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Fourier Analysis of TWM (ProShares UltraShort Russell200)


TWM (ProShares UltraShort Russell200) appears to have interesting cyclic behaviour every 47 weeks (47.6532*sine), 44 weeks (40.8733*sine), and 52 weeks (30.7569*cosine).

TWM (ProShares UltraShort Russell200) has an average price of 326.28 (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 1/25/2007 to 1/17/2017 for TWM (ProShares UltraShort Russell200), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0326.2846   0 
1182.1617 372.3553 (1*2π)/522522 weeks
2-61.18584 222.1234 (2*2π)/522261 weeks
3-87.13835 50.94814 (3*2π)/522174 weeks
4-1.74041 -3.19248 (4*2π)/522131 weeks
542.24522 30.03698 (5*2π)/522104 weeks
618.03893 70.75704 (6*2π)/52287 weeks
7-31.81383 55.43222 (7*2π)/52275 weeks
8-22.25318 -2.90934 (8*2π)/52265 weeks
920.10722 -.77962 (9*2π)/52258 weeks
1030.75694 17.70144 (10*2π)/52252 weeks
1122.03669 47.65318 (11*2π)/52247 weeks
12-14.49176 40.8733 (12*2π)/52244 weeks
13-14.73367 14.25624 (13*2π)/52240 weeks
14-2.8207 6.29158 (14*2π)/52237 weeks
154.33651 10.43699 (15*2π)/52235 weeks
161.44179 8.45954 (16*2π)/52233 weeks
1711.64752 10.5138 (17*2π)/52231 weeks
186.09073 17.21122 (18*2π)/52229 weeks
196.00468 15.92487 (19*2π)/52227 weeks
202.18197 18.2679 (20*2π)/52226 weeks
21-2.57088 13.69813 (21*2π)/52225 weeks
223.80441 6.16196 (22*2π)/52224 weeks
239.42296 13.39782 (23*2π)/52223 weeks
243.90359 24.20945 (24*2π)/52222 weeks
25-14.36574 20.09478 (25*2π)/52221 weeks
26-14.8067 1.82049 (26*2π)/52220 weeks
27-.40499 -9.95714 (27*2π)/52219 weeks
2820.12103 1.33974 (28*2π)/52219 weeks
2914.71043 25.44938 (29*2π)/52218 weeks
30-9.80557 27.06765 (30*2π)/52217 weeks
31-22.73992 4.65355 (31*2π)/52217 weeks
32-4.25369 -16.05059 (32*2π)/52216 weeks
3316.61659 -3.72588 (33*2π)/52216 weeks
3413.8325 12.70706 (34*2π)/52215 weeks
35.6157 17.81338 (35*2π)/52215 weeks
36-6.23428 7.92509 (36*2π)/52215 weeks
37-1.8601 1.32234 (37*2π)/52214 weeks
384.43454 .87708 (38*2π)/52214 weeks
398.89888 8.18547 (39*2π)/52213 weeks
40.26184 12.69098 (40*2π)/52213 weeks
41-1.70342 5.2085 (41*2π)/52213 weeks
421.3476 4.75175 (42*2π)/52212 weeks
433.13043 7.72167 (43*2π)/52212 weeks
44-2.2829 9.52374 (44*2π)/52212 weeks
45-4.23168 3.57575 (45*2π)/52212 weeks
46-1.74011 .68822 (46*2π)/52211 weeks
473.12877 1.9358 (47*2π)/52211 weeks
482.83667 4.80526 (48*2π)/52211 weeks
49-.59102 5.53207 (49*2π)/52211 weeks
50-.92377 1.92834 (50*2π)/52210 weeks
511.37804 .19401 (51*2π)/52210 weeks
526.21411 .75188 (52*2π)/52210 weeks
536.49306 8.46369 (53*2π)/52210 weeks
54-2.6501 8.35253 (54*2π)/52210 weeks
55-2.86381 1.43494 (55*2π)/5229 weeks
562.62104 .18574 (56*2π)/5229 weeks
574.43494 3.98947 (57*2π)/5229 weeks
58-.29764 7.73051 (58*2π)/5229 weeks
59-4.64343 .60981 (59*2π)/5229 weeks
601.99039 -3.75362 (60*2π)/5229 weeks
618.55999 -.82242 (61*2π)/5229 weeks
627.84241 7.19211 (62*2π)/5228 weeks
63.56194 8.12161 (63*2π)/5228 weeks
64.4422 4.1007 (64*2π)/5228 weeks
651.97847 2.53333 (65*2π)/5228 weeks
664.34662 6.67645 (66*2π)/5228 weeks
67-3.3166 9.25831 (67*2π)/5228 weeks
68-6.92147 .62007 (68*2π)/5228 weeks
69-.60155 -5.3722 (69*2π)/5228 weeks
708.37393 -2.92191 (70*2π)/5227 weeks
717.26658 6.66756 (71*2π)/5227 weeks
721.30122 6.39464 (72*2π)/5227 weeks
73-2.19307 5.93288 (73*2π)/5227 weeks
74-3.55474 -2.62984 (74*2π)/5227 weeks
756.26489 -4.17621 (75*2π)/5227 weeks
768.89441 3.23113 (76*2π)/5227 weeks
774.80635 9.32116 (77*2π)/5227 weeks
78-3.04554 7.01186 (78*2π)/5227 weeks
79-3.32046 .48603 (79*2π)/5227 weeks
80.92301 -4.29617 (80*2π)/5227 weeks
819.47618 -1.24559 (81*2π)/5226 weeks
828.5656 7.71057 (82*2π)/5226 weeks
831.14772 10.16148 (83*2π)/5226 weeks
84-3.1963 4.91784 (84*2π)/5226 weeks
85-.89116 .60483 (85*2π)/5226 weeks
862.06262 1.21413 (86*2π)/5226 weeks
872.04247 3.39747 (87*2π)/5226 weeks
88-.47873 3.10418 (88*2π)/5226 weeks
89.35422 .11981 (89*2π)/5226 weeks
902.40818 2.0481 (90*2π)/5226 weeks
91-.12804 2.26933 (91*2π)/5226 weeks
92-.15002 -.70784 (92*2π)/5226 weeks
933.60193 -2.1308 (93*2π)/5226 weeks
946.79242 1.34729 (94*2π)/5226 weeks
954.79024 6.21253 (95*2π)/5225 weeks
96-.5959 5.94865 (96*2π)/5225 weeks
97-2.59794 .08526 (97*2π)/5225 weeks
983.29263 -3.74553 (98*2π)/5225 weeks
998.35115 .8033 (99*2π)/5225 weeks
1006.97265 7.28166 (100*2π)/5225 weeks
101.01092 8.59043 (101*2π)/5225 weeks
102-4.17184 4.14639 (102*2π)/5225 weeks
103-1.69992 -2.792 (103*2π)/5225 weeks
1046.11619 -1.88093 (104*2π)/5225 weeks
1057.38934 5.28229 (105*2π)/5225 weeks
1061.35115 8.52107 (106*2π)/5225 weeks
107-3.04045 5.29261 (107*2π)/5225 weeks
108-4.15508 .60555 (108*2π)/5225 weeks
109.66932 -3.67943 (109*2π)/5225 weeks
1105.33548 .03407 (110*2π)/5225 weeks
1113.66573 3.98976 (111*2π)/5225 weeks
1121.05403 4.44591 (112*2π)/5225 weeks
113-1.14412 2.54233 (113*2π)/5225 weeks
114-.00407 -.5422 (114*2π)/5225 weeks
1153.93352 -1.19538 (115*2π)/5225 weeks
1165.62974 3.14014 (116*2π)/5225 weeks
1171.73094 6.15701 (117*2π)/5224 weeks
118-1.49198 3.21591 (118*2π)/5224 weeks
119-.74078 .49066 (119*2π)/5224 weeks
1201.28178 .02463 (120*2π)/5224 weeks
1212.22344 .77327 (121*2π)/5224 weeks
1222.95606 1.54461 (122*2π)/5224 weeks
1232.33818 2.80116 (123*2π)/5224 weeks
1241.00209 2.54806 (124*2π)/5224 weeks
1251.6756 1.18395 (125*2π)/5224 weeks
1263.32344 2.54753 (126*2π)/5224 weeks
1271.40251 4.39087 (127*2π)/5224 weeks
128-.61968 3.32735 (128*2π)/5224 weeks
129-1.84686 1.53019 (129*2π)/5224 weeks
130-.16503 -.68212 (130*2π)/5224 weeks
1311.22805 .35419 (131*2π)/5224 weeks
1321.52289 -.45179 (132*2π)/5224 weeks
1333.22185 .8109 (133*2π)/5224 weeks
1343.0531 2.14109 (134*2π)/5224 weeks
135.77135 3.82202 (135*2π)/5224 weeks
136-1.44279 .03542 (136*2π)/5224 weeks
1372.72401 -2.00067 (137*2π)/5224 weeks
1384.74237 1.7717 (138*2π)/5224 weeks
1392.10492 4.69815 (139*2π)/5224 weeks
140-1.7639 3.04289 (140*2π)/5224 weeks
141-.55869 -.85337 (141*2π)/5224 weeks
1422.46232 -1.21958 (142*2π)/5224 weeks
1434.50177 1.85678 (143*2π)/5224 weeks
1441.08921 4.17251 (144*2π)/5224 weeks
145-.5568 1.86353 (145*2π)/5224 weeks
146-.19595 .45378 (146*2π)/5224 weeks
147.83014 .03681 (147*2π)/5224 weeks
1481.48631 .08682 (148*2π)/5224 weeks
1492.49546 .78271 (149*2π)/5224 weeks
1501.49219 2.81557 (150*2π)/5223 weeks
151-.43187 .81738 (151*2π)/5223 weeks
1521.0875 -.01609 (152*2π)/5223 weeks
1531.33168 .04305 (153*2π)/5223 weeks
1542.25134 -.00465 (154*2π)/5223 weeks
1553.09708 1.37814 (155*2π)/5223 weeks
1561.12263 3.32125 (156*2π)/5223 weeks
157-1.11589 1.53434 (157*2π)/5223 weeks
158-.99012 -1.47243 (158*2π)/5223 weeks
1592.63438 -2.8219 (159*2π)/5223 weeks
1605.16006 .11545 (160*2π)/5223 weeks
1613.54503 3.47531 (161*2π)/5223 weeks
162.2863 3.05674 (162*2π)/5223 weeks
163-.77588 .7422 (163*2π)/5223 weeks
164.99328 -1.53852 (164*2π)/5223 weeks
1654.0168 -.77166 (165*2π)/5223 weeks
1664.46996 2.50778 (166*2π)/5223 weeks
1671.52658 4.39727 (167*2π)/5223 weeks
168-1.5911 2.71727 (168*2π)/5223 weeks
169-1.87621 -.6823 (169*2π)/5223 weeks
1701.38727 -2.90558 (170*2π)/5223 weeks
1714.49974 -.59304 (171*2π)/5223 weeks
1723.76942 3.11669 (172*2π)/5223 weeks
173-.04941 3.50471 (173*2π)/5223 weeks
174-1.22797 .38083 (174*2π)/5223 weeks
175.61611 -1.89148 (175*2π)/5223 weeks
1763.19055 -.47259 (176*2π)/5223 weeks
1772.53618 1.16919 (177*2π)/5223 weeks
1781.13228 1.89491 (178*2π)/5223 weeks
179-.16396 -.05316 (179*2π)/5223 weeks
1801.97669 -1.67867 (180*2π)/5223 weeks
1813.64725 -.23633 (181*2π)/5223 weeks
1823.77628 1.66377 (182*2π)/5223 weeks
1832.13499 2.70537 (183*2π)/5223 weeks
1841.60557 3.01385 (184*2π)/5223 weeks
185-1.45909 2.92742 (185*2π)/5223 weeks
186-1.28858 -.84803 (186*2π)/5223 weeks
187.3032 -1.34376 (187*2π)/5223 weeks
1881.81795 -1.2983 (188*2π)/5223 weeks
1891.97054 -.30622 (189*2π)/5223 weeks
1902.21641 -.46172 (190*2π)/5223 weeks
1911.69305 .80372 (191*2π)/5223 weeks
1921.34469 -1.24433 (192*2π)/5223 weeks
1932.97958 -.5546 (193*2π)/5223 weeks
1943.70059 -.30104 (194*2π)/5223 weeks
1954.23368 2.48286 (195*2π)/5223 weeks
196.97561 3.63431 (196*2π)/5223 weeks
197-.92642 .86452 (197*2π)/5223 weeks
198.93943 -1.55827 (198*2π)/5223 weeks
1993.5845 .11546 (199*2π)/5223 weeks
2001.92441 2.49822 (200*2π)/5223 weeks
201-.12849 1.55359 (201*2π)/5223 weeks
202-.83011 -.74743 (202*2π)/5223 weeks
2031.75954 -3.16217 (203*2π)/5223 weeks
2045.16657 -.69987 (204*2π)/5223 weeks
2053.80634 3.13445 (205*2π)/5223 weeks
206-.21496 2.86758 (206*2π)/5223 weeks
207-.43886 -.9155 (207*2π)/5223 weeks
2082.84782 -1.02104 (208*2π)/5223 weeks
2092.59003 1.49914 (209*2π)/5222 weeks
210.80982 1.34214 (210*2π)/5222 weeks
211.0393 .52436 (211*2π)/5222 weeks
212.1671 -1.90849 (212*2π)/5222 weeks
2133.63756 -2.07927 (213*2π)/5222 weeks
2143.88913 .99507 (214*2π)/5222 weeks
2152.01068 2.1494 (215*2π)/5222 weeks
216-.04758 .31359 (216*2π)/5222 weeks
2172.02854 -1.64345 (217*2π)/5222 weeks
2183.6492 -.52508 (218*2π)/5222 weeks
2193.69497 1.51549 (219*2π)/5222 weeks
2201.22683 2.82351 (220*2π)/5222 weeks
221-.61092 .35903 (221*2π)/5222 weeks
222.93508 -2.07754 (222*2π)/5222 weeks
2234.35622 -1.97025 (223*2π)/5222 weeks
2245.33257 2.0261 (224*2π)/5222 weeks
2252.24548 3.742 (225*2π)/5222 weeks
226.16062 2.79814 (226*2π)/5222 weeks
227-1.2209 -.11554 (227*2π)/5222 weeks
2281.78577 -1.10864 (228*2π)/5222 weeks
2292.34955 -.09513 (229*2π)/5222 weeks
2302.49865 1.26707 (230*2π)/5222 weeks
2311.00794 .97125 (231*2π)/5222 weeks
2321.31061 .75943 (232*2π)/5222 weeks
233.32551 .11989 (233*2π)/5222 weeks
2341.63151 -1.37368 (234*2π)/5222 weeks
2353.37814 -.47143 (235*2π)/5222 weeks
2364.1624 1.64437 (236*2π)/5222 weeks
2371.34307 3.71611 (237*2π)/5222 weeks
238-1.49076 1.43132 (238*2π)/5222 weeks
239-.58534 -1.52003 (239*2π)/5222 weeks
2402.02689 -2.76032 (240*2π)/5222 weeks
2415.19061 -1.12235 (241*2π)/5222 weeks
2424.83962 3.19149 (242*2π)/5222 weeks
243.92792 5.36735 (243*2π)/5222 weeks
244-3.51349 1.79573 (244*2π)/5222 weeks
245-1.2713 -3.01002 (245*2π)/5222 weeks
2462.74409 -3.12827 (246*2π)/5222 weeks
2475.4915 .17329 (247*2π)/5222 weeks
2482.80888 4.14516 (248*2π)/5222 weeks
249-1.81785 2.59308 (249*2π)/5222 weeks
250-.90227 -2.24022 (250*2π)/5222 weeks
2512.95179 -2.24443 (251*2π)/5222 weeks
2524.49823 .46746 (252*2π)/5222 weeks
2533.0633 3.37722 (253*2π)/5222 weeks
254-.86379 4.14733 (254*2π)/5222 weeks
255-3.45412 -.2172 (255*2π)/5222 weeks
256.44023 -3.7243 (256*2π)/5222 weeks
2573.79571 -1.26235 (257*2π)/5222 weeks
2583.15019 1.18018 (258*2π)/5222 weeks
2591.46255 1.89663 (259*2π)/5222 weeks
260.17071 1.94794 (260*2π)/5222 weeks
261-1.62436   (261*2π)/5222 weeks
262.17071 -1.94794 (262*2π)/5222 weeks
2631.46255 -1.89663 (263*2π)/5222 weeks
2643.15019 -1.18018 (264*2π)/5222 weeks
2653.79571 1.26235 (265*2π)/5222 weeks
266.44023 3.7243 (266*2π)/5222 weeks
267-3.45412 .2172 (267*2π)/5222 weeks
268-.86379 -4.14733 (268*2π)/5222 weeks
2693.0633 -3.37722 (269*2π)/5222 weeks
2704.49823 -.46746 (270*2π)/5222 weeks
2712.95179 2.24443 (271*2π)/5222 weeks
272-.90227 2.24022 (272*2π)/5222 weeks
273-1.81785 -2.59308 (273*2π)/5222 weeks
2742.80888 -4.14516 (274*2π)/5222 weeks
2755.4915 -.17329 (275*2π)/5222 weeks
2762.74409 3.12827 (276*2π)/5222 weeks
277-1.2713 3.01002 (277*2π)/5222 weeks
278-3.51349 -1.79573 (278*2π)/5222 weeks
279.92792 -5.36735 (279*2π)/5222 weeks
2804.83962 -3.19149 (280*2π)/5222 weeks
2815.19061 1.12235 (281*2π)/5222 weeks
2822.02689 2.76032 (282*2π)/5222 weeks
283-.58534 1.52003 (283*2π)/5222 weeks
284-1.49076 -1.43132 (284*2π)/5222 weeks
2851.34307 -3.71611 (285*2π)/5222 weeks
2864.1624 -1.64437 (286*2π)/5222 weeks
2873.37814 .47143 (287*2π)/5222 weeks
2881.63151 1.37368 (288*2π)/5222 weeks
289.32551 -.11989 (289*2π)/5222 weeks
2901.31061 -.75943 (290*2π)/5222 weeks
2911.00794 -.97125 (291*2π)/5222 weeks
2922.49865 -1.26707 (292*2π)/5222 weeks
2932.34955 .09513 (293*2π)/5222 weeks
2941.78577 1.10864 (294*2π)/5222 weeks
295-1.2209 .11554 (295*2π)/5222 weeks
296.16062 -2.79814 (296*2π)/5222 weeks
2972.24548 -3.742 (297*2π)/5222 weeks
2985.33257 -2.0261 (298*2π)/5222 weeks
2994.35622 1.97025 (299*2π)/5222 weeks
300.93508 2.07754 (300*2π)/5222 weeks
301-.61092 -.35903 (301*2π)/5222 weeks
3021.22683 -2.82351 (302*2π)/5222 weeks
3033.69497 -1.51549 (303*2π)/5222 weeks
3043.6492 .52508 (304*2π)/5222 weeks
3052.02854 1.64345 (305*2π)/5222 weeks
306-.04758 -.31359 (306*2π)/5222 weeks
3072.01068 -2.1494 (307*2π)/5222 weeks
3083.88913 -.99507 (308*2π)/5222 weeks
3093.63756 2.07927 (309*2π)/5222 weeks
310.1671 1.90849 (310*2π)/5222 weeks
311.0393 -.52436 (311*2π)/5222 weeks
312.80982 -1.34214 (312*2π)/5222 weeks
3132.59003 -1.49914 (313*2π)/5222 weeks
3142.84782 1.02104 (314*2π)/5222 weeks
315-.43886 .9155 (315*2π)/5222 weeks
316-.21496 -2.86758 (316*2π)/5222 weeks
3173.80634 -3.13445 (317*2π)/5222 weeks
3185.16657 .69987 (318*2π)/5222 weeks
3191.75954 3.16217 (319*2π)/5222 weeks
320-.83011 .74743 (320*2π)/5222 weeks
321-.12849 -1.55359 (321*2π)/5222 weeks
3221.92441 -2.49822 (322*2π)/5222 weeks
3233.5845 -.11546 (323*2π)/5222 weeks
324.93943 1.55827 (324*2π)/5222 weeks
325-.92642 -.86452 (325*2π)/5222 weeks
326.97561 -3.63431 (326*2π)/5222 weeks
3274.23368 -2.48286 (327*2π)/5222 weeks
3283.70059 .30104 (328*2π)/5222 weeks
3292.97958 .5546 (329*2π)/5222 weeks
3301.34469 1.24433 (330*2π)/5222 weeks
3311.69305 -.80372 (331*2π)/5222 weeks
3322.21641 .46172 (332*2π)/5222 weeks
3331.97054 .30622 (333*2π)/5222 weeks
3341.81795 1.2983 (334*2π)/5222 weeks
335.3032 1.34376 (335*2π)/5222 weeks
336-1.28858 .84803 (336*2π)/5222 weeks
337-1.45909 -2.92742 (337*2π)/5222 weeks
3381.60557 -3.01385 (338*2π)/5222 weeks
3392.13499 -2.70537 (339*2π)/5222 weeks
3403.77628 -1.66377 (340*2π)/5222 weeks
3413.64725 .23633 (341*2π)/5222 weeks
3421.97669 1.67867 (342*2π)/5222 weeks
343-.16396 .05316 (343*2π)/5222 weeks
3441.13228 -1.89491 (344*2π)/5222 weeks
3452.53618 -1.16919 (345*2π)/5222 weeks
3463.19055 .47259 (346*2π)/5222 weeks
347.61611 1.89148 (347*2π)/5222 weeks
348-1.22797 -.38083 (348*2π)/5222 weeks
349-.04941 -3.50471 (349*2π)/5221 weeks
3503.76942 -3.11669 (350*2π)/5221 weeks
3514.49974 .59304 (351*2π)/5221 weeks
3521.38727 2.90558 (352*2π)/5221 weeks
353-1.87621 .6823 (353*2π)/5221 weeks
354-1.5911 -2.71727 (354*2π)/5221 weeks
3551.52658 -4.39727 (355*2π)/5221 weeks
3564.46996 -2.50778 (356*2π)/5221 weeks
3574.0168 .77166 (357*2π)/5221 weeks
358.99328 1.53852 (358*2π)/5221 weeks
359-.77588 -.7422 (359*2π)/5221 weeks
360.2863 -3.05674 (360*2π)/5221 weeks
3613.54503 -3.47531 (361*2π)/5221 weeks
3625.16006 -.11545 (362*2π)/5221 weeks
3632.63438 2.8219 (363*2π)/5221 weeks
364-.99012 1.47243 (364*2π)/5221 weeks
365-1.11589 -1.53434 (365*2π)/5221 weeks
3661.12263 -3.32125 (366*2π)/5221 weeks
3673.09708 -1.37814 (367*2π)/5221 weeks
3682.25134 .00465 (368*2π)/5221 weeks
3691.33168 -.04305 (369*2π)/5221 weeks
3701.0875 .01609 (370*2π)/5221 weeks
371-.43187 -.81738 (371*2π)/5221 weeks
3721.49219 -2.81557 (372*2π)/5221 weeks
3732.49546 -.78271 (373*2π)/5221 weeks
3741.48631 -.08682 (374*2π)/5221 weeks
375.83014 -.03681 (375*2π)/5221 weeks
376-.19595 -.45378 (376*2π)/5221 weeks
377-.5568 -1.86353 (377*2π)/5221 weeks
3781.08921 -4.17251 (378*2π)/5221 weeks
3794.50177 -1.85678 (379*2π)/5221 weeks
3802.46232 1.21958 (380*2π)/5221 weeks
381-.55869 .85337 (381*2π)/5221 weeks
382-1.7639 -3.04289 (382*2π)/5221 weeks
3832.10492 -4.69815 (383*2π)/5221 weeks
3844.74237 -1.7717 (384*2π)/5221 weeks
3852.72401 2.00067 (385*2π)/5221 weeks
386-1.44279 -.03542 (386*2π)/5221 weeks
387.77135 -3.82202 (387*2π)/5221 weeks
3883.0531 -2.14109 (388*2π)/5221 weeks
3893.22185 -.8109 (389*2π)/5221 weeks
3901.52289 .45179 (390*2π)/5221 weeks
3911.22805 -.35419 (391*2π)/5221 weeks
392-.16503 .68212 (392*2π)/5221 weeks
393-1.84686 -1.53019 (393*2π)/5221 weeks
394-.61968 -3.32735 (394*2π)/5221 weeks
3951.40251 -4.39087 (395*2π)/5221 weeks
3963.32344 -2.54753 (396*2π)/5221 weeks
3971.6756 -1.18395 (397*2π)/5221 weeks
3981.00209 -2.54806 (398*2π)/5221 weeks
3992.33818 -2.80116 (399*2π)/5221 weeks
4002.95606 -1.54461 (400*2π)/5221 weeks
4012.22344 -.77327 (401*2π)/5221 weeks
4021.28178 -.02463 (402*2π)/5221 weeks
403-.74078 -.49066 (403*2π)/5221 weeks
404-1.49198 -3.21591 (404*2π)/5221 weeks
4051.73094 -6.15701 (405*2π)/5221 weeks
4065.62974 -3.14014 (406*2π)/5221 weeks
4073.93352 1.19538 (407*2π)/5221 weeks
408-.00407 .5422 (408*2π)/5221 weeks
409-1.14412 -2.54233 (409*2π)/5221 weeks
4101.05403 -4.44591 (410*2π)/5221 weeks
4113.66573 -3.98976 (411*2π)/5221 weeks
4125.33548 -.03407 (412*2π)/5221 weeks
413.66932 3.67943 (413*2π)/5221 weeks
414-4.15508 -.60555 (414*2π)/5221 weeks
415-3.04045 -5.29261 (415*2π)/5221 weeks
4161.35115 -8.52107 (416*2π)/5221 weeks
4177.38934 -5.28229 (417*2π)/5221 weeks
4186.11619 1.88093 (418*2π)/5221 weeks
419-1.69992 2.792 (419*2π)/5221 weeks
420-4.17184 -4.14639 (420*2π)/5221 weeks
421.01092 -8.59043 (421*2π)/5221 weeks
4226.97265 -7.28166 (422*2π)/5221 weeks
4238.35115 -.8033 (423*2π)/5221 weeks
4243.29263 3.74553 (424*2π)/5221 weeks
425-2.59794 -.08526 (425*2π)/5221 weeks
426-.5959 -5.94865 (426*2π)/5221 weeks
4274.79024 -6.21253 (427*2π)/5221 weeks
4286.79242 -1.34729 (428*2π)/5221 weeks
4293.60193 2.1308 (429*2π)/5221 weeks
430-.15002 .70784 (430*2π)/5221 weeks
431-.12804 -2.26933 (431*2π)/5221 weeks
4322.40818 -2.0481 (432*2π)/5221 weeks
433.35422 -.11981 (433*2π)/5221 weeks
434-.47873 -3.10418 (434*2π)/5221 weeks
4352.04247 -3.39747 (435*2π)/5221 weeks
4362.06262 -1.21413 (436*2π)/5221 weeks
437-.89116 -.60483 (437*2π)/5221 weeks
438-3.1963 -4.91784 (438*2π)/5221 weeks
4391.14772 -10.16148 (439*2π)/5221 weeks
4408.5656 -7.71057 (440*2π)/5221 weeks
4419.47618 1.24559 (441*2π)/5221 weeks
442.92301 4.29617 (442*2π)/5221 weeks
443-3.32046 -.48603 (443*2π)/5221 weeks
444-3.04554 -7.01186 (444*2π)/5221 weeks
4454.80635 -9.32116 (445*2π)/5221 weeks
4468.89441 -3.23113 (446*2π)/5221 weeks
4476.26489 4.17621 (447*2π)/5221 weeks
448-3.55474 2.62984 (448*2π)/5221 weeks
449-2.19307 -5.93288 (449*2π)/5221 weeks
4501.30122 -6.39464 (450*2π)/5221 weeks
4517.26658 -6.66756 (451*2π)/5221 weeks
4528.37393 2.92191 (452*2π)/5221 weeks
453-.60155 5.3722 (453*2π)/5221 weeks
454-6.92147 -.62007 (454*2π)/5221 weeks
455-3.3166 -9.25831 (455*2π)/5221 weeks
4564.34662 -6.67645 (456*2π)/5221 weeks
4571.97847 -2.53333 (457*2π)/5221 weeks
458.4422 -4.1007 (458*2π)/5221 weeks
459.56194 -8.12161 (459*2π)/5221 weeks
4607.84241 -7.19211 (460*2π)/5221 weeks
4618.55999 .82242 (461*2π)/5221 weeks
4621.99039 3.75362 (462*2π)/5221 weeks
463-4.64343 -.60981 (463*2π)/5221 weeks
464-.29764 -7.73051 (464*2π)/5221 weeks
4654.43494 -3.98947 (465*2π)/5221 weeks
4662.62104 -.18574 (466*2π)/5221 weeks
467-2.86381 -1.43494 (467*2π)/5221 weeks
468-2.6501 -8.35253 (468*2π)/5221 weeks
4696.49306 -8.46369 (469*2π)/5221 weeks
4706.21411 -.75188 (470*2π)/5221 weeks
4711.37804 -.19401 (471*2π)/5221 weeks
472-.92377 -1.92834 (472*2π)/5221 weeks
473-.59102 -5.53207 (473*2π)/5221 weeks
4742.83667 -4.80526 (474*2π)/5221 weeks
4753.12877 -1.9358 (475*2π)/5221 weeks
476-1.74011 -.68822 (476*2π)/5221 weeks
477-4.23168 -3.57575 (477*2π)/5221 weeks
478-2.2829 -9.52374 (478*2π)/5221 weeks
4793.13043 -7.72167 (479*2π)/5221 weeks
4801.3476 -4.75175 (480*2π)/5221 weeks
481-1.70342 -5.2085 (481*2π)/5221 weeks
482.26184 -12.69098 (482*2π)/5221 weeks
4838.89888 -8.18547 (483*2π)/5221 weeks
4844.43454 -.87708 (484*2π)/5221 weeks
485-1.8601 -1.32234 (485*2π)/5221 weeks
486-6.23428 -7.92509 (486*2π)/5221 weeks
487.6157 -17.81338 (487*2π)/5221 weeks
48813.8325 -12.70706 (488*2π)/5221 weeks
48916.61659 3.72588 (489*2π)/5221 weeks
490-4.25369 16.05059 (490*2π)/5221 weeks
491-22.73992 -4.65355 (491*2π)/5221 weeks
492-9.80557 -27.06765 (492*2π)/5221 weeks
49314.71043 -25.44938 (493*2π)/5221 weeks
49420.12103 -1.33974 (494*2π)/5221 weeks
495-.40499 9.95714 (495*2π)/5221 weeks
496-14.8067 -1.82049 (496*2π)/5221 weeks
497-14.36574 -20.09478 (497*2π)/5221 weeks
4983.90359 -24.20945 (498*2π)/5221 weeks
4999.42296 -13.39782 (499*2π)/5221 weeks
5003.80441 -6.16196 (500*2π)/5221 weeks
501-2.57088 -13.69813 (501*2π)/5221 weeks
5022.18197 -18.2679 (502*2π)/5221 weeks
5036.00468 -15.92487 (503*2π)/5221 weeks
5046.09073 -17.21122 (504*2π)/5221 weeks
50511.64752 -10.5138 (505*2π)/5221 weeks
5061.44179 -8.45954 (506*2π)/5221 weeks
5074.33651 -10.43699 (507*2π)/5221 weeks
508-2.8207 -6.29158 (508*2π)/5221 weeks
509-14.73367 -14.25624 (509*2π)/5221 weeks
510-14.49176 -40.8733 (510*2π)/5221 weeks
51122.03669 -47.65318 (511*2π)/5221 weeks
51230.75694 -17.70144 (512*2π)/5221 weeks
51320.10722 .77962 (513*2π)/5221 weeks
514-22.25318 2.90934 (514*2π)/5221 weeks
515-31.81383 -55.43222 (515*2π)/5221 weeks
51618.03893 -70.75704 (516*2π)/5221 weeks
51742.24522 -30.03698 (517*2π)/5221 weeks
518-1.74041 3.19248 (518*2π)/5221 weeks
519-87.13835 -50.94814 (519*2π)/5221 weeks
520-61.18584 -222.1234 (520*2π)/5221 weeks

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