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Fourier Analysis of ZSL (ProShares UltraShort Silver)


ZSL (ProShares UltraShort Silver) appears to have interesting cyclic behaviour every 66 weeks (229.4995*sine), 60 weeks (213.5662*sine), and 66 weeks (92.8188*cosine).

ZSL (ProShares UltraShort Silver) has an average price of 555.09 (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 12/3/2008 to 7/26/2021 for ZSL (ProShares UltraShort Silver), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0555.0886   0 
1725.5251 247.6491 (1*2π)/661661 weeks
2599.2282 419.362 (2*2π)/661331 weeks
3363.1143 465.6748 (3*2π)/661220 weeks
4250.094 414.0303 (4*2π)/661165 weeks
5179.1676 320.1279 (5*2π)/661132 weeks
6166.1845 275.1194 (6*2π)/661110 weeks
7164.4616 239.6867 (7*2π)/66194 weeks
8158.3428 251.7149 (8*2π)/66183 weeks
9134.1338 252.9832 (9*2π)/66173 weeks
1092.81876 229.4995 (10*2π)/66166 weeks
1174.69497 213.5662 (11*2π)/66160 weeks
1249.80127 178.9234 (12*2π)/66155 weeks
1349.15407 156.4559 (13*2π)/66151 weeks
1455.12521 134.2662 (14*2π)/66147 weeks
1554.29233 131.6804 (15*2π)/66144 weeks
1658.54602 120.3843 (16*2π)/66141 weeks
1767.95911 113.7357 (17*2π)/66139 weeks
1864.68552 110.8139 (18*2π)/66137 weeks
1970.36973 97.25777 (19*2π)/66135 weeks
2069.68854 97.83266 (20*2π)/66133 weeks
2179.74918 99.58976 (21*2π)/66131 weeks
2282.28282 108.0085 (22*2π)/66130 weeks
2373.50708 115.1282 (23*2π)/66129 weeks
2459.37411 118.7786 (24*2π)/66128 weeks
2548.67276 113.6784 (25*2π)/66126 weeks
2632.07848 108.2129 (26*2π)/66125 weeks
2730.91302 87.70377 (27*2π)/66124 weeks
2841.20816 74.62867 (28*2π)/66124 weeks
2946.37313 72.99696 (29*2π)/66123 weeks
3056.20572 69.25005 (30*2π)/66122 weeks
3153.75519 76.50101 (31*2π)/66121 weeks
3253.10554 71.65857 (32*2π)/66121 weeks
3352.18516 74.23004 (33*2π)/66120 weeks
3456.45617 69.72485 (34*2π)/66119 weeks
3558.4034 70.6697 (35*2π)/66119 weeks
3662.41035 73.93568 (36*2π)/66118 weeks
3759.49498 75.4865 (37*2π)/66118 weeks
3861.70329 76.10206 (38*2π)/66117 weeks
3959.43134 76.92581 (39*2π)/66117 weeks
4060.46258 81.40941 (40*2π)/66117 weeks
4159.19083 87.22547 (41*2π)/66116 weeks
4255.14043 94.61028 (42*2π)/66116 weeks
4346.18342 97.54489 (43*2π)/66115 weeks
4442.03301 97.51874 (44*2π)/66115 weeks
4533.96887 98.87594 (45*2π)/66115 weeks
4625.08917 98.14218 (46*2π)/66114 weeks
4716.96673 93.44696 (47*2π)/66114 weeks
487.67616 84.01008 (48*2π)/66114 weeks
495.69315 76.33161 (49*2π)/66113 weeks
502.67779 69.05225 (50*2π)/66113 weeks
512.21009 63.63008 (51*2π)/66113 weeks
526.19523 56.1991 (52*2π)/66113 weeks
537.72681 54.52428 (53*2π)/66112 weeks
548.52343 51.34614 (54*2π)/66112 weeks
558.62921 48.90768 (55*2π)/66112 weeks
568.33946 44.52758 (56*2π)/66112 weeks
5710.79543 36.19901 (57*2π)/66112 weeks
5815.84799 34.18229 (58*2π)/66111 weeks
5919.90526 34.01037 (59*2π)/66111 weeks
6022.41525 32.81765 (60*2π)/66111 weeks
6125.69555 34.23914 (61*2π)/66111 weeks
6228.16728 33.81386 (62*2π)/66111 weeks
6330.74074 35.97115 (63*2π)/66110 weeks
6430.58254 37.26687 (64*2π)/66110 weeks
6531.28712 38.55481 (65*2π)/66110 weeks
6634.10112 41.8369 (66*2π)/66110 weeks
6730.46054 42.42367 (67*2π)/66110 weeks
6828.21769 45.22456 (68*2π)/66110 weeks
6929.30209 43.75087 (69*2π)/66110 weeks
7023.80432 43.9603 (70*2π)/6619 weeks
7127.3075 41.95862 (71*2π)/6619 weeks
7224.16012 43.94576 (72*2π)/6619 weeks
7323.87708 43.01987 (73*2π)/6619 weeks
7422.53478 42.03175 (74*2π)/6619 weeks
7521.68471 41.65513 (75*2π)/6619 weeks
7620.25287 40.64794 (76*2π)/6619 weeks
7717.45287 42.16183 (77*2π)/6619 weeks
7814.38766 40.33733 (78*2π)/6618 weeks
7911.33888 38.16282 (79*2π)/6618 weeks
809.5193 32.31139 (80*2π)/6618 weeks
8112.31702 25.8526 (81*2π)/6618 weeks
8214.59565 23.60458 (82*2π)/6618 weeks
8319.39524 19.74944 (83*2π)/6618 weeks
8423.83843 20.30814 (84*2π)/6618 weeks
8525.376 21.32129 (85*2π)/6618 weeks
8627.58217 25.37497 (86*2π)/6618 weeks
8727.90006 25.84789 (87*2π)/6618 weeks
8826.33888 29.89498 (88*2π)/6618 weeks
8924.68171 29.57523 (89*2π)/6617 weeks
9023.06391 30.48231 (90*2π)/6617 weeks
9120.56035 25.53977 (91*2π)/6617 weeks
9221.2247 23.05973 (92*2π)/6617 weeks
9324.46215 18.38546 (93*2π)/6617 weeks
9427.49191 20.21098 (94*2π)/6617 weeks
9530.01939 21.67447 (95*2π)/6617 weeks
9629.29079 24.24837 (96*2π)/6617 weeks
9728.14112 25.08669 (97*2π)/6617 weeks
9829.31828 24.89992 (98*2π)/6617 weeks
9929.14402 26.07387 (99*2π)/6617 weeks
10028.01691 26.95551 (100*2π)/6617 weeks
10126.05359 25.42663 (101*2π)/6617 weeks
10226.30039 22.30456 (102*2π)/6616 weeks
10328.69807 20.73598 (103*2π)/6616 weeks
10429.70544 21.819 (104*2π)/6616 weeks
10532.09141 21.30004 (105*2π)/6616 weeks
10632.55229 22.37647 (106*2π)/6616 weeks
10736.26033 25.00847 (107*2π)/6616 weeks
10837.87782 27.63347 (108*2π)/6616 weeks
10938.61652 32.74748 (109*2π)/6616 weeks
11035.89801 35.59634 (110*2π)/6616 weeks
11132.71134 39.28727 (111*2π)/6616 weeks
11226.06762 39.99551 (112*2π)/6616 weeks
11322.35528 39.35876 (113*2π)/6616 weeks
11417.38432 37.5295 (114*2π)/6616 weeks
11515.1478 33.52719 (115*2π)/6616 weeks
11614.01868 28.9623 (116*2π)/6616 weeks
11715.78551 25.3159 (117*2π)/6616 weeks
11818.33497 23.79042 (118*2π)/6616 weeks
11922.08895 22.85658 (119*2π)/6616 weeks
12021.87719 25.28192 (120*2π)/6616 weeks
12121.91066 26.11404 (121*2π)/6615 weeks
12219.64043 24.43003 (122*2π)/6615 weeks
12318.6546 25.07598 (123*2π)/6615 weeks
12419.0174 22.42473 (124*2π)/6615 weeks
12520.43156 22.67418 (125*2π)/6615 weeks
12621.75472 23.09546 (126*2π)/6615 weeks
12722.40788 23.85673 (127*2π)/6615 weeks
12822.31222 27.00952 (128*2π)/6615 weeks
12919.44548 26.78688 (129*2π)/6615 weeks
13016.7009 26.69872 (130*2π)/6615 weeks
13115.02765 24.76617 (131*2π)/6615 weeks
13212.24594 21.8829 (132*2π)/6615 weeks
13312.89017 17.88906 (133*2π)/6615 weeks
13413.4365 16.84659 (134*2π)/6615 weeks
13516.85141 13.05324 (135*2π)/6615 weeks
13618.32997 14.22452 (136*2π)/6615 weeks
13719.91059 13.91932 (137*2π)/6615 weeks
13821.15046 13.60106 (138*2π)/6615 weeks
13922.68336 13.56455 (139*2π)/6615 weeks
14024.57543 14.15994 (140*2π)/6615 weeks
14125.29731 15.19698 (141*2π)/6615 weeks
14225.45735 17.78164 (142*2π)/6615 weeks
14324.46685 19.01842 (143*2π)/6615 weeks
14423.93597 20.22686 (144*2π)/6615 weeks
14522.51005 20.25593 (145*2π)/6615 weeks
14621.92509 19.46308 (146*2π)/6615 weeks
14720.93907 18.48166 (147*2π)/6614 weeks
14821.3831 18.23858 (148*2π)/6614 weeks
14920.38922 17.03438 (149*2π)/6614 weeks
15021.34143 16.69398 (150*2π)/6614 weeks
15120.54262 16.99394 (151*2π)/6614 weeks
15222.28314 15.73336 (152*2π)/6614 weeks
15322.86011 16.69878 (153*2π)/6614 weeks
15424.27907 16.55009 (154*2π)/6614 weeks
15523.5654 19.11957 (155*2π)/6614 weeks
15623.3594 18.96627 (156*2π)/6614 weeks
15721.42295 20.61038 (157*2π)/6614 weeks
15820.46538 20.68266 (158*2π)/6614 weeks
15918.61832 19.44618 (159*2π)/6614 weeks
16017.45023 18.37475 (160*2π)/6614 weeks
16117.95961 16.9853 (161*2π)/6614 weeks
16218.45891 16.5177 (162*2π)/6614 weeks
16318.33041 17.27702 (163*2π)/6614 weeks
16417.11551 15.7353 (164*2π)/6614 weeks
16517.13359 14.12211 (165*2π)/6614 weeks
16618.41603 12.73178 (166*2π)/6614 weeks
16720.1539 12.88639 (167*2π)/6614 weeks
16820.50489 13.75538 (168*2π)/6614 weeks
16919.60667 14.18798 (169*2π)/6614 weeks
17019.51237 14.39361 (170*2π)/6614 weeks
17120.24109 13.10755 (171*2π)/6614 weeks
17220.24838 14.41929 (172*2π)/6614 weeks
17320.4243 14.2044 (173*2π)/6614 weeks
17420.98548 14.63799 (174*2π)/6614 weeks
17520.76921 14.96496 (175*2π)/6614 weeks
17620.23143 15.50552 (176*2π)/6614 weeks
17719.16252 16.47958 (177*2π)/6614 weeks
17817.41859 16.66709 (178*2π)/6614 weeks
17915.47004 15.70026 (179*2π)/6614 weeks
18014.3158 14.6335 (180*2π)/6614 weeks
18113.22159 12.59243 (181*2π)/6614 weeks
18213.98041 10.0157 (182*2π)/6614 weeks
18314.41872 8.35907 (183*2π)/6614 weeks
18416.81751 5.62169 (184*2π)/6614 weeks
18517.64549 5.83035 (185*2π)/6614 weeks
18620.05403 6.25385 (186*2π)/6614 weeks
18720.20482 7.43053 (187*2π)/6614 weeks
18820.81431 7.91409 (188*2π)/6614 weeks
18920.57529 8.40958 (189*2π)/6613 weeks
19019.82967 7.71661 (190*2π)/6613 weeks
19120.55415 6.40728 (191*2π)/6613 weeks
19221.72481 6.52215 (192*2π)/6613 weeks
19324.51826 6.37041 (193*2π)/6613 weeks
19424.68746 8.47013 (194*2π)/6613 weeks
19524.25299 9.99627 (195*2π)/6613 weeks
19622.76671 10.6589 (196*2π)/6613 weeks
19721.54949 10.66239 (197*2π)/6613 weeks
19821.28124 9.96923 (198*2π)/6613 weeks
19921.93056 10.05057 (199*2π)/6613 weeks
20021.60304 10.03149 (200*2π)/6613 weeks
20121.25061 10.4947 (201*2π)/6613 weeks
20220.63857 10.31863 (202*2π)/6613 weeks
20319.99321 9.25391 (203*2π)/6613 weeks
20418.86705 9.37393 (204*2π)/6613 weeks
20518.11178 7.09772 (205*2π)/6613 weeks
20618.7352 5.57125 (206*2π)/6613 weeks
20720.0498 4.22047 (207*2π)/6613 weeks
20822.61704 3.66406 (208*2π)/6613 weeks
20923.62136 4.33166 (209*2π)/6613 weeks
21024.66312 4.88562 (210*2π)/6613 weeks
21125.11249 4.96049 (211*2π)/6613 weeks
21226.40631 5.44205 (212*2π)/6613 weeks
21326.96927 5.64373 (213*2π)/6613 weeks
21428.33379 6.51476 (214*2π)/6613 weeks
21528.04656 8.76552 (215*2π)/6613 weeks
21628.24444 10.09122 (216*2π)/6613 weeks
21727.28836 13.06965 (217*2π)/6613 weeks
21826.08306 13.00847 (218*2π)/6613 weeks
21923.54518 12.64929 (219*2π)/6613 weeks
22023.84647 11.55098 (220*2π)/6613 weeks
22123.09198 10.41533 (221*2π)/6613 weeks
22223.96098 9.77123 (222*2π)/6613 weeks
22323.65092 10.95006 (223*2π)/6613 weeks
22423.74364 10.86592 (224*2π)/6613 weeks
22524.01323 11.87586 (225*2π)/6613 weeks
22623.25169 12.08099 (226*2π)/6613 weeks
22722.38026 12.83454 (227*2π)/6613 weeks
22821.75845 11.54411 (228*2π)/6613 weeks
22921.01841 11.38654 (229*2π)/6613 weeks
23021.1547 10.5355 (230*2π)/6613 weeks
23121.36109 10.30333 (231*2π)/6613 weeks
23220.88212 9.4815 (232*2π)/6613 weeks
23321.81291 9.32272 (233*2π)/6613 weeks
23422.11504 9.32042 (234*2π)/6613 weeks
23523.28881 10.78158 (235*2π)/6613 weeks
23622.95893 11.91026 (236*2π)/6613 weeks
23721.6074 13.10446 (237*2π)/6613 weeks
23819.7017 12.92143 (238*2π)/6613 weeks
23918.46595 11.89975 (239*2π)/6613 weeks
24017.05978 10.02837 (240*2π)/6613 weeks
24117.18452 8.17497 (241*2π)/6613 weeks
24217.32846 7.0856 (242*2π)/6613 weeks
24318.68648 6.41011 (243*2π)/6613 weeks
24419.45834 6.87113 (244*2π)/6613 weeks
24519.86748 6.03087 (245*2π)/6613 weeks
24620.73755 5.85395 (246*2π)/6613 weeks
24722.04832 5.22321 (247*2π)/6613 weeks
24822.5508 5.66386 (248*2π)/6613 weeks
24924.02402 6.39032 (249*2π)/6613 weeks
25024.3251 7.27258 (250*2π)/6613 weeks
25124.63994 9.39521 (251*2π)/6613 weeks
25223.30869 10.28336 (252*2π)/6613 weeks
25322.18107 11.88843 (253*2π)/6613 weeks
25420.87755 10.96825 (254*2π)/6613 weeks
25519.95039 10.58876 (255*2π)/6613 weeks
25619.88325 9.01484 (256*2π)/6613 weeks
25719.99636 9.30924 (257*2π)/6613 weeks
25819.9976 8.93113 (258*2π)/6613 weeks
25919.89737 9.21987 (259*2π)/6613 weeks
26020.42118 9.37993 (260*2π)/6613 weeks
26119.87774 10.6114 (261*2π)/6613 weeks
26218.41883 11.45201 (262*2π)/6613 weeks
26316.89174 11.38003 (263*2π)/6613 weeks
26414.75111 9.88554 (264*2π)/6613 weeks
26514.47191 6.70772 (265*2π)/6612 weeks
26614.85667 4.62117 (266*2π)/6612 weeks
26716.71286 3.15942 (267*2π)/6612 weeks
26818.11794 2.99794 (268*2π)/6612 weeks
26919.17003 4.17894 (269*2π)/6612 weeks
27018.87099 4.34711 (270*2π)/6612 weeks
27119.12726 4.91929 (271*2π)/6612 weeks
27218.92476 4.46242 (272*2π)/6612 weeks
27319.36286 3.76657 (273*2π)/6612 weeks
27419.44536 3.21053 (274*2π)/6612 weeks
27520.06169 1.5928 (275*2π)/6612 weeks
27621.79215 1.18466 (276*2π)/6612 weeks
27723.27224 1.30847 (277*2π)/6612 weeks
27824.96907 2.6302 (278*2π)/6612 weeks
27926.1797 4.2303 (279*2π)/6612 weeks
28025.91298 6.3216 (280*2π)/6612 weeks
28126.43047 7.45384 (281*2π)/6612 weeks
28226.3711 9.35711 (282*2π)/6612 weeks
28325.26098 10.46665 (283*2π)/6612 weeks
28424.37444 11.50745 (284*2π)/6612 weeks
28522.63034 12.6255 (285*2π)/6612 weeks
28620.45796 12.81755 (286*2π)/6612 weeks
28719.47705 11.95527 (287*2π)/6612 weeks
28818.59151 12.17826 (288*2π)/6612 weeks
28917.92182 12.29204 (289*2π)/6612 weeks
29016.99752 12.6914 (290*2π)/6612 weeks
29114.98774 11.77588 (291*2π)/6612 weeks
29214.23514 9.81917 (292*2π)/6612 weeks
29314.07776 7.99844 (293*2π)/6612 weeks
29415.48501 7.80048 (294*2π)/6612 weeks
29515.5148 7.42348 (295*2π)/6612 weeks
29615.70012 8.63269 (296*2π)/6612 weeks
29714.02745 8.93528 (297*2π)/6612 weeks
29813.39233 8.81875 (298*2π)/6612 weeks
29911.45025 8.31034 (299*2π)/6612 weeks
30010.50167 7.03861 (300*2π)/6612 weeks
3019.95612 4.54556 (301*2π)/6612 weeks
30210.52902 2.73993 (302*2π)/6612 weeks
30310.73205 .65602 (303*2π)/6612 weeks
30412.53709 -.30857 (304*2π)/6612 weeks
30513.10503 -.5699 (305*2π)/6612 weeks
30613.89399 -1.20057 (306*2π)/6612 weeks
30716.03706 -1.44703 (307*2π)/6612 weeks
30816.74124 -1.12839 (308*2π)/6612 weeks
30917.62775 -.11562 (309*2π)/6612 weeks
31018.08185 .28603 (310*2π)/6612 weeks
31118.24608 .57452 (311*2π)/6612 weeks
31219.01292 .63235 (312*2π)/6612 weeks
31319.21527 1.40828 (313*2π)/6612 weeks
31419.19822 2.30806 (314*2π)/6612 weeks
31517.72561 3.0373 (315*2π)/6612 weeks
31616.54109 3.73169 (316*2π)/6612 weeks
31715.09694 2.39832 (317*2π)/6612 weeks
31815.31301 1.15482 (318*2π)/6612 weeks
31916.40343 -.52802 (319*2π)/6612 weeks
32018.07526 -1.07046 (320*2π)/6612 weeks
32120.2177 .35471 (321*2π)/6612 weeks
32220.25599 3.00898 (322*2π)/6612 weeks
32318.45399 4.12587 (323*2π)/6612 weeks
32417.24628 4.63293 (324*2π)/6612 weeks
32515.39053 4.35863 (325*2π)/6612 weeks
32614.75233 3.52987 (326*2π)/6612 weeks
32713.45839 2.73092 (327*2π)/6612 weeks
32813.60118 1.22053 (328*2π)/6612 weeks
32914.10502 -.1793 (329*2π)/6612 weeks
33014.63618 .02245 (330*2π)/6612 weeks
33114.63618 -.02245 (331*2π)/6612 weeks
33214.10502 .1793 (332*2π)/6612 weeks
33313.60118 -1.22053 (333*2π)/6612 weeks
33413.45839 -2.73092 (334*2π)/6612 weeks
33514.75233 -3.52987 (335*2π)/6612 weeks
33615.39053 -4.35863 (336*2π)/6612 weeks
33717.24628 -4.63293 (337*2π)/6612 weeks
33818.45399 -4.12587 (338*2π)/6612 weeks
33920.25599 -3.00898 (339*2π)/6612 weeks
34020.2177 -.35471 (340*2π)/6612 weeks
34118.07526 1.07046 (341*2π)/6612 weeks
34216.40343 .52802 (342*2π)/6612 weeks
34315.31301 -1.15482 (343*2π)/6612 weeks
34415.09694 -2.39832 (344*2π)/6612 weeks
34516.54109 -3.73169 (345*2π)/6612 weeks
34617.72561 -3.0373 (346*2π)/6612 weeks
34719.19822 -2.30806 (347*2π)/6612 weeks
34819.21527 -1.40828 (348*2π)/6612 weeks
34919.01292 -.63235 (349*2π)/6612 weeks
35018.24608 -.57452 (350*2π)/6612 weeks
35118.08185 -.28603 (351*2π)/6612 weeks
35217.62775 .11562 (352*2π)/6612 weeks
35316.74124 1.12839 (353*2π)/6612 weeks
35416.03706 1.44703 (354*2π)/6612 weeks
35513.89399 1.20057 (355*2π)/6612 weeks
35613.10503 .5699 (356*2π)/6612 weeks
35712.53709 .30857 (357*2π)/6612 weeks
35810.73205 -.65602 (358*2π)/6612 weeks
35910.52902 -2.73993 (359*2π)/6612 weeks
3609.95612 -4.54556 (360*2π)/6612 weeks
36110.50167 -7.03861 (361*2π)/6612 weeks
36211.45025 -8.31034 (362*2π)/6612 weeks
36313.39233 -8.81875 (363*2π)/6612 weeks
36414.02745 -8.93528 (364*2π)/6612 weeks
36515.70012 -8.63269 (365*2π)/6612 weeks
36615.5148 -7.42348 (366*2π)/6612 weeks
36715.48501 -7.80048 (367*2π)/6612 weeks
36814.07776 -7.99844 (368*2π)/6612 weeks
36914.23514 -9.81917 (369*2π)/6612 weeks
37014.98774 -11.77588 (370*2π)/6612 weeks
37116.99752 -12.6914 (371*2π)/6612 weeks
37217.92182 -12.29204 (372*2π)/6612 weeks
37318.59151 -12.17826 (373*2π)/6612 weeks
37419.47705 -11.95527 (374*2π)/6612 weeks
37520.45796 -12.81755 (375*2π)/6612 weeks
37622.63034 -12.6255 (376*2π)/6612 weeks
37724.37444 -11.50745 (377*2π)/6612 weeks
37825.26098 -10.46665 (378*2π)/6612 weeks
37926.3711 -9.35711 (379*2π)/6612 weeks
38026.43047 -7.45384 (380*2π)/6612 weeks
38125.91298 -6.3216 (381*2π)/6612 weeks
38226.1797 -4.2303 (382*2π)/6612 weeks
38324.96907 -2.6302 (383*2π)/6612 weeks
38423.27224 -1.30847 (384*2π)/6612 weeks
38521.79215 -1.18466 (385*2π)/6612 weeks
38620.06169 -1.5928 (386*2π)/6612 weeks
38719.44536 -3.21053 (387*2π)/6612 weeks
38819.36286 -3.76657 (388*2π)/6612 weeks
38918.92476 -4.46242 (389*2π)/6612 weeks
39019.12726 -4.91929 (390*2π)/6612 weeks
39118.87099 -4.34711 (391*2π)/6612 weeks
39219.17003 -4.17894 (392*2π)/6612 weeks
39318.11794 -2.99794 (393*2π)/6612 weeks
39416.71286 -3.15942 (394*2π)/6612 weeks
39514.85667 -4.62117 (395*2π)/6612 weeks
39614.47191 -6.70772 (396*2π)/6612 weeks
39714.75111 -9.88554 (397*2π)/6612 weeks
39816.89174 -11.38003 (398*2π)/6612 weeks
39918.41883 -11.45201 (399*2π)/6612 weeks
40019.87774 -10.6114 (400*2π)/6612 weeks
40120.42118 -9.37993 (401*2π)/6612 weeks
40219.89737 -9.21987 (402*2π)/6612 weeks
40319.9976 -8.93113 (403*2π)/6612 weeks
40419.99636 -9.30924 (404*2π)/6612 weeks
40519.88325 -9.01484 (405*2π)/6612 weeks
40619.95039 -10.58876 (406*2π)/6612 weeks
40720.87755 -10.96825 (407*2π)/6612 weeks
40822.18107 -11.88843 (408*2π)/6612 weeks
40923.30869 -10.28336 (409*2π)/6612 weeks
41024.63994 -9.39521 (410*2π)/6612 weeks
41124.3251 -7.27258 (411*2π)/6612 weeks
41224.02402 -6.39032 (412*2π)/6612 weeks
41322.5508 -5.66386 (413*2π)/6612 weeks
41422.04832 -5.22321 (414*2π)/6612 weeks
41520.73755 -5.85395 (415*2π)/6612 weeks
41619.86748 -6.03087 (416*2π)/6612 weeks
41719.45834 -6.87113 (417*2π)/6612 weeks
41818.68648 -6.41011 (418*2π)/6612 weeks
41917.32846 -7.0856 (419*2π)/6612 weeks
42017.18452 -8.17497 (420*2π)/6612 weeks
42117.05978 -10.02837 (421*2π)/6612 weeks
42218.46595 -11.89975 (422*2π)/6612 weeks
42319.7017 -12.92143 (423*2π)/6612 weeks
42421.6074 -13.10446 (424*2π)/6612 weeks
42522.95893 -11.91026 (425*2π)/6612 weeks
42623.28881 -10.78158 (426*2π)/6612 weeks
42722.11504 -9.32042 (427*2π)/6612 weeks
42821.81291 -9.32272 (428*2π)/6612 weeks
42920.88212 -9.4815 (429*2π)/6612 weeks
43021.36109 -10.30333 (430*2π)/6612 weeks
43121.1547 -10.5355 (431*2π)/6612 weeks
43221.01841 -11.38654 (432*2π)/6612 weeks
43321.75845 -11.54411 (433*2π)/6612 weeks
43422.38026 -12.83454 (434*2π)/6612 weeks
43523.25169 -12.08099 (435*2π)/6612 weeks
43624.01323 -11.87586 (436*2π)/6612 weeks
43723.74364 -10.86592 (437*2π)/6612 weeks
43823.65092 -10.95006 (438*2π)/6612 weeks
43923.96098 -9.77123 (439*2π)/6612 weeks
44023.09198 -10.41533 (440*2π)/6612 weeks
44123.84647 -11.55098 (441*2π)/6611 weeks
44223.54518 -12.64929 (442*2π)/6611 weeks
44326.08306 -13.00847 (443*2π)/6611 weeks
44427.28836 -13.06965 (444*2π)/6611 weeks
44528.24444 -10.09122 (445*2π)/6611 weeks
44628.04656 -8.76552 (446*2π)/6611 weeks
44728.33379 -6.51476 (447*2π)/6611 weeks
44826.96927 -5.64373 (448*2π)/6611 weeks
44926.40631 -5.44205 (449*2π)/6611 weeks
45025.11249 -4.96049 (450*2π)/6611 weeks
45124.66312 -4.88562 (451*2π)/6611 weeks
45223.62136 -4.33166 (452*2π)/6611 weeks
45322.61704 -3.66406 (453*2π)/6611 weeks
45420.0498 -4.22047 (454*2π)/6611 weeks
45518.7352 -5.57125 (455*2π)/6611 weeks
45618.11178 -7.09772 (456*2π)/6611 weeks
45718.86705 -9.37393 (457*2π)/6611 weeks
45819.99321 -9.25391 (458*2π)/6611 weeks
45920.63857 -10.31863 (459*2π)/6611 weeks
46021.25061 -10.4947 (460*2π)/6611 weeks
46121.60304 -10.03149 (461*2π)/6611 weeks
46221.93056 -10.05057 (462*2π)/6611 weeks
46321.28124 -9.96923 (463*2π)/6611 weeks
46421.54949 -10.66239 (464*2π)/6611 weeks
46522.76671 -10.6589 (465*2π)/6611 weeks
46624.25299 -9.99627 (466*2π)/6611 weeks
46724.68746 -8.47013 (467*2π)/6611 weeks
46824.51826 -6.37041 (468*2π)/6611 weeks
46921.72481 -6.52215 (469*2π)/6611 weeks
47020.55415 -6.40728 (470*2π)/6611 weeks
47119.82967 -7.71661 (471*2π)/6611 weeks
47220.57529 -8.40958 (472*2π)/6611 weeks
47320.81431 -7.91409 (473*2π)/6611 weeks
47420.20482 -7.43053 (474*2π)/6611 weeks
47520.05403 -6.25385 (475*2π)/6611 weeks
47617.64549 -5.83035 (476*2π)/6611 weeks
47716.81751 -5.62169 (477*2π)/6611 weeks
47814.41872 -8.35907 (478*2π)/6611 weeks
47913.98041 -10.0157 (479*2π)/6611 weeks
48013.22159 -12.59243 (480*2π)/6611 weeks
48114.3158 -14.6335 (481*2π)/6611 weeks
48215.47004 -15.70026 (482*2π)/6611 weeks
48317.41859 -16.66709 (483*2π)/6611 weeks
48419.16252 -16.47958 (484*2π)/6611 weeks
48520.23143 -15.50552 (485*2π)/6611 weeks
48620.76921 -14.96496 (486*2π)/6611 weeks
48720.98548 -14.63799 (487*2π)/6611 weeks
48820.4243 -14.2044 (488*2π)/6611 weeks
48920.24838 -14.41929 (489*2π)/6611 weeks
49020.24109 -13.10755 (490*2π)/6611 weeks
49119.51237 -14.39361 (491*2π)/6611 weeks
49219.60667 -14.18798 (492*2π)/6611 weeks
49320.50489 -13.75538 (493*2π)/6611 weeks
49420.1539 -12.88639 (494*2π)/6611 weeks
49518.41603 -12.73178 (495*2π)/6611 weeks
49617.13359 -14.12211 (496*2π)/6611 weeks
49717.11551 -15.7353 (497*2π)/6611 weeks
49818.33041 -17.27702 (498*2π)/6611 weeks
49918.45891 -16.5177 (499*2π)/6611 weeks
50017.95961 -16.9853 (500*2π)/6611 weeks
50117.45023 -18.37475 (501*2π)/6611 weeks
50218.61832 -19.44618 (502*2π)/6611 weeks
50320.46538 -20.68266 (503*2π)/6611 weeks
50421.42295 -20.61038 (504*2π)/6611 weeks
50523.3594 -18.96627 (505*2π)/6611 weeks
50623.5654 -19.11957 (506*2π)/6611 weeks
50724.27907 -16.55009 (507*2π)/6611 weeks
50822.86011 -16.69878 (508*2π)/6611 weeks
50922.28314 -15.73336 (509*2π)/6611 weeks
51020.54262 -16.99394 (510*2π)/6611 weeks
51121.34143 -16.69398 (511*2π)/6611 weeks
51220.38922 -17.03438 (512*2π)/6611 weeks
51321.3831 -18.23858 (513*2π)/6611 weeks
51420.93907 -18.48166 (514*2π)/6611 weeks
51521.92509 -19.46308 (515*2π)/6611 weeks
51622.51005 -20.25593 (516*2π)/6611 weeks
51723.93597 -20.22686 (517*2π)/6611 weeks
51824.46685 -19.01842 (518*2π)/6611 weeks
51925.45735 -17.78164 (519*2π)/6611 weeks
52025.29731 -15.19698 (520*2π)/6611 weeks
52124.57543 -14.15994 (521*2π)/6611 weeks
52222.68336 -13.56455 (522*2π)/6611 weeks
52321.15046 -13.60106 (523*2π)/6611 weeks
52419.91059 -13.91932 (524*2π)/6611 weeks
52518.32997 -14.22452 (525*2π)/6611 weeks
52616.85141 -13.05324 (526*2π)/6611 weeks
52713.4365 -16.84659 (527*2π)/6611 weeks
52812.89017 -17.88906 (528*2π)/6611 weeks
52912.24594 -21.8829 (529*2π)/6611 weeks
53015.02765 -24.76617 (530*2π)/6611 weeks
53116.7009 -26.69872 (531*2π)/6611 weeks
53219.44548 -26.78688 (532*2π)/6611 weeks
53322.31222 -27.00952 (533*2π)/6611 weeks
53422.40788 -23.85673 (534*2π)/6611 weeks
53521.75472 -23.09546 (535*2π)/6611 weeks
53620.43156 -22.67418 (536*2π)/6611 weeks
53719.0174 -22.42473 (537*2π)/6611 weeks
53818.6546 -25.07598 (538*2π)/6611 weeks
53919.64043 -24.43003 (539*2π)/6611 weeks
54021.91066 -26.11404 (540*2π)/6611 weeks
54121.87719 -25.28192 (541*2π)/6611 weeks
54222.08895 -22.85658 (542*2π)/6611 weeks
54318.33497 -23.79042 (543*2π)/6611 weeks
54415.78551 -25.3159 (544*2π)/6611 weeks
54514.01868 -28.9623 (545*2π)/6611 weeks
54615.1478 -33.52719 (546*2π)/6611 weeks
54717.38432 -37.5295 (547*2π)/6611 weeks
54822.35528 -39.35876 (548*2π)/6611 weeks
54926.06762 -39.99551 (549*2π)/6611 weeks
55032.71134 -39.28727 (550*2π)/6611 weeks
55135.89801 -35.59634 (551*2π)/6611 weeks
55238.61652 -32.74748 (552*2π)/6611 weeks
55337.87782 -27.63347 (553*2π)/6611 weeks
55436.26033 -25.00847 (554*2π)/6611 weeks
55532.55229 -22.37647 (555*2π)/6611 weeks
55632.09141 -21.30004 (556*2π)/6611 weeks
55729.70544 -21.819 (557*2π)/6611 weeks
55828.69807 -20.73598 (558*2π)/6611 weeks
55926.30039 -22.30456 (559*2π)/6611 weeks
56026.05359 -25.42663 (560*2π)/6611 weeks
56128.01691 -26.95551 (561*2π)/6611 weeks
56229.14402 -26.07387 (562*2π)/6611 weeks
56329.31828 -24.89992 (563*2π)/6611 weeks
56428.14112 -25.08669 (564*2π)/6611 weeks
56529.29079 -24.24837 (565*2π)/6611 weeks
56630.01939 -21.67447 (566*2π)/6611 weeks
56727.49191 -20.21098 (567*2π)/6611 weeks
56824.46215 -18.38546 (568*2π)/6611 weeks
56921.2247 -23.05973 (569*2π)/6611 weeks
57020.56035 -25.53977 (570*2π)/6611 weeks
57123.06391 -30.48231 (571*2π)/6611 weeks
57224.68171 -29.57523 (572*2π)/6611 weeks
57326.33888 -29.89498 (573*2π)/6611 weeks
57427.90006 -25.84789 (574*2π)/6611 weeks
57527.58217 -25.37497 (575*2π)/6611 weeks
57625.376 -21.32129 (576*2π)/6611 weeks
57723.83843 -20.30814 (577*2π)/6611 weeks
57819.39524 -19.74944 (578*2π)/6611 weeks
57914.59565 -23.60458 (579*2π)/6611 weeks
58012.31702 -25.8526 (580*2π)/6611 weeks
5819.5193 -32.31139 (581*2π)/6611 weeks
58211.33888 -38.16282 (582*2π)/6611 weeks
58314.38766 -40.33733 (583*2π)/6611 weeks
58417.45287 -42.16183 (584*2π)/6611 weeks
58520.25287 -40.64794 (585*2π)/6611 weeks
58621.68471 -41.65513 (586*2π)/6611 weeks
58722.53478 -42.03175 (587*2π)/6611 weeks
58823.87708 -43.01987 (588*2π)/6611 weeks
58924.16012 -43.94576 (589*2π)/6611 weeks
59027.3075 -41.95862 (590*2π)/6611 weeks
59123.80432 -43.9603 (591*2π)/6611 weeks
59229.30209 -43.75087 (592*2π)/6611 weeks
59328.21769 -45.22456 (593*2π)/6611 weeks
59430.46054 -42.42367 (594*2π)/6611 weeks
59534.10112 -41.8369 (595*2π)/6611 weeks
59631.28712 -38.55481 (596*2π)/6611 weeks
59730.58254 -37.26687 (597*2π)/6611 weeks
59830.74074 -35.97115 (598*2π)/6611 weeks
59928.16728 -33.81386 (599*2π)/6611 weeks
60025.69555 -34.23914 (600*2π)/6611 weeks
60122.41525 -32.81765 (601*2π)/6611 weeks
60219.90526 -34.01037 (602*2π)/6611 weeks
60315.84799 -34.18229 (603*2π)/6611 weeks
60410.79543 -36.19901 (604*2π)/6611 weeks
6058.33946 -44.52758 (605*2π)/6611 weeks
6068.62921 -48.90768 (606*2π)/6611 weeks
6078.52343 -51.34614 (607*2π)/6611 weeks
6087.72681 -54.52428 (608*2π)/6611 weeks
6096.19523 -56.1991 (609*2π)/6611 weeks
6102.21009 -63.63008 (610*2π)/6611 weeks
6112.67779 -69.05225 (611*2π)/6611 weeks
6125.69315 -76.33161 (612*2π)/6611 weeks
6137.67616 -84.01008 (613*2π)/6611 weeks
61416.96673 -93.44696 (614*2π)/6611 weeks
61525.08917 -98.14218 (615*2π)/6611 weeks
61633.96887 -98.87594 (616*2π)/6611 weeks
61742.03301 -97.51874 (617*2π)/6611 weeks
61846.18342 -97.54489 (618*2π)/6611 weeks
61955.14043 -94.61028 (619*2π)/6611 weeks
62059.19083 -87.22547 (620*2π)/6611 weeks
62160.46258 -81.40941 (621*2π)/6611 weeks
62259.43134 -76.92581 (622*2π)/6611 weeks
62361.70329 -76.10206 (623*2π)/6611 weeks
62459.49498 -75.4865 (624*2π)/6611 weeks
62562.41035 -73.93568 (625*2π)/6611 weeks
62658.4034 -70.6697 (626*2π)/6611 weeks
62756.45617 -69.72485 (627*2π)/6611 weeks
62852.18516 -74.23004 (628*2π)/6611 weeks
62953.10554 -71.65857 (629*2π)/6611 weeks
63053.75519 -76.50101 (630*2π)/6611 weeks
63156.20572 -69.25005 (631*2π)/6611 weeks
63246.37313 -72.99696 (632*2π)/6611 weeks
63341.20816 -74.62867 (633*2π)/6611 weeks
63430.91302 -87.70377 (634*2π)/6611 weeks
63532.07848 -108.2129 (635*2π)/6611 weeks
63648.67276 -113.6784 (636*2π)/6611 weeks
63759.37411 -118.7786 (637*2π)/6611 weeks
63873.50708 -115.1282 (638*2π)/6611 weeks
63982.28282 -108.0085 (639*2π)/6611 weeks
64079.74918 -99.58976 (640*2π)/6611 weeks
64169.68854 -97.83266 (641*2π)/6611 weeks
64270.36973 -97.25777 (642*2π)/6611 weeks
64364.68552 -110.8139 (643*2π)/6611 weeks
64467.95911 -113.7357 (644*2π)/6611 weeks
64558.54602 -120.3843 (645*2π)/6611 weeks
64654.29233 -131.6804 (646*2π)/6611 weeks
64755.12521 -134.2662 (647*2π)/6611 weeks
64849.15407 -156.4559 (648*2π)/6611 weeks
64949.80127 -178.9234 (649*2π)/6611 weeks
65074.69497 -213.5662 (650*2π)/6611 weeks
65192.81876 -229.4995 (651*2π)/6611 weeks
652134.1338 -252.9832 (652*2π)/6611 weeks
653158.3428 -251.7149 (653*2π)/6611 weeks
654164.4616 -239.6867 (654*2π)/6611 weeks
655166.1845 -275.1194 (655*2π)/6611 weeks
656179.1676 -320.1279 (656*2π)/6611 weeks
657250.094 -414.0303 (657*2π)/6611 weeks
658363.1143 -465.6748 (658*2π)/6611 weeks
659599.2282 -419.362 (659*2π)/6611 weeks



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