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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 40 weeks (37.3207*sine), 36 weeks (37.128*sine), and 30 weeks (20.0788*cosine).

SPXU (ProShares UltraPro Short S&P500) has an average price of 244.74 (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 1/9/2017 for SPXU (ProShares UltraPro Short S&P500), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0244.7379   0 
1174.4515 225.552 (1*2π)/395395 weeks
265.37608 140.9144 (2*2π)/395198 weeks
339.24855 107.5812 (3*2π)/395132 weeks
421.91313 82.85353 (4*2π)/39599 weeks
515.15381 57.15332 (5*2π)/39579 weeks
632.49725 39.11889 (6*2π)/39566 weeks
741.65932 55.73676 (7*2π)/39556 weeks
819.23653 61.50457 (8*2π)/39549 weeks
99.30987 45.23725 (9*2π)/39544 weeks
1013.71301 37.32065 (10*2π)/39540 weeks
1111.25733 37.12803 (11*2π)/39536 weeks
128.99116 25.90102 (12*2π)/39533 weeks
1320.07877 26.18239 (13*2π)/39530 weeks
1417.75566 31.69771 (14*2π)/39528 weeks
1515.72065 32.57452 (15*2π)/39526 weeks
1611.08521 33.09657 (16*2π)/39525 weeks
178.27212 26.82757 (17*2π)/39523 weeks
187.7661 28.05298 (18*2π)/39522 weeks
191.42611 22.16896 (19*2π)/39521 weeks
207.99637 15.69071 (20*2π)/39520 weeks
2111.47163 18.70865 (21*2π)/39519 weeks
2210.59545 18.99584 (22*2π)/39518 weeks
2312.57277 16.33144 (23*2π)/39517 weeks
2415.6876 18.67229 (24*2π)/39516 weeks
2513.01386 23.4431 (25*2π)/39516 weeks
269.30611 22.20787 (26*2π)/39515 weeks
278.84152 22.56323 (27*2π)/39515 weeks
285.86738 22.28068 (28*2π)/39514 weeks
291.51711 19.63655 (29*2π)/39514 weeks
303.59408 12.35377 (30*2π)/39513 weeks
319.23558 13.54265 (31*2π)/39513 weeks
326.97192 16.8175 (32*2π)/39512 weeks
336.05578 13.85954 (33*2π)/39512 weeks
349.27683 13.38431 (34*2π)/39512 weeks
357.31824 15.43246 (35*2π)/39511 weeks
367.15277 14.99515 (36*2π)/39511 weeks
376.52286 14.07576 (37*2π)/39511 weeks
388.38788 13.81533 (38*2π)/39510 weeks
398.02444 15.66164 (39*2π)/39510 weeks
405.77915 16.62945 (40*2π)/39510 weeks
413.36234 13.86703 (41*2π)/39510 weeks
424.37005 11.92852 (42*2π)/3959 weeks
436.6587 11.98197 (43*2π)/3959 weeks
445.60549 14.15305 (44*2π)/3959 weeks
453.4213 12.08351 (45*2π)/3959 weeks
465.66794 11.16473 (46*2π)/3959 weeks
475.82774 12.44701 (47*2π)/3958 weeks
482.34237 12.24387 (48*2π)/3958 weeks
495.26233 7.82763 (49*2π)/3958 weeks
508.14389 11.32816 (50*2π)/3958 weeks
515.89826 12.89934 (51*2π)/3958 weeks
524.74369 12.03733 (52*2π)/3958 weeks
536.2095 12.81506 (53*2π)/3957 weeks
543.44334 15.4233 (54*2π)/3957 weeks
55-2.34029 12.37038 (55*2π)/3957 weeks
56.19919 5.77422 (56*2π)/3957 weeks
575.04852 6.62763 (57*2π)/3957 weeks
584.52187 8.55933 (58*2π)/3957 weeks
595.13697 7.40444 (59*2π)/3957 weeks
607.07502 9.87614 (60*2π)/3957 weeks
614.02721 11.70565 (61*2π)/3956 weeks
622.72856 9.35114 (62*2π)/3956 weeks
633.56004 8.90087 (63*2π)/3956 weeks
644.27727 8.60403 (64*2π)/3956 weeks
654.61712 9.05481 (65*2π)/3956 weeks
664.52611 9.43792 (66*2π)/3956 weeks
674.33078 10.83681 (67*2π)/3956 weeks
681.39201 11.10846 (68*2π)/3956 weeks
69.85846 8.31464 (69*2π)/3956 weeks
701.54629 7.97987 (70*2π)/3956 weeks
711.47828 7.41898 (71*2π)/3956 weeks
721.61783 6.73872 (72*2π)/3955 weeks
732.52492 6.78894 (73*2π)/3955 weeks
742.70934 7.05907 (74*2π)/3955 weeks
752.18392 6.72538 (75*2π)/3955 weeks
762.71667 7.09128 (76*2π)/3955 weeks
771.23053 6.43413 (77*2π)/3955 weeks
781.81607 5.11322 (78*2π)/3955 weeks
792.54574 5.17095 (79*2π)/3955 weeks
803.58489 5.06611 (80*2π)/3955 weeks
814.09394 6.25556 (81*2π)/3955 weeks
822.439 6.83273 (82*2π)/3955 weeks
832.02747 5.30467 (83*2π)/3955 weeks
842.66343 4.39861 (84*2π)/3955 weeks
853.67051 5.00301 (85*2π)/3955 weeks
863.19113 5.23638 (86*2π)/3955 weeks
874.1447 5.11887 (87*2π)/3955 weeks
884.446 5.45923 (88*2π)/3954 weeks
894.65037 6.73776 (89*2π)/3954 weeks
903.98968 6.79697 (90*2π)/3954 weeks
913.53676 7.74563 (91*2π)/3954 weeks
921.87904 8.34935 (92*2π)/3954 weeks
93.55548 7.52056 (93*2π)/3954 weeks
94-.26137 6.09398 (94*2π)/3954 weeks
95-.13204 4.80729 (95*2π)/3954 weeks
961.33128 3.89369 (96*2π)/3954 weeks
972.47556 4.95462 (97*2π)/3954 weeks
98.63182 5.89791 (98*2π)/3954 weeks
99-.72216 4.28118 (99*2π)/3954 weeks
100.42703 3.23078 (100*2π)/3954 weeks
101.06318 3.93138 (101*2π)/3954 weeks
102-.7497 1.63478 (102*2π)/3954 weeks
1031.72848 .21843 (103*2π)/3954 weeks
1043.62143 1.41361 (104*2π)/3954 weeks
1052.98003 2.42427 (105*2π)/3954 weeks
1062.87148 2.27061 (106*2π)/3954 weeks
1073.31384 3.21712 (107*2π)/3954 weeks
1081.55585 3.36833 (108*2π)/3954 weeks
1091.50585 .97572 (109*2π)/3954 weeks
1103.66397 .99095 (110*2π)/3954 weeks
1113.6701 1.74921 (111*2π)/3954 weeks
1124.17695 1.43109 (112*2π)/3954 weeks
1135.37752 2.05022 (113*2π)/3953 weeks
1145.24349 4.73949 (114*2π)/3953 weeks
1152.50608 4.75425 (115*2π)/3953 weeks
1162.18923 3.29571 (116*2π)/3953 weeks
1172.49432 3.03772 (117*2π)/3953 weeks
1182.59413 2.12203 (118*2π)/3953 weeks
1193.57406 3.07949 (119*2π)/3953 weeks
1202.46435 3.31692 (120*2π)/3953 weeks
1212.31719 2.86766 (121*2π)/3953 weeks
1222.1584 2.64185 (122*2π)/3953 weeks
1232.3468 2.28427 (123*2π)/3953 weeks
1241.92037 2.31942 (124*2π)/3953 weeks
1252.41117 1.72884 (125*2π)/3953 weeks
1262.61884 2.07774 (126*2π)/3953 weeks
1272.33683 1.95607 (127*2π)/3953 weeks
1282.31987 1.34244 (128*2π)/3953 weeks
1292.88294 1.52098 (129*2π)/3953 weeks
1302.4723 1.71252 (130*2π)/3953 weeks
1312.69213 1.03452 (131*2π)/3953 weeks
1323.06923 1.72156 (132*2π)/3953 weeks
1332.61622 1.12839 (133*2π)/3953 weeks
1343.78891 1.20787 (134*2π)/3953 weeks
1353.10701 2.43055 (135*2π)/3953 weeks
1361.93806 2.00101 (136*2π)/3953 weeks
1372.36266 1.23187 (137*2π)/3953 weeks
1382.23818 1.79442 (138*2π)/3953 weeks
139.58793 .80686 (139*2π)/3953 weeks
1401.84766 -1.808 (140*2π)/3953 weeks
1414.40819 -.44972 (141*2π)/3953 weeks
1423.44878 .63218 (142*2π)/3953 weeks
1433.35997 -.20404 (143*2π)/3953 weeks
1445.04508 .18927 (144*2π)/3953 weeks
1453.504 2.49298 (145*2π)/3953 weeks
1461.4429 .11614 (146*2π)/3953 weeks
1473.77437 -1.43635 (147*2π)/3953 weeks
1484.84007 -.20643 (148*2π)/3953 weeks
1494.37953 .76222 (149*2π)/3953 weeks
1504.36143 .4804 (150*2π)/3953 weeks
1514.7484 1.18907 (151*2π)/3953 weeks
1523.43352 2.0193 (152*2π)/3953 weeks
1532.17887 .84121 (153*2π)/3953 weeks
1543.43486 -.48519 (154*2π)/3953 weeks
1553.71649 .02654 (155*2π)/3953 weeks
1563.56034 -.36846 (156*2π)/3953 weeks
1574.36638 -.73206 (157*2π)/3953 weeks
1585.37287 -.21398 (158*2π)/3953 weeks
1595.75764 .97755 (159*2π)/3952 weeks
1604.48045 2.23358 (160*2π)/3952 weeks
1613.05305 1.3198 (161*2π)/3952 weeks
1623.78149 .34675 (162*2π)/3952 weeks
1633.51147 1.3019 (163*2π)/3952 weeks
1642.54043 .10745 (164*2π)/3952 weeks
1653.90816 -.81987 (165*2π)/3952 weeks
1664.7765 -.0247 (166*2π)/3952 weeks
1674.17169 .20334 (167*2π)/3952 weeks
1684.35045 -.14746 (168*2π)/3952 weeks
1694.80461 .18527 (169*2π)/3952 weeks
1704.635 .78518 (170*2π)/3952 weeks
1713.68897 .42267 (171*2π)/3952 weeks
1725.07603 -.52851 (172*2π)/3952 weeks
1734.85918 1.20687 (173*2π)/3952 weeks
1743.80739 .1393 (174*2π)/3952 weeks
1755.2486 -.02247 (175*2π)/3952 weeks
1765.23452 1.36043 (176*2π)/3952 weeks
1774.07781 1.40746 (177*2π)/3952 weeks
1783.9117 .14216 (178*2π)/3952 weeks
1794.98307 .78896 (179*2π)/3952 weeks
1804.64215 1.68449 (180*2π)/3952 weeks
1813.72497 1.67046 (181*2π)/3952 weeks
1823.05546 1.34564 (182*2π)/3952 weeks
1833.15432 .89809 (183*2π)/3952 weeks
1842.28545 .13452 (184*2π)/3952 weeks
1853.54482 -1.38354 (185*2π)/3952 weeks
1865.21893 -.2516 (186*2π)/3952 weeks
1874.44919 1.12317 (187*2π)/3952 weeks
1883.51741 1.13126 (188*2π)/3952 weeks
1892.33143 .41629 (189*2π)/3952 weeks
1902.87546 -.70166 (190*2π)/3952 weeks
1913.29363 -1.12759 (191*2π)/3952 weeks
1924.62043 -1.97748 (192*2π)/3952 weeks
1936.084 -.73647 (193*2π)/3952 weeks
1945.4981 .9946 (194*2π)/3952 weeks
1954.16653 1.28365 (195*2π)/3952 weeks
1963.93699 1.32031 (196*2π)/3952 weeks
1972.54194 1.03638 (197*2π)/3952 weeks
1982.54194 -1.03638 (198*2π)/3952 weeks
1993.93699 -1.32031 (199*2π)/3952 weeks
2004.16653 -1.28365 (200*2π)/3952 weeks
2015.4981 -.9946 (201*2π)/3952 weeks
2026.084 .73647 (202*2π)/3952 weeks
2034.62043 1.97748 (203*2π)/3952 weeks
2043.29363 1.12759 (204*2π)/3952 weeks
2052.87546 .70166 (205*2π)/3952 weeks
2062.33143 -.41629 (206*2π)/3952 weeks
2073.51741 -1.13126 (207*2π)/3952 weeks
2084.44919 -1.12317 (208*2π)/3952 weeks
2095.21893 .2516 (209*2π)/3952 weeks
2103.54482 1.38354 (210*2π)/3952 weeks
2112.28545 -.13452 (211*2π)/3952 weeks
2123.15432 -.89809 (212*2π)/3952 weeks
2133.05546 -1.34564 (213*2π)/3952 weeks
2143.72497 -1.67046 (214*2π)/3952 weeks
2154.64215 -1.68449 (215*2π)/3952 weeks
2164.98307 -.78896 (216*2π)/3952 weeks
2173.9117 -.14216 (217*2π)/3952 weeks
2184.07781 -1.40746 (218*2π)/3952 weeks
2195.23452 -1.36043 (219*2π)/3952 weeks
2205.2486 .02247 (220*2π)/3952 weeks
2213.80739 -.1393 (221*2π)/3952 weeks
2224.85918 -1.20687 (222*2π)/3952 weeks
2235.07603 .52851 (223*2π)/3952 weeks
2243.68897 -.42267 (224*2π)/3952 weeks
2254.635 -.78518 (225*2π)/3952 weeks
2264.80461 -.18527 (226*2π)/3952 weeks
2274.35045 .14746 (227*2π)/3952 weeks
2284.17169 -.20334 (228*2π)/3952 weeks
2294.7765 .0247 (229*2π)/3952 weeks
2303.90816 .81987 (230*2π)/3952 weeks
2312.54043 -.10745 (231*2π)/3952 weeks
2323.51147 -1.3019 (232*2π)/3952 weeks
2333.78149 -.34675 (233*2π)/3952 weeks
2343.05305 -1.3198 (234*2π)/3952 weeks
2354.48045 -2.23358 (235*2π)/3952 weeks
2365.75764 -.97755 (236*2π)/3952 weeks
2375.37287 .21398 (237*2π)/3952 weeks
2384.36638 .73206 (238*2π)/3952 weeks
2393.56034 .36846 (239*2π)/3952 weeks
2403.71649 -.02654 (240*2π)/3952 weeks
2413.43486 .48519 (241*2π)/3952 weeks
2422.17887 -.84121 (242*2π)/3952 weeks
2433.43352 -2.0193 (243*2π)/3952 weeks
2444.7484 -1.18907 (244*2π)/3952 weeks
2454.36143 -.4804 (245*2π)/3952 weeks
2464.37953 -.76222 (246*2π)/3952 weeks
2474.84007 .20643 (247*2π)/3952 weeks
2483.77437 1.43635 (248*2π)/3952 weeks
2491.4429 -.11614 (249*2π)/3952 weeks
2503.504 -2.49298 (250*2π)/3952 weeks
2515.04508 -.18927 (251*2π)/3952 weeks
2523.35997 .20404 (252*2π)/3952 weeks
2533.44878 -.63218 (253*2π)/3952 weeks
2544.40819 .44972 (254*2π)/3952 weeks
2551.84766 1.808 (255*2π)/3952 weeks
256.58793 -.80686 (256*2π)/3952 weeks
2572.23818 -1.79442 (257*2π)/3952 weeks
2582.36266 -1.23187 (258*2π)/3952 weeks
2591.93806 -2.00101 (259*2π)/3952 weeks
2603.10701 -2.43055 (260*2π)/3952 weeks
2613.78891 -1.20787 (261*2π)/3952 weeks
2622.61622 -1.12839 (262*2π)/3952 weeks
2633.06923 -1.72156 (263*2π)/3952 weeks
2642.69213 -1.03452 (264*2π)/3951 weeks
2652.4723 -1.71252 (265*2π)/3951 weeks
2662.88294 -1.52098 (266*2π)/3951 weeks
2672.31987 -1.34244 (267*2π)/3951 weeks
2682.33683 -1.95607 (268*2π)/3951 weeks
2692.61884 -2.07774 (269*2π)/3951 weeks
2702.41117 -1.72884 (270*2π)/3951 weeks
2711.92037 -2.31942 (271*2π)/3951 weeks
2722.3468 -2.28427 (272*2π)/3951 weeks
2732.1584 -2.64185 (273*2π)/3951 weeks
2742.31719 -2.86766 (274*2π)/3951 weeks
2752.46435 -3.31692 (275*2π)/3951 weeks
2763.57406 -3.07949 (276*2π)/3951 weeks
2772.59413 -2.12203 (277*2π)/3951 weeks
2782.49432 -3.03772 (278*2π)/3951 weeks
2792.18923 -3.29571 (279*2π)/3951 weeks
2802.50608 -4.75425 (280*2π)/3951 weeks
2815.24349 -4.73949 (281*2π)/3951 weeks
2825.37752 -2.05022 (282*2π)/3951 weeks
2834.17695 -1.43109 (283*2π)/3951 weeks
2843.6701 -1.74921 (284*2π)/3951 weeks
2853.66397 -.99095 (285*2π)/3951 weeks
2861.50585 -.97572 (286*2π)/3951 weeks
2871.55585 -3.36833 (287*2π)/3951 weeks
2883.31384 -3.21712 (288*2π)/3951 weeks
2892.87148 -2.27061 (289*2π)/3951 weeks
2902.98003 -2.42427 (290*2π)/3951 weeks
2913.62143 -1.41361 (291*2π)/3951 weeks
2921.72848 -.21843 (292*2π)/3951 weeks
293-.7497 -1.63478 (293*2π)/3951 weeks
294.06318 -3.93138 (294*2π)/3951 weeks
295.42703 -3.23078 (295*2π)/3951 weeks
296-.72216 -4.28118 (296*2π)/3951 weeks
297.63182 -5.89791 (297*2π)/3951 weeks
2982.47556 -4.95462 (298*2π)/3951 weeks
2991.33128 -3.89369 (299*2π)/3951 weeks
300-.13204 -4.80729 (300*2π)/3951 weeks
301-.26137 -6.09398 (301*2π)/3951 weeks
302.55548 -7.52056 (302*2π)/3951 weeks
3031.87904 -8.34935 (303*2π)/3951 weeks
3043.53676 -7.74563 (304*2π)/3951 weeks
3053.98968 -6.79697 (305*2π)/3951 weeks
3064.65037 -6.73776 (306*2π)/3951 weeks
3074.446 -5.45923 (307*2π)/3951 weeks
3084.1447 -5.11887 (308*2π)/3951 weeks
3093.19113 -5.23638 (309*2π)/3951 weeks
3103.67051 -5.00301 (310*2π)/3951 weeks
3112.66343 -4.39861 (311*2π)/3951 weeks
3122.02747 -5.30467 (312*2π)/3951 weeks
3132.439 -6.83273 (313*2π)/3951 weeks
3144.09394 -6.25556 (314*2π)/3951 weeks
3153.58489 -5.06611 (315*2π)/3951 weeks
3162.54574 -5.17095 (316*2π)/3951 weeks
3171.81607 -5.11322 (317*2π)/3951 weeks
3181.23053 -6.43413 (318*2π)/3951 weeks
3192.71667 -7.09128 (319*2π)/3951 weeks
3202.18392 -6.72538 (320*2π)/3951 weeks
3212.70934 -7.05907 (321*2π)/3951 weeks
3222.52492 -6.78894 (322*2π)/3951 weeks
3231.61783 -6.73872 (323*2π)/3951 weeks
3241.47828 -7.41898 (324*2π)/3951 weeks
3251.54629 -7.97987 (325*2π)/3951 weeks
326.85846 -8.31464 (326*2π)/3951 weeks
3271.39201 -11.10846 (327*2π)/3951 weeks
3284.33078 -10.83681 (328*2π)/3951 weeks
3294.52611 -9.43792 (329*2π)/3951 weeks
3304.61712 -9.05481 (330*2π)/3951 weeks
3314.27727 -8.60403 (331*2π)/3951 weeks
3323.56004 -8.90087 (332*2π)/3951 weeks
3332.72856 -9.35114 (333*2π)/3951 weeks
3344.02721 -11.70565 (334*2π)/3951 weeks
3357.07502 -9.87614 (335*2π)/3951 weeks
3365.13697 -7.40444 (336*2π)/3951 weeks
3374.52187 -8.55933 (337*2π)/3951 weeks
3385.04852 -6.62763 (338*2π)/3951 weeks
339.19919 -5.77422 (339*2π)/3951 weeks
340-2.34029 -12.37038 (340*2π)/3951 weeks
3413.44334 -15.4233 (341*2π)/3951 weeks
3426.2095 -12.81506 (342*2π)/3951 weeks
3434.74369 -12.03733 (343*2π)/3951 weeks
3445.89826 -12.89934 (344*2π)/3951 weeks
3458.14389 -11.32816 (345*2π)/3951 weeks
3465.26233 -7.82763 (346*2π)/3951 weeks
3472.34237 -12.24387 (347*2π)/3951 weeks
3485.82774 -12.44701 (348*2π)/3951 weeks
3495.66794 -11.16473 (349*2π)/3951 weeks
3503.4213 -12.08351 (350*2π)/3951 weeks
3515.60549 -14.15305 (351*2π)/3951 weeks
3526.6587 -11.98197 (352*2π)/3951 weeks
3534.37005 -11.92852 (353*2π)/3951 weeks
3543.36234 -13.86703 (354*2π)/3951 weeks
3555.77915 -16.62945 (355*2π)/3951 weeks
3568.02444 -15.66164 (356*2π)/3951 weeks
3578.38788 -13.81533 (357*2π)/3951 weeks
3586.52286 -14.07576 (358*2π)/3951 weeks
3597.15277 -14.99515 (359*2π)/3951 weeks
3607.31824 -15.43246 (360*2π)/3951 weeks
3619.27683 -13.38431 (361*2π)/3951 weeks
3626.05578 -13.85954 (362*2π)/3951 weeks
3636.97192 -16.8175 (363*2π)/3951 weeks
3649.23558 -13.54265 (364*2π)/3951 weeks
3653.59408 -12.35377 (365*2π)/3951 weeks
3661.51711 -19.63655 (366*2π)/3951 weeks
3675.86738 -22.28068 (367*2π)/3951 weeks
3688.84152 -22.56323 (368*2π)/3951 weeks
3699.30611 -22.20787 (369*2π)/3951 weeks
37013.01386 -23.4431 (370*2π)/3951 weeks
37115.6876 -18.67229 (371*2π)/3951 weeks
37212.57277 -16.33144 (372*2π)/3951 weeks
37310.59545 -18.99584 (373*2π)/3951 weeks
37411.47163 -18.70865 (374*2π)/3951 weeks
3757.99637 -15.69071 (375*2π)/3951 weeks
3761.42611 -22.16896 (376*2π)/3951 weeks
3777.7661 -28.05298 (377*2π)/3951 weeks
3788.27212 -26.82757 (378*2π)/3951 weeks
37911.08521 -33.09657 (379*2π)/3951 weeks
38015.72065 -32.57452 (380*2π)/3951 weeks
38117.75566 -31.69771 (381*2π)/3951 weeks
38220.07877 -26.18239 (382*2π)/3951 weeks
3838.99116 -25.90102 (383*2π)/3951 weeks
38411.25733 -37.12803 (384*2π)/3951 weeks
38513.71301 -37.32065 (385*2π)/3951 weeks
3869.30987 -45.23725 (386*2π)/3951 weeks
38719.23653 -61.50457 (387*2π)/3951 weeks
38841.65932 -55.73676 (388*2π)/3951 weeks
38932.49725 -39.11889 (389*2π)/3951 weeks
39015.15381 -57.15332 (390*2π)/3951 weeks
39121.91313 -82.85353 (391*2π)/3951 weeks
39239.24855 -107.5812 (392*2π)/3951 weeks
39365.37608 -140.9144 (393*2π)/3951 weeks

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