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Fourier Analysis of SPXU (ProShares UltraPro Short S&P500)


SPXU (ProShares UltraPro Short S&P500) appears to have interesting cyclic behaviour every 47 weeks (185.6096*sine), 42 weeks (140.4255*sine), and 29 weeks (68.0895*cosine).

SPXU (ProShares UltraPro Short S&P500) has an average price of 835.23 (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 6/25/2009 to 5/21/2018 for SPXU (ProShares UltraPro Short S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0835.2284   0 
1719.3229 787.8193 (1*2π)/466466 weeks
2258.5475 558.6604 (2*2π)/466233 weeks
3173.9769 417.1543 (3*2π)/466155 weeks
4111.3256 333.3802 (4*2π)/466117 weeks
566.43179 260.533 (5*2π)/46693 weeks
651.94904 186.4486 (6*2π)/46678 weeks
7104.9033 133.6821 (7*2π)/46667 weeks
8144.9774 172.3444 (8*2π)/46658 weeks
994.74628 216.9357 (9*2π)/46652 weeks
1039.25873 185.6096 (10*2π)/46647 weeks
1135.5132 140.4255 (11*2π)/46642 weeks
1248.75648 127.2467 (12*2π)/46639 weeks
1338.01307 125.8412 (13*2π)/46636 weeks
1427.00017 94.76174 (14*2π)/46633 weeks
1561.71829 82.23228 (15*2π)/46631 weeks
1668.08949 103.7976 (16*2π)/46629 weeks
1757.31326 106.4968 (17*2π)/46627 weeks
1849.54209 111.2647 (18*2π)/46626 weeks
1934.7514 111.6711 (19*2π)/46625 weeks
2027.12365 91.64365 (20*2π)/46623 weeks
2129.08573 95.06686 (21*2π)/46622 weeks
2210.72217 89.82046 (22*2π)/46621 weeks
2314.95696 57.79464 (23*2π)/46620 weeks
2435.24393 53.83271 (24*2π)/46619 weeks
2537.45759 63.67483 (25*2π)/46619 weeks
2635.39812 64.32086 (26*2π)/46618 weeks
2740.71543 54.93906 (27*2π)/46617 weeks
2849.63234 59.44402 (28*2π)/46617 weeks
2950.33089 75.66179 (29*2π)/46616 weeks
3036.95034 80.30824 (30*2π)/46616 weeks
3131.83867 73.94768 (31*2π)/46615 weeks
3228.77 77.05001 (32*2π)/46615 weeks
3320.29277 75.72198 (33*2π)/46614 weeks
348.13464 70.16482 (34*2π)/46614 weeks
355.60283 48.01487 (35*2π)/46613 weeks
3623.62248 40.38181 (36*2π)/46613 weeks
3731.83442 52.49846 (37*2π)/46613 weeks
3820.95091 55.5234 (38*2π)/46612 weeks
3920.86136 46.66185 (39*2π)/46612 weeks
4030.37264 44.19316 (40*2π)/46612 weeks
4126.85938 53.66148 (41*2π)/46611 weeks
4225.01238 50.44543 (42*2π)/46611 weeks
4322.84992 49.93443 (43*2π)/46611 weeks
4422.70714 45.84664 (44*2π)/46611 weeks
4528.59562 48.24974 (45*2π)/46610 weeks
4627.28309 53.21457 (46*2π)/46610 weeks
4721.23659 56.10133 (47*2π)/46610 weeks
4811.43966 51.38826 (48*2π)/46610 weeks
4913.22648 43.46281 (49*2π)/46610 weeks
5017.57309 39.03329 (50*2π)/4669 weeks
5123.35501 42.87398 (51*2π)/4669 weeks
5218.25768 48.23459 (52*2π)/4669 weeks
5311.55038 42.10722 (53*2π)/4669 weeks
5417.88109 37.06092 (54*2π)/4669 weeks
5519.81361 40.67945 (55*2π)/4668 weeks
5616.39133 45.75624 (56*2π)/4668 weeks
577.30034 34.90168 (57*2π)/4668 weeks
5821.14105 27.1741 (58*2π)/4668 weeks
5927.65638 38.63346 (59*2π)/4668 weeks
6021.04899 43.86961 (60*2π)/4668 weeks
6116.80996 42.40347 (61*2π)/4668 weeks
6219.28501 39.42234 (62*2π)/4668 weeks
6319.06483 47.79932 (63*2π)/4667 weeks
646.9906 52.81974 (64*2π)/4667 weeks
65-8.56287 39.26221 (65*2π)/4667 weeks
66-.29981 20.26446 (66*2π)/4667 weeks
6715.16443 20.23359 (67*2π)/4667 weeks
6817.14482 28.51468 (68*2π)/4667 weeks
6914.72646 27.21491 (69*2π)/4667 weeks
7020.95615 25.69699 (70*2π)/4667 weeks
7123.03825 35.67143 (71*2π)/4667 weeks
7213.21111 39.46327 (72*2π)/4666 weeks
738.93181 32.64954 (73*2π)/4666 weeks
7412.1432 30.08244 (74*2π)/4666 weeks
7512.89313 28.55202 (75*2π)/4666 weeks
7614.53682 29.75651 (76*2π)/4666 weeks
7715.27746 31.63194 (77*2π)/4666 weeks
7815.4914 32.44739 (78*2π)/4666 weeks
7914.86982 36.55123 (79*2π)/4666 weeks
806.66564 38.77967 (80*2π)/4666 weeks
811.52255 31.19099 (81*2π)/4666 weeks
825.07012 27.57081 (82*2π)/4666 weeks
835.34171 26.84396 (83*2π)/4666 weeks
845.4082 24.81986 (84*2π)/4666 weeks
855.68332 22.73741 (85*2π)/4665 weeks
868.72401 22.99483 (86*2π)/4665 weeks
879.38646 23.31079 (87*2π)/4665 weeks
887.73429 23.96401 (88*2π)/4665 weeks
898.52207 22.12717 (89*2π)/4665 weeks
907.75491 25.12942 (90*2π)/4665 weeks
914.36799 21.04069 (91*2π)/4665 weeks
926.13566 17.43867 (92*2π)/4665 weeks
938.78008 17.79889 (93*2π)/4665 weeks
9411.03742 16.44359 (94*2π)/4665 weeks
9513.44028 18.6202 (95*2π)/4665 weeks
9612.29682 23.25266 (96*2π)/4665 weeks
977.20005 22.33398 (97*2π)/4665 weeks
987.12067 17.8297 (98*2π)/4665 weeks
998.58413 15.25233 (99*2π)/4665 weeks
10012.36406 16.5281 (100*2π)/4665 weeks
10112.14611 18.50655 (101*2π)/4665 weeks
10212.277 16.02067 (102*2π)/4665 weeks
10314.09045 17.88841 (103*2π)/4665 weeks
10415.44334 18.83639 (104*2π)/4664 weeks
10515.79628 22.83017 (105*2π)/4664 weeks
10613.23898 22.87574 (106*2π)/4664 weeks
10712.77779 25.60121 (107*2π)/4664 weeks
1089.86884 28.30601 (108*2π)/4664 weeks
1094.51868 27.17347 (109*2π)/4664 weeks
1101.11992 24.55332 (110*2π)/4664 weeks
111-.74835 20.13765 (111*2π)/4664 weeks
112-.28468 16.68835 (112*2π)/4664 weeks
1133.58193 12.88754 (113*2π)/4664 weeks
1147.26965 14.1525 (114*2π)/4664 weeks
1156.00668 20.1563 (115*2π)/4664 weeks
116.40136 19.13654 (116*2π)/4664 weeks
117-1.94235 13.03525 (117*2π)/4664 weeks
1181.60682 10.98067 (118*2π)/4664 weeks
1191.35232 13.3506 (119*2π)/4664 weeks
120-2.77115 8.12896 (120*2π)/4664 weeks
1211.63424 .79553 (121*2π)/4664 weeks
1228.57416 1.42446 (122*2π)/4664 weeks
12312.04009 6.93031 (123*2π)/4664 weeks
12410.02553 8.30406 (124*2π)/4664 weeks
1259.63726 7.79253 (125*2π)/4664 weeks
12611.66049 9.86218 (126*2π)/4664 weeks
1277.64131 12.36698 (127*2π)/4664 weeks
1283.31038 7.59136 (128*2π)/4664 weeks
1297.76772 1.88724 (129*2π)/4664 weeks
13012.8054 4.41826 (130*2π)/4664 weeks
13112.40765 5.98886 (131*2π)/4664 weeks
13213.64315 4.8828 (132*2π)/4664 weeks
13316.77416 6.14574 (133*2π)/4664 weeks
13419.85114 12.14837 (134*2π)/4663 weeks
13513.51135 18.13046 (135*2π)/4663 weeks
1367.5676 14.48871 (136*2π)/4663 weeks
1377.70189 10.86902 (137*2π)/4663 weeks
1388.57175 10.31295 (138*2π)/4663 weeks
1398.02878 7.84803 (139*2π)/4663 weeks
14012.11936 8.65821 (140*2π)/4663 weeks
14110.09225 12.08047 (141*2π)/4663 weeks
1428.08916 10.57577 (142*2π)/4663 weeks
1437.96248 9.64742 (143*2π)/4663 weeks
1447.42191 8.8916 (144*2π)/4663 weeks
1457.91741 7.7475 (145*2π)/4663 weeks
1467.28579 8.55064 (146*2π)/4663 weeks
1477.43407 5.95111 (147*2π)/4663 weeks
1488.99828 6.07317 (148*2π)/4663 weeks
1498.44974 7.04178 (149*2π)/4663 weeks
1507.83039 6.50105 (150*2π)/4663 weeks
1517.90226 4.49525 (151*2π)/4663 weeks
1529.66349 4.82963 (152*2π)/4663 weeks
1539.03059 6.06332 (153*2π)/4663 weeks
1548.13996 4.47921 (154*2π)/4663 weeks
15510.48643 3.74674 (155*2π)/4663 weeks
1569.55204 5.96778 (156*2π)/4663 weeks
1579.02458 3.61432 (157*2π)/4663 weeks
15812.58735 3.71425 (158*2π)/4663 weeks
15911.4501 7.91169 (159*2π)/4663 weeks
1607.89824 8.09497 (160*2π)/4663 weeks
1616.66611 4.72928 (161*2π)/4663 weeks
1628.34092 4.60507 (162*2π)/4663 weeks
1636.7914 6.45685 (163*2π)/4663 weeks
1641.98376 2.71997 (164*2π)/4663 weeks
1654.83692 -5.12241 (165*2π)/4663 weeks
16614.08005 -4.05117 (166*2π)/4663 weeks
16713.60509 1.79413 (167*2π)/4663 weeks
16810.7585 1.14818 (168*2π)/4663 weeks
16912.26577 -1.26578 (169*2π)/4663 weeks
17017.45752 1.67897 (170*2π)/4663 weeks
17112.58411 8.40813 (171*2π)/4663 weeks
1724.93334 2.87841 (172*2π)/4663 weeks
1739.32334 -4.75749 (173*2π)/4663 weeks
17415.46191 -2.54893 (174*2π)/4663 weeks
17516.70994 .91723 (175*2π)/4663 weeks
17614.47241 2.4639 (176*2π)/4663 weeks
17714.88518 1.659 (177*2π)/4663 weeks
17816.10531 3.53775 (178*2π)/4663 weeks
17913.39112 6.97489 (179*2π)/4663 weeks
1808.97855 5.30489 (180*2π)/4663 weeks
1818.1272 -.40981 (181*2π)/4663 weeks
18212.61118 -.87936 (182*2π)/4663 weeks
18312.61627 .14824 (183*2π)/4663 weeks
18412.07944 -1.13604 (184*2π)/4663 weeks
18514.28488 -2.38571 (185*2π)/4663 weeks
18617.32098 -1.80372 (186*2π)/4663 weeks
18719.04384 .98639 (187*2π)/4662 weeks
18818.82949 5.47578 (188*2π)/4662 weeks
18913.93467 7.53491 (189*2π)/4662 weeks
19010.35748 4.16929 (190*2π)/4662 weeks
19112.39664 1.13399 (191*2π)/4662 weeks
19213.25191 4.05387 (192*2π)/4662 weeks
1939.38216 2.77844 (193*2π)/4662 weeks
19410.2098 -2.39838 (194*2π)/4662 weeks
19514.30279 -2.45268 (195*2π)/4662 weeks
19616.0171 .55564 (196*2π)/4662 weeks
19714.20116 .71161 (197*2π)/4662 weeks
19814.4688 -.37539 (198*2π)/4662 weeks
19916.05631 .02879 (199*2π)/4662 weeks
20016.31588 1.58553 (200*2π)/4662 weeks
20114.49915 2.99329 (201*2π)/4662 weeks
20212.37279 .15424 (202*2π)/4662 weeks
20317.67786 -1.36798 (203*2π)/4662 weeks
20416.9434 3.88598 (204*2π)/4662 weeks
20512.6962 1.97847 (205*2π)/4662 weeks
20615.99355 -1.07341 (206*2π)/4662 weeks
20718.6472 2.07022 (207*2π)/4662 weeks
20816.33337 5.40668 (208*2π)/4662 weeks
20913.3844 4.55196 (209*2π)/4662 weeks
21013.33391 .4912 (210*2π)/4662 weeks
21116.89238 2.17737 (211*2π)/4662 weeks
21216.5188 4.80602 (212*2π)/4662 weeks
21313.71645 6.13762 (213*2π)/4662 weeks
21411.94337 5.46316 (214*2π)/4662 weeks
21510.07801 3.76306 (215*2π)/4662 weeks
21610.57714 3.21293 (216*2π)/4662 weeks
2177.83838 .89288 (217*2π)/4662 weeks
21810.41423 -4.12562 (218*2π)/4662 weeks
21916.388 -3.0717 (219*2π)/4662 weeks
22017.12901 2.37689 (220*2π)/4662 weeks
22113.93407 4.20097 (221*2π)/4662 weeks
22211.57529 3.91774 (222*2π)/4662 weeks
2237.95062 1.27753 (223*2π)/4662 weeks
2249.6054 -2.0635 (224*2π)/4662 weeks
22511.12934 -3.3451 (225*2π)/4662 weeks
22612.60934 -6.07962 (226*2π)/4662 weeks
22718.22647 -5.35178 (227*2π)/4662 weeks
22821.08776 -.42234 (228*2π)/4662 weeks
22918.35821 3.67402 (229*2π)/4662 weeks
23014.31977 4.51422 (230*2π)/4662 weeks
23113.9948 4.10464 (231*2π)/4662 weeks
23210.62607 4.5278 (232*2π)/4662 weeks
2337.16422   (233*2π)/4662 weeks
23410.62607 -4.5278 (234*2π)/4662 weeks
23513.9948 -4.10464 (235*2π)/4662 weeks
23614.31977 -4.51422 (236*2π)/4662 weeks
23718.35821 -3.67402 (237*2π)/4662 weeks
23821.08776 .42234 (238*2π)/4662 weeks
23918.22647 5.35178 (239*2π)/4662 weeks
24012.60934 6.07962 (240*2π)/4662 weeks
24111.12934 3.3451 (241*2π)/4662 weeks
2429.6054 2.0635 (242*2π)/4662 weeks
2437.95062 -1.27753 (243*2π)/4662 weeks
24411.57529 -3.91774 (244*2π)/4662 weeks
24513.93407 -4.20097 (245*2π)/4662 weeks
24617.12901 -2.37689 (246*2π)/4662 weeks
24716.388 3.0717 (247*2π)/4662 weeks
24810.41423 4.12562 (248*2π)/4662 weeks
2497.83838 -.89288 (249*2π)/4662 weeks
25010.57714 -3.21293 (250*2π)/4662 weeks
25110.07801 -3.76306 (251*2π)/4662 weeks
25211.94337 -5.46316 (252*2π)/4662 weeks
25313.71645 -6.13762 (253*2π)/4662 weeks
25416.5188 -4.80602 (254*2π)/4662 weeks
25516.89238 -2.17737 (255*2π)/4662 weeks
25613.33391 -.4912 (256*2π)/4662 weeks
25713.3844 -4.55196 (257*2π)/4662 weeks
25816.33337 -5.40668 (258*2π)/4662 weeks
25918.6472 -2.07022 (259*2π)/4662 weeks
26015.99355 1.07341 (260*2π)/4662 weeks
26112.6962 -1.97847 (261*2π)/4662 weeks
26216.9434 -3.88598 (262*2π)/4662 weeks
26317.67786 1.36798 (263*2π)/4662 weeks
26412.37279 -.15424 (264*2π)/4662 weeks
26514.49915 -2.99329 (265*2π)/4662 weeks
26616.31588 -1.58553 (266*2π)/4662 weeks
26716.05631 -.02879 (267*2π)/4662 weeks
26814.4688 .37539 (268*2π)/4662 weeks
26914.20116 -.71161 (269*2π)/4662 weeks
27016.0171 -.55564 (270*2π)/4662 weeks
27114.30279 2.45268 (271*2π)/4662 weeks
27210.2098 2.39838 (272*2π)/4662 weeks
2739.38216 -2.77844 (273*2π)/4662 weeks
27413.25191 -4.05387 (274*2π)/4662 weeks
27512.39664 -1.13399 (275*2π)/4662 weeks
27610.35748 -4.16929 (276*2π)/4662 weeks
27713.93467 -7.53491 (277*2π)/4662 weeks
27818.82949 -5.47578 (278*2π)/4662 weeks
27919.04384 -.98639 (279*2π)/4662 weeks
28017.32098 1.80372 (280*2π)/4662 weeks
28114.28488 2.38571 (281*2π)/4662 weeks
28212.07944 1.13604 (282*2π)/4662 weeks
28312.61627 -.14824 (283*2π)/4662 weeks
28412.61118 .87936 (284*2π)/4662 weeks
2858.1272 .40981 (285*2π)/4662 weeks
2868.97855 -5.30489 (286*2π)/4662 weeks
28713.39112 -6.97489 (287*2π)/4662 weeks
28816.10531 -3.53775 (288*2π)/4662 weeks
28914.88518 -1.659 (289*2π)/4662 weeks
29014.47241 -2.4639 (290*2π)/4662 weeks
29116.70994 -.91723 (291*2π)/4662 weeks
29215.46191 2.54893 (292*2π)/4662 weeks
2939.32334 4.75749 (293*2π)/4662 weeks
2944.93334 -2.87841 (294*2π)/4662 weeks
29512.58411 -8.40813 (295*2π)/4662 weeks
29617.45752 -1.67897 (296*2π)/4662 weeks
29712.26577 1.26578 (297*2π)/4662 weeks
29810.7585 -1.14818 (298*2π)/4662 weeks
29913.60509 -1.79413 (299*2π)/4662 weeks
30014.08005 4.05117 (300*2π)/4662 weeks
3014.83692 5.12241 (301*2π)/4662 weeks
3021.98376 -2.71997 (302*2π)/4662 weeks
3036.7914 -6.45685 (303*2π)/4662 weeks
3048.34092 -4.60507 (304*2π)/4662 weeks
3056.66611 -4.72928 (305*2π)/4662 weeks
3067.89824 -8.09497 (306*2π)/4662 weeks
30711.4501 -7.91169 (307*2π)/4662 weeks
30812.58735 -3.71425 (308*2π)/4662 weeks
3099.02458 -3.61432 (309*2π)/4662 weeks
3109.55204 -5.96778 (310*2π)/4662 weeks
31110.48643 -3.74674 (311*2π)/4661 weeks
3128.13996 -4.47921 (312*2π)/4661 weeks
3139.03059 -6.06332 (313*2π)/4661 weeks
3149.66349 -4.82963 (314*2π)/4661 weeks
3157.90226 -4.49525 (315*2π)/4661 weeks
3167.83039 -6.50105 (316*2π)/4661 weeks
3178.44974 -7.04178 (317*2π)/4661 weeks
3188.99828 -6.07317 (318*2π)/4661 weeks
3197.43407 -5.95111 (319*2π)/4661 weeks
3207.28579 -8.55064 (320*2π)/4661 weeks
3217.91741 -7.7475 (321*2π)/4661 weeks
3227.42191 -8.8916 (322*2π)/4661 weeks
3237.96248 -9.64742 (323*2π)/4661 weeks
3248.08916 -10.57577 (324*2π)/4661 weeks
32510.09225 -12.08047 (325*2π)/4661 weeks
32612.11936 -8.65821 (326*2π)/4661 weeks
3278.02878 -7.84803 (327*2π)/4661 weeks
3288.57175 -10.31295 (328*2π)/4661 weeks
3297.70189 -10.86902 (329*2π)/4661 weeks
3307.5676 -14.48871 (330*2π)/4661 weeks
33113.51135 -18.13046 (331*2π)/4661 weeks
33219.85114 -12.14837 (332*2π)/4661 weeks
33316.77416 -6.14574 (333*2π)/4661 weeks
33413.64315 -4.8828 (334*2π)/4661 weeks
33512.40765 -5.98886 (335*2π)/4661 weeks
33612.8054 -4.41826 (336*2π)/4661 weeks
3377.76772 -1.88724 (337*2π)/4661 weeks
3383.31038 -7.59136 (338*2π)/4661 weeks
3397.64131 -12.36698 (339*2π)/4661 weeks
34011.66049 -9.86218 (340*2π)/4661 weeks
3419.63726 -7.79253 (341*2π)/4661 weeks
34210.02553 -8.30406 (342*2π)/4661 weeks
34312.04009 -6.93031 (343*2π)/4661 weeks
3448.57416 -1.42446 (344*2π)/4661 weeks
3451.63424 -.79553 (345*2π)/4661 weeks
346-2.77115 -8.12896 (346*2π)/4661 weeks
3471.35232 -13.3506 (347*2π)/4661 weeks
3481.60682 -10.98067 (348*2π)/4661 weeks
349-1.94235 -13.03525 (349*2π)/4661 weeks
350.40136 -19.13654 (350*2π)/4661 weeks
3516.00668 -20.1563 (351*2π)/4661 weeks
3527.26965 -14.1525 (352*2π)/4661 weeks
3533.58193 -12.88754 (353*2π)/4661 weeks
354-.28468 -16.68835 (354*2π)/4661 weeks
355-.74835 -20.13765 (355*2π)/4661 weeks
3561.11992 -24.55332 (356*2π)/4661 weeks
3574.51868 -27.17347 (357*2π)/4661 weeks
3589.86884 -28.30601 (358*2π)/4661 weeks
35912.77779 -25.60121 (359*2π)/4661 weeks
36013.23898 -22.87574 (360*2π)/4661 weeks
36115.79628 -22.83017 (361*2π)/4661 weeks
36215.44334 -18.83639 (362*2π)/4661 weeks
36314.09045 -17.88841 (363*2π)/4661 weeks
36412.277 -16.02067 (364*2π)/4661 weeks
36512.14611 -18.50655 (365*2π)/4661 weeks
36612.36406 -16.5281 (366*2π)/4661 weeks
3678.58413 -15.25233 (367*2π)/4661 weeks
3687.12067 -17.8297 (368*2π)/4661 weeks
3697.20005 -22.33398 (369*2π)/4661 weeks
37012.29682 -23.25266 (370*2π)/4661 weeks
37113.44028 -18.6202 (371*2π)/4661 weeks
37211.03742 -16.44359 (372*2π)/4661 weeks
3738.78008 -17.79889 (373*2π)/4661 weeks
3746.13566 -17.43867 (374*2π)/4661 weeks
3754.36799 -21.04069 (375*2π)/4661 weeks
3767.75491 -25.12942 (376*2π)/4661 weeks
3778.52207 -22.12717 (377*2π)/4661 weeks
3787.73429 -23.96401 (378*2π)/4661 weeks
3799.38646 -23.31079 (379*2π)/4661 weeks
3808.72401 -22.99483 (380*2π)/4661 weeks
3815.68332 -22.73741 (381*2π)/4661 weeks
3825.4082 -24.81986 (382*2π)/4661 weeks
3835.34171 -26.84396 (383*2π)/4661 weeks
3845.07012 -27.57081 (384*2π)/4661 weeks
3851.52255 -31.19099 (385*2π)/4661 weeks
3866.66564 -38.77967 (386*2π)/4661 weeks
38714.86982 -36.55123 (387*2π)/4661 weeks
38815.4914 -32.44739 (388*2π)/4661 weeks
38915.27746 -31.63194 (389*2π)/4661 weeks
39014.53682 -29.75651 (390*2π)/4661 weeks
39112.89313 -28.55202 (391*2π)/4661 weeks
39212.1432 -30.08244 (392*2π)/4661 weeks
3938.93181 -32.64954 (393*2π)/4661 weeks
39413.21111 -39.46327 (394*2π)/4661 weeks
39523.03825 -35.67143 (395*2π)/4661 weeks
39620.95615 -25.69699 (396*2π)/4661 weeks
39714.72646 -27.21491 (397*2π)/4661 weeks
39817.14482 -28.51468 (398*2π)/4661 weeks
39915.16443 -20.23359 (399*2π)/4661 weeks
400-.29981 -20.26446 (400*2π)/4661 weeks
401-8.56287 -39.26221 (401*2π)/4661 weeks
4026.9906 -52.81974 (402*2π)/4661 weeks
40319.06483 -47.79932 (403*2π)/4661 weeks
40419.28501 -39.42234 (404*2π)/4661 weeks
40516.80996 -42.40347 (405*2π)/4661 weeks
40621.04899 -43.86961 (406*2π)/4661 weeks
40727.65638 -38.63346 (407*2π)/4661 weeks
40821.14105 -27.1741 (408*2π)/4661 weeks
4097.30034 -34.90168 (409*2π)/4661 weeks
41016.39133 -45.75624 (410*2π)/4661 weeks
41119.81361 -40.67945 (411*2π)/4661 weeks
41217.88109 -37.06092 (412*2π)/4661 weeks
41311.55038 -42.10722 (413*2π)/4661 weeks
41418.25768 -48.23459 (414*2π)/4661 weeks
41523.35501 -42.87398 (415*2π)/4661 weeks
41617.57309 -39.03329 (416*2π)/4661 weeks
41713.22648 -43.46281 (417*2π)/4661 weeks
41811.43966 -51.38826 (418*2π)/4661 weeks
41921.23659 -56.10133 (419*2π)/4661 weeks
42027.28309 -53.21457 (420*2π)/4661 weeks
42128.59562 -48.24974 (421*2π)/4661 weeks
42222.70714 -45.84664 (422*2π)/4661 weeks
42322.84992 -49.93443 (423*2π)/4661 weeks
42425.01238 -50.44543 (424*2π)/4661 weeks
42526.85938 -53.66148 (425*2π)/4661 weeks
42630.37264 -44.19316 (426*2π)/4661 weeks
42720.86136 -46.66185 (427*2π)/4661 weeks
42820.95091 -55.5234 (428*2π)/4661 weeks
42931.83442 -52.49846 (429*2π)/4661 weeks
43023.62248 -40.38181 (430*2π)/4661 weeks
4315.60283 -48.01487 (431*2π)/4661 weeks
4328.13464 -70.16482 (432*2π)/4661 weeks
43320.29277 -75.72198 (433*2π)/4661 weeks
43428.77 -77.05001 (434*2π)/4661 weeks
43531.83867 -73.94768 (435*2π)/4661 weeks
43636.95034 -80.30824 (436*2π)/4661 weeks
43750.33089 -75.66179 (437*2π)/4661 weeks
43849.63234 -59.44402 (438*2π)/4661 weeks
43940.71543 -54.93906 (439*2π)/4661 weeks
44035.39812 -64.32086 (440*2π)/4661 weeks
44137.45759 -63.67483 (441*2π)/4661 weeks
44235.24393 -53.83271 (442*2π)/4661 weeks
44314.95696 -57.79464 (443*2π)/4661 weeks
44410.72217 -89.82046 (444*2π)/4661 weeks
44529.08573 -95.06686 (445*2π)/4661 weeks
44627.12365 -91.64365 (446*2π)/4661 weeks
44734.7514 -111.6711 (447*2π)/4661 weeks
44849.54209 -111.2647 (448*2π)/4661 weeks
44957.31326 -106.4968 (449*2π)/4661 weeks
45068.08949 -103.7976 (450*2π)/4661 weeks
45161.71829 -82.23228 (451*2π)/4661 weeks
45227.00017 -94.76174 (452*2π)/4661 weeks
45338.01307 -125.8412 (453*2π)/4661 weeks
45448.75648 -127.2467 (454*2π)/4661 weeks
45535.5132 -140.4255 (455*2π)/4661 weeks
45639.25873 -185.6096 (456*2π)/4661 weeks
45794.74628 -216.9357 (457*2π)/4661 weeks
458144.9774 -172.3444 (458*2π)/4661 weeks
459104.9033 -133.6821 (459*2π)/4661 weeks
46051.94904 -186.4486 (460*2π)/4661 weeks
46166.43179 -260.533 (461*2π)/4661 weeks
462111.3256 -333.3802 (462*2π)/4661 weeks
463173.9769 -417.1543 (463*2π)/4661 weeks
464258.5475 -558.6604 (464*2π)/4661 weeks



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