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Fourier Analysis of GLL (ProShares UltraShort Gold ETF)


GLL (ProShares UltraShort Gold ETF) appears to have interesting cyclic behaviour every 26 weeks (8.8975*sine), 29 weeks (8.2024*sine), and 27 weeks (7.4661*sine).

GLL (ProShares UltraShort Gold ETF) has an average price of 118.54 (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 10/16/2017 for GLL (ProShares UltraShort Gold ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0118.5362   0 
157.8727 24.56968 (1*2π)/464464 weeks
222.54976 49.85056 (2*2π)/464232 weeks
310.12521 32.17913 (3*2π)/464155 weeks
411.80319 25.72628 (4*2π)/464116 weeks
56.12462 16.82765 (5*2π)/46493 weeks
61.44668 18.49615 (6*2π)/46477 weeks
7-.52953 13.08371 (7*2π)/46466 weeks
82.21485 16.47554 (8*2π)/46458 weeks
91.69354 11.46905 (9*2π)/46452 weeks
102.87808 6.98853 (10*2π)/46446 weeks
112.59463 6.77925 (11*2π)/46442 weeks
124.67856 6.37267 (12*2π)/46439 weeks
132.54529 6.68709 (13*2π)/46436 weeks
144.23611 6.56744 (14*2π)/46433 weeks
154.0753 6.46476 (15*2π)/46431 weeks
162.56032 8.20238 (16*2π)/46429 weeks
17.80525 7.4661 (17*2π)/46427 weeks
181.78865 8.89754 (18*2π)/46426 weeks
19.71384 4.07885 (19*2π)/46424 weeks
203.44875 4.03532 (20*2π)/46423 weeks
214.43622 3.11696 (21*2π)/46422 weeks
221.92451 5.83178 (22*2π)/46421 weeks
233.22109 5.96153 (23*2π)/46420 weeks
243.86586 4.56262 (24*2π)/46419 weeks
253.1076 4.48529 (25*2π)/46419 weeks
261.73921 4.98505 (26*2π)/46418 weeks
272.2906 5.62334 (27*2π)/46417 weeks
282.76049 5.69844 (28*2π)/46417 weeks
292.26425 5.1125 (29*2π)/46416 weeks
301.34887 5.1236 (30*2π)/46415 weeks
312.71649 3.98684 (31*2π)/46415 weeks
321.97769 5.27107 (32*2π)/46415 weeks
331.12757 5.00305 (33*2π)/46414 weeks
34.86099 4.18406 (34*2π)/46414 weeks
35.32904 4.50776 (35*2π)/46413 weeks
36-1.09628 3.66501 (36*2π)/46413 weeks
37.57002 2.80645 (37*2π)/46413 weeks
38.31754 2.69673 (38*2π)/46412 weeks
39.14311 3.33291 (39*2π)/46412 weeks
40.81643 1.43485 (40*2π)/46412 weeks
411.70311 2.13417 (41*2π)/46411 weeks
42.53736 2.13727 (42*2π)/46411 weeks
431.11001 2.13165 (43*2π)/46411 weeks
441.72972 1.71647 (44*2π)/46411 weeks
45.95652 2.03633 (45*2π)/46410 weeks
461.51173 1.33436 (46*2π)/46410 weeks
471.31785 2.05712 (47*2π)/46410 weeks
481.16517 1.62774 (48*2π)/46410 weeks
491.16785 2.66891 (49*2π)/4649 weeks
502.4842 2.51706 (50*2π)/4649 weeks
511.72211 2.66093 (51*2π)/4649 weeks
521.07202 1.92707 (52*2π)/4649 weeks
531.01002 2.12398 (53*2π)/4649 weeks
541.19848 2.54604 (54*2π)/4649 weeks
551.31243 2.66796 (55*2π)/4648 weeks
56.38611 1.96046 (56*2π)/4648 weeks
571.02683 1.71785 (57*2π)/4648 weeks
58.68024 .97633 (58*2π)/4648 weeks
591.47029 1.38437 (59*2π)/4648 weeks
602.06684 1.12184 (60*2π)/4648 weeks
611.51623 1.11695 (61*2π)/4648 weeks
621.33386 1.96746 (62*2π)/4647 weeks
631.61258 1.85341 (63*2π)/4647 weeks
641.04927 .91217 (64*2π)/4647 weeks
65.89683 .94001 (65*2π)/4647 weeks
661.58901 1.20431 (66*2π)/4647 weeks
671.64998 1.77298 (67*2π)/4647 weeks
681.49587 1.5553 (68*2π)/4647 weeks
691.72626 1.30604 (69*2π)/4647 weeks
701.94593 1.96446 (70*2π)/4647 weeks
711.10467 1.89193 (71*2π)/4647 weeks
721.4724 1.34498 (72*2π)/4646 weeks
73.92506 1.35576 (73*2π)/4646 weeks
741.33881 1.54406 (74*2π)/4646 weeks
751.7981 .94278 (75*2π)/4646 weeks
762.41814 1.2566 (76*2π)/4646 weeks
772.02223 1.40073 (77*2π)/4646 weeks
782.0662 2.24638 (78*2π)/4646 weeks
791.35847 1.73689 (79*2π)/4646 weeks
801.10369 2.20144 (80*2π)/4646 weeks
81.86028 1.81124 (81*2π)/4646 weeks
821.27817 1.52732 (82*2π)/4646 weeks
831.0435 .98488 (83*2π)/4646 weeks
841.73457 1.51267 (84*2π)/4646 weeks
851.44578 1.51006 (85*2π)/4645 weeks
861.80618 1.64058 (86*2π)/4645 weeks
871.40464 1.20875 (87*2π)/4645 weeks
881.46046 1.73265 (88*2π)/4645 weeks
891.08995 1.07486 (89*2π)/4645 weeks
901.38093 1.81009 (90*2π)/4645 weeks
911.19848 1.83987 (91*2π)/4645 weeks
921.25796 2.04222 (92*2π)/4645 weeks
93.64939 1.07645 (93*2π)/4645 weeks
94.60784 1.63283 (94*2π)/4645 weeks
951.36434 .69654 (95*2π)/4645 weeks
961.30186 .80383 (96*2π)/4645 weeks
971.32615 .48381 (97*2π)/4645 weeks
981.33792 .79372 (98*2π)/4645 weeks
991.57463 .85421 (99*2π)/4645 weeks
1001.5808 .94338 (100*2π)/4645 weeks
1011.80089 1.08332 (101*2π)/4645 weeks
1021.53755 1.1225 (102*2π)/4645 weeks
1031.3826 1.27822 (103*2π)/4645 weeks
1041.71385 1.43769 (104*2π)/4644 weeks
1051.53008 1.22219 (105*2π)/4644 weeks
1061.15249 1.63531 (106*2π)/4644 weeks
1071.50473 1.31395 (107*2π)/4644 weeks
1081.62634 1.0223 (108*2π)/4644 weeks
1091.1824 1.73713 (109*2π)/4644 weeks
1101.35226 1.91481 (110*2π)/4644 weeks
1111.1813 1.97881 (111*2π)/4644 weeks
1121.06028 1.67304 (112*2π)/4644 weeks
113.66537 1.02343 (113*2π)/4644 weeks
1141.02756 1.29961 (114*2π)/4644 weeks
115.36846 1.38999 (115*2π)/4644 weeks
116.60258 1.00779 (116*2π)/4644 weeks
1171.02451 .70249 (117*2π)/4644 weeks
118.95233 1.05554 (118*2π)/4644 weeks
119.64078 .93836 (119*2π)/4644 weeks
120.7398 .68517 (120*2π)/4644 weeks
121.8703 .97894 (121*2π)/4644 weeks
1221.00437 .68589 (122*2π)/4644 weeks
123.94763 .89218 (123*2π)/4644 weeks
124.67435 1.11476 (124*2π)/4644 weeks
125.58353 1.11865 (125*2π)/4644 weeks
126.62066 .42276 (126*2π)/4644 weeks
127.47626 .60961 (127*2π)/4644 weeks
128.82422 .49364 (128*2π)/4644 weeks
129.74939 .34305 (129*2π)/4644 weeks
130.68182 .11262 (130*2π)/4644 weeks
1311.00717 .46717 (131*2π)/4644 weeks
1321.14571 .22077 (132*2π)/4644 weeks
133.80656 .65746 (133*2π)/4643 weeks
1341.14977 .21937 (134*2π)/4643 weeks
135.84592 .20779 (135*2π)/4643 weeks
1361.146 .64907 (136*2π)/4643 weeks
137.92278 .49587 (137*2π)/4643 weeks
138.94436 .46797 (138*2π)/4643 weeks
1391.10984 .18885 (139*2π)/4643 weeks
1401.23706 .3193 (140*2π)/4643 weeks
1411.39238 .4571 (141*2π)/4643 weeks
1421.21148 .4311 (142*2π)/4643 weeks
1431.16248 .67542 (143*2π)/4643 weeks
144.92452 .23964 (144*2π)/4643 weeks
1451.19141 .24149 (145*2π)/4643 weeks
1461.45869 -.03754 (146*2π)/4643 weeks
1471.26371 .27238 (147*2π)/4643 weeks
1481.38913 .27547 (148*2π)/4643 weeks
1491.43745 .35855 (149*2π)/4643 weeks
1501.56378 .32562 (150*2π)/4643 weeks
1511.38322 .73294 (151*2π)/4643 weeks
1521.65028 .52323 (152*2π)/4643 weeks
1531.51082 .65796 (153*2π)/4643 weeks
1541.36812 .46497 (154*2π)/4643 weeks
1551.04803 .51971 (155*2π)/4643 weeks
1561.40478 .42204 (156*2π)/4643 weeks
1571.35473 .51394 (157*2π)/4643 weeks
1581.45069 .58391 (158*2π)/4643 weeks
1591.28909 .66104 (159*2π)/4643 weeks
1601.14679 .57905 (160*2π)/4643 weeks
161.98402 .577 (161*2π)/4643 weeks
1621.16011 .59717 (162*2π)/4643 weeks
163.90469 .42044 (163*2π)/4643 weeks
1641.01056 .40424 (164*2π)/4643 weeks
1651.30581 .39102 (165*2π)/4643 weeks
1661.14449 .64428 (166*2π)/4643 weeks
1671.08459 .52989 (167*2π)/4643 weeks
1681.19048 .51718 (168*2π)/4643 weeks
1691.17843 .25435 (169*2π)/4643 weeks
1701.11022 .31297 (170*2π)/4643 weeks
1711.15326 .4263 (171*2π)/4643 weeks
172.88064 .25309 (172*2π)/4643 weeks
173.98196 .15036 (173*2π)/4643 weeks
1741.15627 .49794 (174*2π)/4643 weeks
1751.21377 .34675 (175*2π)/4643 weeks
1761.57556 .45025 (176*2π)/4643 weeks
1771.26867 .39009 (177*2π)/4643 weeks
178.75213 .59354 (178*2π)/4643 weeks
179.85739 .40649 (179*2π)/4643 weeks
1801.09138 .44653 (180*2π)/4643 weeks
181.99413 .23354 (181*2π)/4643 weeks
182.99361 .11839 (182*2π)/4643 weeks
1831.02553 .43342 (183*2π)/4643 weeks
184.92213 .50851 (184*2π)/4643 weeks
185.83766 .51908 (185*2π)/4643 weeks
186.73059 .05478 (186*2π)/4642 weeks
187.80939 -.08979 (187*2π)/4642 weeks
188.96527 -.11911 (188*2π)/4642 weeks
1891.08079 .0857 (189*2π)/4642 weeks
1901.23334 -.01921 (190*2π)/4642 weeks
1911.0101 -.17892 (191*2π)/4642 weeks
1921.14639 .07654 (192*2π)/4642 weeks
1931.07055 -.14308 (193*2π)/4642 weeks
1941.47018 -.25319 (194*2π)/4642 weeks
1951.65951 -.0842 (195*2π)/4642 weeks
1961.66432 .12502 (196*2π)/4642 weeks
1971.41278 .07727 (197*2π)/4642 weeks
1981.45847 .47201 (198*2π)/4642 weeks
1991.2401 .39227 (199*2π)/4642 weeks
2001.39285 .49345 (200*2π)/4642 weeks
2011.04076 .43734 (201*2π)/4642 weeks
2021.14877 .22593 (202*2π)/4642 weeks
2031.19053 .31922 (203*2π)/4642 weeks
2041.01174 .50643 (204*2π)/4642 weeks
2051.02814 .2935 (205*2π)/4642 weeks
2061.16091 .07546 (206*2π)/4642 weeks
207.85329 .07804 (207*2π)/4642 weeks
2081.14888 .36162 (208*2π)/4642 weeks
2091.02024 .20947 (209*2π)/4642 weeks
210.82944 .22017 (210*2π)/4642 weeks
211.70593 .15034 (211*2π)/4642 weeks
212.87 .08405 (212*2π)/4642 weeks
213.85716 -.23666 (213*2π)/4642 weeks
214.98276 -.03409 (214*2π)/4642 weeks
215.91304 -.46306 (215*2π)/4642 weeks
2161.2151 -.31616 (216*2π)/4642 weeks
2171.23129 -.09419 (217*2π)/4642 weeks
2181.17168 -.12777 (218*2π)/4642 weeks
2191.2087 -.07737 (219*2π)/4642 weeks
2201.38935 -.17199 (220*2π)/4642 weeks
2211.25759 .07034 (221*2π)/4642 weeks
2221.28512 .10946 (222*2π)/4642 weeks
2231.26904 .03852 (223*2π)/4642 weeks
2241.1771 .05227 (224*2π)/4642 weeks
2251.35755 -.32618 (225*2π)/4642 weeks
2261.53778 .13604 (226*2π)/4642 weeks
2271.10844 -.01727 (227*2π)/4642 weeks
2281.18244 .18145 (228*2π)/4642 weeks
2291.33389 .16523 (229*2π)/4642 weeks
2301.11098 -.02081 (230*2π)/4642 weeks
2311.24607 -.09319 (231*2π)/4642 weeks
2321.19836   (232*2π)/4642 weeks
2331.24607 .09319 (233*2π)/4642 weeks
2341.11098 .02081 (234*2π)/4642 weeks
2351.33389 -.16523 (235*2π)/4642 weeks
2361.18244 -.18145 (236*2π)/4642 weeks
2371.10844 .01727 (237*2π)/4642 weeks
2381.53778 -.13604 (238*2π)/4642 weeks
2391.35755 .32618 (239*2π)/4642 weeks
2401.1771 -.05227 (240*2π)/4642 weeks
2411.26904 -.03852 (241*2π)/4642 weeks
2421.28512 -.10946 (242*2π)/4642 weeks
2431.25759 -.07034 (243*2π)/4642 weeks
2441.38935 .17199 (244*2π)/4642 weeks
2451.2087 .07737 (245*2π)/4642 weeks
2461.17168 .12777 (246*2π)/4642 weeks
2471.23129 .09419 (247*2π)/4642 weeks
2481.2151 .31616 (248*2π)/4642 weeks
249.91304 .46306 (249*2π)/4642 weeks
250.98276 .03409 (250*2π)/4642 weeks
251.85716 .23666 (251*2π)/4642 weeks
252.87 -.08405 (252*2π)/4642 weeks
253.70593 -.15034 (253*2π)/4642 weeks
254.82944 -.22017 (254*2π)/4642 weeks
2551.02024 -.20947 (255*2π)/4642 weeks
2561.14888 -.36162 (256*2π)/4642 weeks
257.85329 -.07804 (257*2π)/4642 weeks
2581.16091 -.07546 (258*2π)/4642 weeks
2591.02814 -.2935 (259*2π)/4642 weeks
2601.01174 -.50643 (260*2π)/4642 weeks
2611.19053 -.31922 (261*2π)/4642 weeks
2621.14877 -.22593 (262*2π)/4642 weeks
2631.04076 -.43734 (263*2π)/4642 weeks
2641.39285 -.49345 (264*2π)/4642 weeks
2651.2401 -.39227 (265*2π)/4642 weeks
2661.45847 -.47201 (266*2π)/4642 weeks
2671.41278 -.07727 (267*2π)/4642 weeks
2681.66432 -.12502 (268*2π)/4642 weeks
2691.65951 .0842 (269*2π)/4642 weeks
2701.47018 .25319 (270*2π)/4642 weeks
2711.07055 .14308 (271*2π)/4642 weeks
2721.14639 -.07654 (272*2π)/4642 weeks
2731.0101 .17892 (273*2π)/4642 weeks
2741.23334 .01921 (274*2π)/4642 weeks
2751.08079 -.0857 (275*2π)/4642 weeks
276.96527 .11911 (276*2π)/4642 weeks
277.80939 .08979 (277*2π)/4642 weeks
278.73059 -.05478 (278*2π)/4642 weeks
279.83766 -.51908 (279*2π)/4642 weeks
280.92213 -.50851 (280*2π)/4642 weeks
2811.02553 -.43342 (281*2π)/4642 weeks
282.99361 -.11839 (282*2π)/4642 weeks
283.99413 -.23354 (283*2π)/4642 weeks
2841.09138 -.44653 (284*2π)/4642 weeks
285.85739 -.40649 (285*2π)/4642 weeks
286.75213 -.59354 (286*2π)/4642 weeks
2871.26867 -.39009 (287*2π)/4642 weeks
2881.57556 -.45025 (288*2π)/4642 weeks
2891.21377 -.34675 (289*2π)/4642 weeks
2901.15627 -.49794 (290*2π)/4642 weeks
291.98196 -.15036 (291*2π)/4642 weeks
292.88064 -.25309 (292*2π)/4642 weeks
2931.15326 -.4263 (293*2π)/4642 weeks
2941.11022 -.31297 (294*2π)/4642 weeks
2951.17843 -.25435 (295*2π)/4642 weeks
2961.19048 -.51718 (296*2π)/4642 weeks
2971.08459 -.52989 (297*2π)/4642 weeks
2981.14449 -.64428 (298*2π)/4642 weeks
2991.30581 -.39102 (299*2π)/4642 weeks
3001.01056 -.40424 (300*2π)/4642 weeks
301.90469 -.42044 (301*2π)/4642 weeks
3021.16011 -.59717 (302*2π)/4642 weeks
303.98402 -.577 (303*2π)/4642 weeks
3041.14679 -.57905 (304*2π)/4642 weeks
3051.28909 -.66104 (305*2π)/4642 weeks
3061.45069 -.58391 (306*2π)/4642 weeks
3071.35473 -.51394 (307*2π)/4642 weeks
3081.40478 -.42204 (308*2π)/4642 weeks
3091.04803 -.51971 (309*2π)/4642 weeks
3101.36812 -.46497 (310*2π)/4641 weeks
3111.51082 -.65796 (311*2π)/4641 weeks
3121.65028 -.52323 (312*2π)/4641 weeks
3131.38322 -.73294 (313*2π)/4641 weeks
3141.56378 -.32562 (314*2π)/4641 weeks
3151.43745 -.35855 (315*2π)/4641 weeks
3161.38913 -.27547 (316*2π)/4641 weeks
3171.26371 -.27238 (317*2π)/4641 weeks
3181.45869 .03754 (318*2π)/4641 weeks
3191.19141 -.24149 (319*2π)/4641 weeks
320.92452 -.23964 (320*2π)/4641 weeks
3211.16248 -.67542 (321*2π)/4641 weeks
3221.21148 -.4311 (322*2π)/4641 weeks
3231.39238 -.4571 (323*2π)/4641 weeks
3241.23706 -.3193 (324*2π)/4641 weeks
3251.10984 -.18885 (325*2π)/4641 weeks
326.94436 -.46797 (326*2π)/4641 weeks
327.92278 -.49587 (327*2π)/4641 weeks
3281.146 -.64907 (328*2π)/4641 weeks
329.84592 -.20779 (329*2π)/4641 weeks
3301.14977 -.21937 (330*2π)/4641 weeks
331.80656 -.65746 (331*2π)/4641 weeks
3321.14571 -.22077 (332*2π)/4641 weeks
3331.00717 -.46717 (333*2π)/4641 weeks
334.68182 -.11262 (334*2π)/4641 weeks
335.74939 -.34305 (335*2π)/4641 weeks
336.82422 -.49364 (336*2π)/4641 weeks
337.47626 -.60961 (337*2π)/4641 weeks
338.62066 -.42276 (338*2π)/4641 weeks
339.58353 -1.11865 (339*2π)/4641 weeks
340.67435 -1.11476 (340*2π)/4641 weeks
341.94763 -.89218 (341*2π)/4641 weeks
3421.00437 -.68589 (342*2π)/4641 weeks
343.8703 -.97894 (343*2π)/4641 weeks
344.7398 -.68517 (344*2π)/4641 weeks
345.64078 -.93836 (345*2π)/4641 weeks
346.95233 -1.05554 (346*2π)/4641 weeks
3471.02451 -.70249 (347*2π)/4641 weeks
348.60258 -1.00779 (348*2π)/4641 weeks
349.36846 -1.38999 (349*2π)/4641 weeks
3501.02756 -1.29961 (350*2π)/4641 weeks
351.66537 -1.02343 (351*2π)/4641 weeks
3521.06028 -1.67304 (352*2π)/4641 weeks
3531.1813 -1.97881 (353*2π)/4641 weeks
3541.35226 -1.91481 (354*2π)/4641 weeks
3551.1824 -1.73713 (355*2π)/4641 weeks
3561.62634 -1.0223 (356*2π)/4641 weeks
3571.50473 -1.31395 (357*2π)/4641 weeks
3581.15249 -1.63531 (358*2π)/4641 weeks
3591.53008 -1.22219 (359*2π)/4641 weeks
3601.71385 -1.43769 (360*2π)/4641 weeks
3611.3826 -1.27822 (361*2π)/4641 weeks
3621.53755 -1.1225 (362*2π)/4641 weeks
3631.80089 -1.08332 (363*2π)/4641 weeks
3641.5808 -.94338 (364*2π)/4641 weeks
3651.57463 -.85421 (365*2π)/4641 weeks
3661.33792 -.79372 (366*2π)/4641 weeks
3671.32615 -.48381 (367*2π)/4641 weeks
3681.30186 -.80383 (368*2π)/4641 weeks
3691.36434 -.69654 (369*2π)/4641 weeks
370.60784 -1.63283 (370*2π)/4641 weeks
371.64939 -1.07645 (371*2π)/4641 weeks
3721.25796 -2.04222 (372*2π)/4641 weeks
3731.19848 -1.83987 (373*2π)/4641 weeks
3741.38093 -1.81009 (374*2π)/4641 weeks
3751.08995 -1.07486 (375*2π)/4641 weeks
3761.46046 -1.73265 (376*2π)/4641 weeks
3771.40464 -1.20875 (377*2π)/4641 weeks
3781.80618 -1.64058 (378*2π)/4641 weeks
3791.44578 -1.51006 (379*2π)/4641 weeks
3801.73457 -1.51267 (380*2π)/4641 weeks
3811.0435 -.98488 (381*2π)/4641 weeks
3821.27817 -1.52732 (382*2π)/4641 weeks
383.86028 -1.81124 (383*2π)/4641 weeks
3841.10369 -2.20144 (384*2π)/4641 weeks
3851.35847 -1.73689 (385*2π)/4641 weeks
3862.0662 -2.24638 (386*2π)/4641 weeks
3872.02223 -1.40073 (387*2π)/4641 weeks
3882.41814 -1.2566 (388*2π)/4641 weeks
3891.7981 -.94278 (389*2π)/4641 weeks
3901.33881 -1.54406 (390*2π)/4641 weeks
391.92506 -1.35576 (391*2π)/4641 weeks
3921.4724 -1.34498 (392*2π)/4641 weeks
3931.10467 -1.89193 (393*2π)/4641 weeks
3941.94593 -1.96446 (394*2π)/4641 weeks
3951.72626 -1.30604 (395*2π)/4641 weeks
3961.49587 -1.5553 (396*2π)/4641 weeks
3971.64998 -1.77298 (397*2π)/4641 weeks
3981.58901 -1.20431 (398*2π)/4641 weeks
399.89683 -.94001 (399*2π)/4641 weeks
4001.04927 -.91217 (400*2π)/4641 weeks
4011.61258 -1.85341 (401*2π)/4641 weeks
4021.33386 -1.96746 (402*2π)/4641 weeks
4031.51623 -1.11695 (403*2π)/4641 weeks
4042.06684 -1.12184 (404*2π)/4641 weeks
4051.47029 -1.38437 (405*2π)/4641 weeks
406.68024 -.97633 (406*2π)/4641 weeks
4071.02683 -1.71785 (407*2π)/4641 weeks
408.38611 -1.96046 (408*2π)/4641 weeks
4091.31243 -2.66796 (409*2π)/4641 weeks
4101.19848 -2.54604 (410*2π)/4641 weeks
4111.01002 -2.12398 (411*2π)/4641 weeks
4121.07202 -1.92707 (412*2π)/4641 weeks
4131.72211 -2.66093 (413*2π)/4641 weeks
4142.4842 -2.51706 (414*2π)/4641 weeks
4151.16785 -2.66891 (415*2π)/4641 weeks
4161.16517 -1.62774 (416*2π)/4641 weeks
4171.31785 -2.05712 (417*2π)/4641 weeks
4181.51173 -1.33436 (418*2π)/4641 weeks
419.95652 -2.03633 (419*2π)/4641 weeks
4201.72972 -1.71647 (420*2π)/4641 weeks
4211.11001 -2.13165 (421*2π)/4641 weeks
422.53736 -2.13727 (422*2π)/4641 weeks
4231.70311 -2.13417 (423*2π)/4641 weeks
424.81643 -1.43485 (424*2π)/4641 weeks
425.14311 -3.33291 (425*2π)/4641 weeks
426.31754 -2.69673 (426*2π)/4641 weeks
427.57002 -2.80645 (427*2π)/4641 weeks
428-1.09628 -3.66501 (428*2π)/4641 weeks
429.32904 -4.50776 (429*2π)/4641 weeks
430.86099 -4.18406 (430*2π)/4641 weeks
4311.12757 -5.00305 (431*2π)/4641 weeks
4321.97769 -5.27107 (432*2π)/4641 weeks
4332.71649 -3.98684 (433*2π)/4641 weeks
4341.34887 -5.1236 (434*2π)/4641 weeks
4352.26425 -5.1125 (435*2π)/4641 weeks
4362.76049 -5.69844 (436*2π)/4641 weeks
4372.2906 -5.62334 (437*2π)/4641 weeks
4381.73921 -4.98505 (438*2π)/4641 weeks
4393.1076 -4.48529 (439*2π)/4641 weeks
4403.86586 -4.56262 (440*2π)/4641 weeks
4413.22109 -5.96153 (441*2π)/4641 weeks
4421.92451 -5.83178 (442*2π)/4641 weeks
4434.43622 -3.11696 (443*2π)/4641 weeks
4443.44875 -4.03532 (444*2π)/4641 weeks
445.71384 -4.07885 (445*2π)/4641 weeks
4461.78865 -8.89754 (446*2π)/4641 weeks
447.80525 -7.4661 (447*2π)/4641 weeks
4482.56032 -8.20238 (448*2π)/4641 weeks
4494.0753 -6.46476 (449*2π)/4641 weeks
4504.23611 -6.56744 (450*2π)/4641 weeks
4512.54529 -6.68709 (451*2π)/4641 weeks
4524.67856 -6.37267 (452*2π)/4641 weeks
4532.59463 -6.77925 (453*2π)/4641 weeks
4542.87808 -6.98853 (454*2π)/4641 weeks
4551.69354 -11.46905 (455*2π)/4641 weeks
4562.21485 -16.47554 (456*2π)/4641 weeks
457-.52953 -13.08371 (457*2π)/4641 weeks
4581.44668 -18.49615 (458*2π)/4641 weeks
4596.12462 -16.82765 (459*2π)/4641 weeks
46011.80319 -25.72628 (460*2π)/4641 weeks
46110.12521 -32.17913 (461*2π)/4641 weeks
46222.54976 -49.85056 (462*2π)/4641 weeks



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