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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 58 weeks (58.2339*sine), 53 weeks (46.9573*sine), and 31 weeks (23.2575*cosine).

ZSL (ProShares UltraShort Silver) has an average price of 156.01 (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 1/13/2020 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0156.0102   0 
1207.304 74.43819 (1*2π)/581581 weeks
2156.8742 127.1914 (2*2π)/581291 weeks
390.25561 119.2114 (3*2π)/581194 weeks
454.40721 100.0328 (4*2π)/581145 weeks
548.11364 79.18516 (5*2π)/581116 weeks
645.12443 67.5724 (6*2π)/58197 weeks
744.57761 70.21253 (7*2π)/58183 weeks
835.85587 71.25111 (8*2π)/58173 weeks
924.81803 63.07113 (9*2π)/58165 weeks
1017.04897 58.23393 (10*2π)/58158 weeks
1114.71514 46.95733 (11*2π)/58153 weeks
1214.51058 39.51769 (12*2π)/58148 weeks
1316.46525 37.68584 (13*2π)/58145 weeks
1416.88244 33.50172 (14*2π)/58142 weeks
1519.22602 31.55169 (15*2π)/58139 weeks
1617.74904 30.31066 (16*2π)/58136 weeks
1720.78764 28.18464 (17*2π)/58134 weeks
1821.679 26.59853 (18*2π)/58132 weeks
1923.25749 28.8452 (19*2π)/58131 weeks
2021.38893 32.07442 (20*2π)/58129 weeks
2117.48232 33.59018 (21*2π)/58128 weeks
2213.9937 31.92825 (22*2π)/58126 weeks
238.64884 29.05237 (23*2π)/58125 weeks
249.12303 22.87911 (24*2π)/58124 weeks
2512.62278 20.70758 (25*2π)/58123 weeks
2614.08674 19.16418 (26*2π)/58122 weeks
2715.77757 21.5271 (27*2π)/58122 weeks
2814.84816 20.31406 (28*2π)/58121 weeks
2914.8783 20.82877 (29*2π)/58120 weeks
3016.16673 19.59657 (30*2π)/58119 weeks
3116.81497 19.7123 (31*2π)/58119 weeks
3217.18472 21.29404 (32*2π)/58118 weeks
3316.91966 21.06288 (33*2π)/58118 weeks
3416.69499 22.1146 (34*2π)/58117 weeks
3517.32392 22.94417 (35*2π)/58117 weeks
3617.01999 24.62264 (36*2π)/58116 weeks
3715.58455 26.8373 (37*2π)/58116 weeks
3812.69007 27.29788 (38*2π)/58115 weeks
3911.11794 27.84045 (39*2π)/58115 weeks
408.42269 27.85947 (40*2π)/58115 weeks
415.36686 26.77512 (41*2π)/58114 weeks
422.274 24.69824 (42*2π)/58114 weeks
431.65203 21.92671 (43*2π)/58114 weeks
44.8799 19.50573 (44*2π)/58113 weeks
45.65714 17.43288 (45*2π)/58113 weeks
462.11674 15.74438 (46*2π)/58113 weeks
472.27646 14.91085 (47*2π)/58112 weeks
482.51651 14.03135 (48*2π)/58112 weeks
492.32548 12.80548 (49*2π)/58112 weeks
502.6725 10.41326 (50*2π)/58112 weeks
514.45364 9.66947 (51*2π)/58111 weeks
525.70019 9.62668 (52*2π)/58111 weeks
536.76654 9.24689 (53*2π)/58111 weeks
547.3882 9.56599 (54*2π)/58111 weeks
558.43172 9.83367 (55*2π)/58111 weeks
568.60608 10.57617 (56*2π)/58110 weeks
578.88828 10.91013 (57*2π)/58110 weeks
589.68155 11.78715 (58*2π)/58110 weeks
598.74021 11.99662 (59*2π)/58110 weeks
607.69122 12.42423 (60*2π)/58110 weeks
617.84964 12.98597 (61*2π)/58110 weeks
627.12945 11.57856 (62*2π)/5819 weeks
637.21086 12.5814 (63*2π)/5819 weeks
646.78282 12.12256 (64*2π)/5819 weeks
656.32883 11.94511 (65*2π)/5819 weeks
666.075 11.89303 (66*2π)/5819 weeks
675.8335 11.68454 (67*2π)/5819 weeks
684.68092 11.74686 (68*2π)/5819 weeks
693.8218 11.0635 (69*2π)/5818 weeks
702.75254 9.62998 (70*2π)/5818 weeks
713.06685 7.47655 (71*2π)/5818 weeks
723.99736 6.73031 (72*2π)/5818 weeks
735.47265 5.59751 (73*2π)/5818 weeks
746.88296 5.96665 (74*2π)/5818 weeks
757.71255 6.20273 (75*2π)/5818 weeks
767.62345 7.21978 (76*2π)/5818 weeks
778.01062 8.10786 (77*2π)/5818 weeks
787.09697 8.23167 (78*2π)/5817 weeks
796.6335 8.43951 (79*2π)/5817 weeks
805.69293 7.11471 (80*2π)/5817 weeks
815.85243 6.32532 (81*2π)/5817 weeks
827.37298 5.34499 (82*2π)/5817 weeks
838.0552 5.76369 (83*2π)/5817 weeks
848.50629 6.70207 (84*2π)/5817 weeks
858.19428 7.06655 (85*2π)/5817 weeks
868.28719 6.85088 (86*2π)/5817 weeks
878.23141 7.25224 (87*2π)/5817 weeks
887.77872 7.53573 (88*2π)/5817 weeks
897.20608 6.95956 (89*2π)/5817 weeks
907.59642 6.10635 (90*2π)/5816 weeks
918.46715 6.12019 (91*2π)/5816 weeks
928.79024 5.91516 (92*2π)/5816 weeks
939.22873 6.39528 (93*2π)/5816 weeks
9410.32959 6.8916 (94*2π)/5816 weeks
9510.75438 7.77105 (95*2π)/5816 weeks
9610.63959 9.51222 (96*2π)/5816 weeks
979.87827 10.47388 (97*2π)/5816 weeks
988.31329 11.60936 (98*2π)/5816 weeks
996.83816 11.21863 (99*2π)/5816 weeks
1005.33839 10.86412 (100*2π)/5816 weeks
1014.41666 9.52599 (101*2π)/5816 weeks
1024.0375 8.04945 (102*2π)/5816 weeks
1034.62985 6.89883 (103*2π)/5816 weeks
1045.31959 6.42038 (104*2π)/5816 weeks
1056.37941 6.9182 (105*2π)/5816 weeks
1066.18525 7.12908 (106*2π)/5815 weeks
1075.4632 7.231 (107*2π)/5815 weeks
1085.46659 7.22951 (108*2π)/5815 weeks
1095.49003 6.35309 (109*2π)/5815 weeks
1105.90434 6.35902 (110*2π)/5815 weeks
1116.24683 6.5562 (111*2π)/5815 weeks
1126.54236 6.92879 (112*2π)/5815 weeks
1135.65739 7.6577 (113*2π)/5815 weeks
1144.99564 7.66476 (114*2π)/5815 weeks
1154.29265 7.0665 (115*2π)/5815 weeks
1163.46996 6.26948 (116*2π)/5815 weeks
1173.7666 5.00215 (117*2π)/5815 weeks
1183.79066 4.40099 (118*2π)/5815 weeks
1195.18082 3.90582 (119*2π)/5815 weeks
1205.45877 3.85488 (120*2π)/5815 weeks
1215.84459 3.82682 (121*2π)/5815 weeks
1226.32638 3.80144 (122*2π)/5815 weeks
1236.93022 3.97103 (123*2π)/5815 weeks
1247.24556 4.34051 (124*2π)/5815 weeks
1257.21997 5.09192 (125*2π)/5815 weeks
1266.95331 5.35347 (126*2π)/5815 weeks
1276.53144 5.66113 (127*2π)/5815 weeks
1286.14561 5.48816 (128*2π)/5815 weeks
1295.87563 5.34754 (129*2π)/5815 weeks
1306.02697 5.16065 (130*2π)/5814 weeks
1315.77313 4.83239 (131*2π)/5814 weeks
1326.10013 4.76627 (132*2π)/5814 weeks
1335.84554 4.53226 (133*2π)/5814 weeks
1346.44608 4.55472 (134*2π)/5814 weeks
1356.52761 4.57123 (135*2π)/5814 weeks
1366.82491 5.31775 (136*2π)/5814 weeks
1376.54163 5.32103 (137*2π)/5814 weeks
1386.04689 5.84731 (138*2π)/5814 weeks
1395.66825 5.88902 (139*2π)/5814 weeks
1405.23175 5.4776 (140*2π)/5814 weeks
1414.97366 4.94321 (141*2π)/5814 weeks
1425.14887 4.6946 (142*2π)/5814 weeks
1435.29167 4.76741 (143*2π)/5814 weeks
1444.79297 4.51579 (144*2π)/5814 weeks
1454.79307 4.01174 (145*2π)/5814 weeks
1465.21821 3.59081 (146*2π)/5814 weeks
1475.72243 3.75588 (147*2π)/5814 weeks
1485.77115 4.06686 (148*2π)/5814 weeks
1495.65173 3.97976 (149*2π)/5814 weeks
1505.50363 3.72718 (150*2π)/5814 weeks
1515.80362 4.04112 (151*2π)/5814 weeks
1525.75776 3.96947 (152*2π)/5814 weeks
1535.88632 4.12949 (153*2π)/5814 weeks
1545.81997 4.29092 (154*2π)/5814 weeks
1555.66917 4.50084 (155*2π)/5814 weeks
1565.19435 4.71626 (156*2π)/5814 weeks
1574.55633 4.61003 (157*2π)/5814 weeks
1584.16695 4.2035 (158*2π)/5814 weeks
1593.75028 3.59735 (159*2π)/5814 weeks
1603.91131 2.77907 (160*2π)/5814 weeks
1614.01372 2.22889 (161*2π)/5814 weeks
1624.96763 1.76517 (162*2π)/5814 weeks
1635.37563 1.54944 (163*2π)/5814 weeks
1645.80396 2.00852 (164*2π)/5814 weeks
1655.90111 2.09621 (165*2π)/5814 weeks
1665.85535 2.29631 (166*2π)/5814 weeks
1675.61313 2.12375 (167*2π)/5813 weeks
1685.88709 1.71124 (168*2π)/5813 weeks
1696.18264 1.64577 (169*2π)/5813 weeks
1706.97875 2.13265 (170*2π)/5813 weeks
1716.93301 2.64695 (171*2π)/5813 weeks
1726.5653 3.04394 (172*2π)/5813 weeks
1736.19999 3.05873 (173*2π)/5813 weeks
1746.05923 2.79793 (174*2π)/5813 weeks
1756.21098 2.81856 (175*2π)/5813 weeks
1766.13096 2.80678 (176*2π)/5813 weeks
1775.90274 2.88818 (177*2π)/5813 weeks
1785.60177 2.79836 (178*2π)/5813 weeks
1795.5489 2.73347 (179*2π)/5813 weeks
1805.11557 2.16016 (180*2π)/5813 weeks
1815.32043 1.6007 (181*2π)/5813 weeks
1825.72809 1.12647 (182*2π)/5813 weeks
1836.51327 1.0635 (183*2π)/5813 weeks
1846.80935 1.20152 (184*2π)/5813 weeks
1857.01839 1.396 (185*2π)/5813 weeks
1867.34592 1.38856 (186*2π)/5813 weeks
1877.53353 1.5886 (187*2π)/5813 weeks
1887.98551 1.80572 (188*2π)/5813 weeks
1898.00187 2.48512 (189*2π)/5813 weeks
1908.09227 2.88782 (190*2π)/5813 weeks
1917.45491 3.60037 (191*2π)/5813 weeks
1927.03788 3.79601 (192*2π)/5813 weeks
1936.63723 3.23864 (193*2π)/5813 weeks
1946.44889 3.12362 (194*2π)/5813 weeks
1956.69609 2.82643 (195*2π)/5813 weeks
1966.72547 3.15218 (196*2π)/5813 weeks
1976.77193 3.09764 (197*2π)/5813 weeks
1986.72855 3.42353 (198*2π)/5813 weeks
1996.57354 3.47931 (199*2π)/5813 weeks
2006.06261 3.42071 (200*2π)/5813 weeks
2016.02841 3.34496 (201*2π)/5813 weeks
2025.96623 3.0353 (202*2π)/5813 weeks
2036.04294 2.95487 (203*2π)/5813 weeks
2045.9509 2.69907 (204*2π)/5813 weeks
2056.2402 2.69797 (205*2π)/5813 weeks
2066.50073 2.65366 (206*2π)/5813 weeks
2076.51978 3.1733 (207*2π)/5813 weeks
2086.27402 3.61168 (208*2π)/5813 weeks
2095.65126 3.70485 (209*2π)/5813 weeks
2105.20731 3.41883 (210*2π)/5813 weeks
2114.79916 2.87443 (211*2π)/5813 weeks
2124.93011 2.32985 (212*2π)/5813 weeks
2135.0924 1.8813 (213*2π)/5813 weeks
2145.51201 1.79301 (214*2π)/5813 weeks
2155.50354 1.73905 (215*2π)/5813 weeks
2165.80178 1.61691 (216*2π)/5813 weeks
2176.11713 1.44092 (217*2π)/5813 weeks
2186.3438 1.61034 (218*2π)/5813 weeks
2196.78685 1.90691 (219*2π)/5813 weeks
2206.98168 2.20607 (220*2π)/5813 weeks
2216.79572 2.88564 (221*2π)/5813 weeks
2226.60064 3.14578 (222*2π)/5813 weeks
2235.91239 3.11995 (223*2π)/5813 weeks
2245.65849 3.02147 (224*2π)/5813 weeks
2255.57902 2.5708 (225*2π)/5813 weeks
2265.62046 2.65192 (226*2π)/5813 weeks
2275.68537 2.57156 (227*2π)/5813 weeks
2285.64876 2.57729 (228*2π)/5813 weeks
2295.75416 2.87855 (229*2π)/5813 weeks
2305.40952 3.18887 (230*2π)/5813 weeks
2314.87113 3.17936 (231*2π)/5813 weeks
2324.13993 2.80663 (232*2π)/5813 weeks
2334.04093 1.86488 (233*2π)/5812 weeks
2344.24392 1.19515 (234*2π)/5812 weeks
2354.87425 .92818 (235*2π)/5812 weeks
2365.39566 .9849 (236*2π)/5812 weeks
2375.36852 1.25848 (237*2π)/5812 weeks
2385.48033 1.30356 (238*2π)/5812 weeks
2395.33692 1.20707 (239*2π)/5812 weeks
2405.42656 1.01184 (240*2π)/5812 weeks
2415.42371 .84068 (241*2π)/5812 weeks
2425.79936 .39697 (242*2π)/5812 weeks
2436.33979 .39821 (243*2π)/5812 weeks
2446.96103 .57228 (244*2π)/5812 weeks
2457.34953 1.02573 (245*2π)/5812 weeks
2467.38737 1.72388 (246*2π)/5812 weeks
2477.47615 2.06363 (247*2π)/5812 weeks
2487.37488 2.70139 (248*2π)/5812 weeks
2497.0356 3.05561 (249*2π)/5812 weeks
2506.70347 3.47221 (250*2π)/5812 weeks
2516.08107 3.70202 (251*2π)/5812 weeks
2525.55639 3.45728 (252*2π)/5812 weeks
2535.35378 3.46617 (253*2π)/5812 weeks
2545.10737 3.44741 (254*2π)/5812 weeks
2554.73018 3.56239 (255*2π)/5812 weeks
2564.09922 3.18873 (256*2π)/5812 weeks
2573.95815 2.64143 (257*2π)/5812 weeks
2584.24214 2.10379 (258*2π)/5812 weeks
2594.29158 2.177 (259*2π)/5812 weeks
2604.50201 2.3868 (260*2π)/5812 weeks
2614.01491 2.5526 (261*2π)/5812 weeks
2623.78287 2.49307 (262*2π)/5812 weeks
2633.17745 2.20255 (263*2π)/5812 weeks
2642.78286 1.72914 (264*2π)/5812 weeks
2652.81438 .98973 (265*2π)/5812 weeks
2662.89591 .50586 (266*2π)/5812 weeks
2673.4392 -.03343 (267*2π)/5812 weeks
2683.7142 -.10546 (268*2π)/5812 weeks
2693.97793 -.3528 (269*2π)/5812 weeks
2704.61888 -.35354 (270*2π)/5812 weeks
2714.92192 -.29649 (271*2π)/5812 weeks
2725.03601 -.05169 (272*2π)/5812 weeks
2735.12449 .10479 (273*2π)/5812 weeks
2745.25541 .11019 (274*2π)/5812 weeks
2755.38995 .39245 (275*2π)/5812 weeks
2765.41759 .70351 (276*2π)/5812 weeks
2775.02574 .89263 (277*2π)/5812 weeks
2784.54077 .99935 (278*2π)/5812 weeks
2794.31056 .44427 (279*2π)/5812 weeks
2804.37266 -.02427 (280*2π)/5812 weeks
2814.89056 -.26801 (281*2π)/5812 weeks
2825.63251 -.01008 (282*2π)/5812 weeks
2835.72786 .83439 (283*2π)/5812 weeks
2845.17257 1.18256 (284*2π)/5812 weeks
2854.74849 1.3449 (285*2π)/5812 weeks
2864.23893 1.09814 (286*2π)/5812 weeks
2873.99051 .94796 (287*2π)/5812 weeks
2883.78664 .40618 (288*2π)/5812 weeks
2893.85681 .00026 (289*2π)/5812 weeks
2904.10734 .00953 (290*2π)/5812 weeks
2914.10734 -.00953 (291*2π)/5812 weeks
2923.85681 -.00026 (292*2π)/5812 weeks
2933.78664 -.40618 (293*2π)/5812 weeks
2943.99051 -.94796 (294*2π)/5812 weeks
2954.23893 -1.09814 (295*2π)/5812 weeks
2964.74849 -1.3449 (296*2π)/5812 weeks
2975.17257 -1.18256 (297*2π)/5812 weeks
2985.72786 -.83439 (298*2π)/5812 weeks
2995.63251 .01008 (299*2π)/5812 weeks
3004.89056 .26801 (300*2π)/5812 weeks
3014.37266 .02427 (301*2π)/5812 weeks
3024.31056 -.44427 (302*2π)/5812 weeks
3034.54077 -.99935 (303*2π)/5812 weeks
3045.02574 -.89263 (304*2π)/5812 weeks
3055.41759 -.70351 (305*2π)/5812 weeks
3065.38995 -.39245 (306*2π)/5812 weeks
3075.25541 -.11019 (307*2π)/5812 weeks
3085.12449 -.10479 (308*2π)/5812 weeks
3095.03601 .05169 (309*2π)/5812 weeks
3104.92192 .29649 (310*2π)/5812 weeks
3114.61888 .35354 (311*2π)/5812 weeks
3123.97793 .3528 (312*2π)/5812 weeks
3133.7142 .10546 (313*2π)/5812 weeks
3143.4392 .03343 (314*2π)/5812 weeks
3152.89591 -.50586 (315*2π)/5812 weeks
3162.81438 -.98973 (316*2π)/5812 weeks
3172.78286 -1.72914 (317*2π)/5812 weeks
3183.17745 -2.20255 (318*2π)/5812 weeks
3193.78287 -2.49307 (319*2π)/5812 weeks
3204.01491 -2.5526 (320*2π)/5812 weeks
3214.50201 -2.3868 (321*2π)/5812 weeks
3224.29158 -2.177 (322*2π)/5812 weeks
3234.24214 -2.10379 (323*2π)/5812 weeks
3243.95815 -2.64143 (324*2π)/5812 weeks
3254.09922 -3.18873 (325*2π)/5812 weeks
3264.73018 -3.56239 (326*2π)/5812 weeks
3275.10737 -3.44741 (327*2π)/5812 weeks
3285.35378 -3.46617 (328*2π)/5812 weeks
3295.55639 -3.45728 (329*2π)/5812 weeks
3306.08107 -3.70202 (330*2π)/5812 weeks
3316.70347 -3.47221 (331*2π)/5812 weeks
3327.0356 -3.05561 (332*2π)/5812 weeks
3337.37488 -2.70139 (333*2π)/5812 weeks
3347.47615 -2.06363 (334*2π)/5812 weeks
3357.38737 -1.72388 (335*2π)/5812 weeks
3367.34953 -1.02573 (336*2π)/5812 weeks
3376.96103 -.57228 (337*2π)/5812 weeks
3386.33979 -.39821 (338*2π)/5812 weeks
3395.79936 -.39697 (339*2π)/5812 weeks
3405.42371 -.84068 (340*2π)/5812 weeks
3415.42656 -1.01184 (341*2π)/5812 weeks
3425.33692 -1.20707 (342*2π)/5812 weeks
3435.48033 -1.30356 (343*2π)/5812 weeks
3445.36852 -1.25848 (344*2π)/5812 weeks
3455.39566 -.9849 (345*2π)/5812 weeks
3464.87425 -.92818 (346*2π)/5812 weeks
3474.24392 -1.19515 (347*2π)/5812 weeks
3484.04093 -1.86488 (348*2π)/5812 weeks
3494.13993 -2.80663 (349*2π)/5812 weeks
3504.87113 -3.17936 (350*2π)/5812 weeks
3515.40952 -3.18887 (351*2π)/5812 weeks
3525.75416 -2.87855 (352*2π)/5812 weeks
3535.64876 -2.57729 (353*2π)/5812 weeks
3545.68537 -2.57156 (354*2π)/5812 weeks
3555.62046 -2.65192 (355*2π)/5812 weeks
3565.57902 -2.5708 (356*2π)/5812 weeks
3575.65849 -3.02147 (357*2π)/5812 weeks
3585.91239 -3.11995 (358*2π)/5812 weeks
3596.60064 -3.14578 (359*2π)/5812 weeks
3606.79572 -2.88564 (360*2π)/5812 weeks
3616.98168 -2.20607 (361*2π)/5812 weeks
3626.78685 -1.90691 (362*2π)/5812 weeks
3636.3438 -1.61034 (363*2π)/5812 weeks
3646.11713 -1.44092 (364*2π)/5812 weeks
3655.80178 -1.61691 (365*2π)/5812 weeks
3665.50354 -1.73905 (366*2π)/5812 weeks
3675.51201 -1.79301 (367*2π)/5812 weeks
3685.0924 -1.8813 (368*2π)/5812 weeks
3694.93011 -2.32985 (369*2π)/5812 weeks
3704.79916 -2.87443 (370*2π)/5812 weeks
3715.20731 -3.41883 (371*2π)/5812 weeks
3725.65126 -3.70485 (372*2π)/5812 weeks
3736.27402 -3.61168 (373*2π)/5812 weeks
3746.51978 -3.1733 (374*2π)/5812 weeks
3756.50073 -2.65366 (375*2π)/5812 weeks
3766.2402 -2.69797 (376*2π)/5812 weeks
3775.9509 -2.69907 (377*2π)/5812 weeks
3786.04294 -2.95487 (378*2π)/5812 weeks
3795.96623 -3.0353 (379*2π)/5812 weeks
3806.02841 -3.34496 (380*2π)/5812 weeks
3816.06261 -3.42071 (381*2π)/5812 weeks
3826.57354 -3.47931 (382*2π)/5812 weeks
3836.72855 -3.42353 (383*2π)/5812 weeks
3846.77193 -3.09764 (384*2π)/5812 weeks
3856.72547 -3.15218 (385*2π)/5812 weeks
3866.69609 -2.82643 (386*2π)/5812 weeks
3876.44889 -3.12362 (387*2π)/5812 weeks
3886.63723 -3.23864 (388*2π)/5811 weeks
3897.03788 -3.79601 (389*2π)/5811 weeks
3907.45491 -3.60037 (390*2π)/5811 weeks
3918.09227 -2.88782 (391*2π)/5811 weeks
3928.00187 -2.48512 (392*2π)/5811 weeks
3937.98551 -1.80572 (393*2π)/5811 weeks
3947.53353 -1.5886 (394*2π)/5811 weeks
3957.34592 -1.38856 (395*2π)/5811 weeks
3967.01839 -1.396 (396*2π)/5811 weeks
3976.80935 -1.20152 (397*2π)/5811 weeks
3986.51327 -1.0635 (398*2π)/5811 weeks
3995.72809 -1.12647 (399*2π)/5811 weeks
4005.32043 -1.6007 (400*2π)/5811 weeks
4015.11557 -2.16016 (401*2π)/5811 weeks
4025.5489 -2.73347 (402*2π)/5811 weeks
4035.60177 -2.79836 (403*2π)/5811 weeks
4045.90274 -2.88818 (404*2π)/5811 weeks
4056.13096 -2.80678 (405*2π)/5811 weeks
4066.21098 -2.81856 (406*2π)/5811 weeks
4076.05923 -2.79793 (407*2π)/5811 weeks
4086.19999 -3.05873 (408*2π)/5811 weeks
4096.5653 -3.04394 (409*2π)/5811 weeks
4106.93301 -2.64695 (410*2π)/5811 weeks
4116.97875 -2.13265 (411*2π)/5811 weeks
4126.18264 -1.64577 (412*2π)/5811 weeks
4135.88709 -1.71124 (413*2π)/5811 weeks
4145.61313 -2.12375 (414*2π)/5811 weeks
4155.85535 -2.29631 (415*2π)/5811 weeks
4165.90111 -2.09621 (416*2π)/5811 weeks
4175.80396 -2.00852 (417*2π)/5811 weeks
4185.37563 -1.54944 (418*2π)/5811 weeks
4194.96763 -1.76517 (419*2π)/5811 weeks
4204.01372 -2.22889 (420*2π)/5811 weeks
4213.91131 -2.77907 (421*2π)/5811 weeks
4223.75028 -3.59735 (422*2π)/5811 weeks
4234.16695 -4.2035 (423*2π)/5811 weeks
4244.55633 -4.61003 (424*2π)/5811 weeks
4255.19435 -4.71626 (425*2π)/5811 weeks
4265.66917 -4.50084 (426*2π)/5811 weeks
4275.81997 -4.29092 (427*2π)/5811 weeks
4285.88632 -4.12949 (428*2π)/5811 weeks
4295.75776 -3.96947 (429*2π)/5811 weeks
4305.80362 -4.04112 (430*2π)/5811 weeks
4315.50363 -3.72718 (431*2π)/5811 weeks
4325.65173 -3.97976 (432*2π)/5811 weeks
4335.77115 -4.06686 (433*2π)/5811 weeks
4345.72243 -3.75588 (434*2π)/5811 weeks
4355.21821 -3.59081 (435*2π)/5811 weeks
4364.79307 -4.01174 (436*2π)/5811 weeks
4374.79297 -4.51579 (437*2π)/5811 weeks
4385.29167 -4.76741 (438*2π)/5811 weeks
4395.14887 -4.6946 (439*2π)/5811 weeks
4404.97366 -4.94321 (440*2π)/5811 weeks
4415.23175 -5.4776 (441*2π)/5811 weeks
4425.66825 -5.88902 (442*2π)/5811 weeks
4436.04689 -5.84731 (443*2π)/5811 weeks
4446.54163 -5.32103 (444*2π)/5811 weeks
4456.82491 -5.31775 (445*2π)/5811 weeks
4466.52761 -4.57123 (446*2π)/5811 weeks
4476.44608 -4.55472 (447*2π)/5811 weeks
4485.84554 -4.53226 (448*2π)/5811 weeks
4496.10013 -4.76627 (449*2π)/5811 weeks
4505.77313 -4.83239 (450*2π)/5811 weeks
4516.02697 -5.16065 (451*2π)/5811 weeks
4525.87563 -5.34754 (452*2π)/5811 weeks
4536.14561 -5.48816 (453*2π)/5811 weeks
4546.53144 -5.66113 (454*2π)/5811 weeks
4556.95331 -5.35347 (455*2π)/5811 weeks
4567.21997 -5.09192 (456*2π)/5811 weeks
4577.24556 -4.34051 (457*2π)/5811 weeks
4586.93022 -3.97103 (458*2π)/5811 weeks
4596.32638 -3.80144 (459*2π)/5811 weeks
4605.84459 -3.82682 (460*2π)/5811 weeks
4615.45877 -3.85488 (461*2π)/5811 weeks
4625.18082 -3.90582 (462*2π)/5811 weeks
4633.79066 -4.40099 (463*2π)/5811 weeks
4643.7666 -5.00215 (464*2π)/5811 weeks
4653.46996 -6.26948 (465*2π)/5811 weeks
4664.29265 -7.0665 (466*2π)/5811 weeks
4674.99564 -7.66476 (467*2π)/5811 weeks
4685.65739 -7.6577 (468*2π)/5811 weeks
4696.54236 -6.92879 (469*2π)/5811 weeks
4706.24683 -6.5562 (470*2π)/5811 weeks
4715.90434 -6.35902 (471*2π)/5811 weeks
4725.49003 -6.35309 (472*2π)/5811 weeks
4735.46659 -7.22951 (473*2π)/5811 weeks
4745.4632 -7.231 (474*2π)/5811 weeks
4756.18525 -7.12908 (475*2π)/5811 weeks
4766.37941 -6.9182 (476*2π)/5811 weeks
4775.31959 -6.42038 (477*2π)/5811 weeks
4784.62985 -6.89883 (478*2π)/5811 weeks
4794.0375 -8.04945 (479*2π)/5811 weeks
4804.41666 -9.52599 (480*2π)/5811 weeks
4815.33839 -10.86412 (481*2π)/5811 weeks
4826.83816 -11.21863 (482*2π)/5811 weeks
4838.31329 -11.60936 (483*2π)/5811 weeks
4849.87827 -10.47388 (484*2π)/5811 weeks
48510.63959 -9.51222 (485*2π)/5811 weeks
48610.75438 -7.77105 (486*2π)/5811 weeks
48710.32959 -6.8916 (487*2π)/5811 weeks
4889.22873 -6.39528 (488*2π)/5811 weeks
4898.79024 -5.91516 (489*2π)/5811 weeks
4908.46715 -6.12019 (490*2π)/5811 weeks
4917.59642 -6.10635 (491*2π)/5811 weeks
4927.20608 -6.95956 (492*2π)/5811 weeks
4937.77872 -7.53573 (493*2π)/5811 weeks
4948.23141 -7.25224 (494*2π)/5811 weeks
4958.28719 -6.85088 (495*2π)/5811 weeks
4968.19428 -7.06655 (496*2π)/5811 weeks
4978.50629 -6.70207 (497*2π)/5811 weeks
4988.0552 -5.76369 (498*2π)/5811 weeks
4997.37298 -5.34499 (499*2π)/5811 weeks
5005.85243 -6.32532 (500*2π)/5811 weeks
5015.69293 -7.11471 (501*2π)/5811 weeks
5026.6335 -8.43951 (502*2π)/5811 weeks
5037.09697 -8.23167 (503*2π)/5811 weeks
5048.01062 -8.10786 (504*2π)/5811 weeks
5057.62345 -7.21978 (505*2π)/5811 weeks
5067.71255 -6.20273 (506*2π)/5811 weeks
5076.88296 -5.96665 (507*2π)/5811 weeks
5085.47265 -5.59751 (508*2π)/5811 weeks
5093.99736 -6.73031 (509*2π)/5811 weeks
5103.06685 -7.47655 (510*2π)/5811 weeks
5112.75254 -9.62998 (511*2π)/5811 weeks
5123.8218 -11.0635 (512*2π)/5811 weeks
5134.68092 -11.74686 (513*2π)/5811 weeks
5145.8335 -11.68454 (514*2π)/5811 weeks
5156.075 -11.89303 (515*2π)/5811 weeks
5166.32883 -11.94511 (516*2π)/5811 weeks
5176.78282 -12.12256 (517*2π)/5811 weeks
5187.21086 -12.5814 (518*2π)/5811 weeks
5197.12945 -11.57856 (519*2π)/5811 weeks
5207.84964 -12.98597 (520*2π)/5811 weeks
5217.69122 -12.42423 (521*2π)/5811 weeks
5228.74021 -11.99662 (522*2π)/5811 weeks
5239.68155 -11.78715 (523*2π)/5811 weeks
5248.88828 -10.91013 (524*2π)/5811 weeks
5258.60608 -10.57617 (525*2π)/5811 weeks
5268.43172 -9.83367 (526*2π)/5811 weeks
5277.3882 -9.56599 (527*2π)/5811 weeks
5286.76654 -9.24689 (528*2π)/5811 weeks
5295.70019 -9.62668 (529*2π)/5811 weeks
5304.45364 -9.66947 (530*2π)/5811 weeks
5312.6725 -10.41326 (531*2π)/5811 weeks
5322.32548 -12.80548 (532*2π)/5811 weeks
5332.51651 -14.03135 (533*2π)/5811 weeks
5342.27646 -14.91085 (534*2π)/5811 weeks
5352.11674 -15.74438 (535*2π)/5811 weeks
536.65714 -17.43288 (536*2π)/5811 weeks
537.8799 -19.50573 (537*2π)/5811 weeks
5381.65203 -21.92671 (538*2π)/5811 weeks
5392.274 -24.69824 (539*2π)/5811 weeks
5405.36686 -26.77512 (540*2π)/5811 weeks
5418.42269 -27.85947 (541*2π)/5811 weeks
54211.11794 -27.84045 (542*2π)/5811 weeks
54312.69007 -27.29788 (543*2π)/5811 weeks
54415.58455 -26.8373 (544*2π)/5811 weeks
54517.01999 -24.62264 (545*2π)/5811 weeks
54617.32392 -22.94417 (546*2π)/5811 weeks
54716.69499 -22.1146 (547*2π)/5811 weeks
54816.91966 -21.06288 (548*2π)/5811 weeks
54917.18472 -21.29404 (549*2π)/5811 weeks
55016.81497 -19.7123 (550*2π)/5811 weeks
55116.16673 -19.59657 (551*2π)/5811 weeks
55214.8783 -20.82877 (552*2π)/5811 weeks
55314.84816 -20.31406 (553*2π)/5811 weeks
55415.77757 -21.5271 (554*2π)/5811 weeks
55514.08674 -19.16418 (555*2π)/5811 weeks
55612.62278 -20.70758 (556*2π)/5811 weeks
5579.12303 -22.87911 (557*2π)/5811 weeks
5588.64884 -29.05237 (558*2π)/5811 weeks
55913.9937 -31.92825 (559*2π)/5811 weeks
56017.48232 -33.59018 (560*2π)/5811 weeks
56121.38893 -32.07442 (561*2π)/5811 weeks
56223.25749 -28.8452 (562*2π)/5811 weeks
56321.679 -26.59853 (563*2π)/5811 weeks
56420.78764 -28.18464 (564*2π)/5811 weeks
56517.74904 -30.31066 (565*2π)/5811 weeks
56619.22602 -31.55169 (566*2π)/5811 weeks
56716.88244 -33.50172 (567*2π)/5811 weeks
56816.46525 -37.68584 (568*2π)/5811 weeks
56914.51058 -39.51769 (569*2π)/5811 weeks
57014.71514 -46.95733 (570*2π)/5811 weeks
57117.04897 -58.23393 (571*2π)/5811 weeks
57224.81803 -63.07113 (572*2π)/5811 weeks
57335.85587 -71.25111 (573*2π)/5811 weeks
57444.57761 -70.21253 (574*2π)/5811 weeks
57545.12443 -67.5724 (575*2π)/5811 weeks
57648.11364 -79.18516 (576*2π)/5811 weeks
57754.40721 -100.0328 (577*2π)/5811 weeks
57890.25561 -119.2114 (578*2π)/5811 weeks
579156.8742 -127.1914 (579*2π)/5811 weeks



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