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Fourier Analysis of GLL (ProShares UltraShort Gold)


GLL (ProShares UltraShort Gold) appears to have interesting cyclic behaviour every 25 weeks (8.6355*sine), 29 weeks (8.2939*sine), and 43 weeks (7.6795*sine).

GLL (ProShares UltraShort Gold) has an average price of 121.79 (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 3/13/2017 for GLL (ProShares UltraShort Gold), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0121.7939   0 
163.68715 28.1088 (1*2π)/433433 weeks
219.17023 48.07122 (2*2π)/433217 weeks
38.70364 30.50208 (3*2π)/433144 weeks
47.95401 29.02184 (4*2π)/433108 weeks
59.38905 21.51337 (5*2π)/43387 weeks
63.05051 17.59143 (6*2π)/43372 weeks
76.23096 11.61241 (7*2π)/43362 weeks
8.44142 10.62442 (8*2π)/43354 weeks
9.01591 7.36547 (9*2π)/43348 weeks
102.12048 7.6795 (10*2π)/43343 weeks
114.07786 6.18295 (11*2π)/43339 weeks
122.67736 7.64051 (12*2π)/43336 weeks
134.54809 6.76005 (13*2π)/43333 weeks
144.47303 6.71737 (14*2π)/43331 weeks
152.79341 8.29388 (15*2π)/43329 weeks
16.96693 6.69363 (16*2π)/43327 weeks
17-.18434 8.63553 (17*2π)/43325 weeks
181.17695 3.75867 (18*2π)/43324 weeks
192.7499 4.80453 (19*2π)/43323 weeks
205.49867 6.27851 (20*2π)/43322 weeks
213.49604 4.45443 (21*2π)/43321 weeks
222.30714 4.45353 (22*2π)/43320 weeks
232.49814 5.55642 (23*2π)/43319 weeks
242.3317 6.43918 (24*2π)/43318 weeks
253.06872 5.96714 (25*2π)/43317 weeks
263.12115 5.70332 (26*2π)/43317 weeks
272.27392 5.3423 (27*2π)/43316 weeks
281.28739 5.43718 (28*2π)/43315 weeks
292.87707 4.4843 (29*2π)/43315 weeks
301.83857 5.73173 (30*2π)/43314 weeks
31.95041 5.41593 (31*2π)/43314 weeks
321.12383 4.8317 (32*2π)/43314 weeks
33.21878 4.93793 (33*2π)/43313 weeks
34-.35814 2.60342 (34*2π)/43313 weeks
35.46222 3.19733 (35*2π)/43312 weeks
36.94291 3.04482 (36*2π)/43312 weeks
37-.12273 1.63364 (37*2π)/43312 weeks
381.48749 1.9223 (38*2π)/43311 weeks
39.6145 2.75399 (39*2π)/43311 weeks
401.29269 2.28034 (40*2π)/43311 weeks
411.78527 1.79566 (41*2π)/43311 weeks
421.067 2.24384 (42*2π)/43310 weeks
431.84598 1.54164 (43*2π)/43310 weeks
441.55539 2.14491 (44*2π)/43310 weeks
451.83421 1.50332 (45*2π)/43310 weeks
461.04565 1.83951 (46*2π)/4339 weeks
471.76942 3.06857 (47*2π)/4339 weeks
481.10486 3.1363 (48*2π)/4339 weeks
491.53888 2.57343 (49*2π)/4339 weeks
501.736 2.37076 (50*2π)/4339 weeks
511.46229 2.34698 (51*2π)/4338 weeks
52.39146 2.43525 (52*2π)/4338 weeks
53.99645 1.65161 (53*2π)/4338 weeks
54.52442 1.24263 (54*2π)/4338 weeks
551.56246 1.4695 (55*2π)/4338 weeks
562.15821 1.26938 (56*2π)/4338 weeks
571.73044 1.23279 (57*2π)/4338 weeks
581.24603 1.98541 (58*2π)/4337 weeks
591.35496 2.3006 (59*2π)/4337 weeks
601.60627 1.33428 (60*2π)/4337 weeks
611.70581 .79122 (61*2π)/4337 weeks
622.08433 1.24991 (62*2π)/4337 weeks
631.60918 1.53224 (63*2π)/4337 weeks
641.61794 1.32324 (64*2π)/4337 weeks
652.1708 1.63526 (65*2π)/4337 weeks
661.35419 2.1073 (66*2π)/4337 weeks
671.36858 1.29933 (67*2π)/4336 weeks
681.0145 1.58179 (68*2π)/4336 weeks
691.51417 1.55537 (69*2π)/4336 weeks
701.9134 .91955 (70*2π)/4336 weeks
712.58033 1.40727 (71*2π)/4336 weeks
722.32084 1.46317 (72*2π)/4336 weeks
731.94674 2.46543 (73*2π)/4336 weeks
741.81398 1.84864 (74*2π)/4336 weeks
751.11621 1.92013 (75*2π)/4336 weeks
76.98229 1.34277 (76*2π)/4336 weeks
77.98339 1.48807 (77*2π)/4336 weeks
781.85173 1.02279 (78*2π)/4336 weeks
791.55419 1.4884 (79*2π)/4335 weeks
801.77912 1.30954 (80*2π)/4335 weeks
811.19417 1.3344 (81*2π)/4335 weeks
821.55177 1.73953 (82*2π)/4335 weeks
831.03008 1.13585 (83*2π)/4335 weeks
841.41292 1.83204 (84*2π)/4335 weeks
851.15496 1.82134 (85*2π)/4335 weeks
861.00842 2.18311 (86*2π)/4335 weeks
87.95493 1.00146 (87*2π)/4335 weeks
88.19138 1.05551 (88*2π)/4335 weeks
891.15948 1.0407 (89*2π)/4335 weeks
901.1139 1.00526 (90*2π)/4335 weeks
911.61537 .95431 (91*2π)/4335 weeks
921.64908 .8403 (92*2π)/4335 weeks
931.70409 1.00791 (93*2π)/4335 weeks
941.86215 1.0233 (94*2π)/4335 weeks
951.6124 1.27809 (95*2π)/4335 weeks
961.55502 1.42862 (96*2π)/4335 weeks
971.87937 1.4686 (97*2π)/4334 weeks
981.66317 1.27598 (98*2π)/4334 weeks
991.17495 1.62161 (99*2π)/4334 weeks
1001.55414 1.46013 (100*2π)/4334 weeks
1012.04007 1.29728 (101*2π)/4334 weeks
1021.37405 1.4544 (102*2π)/4334 weeks
1031.18614 1.76274 (103*2π)/4334 weeks
104.7389 1.79241 (104*2π)/4334 weeks
105.42237 1.7779 (105*2π)/4334 weeks
1061.00809 1.33258 (106*2π)/4334 weeks
107.6949 1.78592 (107*2π)/4334 weeks
108.63402 1.07431 (108*2π)/4334 weeks
109.88481 .68787 (109*2π)/4334 weeks
110.99009 1.13845 (110*2π)/4334 weeks
111.65077 1.06045 (111*2π)/4334 weeks
112.77533 .75317 (112*2π)/4334 weeks
113.84968 1.06014 (113*2π)/4334 weeks
1141.11377 .83765 (114*2π)/4334 weeks
1151.05861 1.008 (115*2π)/4334 weeks
116.6665 1.02109 (116*2π)/4334 weeks
117.25482 .96449 (117*2π)/4334 weeks
118.78394 .73336 (118*2π)/4334 weeks
119.67334 .36171 (119*2π)/4334 weeks
120.65157 .49275 (120*2π)/4334 weeks
121.65835 .40531 (121*2π)/4334 weeks
1221.21024 .38135 (122*2π)/4334 weeks
1231.09015 .20334 (123*2π)/4334 weeks
124.98665 .75168 (124*2π)/4333 weeks
1251.21319 .19031 (125*2π)/4333 weeks
126.94291 .1862 (126*2π)/4333 weeks
1271.179 .66422 (127*2π)/4333 weeks
128.9897 .44375 (128*2π)/4333 weeks
129.93024 .38121 (129*2π)/4333 weeks
1301.24835 .20773 (130*2π)/4333 weeks
1311.32247 .28382 (131*2π)/4333 weeks
1321.28908 .56081 (132*2π)/4333 weeks
1331.35265 .52631 (133*2π)/4333 weeks
134.87614 .48508 (134*2π)/4333 weeks
1351.1972 .16228 (135*2π)/4333 weeks
1361.23217 -.05335 (136*2π)/4333 weeks
1371.33574 .40466 (137*2π)/4333 weeks
1381.44457 .31433 (138*2π)/4333 weeks
1391.49823 .38855 (139*2π)/4333 weeks
1401.62929 .34934 (140*2π)/4333 weeks
1411.33853 .73104 (141*2π)/4333 weeks
1421.64394 .67973 (142*2π)/4333 weeks
1431.4519 .82428 (143*2π)/4333 weeks
1441.49728 .70753 (144*2π)/4333 weeks
1451.24596 .35724 (145*2π)/4333 weeks
1461.45085 .5547 (146*2π)/4333 weeks
1471.44604 .54925 (147*2π)/4333 weeks
1481.37329 .75921 (148*2π)/4333 weeks
1491.19066 .75538 (149*2π)/4333 weeks
1501.12186 .76541 (150*2π)/4333 weeks
1511.26023 .60759 (151*2π)/4333 weeks
152.95167 .53909 (152*2π)/4333 weeks
1531.08948 .46334 (153*2π)/4333 weeks
1541.39295 .43707 (154*2π)/4333 weeks
1551.16638 .67964 (155*2π)/4333 weeks
1561.09184 .55415 (156*2π)/4333 weeks
1571.10412 .63475 (157*2π)/4333 weeks
1581.28466 .48586 (158*2π)/4333 weeks
1591.26785 .44621 (159*2π)/4333 weeks
1601.11449 .62093 (160*2π)/4333 weeks
1611.17165 .32783 (161*2π)/4333 weeks
1621.51927 .2977 (162*2π)/4333 weeks
1631.30882 .2515 (163*2π)/4333 weeks
1641.56528 .19574 (164*2π)/4333 weeks
1651.20445 .45496 (165*2π)/4333 weeks
166.85972 .78024 (166*2π)/4333 weeks
167.94451 .46907 (167*2π)/4333 weeks
1681.16953 .50596 (168*2π)/4333 weeks
1691.10913 .29072 (169*2π)/4333 weeks
1701.21038 .13834 (170*2π)/4333 weeks
1711.10441 .4029 (171*2π)/4333 weeks
172.92394 .43097 (172*2π)/4333 weeks
173.62032 .4192 (173*2π)/4333 weeks
174.81123 .09141 (174*2π)/4332 weeks
1751.01119 -.06549 (175*2π)/4332 weeks
1761.2543 -.04361 (176*2π)/4332 weeks
1771.16788 -.12688 (177*2π)/4332 weeks
178.99234 -.00136 (178*2π)/4332 weeks
1791.31067 .08521 (179*2π)/4332 weeks
1801.1445 -.10535 (180*2π)/4332 weeks
1811.55334 -.27154 (181*2π)/4332 weeks
1821.77003 -.05179 (182*2π)/4332 weeks
1831.78316 .21872 (183*2π)/4332 weeks
1841.6468 .08545 (184*2π)/4332 weeks
1851.48718 .48771 (185*2π)/4332 weeks
1861.36392 .32059 (186*2π)/4332 weeks
1871.30391 .61559 (187*2π)/4332 weeks
1881.1007 .32614 (188*2π)/4332 weeks
1891.28575 .32616 (189*2π)/4332 weeks
1901.28611 .48701 (190*2π)/4332 weeks
1911.04541 .25616 (191*2π)/4332 weeks
1921.03847 .06558 (192*2π)/4332 weeks
193.89198 .27718 (193*2π)/4332 weeks
1941.29523 .36491 (194*2π)/4332 weeks
1951.08677 .23999 (195*2π)/4332 weeks
196.89402 .24645 (196*2π)/4332 weeks
197.74556 .11992 (197*2π)/4332 weeks
198.84978 .11351 (198*2π)/4332 weeks
1991.01871 -.21912 (199*2π)/4332 weeks
200.8889 -.02326 (200*2π)/4332 weeks
2011.23784 -.4136 (201*2π)/4332 weeks
2021.42615 -.20694 (202*2π)/4332 weeks
2031.30611 -.09846 (203*2π)/4332 weeks
2041.3646 -.12948 (204*2π)/4332 weeks
2051.37582 -.23375 (205*2π)/4332 weeks
2061.44987 .08802 (206*2π)/4332 weeks
2071.43066 .06088 (207*2π)/4332 weeks
2081.35675 .00403 (208*2π)/4332 weeks
2091.26288 .04003 (209*2π)/4332 weeks
2101.47345 -.35103 (210*2π)/4332 weeks
2111.61156 .19861 (211*2π)/4332 weeks
2121.30111 -.10437 (212*2π)/4332 weeks
2131.19711 .04274 (213*2π)/4332 weeks
2141.22807 .22546 (214*2π)/4332 weeks
2151.21924 -.04378 (215*2π)/4332 weeks
2161.3715 .01522 (216*2π)/4332 weeks
2171.3715 -.01522 (217*2π)/4332 weeks
2181.21924 .04378 (218*2π)/4332 weeks
2191.22807 -.22546 (219*2π)/4332 weeks
2201.19711 -.04274 (220*2π)/4332 weeks
2211.30111 .10437 (221*2π)/4332 weeks
2221.61156 -.19861 (222*2π)/4332 weeks
2231.47345 .35103 (223*2π)/4332 weeks
2241.26288 -.04003 (224*2π)/4332 weeks
2251.35675 -.00403 (225*2π)/4332 weeks
2261.43066 -.06088 (226*2π)/4332 weeks
2271.44987 -.08802 (227*2π)/4332 weeks
2281.37582 .23375 (228*2π)/4332 weeks
2291.3646 .12948 (229*2π)/4332 weeks
2301.30611 .09846 (230*2π)/4332 weeks
2311.42615 .20694 (231*2π)/4332 weeks
2321.23784 .4136 (232*2π)/4332 weeks
233.8889 .02326 (233*2π)/4332 weeks
2341.01871 .21912 (234*2π)/4332 weeks
235.84978 -.11351 (235*2π)/4332 weeks
236.74556 -.11992 (236*2π)/4332 weeks
237.89402 -.24645 (237*2π)/4332 weeks
2381.08677 -.23999 (238*2π)/4332 weeks
2391.29523 -.36491 (239*2π)/4332 weeks
240.89198 -.27718 (240*2π)/4332 weeks
2411.03847 -.06558 (241*2π)/4332 weeks
2421.04541 -.25616 (242*2π)/4332 weeks
2431.28611 -.48701 (243*2π)/4332 weeks
2441.28575 -.32616 (244*2π)/4332 weeks
2451.1007 -.32614 (245*2π)/4332 weeks
2461.30391 -.61559 (246*2π)/4332 weeks
2471.36392 -.32059 (247*2π)/4332 weeks
2481.48718 -.48771 (248*2π)/4332 weeks
2491.6468 -.08545 (249*2π)/4332 weeks
2501.78316 -.21872 (250*2π)/4332 weeks
2511.77003 .05179 (251*2π)/4332 weeks
2521.55334 .27154 (252*2π)/4332 weeks
2531.1445 .10535 (253*2π)/4332 weeks
2541.31067 -.08521 (254*2π)/4332 weeks
255.99234 .00136 (255*2π)/4332 weeks
2561.16788 .12688 (256*2π)/4332 weeks
2571.2543 .04361 (257*2π)/4332 weeks
2581.01119 .06549 (258*2π)/4332 weeks
259.81123 -.09141 (259*2π)/4332 weeks
260.62032 -.4192 (260*2π)/4332 weeks
261.92394 -.43097 (261*2π)/4332 weeks
2621.10441 -.4029 (262*2π)/4332 weeks
2631.21038 -.13834 (263*2π)/4332 weeks
2641.10913 -.29072 (264*2π)/4332 weeks
2651.16953 -.50596 (265*2π)/4332 weeks
266.94451 -.46907 (266*2π)/4332 weeks
267.85972 -.78024 (267*2π)/4332 weeks
2681.20445 -.45496 (268*2π)/4332 weeks
2691.56528 -.19574 (269*2π)/4332 weeks
2701.30882 -.2515 (270*2π)/4332 weeks
2711.51927 -.2977 (271*2π)/4332 weeks
2721.17165 -.32783 (272*2π)/4332 weeks
2731.11449 -.62093 (273*2π)/4332 weeks
2741.26785 -.44621 (274*2π)/4332 weeks
2751.28466 -.48586 (275*2π)/4332 weeks
2761.10412 -.63475 (276*2π)/4332 weeks
2771.09184 -.55415 (277*2π)/4332 weeks
2781.16638 -.67964 (278*2π)/4332 weeks
2791.39295 -.43707 (279*2π)/4332 weeks
2801.08948 -.46334 (280*2π)/4332 weeks
281.95167 -.53909 (281*2π)/4332 weeks
2821.26023 -.60759 (282*2π)/4332 weeks
2831.12186 -.76541 (283*2π)/4332 weeks
2841.19066 -.75538 (284*2π)/4332 weeks
2851.37329 -.75921 (285*2π)/4332 weeks
2861.44604 -.54925 (286*2π)/4332 weeks
2871.45085 -.5547 (287*2π)/4332 weeks
2881.24596 -.35724 (288*2π)/4332 weeks
2891.49728 -.70753 (289*2π)/4331 weeks
2901.4519 -.82428 (290*2π)/4331 weeks
2911.64394 -.67973 (291*2π)/4331 weeks
2921.33853 -.73104 (292*2π)/4331 weeks
2931.62929 -.34934 (293*2π)/4331 weeks
2941.49823 -.38855 (294*2π)/4331 weeks
2951.44457 -.31433 (295*2π)/4331 weeks
2961.33574 -.40466 (296*2π)/4331 weeks
2971.23217 .05335 (297*2π)/4331 weeks
2981.1972 -.16228 (298*2π)/4331 weeks
299.87614 -.48508 (299*2π)/4331 weeks
3001.35265 -.52631 (300*2π)/4331 weeks
3011.28908 -.56081 (301*2π)/4331 weeks
3021.32247 -.28382 (302*2π)/4331 weeks
3031.24835 -.20773 (303*2π)/4331 weeks
304.93024 -.38121 (304*2π)/4331 weeks
305.9897 -.44375 (305*2π)/4331 weeks
3061.179 -.66422 (306*2π)/4331 weeks
307.94291 -.1862 (307*2π)/4331 weeks
3081.21319 -.19031 (308*2π)/4331 weeks
309.98665 -.75168 (309*2π)/4331 weeks
3101.09015 -.20334 (310*2π)/4331 weeks
3111.21024 -.38135 (311*2π)/4331 weeks
312.65835 -.40531 (312*2π)/4331 weeks
313.65157 -.49275 (313*2π)/4331 weeks
314.67334 -.36171 (314*2π)/4331 weeks
315.78394 -.73336 (315*2π)/4331 weeks
316.25482 -.96449 (316*2π)/4331 weeks
317.6665 -1.02109 (317*2π)/4331 weeks
3181.05861 -1.008 (318*2π)/4331 weeks
3191.11377 -.83765 (319*2π)/4331 weeks
320.84968 -1.06014 (320*2π)/4331 weeks
321.77533 -.75317 (321*2π)/4331 weeks
322.65077 -1.06045 (322*2π)/4331 weeks
323.99009 -1.13845 (323*2π)/4331 weeks
324.88481 -.68787 (324*2π)/4331 weeks
325.63402 -1.07431 (325*2π)/4331 weeks
326.6949 -1.78592 (326*2π)/4331 weeks
3271.00809 -1.33258 (327*2π)/4331 weeks
328.42237 -1.7779 (328*2π)/4331 weeks
329.7389 -1.79241 (329*2π)/4331 weeks
3301.18614 -1.76274 (330*2π)/4331 weeks
3311.37405 -1.4544 (331*2π)/4331 weeks
3322.04007 -1.29728 (332*2π)/4331 weeks
3331.55414 -1.46013 (333*2π)/4331 weeks
3341.17495 -1.62161 (334*2π)/4331 weeks
3351.66317 -1.27598 (335*2π)/4331 weeks
3361.87937 -1.4686 (336*2π)/4331 weeks
3371.55502 -1.42862 (337*2π)/4331 weeks
3381.6124 -1.27809 (338*2π)/4331 weeks
3391.86215 -1.0233 (339*2π)/4331 weeks
3401.70409 -1.00791 (340*2π)/4331 weeks
3411.64908 -.8403 (341*2π)/4331 weeks
3421.61537 -.95431 (342*2π)/4331 weeks
3431.1139 -1.00526 (343*2π)/4331 weeks
3441.15948 -1.0407 (344*2π)/4331 weeks
345.19138 -1.05551 (345*2π)/4331 weeks
346.95493 -1.00146 (346*2π)/4331 weeks
3471.00842 -2.18311 (347*2π)/4331 weeks
3481.15496 -1.82134 (348*2π)/4331 weeks
3491.41292 -1.83204 (349*2π)/4331 weeks
3501.03008 -1.13585 (350*2π)/4331 weeks
3511.55177 -1.73953 (351*2π)/4331 weeks
3521.19417 -1.3344 (352*2π)/4331 weeks
3531.77912 -1.30954 (353*2π)/4331 weeks
3541.55419 -1.4884 (354*2π)/4331 weeks
3551.85173 -1.02279 (355*2π)/4331 weeks
356.98339 -1.48807 (356*2π)/4331 weeks
357.98229 -1.34277 (357*2π)/4331 weeks
3581.11621 -1.92013 (358*2π)/4331 weeks
3591.81398 -1.84864 (359*2π)/4331 weeks
3601.94674 -2.46543 (360*2π)/4331 weeks
3612.32084 -1.46317 (361*2π)/4331 weeks
3622.58033 -1.40727 (362*2π)/4331 weeks
3631.9134 -.91955 (363*2π)/4331 weeks
3641.51417 -1.55537 (364*2π)/4331 weeks
3651.0145 -1.58179 (365*2π)/4331 weeks
3661.36858 -1.29933 (366*2π)/4331 weeks
3671.35419 -2.1073 (367*2π)/4331 weeks
3682.1708 -1.63526 (368*2π)/4331 weeks
3691.61794 -1.32324 (369*2π)/4331 weeks
3701.60918 -1.53224 (370*2π)/4331 weeks
3712.08433 -1.24991 (371*2π)/4331 weeks
3721.70581 -.79122 (372*2π)/4331 weeks
3731.60627 -1.33428 (373*2π)/4331 weeks
3741.35496 -2.3006 (374*2π)/4331 weeks
3751.24603 -1.98541 (375*2π)/4331 weeks
3761.73044 -1.23279 (376*2π)/4331 weeks
3772.15821 -1.26938 (377*2π)/4331 weeks
3781.56246 -1.4695 (378*2π)/4331 weeks
379.52442 -1.24263 (379*2π)/4331 weeks
380.99645 -1.65161 (380*2π)/4331 weeks
381.39146 -2.43525 (381*2π)/4331 weeks
3821.46229 -2.34698 (382*2π)/4331 weeks
3831.736 -2.37076 (383*2π)/4331 weeks
3841.53888 -2.57343 (384*2π)/4331 weeks
3851.10486 -3.1363 (385*2π)/4331 weeks
3861.76942 -3.06857 (386*2π)/4331 weeks
3871.04565 -1.83951 (387*2π)/4331 weeks
3881.83421 -1.50332 (388*2π)/4331 weeks
3891.55539 -2.14491 (389*2π)/4331 weeks
3901.84598 -1.54164 (390*2π)/4331 weeks
3911.067 -2.24384 (391*2π)/4331 weeks
3921.78527 -1.79566 (392*2π)/4331 weeks
3931.29269 -2.28034 (393*2π)/4331 weeks
394.6145 -2.75399 (394*2π)/4331 weeks
3951.48749 -1.9223 (395*2π)/4331 weeks
396-.12273 -1.63364 (396*2π)/4331 weeks
397.94291 -3.04482 (397*2π)/4331 weeks
398.46222 -3.19733 (398*2π)/4331 weeks
399-.35814 -2.60342 (399*2π)/4331 weeks
400.21878 -4.93793 (400*2π)/4331 weeks
4011.12383 -4.8317 (401*2π)/4331 weeks
402.95041 -5.41593 (402*2π)/4331 weeks
4031.83857 -5.73173 (403*2π)/4331 weeks
4042.87707 -4.4843 (404*2π)/4331 weeks
4051.28739 -5.43718 (405*2π)/4331 weeks
4062.27392 -5.3423 (406*2π)/4331 weeks
4073.12115 -5.70332 (407*2π)/4331 weeks
4083.06872 -5.96714 (408*2π)/4331 weeks
4092.3317 -6.43918 (409*2π)/4331 weeks
4102.49814 -5.55642 (410*2π)/4331 weeks
4112.30714 -4.45353 (411*2π)/4331 weeks
4123.49604 -4.45443 (412*2π)/4331 weeks
4135.49867 -6.27851 (413*2π)/4331 weeks
4142.7499 -4.80453 (414*2π)/4331 weeks
4151.17695 -3.75867 (415*2π)/4331 weeks
416-.18434 -8.63553 (416*2π)/4331 weeks
417.96693 -6.69363 (417*2π)/4331 weeks
4182.79341 -8.29388 (418*2π)/4331 weeks
4194.47303 -6.71737 (419*2π)/4331 weeks
4204.54809 -6.76005 (420*2π)/4331 weeks
4212.67736 -7.64051 (421*2π)/4331 weeks
4224.07786 -6.18295 (422*2π)/4331 weeks
4232.12048 -7.6795 (423*2π)/4331 weeks
424.01591 -7.36547 (424*2π)/4331 weeks
425.44142 -10.62442 (425*2π)/4331 weeks
4266.23096 -11.61241 (426*2π)/4331 weeks
4273.05051 -17.59143 (427*2π)/4331 weeks
4289.38905 -21.51337 (428*2π)/4331 weeks
4297.95401 -29.02184 (429*2π)/4331 weeks
4308.70364 -30.50208 (430*2π)/4331 weeks
43119.17023 -48.07122 (431*2π)/4331 weeks

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