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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 62 weeks (58.0922*sine), 56 weeks (50.6968*sine), and 31 weeks (21.4713*cosine).

ZSL (ProShares UltraShort Silver) has an average price of 148.18 (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 9/21/2020 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0148.1808   0 
1195.7103 67.70985 (1*2π)/617617 weeks
2154.9216 115.6879 (2*2π)/617309 weeks
389.67604 116.7816 (3*2π)/617206 weeks
457.05331 102.8122 (4*2π)/617154 weeks
546.46827 78.85259 (5*2π)/617123 weeks
642.23156 68.18837 (6*2π)/617103 weeks
745.17677 64.30732 (7*2π)/61788 weeks
838.05282 65.62885 (8*2π)/61777 weeks
926.11852 64.65133 (9*2π)/61769 weeks
1021.14207 58.09224 (10*2π)/61762 weeks
1113.00793 50.69678 (11*2π)/61756 weeks
1213.12884 43.02325 (12*2π)/61751 weeks
1314.35039 36.30542 (13*2π)/61747 weeks
1414.49556 35.19591 (14*2π)/61744 weeks
1515.45295 31.81437 (15*2π)/61741 weeks
1617.77935 30.5399 (16*2π)/61739 weeks
1716.5156 29.22182 (17*2π)/61736 weeks
1819.43273 27.00027 (18*2π)/61734 weeks
1919.74674 25.55642 (19*2π)/61732 weeks
2021.4713 27.36316 (20*2π)/61731 weeks
2120.61735 30.54714 (21*2π)/61729 weeks
2217.82705 32.23809 (22*2π)/61728 weeks
2313.97744 31.19517 (23*2π)/61727 weeks
2410.5433 30.37032 (24*2π)/61726 weeks
258.36523 24.27858 (25*2π)/61725 weeks
2610.59645 19.98387 (26*2π)/61724 weeks
2712.38775 19.53913 (27*2π)/61723 weeks
2815.02679 18.48238 (28*2π)/61722 weeks
2914.30575 20.4036 (29*2π)/61721 weeks
3014.52712 19.09513 (30*2π)/61721 weeks
3113.77599 19.24195 (31*2π)/61720 weeks
3215.23608 18.7281 (32*2π)/61719 weeks
3315.8656 18.77931 (33*2π)/61719 weeks
3416.06006 20.29139 (34*2π)/61718 weeks
3515.7831 20.10203 (35*2π)/61718 weeks
3615.73433 21.20285 (36*2π)/61717 weeks
3716.33494 21.69408 (37*2π)/61717 weeks
3816.21334 23.13162 (38*2π)/61716 weeks
3915.38618 24.99781 (39*2π)/61716 weeks
4012.86188 26.15325 (40*2π)/61715 weeks
4111.41046 26.00521 (41*2π)/61715 weeks
429.09962 26.48299 (42*2π)/61715 weeks
436.48211 26.28191 (43*2π)/61714 weeks
444.14552 25.07592 (44*2π)/61714 weeks
452.07124 22.14286 (45*2π)/61714 weeks
461.55925 20.18852 (46*2π)/61713 weeks
471.21023 17.85804 (47*2π)/61713 weeks
48.9289 15.73008 (48*2π)/61713 weeks
492.15453 14.74349 (49*2π)/61713 weeks
502.25055 13.93655 (50*2π)/61712 weeks
512.44074 13.17928 (51*2π)/61712 weeks
522.24583 12.07679 (52*2π)/61712 weeks
532.33659 10.01577 (53*2π)/61712 weeks
544.01557 9.23913 (54*2π)/61711 weeks
555.2638 9.09682 (55*2π)/61711 weeks
565.99344 8.78156 (56*2π)/61711 weeks
576.88904 9.16164 (57*2π)/61711 weeks
587.6732 9.09763 (58*2π)/61711 weeks
598.28134 9.80545 (59*2π)/61710 weeks
608.37637 10.01468 (60*2π)/61710 weeks
618.6293 10.20464 (61*2π)/61710 weeks
628.49634 11.70101 (62*2π)/61710 weeks
638.36667 11.76704 (63*2π)/61710 weeks
647.43616 11.37005 (64*2π)/61710 weeks
656.91793 12.27147 (65*2π)/6179 weeks
667.00884 10.92269 (66*2π)/6179 weeks
676.69517 11.85215 (67*2π)/6179 weeks
686.42857 11.43314 (68*2π)/6179 weeks
696.01009 11.24001 (69*2π)/6179 weeks
705.79115 11.15206 (70*2π)/6179 weeks
715.46461 10.88896 (71*2π)/6179 weeks
724.57198 11.16835 (72*2π)/6179 weeks
733.74181 10.5642 (73*2π)/6178 weeks
742.71227 9.68612 (74*2π)/6178 weeks
752.44558 7.87308 (75*2π)/6178 weeks
763.57479 6.6729 (76*2π)/6178 weeks
774.14314 5.63259 (77*2π)/6178 weeks
785.70603 5.41978 (78*2π)/6178 weeks
796.52795 5.97645 (79*2π)/6178 weeks
807.55147 6.54916 (80*2π)/6178 weeks
817.33902 6.8921 (81*2π)/6178 weeks
827.29765 7.99498 (82*2π)/6178 weeks
836.67353 7.90828 (83*2π)/6177 weeks
846.17756 8.14171 (84*2π)/6177 weeks
855.50297 6.79826 (85*2π)/6177 weeks
865.63882 6.09949 (86*2π)/6177 weeks
876.94515 5.06764 (87*2π)/6177 weeks
887.58804 5.4862 (88*2π)/6177 weeks
898.20345 6.19916 (89*2π)/6177 weeks
907.9422 6.59665 (90*2π)/6177 weeks
917.71826 6.41271 (91*2π)/6177 weeks
927.87898 6.74014 (92*2π)/6177 weeks
937.66233 7.01568 (93*2π)/6177 weeks
947.0151 6.89273 (94*2π)/6177 weeks
956.85078 6.09828 (95*2π)/6176 weeks
967.47988 5.57332 (96*2π)/6176 weeks
977.93901 5.87223 (97*2π)/6176 weeks
988.58657 5.69113 (98*2π)/6176 weeks
998.77209 5.91232 (99*2π)/6176 weeks
1009.66754 6.72804 (100*2π)/6176 weeks
10110.12187 7.55767 (101*2π)/6176 weeks
1029.92251 9.15075 (102*2π)/6176 weeks
1039.30114 9.99642 (103*2π)/6176 weeks
1048.00209 11.04836 (104*2π)/6176 weeks
1056.60161 10.69784 (105*2π)/6176 weeks
1065.36558 10.48429 (106*2π)/6176 weeks
1074.31443 9.33589 (107*2π)/6176 weeks
1083.81946 8.16987 (108*2π)/6176 weeks
1094.16861 6.95217 (109*2π)/6176 weeks
1104.89609 6.37709 (110*2π)/6176 weeks
1115.82351 6.02739 (111*2π)/6176 weeks
1125.86047 6.77636 (112*2π)/6176 weeks
1135.84476 7.06918 (113*2π)/6175 weeks
1145.41417 6.54819 (114*2π)/6175 weeks
1154.98164 6.54376 (115*2π)/6175 weeks
1165.36275 5.90389 (116*2π)/6175 weeks
1175.62838 5.93053 (117*2π)/6175 weeks
1185.88044 6.17342 (118*2π)/6175 weeks
1196.15758 6.56787 (119*2π)/6175 weeks
1205.30378 7.20087 (120*2π)/6175 weeks
1214.73903 7.21956 (121*2π)/6175 weeks
1224.03753 6.70183 (122*2π)/6175 weeks
1233.30837 6.1802 (123*2π)/6175 weeks
1243.32916 4.97538 (124*2π)/6175 weeks
1253.64042 4.61035 (125*2π)/6175 weeks
1264.49014 3.49827 (126*2π)/6175 weeks
1274.91208 3.78886 (127*2π)/6175 weeks
1285.33874 3.72714 (128*2π)/6175 weeks
1295.70838 3.65104 (129*2π)/6175 weeks
1306.15593 3.68307 (130*2π)/6175 weeks
1316.6478 4.04039 (131*2π)/6175 weeks
1327.02127 4.40963 (132*2π)/6175 weeks
1336.81054 4.94785 (133*2π)/6175 weeks
1346.61668 5.1395 (134*2π)/6175 weeks
1356.16362 5.33597 (135*2π)/6175 weeks
1365.83228 5.15343 (136*2π)/6175 weeks
1375.56204 5.03078 (137*2π)/6175 weeks
1385.69673 4.84725 (138*2π)/6174 weeks
1395.40977 4.62282 (139*2π)/6174 weeks
1405.70253 4.4811 (140*2π)/6174 weeks
1415.48277 4.50962 (141*2π)/6174 weeks
1426.00423 4.24026 (142*2π)/6174 weeks
1436.07701 4.4557 (143*2π)/6174 weeks
1446.59214 4.67106 (144*2π)/6174 weeks
1456.13603 5.10648 (145*2π)/6174 weeks
1466.21454 5.41415 (146*2π)/6174 weeks
1475.63367 5.41095 (147*2π)/6174 weeks
1485.07681 5.43959 (148*2π)/6174 weeks
1494.82978 5.13835 (149*2π)/6174 weeks
1504.79288 4.60621 (150*2π)/6174 weeks
1514.92965 4.4317 (151*2π)/6174 weeks
1524.99879 4.57384 (152*2π)/6174 weeks
1534.5779 4.23932 (153*2π)/6174 weeks
1544.58049 3.79004 (154*2π)/6174 weeks
1554.95604 3.40709 (155*2π)/6174 weeks
1565.4384 3.50925 (156*2π)/6174 weeks
1575.52837 3.76508 (157*2π)/6174 weeks
1585.3277 3.72878 (158*2π)/6174 weeks
1595.1623 3.69179 (159*2π)/6174 weeks
1605.606 3.65306 (160*2π)/6174 weeks
1615.42672 3.71275 (161*2π)/6174 weeks
1625.52468 3.72026 (162*2π)/6174 weeks
1635.46885 3.92776 (163*2π)/6174 weeks
1645.37862 4.12907 (164*2π)/6174 weeks
1655.19561 4.39375 (165*2π)/6174 weeks
1664.7257 4.48352 (166*2π)/6174 weeks
1674.15974 4.25477 (167*2π)/6174 weeks
1683.8288 3.92501 (168*2π)/6174 weeks
1693.50095 3.32482 (169*2π)/6174 weeks
1703.72401 2.64899 (170*2π)/6174 weeks
1713.81906 2.14136 (171*2π)/6174 weeks
1724.71206 1.6948 (172*2π)/6174 weeks
1735.0176 1.49777 (173*2π)/6174 weeks
1745.50903 1.86545 (174*2π)/6174 weeks
1755.53527 1.96087 (175*2π)/6174 weeks
1765.56023 2.16688 (176*2π)/6174 weeks
1775.34975 2.1835 (177*2π)/6173 weeks
1785.40387 1.81119 (178*2π)/6173 weeks
1795.83242 1.73693 (179*2π)/6173 weeks
1806.42185 1.54664 (180*2π)/6173 weeks
1816.58875 2.22228 (181*2π)/6173 weeks
1826.49191 2.66727 (182*2π)/6173 weeks
1836.09368 2.84925 (183*2π)/6173 weeks
1845.75674 2.7972 (184*2π)/6173 weeks
1855.71073 2.58247 (185*2π)/6173 weeks
1865.80307 2.69672 (186*2π)/6173 weeks
1875.76642 2.68871 (187*2π)/6173 weeks
1885.54607 2.75239 (188*2π)/6173 weeks
1895.27804 2.69417 (189*2π)/6173 weeks
1905.27376 2.61656 (190*2π)/6173 weeks
1914.83107 2.20523 (191*2π)/6173 weeks
1925.00234 1.66817 (192*2π)/6173 weeks
1935.32518 1.22072 (193*2π)/6173 weeks
1945.96676 .92518 (194*2π)/6173 weeks
1956.30593 1.14986 (195*2π)/6173 weeks
1966.59924 1.30125 (196*2π)/6173 weeks
1976.73137 1.33313 (197*2π)/6173 weeks
1987.07895 1.51981 (198*2π)/6173 weeks
1997.31533 1.58806 (199*2π)/6173 weeks
2007.7571 1.96842 (200*2π)/6173 weeks
2017.62488 2.38956 (201*2π)/6173 weeks
2027.7169 2.86366 (202*2π)/6173 weeks
2036.97897 3.28339 (203*2π)/6173 weeks
2046.53326 3.52799 (204*2π)/6173 weeks
2056.25723 3.01431 (205*2π)/6173 weeks
2066.05906 2.93474 (206*2π)/6173 weeks
2076.25037 2.67019 (207*2π)/6173 weeks
2086.37184 2.99257 (208*2π)/6173 weeks
2096.35733 2.93318 (209*2π)/6173 weeks
2106.44063 3.1777 (210*2π)/6173 weeks
2116.21867 3.23593 (211*2π)/6173 weeks
2125.89956 3.42524 (212*2π)/6173 weeks
2135.82483 3.12435 (213*2π)/6173 weeks
2145.59343 2.97443 (214*2π)/6173 weeks
2155.65804 2.81132 (215*2π)/6173 weeks
2165.63852 2.81072 (216*2π)/6173 weeks
2175.77128 2.51036 (217*2π)/6173 weeks
2185.93433 2.57623 (218*2π)/6173 weeks
2196.29639 2.62789 (219*2π)/6173 weeks
2206.19958 3.02423 (220*2π)/6173 weeks
2215.91414 3.41322 (221*2π)/6173 weeks
2225.3515 3.45251 (222*2π)/6173 weeks
2234.95891 3.181 (223*2π)/6173 weeks
2244.55948 2.70252 (224*2π)/6173 weeks
2254.62847 2.1784 (225*2π)/6173 weeks
2264.70622 1.81527 (226*2π)/6173 weeks
2275.08567 1.64961 (227*2π)/6173 weeks
2285.15727 1.73878 (228*2π)/6173 weeks
2295.3648 1.52871 (229*2π)/6173 weeks
2305.52931 1.45484 (230*2π)/6173 weeks
2315.95144 1.55946 (231*2π)/6173 weeks
2326.23942 1.55634 (232*2π)/6173 weeks
2336.41545 1.93674 (233*2π)/6173 weeks
2346.65749 2.35264 (234*2π)/6173 weeks
2356.2982 2.78203 (235*2π)/6173 weeks
2366.10798 3.1462 (236*2π)/6173 weeks
2375.61165 2.93665 (237*2π)/6173 weeks
2385.35285 2.84134 (238*2π)/6173 weeks
2395.34649 2.42022 (239*2π)/6173 weeks
2405.35911 2.49358 (240*2π)/6173 weeks
2415.40994 2.40355 (241*2π)/6173 weeks
2425.36395 2.42568 (242*2π)/6173 weeks
2435.51393 2.61224 (243*2π)/6173 weeks
2445.26474 2.89167 (244*2π)/6173 weeks
2454.75943 2.93362 (245*2π)/6173 weeks
2464.13686 2.79289 (246*2π)/6173 weeks
2473.67806 2.03475 (247*2π)/6172 weeks
2483.83013 1.46359 (248*2π)/6172 weeks
2494.28122 .91738 (249*2π)/6172 weeks
2504.74322 .8537 (250*2π)/6172 weeks
2515.13215 1.11319 (251*2π)/6172 weeks
2525.04849 1.17322 (252*2π)/6172 weeks
2535.09677 1.30576 (253*2π)/6172 weeks
2545.02302 1.16513 (254*2π)/6172 weeks
2555.13885 1.01494 (255*2π)/6172 weeks
2565.14166 .83552 (256*2π)/6172 weeks
2575.51419 .4368 (257*2π)/6172 weeks
2586.00925 .42801 (258*2π)/6172 weeks
2596.56319 .53086 (259*2π)/6172 weeks
2606.92359 .92249 (260*2π)/6172 weeks
2617.10954 1.54618 (261*2π)/6172 weeks
2627.09025 1.79158 (262*2π)/6172 weeks
2637.11266 2.29815 (263*2π)/6172 weeks
2646.77896 2.72052 (264*2π)/6172 weeks
2656.52909 3.03207 (265*2π)/6172 weeks
2666.06715 3.37833 (266*2π)/6172 weeks
2675.46572 3.42468 (267*2π)/6172 weeks
2685.23451 3.1875 (268*2π)/6172 weeks
2694.9621 3.19592 (269*2π)/6172 weeks
2704.72672 3.2205 (270*2π)/6172 weeks
2714.28883 3.33857 (271*2π)/6172 weeks
2723.78946 2.93886 (272*2π)/6172 weeks
2733.69879 2.48069 (273*2π)/6172 weeks
2743.99256 2.01398 (274*2π)/6172 weeks
2754.03104 2.10012 (275*2π)/6172 weeks
2764.25331 2.24286 (276*2π)/6172 weeks
2773.86697 2.48597 (277*2π)/6172 weeks
2783.65289 2.36611 (278*2π)/6172 weeks
2793.1289 2.29063 (279*2π)/6172 weeks
2802.83332 1.90459 (280*2π)/6172 weeks
2812.66404 1.21223 (281*2π)/6172 weeks
2822.82624 .73896 (282*2π)/6172 weeks
2832.99174 .11642 (283*2π)/6172 weeks
2843.48359 -.04371 (284*2π)/6172 weeks
2853.66314 -.21486 (285*2π)/6172 weeks
2863.95505 -.49896 (286*2π)/6172 weeks
2874.39725 -.30361 (287*2π)/6172 weeks
2884.73473 -.22015 (288*2π)/6172 weeks
2894.8004 -.05933 (289*2π)/6172 weeks
2904.85601 .07449 (290*2π)/6172 weeks
2914.97735 .07126 (291*2π)/6172 weeks
2925.08473 .32339 (292*2π)/6172 weeks
2935.10059 .58149 (293*2π)/6172 weeks
2944.7348 .83332 (294*2π)/6172 weeks
2954.40328 .99696 (295*2π)/6172 weeks
2964.02839 .5705 (296*2π)/6172 weeks
2974.06299 .2172 (297*2π)/6172 weeks
2984.46795 -.16252 (298*2π)/6172 weeks
2995.04847 -.23473 (299*2π)/6172 weeks
3005.48523 .37274 (300*2π)/6172 weeks
3015.18139 1.04653 (301*2π)/6172 weeks
3024.78274 1.17384 (302*2π)/6172 weeks
3034.31013 1.26672 (303*2π)/6172 weeks
3043.99362 .97368 (304*2π)/6172 weeks
3053.69395 .83788 (305*2π)/6172 weeks
3063.62671 .34804 (306*2π)/6172 weeks
3073.71229 -.03173 (307*2π)/6172 weeks
3083.90397 .00701 (308*2π)/6172 weeks
3093.90397 -.00701 (309*2π)/6172 weeks
3103.71229 .03173 (310*2π)/6172 weeks
3113.62671 -.34804 (311*2π)/6172 weeks
3123.69395 -.83788 (312*2π)/6172 weeks
3133.99362 -.97368 (313*2π)/6172 weeks
3144.31013 -1.26672 (314*2π)/6172 weeks
3154.78274 -1.17384 (315*2π)/6172 weeks
3165.18139 -1.04653 (316*2π)/6172 weeks
3175.48523 -.37274 (317*2π)/6172 weeks
3185.04847 .23473 (318*2π)/6172 weeks
3194.46795 .16252 (319*2π)/6172 weeks
3204.06299 -.2172 (320*2π)/6172 weeks
3214.02839 -.5705 (321*2π)/6172 weeks
3224.40328 -.99696 (322*2π)/6172 weeks
3234.7348 -.83332 (323*2π)/6172 weeks
3245.10059 -.58149 (324*2π)/6172 weeks
3255.08473 -.32339 (325*2π)/6172 weeks
3264.97735 -.07126 (326*2π)/6172 weeks
3274.85601 -.07449 (327*2π)/6172 weeks
3284.8004 .05933 (328*2π)/6172 weeks
3294.73473 .22015 (329*2π)/6172 weeks
3304.39725 .30361 (330*2π)/6172 weeks
3313.95505 .49896 (331*2π)/6172 weeks
3323.66314 .21486 (332*2π)/6172 weeks
3333.48359 .04371 (333*2π)/6172 weeks
3342.99174 -.11642 (334*2π)/6172 weeks
3352.82624 -.73896 (335*2π)/6172 weeks
3362.66404 -1.21223 (336*2π)/6172 weeks
3372.83332 -1.90459 (337*2π)/6172 weeks
3383.1289 -2.29063 (338*2π)/6172 weeks
3393.65289 -2.36611 (339*2π)/6172 weeks
3403.86697 -2.48597 (340*2π)/6172 weeks
3414.25331 -2.24286 (341*2π)/6172 weeks
3424.03104 -2.10012 (342*2π)/6172 weeks
3433.99256 -2.01398 (343*2π)/6172 weeks
3443.69879 -2.48069 (344*2π)/6172 weeks
3453.78946 -2.93886 (345*2π)/6172 weeks
3464.28883 -3.33857 (346*2π)/6172 weeks
3474.72672 -3.2205 (347*2π)/6172 weeks
3484.9621 -3.19592 (348*2π)/6172 weeks
3495.23451 -3.1875 (349*2π)/6172 weeks
3505.46572 -3.42468 (350*2π)/6172 weeks
3516.06715 -3.37833 (351*2π)/6172 weeks
3526.52909 -3.03207 (352*2π)/6172 weeks
3536.77896 -2.72052 (353*2π)/6172 weeks
3547.11266 -2.29815 (354*2π)/6172 weeks
3557.09025 -1.79158 (355*2π)/6172 weeks
3567.10954 -1.54618 (356*2π)/6172 weeks
3576.92359 -.92249 (357*2π)/6172 weeks
3586.56319 -.53086 (358*2π)/6172 weeks
3596.00925 -.42801 (359*2π)/6172 weeks
3605.51419 -.4368 (360*2π)/6172 weeks
3615.14166 -.83552 (361*2π)/6172 weeks
3625.13885 -1.01494 (362*2π)/6172 weeks
3635.02302 -1.16513 (363*2π)/6172 weeks
3645.09677 -1.30576 (364*2π)/6172 weeks
3655.04849 -1.17322 (365*2π)/6172 weeks
3665.13215 -1.11319 (366*2π)/6172 weeks
3674.74322 -.8537 (367*2π)/6172 weeks
3684.28122 -.91738 (368*2π)/6172 weeks
3693.83013 -1.46359 (369*2π)/6172 weeks
3703.67806 -2.03475 (370*2π)/6172 weeks
3714.13686 -2.79289 (371*2π)/6172 weeks
3724.75943 -2.93362 (372*2π)/6172 weeks
3735.26474 -2.89167 (373*2π)/6172 weeks
3745.51393 -2.61224 (374*2π)/6172 weeks
3755.36395 -2.42568 (375*2π)/6172 weeks
3765.40994 -2.40355 (376*2π)/6172 weeks
3775.35911 -2.49358 (377*2π)/6172 weeks
3785.34649 -2.42022 (378*2π)/6172 weeks
3795.35285 -2.84134 (379*2π)/6172 weeks
3805.61165 -2.93665 (380*2π)/6172 weeks
3816.10798 -3.1462 (381*2π)/6172 weeks
3826.2982 -2.78203 (382*2π)/6172 weeks
3836.65749 -2.35264 (383*2π)/6172 weeks
3846.41545 -1.93674 (384*2π)/6172 weeks
3856.23942 -1.55634 (385*2π)/6172 weeks
3865.95144 -1.55946 (386*2π)/6172 weeks
3875.52931 -1.45484 (387*2π)/6172 weeks
3885.3648 -1.52871 (388*2π)/6172 weeks
3895.15727 -1.73878 (389*2π)/6172 weeks
3905.08567 -1.64961 (390*2π)/6172 weeks
3914.70622 -1.81527 (391*2π)/6172 weeks
3924.62847 -2.1784 (392*2π)/6172 weeks
3934.55948 -2.70252 (393*2π)/6172 weeks
3944.95891 -3.181 (394*2π)/6172 weeks
3955.3515 -3.45251 (395*2π)/6172 weeks
3965.91414 -3.41322 (396*2π)/6172 weeks
3976.19958 -3.02423 (397*2π)/6172 weeks
3986.29639 -2.62789 (398*2π)/6172 weeks
3995.93433 -2.57623 (399*2π)/6172 weeks
4005.77128 -2.51036 (400*2π)/6172 weeks
4015.63852 -2.81072 (401*2π)/6172 weeks
4025.65804 -2.81132 (402*2π)/6172 weeks
4035.59343 -2.97443 (403*2π)/6172 weeks
4045.82483 -3.12435 (404*2π)/6172 weeks
4055.89956 -3.42524 (405*2π)/6172 weeks
4066.21867 -3.23593 (406*2π)/6172 weeks
4076.44063 -3.1777 (407*2π)/6172 weeks
4086.35733 -2.93318 (408*2π)/6172 weeks
4096.37184 -2.99257 (409*2π)/6172 weeks
4106.25037 -2.67019 (410*2π)/6172 weeks
4116.05906 -2.93474 (411*2π)/6172 weeks
4126.25723 -3.01431 (412*2π)/6171 weeks
4136.53326 -3.52799 (413*2π)/6171 weeks
4146.97897 -3.28339 (414*2π)/6171 weeks
4157.7169 -2.86366 (415*2π)/6171 weeks
4167.62488 -2.38956 (416*2π)/6171 weeks
4177.7571 -1.96842 (417*2π)/6171 weeks
4187.31533 -1.58806 (418*2π)/6171 weeks
4197.07895 -1.51981 (419*2π)/6171 weeks
4206.73137 -1.33313 (420*2π)/6171 weeks
4216.59924 -1.30125 (421*2π)/6171 weeks
4226.30593 -1.14986 (422*2π)/6171 weeks
4235.96676 -.92518 (423*2π)/6171 weeks
4245.32518 -1.22072 (424*2π)/6171 weeks
4255.00234 -1.66817 (425*2π)/6171 weeks
4264.83107 -2.20523 (426*2π)/6171 weeks
4275.27376 -2.61656 (427*2π)/6171 weeks
4285.27804 -2.69417 (428*2π)/6171 weeks
4295.54607 -2.75239 (429*2π)/6171 weeks
4305.76642 -2.68871 (430*2π)/6171 weeks
4315.80307 -2.69672 (431*2π)/6171 weeks
4325.71073 -2.58247 (432*2π)/6171 weeks
4335.75674 -2.7972 (433*2π)/6171 weeks
4346.09368 -2.84925 (434*2π)/6171 weeks
4356.49191 -2.66727 (435*2π)/6171 weeks
4366.58875 -2.22228 (436*2π)/6171 weeks
4376.42185 -1.54664 (437*2π)/6171 weeks
4385.83242 -1.73693 (438*2π)/6171 weeks
4395.40387 -1.81119 (439*2π)/6171 weeks
4405.34975 -2.1835 (440*2π)/6171 weeks
4415.56023 -2.16688 (441*2π)/6171 weeks
4425.53527 -1.96087 (442*2π)/6171 weeks
4435.50903 -1.86545 (443*2π)/6171 weeks
4445.0176 -1.49777 (444*2π)/6171 weeks
4454.71206 -1.6948 (445*2π)/6171 weeks
4463.81906 -2.14136 (446*2π)/6171 weeks
4473.72401 -2.64899 (447*2π)/6171 weeks
4483.50095 -3.32482 (448*2π)/6171 weeks
4493.8288 -3.92501 (449*2π)/6171 weeks
4504.15974 -4.25477 (450*2π)/6171 weeks
4514.7257 -4.48352 (451*2π)/6171 weeks
4525.19561 -4.39375 (452*2π)/6171 weeks
4535.37862 -4.12907 (453*2π)/6171 weeks
4545.46885 -3.92776 (454*2π)/6171 weeks
4555.52468 -3.72026 (455*2π)/6171 weeks
4565.42672 -3.71275 (456*2π)/6171 weeks
4575.606 -3.65306 (457*2π)/6171 weeks
4585.1623 -3.69179 (458*2π)/6171 weeks
4595.3277 -3.72878 (459*2π)/6171 weeks
4605.52837 -3.76508 (460*2π)/6171 weeks
4615.4384 -3.50925 (461*2π)/6171 weeks
4624.95604 -3.40709 (462*2π)/6171 weeks
4634.58049 -3.79004 (463*2π)/6171 weeks
4644.5779 -4.23932 (464*2π)/6171 weeks
4654.99879 -4.57384 (465*2π)/6171 weeks
4664.92965 -4.4317 (466*2π)/6171 weeks
4674.79288 -4.60621 (467*2π)/6171 weeks
4684.82978 -5.13835 (468*2π)/6171 weeks
4695.07681 -5.43959 (469*2π)/6171 weeks
4705.63367 -5.41095 (470*2π)/6171 weeks
4716.21454 -5.41415 (471*2π)/6171 weeks
4726.13603 -5.10648 (472*2π)/6171 weeks
4736.59214 -4.67106 (473*2π)/6171 weeks
4746.07701 -4.4557 (474*2π)/6171 weeks
4756.00423 -4.24026 (475*2π)/6171 weeks
4765.48277 -4.50962 (476*2π)/6171 weeks
4775.70253 -4.4811 (477*2π)/6171 weeks
4785.40977 -4.62282 (478*2π)/6171 weeks
4795.69673 -4.84725 (479*2π)/6171 weeks
4805.56204 -5.03078 (480*2π)/6171 weeks
4815.83228 -5.15343 (481*2π)/6171 weeks
4826.16362 -5.33597 (482*2π)/6171 weeks
4836.61668 -5.1395 (483*2π)/6171 weeks
4846.81054 -4.94785 (484*2π)/6171 weeks
4857.02127 -4.40963 (485*2π)/6171 weeks
4866.6478 -4.04039 (486*2π)/6171 weeks
4876.15593 -3.68307 (487*2π)/6171 weeks
4885.70838 -3.65104 (488*2π)/6171 weeks
4895.33874 -3.72714 (489*2π)/6171 weeks
4904.91208 -3.78886 (490*2π)/6171 weeks
4914.49014 -3.49827 (491*2π)/6171 weeks
4923.64042 -4.61035 (492*2π)/6171 weeks
4933.32916 -4.97538 (493*2π)/6171 weeks
4943.30837 -6.1802 (494*2π)/6171 weeks
4954.03753 -6.70183 (495*2π)/6171 weeks
4964.73903 -7.21956 (496*2π)/6171 weeks
4975.30378 -7.20087 (497*2π)/6171 weeks
4986.15758 -6.56787 (498*2π)/6171 weeks
4995.88044 -6.17342 (499*2π)/6171 weeks
5005.62838 -5.93053 (500*2π)/6171 weeks
5015.36275 -5.90389 (501*2π)/6171 weeks
5024.98164 -6.54376 (502*2π)/6171 weeks
5035.41417 -6.54819 (503*2π)/6171 weeks
5045.84476 -7.06918 (504*2π)/6171 weeks
5055.86047 -6.77636 (505*2π)/6171 weeks
5065.82351 -6.02739 (506*2π)/6171 weeks
5074.89609 -6.37709 (507*2π)/6171 weeks
5084.16861 -6.95217 (508*2π)/6171 weeks
5093.81946 -8.16987 (509*2π)/6171 weeks
5104.31443 -9.33589 (510*2π)/6171 weeks
5115.36558 -10.48429 (511*2π)/6171 weeks
5126.60161 -10.69784 (512*2π)/6171 weeks
5138.00209 -11.04836 (513*2π)/6171 weeks
5149.30114 -9.99642 (514*2π)/6171 weeks
5159.92251 -9.15075 (515*2π)/6171 weeks
51610.12187 -7.55767 (516*2π)/6171 weeks
5179.66754 -6.72804 (517*2π)/6171 weeks
5188.77209 -5.91232 (518*2π)/6171 weeks
5198.58657 -5.69113 (519*2π)/6171 weeks
5207.93901 -5.87223 (520*2π)/6171 weeks
5217.47988 -5.57332 (521*2π)/6171 weeks
5226.85078 -6.09828 (522*2π)/6171 weeks
5237.0151 -6.89273 (523*2π)/6171 weeks
5247.66233 -7.01568 (524*2π)/6171 weeks
5257.87898 -6.74014 (525*2π)/6171 weeks
5267.71826 -6.41271 (526*2π)/6171 weeks
5277.9422 -6.59665 (527*2π)/6171 weeks
5288.20345 -6.19916 (528*2π)/6171 weeks
5297.58804 -5.4862 (529*2π)/6171 weeks
5306.94515 -5.06764 (530*2π)/6171 weeks
5315.63882 -6.09949 (531*2π)/6171 weeks
5325.50297 -6.79826 (532*2π)/6171 weeks
5336.17756 -8.14171 (533*2π)/6171 weeks
5346.67353 -7.90828 (534*2π)/6171 weeks
5357.29765 -7.99498 (535*2π)/6171 weeks
5367.33902 -6.8921 (536*2π)/6171 weeks
5377.55147 -6.54916 (537*2π)/6171 weeks
5386.52795 -5.97645 (538*2π)/6171 weeks
5395.70603 -5.41978 (539*2π)/6171 weeks
5404.14314 -5.63259 (540*2π)/6171 weeks
5413.57479 -6.6729 (541*2π)/6171 weeks
5422.44558 -7.87308 (542*2π)/6171 weeks
5432.71227 -9.68612 (543*2π)/6171 weeks
5443.74181 -10.5642 (544*2π)/6171 weeks
5454.57198 -11.16835 (545*2π)/6171 weeks
5465.46461 -10.88896 (546*2π)/6171 weeks
5475.79115 -11.15206 (547*2π)/6171 weeks
5486.01009 -11.24001 (548*2π)/6171 weeks
5496.42857 -11.43314 (549*2π)/6171 weeks
5506.69517 -11.85215 (550*2π)/6171 weeks
5517.00884 -10.92269 (551*2π)/6171 weeks
5526.91793 -12.27147 (552*2π)/6171 weeks
5537.43616 -11.37005 (553*2π)/6171 weeks
5548.36667 -11.76704 (554*2π)/6171 weeks
5558.49634 -11.70101 (555*2π)/6171 weeks
5568.6293 -10.20464 (556*2π)/6171 weeks
5578.37637 -10.01468 (557*2π)/6171 weeks
5588.28134 -9.80545 (558*2π)/6171 weeks
5597.6732 -9.09763 (559*2π)/6171 weeks
5606.88904 -9.16164 (560*2π)/6171 weeks
5615.99344 -8.78156 (561*2π)/6171 weeks
5625.2638 -9.09682 (562*2π)/6171 weeks
5634.01557 -9.23913 (563*2π)/6171 weeks
5642.33659 -10.01577 (564*2π)/6171 weeks
5652.24583 -12.07679 (565*2π)/6171 weeks
5662.44074 -13.17928 (566*2π)/6171 weeks
5672.25055 -13.93655 (567*2π)/6171 weeks
5682.15453 -14.74349 (568*2π)/6171 weeks
569.9289 -15.73008 (569*2π)/6171 weeks
5701.21023 -17.85804 (570*2π)/6171 weeks
5711.55925 -20.18852 (571*2π)/6171 weeks
5722.07124 -22.14286 (572*2π)/6171 weeks
5734.14552 -25.07592 (573*2π)/6171 weeks
5746.48211 -26.28191 (574*2π)/6171 weeks
5759.09962 -26.48299 (575*2π)/6171 weeks
57611.41046 -26.00521 (576*2π)/6171 weeks
57712.86188 -26.15325 (577*2π)/6171 weeks
57815.38618 -24.99781 (578*2π)/6171 weeks
57916.21334 -23.13162 (579*2π)/6171 weeks
58016.33494 -21.69408 (580*2π)/6171 weeks
58115.73433 -21.20285 (581*2π)/6171 weeks
58215.7831 -20.10203 (582*2π)/6171 weeks
58316.06006 -20.29139 (583*2π)/6171 weeks
58415.8656 -18.77931 (584*2π)/6171 weeks
58515.23608 -18.7281 (585*2π)/6171 weeks
58613.77599 -19.24195 (586*2π)/6171 weeks
58714.52712 -19.09513 (587*2π)/6171 weeks
58814.30575 -20.4036 (588*2π)/6171 weeks
58915.02679 -18.48238 (589*2π)/6171 weeks
59012.38775 -19.53913 (590*2π)/6171 weeks
59110.59645 -19.98387 (591*2π)/6171 weeks
5928.36523 -24.27858 (592*2π)/6171 weeks
59310.5433 -30.37032 (593*2π)/6171 weeks
59413.97744 -31.19517 (594*2π)/6171 weeks
59517.82705 -32.23809 (595*2π)/6171 weeks
59620.61735 -30.54714 (596*2π)/6171 weeks
59721.4713 -27.36316 (597*2π)/6171 weeks
59819.74674 -25.55642 (598*2π)/6171 weeks
59919.43273 -27.00027 (599*2π)/6171 weeks
60016.5156 -29.22182 (600*2π)/6171 weeks
60117.77935 -30.5399 (601*2π)/6171 weeks
60215.45295 -31.81437 (602*2π)/6171 weeks
60314.49556 -35.19591 (603*2π)/6171 weeks
60414.35039 -36.30542 (604*2π)/6171 weeks
60513.12884 -43.02325 (605*2π)/6171 weeks
60613.00793 -50.69678 (606*2π)/6171 weeks
60721.14207 -58.09224 (607*2π)/6171 weeks
60826.11852 -64.65133 (608*2π)/6171 weeks
60938.05282 -65.62885 (609*2π)/6171 weeks
61045.17677 -64.30732 (610*2π)/6171 weeks
61142.23156 -68.18837 (611*2π)/6171 weeks
61246.46827 -78.85259 (612*2π)/6171 weeks
61357.05331 -102.8122 (613*2π)/6171 weeks
61489.67604 -116.7816 (614*2π)/6171 weeks
615154.9216 -115.6879 (615*2π)/6171 weeks



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