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Fourier Analysis of QID (ProShares UltraShort QQQ)


QID (ProShares UltraShort QQQ) appears to have interesting cyclic behaviour every 62 weeks (53.9557*sine), 56 weeks (44.9979*sine), and 44 weeks (30.2346*cosine).

QID (ProShares UltraShort QQQ) has an average price of 314.61 (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 4/16/2018 for QID (ProShares UltraShort QQQ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0314.6147   0 
1178.7989 356.381 (1*2π)/615615 weeks
2-39.4355 191.7773 (2*2π)/615308 weeks
3-33.65918 41.54296 (3*2π)/615205 weeks
449.62025 19.90663 (4*2π)/615154 weeks
569.86902 74.45375 (5*2π)/615123 weeks
614.63607 100.1199 (6*2π)/615103 weeks
7-26.59462 59.18282 (7*2π)/61588 weeks
8-9.02897 8.94463 (8*2π)/61577 weeks
936.19853 22.27728 (9*2π)/61568 weeks
1019.16327 53.95573 (10*2π)/61562 weeks
11-6.40989 44.99787 (11*2π)/61556 weeks
12-14.35156 21.89796 (12*2π)/61551 weeks
133.03019 -.78758 (13*2π)/61547 weeks
1430.23458 10.60405 (14*2π)/61544 weeks
1526.86631 35.91439 (15*2π)/61541 weeks
166.1736 40.80065 (16*2π)/61538 weeks
17-5.2434 28.74698 (17*2π)/61536 weeks
18-3.43813 16.74564 (18*2π)/61534 weeks
192.08432 8.48565 (19*2π)/61532 weeks
2015.21205 11.97139 (20*2π)/61531 weeks
2113.72998 21.691 (21*2π)/61529 weeks
228.34235 24.405 (22*2π)/61528 weeks
233.98467 22.34993 (23*2π)/61527 weeks
241.65429 21.65441 (24*2π)/61526 weeks
25-1.10751 15.82242 (25*2π)/61525 weeks
264.62644 16.39193 (26*2π)/61524 weeks
27-.549 17.38551 (27*2π)/61523 weeks
28-3.17717 12.42494 (28*2π)/61522 weeks
29-.01714 4.74246 (29*2π)/61521 weeks
3011.27784 7.87084 (30*2π)/61521 weeks
3110.30356 16.66043 (31*2π)/61520 weeks
323.79615 21.81385 (32*2π)/61519 weeks
33-7.21423 15.35877 (33*2π)/61519 weeks
34-4.23452 2.32493 (34*2π)/61518 weeks
359.6157 1.54996 (35*2π)/61518 weeks
3615.26457 14.17682 (36*2π)/61517 weeks
374.05676 24.05626 (37*2π)/61517 weeks
38-9.40946 14.78214 (38*2π)/61516 weeks
39-3.56849 2.34747 (39*2π)/61516 weeks
405.6573 3.53264 (40*2π)/61515 weeks
417.73356 10.20225 (41*2π)/61515 weeks
423.33923 12.20533 (42*2π)/61515 weeks
431.28233 11.1254 (43*2π)/61514 weeks
44.18523 8.64905 (44*2π)/61514 weeks
452.47953 6.26874 (45*2π)/61514 weeks
463.98625 10.32096 (46*2π)/61513 weeks
47-.38847 8.78836 (47*2π)/61513 weeks
481.91857 5.8164 (48*2π)/61513 weeks
492.37374 7.78998 (49*2π)/61513 weeks
501.89762 6.784 (50*2π)/61512 weeks
511.06723 5.48043 (51*2π)/61512 weeks
524.6853 2.7518 (52*2π)/61512 weeks
538.49234 8.02779 (53*2π)/61512 weeks
545.47276 11.02002 (54*2π)/61511 weeks
551.36687 11.65185 (55*2π)/61511 weeks
56-.90342 8.46249 (56*2π)/61511 weeks
57.96273 5.39317 (57*2π)/61511 weeks
583.46685 7.20044 (58*2π)/61511 weeks
591.30445 8.20327 (59*2π)/61510 weeks
60-.57517 7.21669 (60*2π)/61510 weeks
61-.82407 3.44768 (61*2π)/61510 weeks
624.46489 2.0599 (62*2π)/61510 weeks
635.69203 8.26054 (63*2π)/61510 weeks
64.93303 8.275 (64*2π)/61510 weeks
65.09177 5.55692 (65*2π)/6159 weeks
661.81843 4.01023 (66*2π)/6159 weeks
673.24555 5.08695 (67*2π)/6159 weeks
681.57625 6.36189 (68*2π)/6159 weeks
69.92119 3.54648 (69*2π)/6159 weeks
704.47792 3.34238 (70*2π)/6159 weeks
715.21318 6.33944 (71*2π)/6159 weeks
722.09302 8.85025 (72*2π)/6159 weeks
73-1.33547 5.67042 (73*2π)/6158 weeks
741.14713 1.62727 (74*2π)/6158 weeks
754.11464 3.94409 (75*2π)/6158 weeks
763.61169 5.34766 (76*2π)/6158 weeks
771.24955 6.11482 (77*2π)/6158 weeks
781.58484 1.63136 (78*2π)/6158 weeks
797.10742 3.48397 (79*2π)/6158 weeks
805.59356 9.6499 (80*2π)/6158 weeks
81-1.47606 9.55042 (81*2π)/6158 weeks
82-3.28378 2.76385 (82*2π)/6158 weeks
833.16484 -.29681 (83*2π)/6157 weeks
845.81213 4.53307 (84*2π)/6157 weeks
853.30259 5.99086 (85*2π)/6157 weeks
862.06169 7.03956 (86*2π)/6157 weeks
87-1.13749 4.08264 (87*2π)/6157 weeks
883.50288 .72681 (88*2π)/6157 weeks
896.25347 5.38414 (89*2π)/6157 weeks
903.27224 8.74157 (90*2π)/6157 weeks
91-1.5135 7.65724 (91*2π)/6157 weeks
92-1.78049 2.66497 (92*2π)/6157 weeks
931.67302 1.16229 (93*2π)/6157 weeks
944.83935 2.93314 (94*2π)/6157 weeks
953.78479 8.12539 (95*2π)/6156 weeks
96-2.35995 7.11167 (96*2π)/6156 weeks
97-2.48687 1.23478 (97*2π)/6156 weeks
982.20659 -.64947 (98*2π)/6156 weeks
995.09108 2.79059 (99*2π)/6156 weeks
1003.10352 6.30455 (100*2π)/6156 weeks
101-.34756 5.3515 (101*2π)/6156 weeks
102-.53595 1.83763 (102*2π)/6156 weeks
1032.32661 1.11559 (103*2π)/6156 weeks
1042.84921 3.43122 (104*2π)/6156 weeks
1051.02034 2.78626 (105*2π)/6156 weeks
1062.78234 2.07997 (106*2π)/6156 weeks
1072.2893 3.459 (107*2π)/6156 weeks
1081.53783 2.61845 (108*2π)/6156 weeks
1092.0533 1.29396 (109*2π)/6156 weeks
1104.65578 1.55335 (110*2π)/6156 weeks
1115.03217 4.83756 (111*2π)/6156 weeks
1121.63891 6.28299 (112*2π)/6155 weeks
113-.53683 3.61538 (113*2π)/6155 weeks
1141.54888 .57518 (114*2π)/6155 weeks
1154.90101 2.12686 (115*2π)/6155 weeks
1163.9676 6.13247 (116*2π)/6155 weeks
117-.20564 6.86673 (117*2π)/6155 weeks
118-3.65887 2.34783 (118*2π)/6155 weeks
119.38489 -2.22609 (119*2π)/6155 weeks
1205.29486 -.82277 (120*2π)/6155 weeks
1215.86702 4.30534 (121*2π)/6155 weeks
1221.17908 6.17072 (122*2π)/6155 weeks
123-1.53703 2.12677 (123*2π)/6155 weeks
1241.98956 -1.63154 (124*2π)/6155 weeks
1255.94938 .9784 (125*2π)/6155 weeks
1265.06574 4.84828 (126*2π)/6155 weeks
1271.59453 6.05573 (127*2π)/6155 weeks
128-1.00684 2.7286 (128*2π)/6155 weeks
1291.80018 -.25654 (129*2π)/6155 weeks
1304.74073 1.54217 (130*2π)/6155 weeks
1313.85848 4.31001 (131*2π)/6155 weeks
1321.60801 4.76621 (132*2π)/6155 weeks
133.44997 2.76273 (133*2π)/6155 weeks
1342.19085 1.77986 (134*2π)/6155 weeks
1353.03686 2.58403 (135*2π)/6155 weeks
1362.38594 4.63059 (136*2π)/6155 weeks
137-.55698 4.18997 (137*2π)/6154 weeks
138-1.04113 .67739 (138*2π)/6154 weeks
1392.34152 -.23163 (139*2π)/6154 weeks
1403.34149 1.60941 (140*2π)/6154 weeks
1412.27818 2.80772 (141*2π)/6154 weeks
1421.33704 2.2309 (142*2π)/6154 weeks
1431.77119 1.97503 (143*2π)/6154 weeks
1441.41648 1.34228 (144*2π)/6154 weeks
1452.31218 1.08998 (145*2π)/6154 weeks
1462.38732 2.0154 (146*2π)/6154 weeks
1471.16619 1.32768 (147*2π)/6154 weeks
1482.28547 -.32343 (148*2π)/6154 weeks
1494.71974 .78253 (149*2π)/6154 weeks
1504.13967 3.17213 (150*2π)/6154 weeks
1512.55196 3.38444 (151*2π)/6154 weeks
152.84823 2.4692 (152*2π)/6154 weeks
1532.23726 .53668 (153*2π)/6154 weeks
1543.6138 2.00276 (154*2π)/6154 weeks
1552.1816 2.29456 (155*2π)/6154 weeks
1562.52551 1.54705 (156*2π)/6154 weeks
1572.76631 1.78565 (157*2π)/6154 weeks
1583.14041 2.62353 (158*2π)/6154 weeks
1591.59038 2.30514 (159*2π)/6154 weeks
1603.0002 .82145 (160*2π)/6154 weeks
1613.90785 2.62073 (161*2π)/6154 weeks
1622.11476 3.44594 (162*2π)/6154 weeks
1631.09893 2.36229 (163*2π)/6154 weeks
1641.9382 .91783 (164*2π)/6154 weeks
1653.43936 1.56094 (165*2π)/6154 weeks
1662.74996 2.96114 (166*2π)/6154 weeks
1671.56711 2.95004 (167*2π)/6154 weeks
168.74466 1.2495 (168*2π)/6154 weeks
1693.20833 .30651 (169*2π)/6154 weeks
1703.33808 2.83447 (170*2π)/6154 weeks
1711.99414 2.57455 (171*2π)/6154 weeks
1721.37353 2.20163 (172*2π)/6154 weeks
1731.59242 1.01206 (173*2π)/6154 weeks
1742.60413 1.0777 (174*2π)/6154 weeks
1752.93164 1.60545 (175*2π)/6154 weeks
1762.8923 2.29365 (176*2π)/6153 weeks
1771.27152 2.35488 (177*2π)/6153 weeks
1781.91287 .33571 (178*2π)/6153 weeks
1793.1719 1.34466 (179*2π)/6153 weeks
1802.81952 1.6227 (180*2π)/6153 weeks
1813.02746 1.82411 (181*2π)/6153 weeks
1822.62111 2.21564 (182*2π)/6153 weeks
1831.92826 1.92524 (183*2π)/6153 weeks
1842.92326 .80675 (184*2π)/6153 weeks
1853.87888 1.92648 (185*2π)/6153 weeks
1863.83282 3.2716 (186*2π)/6153 weeks
1872.02466 4.24453 (187*2π)/6153 weeks
188.2576 2.76508 (188*2π)/6153 weeks
1891.31032 .89257 (189*2π)/6153 weeks
1902.6974 1.70082 (190*2π)/6153 weeks
1912.24967 2.44953 (191*2π)/6153 weeks
1921.57314 2.73687 (192*2π)/6153 weeks
193.77342 1.91008 (193*2π)/6153 weeks
1941.05383 .78419 (194*2π)/6153 weeks
1952.56311 .40249 (195*2π)/6153 weeks
1963.588 2.08455 (196*2π)/6153 weeks
1971.92536 3.69191 (197*2π)/6153 weeks
198-.1006 2.3555 (198*2π)/6153 weeks
199-.01967 .30876 (199*2π)/6153 weeks
2002.34794 -.86267 (200*2π)/6153 weeks
2014.13814 1.18128 (201*2π)/6153 weeks
2022.69827 3.17119 (202*2π)/6153 weeks
203.66094 2.3002 (203*2π)/6153 weeks
204.91733 .21927 (204*2π)/6153 weeks
2052.97224 .06612 (205*2π)/6153 weeks
2063.97025 1.85903 (206*2π)/6153 weeks
2072.2485 3.25341 (207*2π)/6153 weeks
2081.06542 2.28089 (208*2π)/6153 weeks
209.91295 1.28034 (209*2π)/6153 weeks
2102.24427 .94529 (210*2π)/6153 weeks
2112.16399 2.23924 (211*2π)/6153 weeks
212.76178 2.02343 (212*2π)/6153 weeks
213.49995 .71873 (213*2π)/6153 weeks
2141.66212 -.30951 (214*2π)/6153 weeks
2152.91428 .31921 (215*2π)/6153 weeks
2163.14691 .90056 (216*2π)/6153 weeks
2173.68126 2.59038 (217*2π)/6153 weeks
218.80952 3.82821 (218*2π)/6153 weeks
219-.50678 .77902 (219*2π)/6153 weeks
2201.02815 -.61306 (220*2π)/6153 weeks
2212.91654 -.60238 (221*2π)/6153 weeks
2223.65292 1.26811 (222*2π)/6153 weeks
2232.55995 2.19554 (223*2π)/6153 weeks
2241.85818 1.83293 (224*2π)/6153 weeks
2251.33346 .96864 (225*2π)/6153 weeks
2263.17075 .83114 (226*2π)/6153 weeks
2272.31671 2.78483 (227*2π)/6153 weeks
2281.16429 2.18468 (228*2π)/6153 weeks
229.28211 1.76475 (229*2π)/6153 weeks
230.4739 -.38278 (230*2π)/6153 weeks
2313.26873 -.69957 (231*2π)/6153 weeks
2323.73511 2.3013 (232*2π)/6153 weeks
2331.28169 3.36523 (233*2π)/6153 weeks
234-.61599 1.20954 (234*2π)/6153 weeks
2351.24915 -.79092 (235*2π)/6153 weeks
2362.71601 .4795 (236*2π)/6153 weeks
2372.5713 1.6698 (237*2π)/6153 weeks
2381.06924 2.1385 (238*2π)/6153 weeks
239-.04012 .17156 (239*2π)/6153 weeks
2402.25571 -.81204 (240*2π)/6153 weeks
2413.42359 .7714 (241*2π)/6153 weeks
2422.36998 2.38023 (242*2π)/6153 weeks
243.4603 1.71025 (243*2π)/6153 weeks
244.85483 .07956 (244*2π)/6153 weeks
2452.04639 .12046 (245*2π)/6153 weeks
2462.01082 .53705 (246*2π)/6153 weeks
2472.24804 .51811 (247*2π)/6152 weeks
2482.41862 1.07235 (248*2π)/6152 weeks
2492.27815 1.13821 (249*2π)/6152 weeks
2502.46965 2.05647 (250*2π)/6152 weeks
251.50955 2.43182 (251*2π)/6152 weeks
252.15527 .46256 (252*2π)/6152 weeks
2531.3357 -.01914 (253*2π)/6152 weeks
2542.30331 .99245 (254*2π)/6152 weeks
255.57404 2.00273 (255*2π)/6152 weeks
256-.41651 .10107 (256*2π)/6152 weeks
257.61812 -1.23188 (257*2π)/6152 weeks
2582.24389 -1.40097 (258*2π)/6152 weeks
2593.70875 .33747 (259*2π)/6152 weeks
2601.98935 2.28595 (260*2π)/6152 weeks
261-.23562 .83166 (261*2π)/6152 weeks
262.55249 -1.69961 (262*2π)/6152 weeks
2633.59376 -1.62265 (263*2π)/6152 weeks
2644.21489 1.49965 (264*2π)/6152 weeks
2651.65693 2.74925 (265*2π)/6152 weeks
266-.31293 1.33981 (266*2π)/6152 weeks
267-.09875 -1.38858 (267*2π)/6152 weeks
2683.26182 -1.50862 (268*2π)/6152 weeks
2693.38906 1.00445 (269*2π)/6152 weeks
2702.00397 1.91185 (270*2π)/6152 weeks
271.30132 1.13943 (271*2π)/6152 weeks
272.79121 -.34518 (272*2π)/6152 weeks
2731.52236 -.46234 (273*2π)/6152 weeks
2742.23364 -.25197 (274*2π)/6152 weeks
2752.01376 .93476 (275*2π)/6152 weeks
276.5072 .49942 (276*2π)/6152 weeks
2771.11873 -1.07629 (277*2π)/6152 weeks
2782.42179 -1.33695 (278*2π)/6152 weeks
2793.661 .18226 (279*2π)/6152 weeks
2802.4686 2.18334 (280*2π)/6152 weeks
281-.13037 1.55565 (281*2π)/6152 weeks
282-.39078 -.94796 (282*2π)/6152 weeks
2831.29282 -2.30091 (283*2π)/6152 weeks
2843.71404 -1.89504 (284*2π)/6152 weeks
2854.29465 1.12647 (285*2π)/6152 weeks
2861.76717 2.76456 (286*2π)/6152 weeks
287-1.13453 .89593 (287*2π)/6152 weeks
288.16945 -2.49604 (288*2π)/6152 weeks
2893.00372 -2.00348 (289*2π)/6152 weeks
2903.41264 -.06939 (290*2π)/6152 weeks
2911.96295 1.25065 (291*2π)/6152 weeks
292.18911 -.21283 (292*2π)/6152 weeks
2931.293 -2.28291 (293*2π)/6152 weeks
2943.86263 -1.54699 (294*2π)/6152 weeks
2953.33308 .5811 (295*2π)/6152 weeks
2961.68487 .675 (296*2π)/6152 weeks
297.96897 -.81073 (297*2π)/6152 weeks
2982.35037 -1.94248 (298*2π)/6152 weeks
2994.25128 -1.65349 (299*2π)/6152 weeks
3004.90444 1.14863 (300*2π)/6152 weeks
3011.74412 2.58345 (301*2π)/6152 weeks
302.40577 -.23502 (302*2π)/6152 weeks
3032.2901 -1.37172 (303*2π)/6152 weeks
3043.62478 -.86802 (304*2π)/6152 weeks
3053.77872 .92031 (305*2π)/6152 weeks
3062.54111 2.16789 (306*2π)/6152 weeks
307-.00797 1.60127 (307*2π)/6152 weeks
308-.00797 -1.60127 (308*2π)/6152 weeks
3092.54111 -2.16789 (309*2π)/6152 weeks
3103.77872 -.92031 (310*2π)/6152 weeks
3113.62478 .86802 (311*2π)/6152 weeks
3122.2901 1.37172 (312*2π)/6152 weeks
313.40577 .23502 (313*2π)/6152 weeks
3141.74412 -2.58345 (314*2π)/6152 weeks
3154.90444 -1.14863 (315*2π)/6152 weeks
3164.25128 1.65349 (316*2π)/6152 weeks
3172.35037 1.94248 (317*2π)/6152 weeks
318.96897 .81073 (318*2π)/6152 weeks
3191.68487 -.675 (319*2π)/6152 weeks
3203.33308 -.5811 (320*2π)/6152 weeks
3213.86263 1.54699 (321*2π)/6152 weeks
3221.293 2.28291 (322*2π)/6152 weeks
323.18911 .21283 (323*2π)/6152 weeks
3241.96295 -1.25065 (324*2π)/6152 weeks
3253.41264 .06939 (325*2π)/6152 weeks
3263.00372 2.00348 (326*2π)/6152 weeks
327.16945 2.49604 (327*2π)/6152 weeks
328-1.13453 -.89593 (328*2π)/6152 weeks
3291.76717 -2.76456 (329*2π)/6152 weeks
3304.29465 -1.12647 (330*2π)/6152 weeks
3313.71404 1.89504 (331*2π)/6152 weeks
3321.29282 2.30091 (332*2π)/6152 weeks
333-.39078 .94796 (333*2π)/6152 weeks
334-.13037 -1.55565 (334*2π)/6152 weeks
3352.4686 -2.18334 (335*2π)/6152 weeks
3363.661 -.18226 (336*2π)/6152 weeks
3372.42179 1.33695 (337*2π)/6152 weeks
3381.11873 1.07629 (338*2π)/6152 weeks
339.5072 -.49942 (339*2π)/6152 weeks
3402.01376 -.93476 (340*2π)/6152 weeks
3412.23364 .25197 (341*2π)/6152 weeks
3421.52236 .46234 (342*2π)/6152 weeks
343.79121 .34518 (343*2π)/6152 weeks
344.30132 -1.13943 (344*2π)/6152 weeks
3452.00397 -1.91185 (345*2π)/6152 weeks
3463.38906 -1.00445 (346*2π)/6152 weeks
3473.26182 1.50862 (347*2π)/6152 weeks
348-.09875 1.38858 (348*2π)/6152 weeks
349-.31293 -1.33981 (349*2π)/6152 weeks
3501.65693 -2.74925 (350*2π)/6152 weeks
3514.21489 -1.49965 (351*2π)/6152 weeks
3523.59376 1.62265 (352*2π)/6152 weeks
353.55249 1.69961 (353*2π)/6152 weeks
354-.23562 -.83166 (354*2π)/6152 weeks
3551.98935 -2.28595 (355*2π)/6152 weeks
3563.70875 -.33747 (356*2π)/6152 weeks
3572.24389 1.40097 (357*2π)/6152 weeks
358.61812 1.23188 (358*2π)/6152 weeks
359-.41651 -.10107 (359*2π)/6152 weeks
360.57404 -2.00273 (360*2π)/6152 weeks
3612.30331 -.99245 (361*2π)/6152 weeks
3621.3357 .01914 (362*2π)/6152 weeks
363.15527 -.46256 (363*2π)/6152 weeks
364.50955 -2.43182 (364*2π)/6152 weeks
3652.46965 -2.05647 (365*2π)/6152 weeks
3662.27815 -1.13821 (366*2π)/6152 weeks
3672.41862 -1.07235 (367*2π)/6152 weeks
3682.24804 -.51811 (368*2π)/6152 weeks
3692.01082 -.53705 (369*2π)/6152 weeks
3702.04639 -.12046 (370*2π)/6152 weeks
371.85483 -.07956 (371*2π)/6152 weeks
372.4603 -1.71025 (372*2π)/6152 weeks
3732.36998 -2.38023 (373*2π)/6152 weeks
3743.42359 -.7714 (374*2π)/6152 weeks
3752.25571 .81204 (375*2π)/6152 weeks
376-.04012 -.17156 (376*2π)/6152 weeks
3771.06924 -2.1385 (377*2π)/6152 weeks
3782.5713 -1.6698 (378*2π)/6152 weeks
3792.71601 -.4795 (379*2π)/6152 weeks
3801.24915 .79092 (380*2π)/6152 weeks
381-.61599 -1.20954 (381*2π)/6152 weeks
3821.28169 -3.36523 (382*2π)/6152 weeks
3833.73511 -2.3013 (383*2π)/6152 weeks
3843.26873 .69957 (384*2π)/6152 weeks
385.4739 .38278 (385*2π)/6152 weeks
386.28211 -1.76475 (386*2π)/6152 weeks
3871.16429 -2.18468 (387*2π)/6152 weeks
3882.31671 -2.78483 (388*2π)/6152 weeks
3893.17075 -.83114 (389*2π)/6152 weeks
3901.33346 -.96864 (390*2π)/6152 weeks
3911.85818 -1.83293 (391*2π)/6152 weeks
3922.55995 -2.19554 (392*2π)/6152 weeks
3933.65292 -1.26811 (393*2π)/6152 weeks
3942.91654 .60238 (394*2π)/6152 weeks
3951.02815 .61306 (395*2π)/6152 weeks
396-.50678 -.77902 (396*2π)/6152 weeks
397.80952 -3.82821 (397*2π)/6152 weeks
3983.68126 -2.59038 (398*2π)/6152 weeks
3993.14691 -.90056 (399*2π)/6152 weeks
4002.91428 -.31921 (400*2π)/6152 weeks
4011.66212 .30951 (401*2π)/6152 weeks
402.49995 -.71873 (402*2π)/6152 weeks
403.76178 -2.02343 (403*2π)/6152 weeks
4042.16399 -2.23924 (404*2π)/6152 weeks
4052.24427 -.94529 (405*2π)/6152 weeks
406.91295 -1.28034 (406*2π)/6152 weeks
4071.06542 -2.28089 (407*2π)/6152 weeks
4082.2485 -3.25341 (408*2π)/6152 weeks
4093.97025 -1.85903 (409*2π)/6152 weeks
4102.97224 -.06612 (410*2π)/6152 weeks
411.91733 -.21927 (411*2π)/6151 weeks
412.66094 -2.3002 (412*2π)/6151 weeks
4132.69827 -3.17119 (413*2π)/6151 weeks
4144.13814 -1.18128 (414*2π)/6151 weeks
4152.34794 .86267 (415*2π)/6151 weeks
416-.01967 -.30876 (416*2π)/6151 weeks
417-.1006 -2.3555 (417*2π)/6151 weeks
4181.92536 -3.69191 (418*2π)/6151 weeks
4193.588 -2.08455 (419*2π)/6151 weeks
4202.56311 -.40249 (420*2π)/6151 weeks
4211.05383 -.78419 (421*2π)/6151 weeks
422.77342 -1.91008 (422*2π)/6151 weeks
4231.57314 -2.73687 (423*2π)/6151 weeks
4242.24967 -2.44953 (424*2π)/6151 weeks
4252.6974 -1.70082 (425*2π)/6151 weeks
4261.31032 -.89257 (426*2π)/6151 weeks
427.2576 -2.76508 (427*2π)/6151 weeks
4282.02466 -4.24453 (428*2π)/6151 weeks
4293.83282 -3.2716 (429*2π)/6151 weeks
4303.87888 -1.92648 (430*2π)/6151 weeks
4312.92326 -.80675 (431*2π)/6151 weeks
4321.92826 -1.92524 (432*2π)/6151 weeks
4332.62111 -2.21564 (433*2π)/6151 weeks
4343.02746 -1.82411 (434*2π)/6151 weeks
4352.81952 -1.6227 (435*2π)/6151 weeks
4363.1719 -1.34466 (436*2π)/6151 weeks
4371.91287 -.33571 (437*2π)/6151 weeks
4381.27152 -2.35488 (438*2π)/6151 weeks
4392.8923 -2.29365 (439*2π)/6151 weeks
4402.93164 -1.60545 (440*2π)/6151 weeks
4412.60413 -1.0777 (441*2π)/6151 weeks
4421.59242 -1.01206 (442*2π)/6151 weeks
4431.37353 -2.20163 (443*2π)/6151 weeks
4441.99414 -2.57455 (444*2π)/6151 weeks
4453.33808 -2.83447 (445*2π)/6151 weeks
4463.20833 -.30651 (446*2π)/6151 weeks
447.74466 -1.2495 (447*2π)/6151 weeks
4481.56711 -2.95004 (448*2π)/6151 weeks
4492.74996 -2.96114 (449*2π)/6151 weeks
4503.43936 -1.56094 (450*2π)/6151 weeks
4511.9382 -.91783 (451*2π)/6151 weeks
4521.09893 -2.36229 (452*2π)/6151 weeks
4532.11476 -3.44594 (453*2π)/6151 weeks
4543.90785 -2.62073 (454*2π)/6151 weeks
4553.0002 -.82145 (455*2π)/6151 weeks
4561.59038 -2.30514 (456*2π)/6151 weeks
4573.14041 -2.62353 (457*2π)/6151 weeks
4582.76631 -1.78565 (458*2π)/6151 weeks
4592.52551 -1.54705 (459*2π)/6151 weeks
4602.1816 -2.29456 (460*2π)/6151 weeks
4613.6138 -2.00276 (461*2π)/6151 weeks
4622.23726 -.53668 (462*2π)/6151 weeks
463.84823 -2.4692 (463*2π)/6151 weeks
4642.55196 -3.38444 (464*2π)/6151 weeks
4654.13967 -3.17213 (465*2π)/6151 weeks
4664.71974 -.78253 (466*2π)/6151 weeks
4672.28547 .32343 (467*2π)/6151 weeks
4681.16619 -1.32768 (468*2π)/6151 weeks
4692.38732 -2.0154 (469*2π)/6151 weeks
4702.31218 -1.08998 (470*2π)/6151 weeks
4711.41648 -1.34228 (471*2π)/6151 weeks
4721.77119 -1.97503 (472*2π)/6151 weeks
4731.33704 -2.2309 (473*2π)/6151 weeks
4742.27818 -2.80772 (474*2π)/6151 weeks
4753.34149 -1.60941 (475*2π)/6151 weeks
4762.34152 .23163 (476*2π)/6151 weeks
477-1.04113 -.67739 (477*2π)/6151 weeks
478-.55698 -4.18997 (478*2π)/6151 weeks
4792.38594 -4.63059 (479*2π)/6151 weeks
4803.03686 -2.58403 (480*2π)/6151 weeks
4812.19085 -1.77986 (481*2π)/6151 weeks
482.44997 -2.76273 (482*2π)/6151 weeks
4831.60801 -4.76621 (483*2π)/6151 weeks
4843.85848 -4.31001 (484*2π)/6151 weeks
4854.74073 -1.54217 (485*2π)/6151 weeks
4861.80018 .25654 (486*2π)/6151 weeks
487-1.00684 -2.7286 (487*2π)/6151 weeks
4881.59453 -6.05573 (488*2π)/6151 weeks
4895.06574 -4.84828 (489*2π)/6151 weeks
4905.94938 -.9784 (490*2π)/6151 weeks
4911.98956 1.63154 (491*2π)/6151 weeks
492-1.53703 -2.12677 (492*2π)/6151 weeks
4931.17908 -6.17072 (493*2π)/6151 weeks
4945.86702 -4.30534 (494*2π)/6151 weeks
4955.29486 .82277 (495*2π)/6151 weeks
496.38489 2.22609 (496*2π)/6151 weeks
497-3.65887 -2.34783 (497*2π)/6151 weeks
498-.20564 -6.86673 (498*2π)/6151 weeks
4993.9676 -6.13247 (499*2π)/6151 weeks
5004.90101 -2.12686 (500*2π)/6151 weeks
5011.54888 -.57518 (501*2π)/6151 weeks
502-.53683 -3.61538 (502*2π)/6151 weeks
5031.63891 -6.28299 (503*2π)/6151 weeks
5045.03217 -4.83756 (504*2π)/6151 weeks
5054.65578 -1.55335 (505*2π)/6151 weeks
5062.0533 -1.29396 (506*2π)/6151 weeks
5071.53783 -2.61845 (507*2π)/6151 weeks
5082.2893 -3.459 (508*2π)/6151 weeks
5092.78234 -2.07997 (509*2π)/6151 weeks
5101.02034 -2.78626 (510*2π)/6151 weeks
5112.84921 -3.43122 (511*2π)/6151 weeks
5122.32661 -1.11559 (512*2π)/6151 weeks
513-.53595 -1.83763 (513*2π)/6151 weeks
514-.34756 -5.3515 (514*2π)/6151 weeks
5153.10352 -6.30455 (515*2π)/6151 weeks
5165.09108 -2.79059 (516*2π)/6151 weeks
5172.20659 .64947 (517*2π)/6151 weeks
518-2.48687 -1.23478 (518*2π)/6151 weeks
519-2.35995 -7.11167 (519*2π)/6151 weeks
5203.78479 -8.12539 (520*2π)/6151 weeks
5214.83935 -2.93314 (521*2π)/6151 weeks
5221.67302 -1.16229 (522*2π)/6151 weeks
523-1.78049 -2.66497 (523*2π)/6151 weeks
524-1.5135 -7.65724 (524*2π)/6151 weeks
5253.27224 -8.74157 (525*2π)/6151 weeks
5266.25347 -5.38414 (526*2π)/6151 weeks
5273.50288 -.72681 (527*2π)/6151 weeks
528-1.13749 -4.08264 (528*2π)/6151 weeks
5292.06169 -7.03956 (529*2π)/6151 weeks
5303.30259 -5.99086 (530*2π)/6151 weeks
5315.81213 -4.53307 (531*2π)/6151 weeks
5323.16484 .29681 (532*2π)/6151 weeks
533-3.28378 -2.76385 (533*2π)/6151 weeks
534-1.47606 -9.55042 (534*2π)/6151 weeks
5355.59356 -9.6499 (535*2π)/6151 weeks
5367.10742 -3.48397 (536*2π)/6151 weeks
5371.58484 -1.63136 (537*2π)/6151 weeks
5381.24955 -6.11482 (538*2π)/6151 weeks
5393.61169 -5.34766 (539*2π)/6151 weeks
5404.11464 -3.94409 (540*2π)/6151 weeks
5411.14713 -1.62727 (541*2π)/6151 weeks
542-1.33547 -5.67042 (542*2π)/6151 weeks
5432.09302 -8.85025 (543*2π)/6151 weeks
5445.21318 -6.33944 (544*2π)/6151 weeks
5454.47792 -3.34238 (545*2π)/6151 weeks
546.92119 -3.54648 (546*2π)/6151 weeks
5471.57625 -6.36189 (547*2π)/6151 weeks
5483.24555 -5.08695 (548*2π)/6151 weeks
5491.81843 -4.01023 (549*2π)/6151 weeks
550.09177 -5.55692 (550*2π)/6151 weeks
551.93303 -8.275 (551*2π)/6151 weeks
5525.69203 -8.26054 (552*2π)/6151 weeks
5534.46489 -2.0599 (553*2π)/6151 weeks
554-.82407 -3.44768 (554*2π)/6151 weeks
555-.57517 -7.21669 (555*2π)/6151 weeks
5561.30445 -8.20327 (556*2π)/6151 weeks
5573.46685 -7.20044 (557*2π)/6151 weeks
558.96273 -5.39317 (558*2π)/6151 weeks
559-.90342 -8.46249 (559*2π)/6151 weeks
5601.36687 -11.65185 (560*2π)/6151 weeks
5615.47276 -11.02002 (561*2π)/6151 weeks
5628.49234 -8.02779 (562*2π)/6151 weeks
5634.6853 -2.7518 (563*2π)/6151 weeks
5641.06723 -5.48043 (564*2π)/6151 weeks
5651.89762 -6.784 (565*2π)/6151 weeks
5662.37374 -7.78998 (566*2π)/6151 weeks
5671.91857 -5.8164 (567*2π)/6151 weeks
568-.38847 -8.78836 (568*2π)/6151 weeks
5693.98625 -10.32096 (569*2π)/6151 weeks
5702.47953 -6.26874 (570*2π)/6151 weeks
571.18523 -8.64905 (571*2π)/6151 weeks
5721.28233 -11.1254 (572*2π)/6151 weeks
5733.33923 -12.20533 (573*2π)/6151 weeks
5747.73356 -10.20225 (574*2π)/6151 weeks
5755.6573 -3.53264 (575*2π)/6151 weeks
576-3.56849 -2.34747 (576*2π)/6151 weeks
577-9.40946 -14.78214 (577*2π)/6151 weeks
5784.05676 -24.05626 (578*2π)/6151 weeks
57915.26457 -14.17682 (579*2π)/6151 weeks
5809.6157 -1.54996 (580*2π)/6151 weeks
581-4.23452 -2.32493 (581*2π)/6151 weeks
582-7.21423 -15.35877 (582*2π)/6151 weeks
5833.79615 -21.81385 (583*2π)/6151 weeks
58410.30356 -16.66043 (584*2π)/6151 weeks
58511.27784 -7.87084 (585*2π)/6151 weeks
586-.01714 -4.74246 (586*2π)/6151 weeks
587-3.17717 -12.42494 (587*2π)/6151 weeks
588-.549 -17.38551 (588*2π)/6151 weeks
5894.62644 -16.39193 (589*2π)/6151 weeks
590-1.10751 -15.82242 (590*2π)/6151 weeks
5911.65429 -21.65441 (591*2π)/6151 weeks
5923.98467 -22.34993 (592*2π)/6151 weeks
5938.34235 -24.405 (593*2π)/6151 weeks
59413.72998 -21.691 (594*2π)/6151 weeks
59515.21205 -11.97139 (595*2π)/6151 weeks
5962.08432 -8.48565 (596*2π)/6151 weeks
597-3.43813 -16.74564 (597*2π)/6151 weeks
598-5.2434 -28.74698 (598*2π)/6151 weeks
5996.1736 -40.80065 (599*2π)/6151 weeks
60026.86631 -35.91439 (600*2π)/6151 weeks
60130.23458 -10.60405 (601*2π)/6151 weeks
6023.03019 .78758 (602*2π)/6151 weeks
603-14.35156 -21.89796 (603*2π)/6151 weeks
604-6.40989 -44.99787 (604*2π)/6151 weeks
60519.16327 -53.95573 (605*2π)/6151 weeks
60636.19853 -22.27728 (606*2π)/6151 weeks
607-9.02897 -8.94463 (607*2π)/6151 weeks
608-26.59462 -59.18282 (608*2π)/6151 weeks
60914.63607 -100.1199 (609*2π)/6151 weeks
61069.86902 -74.45375 (610*2π)/6151 weeks
61149.62025 -19.90663 (611*2π)/6151 weeks
612-33.65918 -41.54296 (612*2π)/6151 weeks
613-39.4355 -191.7773 (613*2π)/6151 weeks



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