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Fourier Analysis of DUG (ProShares UltraShort Oil & Gas)


DUG (ProShares UltraShort Oil & Gas) appears to have interesting cyclic behaviour every 44 weeks (35.9393*sine), 41 weeks (35.651*sine), and 53 weeks (21.5238*sine).

DUG (ProShares UltraShort Oil & Gas) has an average price of 232.24 (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 2/1/2007 to 3/20/2017 for DUG (ProShares UltraShort Oil & Gas), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0232.2363   0 
1162.2578 206.8651 (1*2π)/530530 weeks
232.03039 135.0077 (2*2π)/530265 weeks
36.02164 72.85248 (3*2π)/530177 weeks
413.50448 52.79138 (4*2π)/530133 weeks
529.41205 41.66487 (5*2π)/530106 weeks
634.8084 59.6034 (6*2π)/53088 weeks
75.38691 61.00808 (7*2π)/53076 weeks
8-1.43688 34.11396 (8*2π)/53066 weeks
910.29756 28.11571 (9*2π)/53059 weeks
107.45014 21.52381 (10*2π)/53053 weeks
1119.96111 21.36834 (11*2π)/53048 weeks
1216.59508 35.93926 (12*2π)/53044 weeks
139.90534 35.651 (13*2π)/53041 weeks
14.13205 33.89447 (14*2π)/53038 weeks
15-5.10642 23.87154 (15*2π)/53035 weeks
16-4.07812 15.66988 (16*2π)/53033 weeks
178.57723 8.23707 (17*2π)/53031 weeks
1814.76996 15.54224 (18*2π)/53029 weeks
1916.07573 20.89398 (19*2π)/53028 weeks
208.79149 26.97926 (20*2π)/53027 weeks
21-.61871 26.10747 (21*2π)/53025 weeks
22-5.98848 16.49768 (22*2π)/53024 weeks
232.86307 11.29634 (23*2π)/53023 weeks
249.14751 15.99961 (24*2π)/53022 weeks
253.95231 23.66153 (25*2π)/53021 weeks
26-3.39016 17.68035 (26*2π)/53020 weeks
27-5.17942 10.93894 (27*2π)/53020 weeks
281.11487 5.17214 (28*2π)/53019 weeks
296.67393 10.63888 (29*2π)/53018 weeks
304.60056 15.7441 (30*2π)/53018 weeks
31-.82971 18.07074 (31*2π)/53017 weeks
32-6.02677 10.74065 (32*2π)/53017 weeks
33-.26404 5.44296 (33*2π)/53016 weeks
342.05547 6.56859 (34*2π)/53016 weeks
354.01617 7.4198 (35*2π)/53015 weeks
363.86927 9.26385 (36*2π)/53015 weeks
372.97222 10.48226 (37*2π)/53014 weeks
38.63512 10.53974 (38*2π)/53014 weeks
391.04451 7.22651 (39*2π)/53014 weeks
403.52873 8.0917 (40*2π)/53013 weeks
413.91005 7.47109 (41*2π)/53013 weeks
426.19138 10.78377 (42*2π)/53013 weeks
432.36509 15.01029 (43*2π)/53012 weeks
44-3.05193 14.54277 (44*2π)/53012 weeks
45-6.36399 8.90316 (45*2π)/53012 weeks
46-3.28509 3.32564 (46*2π)/53012 weeks
47.10476 2.59476 (47*2π)/53011 weeks
482.84289 5.0261 (48*2π)/53011 weeks
492.69036 7.76289 (49*2π)/53011 weeks
50-.784 8.30912 (50*2π)/53011 weeks
51-2.70245 4.61308 (51*2π)/53010 weeks
52-.22052 .17768 (52*2π)/53010 weeks
536.39956 .81755 (53*2π)/53010 weeks
549.22671 7.49482 (54*2π)/53010 weeks
553.14879 13.28838 (55*2π)/53010 weeks
56-4.46489 10.36817 (56*2π)/5309 weeks
57-5.17529 3.66978 (57*2π)/5309 weeks
58-.7129 -.9743 (58*2π)/5309 weeks
594.8318 1.94437 (59*2π)/5309 weeks
604.16655 4.93107 (60*2π)/5309 weeks
613.60403 6.25242 (61*2π)/5309 weeks
621.70518 6.0677 (62*2π)/5309 weeks
63.86307 5.63935 (63*2π)/5308 weeks
64.37262 5.45011 (64*2π)/5308 weeks
651.7545 4.86843 (65*2π)/5308 weeks
66-.13456 5.25095 (66*2π)/5308 weeks
671.42364 4.16727 (67*2π)/5308 weeks
68-.52999 6.5864 (68*2π)/5308 weeks
69-3.69513 3.98226 (69*2π)/5308 weeks
70-1.7782 -.76997 (70*2π)/5308 weeks
713.62546 -2.13292 (71*2π)/5307 weeks
726.21441 3.12829 (72*2π)/5307 weeks
733.45631 5.31605 (73*2π)/5307 weeks
742.777 6.10581 (74*2π)/5307 weeks
75-1.75206 4.57598 (75*2π)/5307 weeks
76-.08982 -.60527 (76*2π)/5307 weeks
773.77364 .78358 (77*2π)/5307 weeks
785.15244 3.08189 (78*2π)/5307 weeks
793.40666 5.93365 (79*2π)/5307 weeks
80.86761 4.21085 (80*2π)/5307 weeks
81-.06937 2.95663 (81*2π)/5307 weeks
821.53861 -.59201 (82*2π)/5306 weeks
836.53891 1.18907 (83*2π)/5306 weeks
846.15561 5.82223 (84*2π)/5306 weeks
851.73738 7.65826 (85*2π)/5306 weeks
86-1.8663 5.22475 (86*2π)/5306 weeks
87-.98367 .97131 (87*2π)/5306 weeks
882.35113 .36085 (88*2π)/5306 weeks
893.98171 2.27854 (89*2π)/5306 weeks
902.88175 4.20862 (90*2π)/5306 weeks
912.50568 3.59644 (91*2π)/5306 weeks
922.35875 5.28146 (92*2π)/5306 weeks
93-.4859 4.00034 (93*2π)/5306 weeks
94-.90861 .40553 (94*2π)/5306 weeks
952.4858 -1.38729 (95*2π)/5306 weeks
965.26175 .81265 (96*2π)/5306 weeks
974.79413 4.1455 (97*2π)/5305 weeks
981.9026 5.76611 (98*2π)/5305 weeks
99-1.14983 3.47569 (99*2π)/5305 weeks
100.73398 -.43252 (100*2π)/5305 weeks
1014.49791 -.62349 (101*2π)/5305 weeks
1026.56101 2.44378 (102*2π)/5305 weeks
1034.72187 5.28033 (103*2π)/5305 weeks
1041.33853 5.88359 (104*2π)/5305 weeks
105-.82766 2.88625 (105*2π)/5305 weeks
1061.47262 .39804 (106*2π)/5305 weeks
1074.46397 1.46987 (107*2π)/5305 weeks
1084.72076 3.97817 (108*2π)/5305 weeks
1093.37437 5.94275 (109*2π)/5305 weeks
110-.49012 6.26389 (110*2π)/5305 weeks
111-2.1237 2.21331 (111*2π)/5305 weeks
112-.46401 -.53451 (112*2π)/5305 weeks
1132.86305 -1.0051 (113*2π)/5305 weeks
1145.10284 1.77769 (114*2π)/5305 weeks
1153.23181 4.61788 (115*2π)/5305 weeks
116.72026 4.00966 (116*2π)/5305 weeks
117-.4242 1.45169 (117*2π)/5305 weeks
1181.74044 -.71832 (118*2π)/5304 weeks
1194.49577 .41724 (119*2π)/5304 weeks
1204.57552 2.4285 (120*2π)/5304 weeks
1213.15584 3.73925 (121*2π)/5304 weeks
1222.05647 3.93665 (122*2π)/5304 weeks
123.72993 3.29883 (123*2π)/5304 weeks
124.72378 .82454 (124*2π)/5304 weeks
1253.59091 .07173 (125*2π)/5304 weeks
1264.93428 2.89821 (126*2π)/5304 weeks
1273.24363 4.06816 (127*2π)/5304 weeks
1282.29352 3.61495 (128*2π)/5304 weeks
1291.26096 4.0273 (129*2π)/5304 weeks
130-.20708 2.6068 (130*2π)/5304 weeks
1311.39056 1.65108 (131*2π)/5304 weeks
1322.29666 1.81305 (132*2π)/5304 weeks
1333.52814 3.07413 (133*2π)/5304 weeks
1341.258 4.96953 (134*2π)/5304 weeks
135-1.23749 2.98383 (135*2π)/5304 weeks
136-1.02967 -.02519 (136*2π)/5304 weeks
1372.18961 -1.15784 (137*2π)/5304 weeks
1383.28281 1.40346 (138*2π)/5304 weeks
1392.57729 2.20531 (139*2π)/5304 weeks
1402.38759 3.04702 (140*2π)/5304 weeks
1411.05841 2.79366 (141*2π)/5304 weeks
142.37087 1.71197 (142*2π)/5304 weeks
143.54381 .30438 (143*2π)/5304 weeks
1441.89151 -.04024 (144*2π)/5304 weeks
1453.03446 .12218 (145*2π)/5304 weeks
1464.01727 2.4197 (146*2π)/5304 weeks
1471.35526 3.43921 (147*2π)/5304 weeks
148.8727 1.27408 (148*2π)/5304 weeks
1492.31945 .74565 (149*2π)/5304 weeks
1502.87576 1.64109 (150*2π)/5304 weeks
1512.17181 1.93786 (151*2π)/5304 weeks
1522.39437 1.73372 (152*2π)/5303 weeks
1531.65726 2.66884 (153*2π)/5303 weeks
1541.07697 1.29635 (154*2π)/5303 weeks
1552.27401 1.23271 (155*2π)/5303 weeks
1562.20494 1.9113 (156*2π)/5303 weeks
1571.76786 1.98038 (157*2π)/5303 weeks
1581.79728 1.54168 (158*2π)/5303 weeks
1591.41484 1.72072 (159*2π)/5303 weeks
1601.71053 1.3381 (160*2π)/5303 weeks
1611.30325 1.49909 (161*2π)/5303 weeks
1621.55514 1.16722 (162*2π)/5303 weeks
1631.60036 1.24707 (163*2π)/5303 weeks
1641.85707 1.26097 (164*2π)/5303 weeks
1651.25608 1.31944 (165*2π)/5303 weeks
166.92606 .83936 (166*2π)/5303 weeks
1671.64982 .24196 (167*2π)/5303 weeks
1682.55733 .37686 (168*2π)/5303 weeks
1692.96727 1.08567 (169*2π)/5303 weeks
1702.823 1.4817 (170*2π)/5303 weeks
1712.73711 1.97929 (171*2π)/5303 weeks
1721.47876 2.63671 (172*2π)/5303 weeks
173.7546 1.2436 (173*2π)/5303 weeks
1741.26914 .77228 (174*2π)/5303 weeks
1751.94437 .58839 (175*2π)/5303 weeks
1761.96149 1.38129 (176*2π)/5303 weeks
1771.62115 1.11557 (177*2π)/5303 weeks
1781.40315 .62796 (178*2π)/5303 weeks
1791.95463 .29232 (179*2π)/5303 weeks
1801.98632 .29459 (180*2π)/5303 weeks
1813.21547 .61639 (181*2π)/5303 weeks
1822.65237 2.38055 (182*2π)/5303 weeks
1831.23502 1.89556 (183*2π)/5303 weeks
184.61765 .74496 (184*2π)/5303 weeks
1851.26124 -.73673 (185*2π)/5303 weeks
1862.98733 -.67057 (186*2π)/5303 weeks
1874.28074 .38 (187*2π)/5303 weeks
1884.48417 3.04824 (188*2π)/5303 weeks
1891.30377 3.81255 (189*2π)/5303 weeks
190.08653 1.91185 (190*2π)/5303 weeks
191.64295 .19463 (191*2π)/5303 weeks
1922.29454 -.03275 (192*2π)/5303 weeks
1932.62014 1.34174 (193*2π)/5303 weeks
1942.53685 2.03981 (194*2π)/5303 weeks
195.53797 2.60452 (195*2π)/5303 weeks
196.04925 .23625 (196*2π)/5303 weeks
197.91693 -.6205 (197*2π)/5303 weeks
1982.74775 -1.22531 (198*2π)/5303 weeks
1994.34271 .5371 (199*2π)/5303 weeks
2003.13614 3.17985 (200*2π)/5303 weeks
201.16526 3.13882 (201*2π)/5303 weeks
202-.84194 .17323 (202*2π)/5303 weeks
2031.80993 -1.84432 (203*2π)/5303 weeks
2043.92912 -.20967 (204*2π)/5303 weeks
2053.86996 1.9497 (205*2π)/5303 weeks
2061.52006 3.59583 (206*2π)/5303 weeks
207-.32447 1.58517 (207*2π)/5303 weeks
208.36681 -.37436 (208*2π)/5303 weeks
2092.44493 -.61711 (209*2π)/5303 weeks
2102.6922 1.16206 (210*2π)/5303 weeks
2111.72972 1.44776 (211*2π)/5303 weeks
2121.70018 1.23419 (212*2π)/5303 weeks
2131.40799 1.68777 (213*2π)/5302 weeks
214.49974 .89552 (214*2π)/5302 weeks
2151.16228 .42731 (215*2π)/5302 weeks
216.98777 .50192 (216*2π)/5302 weeks
2171.38215 .23186 (217*2π)/5302 weeks
218.944 .82153 (218*2π)/5302 weeks
219.49449 .86226 (219*2π)/5302 weeks
220-.1317 .01137 (220*2π)/5302 weeks
2211.11803 -1.31154 (221*2π)/5302 weeks
2222.37096 -.94609 (222*2π)/5302 weeks
2232.58148 -.20988 (223*2π)/5302 weeks
2242.08178 .99276 (224*2π)/5302 weeks
225.92931 1.12288 (225*2π)/5302 weeks
226-.02661 .20266 (226*2π)/5302 weeks
227.15982 -1.47918 (227*2π)/5302 weeks
2281.77083 -2.15256 (228*2π)/5302 weeks
2293.13981 -1.35203 (229*2π)/5302 weeks
2303.6745 .00018 (230*2π)/5302 weeks
2311.92974 1.12286 (231*2π)/5302 weeks
2321.52282 .19965 (232*2π)/5302 weeks
2331.1604 -.3643 (233*2π)/5302 weeks
2342.66949 -1.01521 (234*2π)/5302 weeks
2353.00455 .0653 (235*2π)/5302 weeks
2362.55725 .90113 (236*2π)/5302 weeks
2371.05406 1.49263 (237*2π)/5302 weeks
238-.08116 .0704 (238*2π)/5302 weeks
239.68588 -1.65033 (239*2π)/5302 weeks
2402.26991 -2.54806 (240*2π)/5302 weeks
2414.03105 -1.26634 (241*2π)/5302 weeks
2423.65674 .80996 (242*2π)/5302 weeks
2432.25592 1.33145 (243*2π)/5302 weeks
244.97245 .66712 (244*2π)/5302 weeks
245.52293 -.82778 (245*2π)/5302 weeks
2461.83721 -1.88306 (246*2π)/5302 weeks
2474.12511 -1.68009 (247*2π)/5302 weeks
2484.34389 1.21497 (248*2π)/5302 weeks
2491.75522 1.89871 (249*2π)/5302 weeks
250.28566 .90933 (250*2π)/5302 weeks
251.18076 -1.23686 (251*2π)/5302 weeks
2522.52665 -2.59889 (252*2π)/5302 weeks
2534.42174 -.9118 (253*2π)/5302 weeks
2543.02993 1.19364 (254*2π)/5302 weeks
2551.12338 1.2342 (255*2π)/5302 weeks
256.08623 -.53969 (256*2π)/5302 weeks
2571.03098 -2.60168 (257*2π)/5302 weeks
2583.91837 -3.39176 (258*2π)/5302 weeks
2595.7754 -.36023 (259*2π)/5302 weeks
2603.90941 1.81301 (260*2π)/5302 weeks
2611.86912 1.33488 (261*2π)/5302 weeks
262.95414 .06914 (262*2π)/5302 weeks
2631.65936 -1.3683 (263*2π)/5302 weeks
2643.38825 -1.84512 (264*2π)/5302 weeks
2655.28057   (265*2π)/5302 weeks
2663.38825 1.84512 (266*2π)/5302 weeks
2671.65936 1.3683 (267*2π)/5302 weeks
268.95414 -.06914 (268*2π)/5302 weeks
2691.86912 -1.33488 (269*2π)/5302 weeks
2703.90941 -1.81301 (270*2π)/5302 weeks
2715.7754 .36023 (271*2π)/5302 weeks
2723.91837 3.39176 (272*2π)/5302 weeks
2731.03098 2.60168 (273*2π)/5302 weeks
274.08623 .53969 (274*2π)/5302 weeks
2751.12338 -1.2342 (275*2π)/5302 weeks
2763.02993 -1.19364 (276*2π)/5302 weeks
2774.42174 .9118 (277*2π)/5302 weeks
2782.52665 2.59889 (278*2π)/5302 weeks
279.18076 1.23686 (279*2π)/5302 weeks
280.28566 -.90933 (280*2π)/5302 weeks
2811.75522 -1.89871 (281*2π)/5302 weeks
2824.34389 -1.21497 (282*2π)/5302 weeks
2834.12511 1.68009 (283*2π)/5302 weeks
2841.83721 1.88306 (284*2π)/5302 weeks
285.52293 .82778 (285*2π)/5302 weeks
286.97245 -.66712 (286*2π)/5302 weeks
2872.25592 -1.33145 (287*2π)/5302 weeks
2883.65674 -.80996 (288*2π)/5302 weeks
2894.03105 1.26634 (289*2π)/5302 weeks
2902.26991 2.54806 (290*2π)/5302 weeks
291.68588 1.65033 (291*2π)/5302 weeks
292-.08116 -.0704 (292*2π)/5302 weeks
2931.05406 -1.49263 (293*2π)/5302 weeks
2942.55725 -.90113 (294*2π)/5302 weeks
2953.00455 -.0653 (295*2π)/5302 weeks
2962.66949 1.01521 (296*2π)/5302 weeks
2971.1604 .3643 (297*2π)/5302 weeks
2981.52282 -.19965 (298*2π)/5302 weeks
2991.92974 -1.12286 (299*2π)/5302 weeks
3003.6745 -.00018 (300*2π)/5302 weeks
3013.13981 1.35203 (301*2π)/5302 weeks
3021.77083 2.15256 (302*2π)/5302 weeks
303.15982 1.47918 (303*2π)/5302 weeks
304-.02661 -.20266 (304*2π)/5302 weeks
305.92931 -1.12288 (305*2π)/5302 weeks
3062.08178 -.99276 (306*2π)/5302 weeks
3072.58148 .20988 (307*2π)/5302 weeks
3082.37096 .94609 (308*2π)/5302 weeks
3091.11803 1.31154 (309*2π)/5302 weeks
310-.1317 -.01137 (310*2π)/5302 weeks
311.49449 -.86226 (311*2π)/5302 weeks
312.944 -.82153 (312*2π)/5302 weeks
3131.38215 -.23186 (313*2π)/5302 weeks
314.98777 -.50192 (314*2π)/5302 weeks
3151.16228 -.42731 (315*2π)/5302 weeks
316.49974 -.89552 (316*2π)/5302 weeks
3171.40799 -1.68777 (317*2π)/5302 weeks
3181.70018 -1.23419 (318*2π)/5302 weeks
3191.72972 -1.44776 (319*2π)/5302 weeks
3202.6922 -1.16206 (320*2π)/5302 weeks
3212.44493 .61711 (321*2π)/5302 weeks
322.36681 .37436 (322*2π)/5302 weeks
323-.32447 -1.58517 (323*2π)/5302 weeks
3241.52006 -3.59583 (324*2π)/5302 weeks
3253.86996 -1.9497 (325*2π)/5302 weeks
3263.92912 .20967 (326*2π)/5302 weeks
3271.80993 1.84432 (327*2π)/5302 weeks
328-.84194 -.17323 (328*2π)/5302 weeks
329.16526 -3.13882 (329*2π)/5302 weeks
3303.13614 -3.17985 (330*2π)/5302 weeks
3314.34271 -.5371 (331*2π)/5302 weeks
3322.74775 1.22531 (332*2π)/5302 weeks
333.91693 .6205 (333*2π)/5302 weeks
334.04925 -.23625 (334*2π)/5302 weeks
335.53797 -2.60452 (335*2π)/5302 weeks
3362.53685 -2.03981 (336*2π)/5302 weeks
3372.62014 -1.34174 (337*2π)/5302 weeks
3382.29454 .03275 (338*2π)/5302 weeks
339.64295 -.19463 (339*2π)/5302 weeks
340.08653 -1.91185 (340*2π)/5302 weeks
3411.30377 -3.81255 (341*2π)/5302 weeks
3424.48417 -3.04824 (342*2π)/5302 weeks
3434.28074 -.38 (343*2π)/5302 weeks
3442.98733 .67057 (344*2π)/5302 weeks
3451.26124 .73673 (345*2π)/5302 weeks
346.61765 -.74496 (346*2π)/5302 weeks
3471.23502 -1.89556 (347*2π)/5302 weeks
3482.65237 -2.38055 (348*2π)/5302 weeks
3493.21547 -.61639 (349*2π)/5302 weeks
3501.98632 -.29459 (350*2π)/5302 weeks
3511.95463 -.29232 (351*2π)/5302 weeks
3521.40315 -.62796 (352*2π)/5302 weeks
3531.62115 -1.11557 (353*2π)/5302 weeks
3541.96149 -1.38129 (354*2π)/5301 weeks
3551.94437 -.58839 (355*2π)/5301 weeks
3561.26914 -.77228 (356*2π)/5301 weeks
357.7546 -1.2436 (357*2π)/5301 weeks
3581.47876 -2.63671 (358*2π)/5301 weeks
3592.73711 -1.97929 (359*2π)/5301 weeks
3602.823 -1.4817 (360*2π)/5301 weeks
3612.96727 -1.08567 (361*2π)/5301 weeks
3622.55733 -.37686 (362*2π)/5301 weeks
3631.64982 -.24196 (363*2π)/5301 weeks
364.92606 -.83936 (364*2π)/5301 weeks
3651.25608 -1.31944 (365*2π)/5301 weeks
3661.85707 -1.26097 (366*2π)/5301 weeks
3671.60036 -1.24707 (367*2π)/5301 weeks
3681.55514 -1.16722 (368*2π)/5301 weeks
3691.30325 -1.49909 (369*2π)/5301 weeks
3701.71053 -1.3381 (370*2π)/5301 weeks
3711.41484 -1.72072 (371*2π)/5301 weeks
3721.79728 -1.54168 (372*2π)/5301 weeks
3731.76786 -1.98038 (373*2π)/5301 weeks
3742.20494 -1.9113 (374*2π)/5301 weeks
3752.27401 -1.23271 (375*2π)/5301 weeks
3761.07697 -1.29635 (376*2π)/5301 weeks
3771.65726 -2.66884 (377*2π)/5301 weeks
3782.39437 -1.73372 (378*2π)/5301 weeks
3792.17181 -1.93786 (379*2π)/5301 weeks
3802.87576 -1.64109 (380*2π)/5301 weeks
3812.31945 -.74565 (381*2π)/5301 weeks
382.8727 -1.27408 (382*2π)/5301 weeks
3831.35526 -3.43921 (383*2π)/5301 weeks
3844.01727 -2.4197 (384*2π)/5301 weeks
3853.03446 -.12218 (385*2π)/5301 weeks
3861.89151 .04024 (386*2π)/5301 weeks
387.54381 -.30438 (387*2π)/5301 weeks
388.37087 -1.71197 (388*2π)/5301 weeks
3891.05841 -2.79366 (389*2π)/5301 weeks
3902.38759 -3.04702 (390*2π)/5301 weeks
3912.57729 -2.20531 (391*2π)/5301 weeks
3923.28281 -1.40346 (392*2π)/5301 weeks
3932.18961 1.15784 (393*2π)/5301 weeks
394-1.02967 .02519 (394*2π)/5301 weeks
395-1.23749 -2.98383 (395*2π)/5301 weeks
3961.258 -4.96953 (396*2π)/5301 weeks
3973.52814 -3.07413 (397*2π)/5301 weeks
3982.29666 -1.81305 (398*2π)/5301 weeks
3991.39056 -1.65108 (399*2π)/5301 weeks
400-.20708 -2.6068 (400*2π)/5301 weeks
4011.26096 -4.0273 (401*2π)/5301 weeks
4022.29352 -3.61495 (402*2π)/5301 weeks
4033.24363 -4.06816 (403*2π)/5301 weeks
4044.93428 -2.89821 (404*2π)/5301 weeks
4053.59091 -.07173 (405*2π)/5301 weeks
406.72378 -.82454 (406*2π)/5301 weeks
407.72993 -3.29883 (407*2π)/5301 weeks
4082.05647 -3.93665 (408*2π)/5301 weeks
4093.15584 -3.73925 (409*2π)/5301 weeks
4104.57552 -2.4285 (410*2π)/5301 weeks
4114.49577 -.41724 (411*2π)/5301 weeks
4121.74044 .71832 (412*2π)/5301 weeks
413-.4242 -1.45169 (413*2π)/5301 weeks
414.72026 -4.00966 (414*2π)/5301 weeks
4153.23181 -4.61788 (415*2π)/5301 weeks
4165.10284 -1.77769 (416*2π)/5301 weeks
4172.86305 1.0051 (417*2π)/5301 weeks
418-.46401 .53451 (418*2π)/5301 weeks
419-2.1237 -2.21331 (419*2π)/5301 weeks
420-.49012 -6.26389 (420*2π)/5301 weeks
4213.37437 -5.94275 (421*2π)/5301 weeks
4224.72076 -3.97817 (422*2π)/5301 weeks
4234.46397 -1.46987 (423*2π)/5301 weeks
4241.47262 -.39804 (424*2π)/5301 weeks
425-.82766 -2.88625 (425*2π)/5301 weeks
4261.33853 -5.88359 (426*2π)/5301 weeks
4274.72187 -5.28033 (427*2π)/5301 weeks
4286.56101 -2.44378 (428*2π)/5301 weeks
4294.49791 .62349 (429*2π)/5301 weeks
430.73398 .43252 (430*2π)/5301 weeks
431-1.14983 -3.47569 (431*2π)/5301 weeks
4321.9026 -5.76611 (432*2π)/5301 weeks
4334.79413 -4.1455 (433*2π)/5301 weeks
4345.26175 -.81265 (434*2π)/5301 weeks
4352.4858 1.38729 (435*2π)/5301 weeks
436-.90861 -.40553 (436*2π)/5301 weeks
437-.4859 -4.00034 (437*2π)/5301 weeks
4382.35875 -5.28146 (438*2π)/5301 weeks
4392.50568 -3.59644 (439*2π)/5301 weeks
4402.88175 -4.20862 (440*2π)/5301 weeks
4413.98171 -2.27854 (441*2π)/5301 weeks
4422.35113 -.36085 (442*2π)/5301 weeks
443-.98367 -.97131 (443*2π)/5301 weeks
444-1.8663 -5.22475 (444*2π)/5301 weeks
4451.73738 -7.65826 (445*2π)/5301 weeks
4466.15561 -5.82223 (446*2π)/5301 weeks
4476.53891 -1.18907 (447*2π)/5301 weeks
4481.53861 .59201 (448*2π)/5301 weeks
449-.06937 -2.95663 (449*2π)/5301 weeks
450.86761 -4.21085 (450*2π)/5301 weeks
4513.40666 -5.93365 (451*2π)/5301 weeks
4525.15244 -3.08189 (452*2π)/5301 weeks
4533.77364 -.78358 (453*2π)/5301 weeks
454-.08982 .60527 (454*2π)/5301 weeks
455-1.75206 -4.57598 (455*2π)/5301 weeks
4562.777 -6.10581 (456*2π)/5301 weeks
4573.45631 -5.31605 (457*2π)/5301 weeks
4586.21441 -3.12829 (458*2π)/5301 weeks
4593.62546 2.13292 (459*2π)/5301 weeks
460-1.7782 .76997 (460*2π)/5301 weeks
461-3.69513 -3.98226 (461*2π)/5301 weeks
462-.52999 -6.5864 (462*2π)/5301 weeks
4631.42364 -4.16727 (463*2π)/5301 weeks
464-.13456 -5.25095 (464*2π)/5301 weeks
4651.7545 -4.86843 (465*2π)/5301 weeks
466.37262 -5.45011 (466*2π)/5301 weeks
467.86307 -5.63935 (467*2π)/5301 weeks
4681.70518 -6.0677 (468*2π)/5301 weeks
4693.60403 -6.25242 (469*2π)/5301 weeks
4704.16655 -4.93107 (470*2π)/5301 weeks
4714.8318 -1.94437 (471*2π)/5301 weeks
472-.7129 .9743 (472*2π)/5301 weeks
473-5.17529 -3.66978 (473*2π)/5301 weeks
474-4.46489 -10.36817 (474*2π)/5301 weeks
4753.14879 -13.28838 (475*2π)/5301 weeks
4769.22671 -7.49482 (476*2π)/5301 weeks
4776.39956 -.81755 (477*2π)/5301 weeks
478-.22052 -.17768 (478*2π)/5301 weeks
479-2.70245 -4.61308 (479*2π)/5301 weeks
480-.784 -8.30912 (480*2π)/5301 weeks
4812.69036 -7.76289 (481*2π)/5301 weeks
4822.84289 -5.0261 (482*2π)/5301 weeks
483.10476 -2.59476 (483*2π)/5301 weeks
484-3.28509 -3.32564 (484*2π)/5301 weeks
485-6.36399 -8.90316 (485*2π)/5301 weeks
486-3.05193 -14.54277 (486*2π)/5301 weeks
4872.36509 -15.01029 (487*2π)/5301 weeks
4886.19138 -10.78377 (488*2π)/5301 weeks
4893.91005 -7.47109 (489*2π)/5301 weeks
4903.52873 -8.0917 (490*2π)/5301 weeks
4911.04451 -7.22651 (491*2π)/5301 weeks
492.63512 -10.53974 (492*2π)/5301 weeks
4932.97222 -10.48226 (493*2π)/5301 weeks
4943.86927 -9.26385 (494*2π)/5301 weeks
4954.01617 -7.4198 (495*2π)/5301 weeks
4962.05547 -6.56859 (496*2π)/5301 weeks
497-.26404 -5.44296 (497*2π)/5301 weeks
498-6.02677 -10.74065 (498*2π)/5301 weeks
499-.82971 -18.07074 (499*2π)/5301 weeks
5004.60056 -15.7441 (500*2π)/5301 weeks
5016.67393 -10.63888 (501*2π)/5301 weeks
5021.11487 -5.17214 (502*2π)/5301 weeks
503-5.17942 -10.93894 (503*2π)/5301 weeks
504-3.39016 -17.68035 (504*2π)/5301 weeks
5053.95231 -23.66153 (505*2π)/5301 weeks
5069.14751 -15.99961 (506*2π)/5301 weeks
5072.86307 -11.29634 (507*2π)/5301 weeks
508-5.98848 -16.49768 (508*2π)/5301 weeks
509-.61871 -26.10747 (509*2π)/5301 weeks
5108.79149 -26.97926 (510*2π)/5301 weeks
51116.07573 -20.89398 (511*2π)/5301 weeks
51214.76996 -15.54224 (512*2π)/5301 weeks
5138.57723 -8.23707 (513*2π)/5301 weeks
514-4.07812 -15.66988 (514*2π)/5301 weeks
515-5.10642 -23.87154 (515*2π)/5301 weeks
516.13205 -33.89447 (516*2π)/5301 weeks
5179.90534 -35.651 (517*2π)/5301 weeks
51816.59508 -35.93926 (518*2π)/5301 weeks
51919.96111 -21.36834 (519*2π)/5301 weeks
5207.45014 -21.52381 (520*2π)/5301 weeks
52110.29756 -28.11571 (521*2π)/5301 weeks
522-1.43688 -34.11396 (522*2π)/5301 weeks
5235.38691 -61.00808 (523*2π)/5301 weeks
52434.8084 -59.6034 (524*2π)/5301 weeks
52529.41205 -41.66487 (525*2π)/5301 weeks
52613.50448 -52.79138 (526*2π)/5301 weeks
5276.02164 -72.85248 (527*2π)/5301 weeks
52832.03039 -135.0077 (528*2π)/5301 weeks

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