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Fourier Analysis of GAZ (iPath Bloomberg Natural Gas SubTR ETN)


GAZ (iPath Bloomberg Natural Gas SubTR ETN) appears to have interesting cyclic behaviour every 46 weeks (98.3435*sine), 50 weeks (97.734*sine), and 55 weeks (95.0468*sine).

GAZ (iPath Bloomberg Natural Gas SubTR ETN) has an average price of 82.14 (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 10/25/2007 to 4/16/2018 for GAZ (iPath Bloomberg Natural Gas SubTR ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
082.14438   0 
1153.7103 -4.345 (1*2π)/548548 weeks
2146.2245 -17.41897 (2*2π)/548274 weeks
3139.68 -30.91483 (3*2π)/548183 weeks
4131.2235 -43.26069 (4*2π)/548137 weeks
5122.6379 -55.34349 (5*2π)/548110 weeks
6113.3098 -66.34173 (6*2π)/54891 weeks
7103.0258 -76.07534 (7*2π)/54878 weeks
892.96707 -84.51403 (8*2π)/54869 weeks
982.42382 -90.73865 (9*2π)/54861 weeks
1071.47429 -95.04682 (10*2π)/54855 weeks
1160.59802 -97.73401 (11*2π)/54850 weeks
1249.69753 -98.34349 (12*2π)/54846 weeks
1338.96025 -97.6685 (13*2π)/54842 weeks
1428.95368 -95.34113 (14*2π)/54839 weeks
1519.63233 -91.42596 (15*2π)/54837 weeks
1610.9134 -86.59226 (16*2π)/54834 weeks
173.29477 -80.68786 (17*2π)/54832 weeks
18-3.14308 -74.18627 (18*2π)/54830 weeks
19-8.19655 -66.99762 (19*2π)/54829 weeks
20-12.34712 -59.45229 (20*2π)/54827 weeks
21-15.0756 -52.04206 (21*2π)/54826 weeks
22-16.56258 -44.88657 (22*2π)/54825 weeks
23-16.54479 -38.13017 (23*2π)/54824 weeks
24-15.39414 -31.62087 (24*2π)/54823 weeks
25-13.36806 -25.972 (25*2π)/54822 weeks
26-10.22873 -21.18788 (26*2π)/54821 weeks
27-6.27841 -16.97839 (27*2π)/54820 weeks
28-2.02554 -13.81862 (28*2π)/54820 weeks
292.54253 -11.60776 (29*2π)/54819 weeks
307.21185 -10.6006 (30*2π)/54818 weeks
3111.97009 -10.47892 (31*2π)/54818 weeks
3216.32381 -11.2685 (32*2π)/54817 weeks
3320.26438 -12.98763 (33*2π)/54817 weeks
3423.46395 -15.40619 (34*2π)/54816 weeks
3525.93979 -18.78498 (35*2π)/54816 weeks
3627.8099 -22.64568 (36*2π)/54815 weeks
3728.72864 -26.84338 (37*2π)/54815 weeks
3828.80731 -31.31572 (38*2π)/54814 weeks
3927.94305 -35.76256 (39*2π)/54814 weeks
4026.20753 -40.17861 (40*2π)/54814 weeks
4123.69132 -44.34009 (41*2π)/54813 weeks
4220.50903 -48.01564 (42*2π)/54813 weeks
4316.6736 -50.97736 (43*2π)/54813 weeks
4412.19327 -53.2363 (44*2π)/54812 weeks
457.29404 -54.73118 (45*2π)/54812 weeks
462.14578 -55.3388 (46*2π)/54812 weeks
47-3.26632 -55.11447 (47*2π)/54812 weeks
48-8.53481 -54.006 (48*2π)/54811 weeks
49-13.74833 -51.93563 (49*2π)/54811 weeks
50-18.66647 -49.2526 (50*2π)/54811 weeks
51-23.01597 -45.81723 (51*2π)/54811 weeks
52-26.7714 -41.6985 (52*2π)/54811 weeks
53-29.83137 -37.06426 (53*2π)/54810 weeks
54-32.11064 -32.00333 (54*2π)/54810 weeks
55-33.5159 -26.67459 (55*2π)/54810 weeks
56-34.16055 -21.20252 (56*2π)/54810 weeks
57-33.82304 -15.84872 (57*2π)/54810 weeks
58-32.50948 -10.55191 (58*2π)/5489 weeks
59-30.52142 -5.43832 (59*2π)/5489 weeks
60-27.73271 -.7777 (60*2π)/5489 weeks
61-24.41145 3.37058 (61*2π)/5489 weeks
62-20.54555 6.84309 (62*2π)/5489 weeks
63-16.2156 9.56693 (63*2π)/5489 weeks
64-11.57439 11.51764 (64*2π)/5489 weeks
65-6.78317 12.69772 (65*2π)/5488 weeks
66-2.03746 12.98147 (66*2π)/5488 weeks
672.78637 12.37933 (67*2π)/5488 weeks
687.40928 11.11845 (68*2π)/5488 weeks
6911.58128 9.12351 (69*2π)/5488 weeks
7015.41216 6.46615 (70*2π)/5488 weeks
7118.66691 3.23602 (71*2π)/5488 weeks
7221.36522 -.37326 (72*2π)/5488 weeks
7323.32608 -4.33202 (73*2π)/5488 weeks
7424.62372 -8.61108 (74*2π)/5487 weeks
7525.27844 -12.94362 (75*2π)/5487 weeks
7625.24523 -17.18737 (76*2π)/5487 weeks
7724.46204 -21.30081 (77*2π)/5487 weeks
7823.03188 -25.23002 (78*2π)/5487 weeks
7921.10317 -28.77569 (79*2π)/5487 weeks
8018.59014 -31.92454 (80*2π)/5487 weeks
8115.69471 -34.5867 (81*2π)/5487 weeks
8212.4488 -36.72598 (82*2π)/5487 weeks
838.94393 -38.34874 (83*2π)/5487 weeks
845.35712 -39.40569 (84*2π)/5487 weeks
851.70296 -39.92344 (85*2π)/5486 weeks
86-1.77644 -39.97595 (86*2π)/5486 weeks
87-5.06428 -39.42399 (87*2π)/5486 weeks
88-8.12957 -38.33856 (88*2π)/5486 weeks
89-10.93864 -36.84435 (89*2π)/5486 weeks
90-13.45112 -35.02666 (90*2π)/5486 weeks
91-15.62312 -32.96241 (91*2π)/5486 weeks
92-17.39096 -30.8076 (92*2π)/5486 weeks
93-18.7211 -28.57168 (93*2π)/5486 weeks
94-19.59076 -26.31592 (94*2π)/5486 weeks
95-20.05153 -24.10225 (95*2π)/5486 weeks
96-20.2061 -21.93738 (96*2π)/5486 weeks
97-20.10524 -20.03232 (97*2π)/5486 weeks
98-19.71275 -18.34477 (98*2π)/5486 weeks
99-19.12968 -16.9219 (99*2π)/5486 weeks
100-18.42068 -15.80821 (100*2π)/5485 weeks
101-17.62045 -14.99292 (101*2π)/5485 weeks
102-16.79744 -14.41983 (102*2π)/5485 weeks
103-16.04674 -14.11559 (103*2π)/5485 weeks
104-15.41844 -14.06139 (104*2π)/5485 weeks
105-14.94184 -14.19113 (105*2π)/5485 weeks
106-14.69061 -14.44078 (106*2π)/5485 weeks
107-14.67583 -14.83457 (107*2π)/5485 weeks
108-14.93325 -15.2062 (108*2π)/5485 weeks
109-15.48683 -15.67753 (109*2π)/5485 weeks
110-16.2238 -16.06299 (110*2π)/5485 weeks
111-17.22601 -16.28881 (111*2π)/5485 weeks
112-18.43429 -16.4101 (112*2π)/5485 weeks
113-19.73784 -16.28815 (113*2π)/5485 weeks
114-21.18142 -15.87049 (114*2π)/5485 weeks
115-22.70467 -15.15506 (115*2π)/5485 weeks
116-24.27257 -14.12258 (116*2π)/5485 weeks
117-25.82694 -12.82728 (117*2π)/5485 weeks
118-27.27567 -11.23884 (118*2π)/5485 weeks
119-28.53238 -9.4423 (119*2π)/5485 weeks
120-29.51481 -7.32401 (120*2π)/5485 weeks
121-30.24003 -4.94596 (121*2π)/5485 weeks
122-30.66236 -2.38524 (122*2π)/5484 weeks
123-30.80774 .38773 (123*2π)/5484 weeks
124-30.62838 3.15036 (124*2π)/5484 weeks
125-30.07298 5.93353 (125*2π)/5484 weeks
126-29.12089 8.63782 (126*2π)/5484 weeks
127-27.79701 11.28548 (127*2π)/5484 weeks
128-26.13549 13.75684 (128*2π)/5484 weeks
129-24.16612 16.00567 (129*2π)/5484 weeks
130-21.90563 17.97114 (130*2π)/5484 weeks
131-19.3419 19.64182 (131*2π)/5484 weeks
132-16.5728 21.04852 (132*2π)/5484 weeks
133-13.73503 22.09197 (133*2π)/5484 weeks
134-10.80071 22.74421 (134*2π)/5484 weeks
135-7.80334 23.01914 (135*2π)/5484 weeks
136-4.82445 22.94667 (136*2π)/5484 weeks
137-1.94113 22.54716 (137*2π)/5484 weeks
138.79908 21.82033 (138*2π)/5484 weeks
1393.33088 20.76326 (139*2π)/5484 weeks
1405.6537 19.38006 (140*2π)/5484 weeks
1417.84318 17.77226 (141*2π)/5484 weeks
1429.71999 16.03471 (142*2π)/5484 weeks
14311.32699 14.11658 (143*2π)/5484 weeks
14412.66582 12.10307 (144*2π)/5484 weeks
14513.71697 10.02623 (145*2π)/5484 weeks
14614.51741 7.93187 (146*2π)/5484 weeks
14715.04102 5.84444 (147*2π)/5484 weeks
14815.3883 3.81081 (148*2π)/5484 weeks
14915.51361 1.90015 (149*2π)/5484 weeks
15015.42957 .0845 (150*2π)/5484 weeks
15115.19924 -1.58842 (151*2π)/5484 weeks
15214.75557 -3.15354 (152*2π)/5484 weeks
15314.23924 -4.63027 (153*2π)/5484 weeks
15413.63385 -5.99937 (154*2π)/5484 weeks
15513.01685 -7.27725 (155*2π)/5484 weeks
15612.38557 -8.39711 (156*2π)/5484 weeks
15711.69542 -9.41963 (157*2π)/5483 weeks
15810.9875 -10.38715 (158*2π)/5483 weeks
15910.26004 -11.31994 (159*2π)/5483 weeks
1609.58828 -12.20052 (160*2π)/5483 weeks
1618.88643 -13.03145 (161*2π)/5483 weeks
1628.18372 -13.85553 (162*2π)/5483 weeks
1637.48249 -14.61429 (163*2π)/5483 weeks
1646.69844 -15.36225 (164*2π)/5483 weeks
1655.86638 -16.07458 (165*2π)/5483 weeks
1664.91555 -16.7772 (166*2π)/5483 weeks
1673.88112 -17.51634 (167*2π)/5483 weeks
1682.79401 -18.21902 (168*2π)/5483 weeks
1691.644 -18.86298 (169*2π)/5483 weeks
170.41599 -19.37622 (170*2π)/5483 weeks
171-.94944 -19.76669 (171*2π)/5483 weeks
172-2.42114 -20.02633 (172*2π)/5483 weeks
173-4.00041 -20.14063 (173*2π)/5483 weeks
174-5.65173 -20.13057 (174*2π)/5483 weeks
175-7.29606 -19.90599 (175*2π)/5483 weeks
176-8.98099 -19.48295 (176*2π)/5483 weeks
177-10.61062 -18.80674 (177*2π)/5483 weeks
178-12.22582 -17.88179 (178*2π)/5483 weeks
179-13.76986 -16.78388 (179*2π)/5483 weeks
180-15.14301 -15.45365 (180*2π)/5483 weeks
181-16.3492 -13.92462 (181*2π)/5483 weeks
182-17.32458 -12.20182 (182*2π)/5483 weeks
183-18.07141 -10.31017 (183*2π)/5483 weeks
184-18.54753 -8.328 (184*2π)/5483 weeks
185-18.69708 -6.24299 (185*2π)/5483 weeks
186-18.5514 -4.13186 (186*2π)/5483 weeks
187-18.06622 -2.0494 (187*2π)/5483 weeks
188-17.25615 -.05199 (188*2π)/5483 weeks
189-16.11421 1.82403 (189*2π)/5483 weeks
190-14.66123 3.51721 (190*2π)/5483 weeks
191-12.94184 4.96605 (191*2π)/5483 weeks
192-10.96998 6.15028 (192*2π)/5483 weeks
193-8.79975 6.99077 (193*2π)/5483 weeks
194-6.48138 7.48936 (194*2π)/5483 weeks
195-4.08601 7.62166 (195*2π)/5483 weeks
196-1.68731 7.32937 (196*2π)/5483 weeks
197.6791 6.61276 (197*2π)/5483 weeks
1982.93508 5.50477 (198*2π)/5483 weeks
1994.98002 3.98807 (199*2π)/5483 weeks
2006.83222 2.07287 (200*2π)/5483 weeks
2018.40073 -.13814 (201*2π)/5483 weeks
2029.60326 -2.59889 (202*2π)/5483 weeks
20310.38211 -5.29011 (203*2π)/5483 weeks
20410.70598 -8.16435 (204*2π)/5483 weeks
20510.62138 -11.1074 (205*2π)/5483 weeks
2069.99819 -14.043 (206*2π)/5483 weeks
2078.85555 -16.95074 (207*2π)/5483 weeks
2087.25514 -19.76422 (208*2π)/5483 weeks
2095.25278 -22.40374 (209*2π)/5483 weeks
2102.87373 -24.72336 (210*2π)/5483 weeks
211.11346 -26.63769 (211*2π)/5483 weeks
212-2.9814 -28.16875 (212*2π)/5483 weeks
213-6.36684 -29.22751 (213*2π)/5483 weeks
214-9.92345 -29.83631 (214*2π)/5483 weeks
215-13.56207 -29.90927 (215*2π)/5483 weeks
216-17.26466 -29.47149 (216*2π)/5483 weeks
217-20.86201 -28.48368 (217*2π)/5483 weeks
218-24.37078 -26.95977 (218*2π)/5483 weeks
219-27.66862 -24.97514 (219*2π)/5483 weeks
220-30.67869 -22.50225 (220*2π)/5482 weeks
221-33.36856 -19.63223 (221*2π)/5482 weeks
222-35.65933 -16.42703 (222*2π)/5482 weeks
223-37.4912 -12.93714 (223*2π)/5482 weeks
224-38.79747 -9.23412 (224*2π)/5482 weeks
225-39.63821 -5.34251 (225*2π)/5482 weeks
226-39.9586 -1.4237 (226*2π)/5482 weeks
227-39.73201 2.48801 (227*2π)/5482 weeks
228-39.03693 6.32379 (228*2π)/5482 weeks
229-37.82734 9.96189 (229*2π)/5482 weeks
230-36.14735 13.3846 (230*2π)/5482 weeks
231-34.06068 16.54009 (231*2π)/5482 weeks
232-31.62137 19.36042 (232*2π)/5482 weeks
233-28.88786 21.78303 (233*2π)/5482 weeks
234-25.88495 23.82197 (234*2π)/5482 weeks
235-22.7629 25.44365 (235*2π)/5482 weeks
236-19.53036 26.59368 (236*2π)/5482 weeks
237-16.27386 27.29548 (237*2π)/5482 weeks
238-13.04419 27.55248 (238*2π)/5482 weeks
239-9.88394 27.38853 (239*2π)/5482 weeks
240-6.86845 26.84202 (240*2π)/5482 weeks
241-4.04458 25.95616 (241*2π)/5482 weeks
242-1.44751 24.75584 (242*2π)/5482 weeks
243.89184 23.29224 (243*2π)/5482 weeks
2442.93782 21.65261 (244*2π)/5482 weeks
2454.65702 19.83321 (245*2π)/5482 weeks
2466.09154 17.91292 (246*2π)/5482 weeks
2477.19104 15.95648 (247*2π)/5482 weeks
2487.98641 13.97896 (248*2π)/5482 weeks
2498.48046 12.05372 (249*2π)/5482 weeks
2508.69311 10.15878 (250*2π)/5482 weeks
2518.71261 8.37847 (251*2π)/5482 weeks
2528.50164 6.74636 (252*2π)/5482 weeks
2538.10235 5.2444 (253*2π)/5482 weeks
2547.60991 3.89817 (254*2π)/5482 weeks
2557.00895 2.76557 (255*2π)/5482 weeks
2566.31831 1.80862 (256*2π)/5482 weeks
2575.6037 1.02665 (257*2π)/5482 weeks
2584.86316 .43367 (258*2π)/5482 weeks
2594.09022 -.00495 (259*2π)/5482 weeks
2603.35078 -.35419 (260*2π)/5482 weeks
2612.6895 -.5873 (261*2π)/5482 weeks
2622.06949 -.70834 (262*2π)/5482 weeks
2631.51377 -.73971 (263*2π)/5482 weeks
2641.00612 -.75527 (264*2π)/5482 weeks
265.61111 -.77159 (265*2π)/5482 weeks
266.31719 -.70042 (266*2π)/5482 weeks
267.06556 -.64214 (267*2π)/5482 weeks
268-.08548 -.57563 (268*2π)/5482 weeks
269-.19234 -.47893 (269*2π)/5482 weeks
270-.25636 -.37226 (270*2π)/5482 weeks
271-.30543 -.26869 (271*2π)/5482 weeks
272-.33314 -.17663 (272*2π)/5482 weeks
273-.35381 -.05658 (273*2π)/5482 weeks
274-.40357   (274*2π)/5482 weeks
275-.35381 .05658 (275*2π)/5482 weeks
276-.33314 .17663 (276*2π)/5482 weeks
277-.30543 .26869 (277*2π)/5482 weeks
278-.25636 .37226 (278*2π)/5482 weeks
279-.19234 .47893 (279*2π)/5482 weeks
280-.08548 .57563 (280*2π)/5482 weeks
281.06556 .64214 (281*2π)/5482 weeks
282.31719 .70042 (282*2π)/5482 weeks
283.61111 .77159 (283*2π)/5482 weeks
2841.00612 .75527 (284*2π)/5482 weeks
2851.51377 .73971 (285*2π)/5482 weeks
2862.06949 .70834 (286*2π)/5482 weeks
2872.6895 .5873 (287*2π)/5482 weeks
2883.35078 .35419 (288*2π)/5482 weeks
2894.09022 .00495 (289*2π)/5482 weeks
2904.86316 -.43367 (290*2π)/5482 weeks
2915.6037 -1.02665 (291*2π)/5482 weeks
2926.31831 -1.80862 (292*2π)/5482 weeks
2937.00895 -2.76557 (293*2π)/5482 weeks
2947.60991 -3.89817 (294*2π)/5482 weeks
2958.10235 -5.2444 (295*2π)/5482 weeks
2968.50164 -6.74636 (296*2π)/5482 weeks
2978.71261 -8.37847 (297*2π)/5482 weeks
2988.69311 -10.15878 (298*2π)/5482 weeks
2998.48046 -12.05372 (299*2π)/5482 weeks
3007.98641 -13.97896 (300*2π)/5482 weeks
3017.19104 -15.95648 (301*2π)/5482 weeks
3026.09154 -17.91292 (302*2π)/5482 weeks
3034.65702 -19.83321 (303*2π)/5482 weeks
3042.93782 -21.65261 (304*2π)/5482 weeks
305.89184 -23.29224 (305*2π)/5482 weeks
306-1.44751 -24.75584 (306*2π)/5482 weeks
307-4.04458 -25.95616 (307*2π)/5482 weeks
308-6.86845 -26.84202 (308*2π)/5482 weeks
309-9.88394 -27.38853 (309*2π)/5482 weeks
310-13.04419 -27.55248 (310*2π)/5482 weeks
311-16.27386 -27.29548 (311*2π)/5482 weeks
312-19.53036 -26.59368 (312*2π)/5482 weeks
313-22.7629 -25.44365 (313*2π)/5482 weeks
314-25.88495 -23.82197 (314*2π)/5482 weeks
315-28.88786 -21.78303 (315*2π)/5482 weeks
316-31.62137 -19.36042 (316*2π)/5482 weeks
317-34.06068 -16.54009 (317*2π)/5482 weeks
318-36.14735 -13.3846 (318*2π)/5482 weeks
319-37.82734 -9.96189 (319*2π)/5482 weeks
320-39.03693 -6.32379 (320*2π)/5482 weeks
321-39.73201 -2.48801 (321*2π)/5482 weeks
322-39.9586 1.4237 (322*2π)/5482 weeks
323-39.63821 5.34251 (323*2π)/5482 weeks
324-38.79747 9.23412 (324*2π)/5482 weeks
325-37.4912 12.93714 (325*2π)/5482 weeks
326-35.65933 16.42703 (326*2π)/5482 weeks
327-33.36856 19.63223 (327*2π)/5482 weeks
328-30.67869 22.50225 (328*2π)/5482 weeks
329-27.66862 24.97514 (329*2π)/5482 weeks
330-24.37078 26.95977 (330*2π)/5482 weeks
331-20.86201 28.48368 (331*2π)/5482 weeks
332-17.26466 29.47149 (332*2π)/5482 weeks
333-13.56207 29.90927 (333*2π)/5482 weeks
334-9.92345 29.83631 (334*2π)/5482 weeks
335-6.36684 29.22751 (335*2π)/5482 weeks
336-2.9814 28.16875 (336*2π)/5482 weeks
337.11346 26.63769 (337*2π)/5482 weeks
3382.87373 24.72336 (338*2π)/5482 weeks
3395.25278 22.40374 (339*2π)/5482 weeks
3407.25514 19.76422 (340*2π)/5482 weeks
3418.85555 16.95074 (341*2π)/5482 weeks
3429.99819 14.043 (342*2π)/5482 weeks
34310.62138 11.1074 (343*2π)/5482 weeks
34410.70598 8.16435 (344*2π)/5482 weeks
34510.38211 5.29011 (345*2π)/5482 weeks
3469.60326 2.59889 (346*2π)/5482 weeks
3478.40073 .13814 (347*2π)/5482 weeks
3486.83222 -2.07287 (348*2π)/5482 weeks
3494.98002 -3.98807 (349*2π)/5482 weeks
3502.93508 -5.50477 (350*2π)/5482 weeks
351.6791 -6.61276 (351*2π)/5482 weeks
352-1.68731 -7.32937 (352*2π)/5482 weeks
353-4.08601 -7.62166 (353*2π)/5482 weeks
354-6.48138 -7.48936 (354*2π)/5482 weeks
355-8.79975 -6.99077 (355*2π)/5482 weeks
356-10.96998 -6.15028 (356*2π)/5482 weeks
357-12.94184 -4.96605 (357*2π)/5482 weeks
358-14.66123 -3.51721 (358*2π)/5482 weeks
359-16.11421 -1.82403 (359*2π)/5482 weeks
360-17.25615 .05199 (360*2π)/5482 weeks
361-18.06622 2.0494 (361*2π)/5482 weeks
362-18.5514 4.13186 (362*2π)/5482 weeks
363-18.69708 6.24299 (363*2π)/5482 weeks
364-18.54753 8.328 (364*2π)/5482 weeks
365-18.07141 10.31017 (365*2π)/5482 weeks
366-17.32458 12.20182 (366*2π)/5481 weeks
367-16.3492 13.92462 (367*2π)/5481 weeks
368-15.14301 15.45365 (368*2π)/5481 weeks
369-13.76986 16.78388 (369*2π)/5481 weeks
370-12.22582 17.88179 (370*2π)/5481 weeks
371-10.61062 18.80674 (371*2π)/5481 weeks
372-8.98099 19.48295 (372*2π)/5481 weeks
373-7.29606 19.90599 (373*2π)/5481 weeks
374-5.65173 20.13057 (374*2π)/5481 weeks
375-4.00041 20.14063 (375*2π)/5481 weeks
376-2.42114 20.02633 (376*2π)/5481 weeks
377-.94944 19.76669 (377*2π)/5481 weeks
378.41599 19.37622 (378*2π)/5481 weeks
3791.644 18.86298 (379*2π)/5481 weeks
3802.79401 18.21902 (380*2π)/5481 weeks
3813.88112 17.51634 (381*2π)/5481 weeks
3824.91555 16.7772 (382*2π)/5481 weeks
3835.86638 16.07458 (383*2π)/5481 weeks
3846.69844 15.36225 (384*2π)/5481 weeks
3857.48249 14.61429 (385*2π)/5481 weeks
3868.18372 13.85553 (386*2π)/5481 weeks
3878.88643 13.03145 (387*2π)/5481 weeks
3889.58828 12.20052 (388*2π)/5481 weeks
38910.26004 11.31994 (389*2π)/5481 weeks
39010.9875 10.38715 (390*2π)/5481 weeks
39111.69542 9.41963 (391*2π)/5481 weeks
39212.38557 8.39711 (392*2π)/5481 weeks
39313.01685 7.27725 (393*2π)/5481 weeks
39413.63385 5.99937 (394*2π)/5481 weeks
39514.23924 4.63027 (395*2π)/5481 weeks
39614.75557 3.15354 (396*2π)/5481 weeks
39715.19924 1.58842 (397*2π)/5481 weeks
39815.42957 -.0845 (398*2π)/5481 weeks
39915.51361 -1.90015 (399*2π)/5481 weeks
40015.3883 -3.81081 (400*2π)/5481 weeks
40115.04102 -5.84444 (401*2π)/5481 weeks
40214.51741 -7.93187 (402*2π)/5481 weeks
40313.71697 -10.02623 (403*2π)/5481 weeks
40412.66582 -12.10307 (404*2π)/5481 weeks
40511.32699 -14.11658 (405*2π)/5481 weeks
4069.71999 -16.03471 (406*2π)/5481 weeks
4077.84318 -17.77226 (407*2π)/5481 weeks
4085.6537 -19.38006 (408*2π)/5481 weeks
4093.33088 -20.76326 (409*2π)/5481 weeks
410.79908 -21.82033 (410*2π)/5481 weeks
411-1.94113 -22.54716 (411*2π)/5481 weeks
412-4.82445 -22.94667 (412*2π)/5481 weeks
413-7.80334 -23.01914 (413*2π)/5481 weeks
414-10.80071 -22.74421 (414*2π)/5481 weeks
415-13.73503 -22.09197 (415*2π)/5481 weeks
416-16.5728 -21.04852 (416*2π)/5481 weeks
417-19.3419 -19.64182 (417*2π)/5481 weeks
418-21.90563 -17.97114 (418*2π)/5481 weeks
419-24.16612 -16.00567 (419*2π)/5481 weeks
420-26.13549 -13.75684 (420*2π)/5481 weeks
421-27.79701 -11.28548 (421*2π)/5481 weeks
422-29.12089 -8.63782 (422*2π)/5481 weeks
423-30.07298 -5.93353 (423*2π)/5481 weeks
424-30.62838 -3.15036 (424*2π)/5481 weeks
425-30.80774 -.38773 (425*2π)/5481 weeks
426-30.66236 2.38524 (426*2π)/5481 weeks
427-30.24003 4.94596 (427*2π)/5481 weeks
428-29.51481 7.32401 (428*2π)/5481 weeks
429-28.53238 9.4423 (429*2π)/5481 weeks
430-27.27567 11.23884 (430*2π)/5481 weeks
431-25.82694 12.82728 (431*2π)/5481 weeks
432-24.27257 14.12258 (432*2π)/5481 weeks
433-22.70467 15.15506 (433*2π)/5481 weeks
434-21.18142 15.87049 (434*2π)/5481 weeks
435-19.73784 16.28815 (435*2π)/5481 weeks
436-18.43429 16.4101 (436*2π)/5481 weeks
437-17.22601 16.28881 (437*2π)/5481 weeks
438-16.2238 16.06299 (438*2π)/5481 weeks
439-15.48683 15.67753 (439*2π)/5481 weeks
440-14.93325 15.2062 (440*2π)/5481 weeks
441-14.67583 14.83457 (441*2π)/5481 weeks
442-14.69061 14.44078 (442*2π)/5481 weeks
443-14.94184 14.19113 (443*2π)/5481 weeks
444-15.41844 14.06139 (444*2π)/5481 weeks
445-16.04674 14.11559 (445*2π)/5481 weeks
446-16.79744 14.41983 (446*2π)/5481 weeks
447-17.62045 14.99292 (447*2π)/5481 weeks
448-18.42068 15.80821 (448*2π)/5481 weeks
449-19.12968 16.9219 (449*2π)/5481 weeks
450-19.71275 18.34477 (450*2π)/5481 weeks
451-20.10524 20.03232 (451*2π)/5481 weeks
452-20.2061 21.93738 (452*2π)/5481 weeks
453-20.05153 24.10225 (453*2π)/5481 weeks
454-19.59076 26.31592 (454*2π)/5481 weeks
455-18.7211 28.57168 (455*2π)/5481 weeks
456-17.39096 30.8076 (456*2π)/5481 weeks
457-15.62312 32.96241 (457*2π)/5481 weeks
458-13.45112 35.02666 (458*2π)/5481 weeks
459-10.93864 36.84435 (459*2π)/5481 weeks
460-8.12957 38.33856 (460*2π)/5481 weeks
461-5.06428 39.42399 (461*2π)/5481 weeks
462-1.77644 39.97595 (462*2π)/5481 weeks
4631.70296 39.92344 (463*2π)/5481 weeks
4645.35712 39.40569 (464*2π)/5481 weeks
4658.94393 38.34874 (465*2π)/5481 weeks
46612.4488 36.72598 (466*2π)/5481 weeks
46715.69471 34.5867 (467*2π)/5481 weeks
46818.59014 31.92454 (468*2π)/5481 weeks
46921.10317 28.77569 (469*2π)/5481 weeks
47023.03188 25.23002 (470*2π)/5481 weeks
47124.46204 21.30081 (471*2π)/5481 weeks
47225.24523 17.18737 (472*2π)/5481 weeks
47325.27844 12.94362 (473*2π)/5481 weeks
47424.62372 8.61108 (474*2π)/5481 weeks
47523.32608 4.33202 (475*2π)/5481 weeks
47621.36522 .37326 (476*2π)/5481 weeks
47718.66691 -3.23602 (477*2π)/5481 weeks
47815.41216 -6.46615 (478*2π)/5481 weeks
47911.58128 -9.12351 (479*2π)/5481 weeks
4807.40928 -11.11845 (480*2π)/5481 weeks
4812.78637 -12.37933 (481*2π)/5481 weeks
482-2.03746 -12.98147 (482*2π)/5481 weeks
483-6.78317 -12.69772 (483*2π)/5481 weeks
484-11.57439 -11.51764 (484*2π)/5481 weeks
485-16.2156 -9.56693 (485*2π)/5481 weeks
486-20.54555 -6.84309 (486*2π)/5481 weeks
487-24.41145 -3.37058 (487*2π)/5481 weeks
488-27.73271 .7777 (488*2π)/5481 weeks
489-30.52142 5.43832 (489*2π)/5481 weeks
490-32.50948 10.55191 (490*2π)/5481 weeks
491-33.82304 15.84872 (491*2π)/5481 weeks
492-34.16055 21.20252 (492*2π)/5481 weeks
493-33.5159 26.67459 (493*2π)/5481 weeks
494-32.11064 32.00333 (494*2π)/5481 weeks
495-29.83137 37.06426 (495*2π)/5481 weeks
496-26.7714 41.6985 (496*2π)/5481 weeks
497-23.01597 45.81723 (497*2π)/5481 weeks
498-18.66647 49.2526 (498*2π)/5481 weeks
499-13.74833 51.93563 (499*2π)/5481 weeks
500-8.53481 54.006 (500*2π)/5481 weeks
501-3.26632 55.11447 (501*2π)/5481 weeks
5022.14578 55.3388 (502*2π)/5481 weeks
5037.29404 54.73118 (503*2π)/5481 weeks
50412.19327 53.2363 (504*2π)/5481 weeks
50516.6736 50.97736 (505*2π)/5481 weeks
50620.50903 48.01564 (506*2π)/5481 weeks
50723.69132 44.34009 (507*2π)/5481 weeks
50826.20753 40.17861 (508*2π)/5481 weeks
50927.94305 35.76256 (509*2π)/5481 weeks
51028.80731 31.31572 (510*2π)/5481 weeks
51128.72864 26.84338 (511*2π)/5481 weeks
51227.8099 22.64568 (512*2π)/5481 weeks
51325.93979 18.78498 (513*2π)/5481 weeks
51423.46395 15.40619 (514*2π)/5481 weeks
51520.26438 12.98763 (515*2π)/5481 weeks
51616.32381 11.2685 (516*2π)/5481 weeks
51711.97009 10.47892 (517*2π)/5481 weeks
5187.21185 10.6006 (518*2π)/5481 weeks
5192.54253 11.60776 (519*2π)/5481 weeks
520-2.02554 13.81862 (520*2π)/5481 weeks
521-6.27841 16.97839 (521*2π)/5481 weeks
522-10.22873 21.18788 (522*2π)/5481 weeks
523-13.36806 25.972 (523*2π)/5481 weeks
524-15.39414 31.62087 (524*2π)/5481 weeks
525-16.54479 38.13017 (525*2π)/5481 weeks
526-16.56258 44.88657 (526*2π)/5481 weeks
527-15.0756 52.04206 (527*2π)/5481 weeks
528-12.34712 59.45229 (528*2π)/5481 weeks
529-8.19655 66.99762 (529*2π)/5481 weeks
530-3.14308 74.18627 (530*2π)/5481 weeks
5313.29477 80.68786 (531*2π)/5481 weeks
53210.9134 86.59226 (532*2π)/5481 weeks
53319.63233 91.42596 (533*2π)/5481 weeks
53428.95368 95.34113 (534*2π)/5481 weeks
53538.96025 97.6685 (535*2π)/5481 weeks
53649.69753 98.34349 (536*2π)/5481 weeks
53760.59802 97.73401 (537*2π)/5481 weeks
53871.47429 95.04682 (538*2π)/5481 weeks
53982.42382 90.73865 (539*2π)/5481 weeks
54092.96707 84.51403 (540*2π)/5481 weeks
541103.0258 76.07534 (541*2π)/5481 weeks
542113.3098 66.34173 (542*2π)/5481 weeks
543122.6379 55.34349 (543*2π)/5481 weeks
544131.2235 43.26069 (544*2π)/5481 weeks
545139.68 30.91483 (545*2π)/5481 weeks
546146.2245 17.41897 (546*2π)/5481 weeks



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