π)/5764 weeks
1351.60869 1.30237 (135*2π)/5764 weeks
1362.63491 1.30415 (136*2π)/5764 weeks
1372.15151 2.28645 (137*2π)/5764 weeks
1381.35453 .6885 (138*2π)/5764 weeks
1393.67158 -.44135 (139*2π)/5764 weeks
1405.13297 2.19904 (140*2π)/5764 weeks
1413.25903 3.68277 (141*2π)/5764 weeks
1421.58658 3.4932 (142*2π)/5764 weeks
1431.58391 .81425 (143*2π)/5764 weeks
1443.84231 1.51753 (144*2π)/5764 weeks
1452.47214 2.66914 (145*2π)/5764 weeks
1462.57236 1.66658 (146*2π)/5764 weeks
1472.93727 1.91248 (147*2π)/5764 weeks
1483.32465 2.82942 (148*2π)/5764 weeks
1491.61247 2.26556 (149*2π)/5764 weeks
1503.55201 1.06774 (150*2π)/5764 weeks
1513.91845 3.31143 (151*2π)/5764 weeks
1521.85892 3.41908 (152*2π)/5764 weeks
1531.18257 1.81499 (153*2π)/5764 weeks
1542.82317 .97417 (154*2π)/5764 weeks
1553.60666 2.6668 (155*2π)/5764 weeks
1562.27349 3.23839 (156*2π)/5764 weeks
157.83636 2.27713 (157*2π)/5764 weeks
1582.42579 .05635 (158*2π)/5764 weeks
1594.01996 2.55706 (159*2π)/5764 weeks
1602.1858 2.84624 (160*2π)/5764 weeks
1611.5426 2.44577 (161*2π)/5764 weeks
1621.66214 1.10991 (162*2π)/5764 weeks
1632.79035 1.17467 (163*2π)/5764 weeks
1643.11699 1.7838 (164*2π)/5764 weeks
1652.94096 2.67337 (165*2π)/5763 weeks
1661.08911 1.97385 (166*2π)/5763 weeks
1672.81299 .41989 (167*2π)/5763 weeks
1683.18515 1.73144 (168*2π)/5763 weeks
1693.08798 1.73664 (169*2π)/5763 weeks
1703.10945 2.28394 (170*2π)/5763 weeks
1712.47261 2.37056 (171*2π)/5763 weeks
1722.41842 1.0003 (172*2π)/5763 weeks
1734.06083 1.66475 (173*2π)/5763 weeks
1744.20116 3.08187 (174*2π)/5763 weeks
1752.52852 4.53779 (175*2π)/5763 weeks
176.33327 3.18536 (176*2π)/5763 weeks
1771.36478 .96961 (177*2π)/5763 weeks
1782.88618 1.89519 (178*2π)/5763 weeks
1792.35282 2.65394 (179*2π)/5763 weeks
1801.45559 2.88786 (180*2π)/5763 weeks
181.8293 1.7509 (181*2π)/5763 weeks
1821.53916 .50288 (182*2π)/5763 weeks
1833.42568 .86974 (183*2π)/5763 weeks
1843.35909 3.27738 (184*2π)/5763 weeks
185.62335 3.5676 (185*2π)/5763 weeks
186-.18778 1.25435 (186*2π)/5763 weeks
1871.47465 -.93836 (187*2π)/5763 weeks
1884.25542 .40332 (188*2π)/5763 weeks
1893.38502 3.13786 (189*2π)/5763 weeks
190.86806 2.70755 (190*2π)/5763 weeks
191.85062 .34062 (191*2π)/5763 weeks
1923.16963 .04663 (192*2π)/5763 weeks
1934.20856 2.15362 (193*2π)/5763 weeks
1942.10736 3.41338 (194*2π)/5763 weeks
1951.09685 2.22759 (195*2π)/5763 weeks
1961.21723 .9534 (196*2π)/5763 weeks
1972.64202 1.4484 (197*2π)/5763 weeks
1981.66233 2.59469 (198*2π)/5763 weeks
199.52658 1.51483 (199*2π)/5763 weeks
2001.00187 -.04414 (200*2π)/5763 weeks
2012.73069 -.11369 (201*2π)/5763 weeks
2023.18958 .8612 (202*2π)/5763 weeks
2034.02456 2.04146 (203*2π)/5763 weeks
2041.60748 4.23078 (204*2π)/5763 weeks
205-.70537 1.19334 (205*2π)/5763 weeks
206.99165 -.62123 (206*2π)/5763 weeks
2073.1354 -.63249 (207*2π)/5763 weeks
2083.81928 1.49688 (208*2π)/5763 weeks
2092.50217 2.32944 (209*2π)/5763 weeks
2101.84129 1.92815 (210*2π)/5763 weeks
2111.76303 .54773 (211*2π)/5763 weeks
2123.59388 1.85026 (212*2π)/5763 weeks
2131.65334 2.81698 (213*2π)/5763 weeks
214.9761 2.23299 (214*2π)/5763 weeks
215-.0382 .61709 (215*2π)/5763 weeks
2162.19593 -1.17536 (216*2π)/5763 weeks
2174.36148 1.52331 (217*2π)/5763 weeks
2182.07068 3.61296 (218*2π)/5763 weeks
219-.59996 1.88485 (219*2π)/5763 weeks
2201.02063 -.81253 (220*2π)/5763 weeks
2212.89411 .46249 (221*2π)/5763 weeks
2222.70699 1.83021 (222*2π)/5763 weeks
223.93731 2.22106 (223*2π)/5763 weeks
224.19355 -.32027 (224*2π)/5763 weeks
2252.86327 -.59387 (225*2π)/5763 weeks
2263.54483 1.49157 (226*2π)/5763 weeks
2271.68087 2.67401 (227*2π)/5763 weeks
228.37916 .89205 (228*2π)/5763 weeks
2291.61759 -.16268 (229*2π)/5763 weeks
2302.20809 .5512 (230*2π)/5763 weeks
2312.24232 .54464 (231*2π)/5762 weeks
2322.64835 .94993 (232*2π)/5762 weeks
2332.37358 1.21421 (233*2π)/5762 weeks
2342.72537 1.93651 (234*2π)/5762 weeks
235.73568 2.73162 (235*2π)/5762 weeks
236.12884 .53066 (236*2π)/5762 weeks
2371.47364 -.02233 (237*2π)/5762 weeks
2382.41211 1.31226 (238*2π)/5762 weeks
239.18129 1.92763 (239*2π)/5762 weeks
240-.25629 -.35925 (240*2π)/5762 weeks
2411.19744 -1.53068 (241*2π)/5762 weeks
2423.18914 -1.18917 (242*2π)/5762 weeks
2433.49417 1.61253 (243*2π)/5762 weeks
244.53923 2.07845 (244*2π)/5762 weeks
245-.19383 -.78079 (245*2π)/5762 weeks
2462.72045 -2.28323 (246*2π)/5762 weeks
2474.79414 .65101 (247*2π)/5762 weeks
2482.36534 2.9777 (248*2π)/5762 weeks
249-.15211 1.76898 (249*2π)/5762 weeks
250-.26686 -1.25793 (250*2π)/5762 weeks
2513.47192 -1.62681 (251*2π)/5762 weeks
2523.54091 1.1875 (252*2π)/5762 weeks
2531.8986 2.09765 (253*2π)/5762 weeks
254.21432 .79065 (254*2π)/5762 weeks
2551.11825 -.46562 (255*2π)/5762 weeks
2561.83343 -.50131 (256*2π)/5762 weeks
2572.59018 .21392 (257*2π)/5762 weeks
2581.37034 1.13388 (258*2π)/5762 weeks
259.5374 -.61907 (259*2π)/5762 weeks
2601.91775 -1.37824 (260*2π)/5762 weeks
2613.71445 -.54367 (261*2π)/5762 weeks
2623.24554 1.91692 (262*2π)/5762 weeks
263.27672 2.07667 (263*2π)/5762 weeks
264-.5533 -.71201 (264*2π)/5762 weeks
2651.25215 -2.4165 (265*2π)/5762 weeks
2663.99186 -1.99764 (266*2π)/5762 weeks
2674.44827 1.44154 (267*2π)/5762 weeks
2681.35102 2.94747 (268*2π)/5762 weeks
269-1.40856 .05597 (269*2π)/5762 weeks
2701.18432 -2.92997 (270*2π)/5762 weeks
2713.63258 -1.35998 (271*2π)/5762 weeks
2723.29651 .69336 (272*2π)/5762 weeks
273.89463 .96839 (273*2π)/5762 weeks
274.52881 -1.63327 (274*2π)/5762 weeks
2753.24801 -2.52922 (275*2π)/5762 weeks
2763.99554 .13687 (276*2π)/5762 weeks
2772.17634 .90194 (277*2π)/5762 weeks
2781.01749 -.48756 (278*2π)/5762 weeks
2792.33094 -2.04572 (279*2π)/5762 weeks
2804.43854 -1.82837 (280*2π)/5762 weeks
2815.19738 1.3222 (281*2π)/5762 weeks
2821.50004 2.58667 (282*2π)/5762 weeks
283.63758 -.69822 (283*2π)/5762 weeks
2842.76201 -1.3431 (284*2π)/5762 weeks
2854.23226 -.3531 (285*2π)/5762 weeks
2863.72565 1.51023 (286*2π)/5762 weeks
2871.62251 2.48989 (287*2π)/5762 weeks
288-.66478   (288*2π)/5762 weeks
2891.62251 -2.48989 (289*2π)/5762 weeks
2903.72565 -1.51023 (290*2π)/5762 weeks
2914.23226 .3531 (291*2π)/5762 weeks
2922.76201 1.3431 (292*2π)/5762 weeks
293.63758 .69822 (293*2π)/5762 weeks
2941.50004 -2.58667 (294*2π)/5762 weeks
2955.19738 -1.3222 (295*2π)/5762 weeks
2964.43854 1.82837 (296*2π)/5762 weeks
2972.33094 2.04572 (297*2π)/5762 weeks
2981.01749 .48756 (298*2π)/5762 weeks
2992.17634 -.90194 (299*2π)/5762 weeks
3003.99554 -.13687 (300*2π)/5762 weeks
3013.24801 2.52922 (301*2π)/5762 weeks
302.52881 1.63327 (302*2π)/5762 weeks
303.89463 -.96839 (303*2π)/5762 weeks
3043.29651 -.69336 (304*2π)/5762 weeks
3053.63258 1.35998 (305*2π)/5762 weeks
3061.18432 2.92997 (306*2π)/5762 weeks
307-1.40856 -.05597 (307*2π)/5762 weeks
3081.35102 -2.94747 (308*2π)/5762 weeks
3094.44827 -1.44154 (309*2π)/5762 weeks
3103.99186 1.99764 (310*2π)/5762 weeks
3111.25215 2.4165 (311*2π)/5762 weeks
312-.5533 .71201 (312*2π)/5762 weeks
313.27672 -2.07667 (313*2π)/5762 weeks
3143.24554 -1.91692 (314*2π)/5762 weeks
3153.71445 .54367 (315*2π)/5762 weeks
3161.91775 1.37824 (316*2π)/5762 weeks
317.5374 .61907 (317*2π)/5762 weeks
3181.37034 -1.13388 (318*2π)/5762 weeks
3192.59018 -.21392 (319*2π)/5762 weeks
3201.83343 .50131 (320*2π)/5762 weeks
3211.11825 .46562 (321*2π)/5762 weeks
322.21432 -.79065 (322*2π)/5762 weeks
3231.8986 -2.09765 (323*2π)/5762 weeks
3243.54091 -1.1875 (324*2π)/5762 weeks
3253.47192 1.62681 (325*2π)/5762 weeks
326-.26686 1.25793 (326*2π)/5762 weeks
327-.15211 -1.76898 (327*2π)/5762 weeks
3282.36534 -2.9777 (328*2π)/5762 weeks
3294.79414 -.65101 (329*2π)/5762 weeks
3302.72045 2.28323 (330*2π)/5762 weeks
331-.19383 .78079 (331*2π)/5762 weeks
332.53923 -2.07845 (332*2π)/5762 weeks
3333.49417 -1.61253 (333*2π)/5762 weeks
3343.18914 1.18917 (334*2π)/5762 weeks
3351.19744 1.53068 (335*2π)/5762 weeks
336-.25629 .35925 (336*2π)/5762 weeks
337.18129 -1.92763 (337*2π)/5762 weeks
3382.41211 -1.31226 (338*2π)/5762 weeks
3391.47364 .02233 (339*2π)/5762 weeks
340.12884 -.53066 (340*2π)/5762 weeks
341.73568 -2.73162 (341*2π)/5762 weeks
3422.72537 -1.93651 (342*2π)/5762 weeks
3432.37358 -1.21421 (343*2π)/5762 weeks
3442.64835 -.94993 (344*2π)/5762 weeks
3452.24232 -.54464 (345*2π)/5762 weeks
3462.20809 -.5512 (346*2π)/5762 weeks
3471.61759 .16268 (347*2π)/5762 weeks
348.37916 -.89205 (348*2π)/5762 weeks
3491.68087 -2.67401 (349*2π)/5762 weeks
3503.54483 -1.49157 (350*2π)/5762 weeks
3512.86327 .59387 (351*2π)/5762 weeks
352.19355 .32027 (352*2π)/5762 weeks
353.93731 -2.22106 (353*2π)/5762 weeks
3542.70699 -1.83021 (354*2π)/5762 weeks
3552.89411 -.46249 (355*2π)/5762 weeks
3561.02063 .81253 (356*2π)/5762 weeks
357-.59996 -1.88485 (357*2π)/5762 weeks
3582.07068 -3.61296 (358*2π)/5762 weeks
3594.36148 -1.52331 (359*2π)/5762 weeks
3602.19593 1.17536 (360*2π)/5762 weeks
361-.0382 -.61709 (361*2π)/5762 weeks
362.9761 -2.23299 (362*2π)/5762 weeks
3631.65334 -2.81698 (363*2π)/5762 weeks
3643.59388 -1.85026 (364*2π)/5762 weeks
3651.76303 -.54773 (365*2π)/5762 weeks
3661.84129 -1.92815 (366*2π)/5762 weeks
3672.50217 -2.32944 (367*2π)/5762 weeks
3683.81928 -1.49688 (368*2π)/5762 weeks
3693.1354 .63249 (369*2π)/5762 weeks
370.99165 .62123 (370*2π)/5762 weeks
371-.70537 -1.19334 (371*2π)/5762 weeks
3721.60748 -4.23078 (372*2π)/5762 weeks
3734.02456 -2.04146 (373*2π)/5762 weeks
3743.18958 -.8612 (374*2π)/5762 weeks
3752.73069 .11369 (375*2π)/5762 weeks
3761.00187 .04414 (376*2π)/5762 weeks
377.52658 -1.51483 (377*2π)/5762 weeks
3781.66233 -2.59469 (378*2π)/5762 weeks
3792.64202 -1.4484 (379*2π)/5762 weeks
3801.21723 -.9534 (380*2π)/5762 weeks
3811.09685 -2.22759 (381*2π)/5762 weeks
3822.10736 -3.41338 (382*2π)/5762 weeks
3834.20856 -2.15362 (383*2π)/5762 weeks
3843.16963 -.04663 (384*2π)/5762 weeks
385.85062 -.34062 (385*2π)/5761 weeks
386.86806 -2.70755 (386*2π)/5761 weeks
3873.38502 -3.13786 (387*2π)/5761 weeks
3884.25542 -.40332 (388*2π)/5761 weeks
3891.47465 .93836 (389*2π)/5761 weeks
390-.18778 -1.25435 (390*2π)/5761 weeks
391.62335 -3.5676 (391*2π)/5761 weeks
3923.35909 -3.27738 (392*2π)/5761 weeks
3933.42568 -.86974 (393*2π)/5761 weeks
3941.53916 -.50288 (394*2π)/5761 weeks
395.8293 -1.7509 (395*2π)/5761 weeks
3961.45559 -2.88786 (396*2π)/5761 weeks
3972.35282 -2.65394 (397*2π)/5761 weeks
3982.88618 -1.89519 (398*2π)/5761 weeks
3991.36478 -.96961 (399*2π)/5761 weeks
400.33327 -3.18536 (400*2π)/5761 weeks
4012.52852 -4.53779 (401*2π)/5761 weeks
4024.20116 -3.08187 (402*2π)/5761 weeks
4034.06083 -1.66475 (403*2π)/5761 weeks
4042.41842 -1.0003 (404*2π)/5761 weeks
4052.47261 -2.37056 (405*2π)/5761 weeks
4063.10945 -2.28394 (406*2π)/5761 weeks
4073.08798 -1.73664 (407*2π)/5761 weeks
4083.18515 -1.73144 (408*2π)/5761 weeks
4092.81299 -.41989 (409*2π)/5761 weeks
4101.08911 -1.97385 (410*2π)/5761 weeks
4112.94096 -2.67337 (411*2π)/5761 weeks
4123.11699 -1.7838 (412*2π)/5761 weeks
4132.79035 -1.17467 (413*2π)/5761 weeks
4141.66214 -1.10991 (414*2π)/5761 weeks
4151.5426 -2.44577 (415*2π)/5761 weeks
4162.1858 -2.84624 (416*2π)/5761 weeks
4174.01996 -2.55706 (417*2π)/5761 weeks
4182.42579 -.05635 (418*2π)/5761 weeks
419.83636 -2.27713 (419*2π)/5761 weeks
4202.27349 -3.23839 (420*2π)/5761 weeks
4213.60666 -2.6668 (421*2π)/5761 weeks
4222.82317 -.97417 (422*2π)/5761 weeks
4231.18257 -1.81499 (423*2π)/5761 weeks
4241.85892 -3.41908 (424*2π)/5761 weeks
4253.91845 -3.31143 (425*2π)/5761 weeks
4263.55201 -1.06774 (426*2π)/5761 weeks
4271.61247 -2.26556 (427*2π)/5761 weeks
4283.32465 -2.82942 (428*2π)/5761 weeks
4292.93727 -1.91248 (429*2π)/5761 weeks
4302.57236 -1.66658 (430*2π)/5761 weeks
4312.47214 -2.66914 (431*2π)/5761 weeks
4323.84231 -1.51753 (432*2π)/5761 weeks
4331.58391 -.81425 (433*2π)/5761 weeks
4341.58658 -3.4932 (434*2π)/5761 weeks
4353.25903 -3.68277 (435*2π)/5761 weeks
4365.13297 -2.19904 (436*2π)/5761 weeks
4373.67158 .44135 (437*2π)/5761 weeks
4381.35453 -.6885 (438*2π)/5761 weeks
4392.15151 -2.28645 (439*2π)/5761 weeks
4402.63491 -1.30415 (440*2π)/5761 weeks
4411.60869 -1.30237 (441*2π)/5761 weeks
4421.84774 -2.13088 (442*2π)/5761 weeks
4431.42021 -2.36189 (443*2π)/5761 weeks
4442.51206 -2.99539 (444*2π)/5761 weeks
4453.52674 -1.45847 (445*2π)/5761 weeks
4461.86227 .57396 (446*2π)/5761 weeks
447-1.48975 -1.79449 (447*2π)/5761 weeks
448.41244 -5.12208 (448*2π)/5761 weeks
4493.30756 -4.10126 (449*2π)/5761 weeks
4502.78538 -2.34883 (450*2π)/5761 weeks
4511.14553 -1.88923 (451*2π)/5761 weeks
452.86965 -4.40703 (452*2π)/5761 weeks
4533.44202 -4.97222 (453*2π)/5761 weeks
4545.26515 -2.61586 (454*2π)/5761 weeks
4552.7485 .21828 (455*2π)/5761 weeks
456-1.00243 -2.29309 (456*2π)/5761 weeks
4571.43507 -6.40444 (457*2π)/5761 weeks
4585.43898 -5.1545 (458*2π)/5761 weeks
4596.21164 -.68918 (459*2π)/5761 weeks
4601.24733 1.59624 (460*2π)/5761 weeks
461-1.52939 -3.43335 (461*2π)/5761 weeks
4622.89025 -6.7975 (462*2π)/5761 weeks
4636.88517 -2.70523 (463*2π)/5761 weeks
4643.63071 2.14948 (464*2π)/5761 weeks
465-2.41225 .98009 (465*2π)/5761 weeks
466-2.4756 -6.05375 (466*2π)/5761 weeks
4672.67828 -7.33351 (467*2π)/5761 weeks
4685.61171 -3.68086 (468*2π)/5761 weeks
4692.65455 -.5599 (469*2π)/5761 weeks
470-.62585 -3.12357 (470*2π)/5761 weeks
4711.3076 -6.5205 (471*2π)/5761 weeks
4725.29362 -5.29831 (472*2π)/5761 weeks
4734.90759 -1.5752 (473*2π)/5761 weeks
4742.03272 -1.50628 (474*2π)/5761 weeks
4751.6522 -2.95136 (475*2π)/5761 weeks
4762.81643 -3.56458 (476*2π)/5761 weeks
4772.35516 -1.86382 (477*2π)/5761 weeks
4781.53223 -3.82293 (478*2π)/5761 weeks
4793.42395 -2.58476 (479*2π)/5761 weeks
480.86229 -1.03773 (480*2π)/5761 weeks
481-1.21375 -4.13481 (481*2π)/5761 weeks
4821.71714 -6.80223 (482*2π)/5761 weeks
4835.38643 -4.24479 (483*2π)/5761 weeks
4843.57398 .24012 (484*2π)/5761 weeks
485-2.01072 -.59253 (485*2π)/5761 weeks
486-2.91178 -7.04118 (486*2π)/5761 weeks
4873.90154 -8.76556 (487*2π)/5761 weeks
4885.07464 -2.94376 (488*2π)/5761 weeks
4891.40062 -1.22654 (489*2π)/5761 weeks
490-2.37531 -3.65181 (490*2π)/5761 weeks
491-.47329 -9.08889 (491*2π)/5761 weeks
4924.82451 -8.58371 (492*2π)/5761 weeks
4936.59522 -3.53365 (493*2π)/5761 weeks
494.62821 -1.17974 (494*2π)/5761 weeks
495.08315 -7.03704 (495*2π)/5761 weeks
4963.40189 -6.54256 (496*2π)/5761 weeks
4975.2206 -6.19776 (497*2π)/5761 weeks
4985.07936 -.77637 (498*2π)/5761 weeks
499-2.60984 -1.33754 (499*2π)/5761 weeks
500-2.3658 -9.35395 (500*2π)/5761 weeks
5015.51729 -10.6684 (501*2π)/5761 weeks
5027.64049 -3.77499 (502*2π)/5761 weeks
5031.3907 -1.95919 (503*2π)/5761 weeks
5041.86393 -6.75655 (504*2π)/5761 weeks
5053.96721 -5.45377 (505*2π)/5761 weeks
5064.33998 -3.35635 (506*2π)/5761 weeks
507-.45411 -2.7094 (507*2π)/5761 weeks
508-.66502 -8.01848 (508*2π)/5761 weeks
5094.4262 -8.7092 (509*2π)/5761 weeks
5105.48818 -5.01992 (510*2π)/5761 weeks
5112.36249 -2.78174 (511*2π)/5761 weeks
512.86425 -6.08689 (512*2π)/5761 weeks
5133.44823 -6.0621 (513*2π)/5761 weeks
5142.38638 -4.34448 (514*2π)/5761 weeks
515.18211 -5.57091 (515*2π)/5761 weeks
516.80524 -8.65907 (516*2π)/5761 weeks
5176.09885 -8.80564 (517*2π)/5761 weeks
5184.2954 -1.99249 (518*2π)/5761 weeks
519-1.2077 -4.3698 (519*2π)/5761 weeks
520-.2017 -8.15608 (520*2π)/5761 weeks
5211.86572 -8.92044 (521*2π)/5761 weeks
5223.33433 -6.35156 (522*2π)/5761 weeks
523-.31619 -6.61247 (523*2π)/5761 weeks
524-.23337 -10.84815 (524*2π)/5761 weeks
5254.16674 -12.73758 (525*2π)/5761 weeks
5267.66241 -10.50831 (526*2π)/5761 weeks
5277.30045 -3.60475 (527*2π)/5761 weeks
5281.4593 -4.8006 (528*2π)/5761 weeks
5292.02863 -7.23908 (529*2π)/5761 weeks
5302.27165 -8.27424 (530*2π)/5761 weeks
5312.24098 -6.23803 (531*2π)/5761 weeks
532-.39092 -9.48195 (532*2π)/5761 weeks
5334.62987 -10.58044 (533*2π)/5761 weeks
5341.8777 -6.82688 (534*2π)/5761 weeks
535.16252 -9.92129 (535*2π)/5761 weeks
5361.97609 -12.17868 (536*2π)/5761 weeks
5375.09266 -13.16634 (537*2π)/5761 weeks
5388.59748 -7.51986 (538*2π)/5761 weeks
5392.03829 -1.80035 (539*2π)/5761 weeks
540-9.34745 -8.37619 (540*2π)/5761 weeks
541-2.51425 -24.8476 (541*2π)/5761 weeks
54214.21995 -19.72977 (542*2π)/5761 weeks
54312.91934 -3.7611 (543*2π)/5761 weeks
544-2.26085 -.83774 (544*2π)/5761 weeks
545-8.08259 -15.01148 (545*2π)/5761 weeks
5463.67291 -23.37225 (546*2π)/5761 weeks
54711.16295 -17.49213 (547*2π)/5761 weeks
54811.39397 -7.19943 (548*2π)/5761 weeks
549-1.54072 -6.60551 (549*2π)/5761 weeks
550-3.13969 -14.95174 (550*2π)/5761 weeks
551.87599 -19.51093 (551*2π)/5761 weeks
5523.49784 -14.82286 (552*2π)/5761 weeks
553-1.08016 -20.68761 (553*2π)/5761 weeks
5543.64627 -23.26454 (554*2π)/5761 weeks
5556.27064 -25.63629 (555*2π)/5761 weeks
55612.63442 -24.55701 (556*2π)/5761 weeks
55717.26528 -16.47844 (557*2π)/5761 weeks
5585.52413 -7.70255 (558*2π)/5761 weeks
559-2.97184 -16.76566 (559*2π)/5761 weeks
560-5.9926 -29.31636 (560*2π)/5761 weeks
5616.18997 -43.35762 (561*2π)/5761 weeks
56229.63008 -37.29216 (562*2π)/5761 weeks
56330.33896 -8.05475 (563*2π)/5761 weeks
564-2.74624 -1.78006 (564*2π)/5761 weeks
565-15.19366 -30.32836 (565*2π)/5761 weeks
566-.25219 -53.62944 (566*2π)/5761 weeks
56733.48111 -50.09638 (567*2π)/5761 weeks
56821.84259 -6.18516 (568*2π)/5761 weeks
569-28.24873 -34.92375 (569*2π)/5761 weeks
570-9.32969 -94.73006 (570*2π)/5761 weeks
57159.40418 -97.77399 (571*2π)/5761 weeks
57267.40705 -32.29792 (572*2π)/5761 weeks
573-16.65701 -25.83205 (573*2π)/5761 weeks
574-51.42603 -178.6714 (574*2π)/5761 weeks



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