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Fourier Analysis of ZSL (ProShares UltraShort Silver ETF)


ZSL (ProShares UltraShort Silver ETF) appears to have interesting cyclic behaviour every 46 weeks (47.7411*sine), 42 weeks (41.9579*sine), and 31 weeks (29.263*cosine).

ZSL (ProShares UltraShort Silver ETF) has an average price of 188.55 (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 9/5/2017 for ZSL (ProShares UltraShort Silver ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0188.5496   0 
1251.4597 111.2678 (1*2π)/458458 weeks
2143.3731 165.177 (2*2π)/458229 weeks
377.66524 135.3522 (3*2π)/458153 weeks
461.91933 99.5951 (4*2π)/458115 weeks
560.88974 84.43465 (5*2π)/45892 weeks
651.06233 88.50153 (6*2π)/45876 weeks
731.8482 80.93006 (7*2π)/45865 weeks
819.79826 71.2804 (8*2π)/45857 weeks
918.07932 56.21696 (9*2π)/45851 weeks
1021.80236 47.74113 (10*2π)/45846 weeks
1121.32571 41.95788 (11*2π)/45842 weeks
1224.378 39.72521 (12*2π)/45838 weeks
1323.75836 35.05174 (13*2π)/45835 weeks
1425.80976 34.3338 (14*2π)/45833 weeks
1529.26304 37.11531 (15*2π)/45831 weeks
1625.94314 41.58931 (16*2π)/45829 weeks
1718.96896 41.38577 (17*2π)/45827 weeks
1812.03228 38.4752 (18*2π)/45825 weeks
1912.05562 28.37684 (19*2π)/45824 weeks
2016.35166 26.13622 (20*2π)/45823 weeks
2120.69961 25.89008 (21*2π)/45822 weeks
2218.80541 25.81529 (22*2π)/45821 weeks
2318.76915 25.78343 (23*2π)/45820 weeks
2420.74902 25.18971 (24*2π)/45819 weeks
2522.26526 26.45891 (25*2π)/45818 weeks
2621.56408 26.73178 (26*2π)/45818 weeks
2721.36701 27.90583 (27*2π)/45817 weeks
2821.83157 30.06705 (28*2π)/45816 weeks
2920.37791 33.3501 (29*2π)/45816 weeks
3015.94027 34.46549 (30*2π)/45815 weeks
3112.81187 35.362 (31*2π)/45815 weeks
328.083 34.81952 (32*2π)/45814 weeks
333.35652 32.08577 (33*2π)/45814 weeks
341.98044 27.6192 (34*2π)/45813 weeks
351.29083 23.8254 (35*2π)/45813 weeks
362.13244 19.99524 (36*2π)/45813 weeks
372.77814 18.86362 (37*2π)/45812 weeks
382.99837 17.45435 (38*2π)/45812 weeks
392.60343 15.06304 (39*2π)/45812 weeks
405.26556 12.42033 (40*2π)/45811 weeks
417.26129 12.1629 (41*2π)/45811 weeks
429.01605 11.90444 (42*2π)/45811 weeks
4310.11973 12.01265 (43*2π)/45811 weeks
4410.94883 13.21543 (44*2π)/45810 weeks
4511.25134 13.63743 (45*2π)/45810 weeks
4611.49557 15.52 (46*2π)/45810 weeks
4710.60597 16.10423 (47*2π)/45810 weeks
4810.31674 16.13179 (48*2π)/45810 weeks
499.47434 14.54899 (49*2π)/4589 weeks
508.59075 15.47539 (50*2π)/4589 weeks
518.10239 15.23095 (51*2π)/4589 weeks
527.66154 15.02494 (52*2π)/4589 weeks
537.19456 14.97823 (53*2π)/4589 weeks
545.40293 14.36194 (54*2π)/4588 weeks
553.72209 12.7499 (55*2π)/4588 weeks
564.02818 9.36032 (56*2π)/4588 weeks
575.36999 7.84802 (57*2π)/4588 weeks
588.11213 7.16836 (58*2π)/4588 weeks
599.4856 7.76164 (59*2π)/4588 weeks
609.74326 9.11496 (60*2π)/4588 weeks
619.54886 10.60786 (61*2π)/4588 weeks
628.76134 10.49894 (62*2π)/4587 weeks
637.0786 9.22582 (63*2π)/4587 weeks
647.41952 7.61827 (64*2π)/4587 weeks
659.7716 7.28974 (65*2π)/4587 weeks
6610.86796 8.19212 (66*2π)/4587 weeks
6710.36016 8.95655 (67*2π)/4587 weeks
6810.57166 8.87208 (68*2π)/4587 weeks
6910.26032 9.44885 (69*2π)/4587 weeks
709.20011 9.05061 (70*2π)/4587 weeks
719.68052 7.68179 (71*2π)/4586 weeks
7210.70865 7.89129 (72*2π)/4586 weeks
7311.79218 8.01686 (73*2π)/4586 weeks
7413.03651 8.40949 (74*2π)/4586 weeks
7513.77501 10.00568 (75*2π)/4586 weeks
7612.95203 12.49305 (76*2π)/4586 weeks
7711.3701 14.38387 (77*2π)/4586 weeks
788.6472 14.17671 (78*2π)/4586 weeks
796.26672 13.39552 (79*2π)/4586 weeks
805.13255 11.28679 (80*2π)/4586 weeks
815.5839 9.03875 (81*2π)/4586 weeks
826.76095 8.11543 (82*2π)/4586 weeks
837.8473 9.0519 (83*2π)/4586 weeks
847.45458 9.55484 (84*2π)/4585 weeks
857.17255 9.09077 (85*2π)/4585 weeks
867.08158 7.97032 (86*2π)/4585 weeks
877.68436 7.99916 (87*2π)/4585 weeks
888.06202 8.41065 (88*2π)/4585 weeks
897.29758 9.717 (89*2π)/4585 weeks
906.05068 9.62245 (90*2π)/4585 weeks
914.98807 8.75741 (91*2π)/4585 weeks
924.51051 6.66966 (92*2π)/4585 weeks
934.8463 5.59906 (93*2π)/4585 weeks
946.64006 5.08527 (94*2π)/4585 weeks
957.22045 4.92594 (95*2π)/4585 weeks
967.88735 4.83209 (96*2π)/4585 weeks
978.78547 5.10956 (97*2π)/4585 weeks
989.34405 5.85289 (98*2π)/4585 weeks
998.92684 6.69968 (99*2π)/4585 weeks
1008.44066 7.1992 (100*2π)/4585 weeks
1017.83576 6.95922 (101*2π)/4585 weeks
1027.50536 6.52478 (102*2π)/4584 weeks
1037.33075 6.43266 (103*2π)/4584 weeks
1047.76768 6.07159 (104*2π)/4584 weeks
1057.60312 5.62217 (105*2π)/4584 weeks
1068.18009 5.93979 (106*2π)/4584 weeks
1078.86191 6.39738 (107*2π)/4584 weeks
1088.35173 6.73533 (108*2π)/4584 weeks
1097.5704 7.27041 (109*2π)/4584 weeks
1106.71527 7.13365 (110*2π)/4584 weeks
1116.24823 6.43007 (111*2π)/4584 weeks
1126.51514 5.92631 (112*2π)/4584 weeks
1136.45375 6.13172 (113*2π)/4584 weeks
1146.07287 5.33808 (114*2π)/4584 weeks
1156.54894 4.54743 (115*2π)/4584 weeks
1167.29092 4.76574 (116*2π)/4584 weeks
1177.12541 5.12097 (117*2π)/4584 weeks
1186.93746 4.97777 (118*2π)/4584 weeks
1197.43288 5.08429 (119*2π)/4584 weeks
1207.37916 5.00271 (120*2π)/4584 weeks
1217.40816 5.31658 (121*2π)/4584 weeks
1227.22972 5.63058 (122*2π)/4584 weeks
1236.56857 5.99375 (123*2π)/4584 weeks
1245.5916 5.65684 (124*2π)/4584 weeks
1254.94017 4.9527 (125*2π)/4584 weeks
1264.84659 3.59865 (126*2π)/4584 weeks
1275.08614 2.61999 (127*2π)/4584 weeks
1286.29924 2.29889 (128*2π)/4584 weeks
1297.32305 2.3944 (129*2π)/4584 weeks
1307.42138 2.69363 (130*2π)/4584 weeks
1317.33673 2.9992 (131*2π)/4583 weeks
1327.14606 2.49118 (132*2π)/4583 weeks
1337.76839 2.2656 (133*2π)/4583 weeks
1348.89914 2.68757 (134*2π)/4583 weeks
1358.77467 3.55532 (135*2π)/4583 weeks
1368.11622 3.90327 (136*2π)/4583 weeks
1377.68172 3.61259 (137*2π)/4583 weeks
1387.85101 3.58959 (138*2π)/4583 weeks
1397.73568 3.67348 (139*2π)/4583 weeks
1407.3251 3.68189 (140*2π)/4583 weeks
1417.13262 3.42266 (141*2π)/4583 weeks
1426.53373 2.60669 (142*2π)/4583 weeks
1436.93992 1.75816 (143*2π)/4583 weeks
1447.95662 1.19764 (144*2π)/4583 weeks
1458.57387 1.5205 (145*2π)/4583 weeks
1468.89925 1.77586 (146*2π)/4583 weeks
1479.45482 1.99328 (147*2π)/4583 weeks
1489.97764 2.20388 (148*2π)/4583 weeks
14910.20306 3.23041 (149*2π)/4583 weeks
15010.31638 4.09344 (150*2π)/4583 weeks
1519.32281 4.55677 (151*2π)/4583 weeks
1528.35476 4.19398 (152*2π)/4583 weeks
1538.18829 3.93271 (153*2π)/4583 weeks
1548.69865 3.72808 (154*2π)/4583 weeks
1558.5158 3.87149 (155*2π)/4583 weeks
1568.58782 4.26972 (156*2π)/4583 weeks
1578.28199 4.46561 (157*2π)/4583 weeks
1587.76174 4.1305 (158*2π)/4583 weeks
1597.48906 3.87225 (159*2π)/4583 weeks
1607.61748 3.70324 (160*2π)/4583 weeks
1617.61922 3.30137 (161*2π)/4583 weeks
1627.91511 3.3378 (162*2π)/4583 weeks
1638.32725 3.91654 (163*2π)/4583 weeks
1647.92565 4.57065 (164*2π)/4583 weeks
1656.9199 4.56571 (165*2π)/4583 weeks
1666.20451 4.03212 (166*2π)/4583 weeks
1676.19258 3.04149 (167*2π)/4583 weeks
1686.50597 2.36301 (168*2π)/4583 weeks
1697.02748 2.37471 (169*2π)/4583 weeks
1707.2686 2.04211 (170*2π)/4583 weeks
1717.7108 1.83953 (171*2π)/4583 weeks
1728.16989 2.01942 (172*2π)/4583 weeks
1738.62793 2.58685 (173*2π)/4583 weeks
1748.79722 3.50996 (174*2π)/4583 weeks
1758.33607 3.99038 (175*2π)/4583 weeks
1767.43675 3.88181 (176*2π)/4583 weeks
1776.94937 3.53673 (177*2π)/4583 weeks
1787.19945 3.38573 (178*2π)/4583 weeks
1797.24034 3.28025 (179*2π)/4583 weeks
1807.30502 3.29054 (180*2π)/4583 weeks
1817.09142 3.8725 (181*2π)/4583 weeks
1826.23873 4.00472 (182*2π)/4583 weeks
1835.10452 3.36754 (183*2π)/4583 weeks
1845.18457 2.06601 (184*2π)/4582 weeks
1855.98275 1.184 (185*2π)/4582 weeks
1866.82071 1.20947 (186*2π)/4582 weeks
1876.82271 1.529 (187*2π)/4582 weeks
1886.81789 1.65106 (188*2π)/4582 weeks
1896.82688 1.31394 (189*2π)/4582 weeks
1906.86791 1.04223 (190*2π)/4582 weeks
1917.58473 .46204 (191*2π)/4582 weeks
1928.45618 .52672 (192*2π)/4582 weeks
1939.22796 1.19906 (193*2π)/4582 weeks
1949.35606 2.21411 (194*2π)/4582 weeks
1959.50114 2.89555 (195*2π)/4582 weeks
1969.02169 3.74057 (196*2π)/4582 weeks
1978.53612 4.35954 (197*2π)/4582 weeks
1987.53166 4.70842 (198*2π)/4582 weeks
1996.99723 4.35036 (199*2π)/4582 weeks
2006.55987 4.33237 (200*2π)/4582 weeks
2015.99583 4.4746 (201*2π)/4582 weeks
2025.08253 3.80435 (202*2π)/4582 weeks
2034.99512 2.89965 (203*2π)/4582 weeks
2045.43924 2.84466 (204*2π)/4582 weeks
2055.69189 3.07607 (205*2π)/4582 weeks
2064.96392 3.14229 (206*2π)/4582 weeks
2074.27273 3.09796 (207*2π)/4582 weeks
2083.62477 2.34097 (208*2π)/4582 weeks
2093.62601 1.18324 (209*2π)/4582 weeks
2103.83996 .23938 (210*2π)/4582 weeks
2114.62754 -.06086 (211*2π)/4582 weeks
2125.00412 -.44499 (212*2π)/4582 weeks
2135.86214 -.41171 (213*2π)/4582 weeks
2146.34871 -.14629 (214*2π)/4582 weeks
2156.48959 .10153 (215*2π)/4582 weeks
2166.65059 .16292 (216*2π)/4582 weeks
2176.8145 .59772 (217*2π)/4582 weeks
2186.56898 1.19565 (218*2π)/4582 weeks
2195.96558 1.37226 (219*2π)/4582 weeks
2205.50876 .5792 (220*2π)/4582 weeks
2215.82134 -.18325 (221*2π)/4582 weeks
2226.83478 -.29583 (222*2π)/4582 weeks
2237.32345 .9415 (223*2π)/4582 weeks
2246.49905 1.52579 (224*2π)/4582 weeks
2255.68462 1.67059 (225*2π)/4582 weeks
2265.23806 1.26173 (226*2π)/4582 weeks
2274.79795 .56354 (227*2π)/4582 weeks
2285.03644 -.05116 (228*2π)/4582 weeks
2295.21186   (229*2π)/4582 weeks
2305.03644 .05116 (230*2π)/4582 weeks
2314.79795 -.56354 (231*2π)/4582 weeks
2325.23806 -1.26173 (232*2π)/4582 weeks
2335.68462 -1.67059 (233*2π)/4582 weeks
2346.49905 -1.52579 (234*2π)/4582 weeks
2357.32345 -.9415 (235*2π)/4582 weeks
2366.83478 .29583 (236*2π)/4582 weeks
2375.82134 .18325 (237*2π)/4582 weeks
2385.50876 -.5792 (238*2π)/4582 weeks
2395.96558 -1.37226 (239*2π)/4582 weeks
2406.56898 -1.19565 (240*2π)/4582 weeks
2416.8145 -.59772 (241*2π)/4582 weeks
2426.65059 -.16292 (242*2π)/4582 weeks
2436.48959 -.10153 (243*2π)/4582 weeks
2446.34871 .14629 (244*2π)/4582 weeks
2455.86214 .41171 (245*2π)/4582 weeks
2465.00412 .44499 (246*2π)/4582 weeks
2474.62754 .06086 (247*2π)/4582 weeks
2483.83996 -.23938 (248*2π)/4582 weeks
2493.62601 -1.18324 (249*2π)/4582 weeks
2503.62477 -2.34097 (250*2π)/4582 weeks
2514.27273 -3.09796 (251*2π)/4582 weeks
2524.96392 -3.14229 (252*2π)/4582 weeks
2535.69189 -3.07607 (253*2π)/4582 weeks
2545.43924 -2.84466 (254*2π)/4582 weeks
2554.99512 -2.89965 (255*2π)/4582 weeks
2565.08253 -3.80435 (256*2π)/4582 weeks
2575.99583 -4.4746 (257*2π)/4582 weeks
2586.55987 -4.33237 (258*2π)/4582 weeks
2596.99723 -4.35036 (259*2π)/4582 weeks
2607.53166 -4.70842 (260*2π)/4582 weeks
2618.53612 -4.35954 (261*2π)/4582 weeks
2629.02169 -3.74057 (262*2π)/4582 weeks
2639.50114 -2.89555 (263*2π)/4582 weeks
2649.35606 -2.21411 (264*2π)/4582 weeks
2659.22796 -1.19906 (265*2π)/4582 weeks
2668.45618 -.52672 (266*2π)/4582 weeks
2677.58473 -.46204 (267*2π)/4582 weeks
2686.86791 -1.04223 (268*2π)/4582 weeks
2696.82688 -1.31394 (269*2π)/4582 weeks
2706.81789 -1.65106 (270*2π)/4582 weeks
2716.82271 -1.529 (271*2π)/4582 weeks
2726.82071 -1.20947 (272*2π)/4582 weeks
2735.98275 -1.184 (273*2π)/4582 weeks
2745.18457 -2.06601 (274*2π)/4582 weeks
2755.10452 -3.36754 (275*2π)/4582 weeks
2766.23873 -4.00472 (276*2π)/4582 weeks
2777.09142 -3.8725 (277*2π)/4582 weeks
2787.30502 -3.29054 (278*2π)/4582 weeks
2797.24034 -3.28025 (279*2π)/4582 weeks
2807.19945 -3.38573 (280*2π)/4582 weeks
2816.94937 -3.53673 (281*2π)/4582 weeks
2827.43675 -3.88181 (282*2π)/4582 weeks
2838.33607 -3.99038 (283*2π)/4582 weeks
2848.79722 -3.50996 (284*2π)/4582 weeks
2858.62793 -2.58685 (285*2π)/4582 weeks
2868.16989 -2.01942 (286*2π)/4582 weeks
2877.7108 -1.83953 (287*2π)/4582 weeks
2887.2686 -2.04211 (288*2π)/4582 weeks
2897.02748 -2.37471 (289*2π)/4582 weeks
2906.50597 -2.36301 (290*2π)/4582 weeks
2916.19258 -3.04149 (291*2π)/4582 weeks
2926.20451 -4.03212 (292*2π)/4582 weeks
2936.9199 -4.56571 (293*2π)/4582 weeks
2947.92565 -4.57065 (294*2π)/4582 weeks
2958.32725 -3.91654 (295*2π)/4582 weeks
2967.91511 -3.3378 (296*2π)/4582 weeks
2977.61922 -3.30137 (297*2π)/4582 weeks
2987.61748 -3.70324 (298*2π)/4582 weeks
2997.48906 -3.87225 (299*2π)/4582 weeks
3007.76174 -4.1305 (300*2π)/4582 weeks
3018.28199 -4.46561 (301*2π)/4582 weeks
3028.58782 -4.26972 (302*2π)/4582 weeks
3038.5158 -3.87149 (303*2π)/4582 weeks
3048.69865 -3.72808 (304*2π)/4582 weeks
3058.18829 -3.93271 (305*2π)/4582 weeks
3068.35476 -4.19398 (306*2π)/4581 weeks
3079.32281 -4.55677 (307*2π)/4581 weeks
30810.31638 -4.09344 (308*2π)/4581 weeks
30910.20306 -3.23041 (309*2π)/4581 weeks
3109.97764 -2.20388 (310*2π)/4581 weeks
3119.45482 -1.99328 (311*2π)/4581 weeks
3128.89925 -1.77586 (312*2π)/4581 weeks
3138.57387 -1.5205 (313*2π)/4581 weeks
3147.95662 -1.19764 (314*2π)/4581 weeks
3156.93992 -1.75816 (315*2π)/4581 weeks
3166.53373 -2.60669 (316*2π)/4581 weeks
3177.13262 -3.42266 (317*2π)/4581 weeks
3187.3251 -3.68189 (318*2π)/4581 weeks
3197.73568 -3.67348 (319*2π)/4581 weeks
3207.85101 -3.58959 (320*2π)/4581 weeks
3217.68172 -3.61259 (321*2π)/4581 weeks
3228.11622 -3.90327 (322*2π)/4581 weeks
3238.77467 -3.55532 (323*2π)/4581 weeks
3248.89914 -2.68757 (324*2π)/4581 weeks
3257.76839 -2.2656 (325*2π)/4581 weeks
3267.14606 -2.49118 (326*2π)/4581 weeks
3277.33673 -2.9992 (327*2π)/4581 weeks
3287.42138 -2.69363 (328*2π)/4581 weeks
3297.32305 -2.3944 (329*2π)/4581 weeks
3306.29924 -2.29889 (330*2π)/4581 weeks
3315.08614 -2.61999 (331*2π)/4581 weeks
3324.84659 -3.59865 (332*2π)/4581 weeks
3334.94017 -4.9527 (333*2π)/4581 weeks
3345.5916 -5.65684 (334*2π)/4581 weeks
3356.56857 -5.99375 (335*2π)/4581 weeks
3367.22972 -5.63058 (336*2π)/4581 weeks
3377.40816 -5.31658 (337*2π)/4581 weeks
3387.37916 -5.00271 (338*2π)/4581 weeks
3397.43288 -5.08429 (339*2π)/4581 weeks
3406.93746 -4.97777 (340*2π)/4581 weeks
3417.12541 -5.12097 (341*2π)/4581 weeks
3427.29092 -4.76574 (342*2π)/4581 weeks
3436.54894 -4.54743 (343*2π)/4581 weeks
3446.07287 -5.33808 (344*2π)/4581 weeks
3456.45375 -6.13172 (345*2π)/4581 weeks
3466.51514 -5.92631 (346*2π)/4581 weeks
3476.24823 -6.43007 (347*2π)/4581 weeks
3486.71527 -7.13365 (348*2π)/4581 weeks
3497.5704 -7.27041 (349*2π)/4581 weeks
3508.35173 -6.73533 (350*2π)/4581 weeks
3518.86191 -6.39738 (351*2π)/4581 weeks
3528.18009 -5.93979 (352*2π)/4581 weeks
3537.60312 -5.62217 (353*2π)/4581 weeks
3547.76768 -6.07159 (354*2π)/4581 weeks
3557.33075 -6.43266 (355*2π)/4581 weeks
3567.50536 -6.52478 (356*2π)/4581 weeks
3577.83576 -6.95922 (357*2π)/4581 weeks
3588.44066 -7.1992 (358*2π)/4581 weeks
3598.92684 -6.69968 (359*2π)/4581 weeks
3609.34405 -5.85289 (360*2π)/4581 weeks
3618.78547 -5.10956 (361*2π)/4581 weeks
3627.88735 -4.83209 (362*2π)/4581 weeks
3637.22045 -4.92594 (363*2π)/4581 weeks
3646.64006 -5.08527 (364*2π)/4581 weeks
3654.8463 -5.59906 (365*2π)/4581 weeks
3664.51051 -6.66966 (366*2π)/4581 weeks
3674.98807 -8.75741 (367*2π)/4581 weeks
3686.05068 -9.62245 (368*2π)/4581 weeks
3697.29758 -9.717 (369*2π)/4581 weeks
3708.06202 -8.41065 (370*2π)/4581 weeks
3717.68436 -7.99916 (371*2π)/4581 weeks
3727.08158 -7.97032 (372*2π)/4581 weeks
3737.17255 -9.09077 (373*2π)/4581 weeks
3747.45458 -9.55484 (374*2π)/4581 weeks
3757.8473 -9.0519 (375*2π)/4581 weeks
3766.76095 -8.11543 (376*2π)/4581 weeks
3775.5839 -9.03875 (377*2π)/4581 weeks
3785.13255 -11.28679 (378*2π)/4581 weeks
3796.26672 -13.39552 (379*2π)/4581 weeks
3808.6472 -14.17671 (380*2π)/4581 weeks
38111.3701 -14.38387 (381*2π)/4581 weeks
38212.95203 -12.49305 (382*2π)/4581 weeks
38313.77501 -10.00568 (383*2π)/4581 weeks
38413.03651 -8.40949 (384*2π)/4581 weeks
38511.79218 -8.01686 (385*2π)/4581 weeks
38610.70865 -7.89129 (386*2π)/4581 weeks
3879.68052 -7.68179 (387*2π)/4581 weeks
3889.20011 -9.05061 (388*2π)/4581 weeks
38910.26032 -9.44885 (389*2π)/4581 weeks
39010.57166 -8.87208 (390*2π)/4581 weeks
39110.36016 -8.95655 (391*2π)/4581 weeks
39210.86796 -8.19212 (392*2π)/4581 weeks
3939.7716 -7.28974 (393*2π)/4581 weeks
3947.41952 -7.61827 (394*2π)/4581 weeks
3957.0786 -9.22582 (395*2π)/4581 weeks
3968.76134 -10.49894 (396*2π)/4581 weeks
3979.54886 -10.60786 (397*2π)/4581 weeks
3989.74326 -9.11496 (398*2π)/4581 weeks
3999.4856 -7.76164 (399*2π)/4581 weeks
4008.11213 -7.16836 (400*2π)/4581 weeks
4015.36999 -7.84802 (401*2π)/4581 weeks
4024.02818 -9.36032 (402*2π)/4581 weeks
4033.72209 -12.7499 (403*2π)/4581 weeks
4045.40293 -14.36194 (404*2π)/4581 weeks
4057.19456 -14.97823 (405*2π)/4581 weeks
4067.66154 -15.02494 (406*2π)/4581 weeks
4078.10239 -15.23095 (407*2π)/4581 weeks
4088.59075 -15.47539 (408*2π)/4581 weeks
4099.47434 -14.54899 (409*2π)/4581 weeks
41010.31674 -16.13179 (410*2π)/4581 weeks
41110.60597 -16.10423 (411*2π)/4581 weeks
41211.49557 -15.52 (412*2π)/4581 weeks
41311.25134 -13.63743 (413*2π)/4581 weeks
41410.94883 -13.21543 (414*2π)/4581 weeks
41510.11973 -12.01265 (415*2π)/4581 weeks
4169.01605 -11.90444 (416*2π)/4581 weeks
4177.26129 -12.1629 (417*2π)/4581 weeks
4185.26556 -12.42033 (418*2π)/4581 weeks
4192.60343 -15.06304 (419*2π)/4581 weeks
4202.99837 -17.45435 (420*2π)/4581 weeks
4212.77814 -18.86362 (421*2π)/4581 weeks
4222.13244 -19.99524 (422*2π)/4581 weeks
4231.29083 -23.8254 (423*2π)/4581 weeks
4241.98044 -27.6192 (424*2π)/4581 weeks
4253.35652 -32.08577 (425*2π)/4581 weeks
4268.083 -34.81952 (426*2π)/4581 weeks
42712.81187 -35.362 (427*2π)/4581 weeks
42815.94027 -34.46549 (428*2π)/4581 weeks
42920.37791 -33.3501 (429*2π)/4581 weeks
43021.83157 -30.06705 (430*2π)/4581 weeks
43121.36701 -27.90583 (431*2π)/4581 weeks
43221.56408 -26.73178 (432*2π)/4581 weeks
43322.26526 -26.45891 (433*2π)/4581 weeks
43420.74902 -25.18971 (434*2π)/4581 weeks
43518.76915 -25.78343 (435*2π)/4581 weeks
43618.80541 -25.81529 (436*2π)/4581 weeks
43720.69961 -25.89008 (437*2π)/4581 weeks
43816.35166 -26.13622 (438*2π)/4581 weeks
43912.05562 -28.37684 (439*2π)/4581 weeks
44012.03228 -38.4752 (440*2π)/4581 weeks
44118.96896 -41.38577 (441*2π)/4581 weeks
44225.94314 -41.58931 (442*2π)/4581 weeks
44329.26304 -37.11531 (443*2π)/4581 weeks
44425.80976 -34.3338 (444*2π)/4581 weeks
44523.75836 -35.05174 (445*2π)/4581 weeks
44624.378 -39.72521 (446*2π)/4581 weeks
44721.32571 -41.95788 (447*2π)/4581 weeks
44821.80236 -47.74113 (448*2π)/4581 weeks
44918.07932 -56.21696 (449*2π)/4581 weeks
45019.79826 -71.2804 (450*2π)/4581 weeks
45131.8482 -80.93006 (451*2π)/4581 weeks
45251.06233 -88.50153 (452*2π)/4581 weeks
45360.88974 -84.43465 (453*2π)/4581 weeks
45461.91933 -99.5951 (454*2π)/4581 weeks
45577.66524 -135.3522 (455*2π)/4581 weeks
456143.3731 -165.177 (456*2π)/4581 weeks



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