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Fourier Analysis of SQQQ (ProShares UltraPro Short QQQ)


SQQQ (ProShares UltraPro Short QQQ) appears to have interesting cyclic behaviour every 43 weeks (99.8818*sine), 39 weeks (88.5182*sine), and 24 weeks (50.9639*cosine).

SQQQ (ProShares UltraPro Short QQQ) has an average price of 743.59 (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 2/11/2010 to 4/16/2018 for SQQQ (ProShares UltraPro Short QQQ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0743.5912   0 
1706.4335 714.3063 (1*2π)/428428 weeks
2296.0326 543.006 (2*2π)/428214 weeks
3178.8981 436.985 (3*2π)/428143 weeks
4114.9632 340.9773 (4*2π)/428107 weeks
5107.7992 305.4649 (5*2π)/42886 weeks
648.00661 318.5258 (6*2π)/42871 weeks
7-30.75615 260.8863 (7*2π)/42861 weeks
8-52.2181 183.4714 (8*2π)/42854 weeks
9-39.0875 123.7381 (9*2π)/42848 weeks
10-15.01061 99.88181 (10*2π)/42843 weeks
11-3.34037 88.51823 (11*2π)/42839 weeks
12-1.09748 78.02699 (12*2π)/42836 weeks
137.10022 51.029 (13*2π)/42833 weeks
1433.76152 54.46938 (14*2π)/42831 weeks
1531.27312 63.43683 (15*2π)/42829 weeks
1631.30329 51.85745 (16*2π)/42827 weeks
1749.69703 51.84367 (17*2π)/42825 weeks
1850.96392 78.14617 (18*2π)/42824 weeks
1924.58069 72.89022 (19*2π)/42823 weeks
2024.93276 52.91042 (20*2π)/42821 weeks
2143.64509 59.13095 (21*2π)/42820 weeks
2233.11116 73.9334 (22*2π)/42819 weeks
2318.72312 62.47005 (23*2π)/42819 weeks
2415.59945 54.10038 (24*2π)/42818 weeks
2521.50805 44.20437 (25*2π)/42817 weeks
2632.00556 40.67156 (26*2π)/42816 weeks
2734.42885 50.74679 (27*2π)/42816 weeks
2825.85913 51.81546 (28*2π)/42815 weeks
2928.53304 43.13393 (29*2π)/42815 weeks
3034.8563 45.53495 (30*2π)/42814 weeks
3139.54246 49.61116 (31*2π)/42814 weeks
3236.23304 65.83081 (32*2π)/42813 weeks
3318.57666 68.11612 (33*2π)/42813 weeks
343.90115 57.6601 (34*2π)/42813 weeks
357.67309 39.09941 (35*2π)/42812 weeks
3620.18375 37.52603 (36*2π)/42812 weeks
3723.77228 50.07677 (37*2π)/42812 weeks
3811.59303 48.99107 (38*2π)/42811 weeks
399.13768 45.70598 (39*2π)/42811 weeks
404.01855 40.69849 (40*2π)/42811 weeks
416.31553 27.86184 (41*2π)/42810 weeks
4215.93822 25.29829 (42*2π)/42810 weeks
4324.49437 28.97627 (43*2π)/42810 weeks
4426.57947 42.00301 (44*2π)/42810 weeks
4515.11868 45.72865 (45*2π)/42810 weeks
469.26154 42.22582 (46*2π)/4289 weeks
474.44068 37.01001 (47*2π)/4289 weeks
485.82228 30.48428 (48*2π)/4289 weeks
4912.05922 30.06765 (49*2π)/4289 weeks
509.20734 34.90355 (50*2π)/4289 weeks
514.4619 34.38791 (51*2π)/4288 weeks
52-5.57283 29.4683 (52*2π)/4288 weeks
53-2.92471 13.42136 (53*2π)/4288 weeks
5410.79659 11.11227 (54*2π)/4288 weeks
5513.42515 18.05175 (55*2π)/4288 weeks
5610.44473 18.22738 (56*2π)/4288 weeks
576.83398 15.52645 (57*2π)/4288 weeks
589.71919 6.11227 (58*2π)/4287 weeks
5921.16519 -.66046 (59*2π)/4287 weeks
6036.38458 7.87286 (60*2π)/4287 weeks
6137.56096 23.7412 (61*2π)/4287 weeks
6227.19794 30.83426 (62*2π)/4287 weeks
6321.33804 26.44595 (63*2π)/4287 weeks
6424.85555 23.98297 (64*2π)/4287 weeks
6527.78065 29.97126 (65*2π)/4287 weeks
6622.09529 37.78334 (66*2π)/4286 weeks
6713.68274 36.38084 (67*2π)/4286 weeks
6810.40272 31.7813 (68*2π)/4286 weeks
698.48156 29.91576 (69*2π)/4286 weeks
707.85118 28.6304 (70*2π)/4286 weeks
715.756 25.83079 (71*2π)/4286 weeks
723.11904 22.81738 (72*2π)/4286 weeks
732.87269 15.70275 (73*2π)/4286 weeks
7410.74476 11.56683 (74*2π)/4286 weeks
7516.11717 16.22437 (75*2π)/4286 weeks
7613.79846 19.85873 (76*2π)/4286 weeks
7712.38174 19.02229 (77*2π)/4286 weeks
7811.70999 18.38979 (78*2π)/4285 weeks
7913.62789 18.1699 (79*2π)/4285 weeks
8013.34198 18.97961 (80*2π)/4285 weeks
8110.93651 20.83585 (81*2π)/4285 weeks
828.25066 15.44875 (82*2π)/4285 weeks
8314.74472 14.32004 (83*2π)/4285 weeks
8414.78144 17.53483 (84*2π)/4285 weeks
8514.19769 18.66309 (85*2π)/4285 weeks
8615.09831 20.44414 (86*2π)/4285 weeks
8711.55477 23.21024 (87*2π)/4285 weeks
886.50285 22.44798 (88*2π)/4285 weeks
894.9051 17.52036 (89*2π)/4285 weeks
906.72004 14.71635 (90*2π)/4285 weeks
918.03603 13.31894 (91*2π)/4285 weeks
9210.56404 15.45727 (92*2π)/4285 weeks
937.7842 18.55889 (93*2π)/4285 weeks
943.7208 13.881 (94*2π)/4285 weeks
955.27216 11.45471 (95*2π)/4285 weeks
965.71325 9.00945 (96*2π)/4284 weeks
9710.22187 8.38246 (97*2π)/4284 weeks
989.18623 10.77192 (98*2π)/4284 weeks
996.41496 10.18817 (99*2π)/4284 weeks
1008.35113 5.5826 (100*2π)/4284 weeks
10110.41425 5.48382 (101*2π)/4284 weeks
10212.32987 4.60266 (102*2π)/4284 weeks
10313.60507 4.70433 (103*2π)/4284 weeks
10417.2759 4.02138 (104*2π)/4284 weeks
10522.54459 7.1316 (105*2π)/4284 weeks
10620.426 15.20892 (106*2π)/4284 weeks
10715.33637 16.94529 (107*2π)/4284 weeks
10810.42327 13.34238 (108*2π)/4284 weeks
10912.11944 7.75482 (109*2π)/4284 weeks
11019.22326 9.95903 (110*2π)/4284 weeks
11118.81188 16.50213 (111*2π)/4284 weeks
11213.84804 17.86355 (112*2π)/4284 weeks
1139.79179 16.26755 (113*2π)/4284 weeks
11410.60086 13.90976 (114*2π)/4284 weeks
11511.94988 14.05814 (115*2π)/4284 weeks
11610.32822 18.02129 (116*2π)/4284 weeks
1173.6489 17.57523 (117*2π)/4284 weeks
118.25802 9.68193 (118*2π)/4284 weeks
1196.6572 4.20077 (119*2π)/4284 weeks
12010.73026 7.81535 (120*2π)/4284 weeks
1219.08768 10.739 (121*2π)/4284 weeks
1226.17903 10.9657 (122*2π)/4284 weeks
1232.11317 6.68122 (123*2π)/4283 weeks
1245.12001 -.11789 (124*2π)/4283 weeks
12511.62838 .15303 (125*2π)/4283 weeks
12613.46576 2.92088 (126*2π)/4283 weeks
12712.93404 3.21998 (127*2π)/4283 weeks
12817.2252 3.78099 (128*2π)/4283 weeks
12917.17961 9.26087 (129*2π)/4283 weeks
13014.33352 10.68072 (130*2π)/4283 weeks
13111.77502 11.60226 (131*2π)/4283 weeks
1328.69832 10.7554 (132*2π)/4283 weeks
1337.84124 7.22451 (133*2π)/4283 weeks
13410.2512 6.43377 (134*2π)/4283 weeks
1359.60899 7.6622 (135*2π)/4283 weeks
1368.36143 7.36284 (136*2π)/4283 weeks
1377.07217 5.9893 (137*2π)/4283 weeks
1386.96234 2.2243 (138*2π)/4283 weeks
13910.72139 1.87664 (139*2π)/4283 weeks
14011.9108 3.1855 (140*2π)/4283 weeks
14111.84625 3.89705 (141*2π)/4283 weeks
14211.25909 3.81402 (142*2π)/4283 weeks
14311.26953 4.77865 (143*2π)/4283 weeks
1448.79996 2.78498 (144*2π)/4283 weeks
14510.99122 -1.16728 (145*2π)/4283 weeks
14615.15511 .86093 (146*2π)/4283 weeks
14714.76735 2.97251 (147*2π)/4283 weeks
14812.97574 2.88359 (148*2π)/4283 weeks
14913.58988 .29746 (149*2π)/4283 weeks
15017.65245 -1.41518 (150*2π)/4283 weeks
15122.74989 2.6549 (151*2π)/4283 weeks
15222.40391 10.19305 (152*2π)/4283 weeks
15315.06098 12.54624 (153*2π)/4283 weeks
15412.01957 8.75086 (154*2π)/4283 weeks
15513.69184 6.67194 (155*2π)/4283 weeks
15617.62931 7.12397 (156*2π)/4283 weeks
15717.05474 15.14999 (157*2π)/4283 weeks
1587.52058 17.19776 (158*2π)/4283 weeks
1592.14277 10.52712 (159*2π)/4283 weeks
1603.63833 5.71277 (160*2π)/4283 weeks
1615.68407 2.6953 (161*2π)/4283 weeks
1628.12856 4.1606 (162*2π)/4283 weeks
1635.46993 4.92748 (163*2π)/4283 weeks
1643.20919 1.19949 (164*2π)/4283 weeks
1656.31872 -2.71429 (165*2π)/4283 weeks
16610.18268 -4.06755 (166*2π)/4283 weeks
16712.99281 .09304 (167*2π)/4283 weeks
16810.69158 1.45096 (168*2π)/4283 weeks
1699.0303 -.03971 (169*2π)/4283 weeks
1709.40285 -1.40439 (170*2π)/4283 weeks
17110.15577 -3.65273 (171*2π)/4283 weeks
17212.19503 -4.93429 (172*2π)/4282 weeks
17315.78556 -5.17855 (173*2π)/4282 weeks
17418.97068 -2.22801 (174*2π)/4282 weeks
17517.61666 2.18455 (175*2π)/4282 weeks
17613.32086 1.63797 (176*2π)/4282 weeks
17714.8832 -2.52358 (177*2π)/4282 weeks
17819.01475 -1.58375 (178*2π)/4282 weeks
17919.96423 1.75357 (179*2π)/4282 weeks
18018.84344 5.29064 (180*2π)/4282 weeks
18115.94998 5.50874 (181*2π)/4282 weeks
18214.76077 3.63933 (182*2π)/4282 weeks
18316.45184 3.30487 (183*2π)/4282 weeks
18417.59644 5.477 (184*2π)/4282 weeks
18515.55727 8.84645 (185*2π)/4282 weeks
1869.5997 9.12303 (186*2π)/4282 weeks
1878.54102 2.44914 (187*2π)/4282 weeks
18813.23331 1.06611 (188*2π)/4282 weeks
18914.03852 4.89204 (189*2π)/4282 weeks
19010.96778 5.91031 (190*2π)/4282 weeks
1918.35315 3.75601 (191*2π)/4282 weeks
1928.18078 .18323 (192*2π)/4282 weeks
19312.56278 -2.37297 (193*2π)/4282 weeks
19414.47836 .02074 (194*2π)/4282 weeks
19515.48476 1.56978 (195*2π)/4282 weeks
19615.1606 3.90527 (196*2π)/4282 weeks
19712.94075 5.41535 (197*2π)/4282 weeks
19810.73328 3.62899 (198*2π)/4282 weeks
19912.83746 3.12908 (199*2π)/4282 weeks
20012.09515 6.23404 (200*2π)/4282 weeks
2017.90107 6.61773 (201*2π)/4282 weeks
2024.71013 3.35145 (202*2π)/4282 weeks
2035.36111 .15081 (203*2π)/4282 weeks
2044.9664 -1.26373 (204*2π)/4282 weeks
2056.84674 -4.86873 (205*2π)/4282 weeks
2068.8455 -4.66549 (206*2π)/4282 weeks
2077.83453 -4.80236 (207*2π)/4282 weeks
2089.24481 -9.05117 (208*2π)/4282 weeks
20913.089 -11.01792 (209*2π)/4282 weeks
21018.60429 -9.49834 (210*2π)/4282 weeks
21121.15657 -4.84148 (211*2π)/4282 weeks
21218.66789 -3.64458 (212*2π)/4282 weeks
21320.95856 -3.55976 (213*2π)/4282 weeks
21422.94225   (214*2π)/4282 weeks
21520.95856 3.55976 (215*2π)/4282 weeks
21618.66789 3.64458 (216*2π)/4282 weeks
21721.15657 4.84148 (217*2π)/4282 weeks
21818.60429 9.49834 (218*2π)/4282 weeks
21913.089 11.01792 (219*2π)/4282 weeks
2209.24481 9.05117 (220*2π)/4282 weeks
2217.83453 4.80236 (221*2π)/4282 weeks
2228.8455 4.66549 (222*2π)/4282 weeks
2236.84674 4.86873 (223*2π)/4282 weeks
2244.9664 1.26373 (224*2π)/4282 weeks
2255.36111 -.15081 (225*2π)/4282 weeks
2264.71013 -3.35145 (226*2π)/4282 weeks
2277.90107 -6.61773 (227*2π)/4282 weeks
22812.09515 -6.23404 (228*2π)/4282 weeks
22912.83746 -3.12908 (229*2π)/4282 weeks
23010.73328 -3.62899 (230*2π)/4282 weeks
23112.94075 -5.41535 (231*2π)/4282 weeks
23215.1606 -3.90527 (232*2π)/4282 weeks
23315.48476 -1.56978 (233*2π)/4282 weeks
23414.47836 -.02074 (234*2π)/4282 weeks
23512.56278 2.37297 (235*2π)/4282 weeks
2368.18078 -.18323 (236*2π)/4282 weeks
2378.35315 -3.75601 (237*2π)/4282 weeks
23810.96778 -5.91031 (238*2π)/4282 weeks
23914.03852 -4.89204 (239*2π)/4282 weeks
24013.23331 -1.06611 (240*2π)/4282 weeks
2418.54102 -2.44914 (241*2π)/4282 weeks
2429.5997 -9.12303 (242*2π)/4282 weeks
24315.55727 -8.84645 (243*2π)/4282 weeks
24417.59644 -5.477 (244*2π)/4282 weeks
24516.45184 -3.30487 (245*2π)/4282 weeks
24614.76077 -3.63933 (246*2π)/4282 weeks
24715.94998 -5.50874 (247*2π)/4282 weeks
24818.84344 -5.29064 (248*2π)/4282 weeks
24919.96423 -1.75357 (249*2π)/4282 weeks
25019.01475 1.58375 (250*2π)/4282 weeks
25114.8832 2.52358 (251*2π)/4282 weeks
25213.32086 -1.63797 (252*2π)/4282 weeks
25317.61666 -2.18455 (253*2π)/4282 weeks
25418.97068 2.22801 (254*2π)/4282 weeks
25515.78556 5.17855 (255*2π)/4282 weeks
25612.19503 4.93429 (256*2π)/4282 weeks
25710.15577 3.65273 (257*2π)/4282 weeks
2589.40285 1.40439 (258*2π)/4282 weeks
2599.0303 .03971 (259*2π)/4282 weeks
26010.69158 -1.45096 (260*2π)/4282 weeks
26112.99281 -.09304 (261*2π)/4282 weeks
26210.18268 4.06755 (262*2π)/4282 weeks
2636.31872 2.71429 (263*2π)/4282 weeks
2643.20919 -1.19949 (264*2π)/4282 weeks
2655.46993 -4.92748 (265*2π)/4282 weeks
2668.12856 -4.1606 (266*2π)/4282 weeks
2675.68407 -2.6953 (267*2π)/4282 weeks
2683.63833 -5.71277 (268*2π)/4282 weeks
2692.14277 -10.52712 (269*2π)/4282 weeks
2707.52058 -17.19776 (270*2π)/4282 weeks
27117.05474 -15.14999 (271*2π)/4282 weeks
27217.62931 -7.12397 (272*2π)/4282 weeks
27313.69184 -6.67194 (273*2π)/4282 weeks
27412.01957 -8.75086 (274*2π)/4282 weeks
27515.06098 -12.54624 (275*2π)/4282 weeks
27622.40391 -10.19305 (276*2π)/4282 weeks
27722.74989 -2.6549 (277*2π)/4282 weeks
27817.65245 1.41518 (278*2π)/4282 weeks
27913.58988 -.29746 (279*2π)/4282 weeks
28012.97574 -2.88359 (280*2π)/4282 weeks
28114.76735 -2.97251 (281*2π)/4282 weeks
28215.15511 -.86093 (282*2π)/4282 weeks
28310.99122 1.16728 (283*2π)/4282 weeks
2848.79996 -2.78498 (284*2π)/4282 weeks
28511.26953 -4.77865 (285*2π)/4282 weeks
28611.25909 -3.81402 (286*2π)/4281 weeks
28711.84625 -3.89705 (287*2π)/4281 weeks
28811.9108 -3.1855 (288*2π)/4281 weeks
28910.72139 -1.87664 (289*2π)/4281 weeks
2906.96234 -2.2243 (290*2π)/4281 weeks
2917.07217 -5.9893 (291*2π)/4281 weeks
2928.36143 -7.36284 (292*2π)/4281 weeks
2939.60899 -7.6622 (293*2π)/4281 weeks
29410.2512 -6.43377 (294*2π)/4281 weeks
2957.84124 -7.22451 (295*2π)/4281 weeks
2968.69832 -10.7554 (296*2π)/4281 weeks
29711.77502 -11.60226 (297*2π)/4281 weeks
29814.33352 -10.68072 (298*2π)/4281 weeks
29917.17961 -9.26087 (299*2π)/4281 weeks
30017.2252 -3.78099 (300*2π)/4281 weeks
30112.93404 -3.21998 (301*2π)/4281 weeks
30213.46576 -2.92088 (302*2π)/4281 weeks
30311.62838 -.15303 (303*2π)/4281 weeks
3045.12001 .11789 (304*2π)/4281 weeks
3052.11317 -6.68122 (305*2π)/4281 weeks
3066.17903 -10.9657 (306*2π)/4281 weeks
3079.08768 -10.739 (307*2π)/4281 weeks
30810.73026 -7.81535 (308*2π)/4281 weeks
3096.6572 -4.20077 (309*2π)/4281 weeks
310.25802 -9.68193 (310*2π)/4281 weeks
3113.6489 -17.57523 (311*2π)/4281 weeks
31210.32822 -18.02129 (312*2π)/4281 weeks
31311.94988 -14.05814 (313*2π)/4281 weeks
31410.60086 -13.90976 (314*2π)/4281 weeks
3159.79179 -16.26755 (315*2π)/4281 weeks
31613.84804 -17.86355 (316*2π)/4281 weeks
31718.81188 -16.50213 (317*2π)/4281 weeks
31819.22326 -9.95903 (318*2π)/4281 weeks
31912.11944 -7.75482 (319*2π)/4281 weeks
32010.42327 -13.34238 (320*2π)/4281 weeks
32115.33637 -16.94529 (321*2π)/4281 weeks
32220.426 -15.20892 (322*2π)/4281 weeks
32322.54459 -7.1316 (323*2π)/4281 weeks
32417.2759 -4.02138 (324*2π)/4281 weeks
32513.60507 -4.70433 (325*2π)/4281 weeks
32612.32987 -4.60266 (326*2π)/4281 weeks
32710.41425 -5.48382 (327*2π)/4281 weeks
3288.35113 -5.5826 (328*2π)/4281 weeks
3296.41496 -10.18817 (329*2π)/4281 weeks
3309.18623 -10.77192 (330*2π)/4281 weeks
33110.22187 -8.38246 (331*2π)/4281 weeks
3325.71325 -9.00945 (332*2π)/4281 weeks
3335.27216 -11.45471 (333*2π)/4281 weeks
3343.7208 -13.881 (334*2π)/4281 weeks
3357.7842 -18.55889 (335*2π)/4281 weeks
33610.56404 -15.45727 (336*2π)/4281 weeks
3378.03603 -13.31894 (337*2π)/4281 weeks
3386.72004 -14.71635 (338*2π)/4281 weeks
3394.9051 -17.52036 (339*2π)/4281 weeks
3406.50285 -22.44798 (340*2π)/4281 weeks
34111.55477 -23.21024 (341*2π)/4281 weeks
34215.09831 -20.44414 (342*2π)/4281 weeks
34314.19769 -18.66309 (343*2π)/4281 weeks
34414.78144 -17.53483 (344*2π)/4281 weeks
34514.74472 -14.32004 (345*2π)/4281 weeks
3468.25066 -15.44875 (346*2π)/4281 weeks
34710.93651 -20.83585 (347*2π)/4281 weeks
34813.34198 -18.97961 (348*2π)/4281 weeks
34913.62789 -18.1699 (349*2π)/4281 weeks
35011.70999 -18.38979 (350*2π)/4281 weeks
35112.38174 -19.02229 (351*2π)/4281 weeks
35213.79846 -19.85873 (352*2π)/4281 weeks
35316.11717 -16.22437 (353*2π)/4281 weeks
35410.74476 -11.56683 (354*2π)/4281 weeks
3552.87269 -15.70275 (355*2π)/4281 weeks
3563.11904 -22.81738 (356*2π)/4281 weeks
3575.756 -25.83079 (357*2π)/4281 weeks
3587.85118 -28.6304 (358*2π)/4281 weeks
3598.48156 -29.91576 (359*2π)/4281 weeks
36010.40272 -31.7813 (360*2π)/4281 weeks
36113.68274 -36.38084 (361*2π)/4281 weeks
36222.09529 -37.78334 (362*2π)/4281 weeks
36327.78065 -29.97126 (363*2π)/4281 weeks
36424.85555 -23.98297 (364*2π)/4281 weeks
36521.33804 -26.44595 (365*2π)/4281 weeks
36627.19794 -30.83426 (366*2π)/4281 weeks
36737.56096 -23.7412 (367*2π)/4281 weeks
36836.38458 -7.87286 (368*2π)/4281 weeks
36921.16519 .66046 (369*2π)/4281 weeks
3709.71919 -6.11227 (370*2π)/4281 weeks
3716.83398 -15.52645 (371*2π)/4281 weeks
37210.44473 -18.22738 (372*2π)/4281 weeks
37313.42515 -18.05175 (373*2π)/4281 weeks
37410.79659 -11.11227 (374*2π)/4281 weeks
375-2.92471 -13.42136 (375*2π)/4281 weeks
376-5.57283 -29.4683 (376*2π)/4281 weeks
3774.4619 -34.38791 (377*2π)/4281 weeks
3789.20734 -34.90355 (378*2π)/4281 weeks
37912.05922 -30.06765 (379*2π)/4281 weeks
3805.82228 -30.48428 (380*2π)/4281 weeks
3814.44068 -37.01001 (381*2π)/4281 weeks
3829.26154 -42.22582 (382*2π)/4281 weeks
38315.11868 -45.72865 (383*2π)/4281 weeks
38426.57947 -42.00301 (384*2π)/4281 weeks
38524.49437 -28.97627 (385*2π)/4281 weeks
38615.93822 -25.29829 (386*2π)/4281 weeks
3876.31553 -27.86184 (387*2π)/4281 weeks
3884.01855 -40.69849 (388*2π)/4281 weeks
3899.13768 -45.70598 (389*2π)/4281 weeks
39011.59303 -48.99107 (390*2π)/4281 weeks
39123.77228 -50.07677 (391*2π)/4281 weeks
39220.18375 -37.52603 (392*2π)/4281 weeks
3937.67309 -39.09941 (393*2π)/4281 weeks
3943.90115 -57.6601 (394*2π)/4281 weeks
39518.57666 -68.11612 (395*2π)/4281 weeks
39636.23304 -65.83081 (396*2π)/4281 weeks
39739.54246 -49.61116 (397*2π)/4281 weeks
39834.8563 -45.53495 (398*2π)/4281 weeks
39928.53304 -43.13393 (399*2π)/4281 weeks
40025.85913 -51.81546 (400*2π)/4281 weeks
40134.42885 -50.74679 (401*2π)/4281 weeks
40232.00556 -40.67156 (402*2π)/4281 weeks
40321.50805 -44.20437 (403*2π)/4281 weeks
40415.59945 -54.10038 (404*2π)/4281 weeks
40518.72312 -62.47005 (405*2π)/4281 weeks
40633.11116 -73.9334 (406*2π)/4281 weeks
40743.64509 -59.13095 (407*2π)/4281 weeks
40824.93276 -52.91042 (408*2π)/4281 weeks
40924.58069 -72.89022 (409*2π)/4281 weeks
41050.96392 -78.14617 (410*2π)/4281 weeks
41149.69703 -51.84367 (411*2π)/4281 weeks
41231.30329 -51.85745 (412*2π)/4281 weeks
41331.27312 -63.43683 (413*2π)/4281 weeks
41433.76152 -54.46938 (414*2π)/4281 weeks
4157.10022 -51.029 (415*2π)/4281 weeks
416-1.09748 -78.02699 (416*2π)/4281 weeks
417-3.34037 -88.51823 (417*2π)/4281 weeks
418-15.01061 -99.88181 (418*2π)/4281 weeks
419-39.0875 -123.7381 (419*2π)/4281 weeks
420-52.2181 -183.4714 (420*2π)/4281 weeks
421-30.75615 -260.8863 (421*2π)/4281 weeks
42248.00661 -318.5258 (422*2π)/4281 weeks
423107.7992 -305.4649 (423*2π)/4281 weeks
424114.9632 -340.9773 (424*2π)/4281 weeks
425178.8981 -436.985 (425*2π)/4281 weeks
426296.0326 -543.006 (426*2π)/4281 weeks



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