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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 57 weeks (57.2413*sine), 52 weeks (46.6427*sine), and 30 weeks (23.8113*cosine).

ZSL (ProShares UltraShort Silver) has an average price of 157.79 (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 11/18/2019 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0157.7944   0 
1209.8847 76.14813 (1*2π)/573573 weeks
2156.9226 129.9348 (2*2π)/573287 weeks
390.39073 120.0811 (3*2π)/573191 weeks
454.25269 99.22676 (4*2π)/573143 weeks
548.48816 79.25793 (5*2π)/573115 weeks
646.27981 67.5848 (6*2π)/57396 weeks
744.11325 70.93573 (7*2π)/57382 weeks
834.38012 72.06386 (8*2π)/57372 weeks
924.71485 63.11843 (9*2π)/57364 weeks
1015.8745 57.2413 (10*2π)/57357 weeks
1114.86438 46.64266 (11*2π)/57352 weeks
1215.52101 38.81863 (12*2π)/57348 weeks
1316.06143 37.20082 (13*2π)/57344 weeks
1416.99451 33.17788 (14*2π)/57341 weeks
1519.13305 32.24452 (15*2π)/57338 weeks
1617.67449 29.6641 (16*2π)/57336 weeks
1720.45169 29.28701 (17*2π)/57334 weeks
1822.80893 28.00562 (18*2π)/57332 weeks
1923.81125 30.7043 (19*2π)/57330 weeks
2021.13022 33.31768 (20*2π)/57329 weeks
2116.44783 33.89731 (21*2π)/57327 weeks
2213.25856 32.60253 (22*2π)/57326 weeks
238.65295 27.02933 (23*2π)/57325 weeks
2410.54908 21.62224 (24*2π)/57324 weeks
2513.1562 20.9238 (25*2π)/57323 weeks
2616.05072 19.7385 (26*2π)/57322 weeks
2715.21871 21.78196 (27*2π)/57321 weeks
2815.90262 20.61703 (28*2π)/57320 weeks
2915.09775 19.95376 (29*2π)/57320 weeks
3016.5221 20.1288 (30*2π)/57319 weeks
3117.72327 20.55774 (31*2π)/57318 weeks
3216.9446 21.64008 (32*2π)/57318 weeks
3317.59111 22.02923 (33*2π)/57317 weeks
3417.37179 22.29248 (34*2π)/57317 weeks
3517.50599 23.89894 (35*2π)/57316 weeks
3616.80668 25.92279 (36*2π)/57316 weeks
3714.1565 27.73734 (37*2π)/57315 weeks
3812.18407 27.55029 (38*2π)/57315 weeks
399.58724 28.18565 (39*2π)/57315 weeks
406.49414 27.89358 (40*2π)/57314 weeks
413.64039 26.51626 (41*2π)/57314 weeks
421.87827 23.10388 (42*2π)/57314 weeks
431.0756 20.97333 (43*2π)/57313 weeks
441.03489 18.68648 (44*2π)/57313 weeks
451.76284 15.99973 (45*2π)/57313 weeks
462.28347 15.37792 (46*2π)/57312 weeks
472.51482 14.3406 (47*2π)/57312 weeks
482.32134 13.3418 (48*2π)/57312 weeks
492.12996 11.44891 (49*2π)/57312 weeks
504.1378 9.9999 (50*2π)/57311 weeks
515.60672 9.70271 (51*2π)/57311 weeks
526.44423 9.36837 (52*2π)/57311 weeks
537.41572 9.76447 (53*2π)/57311 weeks
548.37609 9.77985 (54*2π)/57311 weeks
558.83838 10.63769 (55*2π)/57310 weeks
569.09433 10.91603 (56*2π)/57310 weeks
579.81747 11.35414 (57*2π)/57310 weeks
588.71828 12.14349 (58*2π)/57310 weeks
598.0211 12.84534 (59*2π)/57310 weeks
608.30803 12.87437 (60*2π)/57310 weeks
616.99782 11.84116 (61*2π)/5739 weeks
627.55644 12.64629 (62*2π)/5739 weeks
636.8969 12.19686 (63*2π)/5739 weeks
646.43708 12.08008 (64*2π)/5739 weeks
656.20325 11.98999 (65*2π)/5739 weeks
665.89382 11.74996 (66*2π)/5739 weeks
674.79391 11.91917 (67*2π)/5739 weeks
683.90692 11.21382 (68*2π)/5738 weeks
692.79035 9.80664 (69*2π)/5738 weeks
703.05928 7.59223 (70*2π)/5738 weeks
714.03746 6.80502 (71*2π)/5738 weeks
725.54368 5.64523 (72*2π)/5738 weeks
736.97843 6.03898 (73*2π)/5738 weeks
747.86251 6.29941 (74*2π)/5738 weeks
757.72308 7.26403 (75*2π)/5738 weeks
768.03214 8.26494 (76*2π)/5738 weeks
777.14761 8.30737 (77*2π)/5737 weeks
786.56477 8.55909 (78*2π)/5737 weeks
795.84695 7.07401 (79*2π)/5737 weeks
805.94806 6.18909 (80*2π)/5737 weeks
817.66013 5.5258 (81*2π)/5737 weeks
828.34344 5.87104 (82*2π)/5737 weeks
838.56346 6.84829 (83*2π)/5737 weeks
848.20985 7.12671 (84*2π)/5737 weeks
858.47289 7.02899 (85*2π)/5737 weeks
868.33344 7.39211 (86*2π)/5737 weeks
877.73352 7.56258 (87*2π)/5737 weeks
887.31143 6.78857 (88*2π)/5737 weeks
897.92253 6.03384 (89*2π)/5736 weeks
908.61212 6.28245 (90*2π)/5736 weeks
919.29918 6.05951 (91*2π)/5736 weeks
929.6058 6.24574 (92*2π)/5736 weeks
9310.49627 7.21475 (93*2π)/5736 weeks
9411.0483 8.28907 (94*2π)/5736 weeks
9510.37596 9.91372 (95*2π)/5736 weeks
969.61054 11.04341 (96*2π)/5736 weeks
977.59278 11.64249 (97*2π)/5736 weeks
986.36978 11.35684 (98*2π)/5736 weeks
994.79097 10.52561 (99*2π)/5736 weeks
1004.14691 9.22509 (100*2π)/5736 weeks
1014.25338 7.67186 (101*2π)/5736 weeks
1025.05996 6.8378 (102*2π)/5736 weeks
1036.00083 6.38896 (103*2π)/5736 weeks
1046.18127 7.2719 (104*2π)/5736 weeks
1056.09905 7.64935 (105*2π)/5735 weeks
1065.80851 7.10163 (106*2π)/5735 weeks
1075.25446 6.8176 (107*2π)/5735 weeks
1085.85714 6.4028 (108*2π)/5735 weeks
1096.19132 6.42524 (109*2π)/5735 weeks
1106.37266 6.70249 (110*2π)/5735 weeks
1116.2913 7.68848 (111*2π)/5735 weeks
1125.42625 7.64876 (112*2π)/5735 weeks
1134.44851 7.3765 (113*2π)/5735 weeks
1143.78974 6.89665 (114*2π)/5735 weeks
1153.51682 5.49476 (115*2π)/5735 weeks
1163.9831 4.93807 (116*2π)/5735 weeks
1174.80459 3.66623 (117*2π)/5735 weeks
1185.29894 3.95317 (118*2π)/5735 weeks
1195.76398 3.89202 (119*2π)/5735 weeks
1206.21139 3.80936 (120*2π)/5735 weeks
1216.75742 3.86605 (121*2π)/5735 weeks
1227.1231 4.30865 (122*2π)/5735 weeks
1237.37515 5.03032 (123*2π)/5735 weeks
1247.04633 5.39789 (124*2π)/5735 weeks
1256.74944 5.75384 (125*2π)/5735 weeks
1266.26705 5.66044 (126*2π)/5735 weeks
1276.04521 5.53337 (127*2π)/5735 weeks
1286.09842 5.18031 (128*2π)/5734 weeks
1295.80253 5.03479 (129*2π)/5734 weeks
1306.13453 4.805 (130*2π)/5734 weeks
1315.89422 4.77057 (131*2π)/5734 weeks
1326.50428 4.56961 (132*2π)/5734 weeks
1336.55309 4.68562 (133*2π)/5734 weeks
1347.01574 5.28992 (134*2π)/5734 weeks
1356.59601 5.37809 (135*2π)/5734 weeks
1366.232 5.96171 (136*2π)/5734 weeks
1375.84108 5.95755 (137*2π)/5734 weeks
1385.32935 5.55619 (138*2π)/5734 weeks
1395.03197 5.04073 (139*2π)/5734 weeks
1405.21628 4.763 (140*2π)/5734 weeks
1415.37213 4.8148 (141*2π)/5734 weeks
1424.85942 4.58436 (142*2π)/5734 weeks
1434.85767 4.06362 (143*2π)/5734 weeks
1445.29442 3.63092 (144*2π)/5734 weeks
1455.80132 3.80822 (145*2π)/5734 weeks
1465.8333 4.12804 (146*2π)/5734 weeks
1475.7313 4.03928 (147*2π)/5734 weeks
1485.62267 3.73411 (148*2π)/5734 weeks
1495.84433 4.08797 (149*2π)/5734 weeks
1505.83311 4.00998 (150*2π)/5734 weeks
1515.93598 4.20616 (151*2π)/5734 weeks
1525.86862 4.38011 (152*2π)/5734 weeks
1535.70409 4.61326 (153*2π)/5734 weeks
1545.18158 4.77865 (154*2π)/5734 weeks
1554.51682 4.57786 (155*2π)/5734 weeks
1564.1213 4.171 (156*2π)/5734 weeks
1573.73457 3.45127 (157*2π)/5734 weeks
1583.99144 2.71882 (158*2π)/5734 weeks
1594.11282 2.00145 (159*2π)/5734 weeks
1605.02369 1.89834 (160*2π)/5734 weeks
1615.65944 1.69128 (161*2π)/5734 weeks
1625.84911 2.13036 (162*2π)/5734 weeks
1636.00502 2.26254 (163*2π)/5734 weeks
1645.88084 2.41387 (164*2π)/5733 weeks
1655.74288 2.07305 (165*2π)/5733 weeks
1666.20102 1.79498 (166*2π)/5733 weeks
1676.65752 1.57841 (167*2π)/5733 weeks
1687.05604 2.36344 (168*2π)/5733 weeks
1696.96831 2.87656 (169*2π)/5733 weeks
1706.53221 3.08401 (170*2π)/5733 weeks
1716.17302 2.97715 (171*2π)/5733 weeks
1726.19604 2.73653 (172*2π)/5733 weeks
1736.17715 2.88103 (173*2π)/5733 weeks
1746.14904 2.96411 (174*2π)/5733 weeks
1755.91249 2.94316 (175*2π)/5733 weeks
1765.7037 2.66781 (176*2π)/5733 weeks
1775.29633 2.6204 (177*2π)/5733 weeks
1785.28161 1.87494 (178*2π)/5733 weeks
1795.56659 1.34444 (179*2π)/5733 weeks
1806.18539 .92617 (180*2π)/5733 weeks
1816.68265 1.19278 (181*2π)/5733 weeks
1827.01648 1.35608 (182*2π)/5733 weeks
1837.17211 1.39517 (183*2π)/5733 weeks
1847.5188 1.639 (184*2π)/5733 weeks
1857.83649 1.7479 (185*2π)/5733 weeks
1868.21875 2.39322 (186*2π)/5733 weeks
1878.14758 2.76694 (187*2π)/5733 weeks
1888.00536 3.62098 (188*2π)/5733 weeks
1897.45501 3.67981 (189*2π)/5733 weeks
1906.66273 3.45801 (190*2π)/5733 weeks
1916.65394 3.32475 (191*2π)/5733 weeks
1926.68517 2.92674 (192*2π)/5733 weeks
1936.97745 3.15572 (193*2π)/5733 weeks
1946.86795 3.10737 (194*2π)/5733 weeks
1956.95953 3.35626 (195*2π)/5733 weeks
1966.70261 3.43293 (196*2π)/5733 weeks
1976.2661 3.58802 (197*2π)/5733 weeks
1986.23417 3.35331 (198*2π)/5733 weeks
1996.04532 3.07153 (199*2π)/5733 weeks
2006.12577 2.94077 (200*2π)/5733 weeks
2015.9907 2.79154 (201*2π)/5733 weeks
2026.30862 2.68306 (202*2π)/5733 weeks
2036.48366 2.63696 (203*2π)/5733 weeks
2046.63919 3.16491 (204*2π)/5733 weeks
2056.44385 3.59134 (205*2π)/5733 weeks
2065.81813 3.75267 (206*2π)/5733 weeks
2075.32351 3.46736 (207*2π)/5733 weeks
2084.87078 2.96646 (208*2π)/5733 weeks
2094.9745 2.37293 (209*2π)/5733 weeks
2105.12121 1.92758 (210*2π)/5733 weeks
2115.56424 1.80408 (211*2π)/5733 weeks
2125.56895 1.77476 (212*2π)/5733 weeks
2135.87492 1.63449 (213*2π)/5733 weeks
2146.19101 1.45505 (214*2π)/5733 weeks
2156.43028 1.62693 (215*2π)/5733 weeks
2166.87893 1.93467 (216*2π)/5733 weeks
2177.08566 2.24868 (217*2π)/5733 weeks
2186.86069 2.9304 (218*2π)/5733 weeks
2196.66021 3.22801 (219*2π)/5733 weeks
2205.98637 3.13763 (220*2π)/5733 weeks
2215.70349 3.0373 (221*2π)/5733 weeks
2225.7053 2.58638 (222*2π)/5733 weeks
2235.69046 2.65558 (223*2π)/5733 weeks
2245.77488 2.60823 (224*2π)/5733 weeks
2255.7635 2.58244 (225*2π)/5733 weeks
2265.78568 2.94544 (226*2π)/5733 weeks
2275.36235 3.2347 (227*2π)/5733 weeks
2284.79683 3.20213 (228*2π)/5733 weeks
2294.06221 2.66289 (229*2π)/5733 weeks
2304.13468 1.78072 (230*2π)/5732 weeks
2314.45718 1.06758 (231*2π)/5732 weeks
2325.05089 .91323 (232*2π)/5732 weeks
2335.54708 1.1112 (233*2π)/5732 weeks
2345.45288 1.21509 (234*2π)/5732 weeks
2355.48829 1.33867 (235*2π)/5732 weeks
2365.40544 1.15078 (236*2π)/5732 weeks
2375.51941 .99992 (237*2π)/5732 weeks
2385.52441 .68681 (238*2π)/5732 weeks
2396.0876 .37755 (239*2π)/5732 weeks
2406.61479 .40841 (240*2π)/5732 weeks
2417.21417 .77557 (241*2π)/5732 weeks
2427.60821 1.32164 (242*2π)/5732 weeks
2437.47458 1.8094 (243*2π)/5732 weeks
2447.58757 2.32069 (244*2π)/5732 weeks
2457.28397 2.91071 (245*2π)/5732 weeks
2467.0036 3.26066 (246*2π)/5732 weeks
2476.51106 3.67256 (247*2π)/5732 weeks
2485.82995 3.71708 (248*2π)/5732 weeks
2495.60895 3.48317 (249*2π)/5732 weeks
2505.31319 3.4608 (250*2π)/5732 weeks
2515.04052 3.49667 (251*2π)/5732 weeks
2524.38634 3.46939 (252*2π)/5732 weeks
2534.01017 2.87661 (253*2π)/5732 weeks
2543.97448 2.30622 (254*2π)/5732 weeks
2554.36694 2.29851 (255*2π)/5732 weeks
2564.5219 2.23043 (256*2π)/5732 weeks
2574.2861 2.64204 (257*2π)/5732 weeks
2583.92525 2.48746 (258*2π)/5732 weeks
2593.3881 2.47781 (259*2π)/5732 weeks
2603.00927 2.01979 (260*2π)/5732 weeks
2612.80048 1.23998 (261*2π)/5732 weeks
2622.96159 .72733 (262*2π)/5732 weeks
2633.27542 .02571 (263*2π)/5732 weeks
2643.72671 -.05373 (264*2π)/5732 weeks
2653.97278 -.27683 (265*2π)/5732 weeks
2664.55542 -.51988 (266*2π)/5732 weeks
2674.82248 -.38224 (267*2π)/5732 weeks
2685.05711 -.08917 (268*2π)/5732 weeks
2695.17133 .0584 (269*2π)/5732 weeks
2705.23271 .08548 (270*2π)/5732 weeks
2715.43659 .33144 (271*2π)/5732 weeks
2725.46826 .60856 (272*2π)/5732 weeks
2735.10263 .92746 (273*2π)/5732 weeks
2744.71549 1.07755 (274*2π)/5732 weeks
2754.34221 .54348 (275*2π)/5732 weeks
2764.38013 .09347 (276*2π)/5732 weeks
2774.89456 -.22808 (277*2π)/5732 weeks
2785.65028 -.08484 (278*2π)/5732 weeks
2795.85007 .76041 (279*2π)/5732 weeks
2805.28339 1.19604 (280*2π)/5732 weeks
2814.86344 1.35874 (281*2π)/5732 weeks
2824.31287 1.13961 (282*2π)/5732 weeks
2834.07222 .97253 (283*2π)/5732 weeks
2843.83345 .4265 (284*2π)/5732 weeks
2853.90219 .01165 (285*2π)/5732 weeks
2864.16641 .01056 (286*2π)/5732 weeks
2874.16641 -.01056 (287*2π)/5732 weeks
2883.90219 -.01165 (288*2π)/5732 weeks
2893.83345 -.4265 (289*2π)/5732 weeks
2904.07222 -.97253 (290*2π)/5732 weeks
2914.31287 -1.13961 (291*2π)/5732 weeks
2924.86344 -1.35874 (292*2π)/5732 weeks
2935.28339 -1.19604 (293*2π)/5732 weeks
2945.85007 -.76041 (294*2π)/5732 weeks
2955.65028 .08484 (295*2π)/5732 weeks
2964.89456 .22808 (296*2π)/5732 weeks
2974.38013 -.09347 (297*2π)/5732 weeks
2984.34221 -.54348 (298*2π)/5732 weeks
2994.71549 -1.07755 (299*2π)/5732 weeks
3005.10263 -.92746 (300*2π)/5732 weeks
3015.46826 -.60856 (301*2π)/5732 weeks
3025.43659 -.33144 (302*2π)/5732 weeks
3035.23271 -.08548 (303*2π)/5732 weeks
3045.17133 -.0584 (304*2π)/5732 weeks
3055.05711 .08917 (305*2π)/5732 weeks
3064.82248 .38224 (306*2π)/5732 weeks
3074.55542 .51988 (307*2π)/5732 weeks
3083.97278 .27683 (308*2π)/5732 weeks
3093.72671 .05373 (309*2π)/5732 weeks
3103.27542 -.02571 (310*2π)/5732 weeks
3112.96159 -.72733 (311*2π)/5732 weeks
3122.80048 -1.23998 (312*2π)/5732 weeks
3133.00927 -2.01979 (313*2π)/5732 weeks
3143.3881 -2.47781 (314*2π)/5732 weeks
3153.92525 -2.48746 (315*2π)/5732 weeks
3164.2861 -2.64204 (316*2π)/5732 weeks
3174.5219 -2.23043 (317*2π)/5732 weeks
3184.36694 -2.29851 (318*2π)/5732 weeks
3193.97448 -2.30622 (319*2π)/5732 weeks
3204.01017 -2.87661 (320*2π)/5732 weeks
3214.38634 -3.46939 (321*2π)/5732 weeks
3225.04052 -3.49667 (322*2π)/5732 weeks
3235.31319 -3.4608 (323*2π)/5732 weeks
3245.60895 -3.48317 (324*2π)/5732 weeks
3255.82995 -3.71708 (325*2π)/5732 weeks
3266.51106 -3.67256 (326*2π)/5732 weeks
3277.0036 -3.26066 (327*2π)/5732 weeks
3287.28397 -2.91071 (328*2π)/5732 weeks
3297.58757 -2.32069 (329*2π)/5732 weeks
3307.47458 -1.8094 (330*2π)/5732 weeks
3317.60821 -1.32164 (331*2π)/5732 weeks
3327.21417 -.77557 (332*2π)/5732 weeks
3336.61479 -.40841 (333*2π)/5732 weeks
3346.0876 -.37755 (334*2π)/5732 weeks
3355.52441 -.68681 (335*2π)/5732 weeks
3365.51941 -.99992 (336*2π)/5732 weeks
3375.40544 -1.15078 (337*2π)/5732 weeks
3385.48829 -1.33867 (338*2π)/5732 weeks
3395.45288 -1.21509 (339*2π)/5732 weeks
3405.54708 -1.1112 (340*2π)/5732 weeks
3415.05089 -.91323 (341*2π)/5732 weeks
3424.45718 -1.06758 (342*2π)/5732 weeks
3434.13468 -1.78072 (343*2π)/5732 weeks
3444.06221 -2.66289 (344*2π)/5732 weeks
3454.79683 -3.20213 (345*2π)/5732 weeks
3465.36235 -3.2347 (346*2π)/5732 weeks
3475.78568 -2.94544 (347*2π)/5732 weeks
3485.7635 -2.58244 (348*2π)/5732 weeks
3495.77488 -2.60823 (349*2π)/5732 weeks
3505.69046 -2.65558 (350*2π)/5732 weeks
3515.7053 -2.58638 (351*2π)/5732 weeks
3525.70349 -3.0373 (352*2π)/5732 weeks
3535.98637 -3.13763 (353*2π)/5732 weeks
3546.66021 -3.22801 (354*2π)/5732 weeks
3556.86069 -2.9304 (355*2π)/5732 weeks
3567.08566 -2.24868 (356*2π)/5732 weeks
3576.87893 -1.93467 (357*2π)/5732 weeks
3586.43028 -1.62693 (358*2π)/5732 weeks
3596.19101 -1.45505 (359*2π)/5732 weeks
3605.87492 -1.63449 (360*2π)/5732 weeks
3615.56895 -1.77476 (361*2π)/5732 weeks
3625.56424 -1.80408 (362*2π)/5732 weeks
3635.12121 -1.92758 (363*2π)/5732 weeks
3644.9745 -2.37293 (364*2π)/5732 weeks
3654.87078 -2.96646 (365*2π)/5732 weeks
3665.32351 -3.46736 (366*2π)/5732 weeks
3675.81813 -3.75267 (367*2π)/5732 weeks
3686.44385 -3.59134 (368*2π)/5732 weeks
3696.63919 -3.16491 (369*2π)/5732 weeks
3706.48366 -2.63696 (370*2π)/5732 weeks
3716.30862 -2.68306 (371*2π)/5732 weeks
3725.9907 -2.79154 (372*2π)/5732 weeks
3736.12577 -2.94077 (373*2π)/5732 weeks
3746.04532 -3.07153 (374*2π)/5732 weeks
3756.23417 -3.35331 (375*2π)/5732 weeks
3766.2661 -3.58802 (376*2π)/5732 weeks
3776.70261 -3.43293 (377*2π)/5732 weeks
3786.95953 -3.35626 (378*2π)/5732 weeks
3796.86795 -3.10737 (379*2π)/5732 weeks
3806.97745 -3.15572 (380*2π)/5732 weeks
3816.68517 -2.92674 (381*2π)/5732 weeks
3826.65394 -3.32475 (382*2π)/5732 weeks
3836.66273 -3.45801 (383*2π)/5731 weeks
3847.45501 -3.67981 (384*2π)/5731 weeks
3858.00536 -3.62098 (385*2π)/5731 weeks
3868.14758 -2.76694 (386*2π)/5731 weeks
3878.21875 -2.39322 (387*2π)/5731 weeks
3887.83649 -1.7479 (388*2π)/5731 weeks
3897.5188 -1.639 (389*2π)/5731 weeks
3907.17211 -1.39517 (390*2π)/5731 weeks
3917.01648 -1.35608 (391*2π)/5731 weeks
3926.68265 -1.19278 (392*2π)/5731 weeks
3936.18539 -.92617 (393*2π)/5731 weeks
3945.56659 -1.34444 (394*2π)/5731 weeks
3955.28161 -1.87494 (395*2π)/5731 weeks
3965.29633 -2.6204 (396*2π)/5731 weeks
3975.7037 -2.66781 (397*2π)/5731 weeks
3985.91249 -2.94316 (398*2π)/5731 weeks
3996.14904 -2.96411 (399*2π)/5731 weeks
4006.17715 -2.88103 (400*2π)/5731 weeks
4016.19604 -2.73653 (401*2π)/5731 weeks
4026.17302 -2.97715 (402*2π)/5731 weeks
4036.53221 -3.08401 (403*2π)/5731 weeks
4046.96831 -2.87656 (404*2π)/5731 weeks
4057.05604 -2.36344 (405*2π)/5731 weeks
4066.65752 -1.57841 (406*2π)/5731 weeks
4076.20102 -1.79498 (407*2π)/5731 weeks
4085.74288 -2.07305 (408*2π)/5731 weeks
4095.88084 -2.41387 (409*2π)/5731 weeks
4106.00502 -2.26254 (410*2π)/5731 weeks
4115.84911 -2.13036 (411*2π)/5731 weeks
4125.65944 -1.69128 (412*2π)/5731 weeks
4135.02369 -1.89834 (413*2π)/5731 weeks
4144.11282 -2.00145 (414*2π)/5731 weeks
4153.99144 -2.71882 (415*2π)/5731 weeks
4163.73457 -3.45127 (416*2π)/5731 weeks
4174.1213 -4.171 (417*2π)/5731 weeks
4184.51682 -4.57786 (418*2π)/5731 weeks
4195.18158 -4.77865 (419*2π)/5731 weeks
4205.70409 -4.61326 (420*2π)/5731 weeks
4215.86862 -4.38011 (421*2π)/5731 weeks
4225.93598 -4.20616 (422*2π)/5731 weeks
4235.83311 -4.00998 (423*2π)/5731 weeks
4245.84433 -4.08797 (424*2π)/5731 weeks
4255.62267 -3.73411 (425*2π)/5731 weeks
4265.7313 -4.03928 (426*2π)/5731 weeks
4275.8333 -4.12804 (427*2π)/5731 weeks
4285.80132 -3.80822 (428*2π)/5731 weeks
4295.29442 -3.63092 (429*2π)/5731 weeks
4304.85767 -4.06362 (430*2π)/5731 weeks
4314.85942 -4.58436 (431*2π)/5731 weeks
4325.37213 -4.8148 (432*2π)/5731 weeks
4335.21628 -4.763 (433*2π)/5731 weeks
4345.03197 -5.04073 (434*2π)/5731 weeks
4355.32935 -5.55619 (435*2π)/5731 weeks
4365.84108 -5.95755 (436*2π)/5731 weeks
4376.232 -5.96171 (437*2π)/5731 weeks
4386.59601 -5.37809 (438*2π)/5731 weeks
4397.01574 -5.28992 (439*2π)/5731 weeks
4406.55309 -4.68562 (440*2π)/5731 weeks
4416.50428 -4.56961 (441*2π)/5731 weeks
4425.89422 -4.77057 (442*2π)/5731 weeks
4436.13453 -4.805 (443*2π)/5731 weeks
4445.80253 -5.03479 (444*2π)/5731 weeks
4456.09842 -5.18031 (445*2π)/5731 weeks
4466.04521 -5.53337 (446*2π)/5731 weeks
4476.26705 -5.66044 (447*2π)/5731 weeks
4486.74944 -5.75384 (448*2π)/5731 weeks
4497.04633 -5.39789 (449*2π)/5731 weeks
4507.37515 -5.03032 (450*2π)/5731 weeks
4517.1231 -4.30865 (451*2π)/5731 weeks
4526.75742 -3.86605 (452*2π)/5731 weeks
4536.21139 -3.80936 (453*2π)/5731 weeks
4545.76398 -3.89202 (454*2π)/5731 weeks
4555.29894 -3.95317 (455*2π)/5731 weeks
4564.80459 -3.66623 (456*2π)/5731 weeks
4573.9831 -4.93807 (457*2π)/5731 weeks
4583.51682 -5.49476 (458*2π)/5731 weeks
4593.78974 -6.89665 (459*2π)/5731 weeks
4604.44851 -7.3765 (460*2π)/5731 weeks
4615.42625 -7.64876 (461*2π)/5731 weeks
4626.2913 -7.68848 (462*2π)/5731 weeks
4636.37266 -6.70249 (463*2π)/5731 weeks
4646.19132 -6.42524 (464*2π)/5731 weeks
4655.85714 -6.4028 (465*2π)/5731 weeks
4665.25446 -6.8176 (466*2π)/5731 weeks
4675.80851 -7.10163 (467*2π)/5731 weeks
4686.09905 -7.64935 (468*2π)/5731 weeks
4696.18127 -7.2719 (469*2π)/5731 weeks
4706.00083 -6.38896 (470*2π)/5731 weeks
4715.05996 -6.8378 (471*2π)/5731 weeks
4724.25338 -7.67186 (472*2π)/5731 weeks
4734.14691 -9.22509 (473*2π)/5731 weeks
4744.79097 -10.52561 (474*2π)/5731 weeks
4756.36978 -11.35684 (475*2π)/5731 weeks
4767.59278 -11.64249 (476*2π)/5731 weeks
4779.61054 -11.04341 (477*2π)/5731 weeks
47810.37596 -9.91372 (478*2π)/5731 weeks
47911.0483 -8.28907 (479*2π)/5731 weeks
48010.49627 -7.21475 (480*2π)/5731 weeks
4819.6058 -6.24574 (481*2π)/5731 weeks
4829.29918 -6.05951 (482*2π)/5731 weeks
4838.61212 -6.28245 (483*2π)/5731 weeks
4847.92253 -6.03384 (484*2π)/5731 weeks
4857.31143 -6.78857 (485*2π)/5731 weeks
4867.73352 -7.56258 (486*2π)/5731 weeks
4878.33344 -7.39211 (487*2π)/5731 weeks
4888.47289 -7.02899 (488*2π)/5731 weeks
4898.20985 -7.12671 (489*2π)/5731 weeks
4908.56346 -6.84829 (490*2π)/5731 weeks
4918.34344 -5.87104 (491*2π)/5731 weeks
4927.66013 -5.5258 (492*2π)/5731 weeks
4935.94806 -6.18909 (493*2π)/5731 weeks
4945.84695 -7.07401 (494*2π)/5731 weeks
4956.56477 -8.55909 (495*2π)/5731 weeks
4967.14761 -8.30737 (496*2π)/5731 weeks
4978.03214 -8.26494 (497*2π)/5731 weeks
4987.72308 -7.26403 (498*2π)/5731 weeks
4997.86251 -6.29941 (499*2π)/5731 weeks
5006.97843 -6.03898 (500*2π)/5731 weeks
5015.54368 -5.64523 (501*2π)/5731 weeks
5024.03746 -6.80502 (502*2π)/5731 weeks
5033.05928 -7.59223 (503*2π)/5731 weeks
5042.79035 -9.80664 (504*2π)/5731 weeks
5053.90692 -11.21382 (505*2π)/5731 weeks
5064.79391 -11.91917 (506*2π)/5731 weeks
5075.89382 -11.74996 (507*2π)/5731 weeks
5086.20325 -11.98999 (508*2π)/5731 weeks
5096.43708 -12.08008 (509*2π)/5731 weeks
5106.8969 -12.19686 (510*2π)/5731 weeks
5117.55644 -12.64629 (511*2π)/5731 weeks
5126.99782 -11.84116 (512*2π)/5731 weeks
5138.30803 -12.87437 (513*2π)/5731 weeks
5148.0211 -12.84534 (514*2π)/5731 weeks
5158.71828 -12.14349 (515*2π)/5731 weeks
5169.81747 -11.35414 (516*2π)/5731 weeks
5179.09433 -10.91603 (517*2π)/5731 weeks
5188.83838 -10.63769 (518*2π)/5731 weeks
5198.37609 -9.77985 (519*2π)/5731 weeks
5207.41572 -9.76447 (520*2π)/5731 weeks
5216.44423 -9.36837 (521*2π)/5731 weeks
5225.60672 -9.70271 (522*2π)/5731 weeks
5234.1378 -9.9999 (523*2π)/5731 weeks
5242.12996 -11.44891 (524*2π)/5731 weeks
5252.32134 -13.3418 (525*2π)/5731 weeks
5262.51482 -14.3406 (526*2π)/5731 weeks
5272.28347 -15.37792 (527*2π)/5731 weeks
5281.76284 -15.99973 (528*2π)/5731 weeks
5291.03489 -18.68648 (529*2π)/5731 weeks
5301.0756 -20.97333 (530*2π)/5731 weeks
5311.87827 -23.10388 (531*2π)/5731 weeks
5323.64039 -26.51626 (532*2π)/5731 weeks
5336.49414 -27.89358 (533*2π)/5731 weeks
5349.58724 -28.18565 (534*2π)/5731 weeks
53512.18407 -27.55029 (535*2π)/5731 weeks
53614.1565 -27.73734 (536*2π)/5731 weeks
53716.80668 -25.92279 (537*2π)/5731 weeks
53817.50599 -23.89894 (538*2π)/5731 weeks
53917.37179 -22.29248 (539*2π)/5731 weeks
54017.59111 -22.02923 (540*2π)/5731 weeks
54116.9446 -21.64008 (541*2π)/5731 weeks
54217.72327 -20.55774 (542*2π)/5731 weeks
54316.5221 -20.1288 (543*2π)/5731 weeks
54415.09775 -19.95376 (544*2π)/5731 weeks
54515.90262 -20.61703 (545*2π)/5731 weeks
54615.21871 -21.78196 (546*2π)/5731 weeks
54716.05072 -19.7385 (547*2π)/5731 weeks
54813.1562 -20.9238 (548*2π)/5731 weeks
54910.54908 -21.62224 (549*2π)/5731 weeks
5508.65295 -27.02933 (550*2π)/5731 weeks
55113.25856 -32.60253 (551*2π)/5731 weeks
55216.44783 -33.89731 (552*2π)/5731 weeks
55321.13022 -33.31768 (553*2π)/5731 weeks
55423.81125 -30.7043 (554*2π)/5731 weeks
55522.80893 -28.00562 (555*2π)/5731 weeks
55620.45169 -29.28701 (556*2π)/5731 weeks
55717.67449 -29.6641 (557*2π)/5731 weeks
55819.13305 -32.24452 (558*2π)/5731 weeks
55916.99451 -33.17788 (559*2π)/5731 weeks
56016.06143 -37.20082 (560*2π)/5731 weeks
56115.52101 -38.81863 (561*2π)/5731 weeks
56214.86438 -46.64266 (562*2π)/5731 weeks
56315.8745 -57.2413 (563*2π)/5731 weeks
56424.71485 -63.11843 (564*2π)/5731 weeks
56534.38012 -72.06386 (565*2π)/5731 weeks
56644.11325 -70.93573 (566*2π)/5731 weeks
56746.27981 -67.5848 (567*2π)/5731 weeks
56848.48816 -79.25793 (568*2π)/5731 weeks
56954.25269 -99.22676 (569*2π)/5731 weeks
57090.39073 -120.0811 (570*2π)/5731 weeks
571156.9226 -129.9348 (571*2π)/5731 weeks



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