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# Fourier Analysis of TLL (PROSHARES ULTRASHORT TELECOMMUNICATIONS PROSHARES ULTRASHORT TELECOMMUNICATIONS)

TLL (PROSHARES ULTRASHORT TELECOMMUNICATIONS PROSHARES ULTRASHORT TELECOMMUNICATIONS) appears to have interesting cyclic behaviour every 24 weeks (51.7269*sine), 23 weeks (48.5627*sine), and 26 weeks (46.6587*sine).

TLL (PROSHARES ULTRASHORT TELECOMMUNICATIONS PROSHARES ULTRASHORT TELECOMMUNICATIONS) has an average price of 322.48 (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.

## Fourier Analysis

Using data from 4/1/2008 to 1/22/2018 for TLL (PROSHARES ULTRASHORT TELECOMMUNICATIONS PROSHARES ULTRASHORT TELECOMMUNICATIONS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0322.4799   0
1287.7733 251.313 (1*2π)/409409 weeks
2160.9427 266.5031 (2*2π)/409205 weeks
343.26546 238.7327 (3*2π)/409136 weeks
4-16.64334 195.2257 (4*2π)/409102 weeks
5-64.30586 142.9894 (5*2π)/40982 weeks
6-68.16499 80.49467 (6*2π)/40968 weeks
7-59.11168 48.10869 (7*2π)/40958 weeks
8-44.77372 17.81653 (8*2π)/40951 weeks
9-23.51677 -2.38574 (9*2π)/40945 weeks
10-.8237 -8.95163 (10*2π)/40941 weeks
1124.60162 -6.41709 (11*2π)/40937 weeks
1232.64562 8.56294 (12*2π)/40934 weeks
1343.25616 16.8548 (13*2π)/40931 weeks
1438.19112 33.75432 (14*2π)/40929 weeks
1531.54195 39.87625 (15*2π)/40927 weeks
1622.05591 46.65869 (16*2π)/40926 weeks
1710.6672 51.72687 (17*2π)/40924 weeks
18-7.30681 48.56272 (18*2π)/40923 weeks
19-20.0361 39.20047 (19*2π)/40922 weeks
20-27.73697 19.06594 (20*2π)/40920 weeks
21-22.26945 5.58579 (21*2π)/40919 weeks
22-15.38825 -7.21436 (22*2π)/40919 weeks
23-1.43067 -15.72618 (23*2π)/40918 weeks
2415.16845 -14.2121 (24*2π)/40917 weeks
2528.5659 -6.15018 (25*2π)/40916 weeks
2632.47045 9.60838 (26*2π)/40916 weeks
2730.54751 20.33873 (27*2π)/40915 weeks
2823.30883 27.43656 (28*2π)/40915 weeks
2916.53585 32.69131 (29*2π)/40914 weeks
307.49099 31.74855 (30*2π)/40914 weeks
31-2.8976 25.55961 (31*2π)/40913 weeks
32-.30835 15.69169 (32*2π)/40913 weeks
334.60961 12.34272 (33*2π)/40912 weeks
348.39781 14.96093 (34*2π)/40912 weeks
356.49896 19.74658 (35*2π)/40912 weeks
362.50176 18.69066 (36*2π)/40911 weeks
37-1.06224 15.39253 (37*2π)/40911 weeks
38-1.92226 13.47301 (38*2π)/40911 weeks
39-1.38592 10.99182 (39*2π)/40910 weeks
40-2.3902 8.99043 (40*2π)/40910 weeks
41-1.20568 5.05623 (41*2π)/40910 weeks
423.84853 2.94018 (42*2π)/40910 weeks
437.45298 4.69186 (43*2π)/40910 weeks
4410.10436 6.81426 (44*2π)/4099 weeks
4510.52605 11.6661 (45*2π)/4099 weeks
467.45279 13.88841 (46*2π)/4099 weeks
476.62198 14.6249 (47*2π)/4099 weeks
485.22574 14.6742 (48*2π)/4099 weeks
495.76806 15.25734 (49*2π)/4098 weeks
501.67727 17.79104 (50*2π)/4098 weeks
51-.70875 15.68095 (51*2π)/4098 weeks
52-5.19057 14.75141 (52*2π)/4098 weeks
53-7.76402 9.29188 (53*2π)/4098 weeks
54-6.9824 3.87698 (54*2π)/4098 weeks
55-4.44482 -1.83089 (55*2π)/4097 weeks
561.65507 -3.45823 (56*2π)/4097 weeks
573.57821 -2.44726 (57*2π)/4097 weeks
589.37601 -4.17577 (58*2π)/4097 weeks
5914.06211 2.54449 (59*2π)/4097 weeks
6013.93852 8.1939 (60*2π)/4097 weeks
6111.45965 13.65175 (61*2π)/4097 weeks
626.22637 15.3247 (62*2π)/4097 weeks
631.29207 15.38293 (63*2π)/4096 weeks
64-1.82185 12.45202 (64*2π)/4096 weeks
65-3.05917 9.15273 (65*2π)/4096 weeks
66-1.64926 6.8158 (66*2π)/4096 weeks
67-.93623 4.64435 (67*2π)/4096 weeks
68.12422 4.22532 (68*2π)/4096 weeks
69.53918 3.07506 (69*2π)/4096 weeks
701.13699 2.63924 (70*2π)/4096 weeks
711.26158 .23645 (71*2π)/4096 weeks
724.00684 -1.58366 (72*2π)/4096 weeks
738.02348 -1.85618 (73*2π)/4096 weeks
7411.54167 .27366 (74*2π)/4096 weeks
7513.63297 4.29298 (75*2π)/4095 weeks
7613.33388 9.36562 (76*2π)/4095 weeks
7710.26995 14.41751 (77*2π)/4095 weeks
785.38828 16.81788 (78*2π)/4095 weeks
79-.98569 16.44065 (79*2π)/4095 weeks
80-5.08014 13.64784 (80*2π)/4095 weeks
81-8.50261 8.64112 (81*2π)/4095 weeks
82-8.4935 3.53034 (82*2π)/4095 weeks
83-6.81183 -1.90777 (83*2π)/4095 weeks
84-2.88762 -5.17432 (84*2π)/4095 weeks
852.75495 -7.5042 (85*2π)/4095 weeks
868.84409 -5.97001 (86*2π)/4095 weeks
8712.86714 -1.22999 (87*2π)/4095 weeks
8813.93858 3.00687 (88*2π)/4095 weeks
8913.02622 7.86114 (89*2π)/4095 weeks
9010.66308 11.64455 (90*2π)/4095 weeks
916.58383 13.56217 (91*2π)/4094 weeks
921.44935 13.2758 (92*2π)/4094 weeks
93-2.26346 11.73641 (93*2π)/4094 weeks
94-5.20934 7.47224 (94*2π)/4094 weeks
95-5.28136 3.13038 (95*2π)/4094 weeks
96-3.61411 -1.06055 (96*2π)/4094 weeks
97.49663 -3.53269 (97*2π)/4094 weeks
984.97808 -2.75261 (98*2π)/4094 weeks
996.81126 .57633 (99*2π)/4094 weeks
1007.19438 2.95857 (100*2π)/4094 weeks
1016.60307 5.3505 (101*2π)/4094 weeks
1024.8522 6.77294 (102*2π)/4094 weeks
1033.77439 6.72823 (103*2π)/4094 weeks
1041.7124 7.13226 (104*2π)/4094 weeks
105-.0674 6.28175 (105*2π)/4094 weeks
106-1.68039 4.62446 (106*2π)/4094 weeks
107-2.63743 .60549 (107*2π)/4094 weeks
108.74114 -2.52736 (108*2π)/4094 weeks
1094.63049 -3.03794 (109*2π)/4094 weeks
1108.29186 -1.60147 (110*2π)/4094 weeks
1119.85455 2.0086 (111*2π)/4094 weeks
1129.41697 6.027 (112*2π)/4094 weeks
1136.42741 8.97549 (113*2π)/4094 weeks
1142.93775 9.22631 (114*2π)/4094 weeks
115-.05945 8.26351 (115*2π)/4094 weeks
116-2.21329 5.97437 (116*2π)/4094 weeks
117-3.64956 3.30234 (117*2π)/4093 weeks
118-2.82256 -.64886 (118*2π)/4093 weeks
119-.16426 -1.8282 (119*2π)/4093 weeks
1201.62217 -2.56089 (120*2π)/4093 weeks
1214.51321 -2.67145 (121*2π)/4093 weeks
1227.28657 -2.0829 (122*2π)/4093 weeks
1239.81609 1.22468 (123*2π)/4093 weeks
1249.95843 4.99201 (124*2π)/4093 weeks
1258.2242 8.4726 (125*2π)/4093 weeks
1264.54908 10.51517 (126*2π)/4093 weeks
127.98173 10.05117 (127*2π)/4093 weeks
128-2.57473 8.68394 (128*2π)/4093 weeks
129-4.37776 5.19875 (129*2π)/4093 weeks
130-5.7085 2.50664 (130*2π)/4093 weeks
131-5.24707 -1.4666 (131*2π)/4093 weeks
132-3.19278 -4.51444 (132*2π)/4093 weeks
133-.08201 -7.2696 (133*2π)/4093 weeks
1344.76686 -7.33971 (134*2π)/4093 weeks
1358.24113 -5.8287 (135*2π)/4093 weeks
13611.01043 -1.45728 (136*2π)/4093 weeks
13710.77857 2.26617 (137*2π)/4093 weeks
1389.23097 5.97302 (138*2π)/4093 weeks
1396.54825 7.75236 (139*2π)/4093 weeks
1403.35945 8.64185 (140*2π)/4093 weeks
141-.08612 7.91086 (141*2π)/4093 weeks
142-1.93119 5.22391 (142*2π)/4093 weeks
143-2.4082 2.72116 (143*2π)/4093 weeks
144-1.931 .62943 (144*2π)/4093 weeks
145-1.58913 -.97738 (145*2π)/4093 weeks
146.59845 -3.11209 (146*2π)/4093 weeks
1472.39254 -3.07438 (147*2π)/4093 weeks
1484.44938 -3.07788 (148*2π)/4093 weeks
1495.75053 -1.78329 (149*2π)/4093 weeks
1507.08401 -.88667 (150*2π)/4093 weeks
1517.23186 1.59797 (151*2π)/4093 weeks
1525.51823 2.29316 (152*2π)/4093 weeks
1535.2351 3.24522 (153*2π)/4093 weeks
1544.02086 4.0291 (154*2π)/4093 weeks
1552.49011 4.59525 (155*2π)/4093 weeks
156.38133 4.22057 (156*2π)/4093 weeks
157-.87478 2.27613 (157*2π)/4093 weeks
158-1.38551 .60834 (158*2π)/4093 weeks
159-.84656 -2.3386 (159*2π)/4093 weeks
1601.85699 -3.57301 (160*2π)/4093 weeks
1614.68736 -3.0126 (161*2π)/4093 weeks
1626.15666 -.42937 (162*2π)/4093 weeks
1634.98979 1.13537 (163*2π)/4093 weeks
1643.6162 .99774 (164*2π)/4092 weeks
1653.43618 .15792 (165*2π)/4092 weeks
1663.1375 -.78108 (166*2π)/4092 weeks
1674.10917 -1.70417 (167*2π)/4092 weeks
1685.68341 -1.91961 (168*2π)/4092 weeks
1697.74492 -.98034 (169*2π)/4092 weeks
1707.90896 1.48262 (170*2π)/4092 weeks
1717.39016 3.24006 (171*2π)/4092 weeks
1725.99312 4.9834 (172*2π)/4092 weeks
1733.70466 5.95562 (173*2π)/4092 weeks
1741.1699 5.63534 (174*2π)/4092 weeks
175-1.17337 3.97434 (175*2π)/4092 weeks
176-1.54091 .84596 (176*2π)/4092 weeks
177-.68143 -.47218 (177*2π)/4092 weeks
178-.21549 -2.52427 (178*2π)/4092 weeks
1791.70289 -3.03719 (179*2π)/4092 weeks
1803.44328 -3.88544 (180*2π)/4092 weeks
1815.41748 -2.87643 (181*2π)/4092 weeks
1826.52134 -2.59851 (182*2π)/4092 weeks
1838.44223 -1.36279 (183*2π)/4092 weeks
1848.78724 .98198 (184*2π)/4092 weeks
1859.51607 2.69062 (185*2π)/4092 weeks
1868.10017 5.34912 (186*2π)/4092 weeks
1876.99501 6.7189 (187*2π)/4092 weeks
1884.31049 10.00151 (188*2π)/4092 weeks
189-.90489 10.28101 (189*2π)/4092 weeks
190-5.79204 7.7141 (190*2π)/4092 weeks
191-9.58164 2.54753 (191*2π)/4092 weeks
192-9.03631 -4.14579 (192*2π)/4092 weeks
193-6.06273 -9.54715 (193*2π)/4092 weeks
194.19448 -13.03279 (194*2π)/4092 weeks
1956.62665 -12.27508 (195*2π)/4092 weeks
19611.32911 -8.90369 (196*2π)/4092 weeks
19714.0643 -4.25934 (197*2π)/4092 weeks
19815.70407 .9235 (198*2π)/4092 weeks
19914.27158 6.90846 (199*2π)/4092 weeks
2009.21281 11.43904 (200*2π)/4092 weeks
2013.74365 12.37241 (201*2π)/4092 weeks
202-1.72711 11.07283 (202*2π)/4092 weeks
203-5.27366 7.69048 (203*2π)/4092 weeks
204-8.49781 3.19931 (204*2π)/4092 weeks
205-8.49781 -3.19931 (205*2π)/4092 weeks
206-5.27366 -7.69048 (206*2π)/4092 weeks
207-1.72711 -11.07283 (207*2π)/4092 weeks
2083.74365 -12.37241 (208*2π)/4092 weeks
2099.21281 -11.43904 (209*2π)/4092 weeks
21014.27158 -6.90846 (210*2π)/4092 weeks
21115.70407 -.9235 (211*2π)/4092 weeks
21214.0643 4.25934 (212*2π)/4092 weeks
21311.32911 8.90369 (213*2π)/4092 weeks
2146.62665 12.27508 (214*2π)/4092 weeks
215.19448 13.03279 (215*2π)/4092 weeks
216-6.06273 9.54715 (216*2π)/4092 weeks
217-9.03631 4.14579 (217*2π)/4092 weeks
218-9.58164 -2.54753 (218*2π)/4092 weeks
219-5.79204 -7.7141 (219*2π)/4092 weeks
220-.90489 -10.28101 (220*2π)/4092 weeks
2214.31049 -10.00151 (221*2π)/4092 weeks
2226.99501 -6.7189 (222*2π)/4092 weeks
2238.10017 -5.34912 (223*2π)/4092 weeks
2249.51607 -2.69062 (224*2π)/4092 weeks
2258.78724 -.98198 (225*2π)/4092 weeks
2268.44223 1.36279 (226*2π)/4092 weeks
2276.52134 2.59851 (227*2π)/4092 weeks
2285.41748 2.87643 (228*2π)/4092 weeks
2293.44328 3.88544 (229*2π)/4092 weeks
2301.70289 3.03719 (230*2π)/4092 weeks
231-.21549 2.52427 (231*2π)/4092 weeks
232-.68143 .47218 (232*2π)/4092 weeks
233-1.54091 -.84596 (233*2π)/4092 weeks
234-1.17337 -3.97434 (234*2π)/4092 weeks
2351.1699 -5.63534 (235*2π)/4092 weeks
2363.70466 -5.95562 (236*2π)/4092 weeks
2375.99312 -4.9834 (237*2π)/4092 weeks
2387.39016 -3.24006 (238*2π)/4092 weeks
2397.90896 -1.48262 (239*2π)/4092 weeks
2407.74492 .98034 (240*2π)/4092 weeks
2415.68341 1.91961 (241*2π)/4092 weeks
2424.10917 1.70417 (242*2π)/4092 weeks
2433.1375 .78108 (243*2π)/4092 weeks
2443.43618 -.15792 (244*2π)/4092 weeks
2453.6162 -.99774 (245*2π)/4092 weeks
2464.98979 -1.13537 (246*2π)/4092 weeks
2476.15666 .42937 (247*2π)/4092 weeks
2484.68736 3.0126 (248*2π)/4092 weeks
2491.85699 3.57301 (249*2π)/4092 weeks
250-.84656 2.3386 (250*2π)/4092 weeks
251-1.38551 -.60834 (251*2π)/4092 weeks
252-.87478 -2.27613 (252*2π)/4092 weeks
253.38133 -4.22057 (253*2π)/4092 weeks
2542.49011 -4.59525 (254*2π)/4092 weeks
2554.02086 -4.0291 (255*2π)/4092 weeks
2565.2351 -3.24522 (256*2π)/4092 weeks
2575.51823 -2.29316 (257*2π)/4092 weeks
2587.23186 -1.59797 (258*2π)/4092 weeks
2597.08401 .88667 (259*2π)/4092 weeks
2605.75053 1.78329 (260*2π)/4092 weeks
2614.44938 3.07788 (261*2π)/4092 weeks
2622.39254 3.07438 (262*2π)/4092 weeks
263.59845 3.11209 (263*2π)/4092 weeks
264-1.58913 .97738 (264*2π)/4092 weeks
265-1.931 -.62943 (265*2π)/4092 weeks
266-2.4082 -2.72116 (266*2π)/4092 weeks
267-1.93119 -5.22391 (267*2π)/4092 weeks
268-.08612 -7.91086 (268*2π)/4092 weeks
2693.35945 -8.64185 (269*2π)/4092 weeks
2706.54825 -7.75236 (270*2π)/4092 weeks
2719.23097 -5.97302 (271*2π)/4092 weeks
27210.77857 -2.26617 (272*2π)/4092 weeks
27311.01043 1.45728 (273*2π)/4091 weeks
2748.24113 5.8287 (274*2π)/4091 weeks
2754.76686 7.33971 (275*2π)/4091 weeks
276-.08201 7.2696 (276*2π)/4091 weeks
277-3.19278 4.51444 (277*2π)/4091 weeks
278-5.24707 1.4666 (278*2π)/4091 weeks
279-5.7085 -2.50664 (279*2π)/4091 weeks
280-4.37776 -5.19875 (280*2π)/4091 weeks
281-2.57473 -8.68394 (281*2π)/4091 weeks
282.98173 -10.05117 (282*2π)/4091 weeks
2834.54908 -10.51517 (283*2π)/4091 weeks
2848.2242 -8.4726 (284*2π)/4091 weeks
2859.95843 -4.99201 (285*2π)/4091 weeks
2869.81609 -1.22468 (286*2π)/4091 weeks
2877.28657 2.0829 (287*2π)/4091 weeks
2884.51321 2.67145 (288*2π)/4091 weeks
2891.62217 2.56089 (289*2π)/4091 weeks
290-.16426 1.8282 (290*2π)/4091 weeks
291-2.82256 .64886 (291*2π)/4091 weeks
292-3.64956 -3.30234 (292*2π)/4091 weeks
293-2.21329 -5.97437 (293*2π)/4091 weeks
294-.05945 -8.26351 (294*2π)/4091 weeks
2952.93775 -9.22631 (295*2π)/4091 weeks
2966.42741 -8.97549 (296*2π)/4091 weeks
2979.41697 -6.027 (297*2π)/4091 weeks
2989.85455 -2.0086 (298*2π)/4091 weeks
2998.29186 1.60147 (299*2π)/4091 weeks
3004.63049 3.03794 (300*2π)/4091 weeks
301.74114 2.52736 (301*2π)/4091 weeks
302-2.63743 -.60549 (302*2π)/4091 weeks
303-1.68039 -4.62446 (303*2π)/4091 weeks
304-.0674 -6.28175 (304*2π)/4091 weeks
3051.7124 -7.13226 (305*2π)/4091 weeks
3063.77439 -6.72823 (306*2π)/4091 weeks
3074.8522 -6.77294 (307*2π)/4091 weeks
3086.60307 -5.3505 (308*2π)/4091 weeks
3097.19438 -2.95857 (309*2π)/4091 weeks
3106.81126 -.57633 (310*2π)/4091 weeks
3114.97808 2.75261 (311*2π)/4091 weeks
312.49663 3.53269 (312*2π)/4091 weeks
313-3.61411 1.06055 (313*2π)/4091 weeks
314-5.28136 -3.13038 (314*2π)/4091 weeks
315-5.20934 -7.47224 (315*2π)/4091 weeks
316-2.26346 -11.73641 (316*2π)/4091 weeks
3171.44935 -13.2758 (317*2π)/4091 weeks
3186.58383 -13.56217 (318*2π)/4091 weeks
31910.66308 -11.64455 (319*2π)/4091 weeks
32013.02622 -7.86114 (320*2π)/4091 weeks
32113.93858 -3.00687 (321*2π)/4091 weeks
32212.86714 1.22999 (322*2π)/4091 weeks
3238.84409 5.97001 (323*2π)/4091 weeks
3242.75495 7.5042 (324*2π)/4091 weeks
325-2.88762 5.17432 (325*2π)/4091 weeks
326-6.81183 1.90777 (326*2π)/4091 weeks
327-8.4935 -3.53034 (327*2π)/4091 weeks
328-8.50261 -8.64112 (328*2π)/4091 weeks
329-5.08014 -13.64784 (329*2π)/4091 weeks
330-.98569 -16.44065 (330*2π)/4091 weeks
3315.38828 -16.81788 (331*2π)/4091 weeks
33210.26995 -14.41751 (332*2π)/4091 weeks
33313.33388 -9.36562 (333*2π)/4091 weeks
33413.63297 -4.29298 (334*2π)/4091 weeks
33511.54167 -.27366 (335*2π)/4091 weeks
3368.02348 1.85618 (336*2π)/4091 weeks
3374.00684 1.58366 (337*2π)/4091 weeks
3381.26158 -.23645 (338*2π)/4091 weeks
3391.13699 -2.63924 (339*2π)/4091 weeks
340.53918 -3.07506 (340*2π)/4091 weeks
341.12422 -4.22532 (341*2π)/4091 weeks
342-.93623 -4.64435 (342*2π)/4091 weeks
343-1.64926 -6.8158 (343*2π)/4091 weeks
344-3.05917 -9.15273 (344*2π)/4091 weeks
345-1.82185 -12.45202 (345*2π)/4091 weeks
3461.29207 -15.38293 (346*2π)/4091 weeks
3476.22637 -15.3247 (347*2π)/4091 weeks
34811.45965 -13.65175 (348*2π)/4091 weeks
34913.93852 -8.1939 (349*2π)/4091 weeks
35014.06211 -2.54449 (350*2π)/4091 weeks
3519.37601 4.17577 (351*2π)/4091 weeks
3523.57821 2.44726 (352*2π)/4091 weeks
3531.65507 3.45823 (353*2π)/4091 weeks
354-4.44482 1.83089 (354*2π)/4091 weeks
355-6.9824 -3.87698 (355*2π)/4091 weeks
356-7.76402 -9.29188 (356*2π)/4091 weeks
357-5.19057 -14.75141 (357*2π)/4091 weeks
358-.70875 -15.68095 (358*2π)/4091 weeks
3591.67727 -17.79104 (359*2π)/4091 weeks
3605.76806 -15.25734 (360*2π)/4091 weeks
3615.22574 -14.6742 (361*2π)/4091 weeks
3626.62198 -14.6249 (362*2π)/4091 weeks
3637.45279 -13.88841 (363*2π)/4091 weeks
36410.52605 -11.6661 (364*2π)/4091 weeks
36510.10436 -6.81426 (365*2π)/4091 weeks
3667.45298 -4.69186 (366*2π)/4091 weeks
3673.84853 -2.94018 (367*2π)/4091 weeks
368-1.20568 -5.05623 (368*2π)/4091 weeks
369-2.3902 -8.99043 (369*2π)/4091 weeks
370-1.38592 -10.99182 (370*2π)/4091 weeks
371-1.92226 -13.47301 (371*2π)/4091 weeks
372-1.06224 -15.39253 (372*2π)/4091 weeks
3732.50176 -18.69066 (373*2π)/4091 weeks
3746.49896 -19.74658 (374*2π)/4091 weeks
3758.39781 -14.96093 (375*2π)/4091 weeks
3764.60961 -12.34272 (376*2π)/4091 weeks
377-.30835 -15.69169 (377*2π)/4091 weeks
378-2.8976 -25.55961 (378*2π)/4091 weeks
3797.49099 -31.74855 (379*2π)/4091 weeks
38016.53585 -32.69131 (380*2π)/4091 weeks
38123.30883 -27.43656 (381*2π)/4091 weeks
38230.54751 -20.33873 (382*2π)/4091 weeks
38332.47045 -9.60838 (383*2π)/4091 weeks
38428.5659 6.15018 (384*2π)/4091 weeks
38515.16845 14.2121 (385*2π)/4091 weeks
386-1.43067 15.72618 (386*2π)/4091 weeks
387-15.38825 7.21436 (387*2π)/4091 weeks
388-22.26945 -5.58579 (388*2π)/4091 weeks
389-27.73697 -19.06594 (389*2π)/4091 weeks
390-20.0361 -39.20047 (390*2π)/4091 weeks
391-7.30681 -48.56272 (391*2π)/4091 weeks
39210.6672 -51.72687 (392*2π)/4091 weeks
39322.05591 -46.65869 (393*2π)/4091 weeks
39431.54195 -39.87625 (394*2π)/4091 weeks
39538.19112 -33.75432 (395*2π)/4091 weeks
39643.25616 -16.8548 (396*2π)/4091 weeks
39732.64562 -8.56294 (397*2π)/4091 weeks
39824.60162 6.41709 (398*2π)/4091 weeks
399-.8237 8.95163 (399*2π)/4091 weeks
400-23.51677 2.38574 (400*2π)/4091 weeks
401-44.77372 -17.81653 (401*2π)/4091 weeks
402-59.11168 -48.10869 (402*2π)/4091 weeks
403-68.16499 -80.49467 (403*2π)/4091 weeks
404-64.30586 -142.9894 (404*2π)/4091 weeks
405-16.64334 -195.2257 (405*2π)/4091 weeks
40643.26546 -238.7327 (406*2π)/4091 weeks
407160.9427 -266.5031 (407*2π)/4091 weeks