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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 60 weeks (58.3758*sine), 55 weeks (48.4055*sine), and 30 weeks (22.3914*cosine).

ZSL (ProShares UltraShort Silver) has an average price of 151.13 (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 12/3/2008 to 6/22/2020 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0151.1343   0 
1200.2126 69.94444 (1*2π)/604604 weeks
2156.2406 119.6228 (2*2π)/604302 weeks
390.1358 117.371 (3*2π)/604201 weeks
456.12151 101.998 (4*2π)/604151 weeks
547.42051 78.89494 (5*2π)/604121 weeks
643.285 67.91296 (6*2π)/604101 weeks
745.91473 66.62851 (7*2π)/60486 weeks
838.45393 67.35268 (8*2π)/60476 weeks
925.60734 63.65485 (9*2π)/60467 weeks
1020.6048 58.37579 (10*2π)/60460 weeks
1113.66031 48.40548 (11*2π)/60455 weeks
1213.55755 41.66515 (12*2π)/60450 weeks
1316.42364 36.00418 (13*2π)/60446 weeks
1415.28725 33.40186 (14*2π)/60443 weeks
1516.4222 30.24895 (15*2π)/60440 weeks
1617.58419 30.33873 (16*2π)/60438 weeks
1716.71844 27.31453 (17*2π)/60436 weeks
1818.87222 27.69926 (18*2π)/60434 weeks
1921.43058 26.6778 (19*2π)/60432 weeks
2022.39142 29.00999 (20*2π)/60430 weeks
2120.02251 31.41622 (21*2π)/60429 weeks
2215.93312 32.3266 (22*2π)/60427 weeks
2313.01161 30.84821 (23*2π)/60426 weeks
247.95493 27.39159 (24*2π)/60425 weeks
258.69173 21.91242 (25*2π)/60424 weeks
2611.96112 20.11474 (26*2π)/60423 weeks
2713.25189 18.70343 (27*2π)/60422 weeks
2815.17023 20.86284 (28*2π)/60422 weeks
2914.01307 19.99685 (29*2π)/60421 weeks
3014.5418 20.48416 (30*2π)/60420 weeks
3115.23692 18.95379 (31*2π)/60419 weeks
3215.83751 19.26429 (32*2π)/60419 weeks
3316.80947 20.42565 (33*2π)/60418 weeks
3416.05892 20.64388 (34*2π)/60418 weeks
3516.56131 21.51783 (35*2π)/60417 weeks
3616.76232 21.63342 (36*2π)/60417 weeks
3716.73747 23.08004 (37*2π)/60416 weeks
3816.0392 24.90952 (38*2π)/60416 weeks
3913.59513 26.48446 (39*2π)/60415 weeks
4011.77184 26.24336 (40*2π)/60415 weeks
419.51903 26.91441 (41*2π)/60415 weeks
426.87498 26.79013 (42*2π)/60414 weeks
434.39223 25.53485 (43*2π)/60414 weeks
442.03412 22.63394 (44*2π)/60414 weeks
451.51813 20.57495 (45*2π)/60413 weeks
461.13251 18.18138 (46*2π)/60413 weeks
47.87987 15.97552 (47*2π)/60413 weeks
482.13358 14.99356 (48*2π)/60413 weeks
492.24587 14.13937 (49*2π)/60412 weeks
502.42319 13.38002 (50*2π)/60412 weeks
512.25178 12.19883 (51*2π)/60412 weeks
522.63457 9.92032 (52*2π)/60412 weeks
534.25949 9.26549 (53*2π)/60411 weeks
545.4461 9.22501 (54*2π)/60411 weeks
556.34912 8.85152 (55*2π)/60411 weeks
567.02305 9.24294 (56*2π)/60411 weeks
577.96743 9.34542 (57*2π)/60411 weeks
588.33799 10.13273 (58*2π)/60410 weeks
598.59342 10.3669 (59*2π)/60410 weeks
609.18881 10.63615 (60*2π)/60410 weeks
618.22226 11.68298 (61*2π)/60410 weeks
627.95439 12.33279 (62*2π)/60410 weeks
637.94302 11.7871 (63*2π)/60410 weeks
646.42498 11.85285 (64*2π)/6049 weeks
657.41902 11.58006 (65*2π)/6049 weeks
666.40387 11.74833 (66*2π)/6049 weeks
676.18955 11.71012 (67*2π)/6049 weeks
685.92634 11.47646 (68*2π)/6049 weeks
695.52678 11.45027 (69*2π)/6049 weeks
705.36309 11.62009 (70*2π)/6049 weeks
714.26689 11.21934 (71*2π)/6049 weeks
723.43011 10.57135 (72*2π)/6048 weeks
732.65035 8.93631 (73*2π)/6048 weeks
743.32148 7.01513 (74*2π)/6048 weeks
753.97482 6.32874 (75*2π)/6048 weeks
765.52396 5.4473 (76*2π)/6048 weeks
776.76466 5.84558 (77*2π)/6048 weeks
787.57577 6.02817 (78*2π)/6048 weeks
797.44472 6.96109 (79*2π)/6048 weeks
807.86642 7.73277 (80*2π)/6048 weeks
816.975 7.90691 (81*2π)/6047 weeks
826.6303 8.00914 (82*2π)/6047 weeks
835.46894 7.03852 (83*2π)/6047 weeks
845.7403 6.27482 (84*2π)/6047 weeks
856.68666 4.97847 (85*2π)/6047 weeks
867.57273 5.48913 (86*2π)/6047 weeks
878.31282 6.09361 (87*2π)/6047 weeks
888.05486 6.60707 (88*2π)/6047 weeks
897.76669 6.50294 (89*2π)/6047 weeks
907.99398 6.80742 (90*2π)/6047 weeks
917.79021 7.09888 (91*2π)/6047 weeks
927.1323 7.00115 (92*2π)/6047 weeks
936.96648 6.17603 (93*2π)/6046 weeks
947.64152 5.63088 (94*2π)/6046 weeks
958.08919 5.92504 (95*2π)/6046 weeks
968.82204 5.78637 (96*2π)/6046 weeks
979.05846 5.89871 (97*2π)/6046 weeks
989.85601 6.82252 (98*2π)/6046 weeks
9910.346 7.75457 (99*2π)/6046 weeks
1009.88094 9.35058 (100*2π)/6046 weeks
1019.24057 10.29725 (101*2π)/6046 weeks
1027.61615 11.22172 (102*2π)/6046 weeks
1036.38886 10.85441 (103*2π)/6046 weeks
1044.98299 10.48074 (104*2π)/6046 weeks
1054.16724 9.23314 (105*2π)/6046 weeks
1063.79466 7.87257 (106*2π)/6046 weeks
1074.31358 6.78181 (107*2π)/6046 weeks
1084.97084 6.35298 (108*2π)/6046 weeks
1096.08282 6.562 (109*2π)/6046 weeks
1105.82984 6.91328 (110*2π)/6045 weeks
1115.37439 7.31524 (111*2π)/6045 weeks
1125.4984 7.01052 (112*2π)/6045 weeks
1135.0866 6.37452 (113*2π)/6045 weeks
1145.63421 6.19815 (114*2π)/6045 weeks
1155.96045 6.22457 (115*2π)/6045 weeks
1166.11567 6.45858 (116*2π)/6045 weeks
1176.02938 7.37559 (117*2π)/6045 weeks
1185.2304 7.32445 (118*2π)/6045 weeks
1194.34476 7.16629 (119*2π)/6045 weeks
1203.83708 6.73688 (120*2π)/6045 weeks
1213.35871 5.54609 (121*2π)/6045 weeks
1223.90575 4.76463 (122*2π)/6045 weeks
1234.01099 3.69269 (123*2π)/6045 weeks
1245.04269 3.88826 (124*2π)/6045 weeks
1255.40593 3.73442 (125*2π)/6045 weeks
1265.74374 3.67202 (126*2π)/6045 weeks
1276.19292 3.67262 (127*2π)/6045 weeks
1286.75724 3.89989 (128*2π)/6045 weeks
1297.05955 4.2197 (129*2π)/6045 weeks
1306.95788 4.89647 (130*2π)/6045 weeks
1316.70191 5.1272 (131*2π)/6045 weeks
1326.29647 5.4231 (132*2π)/6045 weeks
1335.90948 5.27989 (133*2π)/6045 weeks
1345.67178 5.18371 (134*2π)/6045 weeks
1355.78169 4.91981 (135*2π)/6044 weeks
1365.48829 4.76055 (136*2π)/6044 weeks
1375.79145 4.56343 (137*2π)/6044 weeks
1385.59274 4.61429 (138*2π)/6044 weeks
1396.11433 4.30767 (139*2π)/6044 weeks
1406.18883 4.52442 (140*2π)/6044 weeks
1416.71687 4.78315 (141*2π)/6044 weeks
1426.2318 5.17539 (142*2π)/6044 weeks
1436.26917 5.56763 (143*2π)/6044 weeks
1445.72726 5.51544 (144*2π)/6044 weeks
1455.10776 5.45282 (145*2π)/6044 weeks
1464.82755 5.15536 (146*2π)/6044 weeks
1474.88487 4.64883 (147*2π)/6044 weeks
1485.02257 4.49292 (148*2π)/6044 weeks
1494.9416 4.70488 (149*2π)/6044 weeks
1504.64358 4.23444 (150*2π)/6044 weeks
1514.70708 3.7378 (151*2π)/6044 weeks
1525.16991 3.44273 (152*2π)/6044 weeks
1535.54584 3.68679 (153*2π)/6044 weeks
1545.52924 3.97581 (154*2π)/6044 weeks
1555.47876 3.88186 (155*2π)/6044 weeks
1565.37477 3.58146 (156*2π)/6044 weeks
1575.61821 3.91247 (157*2π)/6044 weeks
1585.58715 3.83852 (158*2π)/6044 weeks
1595.72316 3.96829 (159*2π)/6044 weeks
1605.66151 4.10452 (160*2π)/6044 weeks
1615.52398 4.28257 (161*2π)/6044 weeks
1625.13208 4.52467 (162*2π)/6044 weeks
1634.57565 4.49697 (163*2π)/6044 weeks
1644.16409 4.09388 (164*2π)/6044 weeks
1653.75927 3.62754 (165*2π)/6044 weeks
1663.68766 2.79562 (166*2π)/6044 weeks
1673.88397 2.33808 (167*2π)/6044 weeks
1684.35733 1.50828 (168*2π)/6044 weeks
1694.76921 1.61458 (169*2π)/6044 weeks
1705.48508 1.71069 (170*2π)/6044 weeks
1715.51857 1.98817 (171*2π)/6044 weeks
1725.65397 2.17059 (172*2π)/6044 weeks
1735.51358 2.2775 (173*2π)/6043 weeks
1745.44004 1.92953 (174*2π)/6043 weeks
1755.87498 1.69343 (175*2π)/6043 weeks
1766.254 1.47594 (176*2π)/6043 weeks
1776.67447 2.19269 (177*2π)/6043 weeks
1786.61514 2.652 (178*2π)/6043 weeks
1796.21787 2.92561 (179*2π)/6043 weeks
1805.87707 2.91165 (180*2π)/6043 weeks
1815.79792 2.67781 (181*2π)/6043 weeks
1825.92842 2.75018 (182*2π)/6043 weeks
1835.87087 2.7351 (183*2π)/6043 weeks
1845.65248 2.81317 (184*2π)/6043 weeks
1855.37838 2.75265 (185*2π)/6043 weeks
1865.36382 2.66228 (186*2π)/6043 weeks
1874.90657 2.221 (187*2π)/6043 weeks
1885.084 1.67151 (188*2π)/6043 weeks
1895.42778 1.2153 (189*2π)/6043 weeks
1906.12653 .96665 (190*2π)/6043 weeks
1916.43691 1.17487 (191*2π)/6043 weeks
1926.71472 1.35636 (192*2π)/6043 weeks
1936.88373 1.35724 (193*2π)/6043 weeks
1947.17973 1.60475 (194*2π)/6043 weeks
1957.48697 1.70307 (195*2π)/6043 weeks
1967.88102 2.26595 (196*2π)/6043 weeks
1977.80122 2.60858 (197*2π)/6043 weeks
1987.82988 3.28997 (198*2π)/6043 weeks
1997.1751 3.38958 (199*2π)/6043 weeks
2006.47871 3.49014 (200*2π)/6043 weeks
2016.49826 3.12919 (201*2π)/6043 weeks
2026.31659 2.83333 (202*2π)/6043 weeks
2036.64776 2.71975 (203*2π)/6043 weeks
2046.4848 2.92373 (204*2π)/6043 weeks
2056.58262 2.93782 (205*2π)/6043 weeks
2066.43219 3.24245 (206*2π)/6043 weeks
2076.3136 3.33243 (207*2π)/6043 weeks
2085.83853 3.18991 (208*2π)/6043 weeks
2095.78547 3.15775 (209*2π)/6043 weeks
2105.74144 2.86794 (210*2π)/6043 weeks
2115.81194 2.78549 (211*2π)/6043 weeks
2125.6944 2.57031 (212*2π)/6043 weeks
2135.97627 2.52802 (213*2π)/6043 weeks
2146.1357 2.47479 (214*2π)/6043 weeks
2156.27508 2.96836 (215*2π)/6043 weeks
2166.11873 3.34589 (216*2π)/6043 weeks
2175.5658 3.54453 (217*2π)/6043 weeks
2185.05644 3.31765 (218*2π)/6043 weeks
2194.61375 2.98767 (219*2π)/6043 weeks
2204.58416 2.3928 (220*2π)/6043 weeks
2214.6993 2.06088 (221*2π)/6043 weeks
2225.09233 1.76699 (222*2π)/6043 weeks
2235.29579 1.86183 (223*2π)/6043 weeks
2245.43055 1.61343 (224*2π)/6043 weeks
2255.62583 1.56038 (225*2π)/6043 weeks
2266.07917 1.56427 (226*2π)/6043 weeks
2276.31196 1.56929 (227*2π)/6043 weeks
2286.54999 1.96784 (228*2π)/6043 weeks
2296.79923 2.35035 (229*2π)/6043 weeks
2306.44586 2.83955 (230*2π)/6043 weeks
2316.25411 3.19682 (231*2π)/6043 weeks
2325.71988 2.99882 (232*2π)/6043 weeks
2335.44777 2.90174 (233*2π)/6043 weeks
2345.46306 2.47771 (234*2π)/6043 weeks
2355.45785 2.54911 (235*2π)/6043 weeks
2365.52672 2.47558 (236*2π)/6043 weeks
2375.48647 2.47793 (237*2π)/6043 weeks
2385.60998 2.73558 (238*2π)/6043 weeks
2395.32287 3.02184 (239*2π)/6043 weeks
2404.81933 3.02101 (240*2π)/6043 weeks
2414.14883 2.77127 (241*2π)/6043 weeks
2423.85459 1.88652 (242*2π)/6042 weeks
2433.99926 1.29871 (243*2π)/6042 weeks
2444.56816 .86091 (244*2π)/6042 weeks
2455.03004 .8125 (245*2π)/6042 weeks
2465.24248 1.15528 (246*2π)/6042 weeks
2475.24846 1.10554 (247*2π)/6042 weeks
2485.14268 1.19214 (248*2π)/6042 weeks
2495.12219 .99833 (249*2π)/6042 weeks
2505.20471 .89686 (250*2π)/6042 weeks
2515.23698 .56007 (251*2π)/6042 weeks
2525.76966 .33976 (252*2π)/6042 weeks
2536.23925 .37683 (253*2π)/6042 weeks
2546.78608 .71498 (254*2π)/6042 weeks
2557.14737 1.18358 (255*2π)/6042 weeks
2567.02784 1.70774 (256*2π)/6042 weeks
2577.14934 2.11725 (257*2π)/6042 weeks
2586.97048 2.71299 (258*2π)/6042 weeks
2596.6912 3.02423 (259*2π)/6042 weeks
2606.36041 3.4234 (260*2π)/6042 weeks
2615.78137 3.61187 (261*2π)/6042 weeks
2625.32209 3.36936 (262*2π)/6042 weeks
2635.1408 3.38891 (263*2π)/6042 weeks
2644.92367 3.3705 (264*2π)/6042 weeks
2654.61643 3.46957 (265*2π)/6042 weeks
2664.00714 3.18527 (266*2π)/6042 weeks
2673.8355 2.64816 (267*2π)/6042 weeks
2683.94714 2.08968 (268*2π)/6042 weeks
2694.13961 2.20484 (269*2π)/6042 weeks
2704.35453 2.21084 (270*2π)/6042 weeks
2714.05159 2.54797 (271*2π)/6042 weeks
2723.76276 2.39593 (272*2π)/6042 weeks
2733.27052 2.38851 (273*2π)/6042 weeks
2742.94123 1.9678 (274*2π)/6042 weeks
2752.70089 1.27179 (275*2π)/6042 weeks
2762.8634 .75992 (276*2π)/6042 weeks
2773.00711 .13366 (277*2π)/6042 weeks
2783.52757 -.04472 (278*2π)/6042 weeks
2793.71808 -.21443 (279*2π)/6042 weeks
2804.03649 -.50818 (280*2π)/6042 weeks
2814.47168 -.29789 (281*2π)/6042 weeks
2824.828 -.17897 (282*2π)/6042 weeks
2834.90366 -.02514 (283*2π)/6042 weeks
2844.95369 .10851 (284*2π)/6042 weeks
2855.12682 .12535 (285*2π)/6042 weeks
2865.21211 .38946 (286*2π)/6042 weeks
2875.22519 .69571 (287*2π)/6042 weeks
2884.85003 .8338 (288*2π)/6042 weeks
2894.38022 .93681 (289*2π)/6042 weeks
2904.14304 .42299 (290*2π)/6042 weeks
2914.17487 .01413 (291*2π)/6042 weeks
2924.64781 -.24119 (292*2π)/6042 weeks
2935.33669 -.12131 (293*2π)/6042 weeks
2945.57067 .62939 (294*2π)/6042 weeks
2955.07419 1.11337 (295*2π)/6042 weeks
2964.71394 1.25108 (296*2π)/6042 weeks
2974.16822 1.17328 (297*2π)/6042 weeks
2983.97512 .94701 (298*2π)/6042 weeks
2993.6008 .60455 (299*2π)/6042 weeks
3003.64723 .23923 (300*2π)/6042 weeks
3013.95655 -.02012 (301*2π)/6042 weeks
3023.98644   (302*2π)/6042 weeks
3033.95655 .02012 (303*2π)/6042 weeks
3043.64723 -.23923 (304*2π)/6042 weeks
3053.6008 -.60455 (305*2π)/6042 weeks
3063.97512 -.94701 (306*2π)/6042 weeks
3074.16822 -1.17328 (307*2π)/6042 weeks
3084.71394 -1.25108 (308*2π)/6042 weeks
3095.07419 -1.11337 (309*2π)/6042 weeks
3105.57067 -.62939 (310*2π)/6042 weeks
3115.33669 .12131 (311*2π)/6042 weeks
3124.64781 .24119 (312*2π)/6042 weeks
3134.17487 -.01413 (313*2π)/6042 weeks
3144.14304 -.42299 (314*2π)/6042 weeks
3154.38022 -.93681 (315*2π)/6042 weeks
3164.85003 -.8338 (316*2π)/6042 weeks
3175.22519 -.69571 (317*2π)/6042 weeks
3185.21211 -.38946 (318*2π)/6042 weeks
3195.12682 -.12535 (319*2π)/6042 weeks
3204.95369 -.10851 (320*2π)/6042 weeks
3214.90366 .02514 (321*2π)/6042 weeks
3224.828 .17897 (322*2π)/6042 weeks
3234.47168 .29789 (323*2π)/6042 weeks
3244.03649 .50818 (324*2π)/6042 weeks
3253.71808 .21443 (325*2π)/6042 weeks
3263.52757 .04472 (326*2π)/6042 weeks
3273.00711 -.13366 (327*2π)/6042 weeks
3282.8634 -.75992 (328*2π)/6042 weeks
3292.70089 -1.27179 (329*2π)/6042 weeks
3302.94123 -1.9678 (330*2π)/6042 weeks
3313.27052 -2.38851 (331*2π)/6042 weeks
3323.76276 -2.39593 (332*2π)/6042 weeks
3334.05159 -2.54797 (333*2π)/6042 weeks
3344.35453 -2.21084 (334*2π)/6042 weeks
3354.13961 -2.20484 (335*2π)/6042 weeks
3363.94714 -2.08968 (336*2π)/6042 weeks
3373.8355 -2.64816 (337*2π)/6042 weeks
3384.00714 -3.18527 (338*2π)/6042 weeks
3394.61643 -3.46957 (339*2π)/6042 weeks
3404.92367 -3.3705 (340*2π)/6042 weeks
3415.1408 -3.38891 (341*2π)/6042 weeks
3425.32209 -3.36936 (342*2π)/6042 weeks
3435.78137 -3.61187 (343*2π)/6042 weeks
3446.36041 -3.4234 (344*2π)/6042 weeks
3456.6912 -3.02423 (345*2π)/6042 weeks
3466.97048 -2.71299 (346*2π)/6042 weeks
3477.14934 -2.11725 (347*2π)/6042 weeks
3487.02784 -1.70774 (348*2π)/6042 weeks
3497.14737 -1.18358 (349*2π)/6042 weeks
3506.78608 -.71498 (350*2π)/6042 weeks
3516.23925 -.37683 (351*2π)/6042 weeks
3525.76966 -.33976 (352*2π)/6042 weeks
3535.23698 -.56007 (353*2π)/6042 weeks
3545.20471 -.89686 (354*2π)/6042 weeks
3555.12219 -.99833 (355*2π)/6042 weeks
3565.14268 -1.19214 (356*2π)/6042 weeks
3575.24846 -1.10554 (357*2π)/6042 weeks
3585.24248 -1.15528 (358*2π)/6042 weeks
3595.03004 -.8125 (359*2π)/6042 weeks
3604.56816 -.86091 (360*2π)/6042 weeks
3613.99926 -1.29871 (361*2π)/6042 weeks
3623.85459 -1.88652 (362*2π)/6042 weeks
3634.14883 -2.77127 (363*2π)/6042 weeks
3644.81933 -3.02101 (364*2π)/6042 weeks
3655.32287 -3.02184 (365*2π)/6042 weeks
3665.60998 -2.73558 (366*2π)/6042 weeks
3675.48647 -2.47793 (367*2π)/6042 weeks
3685.52672 -2.47558 (368*2π)/6042 weeks
3695.45785 -2.54911 (369*2π)/6042 weeks
3705.46306 -2.47771 (370*2π)/6042 weeks
3715.44777 -2.90174 (371*2π)/6042 weeks
3725.71988 -2.99882 (372*2π)/6042 weeks
3736.25411 -3.19682 (373*2π)/6042 weeks
3746.44586 -2.83955 (374*2π)/6042 weeks
3756.79923 -2.35035 (375*2π)/6042 weeks
3766.54999 -1.96784 (376*2π)/6042 weeks
3776.31196 -1.56929 (377*2π)/6042 weeks
3786.07917 -1.56427 (378*2π)/6042 weeks
3795.62583 -1.56038 (379*2π)/6042 weeks
3805.43055 -1.61343 (380*2π)/6042 weeks
3815.29579 -1.86183 (381*2π)/6042 weeks
3825.09233 -1.76699 (382*2π)/6042 weeks
3834.6993 -2.06088 (383*2π)/6042 weeks
3844.58416 -2.3928 (384*2π)/6042 weeks
3854.61375 -2.98767 (385*2π)/6042 weeks
3865.05644 -3.31765 (386*2π)/6042 weeks
3875.5658 -3.54453 (387*2π)/6042 weeks
3886.11873 -3.34589 (388*2π)/6042 weeks
3896.27508 -2.96836 (389*2π)/6042 weeks
3906.1357 -2.47479 (390*2π)/6042 weeks
3915.97627 -2.52802 (391*2π)/6042 weeks
3925.6944 -2.57031 (392*2π)/6042 weeks
3935.81194 -2.78549 (393*2π)/6042 weeks
3945.74144 -2.86794 (394*2π)/6042 weeks
3955.78547 -3.15775 (395*2π)/6042 weeks
3965.83853 -3.18991 (396*2π)/6042 weeks
3976.3136 -3.33243 (397*2π)/6042 weeks
3986.43219 -3.24245 (398*2π)/6042 weeks
3996.58262 -2.93782 (399*2π)/6042 weeks
4006.4848 -2.92373 (400*2π)/6042 weeks
4016.64776 -2.71975 (401*2π)/6042 weeks
4026.31659 -2.83333 (402*2π)/6042 weeks
4036.49826 -3.12919 (403*2π)/6041 weeks
4046.47871 -3.49014 (404*2π)/6041 weeks
4057.1751 -3.38958 (405*2π)/6041 weeks
4067.82988 -3.28997 (406*2π)/6041 weeks
4077.80122 -2.60858 (407*2π)/6041 weeks
4087.88102 -2.26595 (408*2π)/6041 weeks
4097.48697 -1.70307 (409*2π)/6041 weeks
4107.17973 -1.60475 (410*2π)/6041 weeks
4116.88373 -1.35724 (411*2π)/6041 weeks
4126.71472 -1.35636 (412*2π)/6041 weeks
4136.43691 -1.17487 (413*2π)/6041 weeks
4146.12653 -.96665 (414*2π)/6041 weeks
4155.42778 -1.2153 (415*2π)/6041 weeks
4165.084 -1.67151 (416*2π)/6041 weeks
4174.90657 -2.221 (417*2π)/6041 weeks
4185.36382 -2.66228 (418*2π)/6041 weeks
4195.37838 -2.75265 (419*2π)/6041 weeks
4205.65248 -2.81317 (420*2π)/6041 weeks
4215.87087 -2.7351 (421*2π)/6041 weeks
4225.92842 -2.75018 (422*2π)/6041 weeks
4235.79792 -2.67781 (423*2π)/6041 weeks
4245.87707 -2.91165 (424*2π)/6041 weeks
4256.21787 -2.92561 (425*2π)/6041 weeks
4266.61514 -2.652 (426*2π)/6041 weeks
4276.67447 -2.19269 (427*2π)/6041 weeks
4286.254 -1.47594 (428*2π)/6041 weeks
4295.87498 -1.69343 (429*2π)/6041 weeks
4305.44004 -1.92953 (430*2π)/6041 weeks
4315.51358 -2.2775 (431*2π)/6041 weeks
4325.65397 -2.17059 (432*2π)/6041 weeks
4335.51857 -1.98817 (433*2π)/6041 weeks
4345.48508 -1.71069 (434*2π)/6041 weeks
4354.76921 -1.61458 (435*2π)/6041 weeks
4364.35733 -1.50828 (436*2π)/6041 weeks
4373.88397 -2.33808 (437*2π)/6041 weeks
4383.68766 -2.79562 (438*2π)/6041 weeks
4393.75927 -3.62754 (439*2π)/6041 weeks
4404.16409 -4.09388 (440*2π)/6041 weeks
4414.57565 -4.49697 (441*2π)/6041 weeks
4425.13208 -4.52467 (442*2π)/6041 weeks
4435.52398 -4.28257 (443*2π)/6041 weeks
4445.66151 -4.10452 (444*2π)/6041 weeks
4455.72316 -3.96829 (445*2π)/6041 weeks
4465.58715 -3.83852 (446*2π)/6041 weeks
4475.61821 -3.91247 (447*2π)/6041 weeks
4485.37477 -3.58146 (448*2π)/6041 weeks
4495.47876 -3.88186 (449*2π)/6041 weeks
4505.52924 -3.97581 (450*2π)/6041 weeks
4515.54584 -3.68679 (451*2π)/6041 weeks
4525.16991 -3.44273 (452*2π)/6041 weeks
4534.70708 -3.7378 (453*2π)/6041 weeks
4544.64358 -4.23444 (454*2π)/6041 weeks
4554.9416 -4.70488 (455*2π)/6041 weeks
4565.02257 -4.49292 (456*2π)/6041 weeks
4574.88487 -4.64883 (457*2π)/6041 weeks
4584.82755 -5.15536 (458*2π)/6041 weeks
4595.10776 -5.45282 (459*2π)/6041 weeks
4605.72726 -5.51544 (460*2π)/6041 weeks
4616.26917 -5.56763 (461*2π)/6041 weeks
4626.2318 -5.17539 (462*2π)/6041 weeks
4636.71687 -4.78315 (463*2π)/6041 weeks
4646.18883 -4.52442 (464*2π)/6041 weeks
4656.11433 -4.30767 (465*2π)/6041 weeks
4665.59274 -4.61429 (466*2π)/6041 weeks
4675.79145 -4.56343 (467*2π)/6041 weeks
4685.48829 -4.76055 (468*2π)/6041 weeks
4695.78169 -4.91981 (469*2π)/6041 weeks
4705.67178 -5.18371 (470*2π)/6041 weeks
4715.90948 -5.27989 (471*2π)/6041 weeks
4726.29647 -5.4231 (472*2π)/6041 weeks
4736.70191 -5.1272 (473*2π)/6041 weeks
4746.95788 -4.89647 (474*2π)/6041 weeks
4757.05955 -4.2197 (475*2π)/6041 weeks
4766.75724 -3.89989 (476*2π)/6041 weeks
4776.19292 -3.67262 (477*2π)/6041 weeks
4785.74374 -3.67202 (478*2π)/6041 weeks
4795.40593 -3.73442 (479*2π)/6041 weeks
4805.04269 -3.88826 (480*2π)/6041 weeks
4814.01099 -3.69269 (481*2π)/6041 weeks
4823.90575 -4.76463 (482*2π)/6041 weeks
4833.35871 -5.54609 (483*2π)/6041 weeks
4843.83708 -6.73688 (484*2π)/6041 weeks
4854.34476 -7.16629 (485*2π)/6041 weeks
4865.2304 -7.32445 (486*2π)/6041 weeks
4876.02938 -7.37559 (487*2π)/6041 weeks
4886.11567 -6.45858 (488*2π)/6041 weeks
4895.96045 -6.22457 (489*2π)/6041 weeks
4905.63421 -6.19815 (490*2π)/6041 weeks
4915.0866 -6.37452 (491*2π)/6041 weeks
4925.4984 -7.01052 (492*2π)/6041 weeks
4935.37439 -7.31524 (493*2π)/6041 weeks
4945.82984 -6.91328 (494*2π)/6041 weeks
4956.08282 -6.562 (495*2π)/6041 weeks
4964.97084 -6.35298 (496*2π)/6041 weeks
4974.31358 -6.78181 (497*2π)/6041 weeks
4983.79466 -7.87257 (498*2π)/6041 weeks
4994.16724 -9.23314 (499*2π)/6041 weeks
5004.98299 -10.48074 (500*2π)/6041 weeks
5016.38886 -10.85441 (501*2π)/6041 weeks
5027.61615 -11.22172 (502*2π)/6041 weeks
5039.24057 -10.29725 (503*2π)/6041 weeks
5049.88094 -9.35058 (504*2π)/6041 weeks
50510.346 -7.75457 (505*2π)/6041 weeks
5069.85601 -6.82252 (506*2π)/6041 weeks
5079.05846 -5.89871 (507*2π)/6041 weeks
5088.82204 -5.78637 (508*2π)/6041 weeks
5098.08919 -5.92504 (509*2π)/6041 weeks
5107.64152 -5.63088 (510*2π)/6041 weeks
5116.96648 -6.17603 (511*2π)/6041 weeks
5127.1323 -7.00115 (512*2π)/6041 weeks
5137.79021 -7.09888 (513*2π)/6041 weeks
5147.99398 -6.80742 (514*2π)/6041 weeks
5157.76669 -6.50294 (515*2π)/6041 weeks
5168.05486 -6.60707 (516*2π)/6041 weeks
5178.31282 -6.09361 (517*2π)/6041 weeks
5187.57273 -5.48913 (518*2π)/6041 weeks
5196.68666 -4.97847 (519*2π)/6041 weeks
5205.7403 -6.27482 (520*2π)/6041 weeks
5215.46894 -7.03852 (521*2π)/6041 weeks
5226.6303 -8.00914 (522*2π)/6041 weeks
5236.975 -7.90691 (523*2π)/6041 weeks
5247.86642 -7.73277 (524*2π)/6041 weeks
5257.44472 -6.96109 (525*2π)/6041 weeks
5267.57577 -6.02817 (526*2π)/6041 weeks
5276.76466 -5.84558 (527*2π)/6041 weeks
5285.52396 -5.4473 (528*2π)/6041 weeks
5293.97482 -6.32874 (529*2π)/6041 weeks
5303.32148 -7.01513 (530*2π)/6041 weeks
5312.65035 -8.93631 (531*2π)/6041 weeks
5323.43011 -10.57135 (532*2π)/6041 weeks
5334.26689 -11.21934 (533*2π)/6041 weeks
5345.36309 -11.62009 (534*2π)/6041 weeks
5355.52678 -11.45027 (535*2π)/6041 weeks
5365.92634 -11.47646 (536*2π)/6041 weeks
5376.18955 -11.71012 (537*2π)/6041 weeks
5386.40387 -11.74833 (538*2π)/6041 weeks
5397.41902 -11.58006 (539*2π)/6041 weeks
5406.42498 -11.85285 (540*2π)/6041 weeks
5417.94302 -11.7871 (541*2π)/6041 weeks
5427.95439 -12.33279 (542*2π)/6041 weeks
5438.22226 -11.68298 (543*2π)/6041 weeks
5449.18881 -10.63615 (544*2π)/6041 weeks
5458.59342 -10.3669 (545*2π)/6041 weeks
5468.33799 -10.13273 (546*2π)/6041 weeks
5477.96743 -9.34542 (547*2π)/6041 weeks
5487.02305 -9.24294 (548*2π)/6041 weeks
5496.34912 -8.85152 (549*2π)/6041 weeks
5505.4461 -9.22501 (550*2π)/6041 weeks
5514.25949 -9.26549 (551*2π)/6041 weeks
5522.63457 -9.92032 (552*2π)/6041 weeks
5532.25178 -12.19883 (553*2π)/6041 weeks
5542.42319 -13.38002 (554*2π)/6041 weeks
5552.24587 -14.13937 (555*2π)/6041 weeks
5562.13358 -14.99356 (556*2π)/6041 weeks
557.87987 -15.97552 (557*2π)/6041 weeks
5581.13251 -18.18138 (558*2π)/6041 weeks
5591.51813 -20.57495 (559*2π)/6041 weeks
5602.03412 -22.63394 (560*2π)/6041 weeks
5614.39223 -25.53485 (561*2π)/6041 weeks
5626.87498 -26.79013 (562*2π)/6041 weeks
5639.51903 -26.91441 (563*2π)/6041 weeks
56411.77184 -26.24336 (564*2π)/6041 weeks
56513.59513 -26.48446 (565*2π)/6041 weeks
56616.0392 -24.90952 (566*2π)/6041 weeks
56716.73747 -23.08004 (567*2π)/6041 weeks
56816.76232 -21.63342 (568*2π)/6041 weeks
56916.56131 -21.51783 (569*2π)/6041 weeks
57016.05892 -20.64388 (570*2π)/6041 weeks
57116.80947 -20.42565 (571*2π)/6041 weeks
57215.83751 -19.26429 (572*2π)/6041 weeks
57315.23692 -18.95379 (573*2π)/6041 weeks
57414.5418 -20.48416 (574*2π)/6041 weeks
57514.01307 -19.99685 (575*2π)/6041 weeks
57615.17023 -20.86284 (576*2π)/6041 weeks
57713.25189 -18.70343 (577*2π)/6041 weeks
57811.96112 -20.11474 (578*2π)/6041 weeks
5798.69173 -21.91242 (579*2π)/6041 weeks
5807.95493 -27.39159 (580*2π)/6041 weeks
58113.01161 -30.84821 (581*2π)/6041 weeks
58215.93312 -32.3266 (582*2π)/6041 weeks
58320.02251 -31.41622 (583*2π)/6041 weeks
58422.39142 -29.00999 (584*2π)/6041 weeks
58521.43058 -26.6778 (585*2π)/6041 weeks
58618.87222 -27.69926 (586*2π)/6041 weeks
58716.71844 -27.31453 (587*2π)/6041 weeks
58817.58419 -30.33873 (588*2π)/6041 weeks
58916.4222 -30.24895 (589*2π)/6041 weeks
59015.28725 -33.40186 (590*2π)/6041 weeks
59116.42364 -36.00418 (591*2π)/6041 weeks
59213.55755 -41.66515 (592*2π)/6041 weeks
59313.66031 -48.40548 (593*2π)/6041 weeks
59420.6048 -58.37579 (594*2π)/6041 weeks
59525.60734 -63.65485 (595*2π)/6041 weeks
59638.45393 -67.35268 (596*2π)/6041 weeks
59745.91473 -66.62851 (597*2π)/6041 weeks
59843.285 -67.91296 (598*2π)/6041 weeks
59947.42051 -78.89494 (599*2π)/6041 weeks
60056.12151 -101.998 (600*2π)/6041 weeks
60190.1358 -117.371 (601*2π)/6041 weeks
602156.2406 -119.6228 (602*2π)/6041 weeks



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