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Fourier Analysis of ZSL (ProShares UltraShort Silver ETF)


ZSL (ProShares UltraShort Silver ETF) appears to have interesting cyclic behaviour every 47 weeks (46.8512*sine), 42 weeks (42.3669*sine), and 31 weeks (28.4434*cosine).

ZSL (ProShares UltraShort Silver ETF) has an average price of 185.52 (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 11/6/2017 for ZSL (ProShares UltraShort Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0185.5211   0 
1247.4909 107.5321 (1*2π)/467467 weeks
2144.666 163.126 (2*2π)/467234 weeks
379.3485 135.1889 (3*2π)/467156 weeks
461.50299 98.67915 (4*2π)/467117 weeks
559.0139 82.48045 (5*2π)/46793 weeks
651.42214 86.52145 (6*2π)/46778 weeks
732.41367 81.76089 (7*2π)/46767 weeks
821.83002 72.8992 (8*2π)/46758 weeks
918.27709 56.93337 (9*2π)/46752 weeks
1020.88964 46.85122 (10*2π)/46747 weeks
1120.24445 42.36689 (11*2π)/46742 weeks
1223.36938 38.55571 (12*2π)/46739 weeks
1321.65803 35.97625 (13*2π)/46736 weeks
1424.71015 34.84094 (14*2π)/46733 weeks
1528.44341 35.22594 (15*2π)/46731 weeks
1627.00369 40.08492 (16*2π)/46729 weeks
1720.80381 41.95135 (17*2π)/46727 weeks
1815.37399 39.98666 (18*2π)/46726 weeks
1910.80099 30.83845 (19*2π)/46725 weeks
2015.54212 25.6804 (20*2π)/46723 weeks
2118.36118 23.79767 (21*2π)/46722 weeks
2218.57387 26.8084 (22*2π)/46721 weeks
2319.4029 25.81109 (23*2π)/46720 weeks
2419.81255 24.06874 (24*2π)/46719 weeks
2521.12411 24.51312 (25*2π)/46719 weeks
2620.80886 26.53606 (26*2π)/46718 weeks
2721.3597 27.20853 (27*2π)/46717 weeks
2821.6245 27.97922 (28*2π)/46717 weeks
2921.17674 30.65003 (29*2π)/46716 weeks
3018.21295 33.87973 (30*2π)/46716 weeks
3114.9485 33.87557 (31*2π)/46715 weeks
3211.03624 34.55776 (32*2π)/46715 weeks
336.45001 33.21768 (33*2π)/46714 weeks
342.32462 29.26272 (34*2π)/46714 weeks
351.2975 25.76602 (35*2π)/46713 weeks
36.99512 22.29214 (36*2π)/46713 weeks
372.70391 19.35437 (37*2π)/46713 weeks
382.93961 17.97939 (38*2π)/46712 weeks
392.92343 16.59625 (39*2π)/46712 weeks
402.79995 13.69313 (40*2π)/46712 weeks
415.60104 11.97732 (41*2π)/46711 weeks
427.26495 11.80865 (42*2π)/46711 weeks
439.01046 11.81732 (43*2π)/46711 weeks
4410.23294 11.86177 (44*2π)/46711 weeks
4510.75701 12.97284 (45*2π)/46710 weeks
4611.13917 13.32927 (46*2π)/46710 weeks
4711.01238 15.22773 (47*2π)/46710 weeks
4810.15806 15.80761 (48*2π)/46710 weeks
499.95276 15.97585 (49*2π)/46710 weeks
509.38936 14.32708 (50*2π)/4679 weeks
518.41478 15.16201 (51*2π)/4679 weeks
527.94629 14.94102 (52*2π)/4679 weeks
537.53361 14.73634 (53*2π)/4679 weeks
547.09664 14.64286 (54*2π)/4679 weeks
555.34732 14.13988 (55*2π)/4678 weeks
563.74363 12.71488 (56*2π)/4678 weeks
573.70252 9.43779 (57*2π)/4678 weeks
585.08569 7.98528 (58*2π)/4678 weeks
597.62211 6.91837 (59*2π)/4678 weeks
608.97179 7.55587 (60*2π)/4678 weeks
619.5853 9.01387 (61*2π)/4678 weeks
629.81853 10.22502 (62*2π)/4678 weeks
638.74554 10.15666 (63*2π)/4677 weeks
647.04633 9.76403 (64*2π)/4677 weeks
657.33122 8.14633 (65*2π)/4677 weeks
669.38379 6.81117 (66*2π)/4677 weeks
6710.54259 7.47386 (67*2π)/4677 weeks
6810.41639 8.63595 (68*2π)/4677 weeks
6910.21081 8.48001 (69*2π)/4677 weeks
7010.24964 9.05968 (70*2π)/4677 weeks
719.401 9.25898 (71*2π)/4677 weeks
729.14487 7.95843 (72*2π)/4676 weeks
7310.45827 7.47987 (73*2π)/4676 weeks
7411.103 7.3651 (74*2π)/4676 weeks
7511.85927 7.74048 (75*2π)/4676 weeks
7612.99388 9.12466 (76*2π)/4676 weeks
7713.45268 11.36321 (77*2π)/4676 weeks
7812.21719 13.01574 (78*2π)/4676 weeks
799.54975 14.31221 (79*2π)/4676 weeks
807.58247 13.87561 (80*2π)/4676 weeks
815.5917 12.19409 (81*2π)/4676 weeks
824.99626 10.01704 (82*2π)/4676 weeks
836.04742 8.42708 (83*2π)/4676 weeks
847.49258 7.85969 (84*2π)/4676 weeks
857.57028 8.79977 (85*2π)/4675 weeks
866.8286 9.01087 (86*2π)/4675 weeks
876.5428 8.79166 (87*2π)/4675 weeks
887.1784 7.89508 (88*2π)/4675 weeks
897.69947 8.00646 (89*2π)/4675 weeks
908.10324 8.56539 (90*2π)/4675 weeks
916.83478 9.40979 (91*2π)/4675 weeks
925.57025 9.19019 (92*2π)/4675 weeks
934.55075 8.31253 (93*2π)/4675 weeks
944.64191 6.27907 (94*2π)/4675 weeks
954.89577 5.02926 (95*2π)/4675 weeks
966.45488 5.01282 (96*2π)/4675 weeks
977.08624 4.84467 (97*2π)/4675 weeks
987.76608 4.75758 (98*2π)/4675 weeks
998.63085 5.09844 (99*2π)/4675 weeks
1009.15688 5.85221 (100*2π)/4675 weeks
1018.7165 6.59554 (101*2π)/4675 weeks
1028.22299 7.07445 (102*2π)/4675 weeks
1037.65858 6.82783 (103*2π)/4675 weeks
1047.33587 6.40463 (104*2π)/4674 weeks
1057.17744 6.33199 (105*2π)/4674 weeks
1067.58943 5.93502 (106*2π)/4674 weeks
1077.37654 5.57511 (107*2π)/4674 weeks
1088.02491 5.82894 (108*2π)/4674 weeks
1098.66302 6.09598 (109*2π)/4674 weeks
1108.09137 6.56587 (110*2π)/4674 weeks
1117.48249 7.20403 (111*2π)/4674 weeks
1126.70057 7.15994 (112*2π)/4674 weeks
1136.18073 6.53564 (113*2π)/4674 weeks
1146.37321 5.90732 (114*2π)/4674 weeks
1156.5324 5.99164 (115*2π)/4674 weeks
1165.95227 5.43418 (116*2π)/4674 weeks
1176.20379 4.62994 (117*2π)/4674 weeks
1187.04319 4.57193 (118*2π)/4674 weeks
1197.12244 5.06288 (119*2π)/4674 weeks
1206.95543 5.02524 (120*2π)/4674 weeks
1217.3034 4.69923 (121*2π)/4674 weeks
1227.12322 4.88491 (122*2π)/4674 weeks
1237.29862 5.08564 (123*2π)/4674 weeks
1247.16771 5.37252 (124*2π)/4674 weeks
1256.7917 5.78842 (125*2π)/4674 weeks
1265.88497 5.81361 (126*2π)/4674 weeks
1275.19492 5.1899 (127*2π)/4674 weeks
1284.62221 4.15231 (128*2π)/4674 weeks
1294.99017 3.19337 (129*2π)/4674 weeks
1305.83339 2.04405 (130*2π)/4674 weeks
1316.57967 1.92844 (131*2π)/4674 weeks
1327.13776 2.54634 (132*2π)/4674 weeks
1337.32545 2.77312 (133*2π)/4674 weeks
1347.02699 2.82202 (134*2π)/4673 weeks
1357.31669 2.18127 (135*2π)/4673 weeks
1367.94391 1.97842 (136*2π)/4673 weeks
1378.61877 2.98269 (137*2π)/4673 weeks
1388.34071 3.71688 (138*2π)/4673 weeks
1397.73686 3.79803 (139*2π)/4673 weeks
1407.54629 3.40338 (140*2π)/4673 weeks
1417.58699 3.52677 (141*2π)/4673 weeks
1427.44281 3.64537 (142*2π)/4673 weeks
1437.01187 3.53301 (143*2π)/4673 weeks
1446.78503 3.40211 (144*2π)/4673 weeks
1456.46398 2.37905 (145*2π)/4673 weeks
1466.90886 1.60045 (146*2π)/4673 weeks
1477.99315 1.25425 (147*2π)/4673 weeks
1488.50054 1.52288 (148*2π)/4673 weeks
1498.76923 1.71819 (149*2π)/4673 weeks
1509.28538 1.99402 (150*2π)/4673 weeks
1519.85747 2.22339 (151*2π)/4673 weeks
1529.97199 3.2013 (152*2π)/4673 weeks
15310.07051 4.10041 (153*2π)/4673 weeks
1549.12461 4.48288 (154*2π)/4673 weeks
1558.19439 4.0942 (155*2π)/4673 weeks
1568.02719 3.85358 (156*2π)/4673 weeks
1578.5193 3.63162 (157*2π)/4673 weeks
1588.33804 3.79796 (158*2π)/4673 weeks
1598.45208 4.14981 (159*2π)/4673 weeks
1608.15849 4.31996 (160*2π)/4673 weeks
1617.57557 4.06168 (161*2π)/4673 weeks
1627.323 3.86597 (162*2π)/4673 weeks
1637.4541 3.62837 (163*2π)/4673 weeks
1647.35616 3.32041 (164*2π)/4673 weeks
1657.70302 3.33639 (165*2π)/4673 weeks
1668.20804 3.68507 (166*2π)/4673 weeks
1677.93116 4.32761 (167*2π)/4673 weeks
1686.98774 4.56428 (168*2π)/4673 weeks
1696.27885 4.13301 (169*2π)/4673 weeks
1705.97427 3.14982 (170*2π)/4673 weeks
1716.19307 2.50995 (171*2π)/4673 weeks
1726.83795 2.24717 (172*2π)/4673 weeks
1736.90498 2.06888 (173*2π)/4673 weeks
1747.27208 1.91522 (174*2π)/4673 weeks
1757.85722 2.03415 (175*2π)/4673 weeks
1768.45355 2.32708 (176*2π)/4673 weeks
1778.766 2.89689 (177*2π)/4673 weeks
1788.26259 3.60203 (178*2π)/4673 weeks
1797.49415 4.06637 (179*2π)/4673 weeks
1807.06767 3.80061 (180*2π)/4673 weeks
1817.02676 3.20671 (181*2π)/4673 weeks
1826.97779 3.203 (182*2π)/4673 weeks
1837.01938 3.24743 (183*2π)/4673 weeks
1847.19562 3.50778 (184*2π)/4673 weeks
1856.61413 3.9545 (185*2π)/4673 weeks
1865.70299 3.86348 (186*2π)/4673 weeks
1874.90093 2.66336 (187*2π)/4672 weeks
1885.20466 1.60263 (188*2π)/4672 weeks
1896.13425 1.15002 (189*2π)/4672 weeks
1906.81075 1.45837 (190*2π)/4672 weeks
1916.78981 1.51074 (191*2π)/4672 weeks
1926.62532 1.53076 (192*2π)/4672 weeks
1936.75108 1.24141 (193*2π)/4672 weeks
1946.78668 .81786 (194*2π)/4672 weeks
1957.64415 .47857 (195*2π)/4672 weeks
1968.53352 .63087 (196*2π)/4672 weeks
1979.19391 1.35294 (197*2π)/4672 weeks
1989.14838 2.22855 (198*2π)/4672 weeks
1999.28129 3.0101 (199*2π)/4672 weeks
2008.7685 3.7271 (200*2π)/4672 weeks
2018.257 4.35181 (201*2π)/4672 weeks
2027.25743 4.594 (202*2π)/4672 weeks
2036.83117 4.27727 (203*2π)/4672 weeks
2046.40502 4.24978 (204*2π)/4672 weeks
2055.82361 4.39327 (205*2π)/4672 weeks
2064.97172 3.70532 (206*2π)/4672 weeks
2074.89761 2.83564 (207*2π)/4672 weeks
2085.32807 2.79537 (208*2π)/4672 weeks
2095.58453 2.99702 (209*2π)/4672 weeks
2104.87417 3.10223 (210*2π)/4672 weeks
2114.25536 3.08574 (211*2π)/4672 weeks
2123.61395 2.38145 (212*2π)/4672 weeks
2133.51606 1.24042 (213*2π)/4672 weeks
2143.67512 .39182 (214*2π)/4672 weeks
2154.50146 -.02967 (215*2π)/4672 weeks
2164.83982 -.33263 (216*2π)/4672 weeks
2175.69821 -.47956 (217*2π)/4672 weeks
2186.17637 -.27445 (218*2π)/4672 weeks
2196.32676 .01294 (219*2π)/4672 weeks
2206.40907 .12645 (220*2π)/4672 weeks
2216.67704 .49172 (221*2π)/4672 weeks
2226.64513 1.03193 (222*2π)/4672 weeks
2236.1257 1.24713 (223*2π)/4672 weeks
2245.35632 .75525 (224*2π)/4672 weeks
2255.44062 .03591 (225*2π)/4672 weeks
2266.25014 -.36998 (226*2π)/4672 weeks
2277.20213 .38886 (227*2π)/4672 weeks
2286.6418 1.43173 (228*2π)/4672 weeks
2295.98451 1.65848 (229*2π)/4672 weeks
2305.24575 1.30189 (230*2π)/4672 weeks
2314.72724 .95579 (231*2π)/4672 weeks
2324.72797 .24444 (232*2π)/4672 weeks
2335.15734 .00833 (233*2π)/4672 weeks
2345.15734 -.00833 (234*2π)/4672 weeks
2354.72797 -.24444 (235*2π)/4672 weeks
2364.72724 -.95579 (236*2π)/4672 weeks
2375.24575 -1.30189 (237*2π)/4672 weeks
2385.98451 -1.65848 (238*2π)/4672 weeks
2396.6418 -1.43173 (239*2π)/4672 weeks
2407.20213 -.38886 (240*2π)/4672 weeks
2416.25014 .36998 (241*2π)/4672 weeks
2425.44062 -.03591 (242*2π)/4672 weeks
2435.35632 -.75525 (243*2π)/4672 weeks
2446.1257 -1.24713 (244*2π)/4672 weeks
2456.64513 -1.03193 (245*2π)/4672 weeks
2466.67704 -.49172 (246*2π)/4672 weeks
2476.40907 -.12645 (247*2π)/4672 weeks
2486.32676 -.01294 (248*2π)/4672 weeks
2496.17637 .27445 (249*2π)/4672 weeks
2505.69821 .47956 (250*2π)/4672 weeks
2514.83982 .33263 (251*2π)/4672 weeks
2524.50146 .02967 (252*2π)/4672 weeks
2533.67512 -.39182 (253*2π)/4672 weeks
2543.51606 -1.24042 (254*2π)/4672 weeks
2553.61395 -2.38145 (255*2π)/4672 weeks
2564.25536 -3.08574 (256*2π)/4672 weeks
2574.87417 -3.10223 (257*2π)/4672 weeks
2585.58453 -2.99702 (258*2π)/4672 weeks
2595.32807 -2.79537 (259*2π)/4672 weeks
2604.89761 -2.83564 (260*2π)/4672 weeks
2614.97172 -3.70532 (261*2π)/4672 weeks
2625.82361 -4.39327 (262*2π)/4672 weeks
2636.40502 -4.24978 (263*2π)/4672 weeks
2646.83117 -4.27727 (264*2π)/4672 weeks
2657.25743 -4.594 (265*2π)/4672 weeks
2668.257 -4.35181 (266*2π)/4672 weeks
2678.7685 -3.7271 (267*2π)/4672 weeks
2689.28129 -3.0101 (268*2π)/4672 weeks
2699.14838 -2.22855 (269*2π)/4672 weeks
2709.19391 -1.35294 (270*2π)/4672 weeks
2718.53352 -.63087 (271*2π)/4672 weeks
2727.64415 -.47857 (272*2π)/4672 weeks
2736.78668 -.81786 (273*2π)/4672 weeks
2746.75108 -1.24141 (274*2π)/4672 weeks
2756.62532 -1.53076 (275*2π)/4672 weeks
2766.78981 -1.51074 (276*2π)/4672 weeks
2776.81075 -1.45837 (277*2π)/4672 weeks
2786.13425 -1.15002 (278*2π)/4672 weeks
2795.20466 -1.60263 (279*2π)/4672 weeks
2804.90093 -2.66336 (280*2π)/4672 weeks
2815.70299 -3.86348 (281*2π)/4672 weeks
2826.61413 -3.9545 (282*2π)/4672 weeks
2837.19562 -3.50778 (283*2π)/4672 weeks
2847.01938 -3.24743 (284*2π)/4672 weeks
2856.97779 -3.203 (285*2π)/4672 weeks
2867.02676 -3.20671 (286*2π)/4672 weeks
2877.06767 -3.80061 (287*2π)/4672 weeks
2887.49415 -4.06637 (288*2π)/4672 weeks
2898.26259 -3.60203 (289*2π)/4672 weeks
2908.766 -2.89689 (290*2π)/4672 weeks
2918.45355 -2.32708 (291*2π)/4672 weeks
2927.85722 -2.03415 (292*2π)/4672 weeks
2937.27208 -1.91522 (293*2π)/4672 weeks
2946.90498 -2.06888 (294*2π)/4672 weeks
2956.83795 -2.24717 (295*2π)/4672 weeks
2966.19307 -2.50995 (296*2π)/4672 weeks
2975.97427 -3.14982 (297*2π)/4672 weeks
2986.27885 -4.13301 (298*2π)/4672 weeks
2996.98774 -4.56428 (299*2π)/4672 weeks
3007.93116 -4.32761 (300*2π)/4672 weeks
3018.20804 -3.68507 (301*2π)/4672 weeks
3027.70302 -3.33639 (302*2π)/4672 weeks
3037.35616 -3.32041 (303*2π)/4672 weeks
3047.4541 -3.62837 (304*2π)/4672 weeks
3057.323 -3.86597 (305*2π)/4672 weeks
3067.57557 -4.06168 (306*2π)/4672 weeks
3078.15849 -4.31996 (307*2π)/4672 weeks
3088.45208 -4.14981 (308*2π)/4672 weeks
3098.33804 -3.79796 (309*2π)/4672 weeks
3108.5193 -3.63162 (310*2π)/4672 weeks
3118.02719 -3.85358 (311*2π)/4672 weeks
3128.19439 -4.0942 (312*2π)/4671 weeks
3139.12461 -4.48288 (313*2π)/4671 weeks
31410.07051 -4.10041 (314*2π)/4671 weeks
3159.97199 -3.2013 (315*2π)/4671 weeks
3169.85747 -2.22339 (316*2π)/4671 weeks
3179.28538 -1.99402 (317*2π)/4671 weeks
3188.76923 -1.71819 (318*2π)/4671 weeks
3198.50054 -1.52288 (319*2π)/4671 weeks
3207.99315 -1.25425 (320*2π)/4671 weeks
3216.90886 -1.60045 (321*2π)/4671 weeks
3226.46398 -2.37905 (322*2π)/4671 weeks
3236.78503 -3.40211 (323*2π)/4671 weeks
3247.01187 -3.53301 (324*2π)/4671 weeks
3257.44281 -3.64537 (325*2π)/4671 weeks
3267.58699 -3.52677 (326*2π)/4671 weeks
3277.54629 -3.40338 (327*2π)/4671 weeks
3287.73686 -3.79803 (328*2π)/4671 weeks
3298.34071 -3.71688 (329*2π)/4671 weeks
3308.61877 -2.98269 (330*2π)/4671 weeks
3317.94391 -1.97842 (331*2π)/4671 weeks
3327.31669 -2.18127 (332*2π)/4671 weeks
3337.02699 -2.82202 (333*2π)/4671 weeks
3347.32545 -2.77312 (334*2π)/4671 weeks
3357.13776 -2.54634 (335*2π)/4671 weeks
3366.57967 -1.92844 (336*2π)/4671 weeks
3375.83339 -2.04405 (337*2π)/4671 weeks
3384.99017 -3.19337 (338*2π)/4671 weeks
3394.62221 -4.15231 (339*2π)/4671 weeks
3405.19492 -5.1899 (340*2π)/4671 weeks
3415.88497 -5.81361 (341*2π)/4671 weeks
3426.7917 -5.78842 (342*2π)/4671 weeks
3437.16771 -5.37252 (343*2π)/4671 weeks
3447.29862 -5.08564 (344*2π)/4671 weeks
3457.12322 -4.88491 (345*2π)/4671 weeks
3467.3034 -4.69923 (346*2π)/4671 weeks
3476.95543 -5.02524 (347*2π)/4671 weeks
3487.12244 -5.06288 (348*2π)/4671 weeks
3497.04319 -4.57193 (349*2π)/4671 weeks
3506.20379 -4.62994 (350*2π)/4671 weeks
3515.95227 -5.43418 (351*2π)/4671 weeks
3526.5324 -5.99164 (352*2π)/4671 weeks
3536.37321 -5.90732 (353*2π)/4671 weeks
3546.18073 -6.53564 (354*2π)/4671 weeks
3556.70057 -7.15994 (355*2π)/4671 weeks
3567.48249 -7.20403 (356*2π)/4671 weeks
3578.09137 -6.56587 (357*2π)/4671 weeks
3588.66302 -6.09598 (358*2π)/4671 weeks
3598.02491 -5.82894 (359*2π)/4671 weeks
3607.37654 -5.57511 (360*2π)/4671 weeks
3617.58943 -5.93502 (361*2π)/4671 weeks
3627.17744 -6.33199 (362*2π)/4671 weeks
3637.33587 -6.40463 (363*2π)/4671 weeks
3647.65858 -6.82783 (364*2π)/4671 weeks
3658.22299 -7.07445 (365*2π)/4671 weeks
3668.7165 -6.59554 (366*2π)/4671 weeks
3679.15688 -5.85221 (367*2π)/4671 weeks
3688.63085 -5.09844 (368*2π)/4671 weeks
3697.76608 -4.75758 (369*2π)/4671 weeks
3707.08624 -4.84467 (370*2π)/4671 weeks
3716.45488 -5.01282 (371*2π)/4671 weeks
3724.89577 -5.02926 (372*2π)/4671 weeks
3734.64191 -6.27907 (373*2π)/4671 weeks
3744.55075 -8.31253 (374*2π)/4671 weeks
3755.57025 -9.19019 (375*2π)/4671 weeks
3766.83478 -9.40979 (376*2π)/4671 weeks
3778.10324 -8.56539 (377*2π)/4671 weeks
3787.69947 -8.00646 (378*2π)/4671 weeks
3797.1784 -7.89508 (379*2π)/4671 weeks
3806.5428 -8.79166 (380*2π)/4671 weeks
3816.8286 -9.01087 (381*2π)/4671 weeks
3827.57028 -8.79977 (382*2π)/4671 weeks
3837.49258 -7.85969 (383*2π)/4671 weeks
3846.04742 -8.42708 (384*2π)/4671 weeks
3854.99626 -10.01704 (385*2π)/4671 weeks
3865.5917 -12.19409 (386*2π)/4671 weeks
3877.58247 -13.87561 (387*2π)/4671 weeks
3889.54975 -14.31221 (388*2π)/4671 weeks
38912.21719 -13.01574 (389*2π)/4671 weeks
39013.45268 -11.36321 (390*2π)/4671 weeks
39112.99388 -9.12466 (391*2π)/4671 weeks
39211.85927 -7.74048 (392*2π)/4671 weeks
39311.103 -7.3651 (393*2π)/4671 weeks
39410.45827 -7.47987 (394*2π)/4671 weeks
3959.14487 -7.95843 (395*2π)/4671 weeks
3969.401 -9.25898 (396*2π)/4671 weeks
39710.24964 -9.05968 (397*2π)/4671 weeks
39810.21081 -8.48001 (398*2π)/4671 weeks
39910.41639 -8.63595 (399*2π)/4671 weeks
40010.54259 -7.47386 (400*2π)/4671 weeks
4019.38379 -6.81117 (401*2π)/4671 weeks
4027.33122 -8.14633 (402*2π)/4671 weeks
4037.04633 -9.76403 (403*2π)/4671 weeks
4048.74554 -10.15666 (404*2π)/4671 weeks
4059.81853 -10.22502 (405*2π)/4671 weeks
4069.5853 -9.01387 (406*2π)/4671 weeks
4078.97179 -7.55587 (407*2π)/4671 weeks
4087.62211 -6.91837 (408*2π)/4671 weeks
4095.08569 -7.98528 (409*2π)/4671 weeks
4103.70252 -9.43779 (410*2π)/4671 weeks
4113.74363 -12.71488 (411*2π)/4671 weeks
4125.34732 -14.13988 (412*2π)/4671 weeks
4137.09664 -14.64286 (413*2π)/4671 weeks
4147.53361 -14.73634 (414*2π)/4671 weeks
4157.94629 -14.94102 (415*2π)/4671 weeks
4168.41478 -15.16201 (416*2π)/4671 weeks
4179.38936 -14.32708 (417*2π)/4671 weeks
4189.95276 -15.97585 (418*2π)/4671 weeks
41910.15806 -15.80761 (419*2π)/4671 weeks
42011.01238 -15.22773 (420*2π)/4671 weeks
42111.13917 -13.32927 (421*2π)/4671 weeks
42210.75701 -12.97284 (422*2π)/4671 weeks
42310.23294 -11.86177 (423*2π)/4671 weeks
4249.01046 -11.81732 (424*2π)/4671 weeks
4257.26495 -11.80865 (425*2π)/4671 weeks
4265.60104 -11.97732 (426*2π)/4671 weeks
4272.79995 -13.69313 (427*2π)/4671 weeks
4282.92343 -16.59625 (428*2π)/4671 weeks
4292.93961 -17.97939 (429*2π)/4671 weeks
4302.70391 -19.35437 (430*2π)/4671 weeks
431.99512 -22.29214 (431*2π)/4671 weeks
4321.2975 -25.76602 (432*2π)/4671 weeks
4332.32462 -29.26272 (433*2π)/4671 weeks
4346.45001 -33.21768 (434*2π)/4671 weeks
43511.03624 -34.55776 (435*2π)/4671 weeks
43614.9485 -33.87557 (436*2π)/4671 weeks
43718.21295 -33.87973 (437*2π)/4671 weeks
43821.17674 -30.65003 (438*2π)/4671 weeks
43921.6245 -27.97922 (439*2π)/4671 weeks
44021.3597 -27.20853 (440*2π)/4671 weeks
44120.80886 -26.53606 (441*2π)/4671 weeks
44221.12411 -24.51312 (442*2π)/4671 weeks
44319.81255 -24.06874 (443*2π)/4671 weeks
44419.4029 -25.81109 (444*2π)/4671 weeks
44518.57387 -26.8084 (445*2π)/4671 weeks
44618.36118 -23.79767 (446*2π)/4671 weeks
44715.54212 -25.6804 (447*2π)/4671 weeks
44810.80099 -30.83845 (448*2π)/4671 weeks
44915.37399 -39.98666 (449*2π)/4671 weeks
45020.80381 -41.95135 (450*2π)/4671 weeks
45127.00369 -40.08492 (451*2π)/4671 weeks
45228.44341 -35.22594 (452*2π)/4671 weeks
45324.71015 -34.84094 (453*2π)/4671 weeks
45421.65803 -35.97625 (454*2π)/4671 weeks
45523.36938 -38.55571 (455*2π)/4671 weeks
45620.24445 -42.36689 (456*2π)/4671 weeks
45720.88964 -46.85122 (457*2π)/4671 weeks
45818.27709 -56.93337 (458*2π)/4671 weeks
45921.83002 -72.8992 (459*2π)/4671 weeks
46032.41367 -81.76089 (460*2π)/4671 weeks
46151.42214 -86.52145 (461*2π)/4671 weeks
46259.0139 -82.48045 (462*2π)/4671 weeks
46361.50299 -98.67915 (463*2π)/4671 weeks
46479.3485 -135.1889 (464*2π)/4671 weeks
465144.666 -163.126 (465*2π)/4671 weeks



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