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Fourier Analysis of GLL (ProShares UltraShort Gold)


GLL (ProShares UltraShort Gold) appears to have interesting cyclic behaviour every 28 weeks (8.2609*sine), 30 weeks (7.7856*sine), and 33 weeks (7.3576*sine).

GLL (ProShares UltraShort Gold) has an average price of 122.69 (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 1/9/2017 for GLL (ProShares UltraShort Gold), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0122.6933   0 
165.25368 29.49226 (1*2π)/424424 weeks
218.32764 47.33772 (2*2π)/424212 weeks
38.47565 29.64076 (3*2π)/424141 weeks
45.97279 28.79568 (4*2π)/424106 weeks
58.26693 23.32022 (5*2π)/42485 weeks
62.37815 18.18702 (6*2π)/42471 weeks
77.00843 14.42424 (7*2π)/42461 weeks
81.94306 10.82942 (8*2π)/42453 weeks
91.99887 6.77601 (9*2π)/42447 weeks
102.6703 7.17138 (10*2π)/42442 weeks
115.25134 6.88858 (11*2π)/42439 weeks
123.17402 6.64234 (12*2π)/42435 weeks
134.76555 7.3576 (13*2π)/42433 weeks
145.49092 7.78556 (14*2π)/42430 weeks
153.24265 8.26088 (15*2π)/42428 weeks
163.24875 6.06294 (16*2π)/42427 weeks
17-.93784 5.25339 (17*2π)/42425 weeks
182.67434 3.03224 (18*2π)/42424 weeks
193.20961 2.97959 (19*2π)/42422 weeks
202.35569 6.72007 (20*2π)/42421 weeks
213.45098 6.17907 (21*2π)/42420 weeks
224.15147 5.04954 (22*2π)/42419 weeks
233.82889 4.99999 (23*2π)/42418 weeks
242.63569 4.42224 (24*2π)/42418 weeks
252.29776 4.87992 (25*2π)/42417 weeks
261.87965 5.56384 (26*2π)/42416 weeks
271.84546 5.59813 (27*2π)/42416 weeks
281.59878 3.84934 (28*2π)/42415 weeks
292.19186 5.5955 (29*2π)/42415 weeks
301.08866 5.45802 (30*2π)/42414 weeks
31.66729 4.56746 (31*2π)/42414 weeks
32.23395 4.88974 (32*2π)/42413 weeks
33-1.26902 3.49269 (33*2π)/42413 weeks
34.49359 3.16549 (34*2π)/42412 weeks
35.58809 2.71608 (35*2π)/42412 weeks
36-.69141 2.44374 (36*2π)/42412 weeks
371.19282 1.87048 (37*2π)/42411 weeks
38.91991 3.07767 (38*2π)/42411 weeks
391.28271 2.1217 (39*2π)/42411 weeks
401.45628 1.64771 (40*2π)/42411 weeks
411.04402 2.4058 (41*2π)/42410 weeks
421.58847 1.48892 (42*2π)/42410 weeks
431.48938 2.22342 (43*2π)/42410 weeks
441.62158 1.54914 (44*2π)/42410 weeks
45.95697 2.05291 (45*2π)/4249 weeks
461.81121 3.14872 (46*2π)/4249 weeks
471.07539 3.19297 (47*2π)/4249 weeks
481.48072 2.6313 (48*2π)/4249 weeks
491.69289 2.47374 (49*2π)/4249 weeks
501.45864 2.45064 (50*2π)/4248 weeks
51.29249 2.33482 (51*2π)/4248 weeks
52.9811 1.74476 (52*2π)/4248 weeks
53.58603 1.03176 (53*2π)/4248 weeks
541.34461 1.51166 (54*2π)/4248 weeks
552.11824 1.65524 (55*2π)/4248 weeks
562.05106 1.38074 (56*2π)/4248 weeks
571.23977 1.63845 (57*2π)/4247 weeks
58.76725 2.06513 (58*2π)/4247 weeks
591.34381 1.63374 (59*2π)/4247 weeks
601.95151 1.14067 (60*2π)/4247 weeks
612.16022 1.66428 (61*2π)/4247 weeks
621.73496 1.54885 (62*2π)/4247 weeks
631.90365 1.28057 (63*2π)/4247 weeks
642.13859 2.04813 (64*2π)/4247 weeks
651.18777 1.82822 (65*2π)/4247 weeks
661.74769 1.55644 (66*2π)/4246 weeks
671.41477 .96096 (67*2π)/4246 weeks
681.22662 .9724 (68*2π)/4246 weeks
692.04131 .89976 (69*2π)/4246 weeks
702.04945 1.73584 (70*2π)/4246 weeks
712.44739 2.09511 (71*2π)/4246 weeks
721.31949 2.07002 (72*2π)/4246 weeks
731.33307 2.406 (73*2π)/4246 weeks
74.9335 1.8956 (74*2π)/4246 weeks
751.33716 1.61459 (75*2π)/4246 weeks
761.32189 .85342 (76*2π)/4246 weeks
771.64984 1.6116 (77*2π)/4246 weeks
781.47984 1.38785 (78*2π)/4245 weeks
791.29221 1.89895 (79*2π)/4245 weeks
801.74261 1.69265 (80*2π)/4245 weeks
81.98363 1.70444 (81*2π)/4245 weeks
821.81131 1.8379 (82*2π)/4245 weeks
831.41296 1.90939 (83*2π)/4245 weeks
841.39355 2.03777 (84*2π)/4245 weeks
85.65059 1.05777 (85*2π)/4245 weeks
86.35328 1.52348 (86*2π)/4245 weeks
871.34796 .98058 (87*2π)/4245 weeks
881.27084 1.02055 (88*2π)/4245 weeks
891.70946 .83339 (89*2π)/4245 weeks
901.66948 .79202 (90*2π)/4245 weeks
911.75492 .98898 (91*2π)/4245 weeks
921.89472 1.00447 (92*2π)/4245 weeks
931.66262 1.29932 (93*2π)/4245 weeks
941.60525 1.44532 (94*2π)/4245 weeks
951.92429 1.50388 (95*2π)/4244 weeks
961.74184 1.3076 (96*2π)/4244 weeks
971.18071 1.58016 (97*2π)/4244 weeks
981.53598 1.51793 (98*2π)/4244 weeks
992.13947 1.5394 (99*2π)/4244 weeks
1001.5745 1.49405 (100*2π)/4244 weeks
1011.30005 1.75244 (101*2π)/4244 weeks
102.83659 1.64305 (102*2π)/4244 weeks
103.34833 1.45858 (103*2π)/4244 weeks
1041.00287 1.39508 (104*2π)/4244 weeks
105.38823 1.6557 (105*2π)/4244 weeks
106.58325 1.12476 (106*2π)/4244 weeks
1071.09794 .86436 (107*2π)/4244 weeks
108.94518 1.23168 (108*2π)/4244 weeks
109.69637 .96515 (109*2π)/4244 weeks
1101.0002 .75873 (110*2π)/4244 weeks
111.74512 .84745 (111*2π)/4244 weeks
1121.04412 1.02234 (112*2π)/4244 weeks
113.96201 1.25891 (113*2π)/4244 weeks
114.7684 1.11615 (114*2π)/4244 weeks
115.4733 .46837 (115*2π)/4244 weeks
116.49504 .70689 (116*2π)/4244 weeks
117.85177 .56149 (117*2π)/4244 weeks
118.81807 .41167 (118*2π)/4244 weeks
119.93153 .04235 (119*2π)/4244 weeks
120.91029 .42145 (120*2π)/4244 weeks
1211.33388 .55843 (121*2π)/4244 weeks
122.79057 .23587 (122*2π)/4243 weeks
123.99233 .56906 (123*2π)/4243 weeks
1241.45559 .47805 (124*2π)/4243 weeks
1251.0339 .51168 (125*2π)/4243 weeks
1261.05578 .4323 (126*2π)/4243 weeks
1271.17796 .12061 (127*2π)/4243 weeks
1281.31251 .2686 (128*2π)/4243 weeks
1291.43118 .49834 (129*2π)/4243 weeks
1301.33966 .41333 (130*2π)/4243 weeks
131.9739 .60672 (131*2π)/4243 weeks
1321.13768 .10598 (132*2π)/4243 weeks
1331.13462 .0319 (133*2π)/4243 weeks
1341.47907 .42186 (134*2π)/4243 weeks
1351.49951 .28231 (135*2π)/4243 weeks
1361.5577 .35644 (136*2π)/4243 weeks
1371.64179 .31361 (137*2π)/4243 weeks
1381.43898 .75424 (138*2π)/4243 weeks
1391.71022 .62419 (139*2π)/4243 weeks
1401.50726 .79267 (140*2π)/4243 weeks
1411.53473 .67512 (141*2π)/4243 weeks
1421.2877 .32168 (142*2π)/4243 weeks
1431.48663 .53049 (143*2π)/4243 weeks
1441.49909 .52459 (144*2π)/4243 weeks
1451.39939 .72791 (145*2π)/4243 weeks
1461.21437 .69622 (146*2π)/4243 weeks
1471.10251 .69946 (147*2π)/4243 weeks
1481.28336 .63641 (148*2π)/4243 weeks
1491.01543 .41978 (149*2π)/4243 weeks
1501.10722 .35447 (150*2π)/4243 weeks
1511.42961 .4781 (151*2π)/4243 weeks
1521.14045 .56941 (152*2π)/4243 weeks
1531.1155 .4238 (153*2π)/4243 weeks
154.98194 .44699 (154*2π)/4243 weeks
1551.15822 .49096 (155*2π)/4243 weeks
1561.23785 .47776 (156*2π)/4243 weeks
157.92445 .45094 (157*2π)/4243 weeks
1581.05989 .25475 (158*2π)/4243 weeks
1591.26425 .56063 (159*2π)/4243 weeks
1601.28216 .39489 (160*2π)/4243 weeks
1611.59498 .73613 (161*2π)/4243 weeks
1621.5057 .70995 (162*2π)/4243 weeks
163.97914 .41751 (163*2π)/4243 weeks
1641.0709 .23827 (164*2π)/4243 weeks
165.92029 .37405 (165*2π)/4243 weeks
166.98711 .30582 (166*2π)/4243 weeks
1671.24884 .48538 (167*2π)/4243 weeks
1681.0949 .54852 (168*2π)/4243 weeks
169.95567 .53903 (169*2π)/4243 weeks
170.81354 .04834 (170*2π)/4242 weeks
171.93885 -.1276 (171*2π)/4242 weeks
1721.13831 -.17478 (172*2π)/4242 weeks
1731.06933 -.01526 (173*2π)/4242 weeks
1741.17391 .14903 (174*2π)/4242 weeks
1751.41233 -.09396 (175*2π)/4242 weeks
1761.17712 -.08241 (176*2π)/4242 weeks
1771.45564 -.38998 (177*2π)/4242 weeks
1781.73076 -.17727 (178*2π)/4242 weeks
1791.77804 .10277 (179*2π)/4242 weeks
1801.52436 .11034 (180*2π)/4242 weeks
1811.55667 .52269 (181*2π)/4242 weeks
1821.34842 .37333 (182*2π)/4242 weeks
1831.39094 .62568 (183*2π)/4242 weeks
1841.10878 .36467 (184*2π)/4242 weeks
1851.30808 .31888 (185*2π)/4242 weeks
1861.31896 .47181 (186*2π)/4242 weeks
1871.04715 .26087 (187*2π)/4242 weeks
1881.04616 .06716 (188*2π)/4242 weeks
189.90061 .26685 (189*2π)/4242 weeks
1901.29538 .3853 (190*2π)/4242 weeks
1911.11304 .24903 (191*2π)/4242 weeks
192.91325 .22331 (192*2π)/4242 weeks
193.76092 .04848 (193*2π)/4242 weeks
194.79669 .06394 (194*2π)/4242 weeks
1951.06967 -.2102 (195*2π)/4242 weeks
196.81468 -.13735 (196*2π)/4242 weeks
1971.2856 -.37088 (197*2π)/4242 weeks
1981.42481 -.14359 (198*2π)/4242 weeks
1991.30055 -.11786 (199*2π)/4242 weeks
2001.35839 -.10022 (200*2π)/4242 weeks
2011.51242 -.2207 (201*2π)/4242 weeks
2021.36548 .03566 (202*2π)/4242 weeks
2031.34562 .08959 (203*2π)/4242 weeks
2041.34136 .04377 (204*2π)/4242 weeks
2051.14872 -.04599 (205*2π)/4242 weeks
2061.68677 -.13353 (206*2π)/4242 weeks
2071.34468 .3273 (207*2π)/4242 weeks
2081.51843 .11979 (208*2π)/4242 weeks
2091.45795 .00148 (209*2π)/4242 weeks
2101.16526 .01665 (210*2π)/4242 weeks
2111.32494 -.10743 (211*2π)/4242 weeks
2121.30142   (212*2π)/4242 weeks
2131.32494 .10743 (213*2π)/4242 weeks
2141.16526 -.01665 (214*2π)/4242 weeks
2151.45795 -.00148 (215*2π)/4242 weeks
2161.51843 -.11979 (216*2π)/4242 weeks
2171.34468 -.3273 (217*2π)/4242 weeks
2181.68677 .13353 (218*2π)/4242 weeks
2191.14872 .04599 (219*2π)/4242 weeks
2201.34136 -.04377 (220*2π)/4242 weeks
2211.34562 -.08959 (221*2π)/4242 weeks
2221.36548 -.03566 (222*2π)/4242 weeks
2231.51242 .2207 (223*2π)/4242 weeks
2241.35839 .10022 (224*2π)/4242 weeks
2251.30055 .11786 (225*2π)/4242 weeks
2261.42481 .14359 (226*2π)/4242 weeks
2271.2856 .37088 (227*2π)/4242 weeks
228.81468 .13735 (228*2π)/4242 weeks
2291.06967 .2102 (229*2π)/4242 weeks
230.79669 -.06394 (230*2π)/4242 weeks
231.76092 -.04848 (231*2π)/4242 weeks
232.91325 -.22331 (232*2π)/4242 weeks
2331.11304 -.24903 (233*2π)/4242 weeks
2341.29538 -.3853 (234*2π)/4242 weeks
235.90061 -.26685 (235*2π)/4242 weeks
2361.04616 -.06716 (236*2π)/4242 weeks
2371.04715 -.26087 (237*2π)/4242 weeks
2381.31896 -.47181 (238*2π)/4242 weeks
2391.30808 -.31888 (239*2π)/4242 weeks
2401.10878 -.36467 (240*2π)/4242 weeks
2411.39094 -.62568 (241*2π)/4242 weeks
2421.34842 -.37333 (242*2π)/4242 weeks
2431.55667 -.52269 (243*2π)/4242 weeks
2441.52436 -.11034 (244*2π)/4242 weeks
2451.77804 -.10277 (245*2π)/4242 weeks
2461.73076 .17727 (246*2π)/4242 weeks
2471.45564 .38998 (247*2π)/4242 weeks
2481.17712 .08241 (248*2π)/4242 weeks
2491.41233 .09396 (249*2π)/4242 weeks
2501.17391 -.14903 (250*2π)/4242 weeks
2511.06933 .01526 (251*2π)/4242 weeks
2521.13831 .17478 (252*2π)/4242 weeks
253.93885 .1276 (253*2π)/4242 weeks
254.81354 -.04834 (254*2π)/4242 weeks
255.95567 -.53903 (255*2π)/4242 weeks
2561.0949 -.54852 (256*2π)/4242 weeks
2571.24884 -.48538 (257*2π)/4242 weeks
258.98711 -.30582 (258*2π)/4242 weeks
259.92029 -.37405 (259*2π)/4242 weeks
2601.0709 -.23827 (260*2π)/4242 weeks
261.97914 -.41751 (261*2π)/4242 weeks
2621.5057 -.70995 (262*2π)/4242 weeks
2631.59498 -.73613 (263*2π)/4242 weeks
2641.28216 -.39489 (264*2π)/4242 weeks
2651.26425 -.56063 (265*2π)/4242 weeks
2661.05989 -.25475 (266*2π)/4242 weeks
267.92445 -.45094 (267*2π)/4242 weeks
2681.23785 -.47776 (268*2π)/4242 weeks
2691.15822 -.49096 (269*2π)/4242 weeks
270.98194 -.44699 (270*2π)/4242 weeks
2711.1155 -.4238 (271*2π)/4242 weeks
2721.14045 -.56941 (272*2π)/4242 weeks
2731.42961 -.4781 (273*2π)/4242 weeks
2741.10722 -.35447 (274*2π)/4242 weeks
2751.01543 -.41978 (275*2π)/4242 weeks
2761.28336 -.63641 (276*2π)/4242 weeks
2771.10251 -.69946 (277*2π)/4242 weeks
2781.21437 -.69622 (278*2π)/4242 weeks
2791.39939 -.72791 (279*2π)/4242 weeks
2801.49909 -.52459 (280*2π)/4242 weeks
2811.48663 -.53049 (281*2π)/4242 weeks
2821.2877 -.32168 (282*2π)/4242 weeks
2831.53473 -.67512 (283*2π)/4241 weeks
2841.50726 -.79267 (284*2π)/4241 weeks
2851.71022 -.62419 (285*2π)/4241 weeks
2861.43898 -.75424 (286*2π)/4241 weeks
2871.64179 -.31361 (287*2π)/4241 weeks
2881.5577 -.35644 (288*2π)/4241 weeks
2891.49951 -.28231 (289*2π)/4241 weeks
2901.47907 -.42186 (290*2π)/4241 weeks
2911.13462 -.0319 (291*2π)/4241 weeks
2921.13768 -.10598 (292*2π)/4241 weeks
293.9739 -.60672 (293*2π)/4241 weeks
2941.33966 -.41333 (294*2π)/4241 weeks
2951.43118 -.49834 (295*2π)/4241 weeks
2961.31251 -.2686 (296*2π)/4241 weeks
2971.17796 -.12061 (297*2π)/4241 weeks
2981.05578 -.4323 (298*2π)/4241 weeks
2991.0339 -.51168 (299*2π)/4241 weeks
3001.45559 -.47805 (300*2π)/4241 weeks
301.99233 -.56906 (301*2π)/4241 weeks
302.79057 -.23587 (302*2π)/4241 weeks
3031.33388 -.55843 (303*2π)/4241 weeks
304.91029 -.42145 (304*2π)/4241 weeks
305.93153 -.04235 (305*2π)/4241 weeks
306.81807 -.41167 (306*2π)/4241 weeks
307.85177 -.56149 (307*2π)/4241 weeks
308.49504 -.70689 (308*2π)/4241 weeks
309.4733 -.46837 (309*2π)/4241 weeks
310.7684 -1.11615 (310*2π)/4241 weeks
311.96201 -1.25891 (311*2π)/4241 weeks
3121.04412 -1.02234 (312*2π)/4241 weeks
313.74512 -.84745 (313*2π)/4241 weeks
3141.0002 -.75873 (314*2π)/4241 weeks
315.69637 -.96515 (315*2π)/4241 weeks
316.94518 -1.23168 (316*2π)/4241 weeks
3171.09794 -.86436 (317*2π)/4241 weeks
318.58325 -1.12476 (318*2π)/4241 weeks
319.38823 -1.6557 (319*2π)/4241 weeks
3201.00287 -1.39508 (320*2π)/4241 weeks
321.34833 -1.45858 (321*2π)/4241 weeks
322.83659 -1.64305 (322*2π)/4241 weeks
3231.30005 -1.75244 (323*2π)/4241 weeks
3241.5745 -1.49405 (324*2π)/4241 weeks
3252.13947 -1.5394 (325*2π)/4241 weeks
3261.53598 -1.51793 (326*2π)/4241 weeks
3271.18071 -1.58016 (327*2π)/4241 weeks
3281.74184 -1.3076 (328*2π)/4241 weeks
3291.92429 -1.50388 (329*2π)/4241 weeks
3301.60525 -1.44532 (330*2π)/4241 weeks
3311.66262 -1.29932 (331*2π)/4241 weeks
3321.89472 -1.00447 (332*2π)/4241 weeks
3331.75492 -.98898 (333*2π)/4241 weeks
3341.66948 -.79202 (334*2π)/4241 weeks
3351.70946 -.83339 (335*2π)/4241 weeks
3361.27084 -1.02055 (336*2π)/4241 weeks
3371.34796 -.98058 (337*2π)/4241 weeks
338.35328 -1.52348 (338*2π)/4241 weeks
339.65059 -1.05777 (339*2π)/4241 weeks
3401.39355 -2.03777 (340*2π)/4241 weeks
3411.41296 -1.90939 (341*2π)/4241 weeks
3421.81131 -1.8379 (342*2π)/4241 weeks
343.98363 -1.70444 (343*2π)/4241 weeks
3441.74261 -1.69265 (344*2π)/4241 weeks
3451.29221 -1.89895 (345*2π)/4241 weeks
3461.47984 -1.38785 (346*2π)/4241 weeks
3471.64984 -1.6116 (347*2π)/4241 weeks
3481.32189 -.85342 (348*2π)/4241 weeks
3491.33716 -1.61459 (349*2π)/4241 weeks
350.9335 -1.8956 (350*2π)/4241 weeks
3511.33307 -2.406 (351*2π)/4241 weeks
3521.31949 -2.07002 (352*2π)/4241 weeks
3532.44739 -2.09511 (353*2π)/4241 weeks
3542.04945 -1.73584 (354*2π)/4241 weeks
3552.04131 -.89976 (355*2π)/4241 weeks
3561.22662 -.9724 (356*2π)/4241 weeks
3571.41477 -.96096 (357*2π)/4241 weeks
3581.74769 -1.55644 (358*2π)/4241 weeks
3591.18777 -1.82822 (359*2π)/4241 weeks
3602.13859 -2.04813 (360*2π)/4241 weeks
3611.90365 -1.28057 (361*2π)/4241 weeks
3621.73496 -1.54885 (362*2π)/4241 weeks
3632.16022 -1.66428 (363*2π)/4241 weeks
3641.95151 -1.14067 (364*2π)/4241 weeks
3651.34381 -1.63374 (365*2π)/4241 weeks
366.76725 -2.06513 (366*2π)/4241 weeks
3671.23977 -1.63845 (367*2π)/4241 weeks
3682.05106 -1.38074 (368*2π)/4241 weeks
3692.11824 -1.65524 (369*2π)/4241 weeks
3701.34461 -1.51166 (370*2π)/4241 weeks
371.58603 -1.03176 (371*2π)/4241 weeks
372.9811 -1.74476 (372*2π)/4241 weeks
373.29249 -2.33482 (373*2π)/4241 weeks
3741.45864 -2.45064 (374*2π)/4241 weeks
3751.69289 -2.47374 (375*2π)/4241 weeks
3761.48072 -2.6313 (376*2π)/4241 weeks
3771.07539 -3.19297 (377*2π)/4241 weeks
3781.81121 -3.14872 (378*2π)/4241 weeks
379.95697 -2.05291 (379*2π)/4241 weeks
3801.62158 -1.54914 (380*2π)/4241 weeks
3811.48938 -2.22342 (381*2π)/4241 weeks
3821.58847 -1.48892 (382*2π)/4241 weeks
3831.04402 -2.4058 (383*2π)/4241 weeks
3841.45628 -1.64771 (384*2π)/4241 weeks
3851.28271 -2.1217 (385*2π)/4241 weeks
386.91991 -3.07767 (386*2π)/4241 weeks
3871.19282 -1.87048 (387*2π)/4241 weeks
388-.69141 -2.44374 (388*2π)/4241 weeks
389.58809 -2.71608 (389*2π)/4241 weeks
390.49359 -3.16549 (390*2π)/4241 weeks
391-1.26902 -3.49269 (391*2π)/4241 weeks
392.23395 -4.88974 (392*2π)/4241 weeks
393.66729 -4.56746 (393*2π)/4241 weeks
3941.08866 -5.45802 (394*2π)/4241 weeks
3952.19186 -5.5955 (395*2π)/4241 weeks
3961.59878 -3.84934 (396*2π)/4241 weeks
3971.84546 -5.59813 (397*2π)/4241 weeks
3981.87965 -5.56384 (398*2π)/4241 weeks
3992.29776 -4.87992 (399*2π)/4241 weeks
4002.63569 -4.42224 (400*2π)/4241 weeks
4013.82889 -4.99999 (401*2π)/4241 weeks
4024.15147 -5.04954 (402*2π)/4241 weeks
4033.45098 -6.17907 (403*2π)/4241 weeks
4042.35569 -6.72007 (404*2π)/4241 weeks
4053.20961 -2.97959 (405*2π)/4241 weeks
4062.67434 -3.03224 (406*2π)/4241 weeks
407-.93784 -5.25339 (407*2π)/4241 weeks
4083.24875 -6.06294 (408*2π)/4241 weeks
4093.24265 -8.26088 (409*2π)/4241 weeks
4105.49092 -7.78556 (410*2π)/4241 weeks
4114.76555 -7.3576 (411*2π)/4241 weeks
4123.17402 -6.64234 (412*2π)/4241 weeks
4135.25134 -6.88858 (413*2π)/4241 weeks
4142.6703 -7.17138 (414*2π)/4241 weeks
4151.99887 -6.77601 (415*2π)/4241 weeks
4161.94306 -10.82942 (416*2π)/4241 weeks
4177.00843 -14.42424 (417*2π)/4241 weeks
4182.37815 -18.18702 (418*2π)/4241 weeks
4198.26693 -23.32022 (419*2π)/4241 weeks
4205.97279 -28.79568 (420*2π)/4241 weeks
4218.47565 -29.64076 (421*2π)/4241 weeks
42218.32764 -47.33772 (422*2π)/4241 weeks

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