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Fourier Analysis of GLL (ProShares UltraShort Gold ETF)


GLL (ProShares UltraShort Gold ETF) appears to have interesting cyclic behaviour every 45 weeks (8.4574*sine), 38 weeks (8.2731*sine), and 41 weeks (6.9195*sine).

GLL (ProShares UltraShort Gold ETF) has an average price of 119.93 (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 7/17/2017 for GLL (ProShares UltraShort Gold ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0119.9303   0 
160.37022 25.83732 (1*2π)/451451 weeks
221.07295 49.26775 (2*2π)/451226 weeks
39.51685 31.72748 (3*2π)/451150 weeks
410.9601 27.56112 (4*2π)/451113 weeks
58.49267 17.90385 (5*2π)/45190 weeks
62.16414 17.19402 (6*2π)/45175 weeks
71.43078 10.56932 (7*2π)/45164 weeks
8-.67362 14.49791 (8*2π)/45156 weeks
9-.22419 11.19787 (9*2π)/45150 weeks
103.05618 8.45741 (10*2π)/45145 weeks
113.09173 6.91948 (11*2π)/45141 weeks
124.82947 8.27314 (12*2π)/45138 weeks
133.80487 6.26723 (13*2π)/45135 weeks
144.39823 7.33751 (14*2π)/45132 weeks
155.23178 8.04437 (15*2π)/45130 weeks
163.18748 7.98427 (16*2π)/45128 weeks
173.08101 5.69974 (17*2π)/45127 weeks
18-.9885 5.65518 (18*2π)/45125 weeks
191.92178 2.97734 (19*2π)/45124 weeks
202.3516 3.77451 (20*2π)/45123 weeks
214.22911 6.83369 (21*2π)/45121 weeks
223.80238 4.63249 (22*2π)/45121 weeks
232.58103 4.00108 (23*2π)/45120 weeks
242.39476 5.13563 (24*2π)/45119 weeks
252.256 6.14128 (25*2π)/45118 weeks
263.1025 5.61132 (26*2π)/45117 weeks
273.08981 5.19183 (27*2π)/45117 weeks
282.13409 4.99901 (28*2π)/45116 weeks
291.5145 5.2891 (29*2π)/45116 weeks
302.32913 3.72325 (30*2π)/45115 weeks
311.9883 5.33216 (31*2π)/45115 weeks
321.05761 5.12829 (32*2π)/45114 weeks
33.705 4.30772 (33*2π)/45114 weeks
34.25186 4.6583 (34*2π)/45113 weeks
35-1.20648 3.74539 (35*2π)/45113 weeks
36.52057 2.93254 (36*2π)/45113 weeks
37.30393 2.72537 (37*2π)/45112 weeks
38-.19341 3.32684 (38*2π)/45112 weeks
39.96524 1.6416 (39*2π)/45112 weeks
401.70498 2.56465 (40*2π)/45111 weeks
41.70401 1.98086 (41*2π)/45111 weeks
42.96451 2.16303 (42*2π)/45111 weeks
431.84266 2.29509 (43*2π)/45110 weeks
441.08291 1.98436 (44*2π)/45110 weeks
452.0813 1.79845 (45*2π)/45110 weeks
461.61317 2.03439 (46*2π)/45110 weeks
472.15005 1.502 (47*2π)/45110 weeks
481.23039 1.40661 (48*2π)/4519 weeks
491.62076 2.80037 (49*2π)/4519 weeks
501.05148 2.91698 (50*2π)/4519 weeks
511.51305 2.33986 (51*2π)/4519 weeks
521.63583 2.05872 (52*2π)/4519 weeks
531.27158 2.08502 (53*2π)/4519 weeks
54.45915 2.46682 (54*2π)/4518 weeks
55.7363 1.42395 (55*2π)/4518 weeks
56.43198 1.50277 (56*2π)/4518 weeks
571.48431 .98709 (57*2π)/4518 weeks
581.44096 .81522 (58*2π)/4518 weeks
591.23788 1.59136 (59*2π)/4518 weeks
601.75685 2.07959 (60*2π)/4518 weeks
611.59333 1.59061 (61*2π)/4517 weeks
62.64463 1.26038 (62*2π)/4517 weeks
63.89958 1.3904 (63*2π)/4517 weeks
641.72726 1.30432 (64*2π)/4517 weeks
651.89828 1.79683 (65*2π)/4517 weeks
661.61277 1.58427 (66*2π)/4517 weeks
671.77799 1.31144 (67*2π)/4517 weeks
682.05991 1.95315 (68*2π)/4517 weeks
691.16847 1.91945 (69*2π)/4517 weeks
701.55112 1.35531 (70*2π)/4516 weeks
71.9859 1.27295 (71*2π)/4516 weeks
721.28097 1.50309 (72*2π)/4516 weeks
731.86863 .99225 (73*2π)/4516 weeks
742.48358 1.48822 (74*2π)/4516 weeks
752.25857 1.45597 (75*2π)/4516 weeks
761.93718 2.39268 (76*2π)/4516 weeks
771.68586 1.73882 (77*2π)/4516 weeks
781.05487 1.95428 (78*2π)/4516 weeks
79.83713 1.48604 (79*2π)/4516 weeks
801.10259 1.58682 (80*2π)/4516 weeks
811.49543 .82834 (81*2π)/4516 weeks
821.52427 1.5275 (82*2π)/4516 weeks
831.42513 1.31932 (83*2π)/4515 weeks
841.28152 1.85167 (84*2π)/4515 weeks
851.70595 1.55305 (85*2π)/4515 weeks
861.12423 1.79731 (86*2π)/4515 weeks
871.88278 1.39455 (87*2π)/4515 weeks
881.4541 1.62806 (88*2π)/4515 weeks
891.30662 1.53536 (89*2π)/4515 weeks
90.37734 1.64262 (90*2π)/4515 weeks
911.15117 1.41987 (91*2π)/4515 weeks
92.70831 .36544 (92*2π)/4515 weeks
931.01187 .80249 (93*2π)/4515 weeks
94.95432 .70433 (94*2π)/4515 weeks
951.34607 .97139 (95*2π)/4515 weeks
961.54251 .87944 (96*2π)/4515 weeks
971.57276 1.00633 (97*2π)/4515 weeks
981.76704 1.05011 (98*2π)/4515 weeks
991.49881 1.23629 (99*2π)/4515 weeks
1001.43836 1.40572 (100*2π)/4515 weeks
1011.76991 1.4222 (101*2π)/4514 weeks
1021.49786 1.26294 (102*2π)/4514 weeks
1031.17973 1.70919 (103*2π)/4514 weeks
1041.50998 1.34868 (104*2π)/4514 weeks
1051.67054 1.06018 (105*2π)/4514 weeks
1061.14522 1.70685 (106*2π)/4514 weeks
1071.23635 1.95496 (107*2π)/4514 weeks
108.99996 2.07041 (108*2π)/4514 weeks
109.93289 1.88223 (109*2π)/4514 weeks
110.83622 1.08741 (110*2π)/4514 weeks
1111.03601 1.48363 (111*2π)/4514 weeks
112.33863 1.19388 (112*2π)/4514 weeks
113.51475 .95873 (113*2π)/4514 weeks
1141.08687 .97241 (114*2π)/4514 weeks
115.88041 1.20921 (115*2π)/4514 weeks
116.70124 .92088 (116*2π)/4514 weeks
117.97464 .73019 (117*2π)/4514 weeks
118.72763 .86103 (118*2π)/4514 weeks
1191.06004 .94721 (119*2π)/4514 weeks
1201.0316 1.09543 (120*2π)/4514 weeks
121.71753 .95698 (121*2π)/4514 weeks
122.23149 .75634 (122*2π)/4514 weeks
123.71256 .7566 (123*2π)/4514 weeks
124.68641 .35962 (124*2π)/4514 weeks
125.62545 .48382 (125*2π)/4514 weeks
126.64034 .42815 (126*2π)/4514 weeks
1271.16753 .33079 (127*2π)/4514 weeks
128.96629 .24365 (128*2π)/4514 weeks
1291.09034 .74741 (129*2π)/4513 weeks
130.97638 .15918 (130*2π)/4513 weeks
131.85194 .46276 (131*2π)/4513 weeks
1321.34886 .59974 (132*2π)/4513 weeks
1331.00185 .53846 (133*2π)/4513 weeks
1341.03874 .46573 (134*2π)/4513 weeks
1351.1125 .1647 (135*2π)/4513 weeks
1361.27832 .30179 (136*2π)/4513 weeks
1371.43232 .42395 (137*2π)/4513 weeks
1381.23107 .42678 (138*2π)/4513 weeks
1391.17654 .67981 (139*2π)/4513 weeks
140.94483 .22044 (140*2π)/4513 weeks
1411.19064 .24962 (141*2π)/4513 weeks
1421.55897 .01971 (142*2π)/4513 weeks
1431.31109 .21868 (143*2π)/4513 weeks
1441.42462 .25256 (144*2π)/4513 weeks
1451.44279 .33326 (145*2π)/4513 weeks
1461.6465 .35888 (146*2π)/4513 weeks
1471.23179 .57251 (147*2π)/4513 weeks
1481.53596 .68437 (148*2π)/4513 weeks
1491.36958 .80515 (149*2π)/4513 weeks
1501.45226 .69961 (150*2π)/4513 weeks
1511.19818 .35955 (151*2π)/4513 weeks
1521.41708 .53603 (152*2π)/4513 weeks
1531.39084 .54118 (153*2π)/4513 weeks
1541.3827 .7479 (154*2π)/4513 weeks
1551.23057 .77731 (155*2π)/4513 weeks
1561.21753 .73745 (156*2π)/4513 weeks
1571.19433 .50496 (157*2π)/4513 weeks
1581.02677 .66503 (158*2π)/4513 weeks
1591.16008 .42224 (159*2π)/4513 weeks
1601.2736 .26224 (160*2π)/4513 weeks
1611.3457 .58305 (161*2π)/4513 weeks
1621.14813 .48486 (162*2π)/4513 weeks
1631.18431 .36976 (163*2π)/4513 weeks
1641.00146 .26879 (164*2π)/4513 weeks
1651.07264 .40157 (165*2π)/4513 weeks
1661.1639 .44151 (166*2π)/4513 weeks
167.87107 .41869 (167*2π)/4513 weeks
1681.00943 .27631 (168*2π)/4513 weeks
1691.31775 .51361 (169*2π)/4513 weeks
1701.28712 .33809 (170*2π)/4513 weeks
1711.625 .37808 (171*2π)/4513 weeks
1721.27559 .3985 (172*2π)/4513 weeks
173.78413 .63193 (173*2π)/4513 weeks
174.88777 .41701 (174*2π)/4513 weeks
1751.11105 .48218 (175*2π)/4513 weeks
1761.05492 .26097 (176*2π)/4513 weeks
1771.10528 .11084 (177*2π)/4513 weeks
1781.04387 .4027 (178*2π)/4513 weeks
179.89214 .46803 (179*2π)/4513 weeks
180.71601 .5152 (180*2π)/4513 weeks
181.79892 .07681 (181*2π)/4512 weeks
182.92252 -.10811 (182*2π)/4512 weeks
1831.09127 -.15501 (183*2π)/4512 weeks
1841.00498 .00092 (184*2π)/4512 weeks
1851.15665 .14178 (185*2π)/4512 weeks
1861.27763 -.1699 (186*2π)/4512 weeks
1871.09025 -.03047 (187*2π)/4512 weeks
1881.17863 -.3316 (188*2π)/4512 weeks
1891.50955 -.17616 (189*2π)/4512 weeks
1901.62705 .09631 (190*2π)/4512 weeks
1911.51583 .37651 (191*2π)/4512 weeks
1921.73997 .32591 (192*2π)/4512 weeks
1931.4053 .46898 (193*2π)/4512 weeks
1941.43948 .32228 (194*2π)/4512 weeks
1951.17457 .5544 (195*2π)/4512 weeks
1961.10657 .2617 (196*2π)/4512 weeks
1971.24206 .32309 (197*2π)/4512 weeks
1981.21393 .49779 (198*2π)/4512 weeks
1991.03871 .23981 (199*2π)/4512 weeks
2001.02173 .0474 (200*2π)/4512 weeks
201.87382 .27674 (201*2π)/4512 weeks
2021.28227 .30175 (202*2π)/4512 weeks
2031.02764 .2134 (203*2π)/4512 weeks
204.87256 .27572 (204*2π)/4512 weeks
205.76941 .20338 (205*2π)/4512 weeks
206.93275 .0753 (206*2π)/4512 weeks
207.88384 -.23786 (207*2π)/4512 weeks
2081.03031 -.03444 (208*2π)/4512 weeks
209.97717 -.48182 (209*2π)/4512 weeks
2101.28363 -.32601 (210*2π)/4512 weeks
2111.27511 -.10727 (211*2π)/4512 weeks
2121.23142 -.16057 (212*2π)/4512 weeks
2131.23431 -.1161 (213*2π)/4512 weeks
2141.48236 -.13556 (214*2π)/4512 weeks
2151.28129 -.00365 (215*2π)/4512 weeks
2161.24617 .07703 (216*2π)/4512 weeks
2171.26207 .04948 (217*2π)/4512 weeks
2181.10056 -.0061 (218*2π)/4512 weeks
2191.56987 -.18908 (219*2π)/4512 weeks
2201.42632 .30666 (220*2π)/4512 weeks
2211.39556 -.05447 (221*2π)/4512 weeks
2221.20914 -.02897 (222*2π)/4512 weeks
2231.13465 .18556 (223*2π)/4512 weeks
2241.18152 -.04707 (224*2π)/4512 weeks
2251.32273 .01993 (225*2π)/4512 weeks
2261.32273 -.01993 (226*2π)/4512 weeks
2271.18152 .04707 (227*2π)/4512 weeks
2281.13465 -.18556 (228*2π)/4512 weeks
2291.20914 .02897 (229*2π)/4512 weeks
2301.39556 .05447 (230*2π)/4512 weeks
2311.42632 -.30666 (231*2π)/4512 weeks
2321.56987 .18908 (232*2π)/4512 weeks
2331.10056 .0061 (233*2π)/4512 weeks
2341.26207 -.04948 (234*2π)/4512 weeks
2351.24617 -.07703 (235*2π)/4512 weeks
2361.28129 .00365 (236*2π)/4512 weeks
2371.48236 .13556 (237*2π)/4512 weeks
2381.23431 .1161 (238*2π)/4512 weeks
2391.23142 .16057 (239*2π)/4512 weeks
2401.27511 .10727 (240*2π)/4512 weeks
2411.28363 .32601 (241*2π)/4512 weeks
242.97717 .48182 (242*2π)/4512 weeks
2431.03031 .03444 (243*2π)/4512 weeks
244.88384 .23786 (244*2π)/4512 weeks
245.93275 -.0753 (245*2π)/4512 weeks
246.76941 -.20338 (246*2π)/4512 weeks
247.87256 -.27572 (247*2π)/4512 weeks
2481.02764 -.2134 (248*2π)/4512 weeks
2491.28227 -.30175 (249*2π)/4512 weeks
250.87382 -.27674 (250*2π)/4512 weeks
2511.02173 -.0474 (251*2π)/4512 weeks
2521.03871 -.23981 (252*2π)/4512 weeks
2531.21393 -.49779 (253*2π)/4512 weeks
2541.24206 -.32309 (254*2π)/4512 weeks
2551.10657 -.2617 (255*2π)/4512 weeks
2561.17457 -.5544 (256*2π)/4512 weeks
2571.43948 -.32228 (257*2π)/4512 weeks
2581.4053 -.46898 (258*2π)/4512 weeks
2591.73997 -.32591 (259*2π)/4512 weeks
2601.51583 -.37651 (260*2π)/4512 weeks
2611.62705 -.09631 (261*2π)/4512 weeks
2621.50955 .17616 (262*2π)/4512 weeks
2631.17863 .3316 (263*2π)/4512 weeks
2641.09025 .03047 (264*2π)/4512 weeks
2651.27763 .1699 (265*2π)/4512 weeks
2661.15665 -.14178 (266*2π)/4512 weeks
2671.00498 -.00092 (267*2π)/4512 weeks
2681.09127 .15501 (268*2π)/4512 weeks
269.92252 .10811 (269*2π)/4512 weeks
270.79892 -.07681 (270*2π)/4512 weeks
271.71601 -.5152 (271*2π)/4512 weeks
272.89214 -.46803 (272*2π)/4512 weeks
2731.04387 -.4027 (273*2π)/4512 weeks
2741.10528 -.11084 (274*2π)/4512 weeks
2751.05492 -.26097 (275*2π)/4512 weeks
2761.11105 -.48218 (276*2π)/4512 weeks
277.88777 -.41701 (277*2π)/4512 weeks
278.78413 -.63193 (278*2π)/4512 weeks
2791.27559 -.3985 (279*2π)/4512 weeks
2801.625 -.37808 (280*2π)/4512 weeks
2811.28712 -.33809 (281*2π)/4512 weeks
2821.31775 -.51361 (282*2π)/4512 weeks
2831.00943 -.27631 (283*2π)/4512 weeks
284.87107 -.41869 (284*2π)/4512 weeks
2851.1639 -.44151 (285*2π)/4512 weeks
2861.07264 -.40157 (286*2π)/4512 weeks
2871.00146 -.26879 (287*2π)/4512 weeks
2881.18431 -.36976 (288*2π)/4512 weeks
2891.14813 -.48486 (289*2π)/4512 weeks
2901.3457 -.58305 (290*2π)/4512 weeks
2911.2736 -.26224 (291*2π)/4512 weeks
2921.16008 -.42224 (292*2π)/4512 weeks
2931.02677 -.66503 (293*2π)/4512 weeks
2941.19433 -.50496 (294*2π)/4512 weeks
2951.21753 -.73745 (295*2π)/4512 weeks
2961.23057 -.77731 (296*2π)/4512 weeks
2971.3827 -.7479 (297*2π)/4512 weeks
2981.39084 -.54118 (298*2π)/4512 weeks
2991.41708 -.53603 (299*2π)/4512 weeks
3001.19818 -.35955 (300*2π)/4512 weeks
3011.45226 -.69961 (301*2π)/4511 weeks
3021.36958 -.80515 (302*2π)/4511 weeks
3031.53596 -.68437 (303*2π)/4511 weeks
3041.23179 -.57251 (304*2π)/4511 weeks
3051.6465 -.35888 (305*2π)/4511 weeks
3061.44279 -.33326 (306*2π)/4511 weeks
3071.42462 -.25256 (307*2π)/4511 weeks
3081.31109 -.21868 (308*2π)/4511 weeks
3091.55897 -.01971 (309*2π)/4511 weeks
3101.19064 -.24962 (310*2π)/4511 weeks
311.94483 -.22044 (311*2π)/4511 weeks
3121.17654 -.67981 (312*2π)/4511 weeks
3131.23107 -.42678 (313*2π)/4511 weeks
3141.43232 -.42395 (314*2π)/4511 weeks
3151.27832 -.30179 (315*2π)/4511 weeks
3161.1125 -.1647 (316*2π)/4511 weeks
3171.03874 -.46573 (317*2π)/4511 weeks
3181.00185 -.53846 (318*2π)/4511 weeks
3191.34886 -.59974 (319*2π)/4511 weeks
320.85194 -.46276 (320*2π)/4511 weeks
321.97638 -.15918 (321*2π)/4511 weeks
3221.09034 -.74741 (322*2π)/4511 weeks
323.96629 -.24365 (323*2π)/4511 weeks
3241.16753 -.33079 (324*2π)/4511 weeks
325.64034 -.42815 (325*2π)/4511 weeks
326.62545 -.48382 (326*2π)/4511 weeks
327.68641 -.35962 (327*2π)/4511 weeks
328.71256 -.7566 (328*2π)/4511 weeks
329.23149 -.75634 (329*2π)/4511 weeks
330.71753 -.95698 (330*2π)/4511 weeks
3311.0316 -1.09543 (331*2π)/4511 weeks
3321.06004 -.94721 (332*2π)/4511 weeks
333.72763 -.86103 (333*2π)/4511 weeks
334.97464 -.73019 (334*2π)/4511 weeks
335.70124 -.92088 (335*2π)/4511 weeks
336.88041 -1.20921 (336*2π)/4511 weeks
3371.08687 -.97241 (337*2π)/4511 weeks
338.51475 -.95873 (338*2π)/4511 weeks
339.33863 -1.19388 (339*2π)/4511 weeks
3401.03601 -1.48363 (340*2π)/4511 weeks
341.83622 -1.08741 (341*2π)/4511 weeks
342.93289 -1.88223 (342*2π)/4511 weeks
343.99996 -2.07041 (343*2π)/4511 weeks
3441.23635 -1.95496 (344*2π)/4511 weeks
3451.14522 -1.70685 (345*2π)/4511 weeks
3461.67054 -1.06018 (346*2π)/4511 weeks
3471.50998 -1.34868 (347*2π)/4511 weeks
3481.17973 -1.70919 (348*2π)/4511 weeks
3491.49786 -1.26294 (349*2π)/4511 weeks
3501.76991 -1.4222 (350*2π)/4511 weeks
3511.43836 -1.40572 (351*2π)/4511 weeks
3521.49881 -1.23629 (352*2π)/4511 weeks
3531.76704 -1.05011 (353*2π)/4511 weeks
3541.57276 -1.00633 (354*2π)/4511 weeks
3551.54251 -.87944 (355*2π)/4511 weeks
3561.34607 -.97139 (356*2π)/4511 weeks
357.95432 -.70433 (357*2π)/4511 weeks
3581.01187 -.80249 (358*2π)/4511 weeks
359.70831 -.36544 (359*2π)/4511 weeks
3601.15117 -1.41987 (360*2π)/4511 weeks
361.37734 -1.64262 (361*2π)/4511 weeks
3621.30662 -1.53536 (362*2π)/4511 weeks
3631.4541 -1.62806 (363*2π)/4511 weeks
3641.88278 -1.39455 (364*2π)/4511 weeks
3651.12423 -1.79731 (365*2π)/4511 weeks
3661.70595 -1.55305 (366*2π)/4511 weeks
3671.28152 -1.85167 (367*2π)/4511 weeks
3681.42513 -1.31932 (368*2π)/4511 weeks
3691.52427 -1.5275 (369*2π)/4511 weeks
3701.49543 -.82834 (370*2π)/4511 weeks
3711.10259 -1.58682 (371*2π)/4511 weeks
372.83713 -1.48604 (372*2π)/4511 weeks
3731.05487 -1.95428 (373*2π)/4511 weeks
3741.68586 -1.73882 (374*2π)/4511 weeks
3751.93718 -2.39268 (375*2π)/4511 weeks
3762.25857 -1.45597 (376*2π)/4511 weeks
3772.48358 -1.48822 (377*2π)/4511 weeks
3781.86863 -.99225 (378*2π)/4511 weeks
3791.28097 -1.50309 (379*2π)/4511 weeks
380.9859 -1.27295 (380*2π)/4511 weeks
3811.55112 -1.35531 (381*2π)/4511 weeks
3821.16847 -1.91945 (382*2π)/4511 weeks
3832.05991 -1.95315 (383*2π)/4511 weeks
3841.77799 -1.31144 (384*2π)/4511 weeks
3851.61277 -1.58427 (385*2π)/4511 weeks
3861.89828 -1.79683 (386*2π)/4511 weeks
3871.72726 -1.30432 (387*2π)/4511 weeks
388.89958 -1.3904 (388*2π)/4511 weeks
389.64463 -1.26038 (389*2π)/4511 weeks
3901.59333 -1.59061 (390*2π)/4511 weeks
3911.75685 -2.07959 (391*2π)/4511 weeks
3921.23788 -1.59136 (392*2π)/4511 weeks
3931.44096 -.81522 (393*2π)/4511 weeks
3941.48431 -.98709 (394*2π)/4511 weeks
395.43198 -1.50277 (395*2π)/4511 weeks
396.7363 -1.42395 (396*2π)/4511 weeks
397.45915 -2.46682 (397*2π)/4511 weeks
3981.27158 -2.08502 (398*2π)/4511 weeks
3991.63583 -2.05872 (399*2π)/4511 weeks
4001.51305 -2.33986 (400*2π)/4511 weeks
4011.05148 -2.91698 (401*2π)/4511 weeks
4021.62076 -2.80037 (402*2π)/4511 weeks
4031.23039 -1.40661 (403*2π)/4511 weeks
4042.15005 -1.502 (404*2π)/4511 weeks
4051.61317 -2.03439 (405*2π)/4511 weeks
4062.0813 -1.79845 (406*2π)/4511 weeks
4071.08291 -1.98436 (407*2π)/4511 weeks
4081.84266 -2.29509 (408*2π)/4511 weeks
409.96451 -2.16303 (409*2π)/4511 weeks
410.70401 -1.98086 (410*2π)/4511 weeks
4111.70498 -2.56465 (411*2π)/4511 weeks
412.96524 -1.6416 (412*2π)/4511 weeks
413-.19341 -3.32684 (413*2π)/4511 weeks
414.30393 -2.72537 (414*2π)/4511 weeks
415.52057 -2.93254 (415*2π)/4511 weeks
416-1.20648 -3.74539 (416*2π)/4511 weeks
417.25186 -4.6583 (417*2π)/4511 weeks
418.705 -4.30772 (418*2π)/4511 weeks
4191.05761 -5.12829 (419*2π)/4511 weeks
4201.9883 -5.33216 (420*2π)/4511 weeks
4212.32913 -3.72325 (421*2π)/4511 weeks
4221.5145 -5.2891 (422*2π)/4511 weeks
4232.13409 -4.99901 (423*2π)/4511 weeks
4243.08981 -5.19183 (424*2π)/4511 weeks
4253.1025 -5.61132 (425*2π)/4511 weeks
4262.256 -6.14128 (426*2π)/4511 weeks
4272.39476 -5.13563 (427*2π)/4511 weeks
4282.58103 -4.00108 (428*2π)/4511 weeks
4293.80238 -4.63249 (429*2π)/4511 weeks
4304.22911 -6.83369 (430*2π)/4511 weeks
4312.3516 -3.77451 (431*2π)/4511 weeks
4321.92178 -2.97734 (432*2π)/4511 weeks
433-.9885 -5.65518 (433*2π)/4511 weeks
4343.08101 -5.69974 (434*2π)/4511 weeks
4353.18748 -7.98427 (435*2π)/4511 weeks
4365.23178 -8.04437 (436*2π)/4511 weeks
4374.39823 -7.33751 (437*2π)/4511 weeks
4383.80487 -6.26723 (438*2π)/4511 weeks
4394.82947 -8.27314 (439*2π)/4511 weeks
4403.09173 -6.91948 (440*2π)/4511 weeks
4413.05618 -8.45741 (441*2π)/4511 weeks
442-.22419 -11.19787 (442*2π)/4511 weeks
443-.67362 -14.49791 (443*2π)/4511 weeks
4441.43078 -10.56932 (444*2π)/4511 weeks
4452.16414 -17.19402 (445*2π)/4511 weeks
4468.49267 -17.90385 (446*2π)/4511 weeks
44710.9601 -27.56112 (447*2π)/4511 weeks
4489.51685 -31.72748 (448*2π)/4511 weeks
44921.07295 -49.26775 (449*2π)/4511 weeks



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