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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 (52.2301*sine), 23 weeks (48.3599*sine), and 26 weeks (47.1843*sine).

TLL (PROSHARES ULTRASHORT TELECOMMUNICATIONS PROSHARES ULTRASHORT TELECOMMUNICATIONS) has an average price of 323.26 (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 4/1/2008 to 1/16/2018 for TLL (PROSHARES ULTRASHORT TELECOMMUNICATIONS PROSHARES ULTRASHORT TELECOMMUNICATIONS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0323.2649   0 
1288.2102 251.8154 (1*2π)/408408 weeks
2160.8622 267.1116 (2*2π)/408204 weeks
342.94392 238.7306 (3*2π)/408136 weeks
4-17.13611 195.0548 (4*2π)/408102 weeks
5-64.87273 142.2438 (5*2π)/40882 weeks
6-68.20469 79.80936 (6*2π)/40868 weeks
7-59.31963 47.44842 (7*2π)/40858 weeks
8-44.73951 17.25471 (8*2π)/40851 weeks
9-23.24528 -2.77429 (9*2π)/40845 weeks
10-.59468 -9.13783 (10*2π)/40841 weeks
1124.94822 -5.92669 (11*2π)/40837 weeks
1232.49691 8.90177 (12*2π)/40834 weeks
1343.41529 17.87903 (13*2π)/40831 weeks
1437.89221 34.45591 (14*2π)/40829 weeks
1531.47827 40.60474 (15*2π)/40827 weeks
1621.88093 47.18432 (16*2π)/40826 weeks
1710.22727 52.23005 (17*2π)/40824 weeks
18-7.68437 48.35992 (18*2π)/40823 weeks
19-20.50302 38.73032 (19*2π)/40821 weeks
20-27.31497 18.05654 (20*2π)/40820 weeks
21-21.9114 4.86187 (21*2π)/40819 weeks
22-14.63933 -8.04034 (22*2π)/40819 weeks
23-.34902 -16.24822 (23*2π)/40818 weeks
2416.04443 -14.17095 (24*2π)/40817 weeks
2529.33842 -5.5675 (25*2π)/40816 weeks
2632.25021 10.10877 (26*2π)/40816 weeks
2730.06397 20.97265 (27*2π)/40815 weeks
2822.72258 27.64483 (28*2π)/40815 weeks
2915.46379 32.99413 (29*2π)/40814 weeks
306.67455 31.92676 (30*2π)/40814 weeks
31-3.41923 24.66924 (31*2π)/40813 weeks
32-.14487 15.58034 (32*2π)/40813 weeks
335.03856 12.63169 (33*2π)/40812 weeks
348.53982 15.58158 (34*2π)/40812 weeks
355.99647 20.19015 (35*2π)/40812 weeks
362.36335 19.01187 (36*2π)/40811 weeks
37-.70892 15.24827 (37*2π)/40811 weeks
38-1.76064 13.17984 (38*2π)/40811 weeks
39-1.13816 10.90515 (39*2π)/40810 weeks
40-2.19179 8.50641 (40*2π)/40810 weeks
41-.74035 4.46715 (41*2π)/40810 weeks
424.46758 2.89036 (42*2π)/40810 weeks
437.80622 4.73403 (43*2π)/4089 weeks
4410.50979 7.04017 (44*2π)/4089 weeks
4510.3186 11.86949 (45*2π)/4089 weeks
467.13465 13.54018 (46*2π)/4089 weeks
476.13267 14.5401 (47*2π)/4089 weeks
484.81105 14.56322 (48*2π)/4089 weeks
495.43111 15.81571 (49*2π)/4088 weeks
50.75283 17.68929 (50*2π)/4088 weeks
51-1.15536 15.98661 (51*2π)/4088 weeks
52-5.9538 14.39015 (52*2π)/4088 weeks
53-7.99326 8.80376 (53*2π)/4088 weeks
54-6.89706 3.6156 (54*2π)/4088 weeks
55-3.52129 -2.09761 (55*2π)/4087 weeks
562.58051 -2.95805 (56*2π)/4087 weeks
574.14818 -2.72408 (57*2π)/4087 weeks
5810.98044 -3.64572 (58*2π)/4087 weeks
5914.42079 3.29923 (59*2π)/4087 weeks
6013.97653 8.81354 (60*2π)/4087 weeks
6110.79019 14.15071 (61*2π)/4087 weeks
625.79138 15.25493 (62*2π)/4087 weeks
63.62713 14.689 (63*2π)/4086 weeks
64-2.20714 11.64793 (64*2π)/4086 weeks
65-3.26796 8.22601 (65*2π)/4086 weeks
66-2.02692 6.53182 (66*2π)/4086 weeks
67-.90706 4.4932 (67*2π)/4086 weeks
68-.13672 4.18605 (68*2π)/4086 weeks
69.48503 3.04544 (69*2π)/4086 weeks
70.80166 2.67167 (70*2π)/4086 weeks
711.52416 .00502 (71*2π)/4086 weeks
724.49819 -1.54232 (72*2π)/4086 weeks
738.72823 -1.24769 (73*2π)/4086 weeks
7412.24389 1.23645 (74*2π)/4086 weeks
7514.11085 5.45637 (75*2π)/4085 weeks
7613.4088 10.42164 (76*2π)/4085 weeks
779.59943 15.03053 (77*2π)/4085 weeks
784.49411 17.12572 (78*2π)/4085 weeks
79-1.7534 15.74665 (79*2π)/4085 weeks
80-5.85274 12.86169 (80*2π)/4085 weeks
81-8.59023 7.30569 (81*2π)/4085 weeks
82-8.43919 2.34532 (82*2π)/4085 weeks
83-6.0163 -2.99622 (83*2π)/4085 weeks
84-2.14227 -6.06031 (84*2π)/4085 weeks
853.96894 -7.61368 (85*2π)/4085 weeks
869.80735 -5.36156 (86*2π)/4085 weeks
8712.86961 -.19672 (87*2π)/4085 weeks
8813.89163 4.20011 (88*2π)/4085 weeks
8912.41757 8.78446 (89*2π)/4085 weeks
909.54832 12.57147 (90*2π)/4085 weeks
915.48053 14.27916 (91*2π)/4084 weeks
92.77049 13.14394 (92*2π)/4084 weeks
93-3.16194 11.23514 (93*2π)/4084 weeks
94-5.27758 6.59164 (94*2π)/4084 weeks
95-4.97007 2.33284 (95*2π)/4084 weeks
96-2.61949 -1.7517 (96*2π)/4084 weeks
971.89289 -3.54572 (97*2π)/4084 weeks
986.18562 -2.03808 (98*2π)/4084 weeks
997.21337 .96729 (99*2π)/4084 weeks
1007.355 3.30254 (100*2π)/4084 weeks
1016.30308 5.55275 (101*2π)/4084 weeks
1024.27643 6.5753 (102*2π)/4084 weeks
1033.40806 6.93105 (103*2π)/4084 weeks
1041.19657 6.80467 (104*2π)/4084 weeks
105-.62434 5.7789 (105*2π)/4084 weeks
106-2.35745 3.86264 (106*2π)/4084 weeks
107-2.19901 -.70701 (107*2π)/4084 weeks
1081.46645 -2.86914 (108*2π)/4084 weeks
1095.33778 -2.68523 (109*2π)/4084 weeks
1108.94562 -.3715 (110*2π)/4084 weeks
11110.03923 3.27026 (111*2π)/4084 weeks
1128.88195 7.223 (112*2π)/4084 weeks
1135.39483 9.46715 (113*2π)/4084 weeks
1142.1731 9.33154 (114*2π)/4084 weeks
115-.65126 7.97698 (115*2π)/4084 weeks
116-2.31381 5.51523 (116*2π)/4084 weeks
117-3.46224 2.23594 (117*2π)/4083 weeks
118-1.53095 -1.44175 (118*2π)/4083 weeks
119.65861 -2.27384 (119*2π)/4083 weeks
1202.53651 -3.22353 (120*2π)/4083 weeks
1215.1794 -2.81099 (121*2π)/4083 weeks
1228.33127 -1.67119 (122*2π)/4083 weeks
1239.91223 2.08984 (123*2π)/4083 weeks
1249.4272 5.91923 (124*2π)/4083 weeks
1257.01601 9.24949 (125*2π)/4083 weeks
1262.96816 10.56181 (126*2π)/4083 weeks
127-.29148 9.98415 (127*2π)/4083 weeks
128-3.76251 7.855 (128*2π)/4083 weeks
129-4.6879 4.76043 (129*2π)/4083 weeks
130-5.86217 1.33799 (130*2π)/4083 weeks
131-4.71532 -2.43648 (131*2π)/4083 weeks
132-2.44048 -5.21521 (132*2π)/4083 weeks
1331.61186 -7.55885 (133*2π)/4083 weeks
1346.10042 -6.58655 (134*2π)/4083 weeks
1359.97147 -4.69039 (135*2π)/4083 weeks
13611.29161 -.0725 (136*2π)/4083 weeks
13710.86708 3.42197 (137*2π)/4083 weeks
1388.42874 6.56583 (138*2π)/4083 weeks
1395.70009 8.08251 (139*2π)/4083 weeks
1402.32604 8.39364 (140*2π)/4083 weeks
141-1.06806 6.76326 (141*2π)/4083 weeks
142-2.32525 4.16596 (142*2π)/4083 weeks
143-2.46233 1.77554 (143*2π)/4083 weeks
144-1.81885 .01693 (144*2π)/4083 weeks
145-1.38542 -2.10926 (145*2π)/4083 weeks
1461.27443 -3.14087 (146*2π)/4083 weeks
1472.79403 -3.25621 (147*2π)/4083 weeks
1484.91136 -2.59049 (148*2π)/4083 weeks
1495.78349 -1.43962 (149*2π)/4083 weeks
1507.24698 .29512 (150*2π)/4083 weeks
1516.51368 2.73658 (151*2π)/4083 weeks
1525.75485 2.75606 (152*2π)/4083 weeks
1535.06172 3.85104 (153*2π)/4083 weeks
1543.86603 4.40249 (154*2π)/4083 weeks
1552.05731 4.61616 (155*2π)/4083 weeks
156-.09398 3.4925 (156*2π)/4083 weeks
157-.76695 1.54116 (157*2π)/4083 weeks
158-1.33636 -.57811 (158*2π)/4083 weeks
159.41914 -3.37897 (159*2π)/4083 weeks
1603.09385 -3.99173 (160*2π)/4083 weeks
1615.55641 -2.62511 (161*2π)/4083 weeks
1625.55492 .16478 (162*2π)/4083 weeks
1634.11209 1.12237 (163*2π)/4083 weeks
1643.07411 .51379 (164*2π)/4082 weeks
1653.00141 .07404 (165*2π)/4082 weeks
1663.30196 -1.1539 (166*2π)/4082 weeks
1674.55658 -1.80419 (167*2π)/4082 weeks
1686.30884 -1.62833 (168*2π)/4082 weeks
1698.11599 .42927 (169*2π)/4082 weeks
1707.7975 2.4163 (170*2π)/4082 weeks
1717.07998 4.23664 (171*2π)/4082 weeks
1725.32424 5.67311 (172*2π)/4082 weeks
1732.82003 6.03439 (173*2π)/4082 weeks
174.32016 5.14554 (174*2π)/4082 weeks
175-1.61067 2.59551 (175*2π)/4082 weeks
176-.85917 .03712 (176*2π)/4082 weeks
177-.5498 -1.17856 (177*2π)/4082 weeks
1781.11259 -3.22442 (178*2π)/4082 weeks
1792.33284 -3.72224 (179*2π)/4082 weeks
1804.65461 -3.9845 (180*2π)/4082 weeks
1815.6319 -2.98248 (181*2π)/4082 weeks
1827.22476 -2.52004 (182*2π)/4082 weeks
1838.73494 -.3992 (183*2π)/4082 weeks
1848.62846 1.27963 (184*2π)/4082 weeks
1858.85687 4.24148 (185*2π)/4082 weeks
1867.15848 6.02051 (186*2π)/4082 weeks
1876.27859 8.36532 (187*2π)/4082 weeks
1881.72011 10.67484 (188*2π)/4082 weeks
189-3.48301 9.67331 (189*2π)/4082 weeks
190-7.81427 6.09429 (190*2π)/4082 weeks
191-9.82116 -.59662 (191*2π)/4082 weeks
192-7.8136 -6.53157 (192*2π)/4082 weeks
193-3.32478 -11.62319 (193*2π)/4082 weeks
1943.63864 -12.92435 (194*2π)/4082 weeks
1959.53457 -10.8037 (195*2π)/4082 weeks
19613.41402 -6.915 (196*2π)/4082 weeks
19715.27028 -2.44543 (197*2π)/4082 weeks
19815.43178 3.58095 (198*2π)/4082 weeks
19912.29041 9.37519 (199*2π)/4082 weeks
2006.39688 11.78973 (200*2π)/4082 weeks
201.82534 11.82747 (201*2π)/4082 weeks
202-4.09922 9.10994 (202*2π)/4082 weeks
203-7.41164 5.80414 (203*2π)/4082 weeks
204-9.42457   (204*2π)/4082 weeks
205-7.41164 -5.80414 (205*2π)/4082 weeks
206-4.09922 -9.10994 (206*2π)/4082 weeks
207.82534 -11.82747 (207*2π)/4082 weeks
2086.39688 -11.78973 (208*2π)/4082 weeks
20912.29041 -9.37519 (209*2π)/4082 weeks
21015.43178 -3.58095 (210*2π)/4082 weeks
21115.27028 2.44543 (211*2π)/4082 weeks
21213.41402 6.915 (212*2π)/4082 weeks
2139.53457 10.8037 (213*2π)/4082 weeks
2143.63864 12.92435 (214*2π)/4082 weeks
215-3.32478 11.62319 (215*2π)/4082 weeks
216-7.8136 6.53157 (216*2π)/4082 weeks
217-9.82116 .59662 (217*2π)/4082 weeks
218-7.81427 -6.09429 (218*2π)/4082 weeks
219-3.48301 -9.67331 (219*2π)/4082 weeks
2201.72011 -10.67484 (220*2π)/4082 weeks
2216.27859 -8.36532 (221*2π)/4082 weeks
2227.15848 -6.02051 (222*2π)/4082 weeks
2238.85687 -4.24148 (223*2π)/4082 weeks
2248.62846 -1.27963 (224*2π)/4082 weeks
2258.73494 .3992 (225*2π)/4082 weeks
2267.22476 2.52004 (226*2π)/4082 weeks
2275.6319 2.98248 (227*2π)/4082 weeks
2284.65461 3.9845 (228*2π)/4082 weeks
2292.33284 3.72224 (229*2π)/4082 weeks
2301.11259 3.22442 (230*2π)/4082 weeks
231-.5498 1.17856 (231*2π)/4082 weeks
232-.85917 -.03712 (232*2π)/4082 weeks
233-1.61067 -2.59551 (233*2π)/4082 weeks
234.32016 -5.14554 (234*2π)/4082 weeks
2352.82003 -6.03439 (235*2π)/4082 weeks
2365.32424 -5.67311 (236*2π)/4082 weeks
2377.07998 -4.23664 (237*2π)/4082 weeks
2387.7975 -2.4163 (238*2π)/4082 weeks
2398.11599 -.42927 (239*2π)/4082 weeks
2406.30884 1.62833 (240*2π)/4082 weeks
2414.55658 1.80419 (241*2π)/4082 weeks
2423.30196 1.1539 (242*2π)/4082 weeks
2433.00141 -.07404 (243*2π)/4082 weeks
2443.07411 -.51379 (244*2π)/4082 weeks
2454.11209 -1.12237 (245*2π)/4082 weeks
2465.55492 -.16478 (246*2π)/4082 weeks
2475.55641 2.62511 (247*2π)/4082 weeks
2483.09385 3.99173 (248*2π)/4082 weeks
249.41914 3.37897 (249*2π)/4082 weeks
250-1.33636 .57811 (250*2π)/4082 weeks
251-.76695 -1.54116 (251*2π)/4082 weeks
252-.09398 -3.4925 (252*2π)/4082 weeks
2532.05731 -4.61616 (253*2π)/4082 weeks
2543.86603 -4.40249 (254*2π)/4082 weeks
2555.06172 -3.85104 (255*2π)/4082 weeks
2565.75485 -2.75606 (256*2π)/4082 weeks
2576.51368 -2.73658 (257*2π)/4082 weeks
2587.24698 -.29512 (258*2π)/4082 weeks
2595.78349 1.43962 (259*2π)/4082 weeks
2604.91136 2.59049 (260*2π)/4082 weeks
2612.79403 3.25621 (261*2π)/4082 weeks
2621.27443 3.14087 (262*2π)/4082 weeks
263-1.38542 2.10926 (263*2π)/4082 weeks
264-1.81885 -.01693 (264*2π)/4082 weeks
265-2.46233 -1.77554 (265*2π)/4082 weeks
266-2.32525 -4.16596 (266*2π)/4082 weeks
267-1.06806 -6.76326 (267*2π)/4082 weeks
2682.32604 -8.39364 (268*2π)/4082 weeks
2695.70009 -8.08251 (269*2π)/4082 weeks
2708.42874 -6.56583 (270*2π)/4082 weeks
27110.86708 -3.42197 (271*2π)/4082 weeks
27211.29161 .0725 (272*2π)/4082 weeks
2739.97147 4.69039 (273*2π)/4081 weeks
2746.10042 6.58655 (274*2π)/4081 weeks
2751.61186 7.55885 (275*2π)/4081 weeks
276-2.44048 5.21521 (276*2π)/4081 weeks
277-4.71532 2.43648 (277*2π)/4081 weeks
278-5.86217 -1.33799 (278*2π)/4081 weeks
279-4.6879 -4.76043 (279*2π)/4081 weeks
280-3.76251 -7.855 (280*2π)/4081 weeks
281-.29148 -9.98415 (281*2π)/4081 weeks
2822.96816 -10.56181 (282*2π)/4081 weeks
2837.01601 -9.24949 (283*2π)/4081 weeks
2849.4272 -5.91923 (284*2π)/4081 weeks
2859.91223 -2.08984 (285*2π)/4081 weeks
2868.33127 1.67119 (286*2π)/4081 weeks
2875.1794 2.81099 (287*2π)/4081 weeks
2882.53651 3.22353 (288*2π)/4081 weeks
289.65861 2.27384 (289*2π)/4081 weeks
290-1.53095 1.44175 (290*2π)/4081 weeks
291-3.46224 -2.23594 (291*2π)/4081 weeks
292-2.31381 -5.51523 (292*2π)/4081 weeks
293-.65126 -7.97698 (293*2π)/4081 weeks
2942.1731 -9.33154 (294*2π)/4081 weeks
2955.39483 -9.46715 (295*2π)/4081 weeks
2968.88195 -7.223 (296*2π)/4081 weeks
29710.03923 -3.27026 (297*2π)/4081 weeks
2988.94562 .3715 (298*2π)/4081 weeks
2995.33778 2.68523 (299*2π)/4081 weeks
3001.46645 2.86914 (300*2π)/4081 weeks
301-2.19901 .70701 (301*2π)/4081 weeks
302-2.35745 -3.86264 (302*2π)/4081 weeks
303-.62434 -5.7789 (303*2π)/4081 weeks
3041.19657 -6.80467 (304*2π)/4081 weeks
3053.40806 -6.93105 (305*2π)/4081 weeks
3064.27643 -6.5753 (306*2π)/4081 weeks
3076.30308 -5.55275 (307*2π)/4081 weeks
3087.355 -3.30254 (308*2π)/4081 weeks
3097.21337 -.96729 (309*2π)/4081 weeks
3106.18562 2.03808 (310*2π)/4081 weeks
3111.89289 3.54572 (311*2π)/4081 weeks
312-2.61949 1.7517 (312*2π)/4081 weeks
313-4.97007 -2.33284 (313*2π)/4081 weeks
314-5.27758 -6.59164 (314*2π)/4081 weeks
315-3.16194 -11.23514 (315*2π)/4081 weeks
316.77049 -13.14394 (316*2π)/4081 weeks
3175.48053 -14.27916 (317*2π)/4081 weeks
3189.54832 -12.57147 (318*2π)/4081 weeks
31912.41757 -8.78446 (319*2π)/4081 weeks
32013.89163 -4.20011 (320*2π)/4081 weeks
32112.86961 .19672 (321*2π)/4081 weeks
3229.80735 5.36156 (322*2π)/4081 weeks
3233.96894 7.61368 (323*2π)/4081 weeks
324-2.14227 6.06031 (324*2π)/4081 weeks
325-6.0163 2.99622 (325*2π)/4081 weeks
326-8.43919 -2.34532 (326*2π)/4081 weeks
327-8.59023 -7.30569 (327*2π)/4081 weeks
328-5.85274 -12.86169 (328*2π)/4081 weeks
329-1.7534 -15.74665 (329*2π)/4081 weeks
3304.49411 -17.12572 (330*2π)/4081 weeks
3319.59943 -15.03053 (331*2π)/4081 weeks
33213.4088 -10.42164 (332*2π)/4081 weeks
33314.11085 -5.45637 (333*2π)/4081 weeks
33412.24389 -1.23645 (334*2π)/4081 weeks
3358.72823 1.24769 (335*2π)/4081 weeks
3364.49819 1.54232 (336*2π)/4081 weeks
3371.52416 -.00502 (337*2π)/4081 weeks
338.80166 -2.67167 (338*2π)/4081 weeks
339.48503 -3.04544 (339*2π)/4081 weeks
340-.13672 -4.18605 (340*2π)/4081 weeks
341-.90706 -4.4932 (341*2π)/4081 weeks
342-2.02692 -6.53182 (342*2π)/4081 weeks
343-3.26796 -8.22601 (343*2π)/4081 weeks
344-2.20714 -11.64793 (344*2π)/4081 weeks
345.62713 -14.689 (345*2π)/4081 weeks
3465.79138 -15.25493 (346*2π)/4081 weeks
34710.79019 -14.15071 (347*2π)/4081 weeks
34813.97653 -8.81354 (348*2π)/4081 weeks
34914.42079 -3.29923 (349*2π)/4081 weeks
35010.98044 3.64572 (350*2π)/4081 weeks
3514.14818 2.72408 (351*2π)/4081 weeks
3522.58051 2.95805 (352*2π)/4081 weeks
353-3.52129 2.09761 (353*2π)/4081 weeks
354-6.89706 -3.6156 (354*2π)/4081 weeks
355-7.99326 -8.80376 (355*2π)/4081 weeks
356-5.9538 -14.39015 (356*2π)/4081 weeks
357-1.15536 -15.98661 (357*2π)/4081 weeks
358.75283 -17.68929 (358*2π)/4081 weeks
3595.43111 -15.81571 (359*2π)/4081 weeks
3604.81105 -14.56322 (360*2π)/4081 weeks
3616.13267 -14.5401 (361*2π)/4081 weeks
3627.13465 -13.54018 (362*2π)/4081 weeks
36310.3186 -11.86949 (363*2π)/4081 weeks
36410.50979 -7.04017 (364*2π)/4081 weeks
3657.80622 -4.73403 (365*2π)/4081 weeks
3664.46758 -2.89036 (366*2π)/4081 weeks
367-.74035 -4.46715 (367*2π)/4081 weeks
368-2.19179 -8.50641 (368*2π)/4081 weeks
369-1.13816 -10.90515 (369*2π)/4081 weeks
370-1.76064 -13.17984 (370*2π)/4081 weeks
371-.70892 -15.24827 (371*2π)/4081 weeks
3722.36335 -19.01187 (372*2π)/4081 weeks
3735.99647 -20.19015 (373*2π)/4081 weeks
3748.53982 -15.58158 (374*2π)/4081 weeks
3755.03856 -12.63169 (375*2π)/4081 weeks
376-.14487 -15.58034 (376*2π)/4081 weeks
377-3.41923 -24.66924 (377*2π)/4081 weeks
3786.67455 -31.92676 (378*2π)/4081 weeks
37915.46379 -32.99413 (379*2π)/4081 weeks
38022.72258 -27.64483 (380*2π)/4081 weeks
38130.06397 -20.97265 (381*2π)/4081 weeks
38232.25021 -10.10877 (382*2π)/4081 weeks
38329.33842 5.5675 (383*2π)/4081 weeks
38416.04443 14.17095 (384*2π)/4081 weeks
385-.34902 16.24822 (385*2π)/4081 weeks
386-14.63933 8.04034 (386*2π)/4081 weeks
387-21.9114 -4.86187 (387*2π)/4081 weeks
388-27.31497 -18.05654 (388*2π)/4081 weeks
389-20.50302 -38.73032 (389*2π)/4081 weeks
390-7.68437 -48.35992 (390*2π)/4081 weeks
39110.22727 -52.23005 (391*2π)/4081 weeks
39221.88093 -47.18432 (392*2π)/4081 weeks
39331.47827 -40.60474 (393*2π)/4081 weeks
39437.89221 -34.45591 (394*2π)/4081 weeks
39543.41529 -17.87903 (395*2π)/4081 weeks
39632.49691 -8.90177 (396*2π)/4081 weeks
39724.94822 5.92669 (397*2π)/4081 weeks
398-.59468 9.13783 (398*2π)/4081 weeks
399-23.24528 2.77429 (399*2π)/4081 weeks
400-44.73951 -17.25471 (400*2π)/4081 weeks
401-59.31963 -47.44842 (401*2π)/4081 weeks
402-68.20469 -79.80936 (402*2π)/4081 weeks
403-64.87273 -142.2438 (403*2π)/4081 weeks
404-17.13611 -195.0548 (404*2π)/4081 weeks
40542.94392 -238.7306 (405*2π)/4081 weeks
406160.8622 -267.1116 (406*2π)/4081 weeks



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