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Fourier Analysis of QID (ProShares UltraShort QQQ)


QID (ProShares UltraShort QQQ) appears to have interesting cyclic behaviour every 39 weeks (46.6492*sine), 55 weeks (45.737*sine), and 42 weeks (36.2739*cosine).

QID (ProShares UltraShort QQQ) has an average price of 351.29 (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 1/9/2017 for QID (ProShares UltraShort QQQ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0351.2881   0 
1149.3428 384.7571 (1*2π)/549549 weeks
2-59.09327 166.8127 (2*2π)/549275 weeks
3-.54709 17.92824 (3*2π)/549183 weeks
478.64825 45.92649 (4*2π)/549137 weeks
544.99799 110.7179 (5*2π)/549110 weeks
6-23.49462 82.57439 (6*2π)/54992 weeks
7-18.21248 15.99758 (7*2π)/54978 weeks
839.8773 22.68448 (8*2π)/54969 weeks
918.42241 60.72203 (9*2π)/54961 weeks
10-10.65391 45.73695 (10*2π)/54955 weeks
11-13.6831 14.54039 (11*2π)/54950 weeks
1219.70863 -.78165 (12*2π)/54946 weeks
1336.27394 28.90313 (13*2π)/54942 weeks
1414.09691 46.64915 (14*2π)/54939 weeks
15-4.70284 35.01275 (15*2π)/54937 weeks
16-4.31859 19.20046 (16*2π)/54934 weeks
172.8967 8.99731 (17*2π)/54932 weeks
1817.82828 15.50757 (18*2π)/54931 weeks
1913.64709 25.42297 (19*2π)/54929 weeks
206.66896 26.87203 (20*2π)/54927 weeks
213.71531 24.34619 (21*2π)/54926 weeks
22-1.45206 20.90935 (22*2π)/54925 weeks
234.62235 16.27789 (23*2π)/54924 weeks
24-.11627 19.77804 (24*2π)/54923 weeks
25-3.56208 13.81745 (25*2π)/54922 weeks
261.49449 4.29826 (26*2π)/54921 weeks
2713.31953 11.55927 (27*2π)/54920 weeks
289.51832 20.75292 (28*2π)/54920 weeks
29-3.01192 23.5508 (29*2π)/54919 weeks
30-8.22338 8.14849 (30*2π)/54918 weeks
316.85891 -.05005 (31*2π)/54918 weeks
3217.38088 13.10672 (32*2π)/54917 weeks
335.15082 26.80346 (33*2π)/54917 weeks
34-10.80224 14.87709 (34*2π)/54916 weeks
35-1.39244 1.77996 (35*2π)/54916 weeks
368.14179 5.9394 (36*2π)/54915 weeks
376.36636 13.4931 (37*2π)/54915 weeks
382.33023 12.87398 (38*2π)/54914 weeks
39.19895 10.68417 (39*2π)/54914 weeks
401.7774 7.22652 (40*2π)/54914 weeks
414.73709 11.17281 (41*2π)/54913 weeks
42-.51138 9.52364 (42*2π)/54913 weeks
432.80358 6.70468 (43*2π)/54913 weeks
442.04149 8.45596 (44*2π)/54912 weeks
451.86561 7.56953 (45*2π)/54912 weeks
462.42607 3.9194 (46*2π)/54912 weeks
479.44239 5.99057 (47*2π)/54912 weeks
486.70995 11.81033 (48*2π)/54911 weeks
492.01947 13.25305 (49*2π)/54911 weeks
50-1.07566 9.38559 (50*2π)/54911 weeks
511.52711 5.87539 (51*2π)/54911 weeks
523.36959 8.90707 (52*2π)/54911 weeks
53.79586 8.99655 (53*2π)/54910 weeks
54-1.38588 6.37074 (54*2π)/54910 weeks
552.28774 1.81086 (55*2π)/54910 weeks
567.42462 7.29516 (56*2π)/54910 weeks
571.49036 9.6157 (57*2π)/54910 weeks
58.08151 6.23789 (58*2π)/5499 weeks
592.27017 4.48188 (59*2π)/5499 weeks
603.63002 6.20349 (60*2π)/5499 weeks
61.88525 6.3393 (61*2π)/5499 weeks
622.73466 2.81593 (62*2π)/5499 weeks
635.85131 5.57578 (63*2π)/5499 weeks
643.96964 9.56581 (64*2π)/5499 weeks
65-1.2902 7.35331 (65*2π)/5498 weeks
66.85694 1.89851 (66*2π)/5498 weeks
674.60592 4.52101 (67*2π)/5498 weeks
683.95404 6.28864 (68*2π)/5498 weeks
69.39492 5.72119 (69*2π)/5498 weeks
704.60005 1.26945 (70*2π)/5498 weeks
718.21304 7.79399 (71*2π)/5498 weeks
721.00679 12.03724 (72*2π)/5498 weeks
73-4.03731 4.97985 (73*2π)/5498 weeks
742.7283 -.59631 (74*2π)/5497 weeks
756.45851 5.13469 (75*2π)/5497 weeks
763.61296 6.61898 (76*2π)/5497 weeks
771.17523 7.84613 (77*2π)/5497 weeks
78-.33191 2.07051 (78*2π)/5497 weeks
796.59527 2.95942 (79*2π)/5497 weeks
805.30297 8.76412 (80*2π)/5497 weeks
81-.41825 9.54579 (81*2π)/5497 weeks
82-2.39667 3.61344 (82*2π)/5497 weeks
831.81422 1.27193 (83*2π)/5497 weeks
845.68356 3.69928 (84*2π)/5497 weeks
852.6788 9.76117 (85*2π)/5496 weeks
86-3.78212 5.67845 (86*2π)/5496 weeks
87-.65353 -.37457 (87*2π)/5496 weeks
885.11275 1.15466 (88*2π)/5496 weeks
894.74124 6.22391 (89*2π)/5496 weeks
90.12001 6.4108 (90*2π)/5496 weeks
91-.78299 2.18913 (91*2π)/5496 weeks
922.7785 1.30801 (92*2π)/5496 weeks
932.78846 4.10578 (93*2π)/5496 weeks
941.414 2.29666 (94*2π)/5496 weeks
953.30512 3.1587 (95*2π)/5496 weeks
961.82987 3.41406 (96*2π)/5496 weeks
971.84567 1.98119 (97*2π)/5496 weeks
984.55554 1.24751 (98*2π)/5496 weeks
995.77884 5.03041 (99*2π)/5496 weeks
1001.70061 6.96195 (100*2π)/5495 weeks
101-.67424 3.38838 (101*2π)/5495 weeks
1022.862 .56997 (102*2π)/5495 weeks
1035.87206 4.2084 (103*2π)/5495 weeks
1042.21125 7.80683 (104*2π)/5495 weeks
105-3.38817 5.35221 (105*2π)/5495 weeks
106-1.18683 -2.01844 (106*2π)/5495 weeks
1075.29813 -1.50509 (107*2π)/5495 weeks
1086.60832 4.7365 (108*2π)/5495 weeks
109.70026 6.64959 (109*2π)/5495 weeks
110-1.51862 1.01395 (110*2π)/5495 weeks
1114.29154 -1.49266 (111*2π)/5495 weeks
1126.83973 3.37587 (112*2π)/5495 weeks
1133.65767 6.65811 (113*2π)/5495 weeks
114-.89549 4.52525 (114*2π)/5495 weeks
1151.19791 -.18202 (115*2π)/5495 weeks
1165.23565 1.50128 (116*2π)/5495 weeks
1174.1852 4.9106 (117*2π)/5495 weeks
1181.31213 5.05047 (118*2π)/5495 weeks
119.83815 2.26292 (119*2π)/5495 weeks
1202.84961 2.37333 (120*2π)/5495 weeks
1213.53614 4.15232 (121*2π)/5495 weeks
122.43469 5.37667 (122*2π)/5495 weeks
123-1.53569 1.65249 (123*2π)/5494 weeks
1242.32007 -.45948 (124*2π)/5494 weeks
1253.7423 1.8427 (125*2π)/5494 weeks
1262.35387 3.1131 (126*2π)/5494 weeks
1271.55978 2.11644 (127*2π)/5494 weeks
1281.62664 2.18048 (128*2π)/5494 weeks
1292.02352 1.14024 (129*2π)/5494 weeks
1302.89393 1.81205 (130*2π)/5494 weeks
1311.47612 1.98332 (131*2π)/5494 weeks
1322.21484 -.20644 (132*2π)/5494 weeks
1335.2463 .82726 (133*2π)/5494 weeks
1344.35872 3.68794 (134*2π)/5494 weeks
1352.51605 3.81609 (135*2π)/5494 weeks
136.99439 1.62629 (136*2π)/5494 weeks
1373.61031 .97972 (137*2π)/5494 weeks
1382.94714 2.96561 (138*2π)/5494 weeks
1392.53593 1.81301 (139*2π)/5494 weeks
1403.08604 2.02223 (140*2π)/5494 weeks
1413.56733 2.85407 (141*2π)/5494 weeks
1421.67733 2.41184 (142*2π)/5494 weeks
1433.77392 1.14888 (143*2π)/5494 weeks
1443.94336 3.61964 (144*2π)/5494 weeks
1451.79653 3.43682 (145*2π)/5494 weeks
1461.42362 1.54178 (146*2π)/5494 weeks
1473.37682 1.21179 (147*2π)/5494 weeks
1483.36271 3.16527 (148*2π)/5494 weeks
1491.89893 3.32205 (149*2π)/5494 weeks
150.87241 1.30503 (150*2π)/5494 weeks
1514.00494 .72155 (151*2π)/5494 weeks
1523.04552 3.36477 (152*2π)/5494 weeks
1532.05094 2.76552 (153*2π)/5494 weeks
1541.41207 1.72543 (154*2π)/5494 weeks
1552.62663 1.01276 (155*2π)/5494 weeks
1563.2114 1.63464 (156*2π)/5494 weeks
1573.24022 2.40018 (157*2π)/5493 weeks
1581.41035 2.62599 (158*2π)/5493 weeks
1592.46296 .32667 (159*2π)/5493 weeks
1603.42521 1.75907 (160*2π)/5493 weeks
1613.17992 1.82557 (161*2π)/5493 weeks
1623.24213 2.36101 (162*2π)/5493 weeks
1632.56054 2.45102 (163*2π)/5493 weeks
1642.68083 .96642 (164*2π)/5493 weeks
1654.30591 1.94527 (165*2π)/5493 weeks
1664.29576 3.5842 (166*2π)/5493 weeks
1672.04403 4.71718 (167*2π)/5493 weeks
168.25844 2.51608 (168*2π)/5493 weeks
1692.21358 .97478 (169*2π)/5493 weeks
1702.87133 2.46715 (170*2π)/5493 weeks
1712.1878 2.95262 (171*2π)/5493 weeks
172.96775 2.53591 (172*2π)/5493 weeks
1731.02713 1.11588 (173*2π)/5493 weeks
1742.73953 .39614 (174*2π)/5493 weeks
1754.01729 2.44938 (175*2π)/5493 weeks
1761.66445 4.14339 (176*2π)/5493 weeks
177-.22146 1.94935 (177*2π)/5493 weeks
178.76265 -.66068 (178*2π)/5493 weeks
1794.10094 -.15915 (179*2π)/5493 weeks
1803.88274 3.04625 (180*2π)/5493 weeks
1811.03774 3.04685 (181*2π)/5493 weeks
182.77949 .44251 (182*2π)/5493 weeks
1833.33493 .03172 (183*2π)/5493 weeks
1844.38216 2.42855 (184*2π)/5493 weeks
1851.9658 3.53605 (185*2π)/5493 weeks
1861.07077 2.20125 (186*2π)/5493 weeks
1871.6123 .77681 (187*2π)/5493 weeks
1882.78212 1.92498 (188*2π)/5493 weeks
1891.20475 2.59262 (189*2π)/5493 weeks
190.47736 1.06853 (190*2π)/5493 weeks
1911.73135 -.37224 (191*2π)/5493 weeks
1923.28173 .4058 (192*2π)/5493 weeks
1933.7425 1.11511 (193*2π)/5493 weeks
1943.48772 3.83162 (194*2π)/5493 weeks
195-.6066 3.01972 (195*2π)/5493 weeks
196.34413 -.25136 (196*2π)/5493 weeks
1972.55219 -.93563 (197*2π)/5493 weeks
1984.21123 1.00177 (198*2π)/5493 weeks
1992.96256 2.47155 (199*2π)/5493 weeks
2002.0059 2.05622 (200*2π)/5493 weeks
2011.61281 .74547 (201*2π)/5493 weeks
2023.79251 1.70496 (202*2π)/5493 weeks
2031.77933 2.97976 (203*2π)/5493 weeks
204.97452 2.37077 (204*2π)/5493 weeks
205-.02487 .4213 (205*2π)/5493 weeks
2062.79722 -1.1983 (206*2π)/5493 weeks
2074.3776 2.22435 (207*2π)/5493 weeks
2081.41703 3.78858 (208*2π)/5493 weeks
209-.6746 .92917 (209*2π)/5493 weeks
2102.07366 -.76571 (210*2π)/5493 weeks
2113.01935 .95448 (211*2π)/5493 weeks
2122.16666 2.37706 (212*2π)/5493 weeks
213.03054 1.47269 (213*2π)/5493 weeks
2141.76904 -1.0729 (214*2π)/5493 weeks
2153.73338 .49786 (215*2π)/5493 weeks
2162.6966 2.60763 (216*2π)/5493 weeks
217.43498 1.70441 (217*2π)/5493 weeks
2181.23677 -.06513 (218*2π)/5493 weeks
2192.33402 .45573 (219*2π)/5493 weeks
2202.26475 .55751 (220*2π)/5492 weeks
2212.76745 .84888 (221*2π)/5492 weeks
2222.49954 1.27955 (222*2π)/5492 weeks
2232.86005 1.99597 (223*2π)/5492 weeks
224.69139 2.8502 (224*2π)/5492 weeks
225.19523 .41905 (225*2π)/5492 weeks
2261.71113 -.03147 (226*2π)/5492 weeks
2272.34928 1.77052 (227*2π)/5492 weeks
228-.26615 1.59952 (228*2π)/5492 weeks
229-.00815 -.80624 (229*2π)/5492 weeks
2301.84358 -1.67295 (230*2π)/5492 weeks
2314.04785 -.3669 (231*2π)/5492 weeks
2322.57534 2.49581 (232*2π)/5492 weeks
233-.31509 .92921 (233*2π)/5492 weeks
234.94734 -2.16468 (234*2π)/5492 weeks
2354.63642 -1.11365 (235*2π)/5492 weeks
2363.823 2.67763 (236*2π)/5492 weeks
237.5719 2.60268 (237*2π)/5492 weeks
238-.67409 -.25436 (238*2π)/5492 weeks
2392.7168 -2.36863 (239*2π)/5492 weeks
2403.96829 .79983 (240*2π)/5492 weeks
2412.30531 2.13414 (241*2π)/5492 weeks
242.25426 1.09271 (242*2π)/5492 weeks
2431.08264 -.46727 (243*2π)/5492 weeks
2441.89126 -.54993 (244*2π)/5492 weeks
2452.71995 .27844 (245*2π)/5492 weeks
2461.25708 1.14258 (246*2π)/5492 weeks
247.75967 -.8932 (247*2π)/5492 weeks
2482.30842 -1.50969 (248*2π)/5492 weeks
2494.05778 .01703 (249*2π)/5492 weeks
2502.61086 2.49759 (250*2π)/5492 weeks
251-.44561 1.29289 (251*2π)/5492 weeks
252-.02647 -1.67187 (252*2π)/5492 weeks
2532.44547 -2.72108 (253*2π)/5492 weeks
2545.10096 -.45358 (254*2π)/5492 weeks
2553.18549 2.78202 (255*2π)/5492 weeks
256-.78515 1.88645 (256*2π)/5492 weeks
257-.21604 -2.55904 (257*2π)/5492 weeks
2583.35615 -2.21705 (258*2π)/5492 weeks
2593.73464 .15863 (259*2π)/5492 weeks
2601.51897 1.30853 (260*2π)/5492 weeks
261.33594 -1.26251 (261*2π)/5492 weeks
2622.96446 -2.7783 (262*2π)/5492 weeks
2634.23685 -.02009 (263*2π)/5492 weeks
2642.31242 .92404 (264*2π)/5492 weeks
2651.07998 -.58604 (265*2π)/5492 weeks
2662.58652 -2.14007 (266*2π)/5492 weeks
2674.95633 -1.63509 (267*2π)/5492 weeks
2685.03097 2.0097 (268*2π)/5492 weeks
269.82151 1.97943 (269*2π)/5492 weeks
2701.32511 -1.36249 (270*2π)/5492 weeks
2713.31984 -1.27289 (271*2π)/5492 weeks
2724.39844 .52565 (272*2π)/5492 weeks
2733.20748 2.20331 (273*2π)/5492 weeks
274.17147 1.93256 (274*2π)/5492 weeks
275.17147 -1.93256 (275*2π)/5492 weeks
2763.20748 -2.20331 (276*2π)/5492 weeks
2774.39844 -.52565 (277*2π)/5492 weeks
2783.31984 1.27289 (278*2π)/5492 weeks
2791.32511 1.36249 (279*2π)/5492 weeks
280.82151 -1.97943 (280*2π)/5492 weeks
2815.03097 -2.0097 (281*2π)/5492 weeks
2824.95633 1.63509 (282*2π)/5492 weeks
2832.58652 2.14007 (283*2π)/5492 weeks
2841.07998 .58604 (284*2π)/5492 weeks
2852.31242 -.92404 (285*2π)/5492 weeks
2864.23685 .02009 (286*2π)/5492 weeks
2872.96446 2.7783 (287*2π)/5492 weeks
288.33594 1.26251 (288*2π)/5492 weeks
2891.51897 -1.30853 (289*2π)/5492 weeks
2903.73464 -.15863 (290*2π)/5492 weeks
2913.35615 2.21705 (291*2π)/5492 weeks
292-.21604 2.55904 (292*2π)/5492 weeks
293-.78515 -1.88645 (293*2π)/5492 weeks
2943.18549 -2.78202 (294*2π)/5492 weeks
2955.10096 .45358 (295*2π)/5492 weeks
2962.44547 2.72108 (296*2π)/5492 weeks
297-.02647 1.67187 (297*2π)/5492 weeks
298-.44561 -1.29289 (298*2π)/5492 weeks
2992.61086 -2.49759 (299*2π)/5492 weeks
3004.05778 -.01703 (300*2π)/5492 weeks
3012.30842 1.50969 (301*2π)/5492 weeks
302.75967 .8932 (302*2π)/5492 weeks
3031.25708 -1.14258 (303*2π)/5492 weeks
3042.71995 -.27844 (304*2π)/5492 weeks
3051.89126 .54993 (305*2π)/5492 weeks
3061.08264 .46727 (306*2π)/5492 weeks
307.25426 -1.09271 (307*2π)/5492 weeks
3082.30531 -2.13414 (308*2π)/5492 weeks
3093.96829 -.79983 (309*2π)/5492 weeks
3102.7168 2.36863 (310*2π)/5492 weeks
311-.67409 .25436 (311*2π)/5492 weeks
312.5719 -2.60268 (312*2π)/5492 weeks
3133.823 -2.67763 (313*2π)/5492 weeks
3144.63642 1.11365 (314*2π)/5492 weeks
315.94734 2.16468 (315*2π)/5492 weeks
316-.31509 -.92921 (316*2π)/5492 weeks
3172.57534 -2.49581 (317*2π)/5492 weeks
3184.04785 .3669 (318*2π)/5492 weeks
3191.84358 1.67295 (319*2π)/5492 weeks
320-.00815 .80624 (320*2π)/5492 weeks
321-.26615 -1.59952 (321*2π)/5492 weeks
3222.34928 -1.77052 (322*2π)/5492 weeks
3231.71113 .03147 (323*2π)/5492 weeks
324.19523 -.41905 (324*2π)/5492 weeks
325.69139 -2.8502 (325*2π)/5492 weeks
3262.86005 -1.99597 (326*2π)/5492 weeks
3272.49954 -1.27955 (327*2π)/5492 weeks
3282.76745 -.84888 (328*2π)/5492 weeks
3292.26475 -.55751 (329*2π)/5492 weeks
3302.33402 -.45573 (330*2π)/5492 weeks
3311.23677 .06513 (331*2π)/5492 weeks
332.43498 -1.70441 (332*2π)/5492 weeks
3332.6966 -2.60763 (333*2π)/5492 weeks
3343.73338 -.49786 (334*2π)/5492 weeks
3351.76904 1.0729 (335*2π)/5492 weeks
336.03054 -1.47269 (336*2π)/5492 weeks
3372.16666 -2.37706 (337*2π)/5492 weeks
3383.01935 -.95448 (338*2π)/5492 weeks
3392.07366 .76571 (339*2π)/5492 weeks
340-.6746 -.92917 (340*2π)/5492 weeks
3411.41703 -3.78858 (341*2π)/5492 weeks
3424.3776 -2.22435 (342*2π)/5492 weeks
3432.79722 1.1983 (343*2π)/5492 weeks
344-.02487 -.4213 (344*2π)/5492 weeks
345.97452 -2.37077 (345*2π)/5492 weeks
3461.77933 -2.97976 (346*2π)/5492 weeks
3473.79251 -1.70496 (347*2π)/5492 weeks
3481.61281 -.74547 (348*2π)/5492 weeks
3492.0059 -2.05622 (349*2π)/5492 weeks
3502.96256 -2.47155 (350*2π)/5492 weeks
3514.21123 -1.00177 (351*2π)/5492 weeks
3522.55219 .93563 (352*2π)/5492 weeks
353.34413 .25136 (353*2π)/5492 weeks
354-.6066 -3.01972 (354*2π)/5492 weeks
3553.48772 -3.83162 (355*2π)/5492 weeks
3563.7425 -1.11511 (356*2π)/5492 weeks
3573.28173 -.4058 (357*2π)/5492 weeks
3581.73135 .37224 (358*2π)/5492 weeks
359.47736 -1.06853 (359*2π)/5492 weeks
3601.20475 -2.59262 (360*2π)/5492 weeks
3612.78212 -1.92498 (361*2π)/5492 weeks
3621.6123 -.77681 (362*2π)/5492 weeks
3631.07077 -2.20125 (363*2π)/5492 weeks
3641.9658 -3.53605 (364*2π)/5492 weeks
3654.38216 -2.42855 (365*2π)/5492 weeks
3663.33493 -.03172 (366*2π)/5492 weeks
367.77949 -.44251 (367*2π)/5491 weeks
3681.03774 -3.04685 (368*2π)/5491 weeks
3693.88274 -3.04625 (369*2π)/5491 weeks
3704.10094 .15915 (370*2π)/5491 weeks
371.76265 .66068 (371*2π)/5491 weeks
372-.22146 -1.94935 (372*2π)/5491 weeks
3731.66445 -4.14339 (373*2π)/5491 weeks
3744.01729 -2.44938 (374*2π)/5491 weeks
3752.73953 -.39614 (375*2π)/5491 weeks
3761.02713 -1.11588 (376*2π)/5491 weeks
377.96775 -2.53591 (377*2π)/5491 weeks
3782.1878 -2.95262 (378*2π)/5491 weeks
3792.87133 -2.46715 (379*2π)/5491 weeks
3802.21358 -.97478 (380*2π)/5491 weeks
381.25844 -2.51608 (381*2π)/5491 weeks
3822.04403 -4.71718 (382*2π)/5491 weeks
3834.29576 -3.5842 (383*2π)/5491 weeks
3844.30591 -1.94527 (384*2π)/5491 weeks
3852.68083 -.96642 (385*2π)/5491 weeks
3862.56054 -2.45102 (386*2π)/5491 weeks
3873.24213 -2.36101 (387*2π)/5491 weeks
3883.17992 -1.82557 (388*2π)/5491 weeks
3893.42521 -1.75907 (389*2π)/5491 weeks
3902.46296 -.32667 (390*2π)/5491 weeks
3911.41035 -2.62599 (391*2π)/5491 weeks
3923.24022 -2.40018 (392*2π)/5491 weeks
3933.2114 -1.63464 (393*2π)/5491 weeks
3942.62663 -1.01276 (394*2π)/5491 weeks
3951.41207 -1.72543 (395*2π)/5491 weeks
3962.05094 -2.76552 (396*2π)/5491 weeks
3973.04552 -3.36477 (397*2π)/5491 weeks
3984.00494 -.72155 (398*2π)/5491 weeks
399.87241 -1.30503 (399*2π)/5491 weeks
4001.89893 -3.32205 (400*2π)/5491 weeks
4013.36271 -3.16527 (401*2π)/5491 weeks
4023.37682 -1.21179 (402*2π)/5491 weeks
4031.42362 -1.54178 (403*2π)/5491 weeks
4041.79653 -3.43682 (404*2π)/5491 weeks
4053.94336 -3.61964 (405*2π)/5491 weeks
4063.77392 -1.14888 (406*2π)/5491 weeks
4071.67733 -2.41184 (407*2π)/5491 weeks
4083.56733 -2.85407 (408*2π)/5491 weeks
4093.08604 -2.02223 (409*2π)/5491 weeks
4102.53593 -1.81301 (410*2π)/5491 weeks
4112.94714 -2.96561 (411*2π)/5491 weeks
4123.61031 -.97972 (412*2π)/5491 weeks
413.99439 -1.62629 (413*2π)/5491 weeks
4142.51605 -3.81609 (414*2π)/5491 weeks
4154.35872 -3.68794 (415*2π)/5491 weeks
4165.2463 -.82726 (416*2π)/5491 weeks
4172.21484 .20644 (417*2π)/5491 weeks
4181.47612 -1.98332 (418*2π)/5491 weeks
4192.89393 -1.81205 (419*2π)/5491 weeks
4202.02352 -1.14024 (420*2π)/5491 weeks
4211.62664 -2.18048 (421*2π)/5491 weeks
4221.55978 -2.11644 (422*2π)/5491 weeks
4232.35387 -3.1131 (423*2π)/5491 weeks
4243.7423 -1.8427 (424*2π)/5491 weeks
4252.32007 .45948 (425*2π)/5491 weeks
426-1.53569 -1.65249 (426*2π)/5491 weeks
427.43469 -5.37667 (427*2π)/5491 weeks
4283.53614 -4.15232 (428*2π)/5491 weeks
4292.84961 -2.37333 (429*2π)/5491 weeks
430.83815 -2.26292 (430*2π)/5491 weeks
4311.31213 -5.05047 (431*2π)/5491 weeks
4324.1852 -4.9106 (432*2π)/5491 weeks
4335.23565 -1.50128 (433*2π)/5491 weeks
4341.19791 .18202 (434*2π)/5491 weeks
435-.89549 -4.52525 (435*2π)/5491 weeks
4363.65767 -6.65811 (436*2π)/5491 weeks
4376.83973 -3.37587 (437*2π)/5491 weeks
4384.29154 1.49266 (438*2π)/5491 weeks
439-1.51862 -1.01395 (439*2π)/5491 weeks
440.70026 -6.64959 (440*2π)/5491 weeks
4416.60832 -4.7365 (441*2π)/5491 weeks
4425.29813 1.50509 (442*2π)/5491 weeks
443-1.18683 2.01844 (443*2π)/5491 weeks
444-3.38817 -5.35221 (444*2π)/5491 weeks
4452.21125 -7.80683 (445*2π)/5491 weeks
4465.87206 -4.2084 (446*2π)/5491 weeks
4472.862 -.56997 (447*2π)/5491 weeks
448-.67424 -3.38838 (448*2π)/5491 weeks
4491.70061 -6.96195 (449*2π)/5491 weeks
4505.77884 -5.03041 (450*2π)/5491 weeks
4514.55554 -1.24751 (451*2π)/5491 weeks
4521.84567 -1.98119 (452*2π)/5491 weeks
4531.82987 -3.41406 (453*2π)/5491 weeks
4543.30512 -3.1587 (454*2π)/5491 weeks
4551.414 -2.29666 (455*2π)/5491 weeks
4562.78846 -4.10578 (456*2π)/5491 weeks
4572.7785 -1.30801 (457*2π)/5491 weeks
458-.78299 -2.18913 (458*2π)/5491 weeks
459.12001 -6.4108 (459*2π)/5491 weeks
4604.74124 -6.22391 (460*2π)/5491 weeks
4615.11275 -1.15466 (461*2π)/5491 weeks
462-.65353 .37457 (462*2π)/5491 weeks
463-3.78212 -5.67845 (463*2π)/5491 weeks
4642.6788 -9.76117 (464*2π)/5491 weeks
4655.68356 -3.69928 (465*2π)/5491 weeks
4661.81422 -1.27193 (466*2π)/5491 weeks
467-2.39667 -3.61344 (467*2π)/5491 weeks
468-.41825 -9.54579 (468*2π)/5491 weeks
4695.30297 -8.76412 (469*2π)/5491 weeks
4706.59527 -2.95942 (470*2π)/5491 weeks
471-.33191 -2.07051 (471*2π)/5491 weeks
4721.17523 -7.84613 (472*2π)/5491 weeks
4733.61296 -6.61898 (473*2π)/5491 weeks
4746.45851 -5.13469 (474*2π)/5491 weeks
4752.7283 .59631 (475*2π)/5491 weeks
476-4.03731 -4.97985 (476*2π)/5491 weeks
4771.00679 -12.03724 (477*2π)/5491 weeks
4788.21304 -7.79399 (478*2π)/5491 weeks
4794.60005 -1.26945 (479*2π)/5491 weeks
480.39492 -5.72119 (480*2π)/5491 weeks
4813.95404 -6.28864 (481*2π)/5491 weeks
4824.60592 -4.52101 (482*2π)/5491 weeks
483.85694 -1.89851 (483*2π)/5491 weeks
484-1.2902 -7.35331 (484*2π)/5491 weeks
4853.96964 -9.56581 (485*2π)/5491 weeks
4865.85131 -5.57578 (486*2π)/5491 weeks
4872.73466 -2.81593 (487*2π)/5491 weeks
488.88525 -6.3393 (488*2π)/5491 weeks
4893.63002 -6.20349 (489*2π)/5491 weeks
4902.27017 -4.48188 (490*2π)/5491 weeks
491.08151 -6.23789 (491*2π)/5491 weeks
4921.49036 -9.6157 (492*2π)/5491 weeks
4937.42462 -7.29516 (493*2π)/5491 weeks
4942.28774 -1.81086 (494*2π)/5491 weeks
495-1.38588 -6.37074 (495*2π)/5491 weeks
496.79586 -8.99655 (496*2π)/5491 weeks
4973.36959 -8.90707 (497*2π)/5491 weeks
4981.52711 -5.87539 (498*2π)/5491 weeks
499-1.07566 -9.38559 (499*2π)/5491 weeks
5002.01947 -13.25305 (500*2π)/5491 weeks
5016.70995 -11.81033 (501*2π)/5491 weeks
5029.44239 -5.99057 (502*2π)/5491 weeks
5032.42607 -3.9194 (503*2π)/5491 weeks
5041.86561 -7.56953 (504*2π)/5491 weeks
5052.04149 -8.45596 (505*2π)/5491 weeks
5062.80358 -6.70468 (506*2π)/5491 weeks
507-.51138 -9.52364 (507*2π)/5491 weeks
5084.73709 -11.17281 (508*2π)/5491 weeks
5091.7774 -7.22652 (509*2π)/5491 weeks
510.19895 -10.68417 (510*2π)/5491 weeks
5112.33023 -12.87398 (511*2π)/5491 weeks
5126.36636 -13.4931 (512*2π)/5491 weeks
5138.14179 -5.9394 (513*2π)/5491 weeks
514-1.39244 -1.77996 (514*2π)/5491 weeks
515-10.80224 -14.87709 (515*2π)/5491 weeks
5165.15082 -26.80346 (516*2π)/5491 weeks
51717.38088 -13.10672 (517*2π)/5491 weeks
5186.85891 .05005 (518*2π)/5491 weeks
519-8.22338 -8.14849 (519*2π)/5491 weeks
520-3.01192 -23.5508 (520*2π)/5491 weeks
5219.51832 -20.75292 (521*2π)/5491 weeks
52213.31953 -11.55927 (522*2π)/5491 weeks
5231.49449 -4.29826 (523*2π)/5491 weeks
524-3.56208 -13.81745 (524*2π)/5491 weeks
525-.11627 -19.77804 (525*2π)/5491 weeks
5264.62235 -16.27789 (526*2π)/5491 weeks
527-1.45206 -20.90935 (527*2π)/5491 weeks
5283.71531 -24.34619 (528*2π)/5491 weeks
5296.66896 -26.87203 (529*2π)/5491 weeks
53013.64709 -25.42297 (530*2π)/5491 weeks
53117.82828 -15.50757 (531*2π)/5491 weeks
5322.8967 -8.99731 (532*2π)/5491 weeks
533-4.31859 -19.20046 (533*2π)/5491 weeks
534-4.70284 -35.01275 (534*2π)/5491 weeks
53514.09691 -46.64915 (535*2π)/5491 weeks
53636.27394 -28.90313 (536*2π)/5491 weeks
53719.70863 .78165 (537*2π)/5491 weeks
538-13.6831 -14.54039 (538*2π)/5491 weeks
539-10.65391 -45.73695 (539*2π)/5491 weeks
54018.42241 -60.72203 (540*2π)/5491 weeks
54139.8773 -22.68448 (541*2π)/5491 weeks
542-18.21248 -15.99758 (542*2π)/5491 weeks
543-23.49462 -82.57439 (543*2π)/5491 weeks
54444.99799 -110.7179 (544*2π)/5491 weeks
54578.64825 -45.92649 (545*2π)/5491 weeks
546-.54709 -17.92824 (546*2π)/5491 weeks
547-59.09327 -166.8127 (547*2π)/5491 weeks

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