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Fourier Analysis of SDS (PROSHARES ULTRASHORT S&P500 PROSHARES ULTRASHORT S&P500)


SDS (PROSHARES ULTRASHORT S&P500 PROSHARES ULTRASHORT S&P500) appears to have interesting cyclic behaviour every 60 weeks (50.8945*sine), 55 weeks (28.9641*sine), and 17 weeks (19.02*cosine).

SDS (PROSHARES ULTRASHORT S&P500 PROSHARES ULTRASHORT S&P500) has an average price of 390.63 (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 7/13/2006 to 1/16/2018 for SDS (PROSHARES ULTRASHORT S&P500 PROSHARES ULTRASHORT S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0390.6291   0 
191.09415 402.4055 (1*2π)/602602 weeks
2-90.5679 145.7836 (2*2π)/602301 weeks
3-46.68009 1.29752 (3*2π)/602201 weeks
457.53072 4.65307 (4*2π)/602151 weeks
559.07951 73.9603 (5*2π)/602120 weeks
6-2.0409 85.32735 (6*2π)/602100 weeks
7-33.46786 32.95829 (7*2π)/60286 weeks
85.46966 -7.21623 (8*2π)/60275 weeks
939.88745 33.36695 (9*2π)/60267 weeks
10.37859 50.89452 (10*2π)/60260 weeks
11-8.96288 28.96414 (11*2π)/60255 weeks
12-12.55651 13.46539 (12*2π)/60250 weeks
139.28583 1.15003 (13*2π)/60246 weeks
1417.6027 21.40017 (14*2π)/60243 weeks
154.64214 25.81217 (15*2π)/60240 weeks
16-.75964 21.06713 (16*2π)/60238 weeks
17.37105 14.0228 (17*2π)/60235 weeks
182.35342 17.79853 (18*2π)/60233 weeks
19-1.15573 7.94237 (19*2π)/60232 weeks
207.90977 10.49314 (20*2π)/60230 weeks
216.79016 12.82136 (21*2π)/60229 weeks
226.70466 16.94394 (22*2π)/60227 weeks
231.96073 19.70759 (23*2π)/60226 weeks
24-4.94235 14.33635 (24*2π)/60225 weeks
251.16036 5.14492 (25*2π)/60224 weeks
264.86496 13.359 (26*2π)/60223 weeks
27-1.54494 17.31593 (27*2π)/60222 weeks
28-10.50642 6.90642 (28*2π)/60222 weeks
294.58391 -4.41927 (29*2π)/60221 weeks
3012.39104 6.20553 (30*2π)/60220 weeks
319.27414 16.92741 (31*2π)/60219 weeks
32-6.70523 18.97049 (32*2π)/60219 weeks
33-10.81574 1.3887 (33*2π)/60218 weeks
346.81253 -6.06038 (34*2π)/60218 weeks
3519.02001 7.29684 (35*2π)/60217 weeks
366.90211 24.85476 (36*2π)/60217 weeks
37-13.95268 15.36605 (37*2π)/60216 weeks
38-6.52874 -2.91202 (38*2π)/60216 weeks
396.53735 -.19503 (39*2π)/60215 weeks
408.12357 9.24846 (40*2π)/60215 weeks
41.14432 11.08535 (41*2π)/60215 weeks
42-1.50998 6.87261 (42*2π)/60214 weeks
43-.00362 4.40856 (43*2π)/60214 weeks
442.62761 3.06198 (44*2π)/60214 weeks
454.94922 8.62868 (45*2π)/60213 weeks
46-1.58039 7.00003 (46*2π)/60213 weeks
472.21372 3.9185 (47*2π)/60213 weeks
48.78894 6.73185 (48*2π)/60213 weeks
49.57276 4.69529 (49*2π)/60212 weeks
50-.20511 2.98443 (50*2π)/60212 weeks
513.7661 .68028 (51*2π)/60212 weeks
526.04904 6.42908 (52*2π)/60212 weeks
534.27413 7.77749 (53*2π)/60211 weeks
54.27792 8.01109 (54*2π)/60211 weeks
55-.79098 4.9894 (55*2π)/60211 weeks
562.16159 3.18961 (56*2π)/60211 weeks
573.26093 6.88642 (57*2π)/60211 weeks
58-.03767 7.16325 (58*2π)/60210 weeks
59-3.04593 4.06487 (59*2π)/60210 weeks
60-.21474 -1.70509 (60*2π)/60210 weeks
617.66906 .62909 (61*2π)/60210 weeks
624.88476 9.69499 (62*2π)/60210 weeks
63-1.927 7.43116 (63*2π)/60210 weeks
64-1.65724 1.57679 (64*2π)/6029 weeks
652.69639 .4556 (65*2π)/6029 weeks
665.45106 4.4897 (66*2π)/6029 weeks
67.15108 6.69814 (67*2π)/6029 weeks
68.01694 .95226 (68*2π)/6029 weeks
694.15065 1.88688 (69*2π)/6029 weeks
705.51448 5.28968 (70*2π)/6029 weeks
71.98144 7.81321 (71*2π)/6028 weeks
72-2.12096 3.46393 (72*2π)/6028 weeks
732.95238 1.8783 (73*2π)/6028 weeks
742.16778 3.31302 (74*2π)/6028 weeks
752.51343 5.2366 (75*2π)/6028 weeks
76-1.02716 2.47443 (76*2π)/6028 weeks
774.79223 .4896 (77*2π)/6028 weeks
785.83956 6.90967 (78*2π)/6028 weeks
79-.60672 8.89456 (79*2π)/6028 weeks
80-4.56893 3.87441 (80*2π)/6028 weeks
81.32886 -2.59763 (81*2π)/6027 weeks
825.75378 2.11108 (82*2π)/6027 weeks
832.35257 5.20802 (83*2π)/6027 weeks
841.77532 5.91968 (84*2π)/6027 weeks
85-3.9933 3.25429 (85*2π)/6027 weeks
861.81096 -3.65525 (86*2π)/6027 weeks
877.48594 2.65066 (87*2π)/6027 weeks
883.94198 7.52576 (88*2π)/6027 weeks
89-2.11196 6.84987 (89*2π)/6027 weeks
90-2.44908 .09991 (90*2π)/6027 weeks
912.56237 -.43575 (91*2π)/6027 weeks
925.73502 1.99174 (92*2π)/6027 weeks
933.67045 8.51116 (93*2π)/6026 weeks
94-4.04294 5.93096 (94*2π)/6026 weeks
95-2.67035 -.89125 (95*2π)/6026 weeks
963.33329 -2.14119 (96*2π)/6026 weeks
975.37371 2.82108 (97*2π)/6026 weeks
981.96437 5.9137 (98*2π)/6026 weeks
99-1.16407 3.46629 (99*2π)/6026 weeks
100.95682 .53565 (100*2π)/6026 weeks
1013.1913 2.13335 (101*2π)/6026 weeks
1021.36016 4.30389 (102*2π)/6026 weeks
103-.36369 1.17986 (103*2π)/6026 weeks
1043.12089 1.60726 (104*2π)/6026 weeks
105.94714 3.65007 (105*2π)/6026 weeks
106-.52886 1.87768 (106*2π)/6026 weeks
1071.25244 -.87233 (107*2π)/6026 weeks
1084.99838 .71653 (108*2π)/6026 weeks
1094.24138 4.91713 (109*2π)/6026 weeks
110-.05335 4.86029 (110*2π)/6025 weeks
111-1.67628 1.01529 (111*2π)/6025 weeks
1122.5546 -1.36027 (112*2π)/6025 weeks
1136.15958 2.7067 (113*2π)/6025 weeks
1142.46695 7.06475 (114*2π)/6025 weeks
115-3.11488 5.32511 (115*2π)/6025 weeks
116-2.88202 -1.5869 (116*2π)/6025 weeks
1172.40181 -2.74126 (117*2π)/6025 weeks
1186.29028 1.07417 (118*2π)/6025 weeks
1193.39061 6.22119 (119*2π)/6025 weeks
120-1.97792 3.73195 (120*2π)/6025 weeks
121-.97514 -1.73651 (121*2π)/6025 weeks
1224.62202 -1.38939 (122*2π)/6025 weeks
1235.6384 3.37739 (123*2π)/6025 weeks
1242.55662 5.99439 (124*2π)/6025 weeks
125-2.30141 4.25694 (125*2π)/6025 weeks
126-1.04611 -1.4736 (126*2π)/6025 weeks
1273.78857 -1.12875 (127*2π)/6025 weeks
1284.5167 2.97158 (128*2π)/6025 weeks
1292.16807 4.89587 (129*2π)/6025 weeks
130-1.00804 3.15669 (130*2π)/6025 weeks
131.49954 -.4118 (131*2π)/6025 weeks
1323.36288 .0686 (132*2π)/6025 weeks
1333.86196 3.90424 (133*2π)/6025 weeks
134.02252 4.97805 (134*2π)/6024 weeks
135-2.26936 1.1248 (135*2π)/6024 weeks
1361.44245 -1.27846 (136*2π)/6024 weeks
1373.50691 .5516 (137*2π)/6024 weeks
1382.22658 2.7028 (138*2π)/6024 weeks
1391.06803 2.10633 (139*2π)/6024 weeks
1401.16959 2.07548 (140*2π)/6024 weeks
141.36592 .92771 (141*2π)/6024 weeks
1421.93916 -.27712 (142*2π)/6024 weeks
1433.31339 1.63668 (143*2π)/6024 weeks
1441.382 2.21277 (144*2π)/6024 weeks
1451.31188 .45435 (145*2π)/6024 weeks
1463.20429 1.46892 (146*2π)/6024 weeks
1472.45471 2.80672 (147*2π)/6024 weeks
1481.92077 2.76251 (148*2π)/6024 weeks
149-.1003 2.36227 (149*2π)/6024 weeks
150.77795 .34111 (150*2π)/6024 weeks
1511.75266 1.44099 (151*2π)/6024 weeks
1521.43569 .40083 (152*2π)/6024 weeks
1533.07589 .79536 (153*2π)/6024 weeks
1542.91512 1.98665 (154*2π)/6024 weeks
1551.16333 3.6449 (155*2π)/6024 weeks
156-.66359 .44475 (156*2π)/6024 weeks
1573.1812 -.00464 (157*2π)/6024 weeks
1582.7876 3.31296 (158*2π)/6024 weeks
159.47081 2.19946 (159*2π)/6024 weeks
160.60443 .44295 (160*2π)/6024 weeks
1612.55192 .324 (161*2π)/6024 weeks
1622.85187 2.69796 (162*2π)/6024 weeks
163.79551 2.62213 (163*2π)/6024 weeks
164-.23914 1.29766 (164*2π)/6024 weeks
1651.33689 -1.08855 (165*2π)/6024 weeks
1663.93594 1.59093 (166*2π)/6024 weeks
1671.13099 2.8094 (167*2π)/6024 weeks
168.79243 1.37476 (168*2π)/6024 weeks
1691.40561 .59719 (169*2π)/6024 weeks
1702.22558 1.30216 (170*2π)/6024 weeks
1711.4117 1.53203 (171*2π)/6024 weeks
1721.4849 1.19207 (172*2π)/6024 weeks
173.80627 1.7345 (173*2π)/6023 weeks
1741.32664 -.46703 (174*2π)/6023 weeks
1753.03085 1.54077 (175*2π)/6023 weeks
1761.31844 1.82259 (176*2π)/6023 weeks
1771.56448 1.01342 (177*2π)/6023 weeks
1781.73078 1.36869 (178*2π)/6023 weeks
1791.23505 1.58948 (179*2π)/6023 weeks
1801.4303 .07734 (180*2π)/6023 weeks
1812.46574 .73651 (181*2π)/6023 weeks
1823.19743 1.40079 (182*2π)/6023 weeks
1831.82569 3.21235 (183*2π)/6023 weeks
184.01902 1.95554 (184*2π)/6023 weeks
185.69695 .26131 (185*2π)/6023 weeks
1862.28032 .61264 (186*2π)/6023 weeks
1871.83782 1.95831 (187*2π)/6023 weeks
188.72363 1.78137 (188*2π)/6023 weeks
189.77564 .07743 (189*2π)/6023 weeks
1901.97219 .10368 (190*2π)/6023 weeks
1912.93117 .94107 (191*2π)/6023 weeks
1922.41662 2.6389 (192*2π)/6023 weeks
193.71455 2.70894 (193*2π)/6023 weeks
194-.33885 1.28301 (194*2π)/6023 weeks
195.24844 -.72267 (195*2π)/6023 weeks
1962.91918 -.40232 (196*2π)/6023 weeks
1972.99983 1.95943 (197*2π)/6023 weeks
1981.1404 2.8814 (198*2π)/6023 weeks
199-.62285 1.05493 (199*2π)/6023 weeks
2001.25973 -.7904 (200*2π)/6023 weeks
2012.64603 .14997 (201*2π)/6023 weeks
2022.72876 2.17559 (202*2π)/6023 weeks
203.62556 2.07148 (203*2π)/6023 weeks
204.7475 .84623 (204*2π)/6023 weeks
2051.29223 -.06733 (205*2π)/6023 weeks
2062.71929 1.2388 (206*2π)/6023 weeks
207.81255 2.70583 (207*2π)/6023 weeks
208-.3292 .73963 (208*2π)/6023 weeks
209.36052 -.67233 (209*2π)/6023 weeks
2102.32264 -.97552 (210*2π)/6023 weeks
2112.96157 .98311 (211*2π)/6023 weeks
2122.62872 1.3707 (212*2π)/6023 weeks
2131.54327 3.2734 (213*2π)/6023 weeks
214-1.36408 .76789 (214*2π)/6023 weeks
2151.1785 -.62306 (215*2π)/6023 weeks
2161.7766 -.04013 (216*2π)/6023 weeks
2172.17059 .75091 (217*2π)/6023 weeks
2181.30842 .85812 (218*2π)/6023 weeks
2192.01603 .03045 (219*2π)/6023 weeks
2201.5579 1.14154 (220*2π)/6023 weeks
2212.54858 -.03274 (221*2π)/6023 weeks
2222.44042 2.74322 (222*2π)/6023 weeks
223.58766 1.8108 (223*2π)/6023 weeks
224.08285 1.87914 (224*2π)/6023 weeks
225-.64138 -.76293 (225*2π)/6023 weeks
2262.69412 -1.89737 (226*2π)/6023 weeks
2273.93756 1.69561 (227*2π)/6023 weeks
2281.14792 3.42996 (228*2π)/6023 weeks
229-1.48358 .97539 (229*2π)/6023 weeks
230.90398 -1.98108 (230*2π)/6023 weeks
2313.49465 .31107 (231*2π)/6023 weeks
2322.30794 2.48434 (232*2π)/6023 weeks
233-.34563 2.48576 (233*2π)/6023 weeks
234-1.68816 -1.35098 (234*2π)/6023 weeks
2352.93426 -2.46017 (235*2π)/6023 weeks
2364.44974 1.01412 (236*2π)/6023 weeks
2371.78119 3.24242 (237*2π)/6023 weeks
238-.76132 1.10409 (238*2π)/6023 weeks
2391.04417 -.82822 (239*2π)/6023 weeks
2402.15744 .62905 (240*2π)/6023 weeks
2411.0644 .72269 (241*2π)/6022 weeks
2421.46766 -.12089 (242*2π)/6022 weeks
2432.01651 .5014 (243*2π)/6022 weeks
2442.46304 .7228 (244*2π)/6022 weeks
2451.93304 2.71495 (245*2π)/6022 weeks
246-.89533 1.58376 (246*2π)/6022 weeks
247.26607 -.74537 (247*2π)/6022 weeks
2481.89148 -.74704 (248*2π)/6022 weeks
2492.49388 1.71697 (249*2π)/6022 weeks
250-.55527 1.8265 (250*2π)/6022 weeks
251-.31478 -.6023 (251*2π)/6022 weeks
2521.03701 -1.43771 (252*2π)/6022 weeks
2532.79305 -.99447 (253*2π)/6022 weeks
2542.41063 1.42871 (254*2π)/6022 weeks
255.30997 1.31684 (255*2π)/6022 weeks
256-.0629 -.77145 (256*2π)/6022 weeks
2572.18982 -2.00447 (257*2π)/6022 weeks
2584.20791 .40034 (258*2π)/6022 weeks
2592.11942 2.99015 (259*2π)/6022 weeks
260-.41373 1.64522 (260*2π)/6022 weeks
261-.57422 -.54924 (261*2π)/6022 weeks
2622.38926 -2.04117 (262*2π)/6022 weeks
2632.93073 .92761 (263*2π)/6022 weeks
2641.75007 1.48416 (264*2π)/6022 weeks
265-.04322 1.26504 (265*2π)/6022 weeks
266.79746 -.87081 (266*2π)/6022 weeks
2671.82086 .00161 (267*2π)/6022 weeks
2681.78379 .26739 (268*2π)/6022 weeks
2691.48989 1.37412 (269*2π)/6022 weeks
270-.15667 .77314 (270*2π)/6022 weeks
271.56032 -1.14558 (271*2π)/6022 weeks
2721.40385 -1.3559 (272*2π)/6022 weeks
2733.22643 -.42886 (273*2π)/6022 weeks
2742.53199 1.91532 (274*2π)/6022 weeks
275.01026 1.57241 (275*2π)/6022 weeks
276-.62412 -.39266 (276*2π)/6022 weeks
277.74687 -2.00513 (277*2π)/6022 weeks
2783.22282 -2.06216 (278*2π)/6022 weeks
2794.17775 1.14048 (279*2π)/6022 weeks
2801.64663 3.60104 (280*2π)/6022 weeks
281-2.45552 .98246 (281*2π)/6022 weeks
282.17727 -3.23573 (282*2π)/6022 weeks
2833.4465 -1.65129 (283*2π)/6022 weeks
2843.7855 .97004 (284*2π)/6022 weeks
285.78891 3.01163 (285*2π)/6022 weeks
286-2.01705 -.17231 (286*2π)/6022 weeks
287.61421 -3.4953 (287*2π)/6022 weeks
2884.31092 -1.0548 (288*2π)/6022 weeks
2892.72915 1.54523 (289*2π)/6022 weeks
290.27152 1.11362 (290*2π)/6022 weeks
291-.03938 -1.38943 (291*2π)/6022 weeks
2922.03815 -2.28864 (292*2π)/6022 weeks
2934.83504 -.80308 (293*2π)/6022 weeks
2943.19614 3.13778 (294*2π)/6022 weeks
295-.90653 1.33773 (295*2π)/6022 weeks
296.3633 -1.68163 (296*2π)/6022 weeks
2972.48392 -1.17182 (297*2π)/6022 weeks
2983.39662 .45161 (298*2π)/6022 weeks
2992.29315 1.47767 (299*2π)/6022 weeks
300.87635 2.08173 (300*2π)/6022 weeks
301-1.31264   (301*2π)/6022 weeks
302.87635 -2.08173 (302*2π)/6022 weeks
3032.29315 -1.47767 (303*2π)/6022 weeks
3043.39662 -.45161 (304*2π)/6022 weeks
3052.48392 1.17182 (305*2π)/6022 weeks
306.3633 1.68163 (306*2π)/6022 weeks
307-.90653 -1.33773 (307*2π)/6022 weeks
3083.19614 -3.13778 (308*2π)/6022 weeks
3094.83504 .80308 (309*2π)/6022 weeks
3102.03815 2.28864 (310*2π)/6022 weeks
311-.03938 1.38943 (311*2π)/6022 weeks
312.27152 -1.11362 (312*2π)/6022 weeks
3132.72915 -1.54523 (313*2π)/6022 weeks
3144.31092 1.0548 (314*2π)/6022 weeks
315.61421 3.4953 (315*2π)/6022 weeks
316-2.01705 .17231 (316*2π)/6022 weeks
317.78891 -3.01163 (317*2π)/6022 weeks
3183.7855 -.97004 (318*2π)/6022 weeks
3193.4465 1.65129 (319*2π)/6022 weeks
320.17727 3.23573 (320*2π)/6022 weeks
321-2.45552 -.98246 (321*2π)/6022 weeks
3221.64663 -3.60104 (322*2π)/6022 weeks
3234.17775 -1.14048 (323*2π)/6022 weeks
3243.22282 2.06216 (324*2π)/6022 weeks
325.74687 2.00513 (325*2π)/6022 weeks
326-.62412 .39266 (326*2π)/6022 weeks
327.01026 -1.57241 (327*2π)/6022 weeks
3282.53199 -1.91532 (328*2π)/6022 weeks
3293.22643 .42886 (329*2π)/6022 weeks
3301.40385 1.3559 (330*2π)/6022 weeks
331.56032 1.14558 (331*2π)/6022 weeks
332-.15667 -.77314 (332*2π)/6022 weeks
3331.48989 -1.37412 (333*2π)/6022 weeks
3341.78379 -.26739 (334*2π)/6022 weeks
3351.82086 -.00161 (335*2π)/6022 weeks
336.79746 .87081 (336*2π)/6022 weeks
337-.04322 -1.26504 (337*2π)/6022 weeks
3381.75007 -1.48416 (338*2π)/6022 weeks
3392.93073 -.92761 (339*2π)/6022 weeks
3402.38926 2.04117 (340*2π)/6022 weeks
341-.57422 .54924 (341*2π)/6022 weeks
342-.41373 -1.64522 (342*2π)/6022 weeks
3432.11942 -2.99015 (343*2π)/6022 weeks
3444.20791 -.40034 (344*2π)/6022 weeks
3452.18982 2.00447 (345*2π)/6022 weeks
346-.0629 .77145 (346*2π)/6022 weeks
347.30997 -1.31684 (347*2π)/6022 weeks
3482.41063 -1.42871 (348*2π)/6022 weeks
3492.79305 .99447 (349*2π)/6022 weeks
3501.03701 1.43771 (350*2π)/6022 weeks
351-.31478 .6023 (351*2π)/6022 weeks
352-.55527 -1.8265 (352*2π)/6022 weeks
3532.49388 -1.71697 (353*2π)/6022 weeks
3541.89148 .74704 (354*2π)/6022 weeks
355.26607 .74537 (355*2π)/6022 weeks
356-.89533 -1.58376 (356*2π)/6022 weeks
3571.93304 -2.71495 (357*2π)/6022 weeks
3582.46304 -.7228 (358*2π)/6022 weeks
3592.01651 -.5014 (359*2π)/6022 weeks
3601.46766 .12089 (360*2π)/6022 weeks
3611.0644 -.72269 (361*2π)/6022 weeks
3622.15744 -.62905 (362*2π)/6022 weeks
3631.04417 .82822 (363*2π)/6022 weeks
364-.76132 -1.10409 (364*2π)/6022 weeks
3651.78119 -3.24242 (365*2π)/6022 weeks
3664.44974 -1.01412 (366*2π)/6022 weeks
3672.93426 2.46017 (367*2π)/6022 weeks
368-1.68816 1.35098 (368*2π)/6022 weeks
369-.34563 -2.48576 (369*2π)/6022 weeks
3702.30794 -2.48434 (370*2π)/6022 weeks
3713.49465 -.31107 (371*2π)/6022 weeks
372.90398 1.98108 (372*2π)/6022 weeks
373-1.48358 -.97539 (373*2π)/6022 weeks
3741.14792 -3.42996 (374*2π)/6022 weeks
3753.93756 -1.69561 (375*2π)/6022 weeks
3762.69412 1.89737 (376*2π)/6022 weeks
377-.64138 .76293 (377*2π)/6022 weeks
378.08285 -1.87914 (378*2π)/6022 weeks
379.58766 -1.8108 (379*2π)/6022 weeks
3802.44042 -2.74322 (380*2π)/6022 weeks
3812.54858 .03274 (381*2π)/6022 weeks
3821.5579 -1.14154 (382*2π)/6022 weeks
3832.01603 -.03045 (383*2π)/6022 weeks
3841.30842 -.85812 (384*2π)/6022 weeks
3852.17059 -.75091 (385*2π)/6022 weeks
3861.7766 .04013 (386*2π)/6022 weeks
3871.1785 .62306 (387*2π)/6022 weeks
388-1.36408 -.76789 (388*2π)/6022 weeks
3891.54327 -3.2734 (389*2π)/6022 weeks
3902.62872 -1.3707 (390*2π)/6022 weeks
3912.96157 -.98311 (391*2π)/6022 weeks
3922.32264 .97552 (392*2π)/6022 weeks
393.36052 .67233 (393*2π)/6022 weeks
394-.3292 -.73963 (394*2π)/6022 weeks
395.81255 -2.70583 (395*2π)/6022 weeks
3962.71929 -1.2388 (396*2π)/6022 weeks
3971.29223 .06733 (397*2π)/6022 weeks
398.7475 -.84623 (398*2π)/6022 weeks
399.62556 -2.07148 (399*2π)/6022 weeks
4002.72876 -2.17559 (400*2π)/6022 weeks
4012.64603 -.14997 (401*2π)/6022 weeks
4021.25973 .7904 (402*2π)/6021 weeks
403-.62285 -1.05493 (403*2π)/6021 weeks
4041.1404 -2.8814 (404*2π)/6021 weeks
4052.99983 -1.95943 (405*2π)/6021 weeks
4062.91918 .40232 (406*2π)/6021 weeks
407.24844 .72267 (407*2π)/6021 weeks
408-.33885 -1.28301 (408*2π)/6021 weeks
409.71455 -2.70894 (409*2π)/6021 weeks
4102.41662 -2.6389 (410*2π)/6021 weeks
4112.93117 -.94107 (411*2π)/6021 weeks
4121.97219 -.10368 (412*2π)/6021 weeks
413.77564 -.07743 (413*2π)/6021 weeks
414.72363 -1.78137 (414*2π)/6021 weeks
4151.83782 -1.95831 (415*2π)/6021 weeks
4162.28032 -.61264 (416*2π)/6021 weeks
417.69695 -.26131 (417*2π)/6021 weeks
418.01902 -1.95554 (418*2π)/6021 weeks
4191.82569 -3.21235 (419*2π)/6021 weeks
4203.19743 -1.40079 (420*2π)/6021 weeks
4212.46574 -.73651 (421*2π)/6021 weeks
4221.4303 -.07734 (422*2π)/6021 weeks
4231.23505 -1.58948 (423*2π)/6021 weeks
4241.73078 -1.36869 (424*2π)/6021 weeks
4251.56448 -1.01342 (425*2π)/6021 weeks
4261.31844 -1.82259 (426*2π)/6021 weeks
4273.03085 -1.54077 (427*2π)/6021 weeks
4281.32664 .46703 (428*2π)/6021 weeks
429.80627 -1.7345 (429*2π)/6021 weeks
4301.4849 -1.19207 (430*2π)/6021 weeks
4311.4117 -1.53203 (431*2π)/6021 weeks
4322.22558 -1.30216 (432*2π)/6021 weeks
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434.79243 -1.37476 (434*2π)/6021 weeks
4351.13099 -2.8094 (435*2π)/6021 weeks
4363.93594 -1.59093 (436*2π)/6021 weeks
4371.33689 1.08855 (437*2π)/6021 weeks
438-.23914 -1.29766 (438*2π)/6021 weeks
439.79551 -2.62213 (439*2π)/6021 weeks
4402.85187 -2.69796 (440*2π)/6021 weeks
4412.55192 -.324 (441*2π)/6021 weeks
442.60443 -.44295 (442*2π)/6021 weeks
443.47081 -2.19946 (443*2π)/6021 weeks
4442.7876 -3.31296 (444*2π)/6021 weeks
4453.1812 .00464 (445*2π)/6021 weeks
446-.66359 -.44475 (446*2π)/6021 weeks
4471.16333 -3.6449 (447*2π)/6021 weeks
4482.91512 -1.98665 (448*2π)/6021 weeks
4493.07589 -.79536 (449*2π)/6021 weeks
4501.43569 -.40083 (450*2π)/6021 weeks
4511.75266 -1.44099 (451*2π)/6021 weeks
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453-.1003 -2.36227 (453*2π)/6021 weeks
4541.92077 -2.76251 (454*2π)/6021 weeks
4552.45471 -2.80672 (455*2π)/6021 weeks
4563.20429 -1.46892 (456*2π)/6021 weeks
4571.31188 -.45435 (457*2π)/6021 weeks
4581.382 -2.21277 (458*2π)/6021 weeks
4593.31339 -1.63668 (459*2π)/6021 weeks
4601.93916 .27712 (460*2π)/6021 weeks
461.36592 -.92771 (461*2π)/6021 weeks
4621.16959 -2.07548 (462*2π)/6021 weeks
4631.06803 -2.10633 (463*2π)/6021 weeks
4642.22658 -2.7028 (464*2π)/6021 weeks
4653.50691 -.5516 (465*2π)/6021 weeks
4661.44245 1.27846 (466*2π)/6021 weeks
467-2.26936 -1.1248 (467*2π)/6021 weeks
468.02252 -4.97805 (468*2π)/6021 weeks
4693.86196 -3.90424 (469*2π)/6021 weeks
4703.36288 -.0686 (470*2π)/6021 weeks
471.49954 .4118 (471*2π)/6021 weeks
472-1.00804 -3.15669 (472*2π)/6021 weeks
4732.16807 -4.89587 (473*2π)/6021 weeks
4744.5167 -2.97158 (474*2π)/6021 weeks
4753.78857 1.12875 (475*2π)/6021 weeks
476-1.04611 1.4736 (476*2π)/6021 weeks
477-2.30141 -4.25694 (477*2π)/6021 weeks
4782.55662 -5.99439 (478*2π)/6021 weeks
4795.6384 -3.37739 (479*2π)/6021 weeks
4804.62202 1.38939 (480*2π)/6021 weeks
481-.97514 1.73651 (481*2π)/6021 weeks
482-1.97792 -3.73195 (482*2π)/6021 weeks
4833.39061 -6.22119 (483*2π)/6021 weeks
4846.29028 -1.07417 (484*2π)/6021 weeks
4852.40181 2.74126 (485*2π)/6021 weeks
486-2.88202 1.5869 (486*2π)/6021 weeks
487-3.11488 -5.32511 (487*2π)/6021 weeks
4882.46695 -7.06475 (488*2π)/6021 weeks
4896.15958 -2.7067 (489*2π)/6021 weeks
4902.5546 1.36027 (490*2π)/6021 weeks
491-1.67628 -1.01529 (491*2π)/6021 weeks
492-.05335 -4.86029 (492*2π)/6021 weeks
4934.24138 -4.91713 (493*2π)/6021 weeks
4944.99838 -.71653 (494*2π)/6021 weeks
4951.25244 .87233 (495*2π)/6021 weeks
496-.52886 -1.87768 (496*2π)/6021 weeks
497.94714 -3.65007 (497*2π)/6021 weeks
4983.12089 -1.60726 (498*2π)/6021 weeks
499-.36369 -1.17986 (499*2π)/6021 weeks
5001.36016 -4.30389 (500*2π)/6021 weeks
5013.1913 -2.13335 (501*2π)/6021 weeks
502.95682 -.53565 (502*2π)/6021 weeks
503-1.16407 -3.46629 (503*2π)/6021 weeks
5041.96437 -5.9137 (504*2π)/6021 weeks
5055.37371 -2.82108 (505*2π)/6021 weeks
5063.33329 2.14119 (506*2π)/6021 weeks
507-2.67035 .89125 (507*2π)/6021 weeks
508-4.04294 -5.93096 (508*2π)/6021 weeks
5093.67045 -8.51116 (509*2π)/6021 weeks
5105.73502 -1.99174 (510*2π)/6021 weeks
5112.56237 .43575 (511*2π)/6021 weeks
512-2.44908 -.09991 (512*2π)/6021 weeks
513-2.11196 -6.84987 (513*2π)/6021 weeks
5143.94198 -7.52576 (514*2π)/6021 weeks
5157.48594 -2.65066 (515*2π)/6021 weeks
5161.81096 3.65525 (516*2π)/6021 weeks
517-3.9933 -3.25429 (517*2π)/6021 weeks
5181.77532 -5.91968 (518*2π)/6021 weeks
5192.35257 -5.20802 (519*2π)/6021 weeks
5205.75378 -2.11108 (520*2π)/6021 weeks
521.32886 2.59763 (521*2π)/6021 weeks
522-4.56893 -3.87441 (522*2π)/6021 weeks
523-.60672 -8.89456 (523*2π)/6021 weeks
5245.83956 -6.90967 (524*2π)/6021 weeks
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526-1.02716 -2.47443 (526*2π)/6021 weeks
5272.51343 -5.2366 (527*2π)/6021 weeks
5282.16778 -3.31302 (528*2π)/6021 weeks
5292.95238 -1.8783 (529*2π)/6021 weeks
530-2.12096 -3.46393 (530*2π)/6021 weeks
531.98144 -7.81321 (531*2π)/6021 weeks
5325.51448 -5.28968 (532*2π)/6021 weeks
5334.15065 -1.88688 (533*2π)/6021 weeks
534.01694 -.95226 (534*2π)/6021 weeks
535.15108 -6.69814 (535*2π)/6021 weeks
5365.45106 -4.4897 (536*2π)/6021 weeks
5372.69639 -.4556 (537*2π)/6021 weeks
538-1.65724 -1.57679 (538*2π)/6021 weeks
539-1.927 -7.43116 (539*2π)/6021 weeks
5404.88476 -9.69499 (540*2π)/6021 weeks
5417.66906 -.62909 (541*2π)/6021 weeks
542-.21474 1.70509 (542*2π)/6021 weeks
543-3.04593 -4.06487 (543*2π)/6021 weeks
544-.03767 -7.16325 (544*2π)/6021 weeks
5453.26093 -6.88642 (545*2π)/6021 weeks
5462.16159 -3.18961 (546*2π)/6021 weeks
547-.79098 -4.9894 (547*2π)/6021 weeks
548.27792 -8.01109 (548*2π)/6021 weeks
5494.27413 -7.77749 (549*2π)/6021 weeks
5506.04904 -6.42908 (550*2π)/6021 weeks
5513.7661 -.68028 (551*2π)/6021 weeks
552-.20511 -2.98443 (552*2π)/6021 weeks
553.57276 -4.69529 (553*2π)/6021 weeks
554.78894 -6.73185 (554*2π)/6021 weeks
5552.21372 -3.9185 (555*2π)/6021 weeks
556-1.58039 -7.00003 (556*2π)/6021 weeks
5574.94922 -8.62868 (557*2π)/6021 weeks
5582.62761 -3.06198 (558*2π)/6021 weeks
559-.00362 -4.40856 (559*2π)/6021 weeks
560-1.50998 -6.87261 (560*2π)/6021 weeks
561.14432 -11.08535 (561*2π)/6021 weeks
5628.12357 -9.24846 (562*2π)/6021 weeks
5636.53735 .19503 (563*2π)/6021 weeks
564-6.52874 2.91202 (564*2π)/6021 weeks
565-13.95268 -15.36605 (565*2π)/6021 weeks
5666.90211 -24.85476 (566*2π)/6021 weeks
56719.02001 -7.29684 (567*2π)/6021 weeks
5686.81253 6.06038 (568*2π)/6021 weeks
569-10.81574 -1.3887 (569*2π)/6021 weeks
570-6.70523 -18.97049 (570*2π)/6021 weeks
5719.27414 -16.92741 (571*2π)/6021 weeks
57212.39104 -6.20553 (572*2π)/6021 weeks
5734.58391 4.41927 (573*2π)/6021 weeks
574-10.50642 -6.90642 (574*2π)/6021 weeks
575-1.54494 -17.31593 (575*2π)/6021 weeks
5764.86496 -13.359 (576*2π)/6021 weeks
5771.16036 -5.14492 (577*2π)/6021 weeks
578-4.94235 -14.33635 (578*2π)/6021 weeks
5791.96073 -19.70759 (579*2π)/6021 weeks
5806.70466 -16.94394 (580*2π)/6021 weeks
5816.79016 -12.82136 (581*2π)/6021 weeks
5827.90977 -10.49314 (582*2π)/6021 weeks
583-1.15573 -7.94237 (583*2π)/6021 weeks
5842.35342 -17.79853 (584*2π)/6021 weeks
585.37105 -14.0228 (585*2π)/6021 weeks
586-.75964 -21.06713 (586*2π)/6021 weeks
5874.64214 -25.81217 (587*2π)/6021 weeks
58817.6027 -21.40017 (588*2π)/6021 weeks
5899.28583 -1.15003 (589*2π)/6021 weeks
590-12.55651 -13.46539 (590*2π)/6021 weeks
591-8.96288 -28.96414 (591*2π)/6021 weeks
592.37859 -50.89452 (592*2π)/6021 weeks
59339.88745 -33.36695 (593*2π)/6021 weeks
5945.46966 7.21623 (594*2π)/6021 weeks
595-33.46786 -32.95829 (595*2π)/6021 weeks
596-2.0409 -85.32735 (596*2π)/6021 weeks
59759.07951 -73.9603 (597*2π)/6021 weeks
59857.53072 -4.65307 (598*2π)/6021 weeks
599-46.68009 -1.29752 (599*2π)/6021 weeks
600-90.5679 -145.7836 (600*2π)/6021 weeks



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