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Fourier Analysis of GAZ (iPath Dow Jones-UBS Natural Gas Subindex Total ReturnSM ETN)


GAZ (iPath Dow Jones-UBS Natural Gas Subindex Total ReturnSM ETN) appears to have interesting cyclic behaviour every 38 weeks (22.3023*cosine), 36 weeks (22.2854*cosine), and 33 weeks (22.2415*cosine).

GAZ (iPath Dow Jones-UBS Natural Gas Subindex Total ReturnSM ETN) has an average price of 21.83 (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 1/16/2018 for GAZ (iPath Dow Jones-UBS Natural Gas Subindex Total ReturnSM ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
021.82882   0 
133.53753 8.74824 (1*2π)/535535 weeks
228.44688 8.26262 (2*2π)/535268 weeks
326.10123 6.96902 (3*2π)/535178 weeks
423.27463 5.79618 (4*2π)/535134 weeks
521.78553 4.13177 (5*2π)/535107 weeks
620.85485 2.42622 (6*2π)/53589 weeks
720.03615 .50127 (7*2π)/53576 weeks
820.38271 -1.24584 (8*2π)/53567 weeks
920.75447 -2.41868 (9*2π)/53559 weeks
1021.01097 -3.32451 (10*2π)/53554 weeks
1121.5622 -4.04017 (11*2π)/53549 weeks
1221.74943 -4.3751 (12*2π)/53545 weeks
1322.01287 -4.9423 (13*2π)/53541 weeks
1422.30228 -5.2358 (14*2π)/53538 weeks
1522.28536 -5.2249 (15*2π)/53536 weeks
1622.24146 -5.48966 (16*2π)/53533 weeks
1722.01944 -5.72063 (17*2π)/53531 weeks
1821.9065 -6.02789 (18*2π)/53530 weeks
1921.69195 -6.04845 (19*2π)/53528 weeks
2021.20058 -6.40561 (20*2π)/53527 weeks
2120.75368 -6.82108 (21*2π)/53525 weeks
2220.42726 -7.48378 (22*2π)/53524 weeks
2320.33861 -7.97606 (23*2π)/53523 weeks
2420.01629 -8.42648 (24*2π)/53522 weeks
2519.86304 -9.08857 (25*2π)/53521 weeks
2619.99349 -9.56448 (26*2π)/53521 weeks
2719.85996 -9.85078 (27*2π)/53520 weeks
2819.77615 -10.14589 (28*2π)/53519 weeks
2919.56034 -10.50848 (29*2π)/53518 weeks
3019.54278 -10.8439 (30*2π)/53518 weeks
3119.38996 -11.00382 (31*2π)/53517 weeks
3219.18169 -11.20838 (32*2π)/53517 weeks
3318.86554 -11.27789 (33*2π)/53516 weeks
3418.39001 -11.6139 (34*2π)/53516 weeks
3518.12453 -11.973 (35*2π)/53515 weeks
3617.77372 -12.25347 (36*2π)/53515 weeks
3717.45328 -12.62389 (37*2π)/53514 weeks
3817.11703 -12.92517 (38*2π)/53514 weeks
3916.77881 -13.33377 (39*2π)/53514 weeks
4016.50505 -13.78079 (40*2π)/53513 weeks
4116.34229 -14.18167 (41*2π)/53513 weeks
4216.19848 -14.43103 (42*2π)/53513 weeks
4315.95884 -14.65974 (43*2π)/53512 weeks
4415.71982 -14.8917 (44*2π)/53512 weeks
4515.49869 -15.04995 (45*2π)/53512 weeks
4615.14447 -15.27667 (46*2π)/53512 weeks
4714.89438 -15.45384 (47*2π)/53511 weeks
4814.46373 -15.55879 (48*2π)/53511 weeks
4914.057 -15.85975 (49*2π)/53511 weeks
5013.72662 -16.12574 (50*2π)/53511 weeks
5113.38224 -16.36065 (51*2π)/53510 weeks
5213.0535 -16.6092 (52*2π)/53510 weeks
5312.71671 -16.84788 (53*2π)/53510 weeks
5412.42134 -17.03709 (54*2π)/53510 weeks
5512.03306 -17.31213 (55*2π)/53510 weeks
5611.7999 -17.60832 (56*2π)/53510 weeks
5711.62737 -17.71741 (57*2π)/5359 weeks
5811.31537 -17.84649 (58*2π)/5359 weeks
5911.0204 -17.86974 (59*2π)/5359 weeks
6010.64111 -17.94977 (60*2π)/5359 weeks
6110.24464 -18.06413 (61*2π)/5359 weeks
629.86309 -18.16569 (62*2π)/5359 weeks
639.4863 -18.24394 (63*2π)/5358 weeks
649.02243 -18.31711 (64*2π)/5358 weeks
658.59248 -18.56193 (65*2π)/5358 weeks
668.27963 -18.6988 (66*2π)/5358 weeks
677.88045 -18.75455 (67*2π)/5358 weeks
687.51444 -18.91929 (68*2π)/5358 weeks
697.12572 -19.02301 (69*2π)/5358 weeks
706.81459 -19.12025 (70*2π)/5358 weeks
716.42607 -19.1732 (71*2π)/5358 weeks
726.01871 -19.31655 (72*2π)/5357 weeks
735.71254 -19.43204 (73*2π)/5357 weeks
745.43542 -19.47738 (74*2π)/5357 weeks
755.0805 -19.48287 (75*2π)/5357 weeks
764.70109 -19.52663 (76*2π)/5357 weeks
774.41002 -19.5425 (77*2π)/5357 weeks
784.0271 -19.53172 (78*2π)/5357 weeks
793.681 -19.51832 (79*2π)/5357 weeks
803.30316 -19.4942 (80*2π)/5357 weeks
812.88757 -19.49913 (81*2π)/5357 weeks
822.51707 -19.50499 (82*2π)/5357 weeks
832.10387 -19.53016 (83*2π)/5356 weeks
841.80823 -19.62594 (84*2π)/5356 weeks
851.54955 -19.61472 (85*2π)/5356 weeks
861.27509 -19.51622 (86*2π)/5356 weeks
87.96269 -19.39636 (87*2π)/5356 weeks
88.60248 -19.279 (88*2π)/5356 weeks
89.18921 -19.16856 (89*2π)/5356 weeks
90-.20178 -19.13074 (90*2π)/5356 weeks
91-.56892 -19.10503 (91*2π)/5356 weeks
92-.88656 -19.04935 (92*2π)/5356 weeks
93-1.16702 -18.95356 (93*2π)/5356 weeks
94-1.53053 -18.80166 (94*2π)/5356 weeks
95-1.8862 -18.73068 (95*2π)/5356 weeks
96-2.22769 -18.63442 (96*2π)/5356 weeks
97-2.5712 -18.5348 (97*2π)/5356 weeks
98-2.89276 -18.45714 (98*2π)/5355 weeks
99-3.17091 -18.37266 (99*2π)/5355 weeks
100-3.46057 -18.24358 (100*2π)/5355 weeks
101-3.75216 -18.10353 (101*2π)/5355 weeks
102-4.02284 -17.96218 (102*2π)/5355 weeks
103-4.28493 -17.78631 (103*2π)/5355 weeks
104-4.59382 -17.60783 (104*2π)/5355 weeks
105-4.85858 -17.40679 (105*2π)/5355 weeks
106-5.23153 -17.21812 (106*2π)/5355 weeks
107-5.52077 -17.08349 (107*2π)/5355 weeks
108-5.79797 -16.89339 (108*2π)/5355 weeks
109-6.11975 -16.74096 (109*2π)/5355 weeks
110-6.35948 -16.6098 (110*2π)/5355 weeks
111-6.58903 -16.413 (111*2π)/5355 weeks
112-6.82724 -16.19858 (112*2π)/5355 weeks
113-7.08315 -15.95986 (113*2π)/5355 weeks
114-7.38191 -15.74537 (114*2π)/5355 weeks
115-7.66207 -15.54778 (115*2π)/5355 weeks
116-7.93531 -15.41885 (116*2π)/5355 weeks
117-8.11186 -15.24315 (117*2π)/5355 weeks
118-8.28575 -15.02328 (118*2π)/5355 weeks
119-8.4624 -14.79472 (119*2π)/5354 weeks
120-8.67014 -14.47501 (120*2π)/5354 weeks
121-8.92584 -14.23896 (121*2π)/5354 weeks
122-9.16355 -13.9992 (122*2π)/5354 weeks
123-9.3732 -13.79575 (123*2π)/5354 weeks
124-9.56832 -13.54347 (124*2π)/5354 weeks
125-9.76785 -13.30645 (125*2π)/5354 weeks
126-9.97343 -13.08053 (126*2π)/5354 weeks
127-10.16392 -12.88161 (127*2π)/5354 weeks
128-10.28445 -12.66802 (128*2π)/5354 weeks
129-10.39926 -12.37741 (129*2π)/5354 weeks
130-10.57373 -12.1132 (130*2π)/5354 weeks
131-10.73165 -11.86879 (131*2π)/5354 weeks
132-10.84986 -11.6153 (132*2π)/5354 weeks
133-10.95688 -11.33725 (133*2π)/5354 weeks
134-11.08561 -11.03789 (134*2π)/5354 weeks
135-11.23508 -10.72777 (135*2π)/5354 weeks
136-11.40914 -10.45695 (136*2π)/5354 weeks
137-11.55167 -10.25815 (137*2π)/5354 weeks
138-11.61229 -9.9834 (138*2π)/5354 weeks
139-11.73453 -9.709 (139*2π)/5354 weeks
140-11.8325 -9.44955 (140*2π)/5354 weeks
141-11.92447 -9.18005 (141*2π)/5354 weeks
142-12.00862 -8.92681 (142*2π)/5354 weeks
143-12.08491 -8.65657 (143*2π)/5354 weeks
144-12.1381 -8.42901 (144*2π)/5354 weeks
145-12.15365 -8.15048 (145*2π)/5354 weeks
146-12.19431 -7.84868 (146*2π)/5354 weeks
147-12.22235 -7.55098 (147*2π)/5354 weeks
148-12.29899 -7.20644 (148*2π)/5354 weeks
149-12.38184 -6.93795 (149*2π)/5354 weeks
150-12.45548 -6.66977 (150*2π)/5354 weeks
151-12.50241 -6.44339 (151*2π)/5354 weeks
152-12.49369 -6.1854 (152*2π)/5354 weeks
153-12.51719 -5.8993 (153*2π)/5353 weeks
154-12.55381 -5.63726 (154*2π)/5353 weeks
155-12.59561 -5.39144 (155*2π)/5353 weeks
156-12.57411 -5.17425 (156*2π)/5353 weeks
157-12.55888 -4.92409 (157*2π)/5353 weeks
158-12.53037 -4.69396 (158*2π)/5353 weeks
159-12.45545 -4.42809 (159*2π)/5353 weeks
160-12.42426 -4.14924 (160*2π)/5353 weeks
161-12.37821 -3.85761 (161*2π)/5353 weeks
162-12.38153 -3.56984 (162*2π)/5353 weeks
163-12.38959 -3.35152 (163*2π)/5353 weeks
164-12.35038 -3.14464 (164*2π)/5353 weeks
165-12.26902 -2.94161 (165*2π)/5353 weeks
166-12.15891 -2.68756 (166*2π)/5353 weeks
167-12.08308 -2.41765 (167*2π)/5353 weeks
168-12.01693 -2.14623 (168*2π)/5353 weeks
169-11.97464 -1.88609 (169*2π)/5353 weeks
170-11.92489 -1.68427 (170*2π)/5353 weeks
171-11.83196 -1.4517 (171*2π)/5353 weeks
172-11.74929 -1.24913 (172*2π)/5353 weeks
173-11.64148 -1.00416 (173*2π)/5353 weeks
174-11.57914 -.75459 (174*2π)/5353 weeks
175-11.50683 -.57154 (175*2π)/5353 weeks
176-11.41203 -.36987 (176*2π)/5353 weeks
177-11.30784 -.18571 (177*2π)/5353 weeks
178-11.18756 .01537 (178*2π)/5353 weeks
179-11.08681 .21336 (179*2π)/5353 weeks
180-10.95981 .37997 (180*2π)/5353 weeks
181-10.83488 .57608 (181*2π)/5353 weeks
182-10.71649 .75036 (182*2π)/5353 weeks
183-10.5913 .9253 (183*2π)/5353 weeks
184-10.45034 1.08528 (184*2π)/5353 weeks
185-10.30704 1.24538 (185*2π)/5353 weeks
186-10.16372 1.41271 (186*2π)/5353 weeks
187-10.00048 1.56654 (187*2π)/5353 weeks
188-9.85247 1.72027 (188*2π)/5353 weeks
189-9.68103 1.87856 (189*2π)/5353 weeks
190-9.50954 2.04799 (190*2π)/5353 weeks
191-9.36966 2.21217 (191*2π)/5353 weeks
192-9.22525 2.35219 (192*2π)/5353 weeks
193-9.06769 2.49724 (193*2π)/5353 weeks
194-8.93855 2.64086 (194*2π)/5353 weeks
195-8.78557 2.72338 (195*2π)/5353 weeks
196-8.59562 2.83116 (196*2π)/5353 weeks
197-8.40687 2.96584 (197*2π)/5353 weeks
198-8.24628 3.09578 (198*2π)/5353 weeks
199-8.10339 3.20505 (199*2π)/5353 weeks
200-7.90211 3.30489 (200*2π)/5353 weeks
201-7.7539 3.44293 (201*2π)/5353 weeks
202-7.64574 3.54534 (202*2π)/5353 weeks
203-7.52389 3.59311 (203*2π)/5353 weeks
204-7.35352 3.59404 (204*2π)/5353 weeks
205-7.1349 3.62859 (205*2π)/5353 weeks
206-6.92336 3.71958 (206*2π)/5353 weeks
207-6.72849 3.78565 (207*2π)/5353 weeks
208-6.57277 3.86421 (208*2π)/5353 weeks
209-6.40012 3.89847 (209*2π)/5353 weeks
210-6.20502 3.95478 (210*2π)/5353 weeks
211-6.03849 3.97546 (211*2π)/5353 weeks
212-5.82644 4.03007 (212*2π)/5353 weeks
213-5.66081 4.08559 (213*2π)/5353 weeks
214-5.47905 4.10856 (214*2π)/5353 weeks
215-5.30786 4.15998 (215*2π)/5352 weeks
216-5.15544 4.18831 (216*2π)/5352 weeks
217-5.00087 4.19114 (217*2π)/5352 weeks
218-4.84171 4.18076 (218*2π)/5352 weeks
219-4.63911 4.19684 (219*2π)/5352 weeks
220-4.49929 4.20943 (220*2π)/5352 weeks
221-4.34379 4.19106 (221*2π)/5352 weeks
222-4.17653 4.19622 (222*2π)/5352 weeks
223-4.04769 4.16077 (223*2π)/5352 weeks
224-3.88249 4.1155 (224*2π)/5352 weeks
225-3.70528 4.08211 (225*2π)/5352 weeks
226-3.54004 4.05244 (226*2π)/5352 weeks
227-3.38773 4.01867 (227*2π)/5352 weeks
228-3.20838 3.9671 (228*2π)/5352 weeks
229-3.04867 3.96406 (229*2π)/5352 weeks
230-2.92183 3.92218 (230*2π)/5352 weeks
231-2.79507 3.87983 (231*2π)/5352 weeks
232-2.67169 3.81807 (232*2π)/5352 weeks
233-2.54009 3.73568 (233*2π)/5352 weeks
234-2.4048 3.65911 (234*2π)/5352 weeks
235-2.26387 3.58331 (235*2π)/5352 weeks
236-2.12757 3.49517 (236*2π)/5352 weeks
237-1.98773 3.40299 (237*2π)/5352 weeks
238-1.83615 3.3358 (238*2π)/5352 weeks
239-1.71878 3.2558 (239*2π)/5352 weeks
240-1.57577 3.16465 (240*2π)/5352 weeks
241-1.45141 3.09993 (241*2π)/5352 weeks
242-1.33805 3.01827 (242*2π)/5352 weeks
243-1.23644 2.95209 (243*2π)/5352 weeks
244-1.16327 2.84322 (244*2π)/5352 weeks
245-1.04538 2.73284 (245*2π)/5352 weeks
246-.95414 2.63939 (246*2π)/5352 weeks
247-.88207 2.51901 (247*2π)/5352 weeks
248-.76481 2.38429 (248*2π)/5352 weeks
249-.65589 2.28737 (249*2π)/5352 weeks
250-.56866 2.18548 (250*2π)/5352 weeks
251-.46758 2.08842 (251*2π)/5352 weeks
252-.38753 2.01522 (252*2π)/5352 weeks
253-.36137 1.93389 (253*2π)/5352 weeks
254-.3287 1.80676 (254*2π)/5352 weeks
255-.27166 1.68699 (255*2π)/5352 weeks
256-.23988 1.56665 (256*2π)/5352 weeks
257-.23356 1.45693 (257*2π)/5352 weeks
258-.23822 1.29133 (258*2π)/5352 weeks
259-.18141 1.09587 (259*2π)/5352 weeks
260-.14263 .95572 (260*2π)/5352 weeks
261-.09811 .77735 (261*2π)/5352 weeks
262-.02001 .62684 (262*2π)/5352 weeks
263.04392 .49333 (263*2π)/5352 weeks
264.09427 .38342 (264*2π)/5352 weeks
265.12745 .27419 (265*2π)/5352 weeks
266.16321 .17221 (266*2π)/5352 weeks
267.13338 .0836 (267*2π)/5352 weeks
268.13338 -.0836 (268*2π)/5352 weeks
269.16321 -.17221 (269*2π)/5352 weeks
270.12745 -.27419 (270*2π)/5352 weeks
271.09427 -.38342 (271*2π)/5352 weeks
272.04392 -.49333 (272*2π)/5352 weeks
273-.02001 -.62684 (273*2π)/5352 weeks
274-.09811 -.77735 (274*2π)/5352 weeks
275-.14263 -.95572 (275*2π)/5352 weeks
276-.18141 -1.09587 (276*2π)/5352 weeks
277-.23822 -1.29133 (277*2π)/5352 weeks
278-.23356 -1.45693 (278*2π)/5352 weeks
279-.23988 -1.56665 (279*2π)/5352 weeks
280-.27166 -1.68699 (280*2π)/5352 weeks
281-.3287 -1.80676 (281*2π)/5352 weeks
282-.36137 -1.93389 (282*2π)/5352 weeks
283-.38753 -2.01522 (283*2π)/5352 weeks
284-.46758 -2.08842 (284*2π)/5352 weeks
285-.56866 -2.18548 (285*2π)/5352 weeks
286-.65589 -2.28737 (286*2π)/5352 weeks
287-.76481 -2.38429 (287*2π)/5352 weeks
288-.88207 -2.51901 (288*2π)/5352 weeks
289-.95414 -2.63939 (289*2π)/5352 weeks
290-1.04538 -2.73284 (290*2π)/5352 weeks
291-1.16327 -2.84322 (291*2π)/5352 weeks
292-1.23644 -2.95209 (292*2π)/5352 weeks
293-1.33805 -3.01827 (293*2π)/5352 weeks
294-1.45141 -3.09993 (294*2π)/5352 weeks
295-1.57577 -3.16465 (295*2π)/5352 weeks
296-1.71878 -3.2558 (296*2π)/5352 weeks
297-1.83615 -3.3358 (297*2π)/5352 weeks
298-1.98773 -3.40299 (298*2π)/5352 weeks
299-2.12757 -3.49517 (299*2π)/5352 weeks
300-2.26387 -3.58331 (300*2π)/5352 weeks
301-2.4048 -3.65911 (301*2π)/5352 weeks
302-2.54009 -3.73568 (302*2π)/5352 weeks
303-2.67169 -3.81807 (303*2π)/5352 weeks
304-2.79507 -3.87983 (304*2π)/5352 weeks
305-2.92183 -3.92218 (305*2π)/5352 weeks
306-3.04867 -3.96406 (306*2π)/5352 weeks
307-3.20838 -3.9671 (307*2π)/5352 weeks
308-3.38773 -4.01867 (308*2π)/5352 weeks
309-3.54004 -4.05244 (309*2π)/5352 weeks
310-3.70528 -4.08211 (310*2π)/5352 weeks
311-3.88249 -4.1155 (311*2π)/5352 weeks
312-4.04769 -4.16077 (312*2π)/5352 weeks
313-4.17653 -4.19622 (313*2π)/5352 weeks
314-4.34379 -4.19106 (314*2π)/5352 weeks
315-4.49929 -4.20943 (315*2π)/5352 weeks
316-4.63911 -4.19684 (316*2π)/5352 weeks
317-4.84171 -4.18076 (317*2π)/5352 weeks
318-5.00087 -4.19114 (318*2π)/5352 weeks
319-5.15544 -4.18831 (319*2π)/5352 weeks
320-5.30786 -4.15998 (320*2π)/5352 weeks
321-5.47905 -4.10856 (321*2π)/5352 weeks
322-5.66081 -4.08559 (322*2π)/5352 weeks
323-5.82644 -4.03007 (323*2π)/5352 weeks
324-6.03849 -3.97546 (324*2π)/5352 weeks
325-6.20502 -3.95478 (325*2π)/5352 weeks
326-6.40012 -3.89847 (326*2π)/5352 weeks
327-6.57277 -3.86421 (327*2π)/5352 weeks
328-6.72849 -3.78565 (328*2π)/5352 weeks
329-6.92336 -3.71958 (329*2π)/5352 weeks
330-7.1349 -3.62859 (330*2π)/5352 weeks
331-7.35352 -3.59404 (331*2π)/5352 weeks
332-7.52389 -3.59311 (332*2π)/5352 weeks
333-7.64574 -3.54534 (333*2π)/5352 weeks
334-7.7539 -3.44293 (334*2π)/5352 weeks
335-7.90211 -3.30489 (335*2π)/5352 weeks
336-8.10339 -3.20505 (336*2π)/5352 weeks
337-8.24628 -3.09578 (337*2π)/5352 weeks
338-8.40687 -2.96584 (338*2π)/5352 weeks
339-8.59562 -2.83116 (339*2π)/5352 weeks
340-8.78557 -2.72338 (340*2π)/5352 weeks
341-8.93855 -2.64086 (341*2π)/5352 weeks
342-9.06769 -2.49724 (342*2π)/5352 weeks
343-9.22525 -2.35219 (343*2π)/5352 weeks
344-9.36966 -2.21217 (344*2π)/5352 weeks
345-9.50954 -2.04799 (345*2π)/5352 weeks
346-9.68103 -1.87856 (346*2π)/5352 weeks
347-9.85247 -1.72027 (347*2π)/5352 weeks
348-10.00048 -1.56654 (348*2π)/5352 weeks
349-10.16372 -1.41271 (349*2π)/5352 weeks
350-10.30704 -1.24538 (350*2π)/5352 weeks
351-10.45034 -1.08528 (351*2π)/5352 weeks
352-10.5913 -.9253 (352*2π)/5352 weeks
353-10.71649 -.75036 (353*2π)/5352 weeks
354-10.83488 -.57608 (354*2π)/5352 weeks
355-10.95981 -.37997 (355*2π)/5352 weeks
356-11.08681 -.21336 (356*2π)/5352 weeks
357-11.18756 -.01537 (357*2π)/5351 weeks
358-11.30784 .18571 (358*2π)/5351 weeks
359-11.41203 .36987 (359*2π)/5351 weeks
360-11.50683 .57154 (360*2π)/5351 weeks
361-11.57914 .75459 (361*2π)/5351 weeks
362-11.64148 1.00416 (362*2π)/5351 weeks
363-11.74929 1.24913 (363*2π)/5351 weeks
364-11.83196 1.4517 (364*2π)/5351 weeks
365-11.92489 1.68427 (365*2π)/5351 weeks
366-11.97464 1.88609 (366*2π)/5351 weeks
367-12.01693 2.14623 (367*2π)/5351 weeks
368-12.08308 2.41765 (368*2π)/5351 weeks
369-12.15891 2.68756 (369*2π)/5351 weeks
370-12.26902 2.94161 (370*2π)/5351 weeks
371-12.35038 3.14464 (371*2π)/5351 weeks
372-12.38959 3.35152 (372*2π)/5351 weeks
373-12.38153 3.56984 (373*2π)/5351 weeks
374-12.37821 3.85761 (374*2π)/5351 weeks
375-12.42426 4.14924 (375*2π)/5351 weeks
376-12.45545 4.42809 (376*2π)/5351 weeks
377-12.53037 4.69396 (377*2π)/5351 weeks
378-12.55888 4.92409 (378*2π)/5351 weeks
379-12.57411 5.17425 (379*2π)/5351 weeks
380-12.59561 5.39144 (380*2π)/5351 weeks
381-12.55381 5.63726 (381*2π)/5351 weeks
382-12.51719 5.8993 (382*2π)/5351 weeks
383-12.49369 6.1854 (383*2π)/5351 weeks
384-12.50241 6.44339 (384*2π)/5351 weeks
385-12.45548 6.66977 (385*2π)/5351 weeks
386-12.38184 6.93795 (386*2π)/5351 weeks
387-12.29899 7.20644 (387*2π)/5351 weeks
388-12.22235 7.55098 (388*2π)/5351 weeks
389-12.19431 7.84868 (389*2π)/5351 weeks
390-12.15365 8.15048 (390*2π)/5351 weeks
391-12.1381 8.42901 (391*2π)/5351 weeks
392-12.08491 8.65657 (392*2π)/5351 weeks
393-12.00862 8.92681 (393*2π)/5351 weeks
394-11.92447 9.18005 (394*2π)/5351 weeks
395-11.8325 9.44955 (395*2π)/5351 weeks
396-11.73453 9.709 (396*2π)/5351 weeks
397-11.61229 9.9834 (397*2π)/5351 weeks
398-11.55167 10.25815 (398*2π)/5351 weeks
399-11.40914 10.45695 (399*2π)/5351 weeks
400-11.23508 10.72777 (400*2π)/5351 weeks
401-11.08561 11.03789 (401*2π)/5351 weeks
402-10.95688 11.33725 (402*2π)/5351 weeks
403-10.84986 11.6153 (403*2π)/5351 weeks
404-10.73165 11.86879 (404*2π)/5351 weeks
405-10.57373 12.1132 (405*2π)/5351 weeks
406-10.39926 12.37741 (406*2π)/5351 weeks
407-10.28445 12.66802 (407*2π)/5351 weeks
408-10.16392 12.88161 (408*2π)/5351 weeks
409-9.97343 13.08053 (409*2π)/5351 weeks
410-9.76785 13.30645 (410*2π)/5351 weeks
411-9.56832 13.54347 (411*2π)/5351 weeks
412-9.3732 13.79575 (412*2π)/5351 weeks
413-9.16355 13.9992 (413*2π)/5351 weeks
414-8.92584 14.23896 (414*2π)/5351 weeks
415-8.67014 14.47501 (415*2π)/5351 weeks
416-8.4624 14.79472 (416*2π)/5351 weeks
417-8.28575 15.02328 (417*2π)/5351 weeks
418-8.11186 15.24315 (418*2π)/5351 weeks
419-7.93531 15.41885 (419*2π)/5351 weeks
420-7.66207 15.54778 (420*2π)/5351 weeks
421-7.38191 15.74537 (421*2π)/5351 weeks
422-7.08315 15.95986 (422*2π)/5351 weeks
423-6.82724 16.19858 (423*2π)/5351 weeks
424-6.58903 16.413 (424*2π)/5351 weeks
425-6.35948 16.6098 (425*2π)/5351 weeks
426-6.11975 16.74096 (426*2π)/5351 weeks
427-5.79797 16.89339 (427*2π)/5351 weeks
428-5.52077 17.08349 (428*2π)/5351 weeks
429-5.23153 17.21812 (429*2π)/5351 weeks
430-4.85858 17.40679 (430*2π)/5351 weeks
431-4.59382 17.60783 (431*2π)/5351 weeks
432-4.28493 17.78631 (432*2π)/5351 weeks
433-4.02284 17.96218 (433*2π)/5351 weeks
434-3.75216 18.10353 (434*2π)/5351 weeks
435-3.46057 18.24358 (435*2π)/5351 weeks
436-3.17091 18.37266 (436*2π)/5351 weeks
437-2.89276 18.45714 (437*2π)/5351 weeks
438-2.5712 18.5348 (438*2π)/5351 weeks
439-2.22769 18.63442 (439*2π)/5351 weeks
440-1.8862 18.73068 (440*2π)/5351 weeks
441-1.53053 18.80166 (441*2π)/5351 weeks
442-1.16702 18.95356 (442*2π)/5351 weeks
443-.88656 19.04935 (443*2π)/5351 weeks
444-.56892 19.10503 (444*2π)/5351 weeks
445-.20178 19.13074 (445*2π)/5351 weeks
446.18921 19.16856 (446*2π)/5351 weeks
447.60248 19.279 (447*2π)/5351 weeks
448.96269 19.39636 (448*2π)/5351 weeks
4491.27509 19.51622 (449*2π)/5351 weeks
4501.54955 19.61472 (450*2π)/5351 weeks
4511.80823 19.62594 (451*2π)/5351 weeks
4522.10387 19.53016 (452*2π)/5351 weeks
4532.51707 19.50499 (453*2π)/5351 weeks
4542.88757 19.49913 (454*2π)/5351 weeks
4553.30316 19.4942 (455*2π)/5351 weeks
4563.681 19.51832 (456*2π)/5351 weeks
4574.0271 19.53172 (457*2π)/5351 weeks
4584.41002 19.5425 (458*2π)/5351 weeks
4594.70109 19.52663 (459*2π)/5351 weeks
4605.0805 19.48287 (460*2π)/5351 weeks
4615.43542 19.47738 (461*2π)/5351 weeks
4625.71254 19.43204 (462*2π)/5351 weeks
4636.01871 19.31655 (463*2π)/5351 weeks
4646.42607 19.1732 (464*2π)/5351 weeks
4656.81459 19.12025 (465*2π)/5351 weeks
4667.12572 19.02301 (466*2π)/5351 weeks
4677.51444 18.91929 (467*2π)/5351 weeks
4687.88045 18.75455 (468*2π)/5351 weeks
4698.27963 18.6988 (469*2π)/5351 weeks
4708.59248 18.56193 (470*2π)/5351 weeks
4719.02243 18.31711 (471*2π)/5351 weeks
4729.4863 18.24394 (472*2π)/5351 weeks
4739.86309 18.16569 (473*2π)/5351 weeks
47410.24464 18.06413 (474*2π)/5351 weeks
47510.64111 17.94977 (475*2π)/5351 weeks
47611.0204 17.86974 (476*2π)/5351 weeks
47711.31537 17.84649 (477*2π)/5351 weeks
47811.62737 17.71741 (478*2π)/5351 weeks
47911.7999 17.60832 (479*2π)/5351 weeks
48012.03306 17.31213 (480*2π)/5351 weeks
48112.42134 17.03709 (481*2π)/5351 weeks
48212.71671 16.84788 (482*2π)/5351 weeks
48313.0535 16.6092 (483*2π)/5351 weeks
48413.38224 16.36065 (484*2π)/5351 weeks
48513.72662 16.12574 (485*2π)/5351 weeks
48614.057 15.85975 (486*2π)/5351 weeks
48714.46373 15.55879 (487*2π)/5351 weeks
48814.89438 15.45384 (488*2π)/5351 weeks
48915.14447 15.27667 (489*2π)/5351 weeks
49015.49869 15.04995 (490*2π)/5351 weeks
49115.71982 14.8917 (491*2π)/5351 weeks
49215.95884 14.65974 (492*2π)/5351 weeks
49316.19848 14.43103 (493*2π)/5351 weeks
49416.34229 14.18167 (494*2π)/5351 weeks
49516.50505 13.78079 (495*2π)/5351 weeks
49616.77881 13.33377 (496*2π)/5351 weeks
49717.11703 12.92517 (497*2π)/5351 weeks
49817.45328 12.62389 (498*2π)/5351 weeks
49917.77372 12.25347 (499*2π)/5351 weeks
50018.12453 11.973 (500*2π)/5351 weeks
50118.39001 11.6139 (501*2π)/5351 weeks
50218.86554 11.27789 (502*2π)/5351 weeks
50319.18169 11.20838 (503*2π)/5351 weeks
50419.38996 11.00382 (504*2π)/5351 weeks
50519.54278 10.8439 (505*2π)/5351 weeks
50619.56034 10.50848 (506*2π)/5351 weeks
50719.77615 10.14589 (507*2π)/5351 weeks
50819.85996 9.85078 (508*2π)/5351 weeks
50919.99349 9.56448 (509*2π)/5351 weeks
51019.86304 9.08857 (510*2π)/5351 weeks
51120.01629 8.42648 (511*2π)/5351 weeks
51220.33861 7.97606 (512*2π)/5351 weeks
51320.42726 7.48378 (513*2π)/5351 weeks
51420.75368 6.82108 (514*2π)/5351 weeks
51521.20058 6.40561 (515*2π)/5351 weeks
51621.69195 6.04845 (516*2π)/5351 weeks
51721.9065 6.02789 (517*2π)/5351 weeks
51822.01944 5.72063 (518*2π)/5351 weeks
51922.24146 5.48966 (519*2π)/5351 weeks
52022.28536 5.2249 (520*2π)/5351 weeks
52122.30228 5.2358 (521*2π)/5351 weeks
52222.01287 4.9423 (522*2π)/5351 weeks
52321.74943 4.3751 (523*2π)/5351 weeks
52421.5622 4.04017 (524*2π)/5351 weeks
52521.01097 3.32451 (525*2π)/5351 weeks
52620.75447 2.41868 (526*2π)/5351 weeks
52720.38271 1.24584 (527*2π)/5351 weeks
52820.03615 -.50127 (528*2π)/5351 weeks
52920.85485 -2.42622 (529*2π)/5351 weeks
53021.78553 -4.13177 (530*2π)/5351 weeks
53123.27463 -5.79618 (531*2π)/5351 weeks
53226.10123 -6.96902 (532*2π)/5351 weeks
53328.44688 -8.26262 (533*2π)/5351 weeks



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