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Fourier Analysis of SMN (ProShares UltraShort Basic Materials)


SMN (ProShares UltraShort Basic Materials) appears to have interesting cyclic behaviour every 43 weeks (68.1191*sine), 46 weeks (67.0038*sine), and 50 weeks (54.1618*cosine).

SMN (ProShares UltraShort Basic Materials) has an average price of 356.43 (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 2/2/2007 to 6/18/2018 for SMN (ProShares UltraShort Basic Materials), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0356.4261   0 
1319.1909 361.7411 (1*2π)/595595 weeks
233.43454 319.3516 (2*2π)/595298 weeks
3-82.09415 146.5371 (3*2π)/595198 weeks
4-10.41905 17.80644 (4*2π)/595149 weeks
581.34409 14.94152 (5*2π)/595119 weeks
6106.742 89.64767 (6*2π)/59599 weeks
747.56587 153.6183 (7*2π)/59585 weeks
8-44.84182 129.9449 (8*2π)/59574 weeks
9-66.36937 40.86278 (9*2π)/59566 weeks
10-17.58659 -10.0967 (10*2π)/59560 weeks
1127.31963 -3.10262 (11*2π)/59554 weeks
1254.1618 27.42276 (12*2π)/59550 weeks
1339.47009 67.00378 (13*2π)/59546 weeks
141.97123 68.11909 (14*2π)/59543 weeks
15-19.85991 48.33414 (15*2π)/59540 weeks
16-18.35411 19.33935 (16*2π)/59537 weeks
17-.33317 8.85965 (17*2π)/59535 weeks
189.91427 11.33436 (18*2π)/59533 weeks
1922.39386 15.45934 (19*2π)/59531 weeks
2022.74023 29.8598 (20*2π)/59530 weeks
2113.26886 33.84111 (21*2π)/59528 weeks
225.23308 34.97584 (22*2π)/59527 weeks
23-.71027 30.39894 (23*2π)/59526 weeks
24-2.70665 22.10024 (24*2π)/59525 weeks
252.89014 11.97772 (25*2π)/59524 weeks
2615.34002 16.24525 (26*2π)/59523 weeks
2718.06531 32.75042 (27*2π)/59522 weeks
281.2974 44.44947 (28*2π)/59521 weeks
29-19.84798 30.5296 (29*2π)/59521 weeks
30-21.7471 8.93095 (30*2π)/59520 weeks
31-4.88789 -6.43491 (31*2π)/59519 weeks
3218.36325 1.31992 (32*2π)/59519 weeks
3322.68809 22.40986 (33*2π)/59518 weeks
344.33341 37.18237 (34*2π)/59518 weeks
35-19.72877 28.26585 (35*2π)/59517 weeks
36-22.84137 1.21797 (36*2π)/59517 weeks
371.21419 -13.359 (37*2π)/59516 weeks
3819.81741 -1.24465 (38*2π)/59516 weeks
3920.80958 16.28762 (39*2π)/59515 weeks
407.27385 25.49069 (40*2π)/59515 weeks
41-3.22262 18.8737 (41*2π)/59515 weeks
42-3.33415 10.16286 (42*2π)/59514 weeks
431.06207 5.16256 (43*2π)/59514 weeks
448.48383 5.08395 (44*2π)/59514 weeks
4511.00389 13.95783 (45*2π)/59513 weeks
465.94121 17.07339 (46*2π)/59513 weeks
472.95495 16.08751 (47*2π)/59513 weeks
48.08956 15.11009 (48*2π)/59512 weeks
49.10489 13.7523 (49*2π)/59512 weeks
50-2.46826 13.42061 (50*2π)/59512 weeks
51-3.82439 9.72978 (51*2π)/59512 weeks
52-2.5615 7.92184 (52*2π)/59511 weeks
53-.65018 4.11887 (53*2π)/59511 weeks
542.39084 5.34686 (54*2π)/59511 weeks
553.81663 6.99008 (55*2π)/59511 weeks
562.54166 9.84163 (56*2π)/59511 weeks
57-1.96678 8.34138 (57*2π)/59510 weeks
58-2.44465 1.68929 (58*2π)/59510 weeks
593.92255 -2.07478 (59*2π)/59510 weeks
6013.14885 .9148 (60*2π)/59510 weeks
6114.32598 13.35357 (61*2π)/59510 weeks
624.73787 17.95107 (62*2π)/59510 weeks
63-3.51903 13.60918 (63*2π)/5959 weeks
64-4.45158 6.52629 (64*2π)/5959 weeks
65.0213 1.8085 (65*2π)/5959 weeks
665.75723 4.3853 (66*2π)/5959 weeks
673.11608 7.8516 (67*2π)/5959 weeks
681.79128 5.62897 (68*2π)/5959 weeks
692.79679 4.6498 (69*2π)/5959 weeks
706.19123 4.61606 (70*2π)/5959 weeks
716.77728 8.43969 (71*2π)/5958 weeks
721.69798 10.22629 (72*2π)/5958 weeks
73.91465 7.30098 (73*2π)/5958 weeks
741.53596 5.32778 (74*2π)/5958 weeks
756.14569 5.20346 (75*2π)/5958 weeks
765.2964 12.97817 (76*2π)/5958 weeks
77-4.27778 13.95611 (77*2π)/5958 weeks
78-9.68013 4.8196 (78*2π)/5958 weeks
79-5.47838 -4.75969 (79*2π)/5958 weeks
806.14225 -7.03222 (80*2π)/5957 weeks
8112.23855 1.74417 (81*2π)/5957 weeks
828.7901 8.56177 (82*2π)/5957 weeks
834.82197 11.43817 (83*2π)/5957 weeks
84-3.89087 9.9454 (84*2π)/5957 weeks
85-5.17269 -.844 (85*2π)/5957 weeks
864.33825 -5.36987 (86*2π)/5957 weeks
8711.79579 -.90804 (87*2π)/5957 weeks
8813.36988 8.42932 (88*2π)/5957 weeks
894.61073 14.5845 (89*2π)/5957 weeks
90-2.46919 10.03086 (90*2π)/5957 weeks
91-4.69478 2.9864 (91*2π)/5957 weeks
921.0723 -4.40545 (92*2π)/5956 weeks
9310.50696 -1.73222 (93*2π)/5956 weeks
9412.16373 6.49887 (94*2π)/5956 weeks
956.81163 12.76409 (95*2π)/5956 weeks
96-.99875 11.57818 (96*2π)/5956 weeks
97-3.54925 4.14276 (97*2π)/5956 weeks
981.2187 -.25076 (98*2π)/5956 weeks
995.76076 1.357 (99*2π)/5956 weeks
1006.45442 5.56402 (100*2π)/5956 weeks
1013.26693 7.27596 (101*2π)/5956 weeks
1022.54744 5.40417 (102*2π)/5956 weeks
1033.35992 6.50119 (103*2π)/5956 weeks
104-.0721 6.88119 (104*2π)/5956 weeks
105-2.70089 3.65018 (105*2π)/5956 weeks
106-.93324 -1.04572 (106*2π)/5956 weeks
1074.76457 -2.16353 (107*2π)/5956 weeks
1088.5604 1.25352 (108*2π)/5956 weeks
1097.37873 6.2863 (109*2π)/5955 weeks
1102.4723 8.47437 (110*2π)/5955 weeks
111-2.10112 4.97463 (111*2π)/5955 weeks
112-.188 -1.75214 (112*2π)/5955 weeks
1136.15503 -3.15068 (113*2π)/5955 weeks
11411.46141 .91175 (114*2π)/5955 weeks
11510.2972 9.01151 (115*2π)/5955 weeks
1163.97506 11.78856 (116*2π)/5955 weeks
117-2.60432 8.2025 (117*2π)/5955 weeks
118-2.99906 .25651 (118*2π)/5955 weeks
1193.94295 -3.0244 (119*2π)/5955 weeks
12010.52239 1.25869 (120*2π)/5955 weeks
1219.64048 9.05247 (121*2π)/5955 weeks
1223.08368 11.71515 (122*2π)/5955 weeks
123-2.83336 9.59977 (123*2π)/5955 weeks
124-5.73649 2.74498 (124*2π)/5955 weeks
125-.85805 -2.77239 (125*2π)/5955 weeks
1264.76796 -2.47661 (126*2π)/5955 weeks
1277.15126 1.16912 (127*2π)/5955 weeks
1286.31141 4.78935 (128*2π)/5955 weeks
1293.17651 5.7345 (129*2π)/5955 weeks
1301.42808 3.59929 (130*2π)/5955 weeks
1312.1168 1.09719 (131*2π)/5955 weeks
1325.43059 .69528 (132*2π)/5955 weeks
1337.15413 3.9528 (133*2π)/5954 weeks
1344.24674 7.10309 (134*2π)/5954 weeks
1351.44892 5.45267 (135*2π)/5954 weeks
136.7217 2.86102 (136*2π)/5954 weeks
1372.72092 1.57523 (137*2π)/5954 weeks
1383.54225 2.82641 (138*2π)/5954 weeks
1392.96279 2.77204 (139*2π)/5954 weeks
1403.55537 2.14046 (140*2π)/5954 weeks
1414.16318 2.58061 (141*2π)/5954 weeks
1423.64404 2.64339 (142*2π)/5954 weeks
1434.14662 2.20647 (143*2π)/5954 weeks
1446.14617 2.69976 (144*2π)/5954 weeks
1455.97229 5.31054 (145*2π)/5954 weeks
1463.11832 6.04414 (146*2π)/5954 weeks
1471.80633 5.29158 (147*2π)/5954 weeks
1481.14645 3.07207 (148*2π)/5954 weeks
1493.77204 1.87253 (149*2π)/5954 weeks
1504.22253 4.77125 (150*2π)/5954 weeks
1511.34756 4.84088 (151*2π)/5954 weeks
152.94383 2.94989 (152*2π)/5954 weeks
1532.27583 1.17399 (153*2π)/5954 weeks
1544.70508 2.03078 (154*2π)/5954 weeks
1553.3985 4.30626 (155*2π)/5954 weeks
1561.86347 3.27749 (156*2π)/5954 weeks
1573.02215 2.4421 (157*2π)/5954 weeks
1583.63886 2.85902 (158*2π)/5954 weeks
1593.88117 4.03552 (159*2π)/5954 weeks
1601.95371 5.54212 (160*2π)/5954 weeks
161-.33404 3.46558 (161*2π)/5954 weeks
162-.15258 .84655 (162*2π)/5954 weeks
1632.60161 -1.39195 (163*2π)/5954 weeks
1645.9746 1.06169 (164*2π)/5954 weeks
1654.87244 3.89133 (165*2π)/5954 weeks
1663.20147 4.05027 (166*2π)/5954 weeks
1672.39692 3.2718 (167*2π)/5954 weeks
1682.10957 2.61584 (168*2π)/5954 weeks
1692.39765 1.59621 (169*2π)/5954 weeks
1703.88568 1.13959 (170*2π)/5954 weeks
1716.01077 2.50196 (171*2π)/5953 weeks
1724.91922 5.57258 (172*2π)/5953 weeks
1732.35738 5.64343 (173*2π)/5953 weeks
1741.25733 4.98593 (174*2π)/5953 weeks
175-.14501 3.74851 (175*2π)/5953 weeks
176.0794 1.38896 (176*2π)/5953 weeks
1772.07509 .40632 (177*2π)/5953 weeks
1784.24652 1.88275 (178*2π)/5953 weeks
1793.62397 4.04456 (179*2π)/5953 weeks
1801.42644 4.9043 (180*2π)/5953 weeks
181-.70087 3.3092 (181*2π)/5953 weeks
182-.87032 .61099 (182*2π)/5953 weeks
1831.37422 -1.2417 (183*2π)/5953 weeks
1843.91614 -.39939 (184*2π)/5953 weeks
1854.28864 1.59274 (185*2π)/5953 weeks
1863.30936 3.16857 (186*2π)/5953 weeks
1871.51618 2.60795 (187*2π)/5953 weeks
188.7165 .90224 (188*2π)/5953 weeks
1891.96765 -1.14165 (189*2π)/5953 weeks
1905.11771 -1.42237 (190*2π)/5953 weeks
1917.53599 1.16341 (191*2π)/5953 weeks
1926.85727 5.13249 (192*2π)/5953 weeks
1933.127 7.36452 (193*2π)/5953 weeks
194-.59575 5.31285 (194*2π)/5953 weeks
195-1.06011 1.59361 (195*2π)/5953 weeks
1961.31692 -.48103 (196*2π)/5953 weeks
1974.17225 .50057 (197*2π)/5953 weeks
1984.27461 3.06545 (198*2π)/5953 weeks
1992.68157 4.14993 (199*2π)/5953 weeks
200.5996 2.9929 (200*2π)/5953 weeks
2011.03453 1.60782 (201*2π)/5953 weeks
2021.51956 .92689 (202*2π)/5953 weeks
2033.24954 .96083 (203*2π)/5953 weeks
2043.29798 2.86228 (204*2π)/5953 weeks
2051.27084 3.80501 (205*2π)/5953 weeks
206-.58158 2.88316 (206*2π)/5953 weeks
207-1.5749 .01075 (207*2π)/5953 weeks
208.43642 -3.29103 (208*2π)/5953 weeks
2094.03939 -3.56356 (209*2π)/5953 weeks
2107.52763 -1.74299 (210*2π)/5953 weeks
2118.79792 3.76078 (211*2π)/5953 weeks
2123.82949 6.84524 (212*2π)/5953 weeks
213.08902 4.79404 (213*2π)/5953 weeks
214-.79258 1.45855 (214*2π)/5953 weeks
2151.59279 -.61954 (215*2π)/5953 weeks
2163.96434 .63105 (216*2π)/5953 weeks
2173.59698 2.11627 (217*2π)/5953 weeks
2183.19597 3.74649 (218*2π)/5953 weeks
219-.29324 4.09471 (219*2π)/5953 weeks
220-1.06434 .58242 (220*2π)/5953 weeks
221.02944 -1.04601 (221*2π)/5953 weeks
2222.41739 -2.82261 (222*2π)/5953 weeks
2235.62065 -1.13283 (223*2π)/5953 weeks
2245.98499 2.63413 (224*2π)/5953 weeks
2252.75147 5.00726 (225*2π)/5953 weeks
226-1.03513 2.87997 (226*2π)/5953 weeks
227-.59784 -1.56408 (227*2π)/5953 weeks
2283.72769 -2.74297 (228*2π)/5953 weeks
2296.02842 .09978 (229*2π)/5953 weeks
2305.69173 3.42198 (230*2π)/5953 weeks
2311.97586 5.48735 (231*2π)/5953 weeks
232-1.46637 2.1099 (232*2π)/5953 weeks
233.05233 -1.59904 (233*2π)/5953 weeks
2343.82075 -2.12902 (234*2π)/5953 weeks
2355.95149 1.34064 (235*2π)/5953 weeks
2363.30108 3.91592 (236*2π)/5953 weeks
237.54716 2.51755 (237*2π)/5953 weeks
238.89557 -.17011 (238*2π)/5953 weeks
2393.2562 -.39154 (239*2π)/5952 weeks
2404.30886 1.19253 (240*2π)/5952 weeks
2413.87544 3.28223 (241*2π)/5952 weeks
2421.19611 4.16777 (242*2π)/5952 weeks
243-.90834 1.82255 (243*2π)/5952 weeks
244.50262 -.34907 (244*2π)/5952 weeks
2452.23431 -.3779 (245*2π)/5952 weeks
2462.76109 1.41663 (246*2π)/5952 weeks
247.74791 2.15424 (247*2π)/5952 weeks
248-.18571 .41681 (248*2π)/5952 weeks
249.13169 -1.25381 (249*2π)/5952 weeks
2501.71074 -2.28184 (250*2π)/5952 weeks
2513.80644 -1.48067 (251*2π)/5952 weeks
2524.36833 .39967 (252*2π)/5952 weeks
2533.26018 2.19177 (253*2π)/5952 weeks
254.54681 2.26768 (254*2π)/5952 weeks
255-.70162 -.73132 (255*2π)/5952 weeks
2561.09807 -3.13794 (256*2π)/5952 weeks
2573.96929 -3.18826 (257*2π)/5952 weeks
2586.21562 -1.20528 (258*2π)/5952 weeks
2595.2899 2.60132 (259*2π)/5952 weeks
2602.56027 2.72201 (260*2π)/5952 weeks
2611.06617 1.78936 (261*2π)/5952 weeks
262.32608 -.63829 (262*2π)/5952 weeks
2632.64617 -1.80503 (263*2π)/5952 weeks
2644.07654 -.56617 (264*2π)/5952 weeks
2654.4471 .73822 (265*2π)/5952 weeks
2663.3988 2.86563 (266*2π)/5952 weeks
267.32151 3.12028 (267*2π)/5952 weeks
268-1.48319 .21419 (268*2π)/5952 weeks
269-.91736 -3.33245 (269*2π)/5952 weeks
2703.12644 -4.96614 (270*2π)/5952 weeks
2716.70648 -2.58087 (271*2π)/5952 weeks
2726.43325 1.19534 (272*2π)/5952 weeks
2734.36149 3.13052 (273*2π)/5952 weeks
2741.29212 3.37989 (274*2π)/5952 weeks
275-1.49915 .59917 (275*2π)/5952 weeks
276-.17598 -3.45205 (276*2π)/5952 weeks
2774.25511 -5.16104 (277*2π)/5952 weeks
2788.28685 -1.2143 (278*2π)/5952 weeks
2796.35619 3.78226 (279*2π)/5952 weeks
2802.02211 4.48787 (280*2π)/5952 weeks
281-1.53422 2.36902 (281*2π)/5952 weeks
282-1.88468 -2.65477 (282*2π)/5952 weeks
2832.91032 -5.48391 (283*2π)/5952 weeks
2847.7581 -2.90599 (284*2π)/5952 weeks
2856.97831 2.71046 (285*2π)/5952 weeks
2862.82096 4.69872 (286*2π)/5952 weeks
287-1.18386 2.87623 (287*2π)/5952 weeks
288-2.42036 -1.97294 (288*2π)/5952 weeks
289.83662 -6.3515 (289*2π)/5952 weeks
2907.30842 -5.69018 (290*2π)/5952 weeks
2919.69165 .77921 (291*2π)/5952 weeks
2925.379 4.92124 (292*2π)/5952 weeks
293.84529 3.71176 (293*2π)/5952 weeks
294-1.24084 .53006 (294*2π)/5952 weeks
295-.03756 -3.22091 (295*2π)/5952 weeks
2963.66151 -5.23445 (296*2π)/5952 weeks
2978.54195 -3.11923 (297*2π)/5952 weeks
2988.54195 3.11923 (298*2π)/5952 weeks
2993.66151 5.23445 (299*2π)/5952 weeks
300-.03756 3.22091 (300*2π)/5952 weeks
301-1.24084 -.53006 (301*2π)/5952 weeks
302.84529 -3.71176 (302*2π)/5952 weeks
3035.379 -4.92124 (303*2π)/5952 weeks
3049.69165 -.77921 (304*2π)/5952 weeks
3057.30842 5.69018 (305*2π)/5952 weeks
306.83662 6.3515 (306*2π)/5952 weeks
307-2.42036 1.97294 (307*2π)/5952 weeks
308-1.18386 -2.87623 (308*2π)/5952 weeks
3092.82096 -4.69872 (309*2π)/5952 weeks
3106.97831 -2.71046 (310*2π)/5952 weeks
3117.7581 2.90599 (311*2π)/5952 weeks
3122.91032 5.48391 (312*2π)/5952 weeks
313-1.88468 2.65477 (313*2π)/5952 weeks
314-1.53422 -2.36902 (314*2π)/5952 weeks
3152.02211 -4.48787 (315*2π)/5952 weeks
3166.35619 -3.78226 (316*2π)/5952 weeks
3178.28685 1.2143 (317*2π)/5952 weeks
3184.25511 5.16104 (318*2π)/5952 weeks
319-.17598 3.45205 (319*2π)/5952 weeks
320-1.49915 -.59917 (320*2π)/5952 weeks
3211.29212 -3.37989 (321*2π)/5952 weeks
3224.36149 -3.13052 (322*2π)/5952 weeks
3236.43325 -1.19534 (323*2π)/5952 weeks
3246.70648 2.58087 (324*2π)/5952 weeks
3253.12644 4.96614 (325*2π)/5952 weeks
326-.91736 3.33245 (326*2π)/5952 weeks
327-1.48319 -.21419 (327*2π)/5952 weeks
328.32151 -3.12028 (328*2π)/5952 weeks
3293.3988 -2.86563 (329*2π)/5952 weeks
3304.4471 -.73822 (330*2π)/5952 weeks
3314.07654 .56617 (331*2π)/5952 weeks
3322.64617 1.80503 (332*2π)/5952 weeks
333.32608 .63829 (333*2π)/5952 weeks
3341.06617 -1.78936 (334*2π)/5952 weeks
3352.56027 -2.72201 (335*2π)/5952 weeks
3365.2899 -2.60132 (336*2π)/5952 weeks
3376.21562 1.20528 (337*2π)/5952 weeks
3383.96929 3.18826 (338*2π)/5952 weeks
3391.09807 3.13794 (339*2π)/5952 weeks
340-.70162 .73132 (340*2π)/5952 weeks
341.54681 -2.26768 (341*2π)/5952 weeks
3423.26018 -2.19177 (342*2π)/5952 weeks
3434.36833 -.39967 (343*2π)/5952 weeks
3443.80644 1.48067 (344*2π)/5952 weeks
3451.71074 2.28184 (345*2π)/5952 weeks
346.13169 1.25381 (346*2π)/5952 weeks
347-.18571 -.41681 (347*2π)/5952 weeks
348.74791 -2.15424 (348*2π)/5952 weeks
3492.76109 -1.41663 (349*2π)/5952 weeks
3502.23431 .3779 (350*2π)/5952 weeks
351.50262 .34907 (351*2π)/5952 weeks
352-.90834 -1.82255 (352*2π)/5952 weeks
3531.19611 -4.16777 (353*2π)/5952 weeks
3543.87544 -3.28223 (354*2π)/5952 weeks
3554.30886 -1.19253 (355*2π)/5952 weeks
3563.2562 .39154 (356*2π)/5952 weeks
357.89557 .17011 (357*2π)/5952 weeks
358.54716 -2.51755 (358*2π)/5952 weeks
3593.30108 -3.91592 (359*2π)/5952 weeks
3605.95149 -1.34064 (360*2π)/5952 weeks
3613.82075 2.12902 (361*2π)/5952 weeks
362.05233 1.59904 (362*2π)/5952 weeks
363-1.46637 -2.1099 (363*2π)/5952 weeks
3641.97586 -5.48735 (364*2π)/5952 weeks
3655.69173 -3.42198 (365*2π)/5952 weeks
3666.02842 -.09978 (366*2π)/5952 weeks
3673.72769 2.74297 (367*2π)/5952 weeks
368-.59784 1.56408 (368*2π)/5952 weeks
369-1.03513 -2.87997 (369*2π)/5952 weeks
3702.75147 -5.00726 (370*2π)/5952 weeks
3715.98499 -2.63413 (371*2π)/5952 weeks
3725.62065 1.13283 (372*2π)/5952 weeks
3732.41739 2.82261 (373*2π)/5952 weeks
374.02944 1.04601 (374*2π)/5952 weeks
375-1.06434 -.58242 (375*2π)/5952 weeks
376-.29324 -4.09471 (376*2π)/5952 weeks
3773.19597 -3.74649 (377*2π)/5952 weeks
3783.59698 -2.11627 (378*2π)/5952 weeks
3793.96434 -.63105 (379*2π)/5952 weeks
3801.59279 .61954 (380*2π)/5952 weeks
381-.79258 -1.45855 (381*2π)/5952 weeks
382.08902 -4.79404 (382*2π)/5952 weeks
3833.82949 -6.84524 (383*2π)/5952 weeks
3848.79792 -3.76078 (384*2π)/5952 weeks
3857.52763 1.74299 (385*2π)/5952 weeks
3864.03939 3.56356 (386*2π)/5952 weeks
387.43642 3.29103 (387*2π)/5952 weeks
388-1.5749 -.01075 (388*2π)/5952 weeks
389-.58158 -2.88316 (389*2π)/5952 weeks
3901.27084 -3.80501 (390*2π)/5952 weeks
3913.29798 -2.86228 (391*2π)/5952 weeks
3923.24954 -.96083 (392*2π)/5952 weeks
3931.51956 -.92689 (393*2π)/5952 weeks
3941.03453 -1.60782 (394*2π)/5952 weeks
395.5996 -2.9929 (395*2π)/5952 weeks
3962.68157 -4.14993 (396*2π)/5952 weeks
3974.27461 -3.06545 (397*2π)/5951 weeks
3984.17225 -.50057 (398*2π)/5951 weeks
3991.31692 .48103 (399*2π)/5951 weeks
400-1.06011 -1.59361 (400*2π)/5951 weeks
401-.59575 -5.31285 (401*2π)/5951 weeks
4023.127 -7.36452 (402*2π)/5951 weeks
4036.85727 -5.13249 (403*2π)/5951 weeks
4047.53599 -1.16341 (404*2π)/5951 weeks
4055.11771 1.42237 (405*2π)/5951 weeks
4061.96765 1.14165 (406*2π)/5951 weeks
407.7165 -.90224 (407*2π)/5951 weeks
4081.51618 -2.60795 (408*2π)/5951 weeks
4093.30936 -3.16857 (409*2π)/5951 weeks
4104.28864 -1.59274 (410*2π)/5951 weeks
4113.91614 .39939 (411*2π)/5951 weeks
4121.37422 1.2417 (412*2π)/5951 weeks
413-.87032 -.61099 (413*2π)/5951 weeks
414-.70087 -3.3092 (414*2π)/5951 weeks
4151.42644 -4.9043 (415*2π)/5951 weeks
4163.62397 -4.04456 (416*2π)/5951 weeks
4174.24652 -1.88275 (417*2π)/5951 weeks
4182.07509 -.40632 (418*2π)/5951 weeks
419.0794 -1.38896 (419*2π)/5951 weeks
420-.14501 -3.74851 (420*2π)/5951 weeks
4211.25733 -4.98593 (421*2π)/5951 weeks
4222.35738 -5.64343 (422*2π)/5951 weeks
4234.91922 -5.57258 (423*2π)/5951 weeks
4246.01077 -2.50196 (424*2π)/5951 weeks
4253.88568 -1.13959 (425*2π)/5951 weeks
4262.39765 -1.59621 (426*2π)/5951 weeks
4272.10957 -2.61584 (427*2π)/5951 weeks
4282.39692 -3.2718 (428*2π)/5951 weeks
4293.20147 -4.05027 (429*2π)/5951 weeks
4304.87244 -3.89133 (430*2π)/5951 weeks
4315.9746 -1.06169 (431*2π)/5951 weeks
4322.60161 1.39195 (432*2π)/5951 weeks
433-.15258 -.84655 (433*2π)/5951 weeks
434-.33404 -3.46558 (434*2π)/5951 weeks
4351.95371 -5.54212 (435*2π)/5951 weeks
4363.88117 -4.03552 (436*2π)/5951 weeks
4373.63886 -2.85902 (437*2π)/5951 weeks
4383.02215 -2.4421 (438*2π)/5951 weeks
4391.86347 -3.27749 (439*2π)/5951 weeks
4403.3985 -4.30626 (440*2π)/5951 weeks
4414.70508 -2.03078 (441*2π)/5951 weeks
4422.27583 -1.17399 (442*2π)/5951 weeks
443.94383 -2.94989 (443*2π)/5951 weeks
4441.34756 -4.84088 (444*2π)/5951 weeks
4454.22253 -4.77125 (445*2π)/5951 weeks
4463.77204 -1.87253 (446*2π)/5951 weeks
4471.14645 -3.07207 (447*2π)/5951 weeks
4481.80633 -5.29158 (448*2π)/5951 weeks
4493.11832 -6.04414 (449*2π)/5951 weeks
4505.97229 -5.31054 (450*2π)/5951 weeks
4516.14617 -2.69976 (451*2π)/5951 weeks
4524.14662 -2.20647 (452*2π)/5951 weeks
4533.64404 -2.64339 (453*2π)/5951 weeks
4544.16318 -2.58061 (454*2π)/5951 weeks
4553.55537 -2.14046 (455*2π)/5951 weeks
4562.96279 -2.77204 (456*2π)/5951 weeks
4573.54225 -2.82641 (457*2π)/5951 weeks
4582.72092 -1.57523 (458*2π)/5951 weeks
459.7217 -2.86102 (459*2π)/5951 weeks
4601.44892 -5.45267 (460*2π)/5951 weeks
4614.24674 -7.10309 (461*2π)/5951 weeks
4627.15413 -3.9528 (462*2π)/5951 weeks
4635.43059 -.69528 (463*2π)/5951 weeks
4642.1168 -1.09719 (464*2π)/5951 weeks
4651.42808 -3.59929 (465*2π)/5951 weeks
4663.17651 -5.7345 (466*2π)/5951 weeks
4676.31141 -4.78935 (467*2π)/5951 weeks
4687.15126 -1.16912 (468*2π)/5951 weeks
4694.76796 2.47661 (469*2π)/5951 weeks
470-.85805 2.77239 (470*2π)/5951 weeks
471-5.73649 -2.74498 (471*2π)/5951 weeks
472-2.83336 -9.59977 (472*2π)/5951 weeks
4733.08368 -11.71515 (473*2π)/5951 weeks
4749.64048 -9.05247 (474*2π)/5951 weeks
47510.52239 -1.25869 (475*2π)/5951 weeks
4763.94295 3.0244 (476*2π)/5951 weeks
477-2.99906 -.25651 (477*2π)/5951 weeks
478-2.60432 -8.2025 (478*2π)/5951 weeks
4793.97506 -11.78856 (479*2π)/5951 weeks
48010.2972 -9.01151 (480*2π)/5951 weeks
48111.46141 -.91175 (481*2π)/5951 weeks
4826.15503 3.15068 (482*2π)/5951 weeks
483-.188 1.75214 (483*2π)/5951 weeks
484-2.10112 -4.97463 (484*2π)/5951 weeks
4852.4723 -8.47437 (485*2π)/5951 weeks
4867.37873 -6.2863 (486*2π)/5951 weeks
4878.5604 -1.25352 (487*2π)/5951 weeks
4884.76457 2.16353 (488*2π)/5951 weeks
489-.93324 1.04572 (489*2π)/5951 weeks
490-2.70089 -3.65018 (490*2π)/5951 weeks
491-.0721 -6.88119 (491*2π)/5951 weeks
4923.35992 -6.50119 (492*2π)/5951 weeks
4932.54744 -5.40417 (493*2π)/5951 weeks
4943.26693 -7.27596 (494*2π)/5951 weeks
4956.45442 -5.56402 (495*2π)/5951 weeks
4965.76076 -1.357 (496*2π)/5951 weeks
4971.2187 .25076 (497*2π)/5951 weeks
498-3.54925 -4.14276 (498*2π)/5951 weeks
499-.99875 -11.57818 (499*2π)/5951 weeks
5006.81163 -12.76409 (500*2π)/5951 weeks
50112.16373 -6.49887 (501*2π)/5951 weeks
50210.50696 1.73222 (502*2π)/5951 weeks
5031.0723 4.40545 (503*2π)/5951 weeks
504-4.69478 -2.9864 (504*2π)/5951 weeks
505-2.46919 -10.03086 (505*2π)/5951 weeks
5064.61073 -14.5845 (506*2π)/5951 weeks
50713.36988 -8.42932 (507*2π)/5951 weeks
50811.79579 .90804 (508*2π)/5951 weeks
5094.33825 5.36987 (509*2π)/5951 weeks
510-5.17269 .844 (510*2π)/5951 weeks
511-3.89087 -9.9454 (511*2π)/5951 weeks
5124.82197 -11.43817 (512*2π)/5951 weeks
5138.7901 -8.56177 (513*2π)/5951 weeks
51412.23855 -1.74417 (514*2π)/5951 weeks
5156.14225 7.03222 (515*2π)/5951 weeks
516-5.47838 4.75969 (516*2π)/5951 weeks
517-9.68013 -4.8196 (517*2π)/5951 weeks
518-4.27778 -13.95611 (518*2π)/5951 weeks
5195.2964 -12.97817 (519*2π)/5951 weeks
5206.14569 -5.20346 (520*2π)/5951 weeks
5211.53596 -5.32778 (521*2π)/5951 weeks
522.91465 -7.30098 (522*2π)/5951 weeks
5231.69798 -10.22629 (523*2π)/5951 weeks
5246.77728 -8.43969 (524*2π)/5951 weeks
5256.19123 -4.61606 (525*2π)/5951 weeks
5262.79679 -4.6498 (526*2π)/5951 weeks
5271.79128 -5.62897 (527*2π)/5951 weeks
5283.11608 -7.8516 (528*2π)/5951 weeks
5295.75723 -4.3853 (529*2π)/5951 weeks
530.0213 -1.8085 (530*2π)/5951 weeks
531-4.45158 -6.52629 (531*2π)/5951 weeks
532-3.51903 -13.60918 (532*2π)/5951 weeks
5334.73787 -17.95107 (533*2π)/5951 weeks
53414.32598 -13.35357 (534*2π)/5951 weeks
53513.14885 -.9148 (535*2π)/5951 weeks
5363.92255 2.07478 (536*2π)/5951 weeks
537-2.44465 -1.68929 (537*2π)/5951 weeks
538-1.96678 -8.34138 (538*2π)/5951 weeks
5392.54166 -9.84163 (539*2π)/5951 weeks
5403.81663 -6.99008 (540*2π)/5951 weeks
5412.39084 -5.34686 (541*2π)/5951 weeks
542-.65018 -4.11887 (542*2π)/5951 weeks
543-2.5615 -7.92184 (543*2π)/5951 weeks
544-3.82439 -9.72978 (544*2π)/5951 weeks
545-2.46826 -13.42061 (545*2π)/5951 weeks
546.10489 -13.7523 (546*2π)/5951 weeks
547.08956 -15.11009 (547*2π)/5951 weeks
5482.95495 -16.08751 (548*2π)/5951 weeks
5495.94121 -17.07339 (549*2π)/5951 weeks
55011.00389 -13.95783 (550*2π)/5951 weeks
5518.48383 -5.08395 (551*2π)/5951 weeks
5521.06207 -5.16256 (552*2π)/5951 weeks
553-3.33415 -10.16286 (553*2π)/5951 weeks
554-3.22262 -18.8737 (554*2π)/5951 weeks
5557.27385 -25.49069 (555*2π)/5951 weeks
55620.80958 -16.28762 (556*2π)/5951 weeks
55719.81741 1.24465 (557*2π)/5951 weeks
5581.21419 13.359 (558*2π)/5951 weeks
559-22.84137 -1.21797 (559*2π)/5951 weeks
560-19.72877 -28.26585 (560*2π)/5951 weeks
5614.33341 -37.18237 (561*2π)/5951 weeks
56222.68809 -22.40986 (562*2π)/5951 weeks
56318.36325 -1.31992 (563*2π)/5951 weeks
564-4.88789 6.43491 (564*2π)/5951 weeks
565-21.7471 -8.93095 (565*2π)/5951 weeks
566-19.84798 -30.5296 (566*2π)/5951 weeks
5671.2974 -44.44947 (567*2π)/5951 weeks
56818.06531 -32.75042 (568*2π)/5951 weeks
56915.34002 -16.24525 (569*2π)/5951 weeks
5702.89014 -11.97772 (570*2π)/5951 weeks
571-2.70665 -22.10024 (571*2π)/5951 weeks
572-.71027 -30.39894 (572*2π)/5951 weeks
5735.23308 -34.97584 (573*2π)/5951 weeks
57413.26886 -33.84111 (574*2π)/5951 weeks
57522.74023 -29.8598 (575*2π)/5951 weeks
57622.39386 -15.45934 (576*2π)/5951 weeks
5779.91427 -11.33436 (577*2π)/5951 weeks
578-.33317 -8.85965 (578*2π)/5951 weeks
579-18.35411 -19.33935 (579*2π)/5951 weeks
580-19.85991 -48.33414 (580*2π)/5951 weeks
5811.97123 -68.11909 (581*2π)/5951 weeks
58239.47009 -67.00378 (582*2π)/5951 weeks
58354.1618 -27.42276 (583*2π)/5951 weeks
58427.31963 3.10262 (584*2π)/5951 weeks
585-17.58659 10.0967 (585*2π)/5951 weeks
586-66.36937 -40.86278 (586*2π)/5951 weeks
587-44.84182 -129.9449 (587*2π)/5951 weeks
58847.56587 -153.6183 (588*2π)/5951 weeks
589106.742 -89.64767 (589*2π)/5951 weeks
59081.34409 -14.94152 (590*2π)/5951 weeks
591-10.41905 -17.80644 (591*2π)/5951 weeks
592-82.09415 -146.5371 (592*2π)/5951 weeks
59333.43454 -319.3516 (593*2π)/5951 weeks



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