Back to list of Stocks    See Also: Seasonal Analysis of SRSGenetic Algorithms Stock Portfolio Generator, and Best Months to Buy/Sell Stocks

# Fourier Analysis of SRS (ProShares UltraShort Real Estate)

SRS (ProShares UltraShort Real Estate) appears to have interesting cyclic behaviour every 43 weeks (189.6733*sine), 18 weeks (172.6764*sine), and 21 weeks (169.4527*sine).

SRS (ProShares UltraShort Real Estate) has an average price of 1,117.36 (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 2/1/2007 to 6/18/2018 for SRS (ProShares UltraShort Real Estate), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,117.359   0
11,484.208 1,213.63 (1*2π)/595595 weeks
2425.0009 1,459.812 (2*2π)/595298 weeks
3-309.6936 1,007.081 (3*2π)/595198 weeks
4-440.7619 383.1784 (4*2π)/595149 weeks
5-168.9857 55.55598 (5*2π)/595119 weeks
676.12936 93.72879 (6*2π)/59599 weeks
790.91467 261.409 (7*2π)/59585 weeks
8-66.49224 299.2688 (8*2π)/59574 weeks
9-175.3971 159.3468 (9*2π)/59566 weeks
10-119.168 1.21682 (10*2π)/59560 weeks
1119.07068 -42.74208 (11*2π)/59554 weeks
12122.3383 38.35335 (12*2π)/59550 weeks
13105.1455 147.1194 (13*2π)/59546 weeks
1420.70347 189.6733 (14*2π)/59543 weeks
15-56.07814 156.0864 (15*2π)/59540 weeks
16-84.90246 86.3969 (16*2π)/59537 weeks
17-62.62671 28.49278 (17*2π)/59535 weeks
18-22.27052 5.15978 (18*2π)/59533 weeks
1917.62958 6.19929 (19*2π)/59531 weeks
2037.04537 32.585 (20*2π)/59530 weeks
2130.4976 52.79235 (21*2π)/59528 weeks
2212.74008 55.8534 (22*2π)/59527 weeks
233.12907 37.24021 (23*2π)/59526 weeks
2421.41649 12.82118 (24*2π)/59525 weeks
2566.95015 16.38882 (25*2π)/59524 weeks
2699.27813 72.58154 (26*2π)/59523 weeks
2763.65142 150.2608 (27*2π)/59522 weeks
28-36.12742 169.4527 (28*2π)/59521 weeks
29-119.5618 90.9063 (29*2π)/59521 weeks
30-103.3642 -25.6995 (30*2π)/59520 weeks
313.48066 -81.10368 (31*2π)/59519 weeks
32109.9323 -16.39832 (32*2π)/59519 weeks
33106.8357 110.7676 (33*2π)/59518 weeks
34-10.07209 172.6764 (34*2π)/59518 weeks
35-126.6978 102.1778 (35*2π)/59517 weeks
36-128.307 -34.93336 (36*2π)/59517 weeks
37-16.27178 -106.3964 (37*2π)/59516 weeks
3893.75005 -53.78394 (38*2π)/59516 weeks
39104.3935 52.89037 (39*2π)/59515 weeks
4029.98888 109.3963 (40*2π)/59515 weeks
41-44.12499 77.24866 (41*2π)/59515 weeks
42-52.75256 8.3443 (42*2π)/59514 weeks
43-2.7226 -29.85316 (43*2π)/59514 weeks
4449.79985 -8.27638 (44*2π)/59514 weeks
4557.28843 45.45009 (45*2π)/59513 weeks
4617.55602 73.52979 (46*2π)/59513 weeks
47-20.98125 59.30228 (47*2π)/59513 weeks
48-28.45303 22.72541 (48*2π)/59512 weeks
49-3.64109 1.82861 (49*2π)/59512 weeks
5021.10505 12.34599 (50*2π)/59512 weeks
5123.75803 36.58807 (51*2π)/59512 weeks
526.81902 52.74683 (52*2π)/59511 weeks
53-17.79311 49.11225 (53*2π)/59511 weeks
54-32.50764 30.49111 (54*2π)/59511 weeks
55-30.46934 5.50437 (55*2π)/59511 weeks
56-13.56572 -8.60525 (56*2π)/59511 weeks
576.0703 -9.43176 (57*2π)/59510 weeks
5819.15634 1.54957 (58*2π)/59510 weeks
5920.18675 16.28728 (59*2π)/59510 weeks
6010.88635 25.74236 (60*2π)/59510 weeks
61-1.45027 23.03942 (61*2π)/59510 weeks
62-3.90184 7.17762 (62*2π)/59510 weeks
6313.21766 -1.43769 (63*2π)/5959 weeks
6432.13086 13.92591 (64*2π)/5959 weeks
6527.26104 43.00585 (65*2π)/5959 weeks
66-5.45615 58.25051 (66*2π)/5959 weeks
67-41.9572 35.59462 (67*2π)/5959 weeks
68-41.53971 -9.60985 (68*2π)/5959 weeks
69-7.41479 -33.95466 (69*2π)/5959 weeks
7029.83525 -22.34481 (70*2π)/5959 weeks
7137.9981 10.20316 (71*2π)/5958 weeks
7218.47318 26.23986 (72*2π)/5958 weeks
735.48892 16.08494 (73*2π)/5958 weeks
7413.11405 4.99826 (74*2π)/5958 weeks
7530.52011 13.56188 (75*2π)/5958 weeks
7627.82145 40.85002 (76*2π)/5958 weeks
77-2.35682 53.38007 (77*2π)/5958 weeks
78-30.76802 33.99246 (78*2π)/5958 weeks
79-32.7171 .12379 (79*2π)/5958 weeks
80-6.54999 -20.88837 (80*2π)/5957 weeks
8120.99304 -9.82856 (81*2π)/5957 weeks
8225.74679 13.78308 (82*2π)/5957 weeks
839.21979 29.95233 (83*2π)/5957 weeks
84-15.87333 22.49036 (84*2π)/5957 weeks
85-19.55522 -7.2619 (85*2π)/5957 weeks
865.93295 -25.93241 (86*2π)/5957 weeks
8737.76033 -15.58764 (87*2π)/5957 weeks
8848.87752 19.56988 (88*2π)/5957 weeks
8924.97702 49.46443 (89*2π)/5957 weeks
90-13.24557 47.4965 (90*2π)/5957 weeks
91-35.2224 14.74176 (91*2π)/5957 weeks
92-19.1881 -23.50813 (92*2π)/5956 weeks
9320.58844 -29.48863 (93*2π)/5956 weeks
9446.53598 -2.8064 (94*2π)/5956 weeks
9541.05799 31.87741 (95*2π)/5956 weeks
9613.11975 47.05249 (96*2π)/5956 weeks
97-12.76388 35.82346 (97*2π)/5956 weeks
98-18.41385 11.3273 (98*2π)/5956 weeks
99-2.5075 -3.45037 (99*2π)/5956 weeks
10015.1125 3.4578 (100*2π)/5956 weeks
10116.30616 21.76382 (101*2π)/5956 weeks
102-.10943 32.58483 (102*2π)/5956 weeks
103-21.10915 25.85439 (103*2π)/5956 weeks
104-30.79502 1.97638 (104*2π)/5956 weeks
105-17.9803 -22.54651 (105*2π)/5956 weeks
10610.0279 -28.52009 (106*2π)/5956 weeks
10730.67153 -10.82347 (107*2π)/5956 weeks
10828.79109 14.31059 (108*2π)/5956 weeks
1098.39424 26.07274 (109*2π)/5955 weeks
110-12.91435 15.73591 (110*2π)/5955 weeks
111-15.54204 -9.77451 (111*2π)/5955 weeks
1125.59837 -27.23953 (112*2π)/5955 weeks
11333.29047 -20.15192 (113*2π)/5955 weeks
11445.27765 6.5596 (114*2π)/5955 weeks
11530.6411 32.5369 (115*2π)/5955 weeks
1162.02724 35.37625 (116*2π)/5955 weeks
117-15.91222 13.58224 (117*2π)/5955 weeks
118-6.8437 -13.59779 (118*2π)/5955 weeks
11922.27043 -19.66751 (119*2π)/5955 weeks
12043.73365 2.75142 (120*2π)/5955 weeks
12136.91046 33.26731 (121*2π)/5955 weeks
1228.28549 45.1813 (122*2π)/5955 weeks
123-17.14116 30.67412 (123*2π)/5955 weeks
124-20.19956 2.888 (124*2π)/5955 weeks
125.1512 -13.37096 (125*2π)/5955 weeks
12622.88397 -5.36399 (126*2π)/5955 weeks
12726.48168 17.96998 (127*2π)/5955 weeks
1288.1104 32.90386 (128*2π)/5955 weeks
129-15.10939 25.1172 (129*2π)/5955 weeks
130-22.05149 .12668 (130*2π)/5955 weeks
131-4.40295 -21.40066 (131*2π)/5955 weeks
13223.99228 -17.69694 (132*2π)/5955 weeks
13337.00013 7.99857 (133*2π)/5954 weeks
13422.60251 33.15886 (134*2π)/5954 weeks
135-5.4861 34.57881 (135*2π)/5954 weeks
136-22.15326 13.80531 (136*2π)/5954 weeks
137-15.39247 -9.83799 (137*2π)/5954 weeks
1385.76928 -17.58462 (138*2π)/5954 weeks
13921.86189 -5.57935 (139*2π)/5954 weeks
14019.59856 12.1726 (140*2π)/5954 weeks
1413.7877 17.48647 (141*2π)/5954 weeks
142-8.59934 4.77649 (142*2π)/5954 weeks
143-2.42544 -14.758 (143*2π)/5954 weeks
14420.91289 -20.0363 (144*2π)/5954 weeks
14540.3623 -3.10696 (145*2π)/5954 weeks
14640.04165 23.98281 (146*2π)/5954 weeks
14718.78007 43.31843 (147*2π)/5954 weeks
148-10.37333 39.57844 (148*2π)/5954 weeks
149-26.01201 16.05297 (149*2π)/5954 weeks
150-19.55711 -9.01276 (150*2π)/5954 weeks
1511.86705 -20.39377 (151*2π)/5954 weeks
15223.23157 -11.16884 (152*2π)/5954 weeks
15327.60376 9.86527 (153*2π)/5954 weeks
15412.65573 25.07772 (154*2π)/5954 weeks
155-8.72613 18.86886 (155*2π)/5954 weeks
156-12.62449 -4.2433 (156*2π)/5954 weeks
1577.78325 -18.51783 (157*2π)/5954 weeks
15831.15491 -7.49657 (158*2π)/5954 weeks
15934.34498 20.24998 (159*2π)/5954 weeks
16010.84414 38.77736 (160*2π)/5954 weeks
161-18.04267 28.96461 (161*2π)/5954 weeks
162-26.47295 -.43053 (162*2π)/5954 weeks
163-7.21877 -24.17074 (163*2π)/5954 weeks
16422.57483 -21.48042 (164*2π)/5954 weeks
16536.05071 3.21203 (165*2π)/5954 weeks
16624.25405 26.48604 (166*2π)/5954 weeks
167.48506 29.22227 (167*2π)/5954 weeks
168-13.98955 12.45915 (168*2π)/5954 weeks
169-7.50381 -7.53513 (169*2π)/5954 weeks
17012.17602 -11.62179 (170*2π)/5954 weeks
17125.36465 3.6128 (171*2π)/5953 weeks
17218.30206 22.45882 (172*2π)/5953 weeks
173-.62613 26.32524 (173*2π)/5953 weeks
174-15.06339 14.26876 (174*2π)/5953 weeks
175-15.38741 -4.70146 (175*2π)/5953 weeks
176-.75553 -17.69881 (176*2π)/5953 weeks
17719.31381 -14.04154 (177*2π)/5953 weeks
17828.44246 4.315 (178*2π)/5953 weeks
17919.50862 22.06309 (179*2π)/5953 weeks
180-.05527 26.59355 (180*2π)/5953 weeks
181-15.98856 13.38276 (181*2π)/5953 weeks
182-14.74454 -7.19929 (182*2π)/5953 weeks
1832.0389 -18.2713 (183*2π)/5953 weeks
18420.21304 -11.3643 (184*2π)/5953 weeks
18524.2021 7.12957 (185*2π)/5953 weeks
18611.12884 19.85065 (186*2π)/5953 weeks
187-6.76226 14.91528 (187*2π)/5953 weeks
188-12.68695 -3.58762 (188*2π)/5953 weeks
189.99633 -20.26455 (189*2π)/5953 weeks
19024.46386 -18.08625 (190*2π)/5953 weeks
19137.1426 3.29613 (191*2π)/5953 weeks
19227.11517 27.51617 (192*2π)/5953 weeks
193.64581 33.43128 (193*2π)/5953 weeks
194-18.9489 14.77218 (194*2π)/5953 weeks
195-13.97038 -10.83637 (195*2π)/5953 weeks
1969.30092 -20.53399 (196*2π)/5953 weeks
19729.52909 -6.10734 (197*2π)/5953 weeks
19827.86866 17.63936 (198*2π)/5953 weeks
1998.23492 28.18641 (199*2π)/5953 weeks
200-9.17954 17.79356 (200*2π)/5953 weeks
201-8.46011 .74924 (201*2π)/5953 weeks
2024.3815 -4.23097 (202*2π)/5953 weeks
20311.07022 4.70297 (203*2π)/5953 weeks
2044.44943 12.77692 (204*2π)/5953 weeks
205-6.46829 8.88557 (205*2π)/5953 weeks
206-8.13852 -3.14802 (206*2π)/5953 weeks
207.32996 -11.40259 (207*2π)/5953 weeks
20810.60562 -10.22225 (208*2π)/5953 weeks
20916.19305 -4.11466 (209*2π)/5953 weeks
21017.0728 2.0684 (210*2π)/5953 weeks
21115.36008 7.30379 (211*2π)/5953 weeks
21211.51192 9.36653 (212*2π)/5953 weeks
2139.82577 10.76935 (213*2π)/5953 weeks
2146.4937 12.90297 (214*2π)/5953 weeks
215.81602 13.0584 (215*2π)/5953 weeks
216-4.20797 8.18967 (216*2π)/5953 weeks
217-3.154 .55177 (217*2π)/5953 weeks
2183.37592 -.41121 (218*2π)/5953 weeks
2193.76362 4.74673 (219*2π)/5953 weeks
220-2.1302 5.90122 (220*2π)/5953 weeks
221-8.07468 -1.23726 (221*2π)/5953 weeks
222-4.04198 -13.17571 (222*2π)/5953 weeks
2239.71553 -16.28929 (223*2π)/5953 weeks
22419.19455 -7.1615 (224*2π)/5953 weeks
22516.94217 3.52121 (225*2π)/5953 weeks
2268.77597 4.86837 (226*2π)/5953 weeks
2277.7645 -1.59926 (227*2π)/5953 weeks
22815.69585 -2.60814 (228*2π)/5953 weeks
22920.15472 7.10258 (229*2π)/5953 weeks
23012.72135 17.60437 (230*2π)/5953 weeks
231-1.84514 17.529 (231*2π)/5953 weeks
232-10.25686 3.39696 (232*2π)/5953 weeks
233-2.23458 -10.51252 (233*2π)/5953 weeks
23413.03171 -10.39029 (234*2π)/5953 weeks
23519.13394 1.96619 (235*2π)/5953 weeks
23611.03114 10.80066 (236*2π)/5953 weeks
2372.30496 5.86059 (237*2π)/5953 weeks
2385.78472 -2.80904 (238*2π)/5953 weeks
23916.62068 -1.48784 (239*2π)/5952 weeks
24020.61423 11.54019 (240*2π)/5952 weeks
24110.3098 24.25407 (241*2π)/5952 weeks
242-9.07514 22.67595 (242*2π)/5952 weeks
243-18.96685 4.70644 (243*2π)/5952 weeks
244-10.07466 -13.31821 (244*2π)/5952 weeks
2458.81391 -15.91389 (245*2π)/5952 weeks
24620.31327 -1.50409 (246*2π)/5952 weeks
24712.61161 14.14699 (247*2π)/5952 weeks
248-3.49276 14.35455 (248*2π)/5952 weeks
249-11.55107 .55697 (249*2π)/5952 weeks
250-3.24788 -13.57135 (250*2π)/5952 weeks
25113.37388 -12.68107 (251*2π)/5952 weeks
25220.5843 1.89919 (252*2π)/5952 weeks
25311.5153 15.88332 (253*2π)/5952 weeks
254-5.98051 15.07039 (254*2π)/5952 weeks
255-14.54518 -.5094 (255*2π)/5952 weeks
256-6.38742 -15.76075 (256*2π)/5952 weeks
2578.64795 -18.08807 (257*2π)/5952 weeks
25819.6004 -9.69781 (258*2π)/5952 weeks
25920.1806 3.44407 (259*2π)/5952 weeks
26011.43895 10.47113 (260*2π)/5952 weeks
2612.05326 8.77817 (261*2π)/5952 weeks
262-1.56792 .85387 (262*2π)/5952 weeks
2632.79075 -5.07455 (263*2π)/5952 weeks
2648.68564 -4.87028 (264*2π)/5952 weeks
26512.37652 -.05666 (265*2π)/5952 weeks
2669.89838 6.41198 (266*2π)/5952 weeks
2672.18346 8.28195 (267*2π)/5952 weeks
268-4.59012 2.34285 (268*2π)/5952 weeks
269-4.54146 -8.22881 (269*2π)/5952 weeks
2705.85005 -15.49551 (270*2π)/5952 weeks
27118.46735 -10.62705 (271*2π)/5952 weeks
27222.42894 2.54694 (272*2π)/5952 weeks
27314.44322 14.70373 (273*2π)/5952 weeks
274-1.88299 15.89079 (274*2π)/5952 weeks
275-13.29343 1.68292 (275*2π)/5952 weeks
276-7.44266 -17.03848 (276*2π)/5952 weeks
27713.0791 -23.45987 (277*2π)/5952 weeks
27830.71986 -8.31599 (278*2π)/5952 weeks
27926.89199 15.1855 (279*2π)/5952 weeks
2805.35906 24.65216 (280*2π)/5952 weeks
281-14.77746 12.45002 (281*2π)/5952 weeks
282-15.38467 -11.78175 (282*2π)/5952 weeks
2834.76735 -24.45154 (283*2π)/5952 weeks
28424.86243 -14.15695 (284*2π)/5952 weeks
28525.24317 6.69724 (285*2π)/5952 weeks
2869.50872 16.05777 (286*2π)/5952 weeks
287-5.0331 7.6794 (287*2π)/5952 weeks
288-4.52334 -8.08364 (288*2π)/5952 weeks
2899.14392 -15.49105 (289*2π)/5952 weeks
29022.81604 -6.68845 (290*2π)/5952 weeks
29122.06435 10.10704 (291*2π)/5952 weeks
2926.84881 17.88567 (292*2π)/5952 weeks
293-7.06857 9.95714 (293*2π)/5952 weeks
294-9.67503 -4.98596 (294*2π)/5952 weeks
295-.03122 -16.22329 (295*2π)/5952 weeks
29613.97293 -16.97593 (296*2π)/5952 weeks
29724.67374 -7.32388 (297*2π)/5952 weeks
29824.67374 7.32388 (298*2π)/5952 weeks
29913.97293 16.97593 (299*2π)/5952 weeks
300-.03122 16.22329 (300*2π)/5952 weeks
301-9.67503 4.98596 (301*2π)/5952 weeks
302-7.06857 -9.95714 (302*2π)/5952 weeks
3036.84881 -17.88567 (303*2π)/5952 weeks
30422.06435 -10.10704 (304*2π)/5952 weeks
30522.81604 6.68845 (305*2π)/5952 weeks
3069.14392 15.49105 (306*2π)/5952 weeks
307-4.52334 8.08364 (307*2π)/5952 weeks
308-5.0331 -7.6794 (308*2π)/5952 weeks
3099.50872 -16.05777 (309*2π)/5952 weeks
31025.24317 -6.69724 (310*2π)/5952 weeks
31124.86243 14.15695 (311*2π)/5952 weeks
3124.76735 24.45154 (312*2π)/5952 weeks
313-15.38467 11.78175 (313*2π)/5952 weeks
314-14.77746 -12.45002 (314*2π)/5952 weeks
3155.35906 -24.65216 (315*2π)/5952 weeks
31626.89199 -15.1855 (316*2π)/5952 weeks
31730.71986 8.31599 (317*2π)/5952 weeks
31813.0791 23.45987 (318*2π)/5952 weeks
319-7.44266 17.03848 (319*2π)/5952 weeks
320-13.29343 -1.68292 (320*2π)/5952 weeks
321-1.88299 -15.89079 (321*2π)/5952 weeks
32214.44322 -14.70373 (322*2π)/5952 weeks
32322.42894 -2.54694 (323*2π)/5952 weeks
32418.46735 10.62705 (324*2π)/5952 weeks
3255.85005 15.49551 (325*2π)/5952 weeks
326-4.54146 8.22881 (326*2π)/5952 weeks
327-4.59012 -2.34285 (327*2π)/5952 weeks
3282.18346 -8.28195 (328*2π)/5952 weeks
3299.89838 -6.41198 (329*2π)/5952 weeks
33012.37652 .05666 (330*2π)/5952 weeks
3318.68564 4.87028 (331*2π)/5952 weeks
3322.79075 5.07455 (332*2π)/5952 weeks
333-1.56792 -.85387 (333*2π)/5952 weeks
3342.05326 -8.77817 (334*2π)/5952 weeks
33511.43895 -10.47113 (335*2π)/5952 weeks
33620.1806 -3.44407 (336*2π)/5952 weeks
33719.6004 9.69781 (337*2π)/5952 weeks
3388.64795 18.08807 (338*2π)/5952 weeks
339-6.38742 15.76075 (339*2π)/5952 weeks
340-14.54518 .5094 (340*2π)/5952 weeks
341-5.98051 -15.07039 (341*2π)/5952 weeks
34211.5153 -15.88332 (342*2π)/5952 weeks
34320.5843 -1.89919 (343*2π)/5952 weeks
34413.37388 12.68107 (344*2π)/5952 weeks
345-3.24788 13.57135 (345*2π)/5952 weeks
346-11.55107 -.55697 (346*2π)/5952 weeks
347-3.49276 -14.35455 (347*2π)/5952 weeks
34812.61161 -14.14699 (348*2π)/5952 weeks
34920.31327 1.50409 (349*2π)/5952 weeks
3508.81391 15.91389 (350*2π)/5952 weeks
351-10.07466 13.31821 (351*2π)/5952 weeks
352-18.96685 -4.70644 (352*2π)/5952 weeks
353-9.07514 -22.67595 (353*2π)/5952 weeks
35410.3098 -24.25407 (354*2π)/5952 weeks
35520.61423 -11.54019 (355*2π)/5952 weeks
35616.62068 1.48784 (356*2π)/5952 weeks
3575.78472 2.80904 (357*2π)/5952 weeks
3582.30496 -5.86059 (358*2π)/5952 weeks
35911.03114 -10.80066 (359*2π)/5952 weeks
36019.13394 -1.96619 (360*2π)/5952 weeks
36113.03171 10.39029 (361*2π)/5952 weeks
362-2.23458 10.51252 (362*2π)/5952 weeks
363-10.25686 -3.39696 (363*2π)/5952 weeks
364-1.84514 -17.529 (364*2π)/5952 weeks
36512.72135 -17.60437 (365*2π)/5952 weeks
36620.15472 -7.10258 (366*2π)/5952 weeks
36715.69585 2.60814 (367*2π)/5952 weeks
3687.7645 1.59926 (368*2π)/5952 weeks
3698.77597 -4.86837 (369*2π)/5952 weeks
37016.94217 -3.52121 (370*2π)/5952 weeks
37119.19455 7.1615 (371*2π)/5952 weeks
3729.71553 16.28929 (372*2π)/5952 weeks
373-4.04198 13.17571 (373*2π)/5952 weeks
374-8.07468 1.23726 (374*2π)/5952 weeks
375-2.1302 -5.90122 (375*2π)/5952 weeks
3763.76362 -4.74673 (376*2π)/5952 weeks
3773.37592 .41121 (377*2π)/5952 weeks
378-3.154 -.55177 (378*2π)/5952 weeks
379-4.20797 -8.18967 (379*2π)/5952 weeks
380.81602 -13.0584 (380*2π)/5952 weeks
3816.4937 -12.90297 (381*2π)/5952 weeks
3829.82577 -10.76935 (382*2π)/5952 weeks
38311.51192 -9.36653 (383*2π)/5952 weeks
38415.36008 -7.30379 (384*2π)/5952 weeks
38517.0728 -2.0684 (385*2π)/5952 weeks
38616.19305 4.11466 (386*2π)/5952 weeks
38710.60562 10.22225 (387*2π)/5952 weeks
388.32996 11.40259 (388*2π)/5952 weeks
389-8.13852 3.14802 (389*2π)/5952 weeks
390-6.46829 -8.88557 (390*2π)/5952 weeks
3914.44943 -12.77692 (391*2π)/5952 weeks
39211.07022 -4.70297 (392*2π)/5952 weeks
3934.3815 4.23097 (393*2π)/5952 weeks
394-8.46011 -.74924 (394*2π)/5952 weeks
395-9.17954 -17.79356 (395*2π)/5952 weeks
3968.23492 -28.18641 (396*2π)/5952 weeks
39727.86866 -17.63936 (397*2π)/5951 weeks
39829.52909 6.10734 (398*2π)/5951 weeks
3999.30092 20.53399 (399*2π)/5951 weeks
400-13.97038 10.83637 (400*2π)/5951 weeks
401-18.9489 -14.77218 (401*2π)/5951 weeks
402.64581 -33.43128 (402*2π)/5951 weeks
40327.11517 -27.51617 (403*2π)/5951 weeks
40437.1426 -3.29613 (404*2π)/5951 weeks
40524.46386 18.08625 (405*2π)/5951 weeks
406.99633 20.26455 (406*2π)/5951 weeks
407-12.68695 3.58762 (407*2π)/5951 weeks
408-6.76226 -14.91528 (408*2π)/5951 weeks
40911.12884 -19.85065 (409*2π)/5951 weeks
41024.2021 -7.12957 (410*2π)/5951 weeks
41120.21304 11.3643 (411*2π)/5951 weeks
4122.0389 18.2713 (412*2π)/5951 weeks
413-14.74454 7.19929 (413*2π)/5951 weeks
414-15.98856 -13.38276 (414*2π)/5951 weeks
415-.05527 -26.59355 (415*2π)/5951 weeks
41619.50862 -22.06309 (416*2π)/5951 weeks
41728.44246 -4.315 (417*2π)/5951 weeks
41819.31381 14.04154 (418*2π)/5951 weeks
419-.75553 17.69881 (419*2π)/5951 weeks
420-15.38741 4.70146 (420*2π)/5951 weeks
421-15.06339 -14.26876 (421*2π)/5951 weeks
422-.62613 -26.32524 (422*2π)/5951 weeks
42318.30206 -22.45882 (423*2π)/5951 weeks
42425.36465 -3.6128 (424*2π)/5951 weeks
42512.17602 11.62179 (425*2π)/5951 weeks
426-7.50381 7.53513 (426*2π)/5951 weeks
427-13.98955 -12.45915 (427*2π)/5951 weeks
428.48506 -29.22227 (428*2π)/5951 weeks
42924.25405 -26.48604 (429*2π)/5951 weeks
43036.05071 -3.21203 (430*2π)/5951 weeks
43122.57483 21.48042 (431*2π)/5951 weeks
432-7.21877 24.17074 (432*2π)/5951 weeks
433-26.47295 .43053 (433*2π)/5951 weeks
434-18.04267 -28.96461 (434*2π)/5951 weeks
43510.84414 -38.77736 (435*2π)/5951 weeks
43634.34498 -20.24998 (436*2π)/5951 weeks
43731.15491 7.49657 (437*2π)/5951 weeks
4387.78325 18.51783 (438*2π)/5951 weeks
439-12.62449 4.2433 (439*2π)/5951 weeks
440-8.72613 -18.86886 (440*2π)/5951 weeks
44112.65573 -25.07772 (441*2π)/5951 weeks
44227.60376 -9.86527 (442*2π)/5951 weeks
44323.23157 11.16884 (443*2π)/5951 weeks
4441.86705 20.39377 (444*2π)/5951 weeks
445-19.55711 9.01276 (445*2π)/5951 weeks
446-26.01201 -16.05297 (446*2π)/5951 weeks
447-10.37333 -39.57844 (447*2π)/5951 weeks
44818.78007 -43.31843 (448*2π)/5951 weeks
44940.04165 -23.98281 (449*2π)/5951 weeks
45040.3623 3.10696 (450*2π)/5951 weeks
45120.91289 20.0363 (451*2π)/5951 weeks
452-2.42544 14.758 (452*2π)/5951 weeks
453-8.59934 -4.77649 (453*2π)/5951 weeks
4543.7877 -17.48647 (454*2π)/5951 weeks
45519.59856 -12.1726 (455*2π)/5951 weeks
45621.86189 5.57935 (456*2π)/5951 weeks
4575.76928 17.58462 (457*2π)/5951 weeks
458-15.39247 9.83799 (458*2π)/5951 weeks
459-22.15326 -13.80531 (459*2π)/5951 weeks
460-5.4861 -34.57881 (460*2π)/5951 weeks
46122.60251 -33.15886 (461*2π)/5951 weeks
46237.00013 -7.99857 (462*2π)/5951 weeks
46323.99228 17.69694 (463*2π)/5951 weeks
464-4.40295 21.40066 (464*2π)/5951 weeks
465-22.05149 -.12668 (465*2π)/5951 weeks
466-15.10939 -25.1172 (466*2π)/5951 weeks
4678.1104 -32.90386 (467*2π)/5951 weeks
46826.48168 -17.96998 (468*2π)/5951 weeks
46922.88397 5.36399 (469*2π)/5951 weeks
470.1512 13.37096 (470*2π)/5951 weeks
471-20.19956 -2.888 (471*2π)/5951 weeks
472-17.14116 -30.67412 (472*2π)/5951 weeks
4738.28549 -45.1813 (473*2π)/5951 weeks
47436.91046 -33.26731 (474*2π)/5951 weeks
47543.73365 -2.75142 (475*2π)/5951 weeks
47622.27043 19.66751 (476*2π)/5951 weeks
477-6.8437 13.59779 (477*2π)/5951 weeks
478-15.91222 -13.58224 (478*2π)/5951 weeks
4792.02724 -35.37625 (479*2π)/5951 weeks
48030.6411 -32.5369 (480*2π)/5951 weeks
48145.27765 -6.5596 (481*2π)/5951 weeks
48233.29047 20.15192 (482*2π)/5951 weeks
4835.59837 27.23953 (483*2π)/5951 weeks
484-15.54204 9.77451 (484*2π)/5951 weeks
485-12.91435 -15.73591 (485*2π)/5951 weeks
4868.39424 -26.07274 (486*2π)/5951 weeks
48728.79109 -14.31059 (487*2π)/5951 weeks
48830.67153 10.82347 (488*2π)/5951 weeks
48910.0279 28.52009 (489*2π)/5951 weeks
490-17.9803 22.54651 (490*2π)/5951 weeks
491-30.79502 -1.97638 (491*2π)/5951 weeks
492-21.10915 -25.85439 (492*2π)/5951 weeks
493-.10943 -32.58483 (493*2π)/5951 weeks
49416.30616 -21.76382 (494*2π)/5951 weeks
49515.1125 -3.4578 (495*2π)/5951 weeks
496-2.5075 3.45037 (496*2π)/5951 weeks
497-18.41385 -11.3273 (497*2π)/5951 weeks
498-12.76388 -35.82346 (498*2π)/5951 weeks
49913.11975 -47.05249 (499*2π)/5951 weeks
50041.05799 -31.87741 (500*2π)/5951 weeks
50146.53598 2.8064 (501*2π)/5951 weeks
50220.58844 29.48863 (502*2π)/5951 weeks
503-19.1881 23.50813 (503*2π)/5951 weeks
504-35.2224 -14.74176 (504*2π)/5951 weeks
505-13.24557 -47.4965 (505*2π)/5951 weeks
50624.97702 -49.46443 (506*2π)/5951 weeks
50748.87752 -19.56988 (507*2π)/5951 weeks
50837.76033 15.58764 (508*2π)/5951 weeks
5095.93295 25.93241 (509*2π)/5951 weeks
510-19.55522 7.2619 (510*2π)/5951 weeks
511-15.87333 -22.49036 (511*2π)/5951 weeks
5129.21979 -29.95233 (512*2π)/5951 weeks
51325.74679 -13.78308 (513*2π)/5951 weeks
51420.99304 9.82856 (514*2π)/5951 weeks
515-6.54999 20.88837 (515*2π)/5951 weeks
516-32.7171 -.12379 (516*2π)/5951 weeks
517-30.76802 -33.99246 (517*2π)/5951 weeks
518-2.35682 -53.38007 (518*2π)/5951 weeks
51927.82145 -40.85002 (519*2π)/5951 weeks
52030.52011 -13.56188 (520*2π)/5951 weeks
52113.11405 -4.99826 (521*2π)/5951 weeks
5225.48892 -16.08494 (522*2π)/5951 weeks
52318.47318 -26.23986 (523*2π)/5951 weeks
52437.9981 -10.20316 (524*2π)/5951 weeks
52529.83525 22.34481 (525*2π)/5951 weeks
526-7.41479 33.95466 (526*2π)/5951 weeks
527-41.53971 9.60985 (527*2π)/5951 weeks
528-41.9572 -35.59462 (528*2π)/5951 weeks
529-5.45615 -58.25051 (529*2π)/5951 weeks
53027.26104 -43.00585 (530*2π)/5951 weeks
53132.13086 -13.92591 (531*2π)/5951 weeks
53213.21766 1.43769 (532*2π)/5951 weeks
533-3.90184 -7.17762 (533*2π)/5951 weeks
534-1.45027 -23.03942 (534*2π)/5951 weeks
53510.88635 -25.74236 (535*2π)/5951 weeks
53620.18675 -16.28728 (536*2π)/5951 weeks
53719.15634 -1.54957 (537*2π)/5951 weeks
5386.0703 9.43176 (538*2π)/5951 weeks
539-13.56572 8.60525 (539*2π)/5951 weeks
540-30.46934 -5.50437 (540*2π)/5951 weeks
541-32.50764 -30.49111 (541*2π)/5951 weeks
542-17.79311 -49.11225 (542*2π)/5951 weeks
5436.81902 -52.74683 (543*2π)/5951 weeks
54423.75803 -36.58807 (544*2π)/5951 weeks
54521.10505 -12.34599 (545*2π)/5951 weeks
546-3.64109 -1.82861 (546*2π)/5951 weeks
547-28.45303 -22.72541 (547*2π)/5951 weeks
548-20.98125 -59.30228 (548*2π)/5951 weeks
54917.55602 -73.52979 (549*2π)/5951 weeks
55057.28843 -45.45009 (550*2π)/5951 weeks
55149.79985 8.27638 (551*2π)/5951 weeks
552-2.7226 29.85316 (552*2π)/5951 weeks
553-52.75256 -8.3443 (553*2π)/5951 weeks
554-44.12499 -77.24866 (554*2π)/5951 weeks
55529.98888 -109.3963 (555*2π)/5951 weeks
556104.3935 -52.89037 (556*2π)/5951 weeks
55793.75005 53.78394 (557*2π)/5951 weeks
558-16.27178 106.3964 (558*2π)/5951 weeks
559-128.307 34.93336 (559*2π)/5951 weeks
560-126.6978 -102.1778 (560*2π)/5951 weeks
561-10.07209 -172.6764 (561*2π)/5951 weeks
562106.8357 -110.7676 (562*2π)/5951 weeks
563109.9323 16.39832 (563*2π)/5951 weeks
5643.48066 81.10368 (564*2π)/5951 weeks
565-103.3642 25.6995 (565*2π)/5951 weeks
566-119.5618 -90.9063 (566*2π)/5951 weeks
567-36.12742 -169.4527 (567*2π)/5951 weeks
56863.65142 -150.2608 (568*2π)/5951 weeks
56999.27813 -72.58154 (569*2π)/5951 weeks
57066.95015 -16.38882 (570*2π)/5951 weeks
57121.41649 -12.82118 (571*2π)/5951 weeks
5723.12907 -37.24021 (572*2π)/5951 weeks
57312.74008 -55.8534 (573*2π)/5951 weeks
57430.4976 -52.79235 (574*2π)/5951 weeks
57537.04537 -32.585 (575*2π)/5951 weeks
57617.62958 -6.19929 (576*2π)/5951 weeks
577-22.27052 -5.15978 (577*2π)/5951 weeks
578-62.62671 -28.49278 (578*2π)/5951 weeks
579-84.90246 -86.3969 (579*2π)/5951 weeks
580-56.07814 -156.0864 (580*2π)/5951 weeks
58120.70347 -189.6733 (581*2π)/5951 weeks
582105.1455 -147.1194 (582*2π)/5951 weeks
583122.3383 -38.35335 (583*2π)/5951 weeks
58419.07068 42.74208 (584*2π)/5951 weeks
585-119.168 -1.21682 (585*2π)/5951 weeks
586-175.3971 -159.3468 (586*2π)/5951 weeks
587-66.49224 -299.2688 (587*2π)/5951 weeks
58890.91467 -261.409 (588*2π)/5951 weeks
58976.12936 -93.72879 (589*2π)/5951 weeks
590-168.9857 -55.55598 (590*2π)/5951 weeks
591-440.7619 -383.1784 (591*2π)/5951 weeks
592-309.6936 -1,007.081 (592*2π)/5951 weeks
593425.0009 -1,459.812 (593*2π)/5951 weeks