henon_map: A function to generate a time series from the Henon Map

Description Usage Arguments Value Author(s) References Examples

View source: R/chaotic_maps.R

Description

Generates a time series from the Henon map

Usage

1
henon_map(N, a, b, startx="rand", starty="rand", disregard_N=0)

Arguments

N

length of the time series that is to be generated

a

Henon map parameter a

b

Henon map parameter b

startx

start value in x direction. Default is to random.

starty

start value in y direction. Default is to random.

disregard_N

Number of values at the beginning of the series to disregard

Value

A vector of length N

Author(s)

Sebastian Sippel

References

Schuster, H.G., 1988. Deterministic chaos. An Introduction.

Examples

1
henon_map(N = 10^4, a=1.4, b=0.3)

Example output

               x_ts          y_ts
1      0.6568854710  0.2831266499
2      0.6790287192  0.1970656413
3      0.5515536393  0.2037086158
4      0.7778126320  0.1654660918
5      0.3184766051  0.2333437896
6      1.0913455024  0.0955429815
7     -0.5719060263  0.3274036507
8      0.8694965466 -0.1715718079
9     -0.2300057503  0.2608489640
10     1.1867852607 -0.0690017251
11    -1.0408446822  0.3560355782
12    -0.1606651353 -0.3122534047
13     0.6516079954 -0.0481995406
14     0.3573702879  0.1954823986
15     1.0166834668  0.1072110864
16    -0.3398922940  0.3050050400
17     1.1432675599 -0.1019676882
18    -0.9318526871  0.3429802680
19     0.1272910654 -0.2795558061
20     0.6977599724  0.0381873196
21     0.3565707489  0.2093279917
22     1.0313282132  0.1069712247
23    -0.3821218121  0.3093984640
24     1.1049745530 -0.1146365436
25    -0.8239928116  0.3314923659
26     0.3809425510 -0.2471978435
27     0.5496380385  0.1142827653
28     0.6913400026  0.1648914115
29     0.4957600126  0.2074020008
30     0.8633128146  0.1487280038
31     0.1052953816  0.2589938444
32     1.2434718800  0.0315886145
33    -1.1331226285  0.3730415640
34    -0.4245120837 -0.3399367885
35     0.4077684986 -0.1273536251
36     0.6398611671  0.1223305496
37     0.5491393112  0.1919583501
38     0.7697827737  0.1647417934
39     0.3351500671  0.2309348321
40     1.0736790376  0.1005450201
41    -0.5133563261  0.3221037113
42     0.9531551067 -0.1540068978
43    -0.4259134183  0.2859465320
44     1.0319833961 -0.1277740255
45    -0.6187596474  0.3095950188
46     0.7735861171 -0.1856278942
47    -0.0234375670  0.2320758351
48     1.2313067878 -0.0070312701
49    -1.1295942379  0.3693920363
50    -0.4169843630 -0.3388782714
51     0.4176953860 -0.1250953089
52     0.6306474814  0.1253086158
53     0.5685058717  0.1891942444
54     0.7367157478  0.1705517615
55     0.4107016313  0.2210147243
56     0.9848685625  0.1232104894
57    -0.2347420301  0.2954605687
58     1.2183152198 -0.0704226090
59    -1.1484313737  0.3654945659
60    -0.4809579022 -0.3445294121
61     0.3316218828 -0.1442873707
62     0.7017503270  0.0994865648
63     0.4100516348  0.2105250981
64     0.9751258176  0.1230154905
65    -0.2082030136  0.2925377453
66     1.2318498524 -0.0624609041
67    -1.1868965866  0.3695549557
68    -0.6026579544 -0.3560689760
69     0.1354557700 -0.1807973863
70     0.7935150418  0.0406367310
71     0.1591041609  0.2380545125
72     1.2026147249  0.0477312483
73    -0.9770637990  0.3607844175
74     0.0242692831 -0.2931191397
75     0.7060562629  0.0072807849
76     0.3093591599  0.2118168789
77     1.0778325531  0.0928077480
78    -0.5336044696  0.3233497659
79     0.9247225439 -0.1600813409
80    -0.3572378375  0.2774167632
81     1.0987503417 -0.1071713512
82    -0.7973245899  0.3296251025
83     0.4396080003 -0.2391973770
84     0.4902453516  0.1318824001
85     0.7954056934  0.1470736055
86     0.2613353015  0.2386217080
87     1.1430071123  0.0784005905
88    -0.7506507717  0.3429021337
89     0.5540349201 -0.2251952315
90     0.3450681987  0.1662104760
91     0.9995095896  0.1035204596
92    -0.2951067280  0.2998528769
93     1.1779297036 -0.0885320184
94    -1.0310577598  0.3533789111
95    -0.1349332345 -0.3093173279
96     0.6651929032 -0.0404799704
97     0.3400457918  0.1995578710
98     1.0376742742  0.1020137375
99    -0.4054613215  0.3113022823
100    1.0811438457 -0.1216383965
101   -0.7580592177  0.3243431537
102    0.5198278653 -0.2274177653
103    0.3942728214  0.1559483596
104    0.9383168788  0.1182818464
105   -0.1143321446  0.2814950636
106    1.2631944886 -0.0342996434
107   -1.2682240859  0.3789583466
108   -0.8727909183 -0.3804672258
109   -0.4469368078 -0.2618372755
110    0.4585092103 -0.1340810423
111    0.5715959834  0.1375527631
112    0.6801420076  0.1714787950
113    0.5238483844  0.2040426023
114    0.8198586205  0.1571545153
115    0.2161190946  0.2459575862
116    1.1805671379  0.0648357284
117   -0.8863985455  0.3541701414
118    0.2541868072 -0.2659195637
119    0.6436251302  0.0762560422
120    0.4963014107  0.1930875391
121    0.8482464127  0.1488904232
122    0.1415596558  0.2544739238
123    1.2264191332  0.0424678967
124   -1.0632775497  0.3679257400
125   -0.2148570669 -0.3189832649
126    0.6163877522 -0.0644571201
127    0.4036354744  0.1849163257
128    0.9568260910  0.1210906423
129   -0.1606319934  0.2870478273
130    1.2509241351 -0.0481895980
131   -1.2389252664  0.3752772405
132   -0.7736329015 -0.3716775799
133   -0.2095885927 -0.2320898704
134    0.7064118001 -0.0628765778
135    0.2384987384  0.2119235400
136    1.1322892326  0.0715496215
137   -0.7233608471  0.3396867698
138    0.6071354886 -0.2170082541
139    0.2669328438  0.1821406466
140    1.0823862462  0.0800798531
141   -0.5601041273  0.3247158739
142    0.8855125870 -0.1680312382
143   -0.2658167967  0.2656537761
144    1.1667317789 -0.0797450390
145   -0.9855133006  0.3500195337
146   -0.0097115181 -0.2956539902
147    0.7042139708 -0.0029134554
148    0.3028023012  0.2112641912
149    1.0828992642  0.0908406904
150   -0.5508984526  0.3248697793
151    0.8999850322 -0.1652695358
152   -0.2992318172  0.2699955097
153    1.1446399571 -0.0897695452
154   -0.9240504290  0.3433919871
155    0.1479751135 -0.2772151287
156    0.6921295834  0.0443925341
157    0.3737318298  0.2076388750
158    1.0120932022  0.1121195489
159   -0.3219461608  0.3036279606
160    1.1585188980 -0.0965838483
161   -0.9756163000  0.3475556694
162    0.0149976386 -0.2926848900
163    0.7070002092  0.0044992916
164    0.3047102775  0.2121000628
165    1.0821123682  0.0914130833
166   -0.5479409652  0.3246337105
167    0.9042986885 -0.1643822896
168   -0.3092408549  0.2712896066
169    1.1374077377 -0.0927722565
170   -0.9039471629  0.3412223213
171    0.1972536586 -0.2711841489
172    0.6743432430  0.0591760976
173    0.4225417645  0.2023029729
174    0.9523448130  0.1267625294
175   -0.1429823708  0.2857034439
176    1.2570819022 -0.0428947112
177   -1.2552515837  0.3771245707
178   -0.8287945831 -0.3765754751
179   -0.3382361204 -0.2486383749
180    0.5911964827 -0.1014708361
181    0.4092105703  0.1773589448
182    0.9429243376  0.1227631711
183   -0.1219856580  0.2828773013
184    1.2620446002 -0.0365956974
185   -1.2664548995  0.3786133801
186   -0.8668578375 -0.3799364699
187   -0.4319559845 -0.2600573513
188    0.4787222872 -0.1295867954
189    0.5495681651  0.1436166862
190    0.7207814508  0.1648704495
191    0.4375341898  0.2162344352
192    0.9482238011  0.1312602569
193   -0.1275194709  0.2844671403
194    1.2617014387 -0.0382558413
195   -1.2669025699  0.3785104316
196   -0.8685485385 -0.3800707710
197   -0.4361979603 -0.2605645616
198    0.4730593137 -0.1308593881
199    0.5558414520  0.1419177941
200    0.7093741865  0.1667524356
201    0.4622560046  0.2128122559
202    0.9136593966  0.1386768014
203   -0.0300060889  0.2740978190
204    1.2728373075 -0.0090018267
205   -1.2771625625  0.3818511922
206   -0.9017507032 -0.3831487687
207   -0.5215648317 -0.2705252110
208    0.3486329659 -0.1564694495
209    0.6733676276  0.1045898898
210    0.4697963432  0.2020102883
211    0.8930182426  0.1409389030
212    0.0244646887  0.2679054728
213    1.2670675434  0.0073394066
214   -1.2403048167  0.3801202630
215   -0.7735781906 -0.3720914450
216   -0.2098839488 -0.2320734572
217    0.7062547621 -0.0629651846
218    0.2387207109  0.2118764286
219    1.1320938197  0.0716162133
220   -0.7226747700  0.3396281459
221    0.6084657934 -0.2168024310
222    0.2648746986  0.1825397380
223    1.0843176897  0.0794624096
224   -0.5665803835  0.3252953069
225    0.8758766436 -0.1699741150
226   -0.2439979678  0.2627629931
227    1.1794139815 -0.0731993903
228   -1.0206236659  0.3538241944
229   -0.1045175400 -0.3061870998
230    0.6785194176 -0.0313552620
231    0.3241006979  0.2035558253
232    1.0564980579  0.0972302094
233   -0.4654331956  0.3169494174
234    1.0136701340 -0.1396299587
235   -0.5781679555  0.3041010402
236    0.8361115815 -0.1734503866
237   -0.1521659941  0.2508334745
238    1.2184171888 -0.0456497982
239   -1.1240064225  0.3655251566
240   -0.4032214564 -0.3372019268
241    0.4351755132 -0.1209664369
242    0.6139047449  0.1305526540
243    0.6029220039  0.1841714235
244    0.6752505036  0.1808766012
245    0.5425280615  0.2025751511
246    0.7905037746  0.1627584184
247    0.2879037137  0.2371511324
248    1.1211071647  0.0863711141
249   -0.6732626705  0.3363321494
250    0.7017364766 -0.2019788011
251    0.1086134832  0.2105209430
252    1.1940052987  0.0325840450
253   -0.9633240698  0.3582015896
254    0.0590110208 -0.2889972209
255    0.7061275583  0.0177033062
256    0.3196407263  0.2118382675
257    1.0687999960  0.0958922179
258   -0.5033745862  0.3206399988
259    0.9658996352 -0.1510123759
260   -0.4571593232  0.2897698906
261    0.9971773851 -0.1371477970
262   -0.5292556291  0.2991532155
263    0.9069970861 -0.1587766887
264   -0.3104778887  0.2720991258
265    1.1371439987 -0.0931433666
266   -0.9034784299  0.3411431996
267    0.1983606170 -0.2710435290
268    0.6738707629  0.0595081851
269    0.4237656580  0.2021612289
270    0.9507529628  0.1271296974
271   -0.1383739775  0.2852258889
272    1.2584195881 -0.0415121933
273   -1.2585799970  0.3775258764
274   -0.8401071759 -0.3775739991
275   -0.3656660929 -0.2520321528
276    0.5607714791 -0.1096998279
277    0.4500496596  0.1682314437
278    0.8846688691  0.1350148979
279    0.0393202867  0.2654006607
280    1.2632361418  0.0117960860
281   -1.2222756840  0.3789708425
282   -0.7125701443 -0.3666827052
283   -0.0775413999 -0.2137710433
284    0.7778112206 -0.0232624200
285    0.1297511673  0.2333433662
286    1.2097738546  0.0389253502
287   -1.0100485407  0.3629321564
288   -0.0653451202 -0.3030145622
289    0.6910074592 -0.0196035360
290    0.3119086319  0.2073022377
291    1.0711004452  0.0935725896
292   -0.5125860397  0.3213301336
293    0.9534879062 -0.1537758119
294   -0.4265706741  0.2860463719
295    1.0312988158 -0.1279712022
296   -0.6169793487  0.3093896447
297    0.7764607213 -0.1850938046
298   -0.0291415569  0.2329382164
299    1.2317492939 -0.0087424671
300   -1.1328313193  0.3695247882
301   -0.4271047291 -0.3398493958
302    0.4047647748 -0.1281314187
303    0.6425002492  0.1214294324
304    0.5435002341  0.1927500748
305    0.7792005685  0.1630500702
306    0.3130351338  0.2337601706
307    1.0965727776  0.0939105401
308   -0.5895500590  0.3289718333
309    0.8423748524 -0.1768650177
310   -0.1702985664  0.2527124557
311    1.2121102133 -0.0510895699
312   -1.1079852068  0.3636330640
313   -0.3550506420 -0.3323955620
314    0.4911190962 -0.1065151926
315    0.5558076541  0.1473357289
316    0.7148447212  0.1667422962
317    0.4513381306  0.2144534164
318    0.9292648650  0.1354014392
319   -0.0735450260  0.2787794595
320    1.2712070403 -0.0220635078
321   -1.2844177829  0.3813621121
322   -0.9282585454 -0.3853253349
323   -0.5916548329 -0.2784775636
324    0.2314448186 -0.1774964499
325    0.7475101644  0.0694334456
326    0.2871534213  0.2242530493
327    1.1088131270  0.0861460264
328   -0.6351071446  0.3326439381
329    0.7679384190 -0.1905321434
330   -0.0161533249  0.2303815257
331    1.2300162238 -0.0048459975
332   -1.1229618727  0.3690048671
333   -0.3964558474 -0.3368885618
334    0.4430633037 -0.1189367542
335    0.6062361183  0.1329189911
336    0.6183878675  0.1818708355
337    0.6465058590  0.1855163602
338    0.6003586043  0.1939517577
339    0.6893491225  0.1801075813
340    0.5148244836  0.2068047367
341    0.8357427883  0.1544473451
342    0.1765949336  0.2507228365
343    1.2070627577  0.0529784801
344   -0.9868222213  0.3621188273
345   -0.0012265078 -0.2960466664
346    0.7039512275 -0.0003679524
347    0.3058657846  0.2111853683
348    1.0802099388  0.0917597354
349   -0.5418351813  0.3240629816
350    0.9130434724 -0.1625505544
351   -0.3296582900  0.2739130417
352    1.1217686183 -0.0988974870
353   -0.8606082532  0.3365305855
354    0.2996253937 -0.2581824760
355    0.6161319968  0.0898876181
356    0.5584215256  0.1848395990
357    0.7482711587  0.1675264577
358    0.3836528400  0.2244813476
359    1.0184160453  0.1150958520
360   -0.3369438858  0.3055248136
361    1.1465811585 -0.1010831657
362   -0.9415908601  0.3439743476
363    0.1027436606 -0.2824772580
364    0.7027439783  0.0308230982
365    0.3394343596  0.2108231935
366    1.0495212352  0.1018303079
367   -0.4402624446  0.3148563706
368    1.0434929424 -0.1320787334
369   -0.6565072626  0.3130478827
370    0.7096453825 -0.1969521788
371    0.0980126248  0.2128936147
372    1.1994445503  0.0294037874
373   -0.9847303334  0.3598333651
374    0.0022620036 -0.2954191000
375    0.7045737366  0.0006786011
376    0.3056847906  0.2113721210
377    1.0805516533  0.0917054372
378   -0.5429231885  0.3241654960
379    0.9114936719 -0.1628769566
380   -0.3260259560  0.2734481016
381    1.1246380080 -0.0978077868
382   -0.8685426954  0.3373914024
383    0.2812784233 -0.2605628086
384    0.6286726194  0.0843835270
385    0.5310625596  0.1886017858
386    0.7937633668  0.1593187679
387    0.2772343724  0.2381290100
388    1.1305265539  0.0831703117
389   -0.7061560929  0.3391579662
390    0.6410389675 -0.2118468279
391    0.2128498311  0.1923116903
392    1.1288846194  0.0638549493
393   -0.7202777283  0.3386653858
394    0.6123453776 -0.2160833185
395    0.2589630755  0.1837036133
396    1.0898169890  0.0776889227
397   -0.5850925746  0.3269450967
398    0.8476784475 -0.1755277724
399   -0.1815100229  0.2543035343
400    1.2081792905 -0.0544530069
401   -1.0980290840  0.3624537871
402   -0.3254812299 -0.3294087252
403    0.5222780314 -0.0976443690
404    0.5204715521  0.1566834094
405    0.7774365183  0.1561414656
406    0.3099709098  0.2332309555
407    1.0987162046  0.0929912729
408   -0.5970569447  0.3296148614
409    0.8305470681 -0.1791170834
410   -0.1448488886  0.2491641204
411    1.2197904397 -0.0434546666
412   -1.1264988700  0.3659371319
413   -0.4106624539 -0.3379496610
414    0.4259492276 -0.1231987362
415    0.6227954216  0.1277847683
416    0.5847609763  0.1868386265
417    0.7081150673  0.1754282929
418    0.4734305648  0.2124345202
419    0.8986434206  0.1420291695
420    0.0114451731  0.2695930262
421    1.2694096374  0.0034335519
422   -1.2525276066  0.3808228912
423   -0.8155326761 -0.3757582820
424   -0.3068892461 -0.2446598028
425    0.6234867841 -0.0920667738
426    0.3637031483  0.1870460352
427    1.0018540631  0.1091109445
428   -0.2960852448  0.3005562189
429    1.1778231578 -0.0888255734
430   -1.0309999211  0.3533469474
431   -0.1347982248 -0.3092999763
432    0.6652612377 -0.0404394674
433    0.3399590124  0.1995783713
434    1.0377773891  0.1019877037
435   -0.4057869694  0.3113332167
436    1.0808049264 -0.1217360908
437   -0.7571310952  0.3242414779
438    0.5216949844 -0.2271393286
439    0.3918287519  0.1565084953
440    0.9415668161  0.1175486256
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1779   0.6982800247 -0.0127733558
1780   0.3045936542  0.2094840074
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1798   0.6678866399  0.1685006015
1799   0.5439990122  0.2003659920
1800   0.7860570966  0.1631997037
1801   0.2981596410  0.2358171290
1802   1.1113582888  0.0894478923
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1812   0.4919773720  0.2087503653
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1818   0.2830520582 -0.1539245631
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1820   0.3308430327  0.2201728747
1821   1.0669329175  0.0992529098
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1823   0.9778326672 -0.1483293843
1824  -0.4869487993  0.2933498002
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1829   0.8327269711 -0.1742785184
1830  -0.1450864101  0.2498180913
1831   1.2203479984 -0.0435259230
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1834   0.4183242449 -0.1250199895
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1836   0.5698606160  0.1889960301
1837   0.7343584597  0.1709581848
1838   0.4159628985  0.2203075379
1839   0.9780723518  0.1247888696
1840  -0.2144868660  0.2934217055
1841   1.2290152436 -0.0643460598
1842  -1.1790159164  0.3687045731
1843  -0.5774053705 -0.3537047749
1844   0.1795394784 -0.1732216112
1845   0.7816501948  0.0538618435
1846   0.1984940057  0.2344950584
1847   1.1793352400  0.0595482017
1848  -0.8876160501  0.3538005720
1849   0.2507934187 -0.2662848150
1850   0.6456589106  0.0752380256
1851   0.4916124253  0.1936976732
1852   0.8553417857  0.1474837276
1853   0.1232303290  0.2566025357
1854   1.2353425361  0.0369690987
1855  -1.0995305555  0.3706027608
1856  -0.3219516587 -0.3298591667
1857   0.5250268146 -0.0965854976
1858   0.5175000839  0.1575080444
1859   0.7825791728  0.1552500252
1860   0.2978477987  0.2347737518
1861   1.1105751162  0.0893543396
1862  -0.6373735845  0.3331725348
1863   0.7644294142 -0.1912120753
1864  -0.0093053363  0.2293288243
1865   1.2292075993 -0.0027916009
1866  -1.1181234518  0.3687622798
1867  -0.3815177951 -0.3354370355
1868   0.4607848053 -0.1144553385
1869   0.5882929699  0.1382354416
1870   0.6537113758  0.1764878910
1871   0.5782139031  0.1961134127
1872   0.7280495679  0.1734641709
1873   0.4313855282  0.2184148704
1874   0.9578840068  0.1294156585
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1876   1.2536681895 -0.0465428461
1877  -1.2469003471  0.3761004568
1878  -0.8005642090 -0.3740701041
1879  -0.2713343781 -0.2401692627
1880   0.6567594547 -0.0814003134
1881   0.3147335127  0.1970278364
1882   1.0583477787  0.0944200538
1883  -0.4737199753  0.3175043336
1884   1.0033294727 -0.1421159926
1885  -0.5514540356  0.3009988418
1886   0.8752566671 -0.1654362107
1887  -0.2379401373  0.2625770001
1888   1.1833152876 -0.0713820412
1889  -1.0317111390  0.3549945863
1890  -0.1352044379 -0.3095133417
1891   0.6648943223 -0.0405613314
1892   0.3405204250  0.1994682967
1893   1.0371324729  0.1021561275
1894  -0.4037451455  0.3111397419
1895   1.0829255424 -0.1211235436
1896  -0.7629423661  0.3248776627
1897   0.5099641871 -0.2288827098
1898   0.4070284292  0.1529892561
1899   0.9210482571  0.1221085288
1900  -0.0655533199  0.2763144771
1901   1.2702983443 -0.0196659960
1902  -1.2787870328  0.3810895033
1903  -0.9083252822 -0.3836361099
1904  -0.5387128555 -0.2724975847
1905   0.3212062584 -0.1616138566
1906   0.6939432987  0.0963618775
1907   0.4221816549  0.2081829896
1908   0.9586507000  0.1266544965
1909  -0.1599611340  0.2875952100
1910   1.2517726199 -0.0479883402
1911  -1.2416969087  0.3755317860
1912  -0.7830039125 -0.3725090726
1913  -0.2308422504 -0.2349011738
1914   0.6904954238 -0.0692526751
1915   0.2632498224  0.2071486271
1916   1.1101279705  0.0789749467
1917  -0.6463628086  0.3330383912
1918   0.7481395586 -0.1939088426
1919   0.0224932386  0.2244418676
1920   1.2237335435  0.0067479716
1921  -1.0897853281  0.3671200630
1922  -0.2955648227 -0.3269355984
1923   0.5507624114 -0.0886694468
1924   0.4866556259  0.1652287234
1925   0.8336615459  0.1459966878
1926   0.1730084854  0.2500984638
1927   1.2081937533  0.0519025456
1928  -0.9917224582  0.3624581260
1929  -0.0144606818 -0.2975167375
1930   0.7021905067 -0.0043382045
1931   0.3053616847  0.2106571520
1932   1.0801130901  0.0916085054
1933  -0.5416934970  0.3240339270
1934   0.9132293444 -0.1625080491
1935  -0.3300910188  0.2739688033
1936   1.1214246904 -0.0990273056
1937  -0.8596579762  0.3364274071
1938   0.3018108366 -0.2578973929
1939   0.6145769136  0.0905432510
1940   0.5617565551  0.1843730741
1941   0.7425744760  0.1685269665
1942   0.3965433731  0.2227723428
1943   1.0026270373  0.1189630119
1944  -0.2884023545  0.3007881112
1945   1.1843418259 -0.0865207063
1946  -1.0502524912  0.3553025478
1947  -0.1889398656 -0.3150757474
1948   0.6349466707 -0.0566819597
1949   0.3788978558  0.1904840012
1950   0.9894949820  0.1136693568
1951  -0.2570710904  0.2968484946
1952   1.2043287309 -0.0771213271
1953  -1.1076920959  0.3612986193
1954  -0.3564758719 -0.3323076288
1955   0.4897873051 -0.1069427616
1956   0.5572089926  0.1469361915
1957   0.7122615856  0.1671626978
1958   0.4569195050  0.2136784757
1959   0.9213928680  0.1370758515
1960  -0.0514748927  0.2764178604
1961   1.2727083300 -0.0154424678
1962  -1.2831435584  0.3818124990
1963  -0.9232278489 -0.3849430675
1964  -0.5782325930 -0.2769683547
1965   0.2549375411 -0.1734697779
1966   0.7355398123  0.0764812623
1967   0.3190549206  0.2206619437
1968   1.0781474844  0.0957164762
1969  -0.5316463211  0.3234442453
1970   0.9277373103 -0.1594938963
1971  -0.3644690200  0.2783211931
1972   1.0923484599 -0.1093407060
1973  -0.7798559271  0.3277045380
1974   0.4762591641 -0.2339567781
1975   0.4484913139  0.1428777492
1976   0.8612755072  0.1345473942
1977   0.0960336952  0.2583826522
1978   1.2454711933  0.0288101086
1979  -1.1428677821  0.3736413580
1980  -0.4549641162 -0.3428603346
1981   0.3673503796 -0.1364892349
1982   0.6745859432  0.1102051139
1983   0.4731124411  0.2023757830
1984   0.8890062483  0.1419337323
1985   0.0354687791  0.2667018745
1986   1.2649406265  0.0106406337
1987  -1.2294640702  0.3794821879
1988  -0.7367324718 -0.3688392210
1989  -0.1287238500 -0.2210197415
1990   0.7557824971 -0.0386171550
1991   0.1616927890  0.2267347491
1992   1.1901323679  0.0485078367
1993  -0.9344732378  0.3570397104
1994   0.1345033855 -0.2803419713
1995   0.6943304037  0.0403510156
1996   0.3654184223  0.2082991211
1997   1.0213562484  0.1096255267
1998  -0.3508104938  0.3064068745
1999   1.1341116709 -0.1052431481
2000  -0.9059361431  0.3402335013
2001   0.1912250876 -0.2717808429
2002   0.6770253093  0.0573675263
2003   0.4156589492  0.2031075928
2004   0.9612262859  0.1246976848
2005  -0.1688406772  0.2883678858
2006   1.2484578418 -0.0506522031
2007  -1.2327579791  0.3745373525
2008  -0.7530317763 -0.3698273937
2009  -0.1637069924 -0.2259095329
2010   0.7365704960 -0.0491120977
2011   0.1913373685  0.2209711488
2012   1.1697171648  0.0574012105
2013  -0.8581323333  0.3509151494
2014   0.3199676074 -0.2574397000
2015   0.5992293223  0.0959902822
2016   0.5932841892  0.1797687967
2017   0.6869882159  0.1779852568
2018   0.5172513245  0.2060964648
2019   0.8315279590  0.1551753974
2020   0.1871611522  0.2494583877
2021   1.2004173721  0.0561483457
2022  -0.9612542683  0.3601252116
2023   0.0665115359 -0.2883762805
2024   0.7054304213  0.0199534608
2025   0.3232685497  0.2116291264
2026   1.0653255491  0.0969805649
2027  -0.4919053709  0.3195976647
2028   0.9808384132 -0.1475716113
2029  -0.4944332013  0.2942515240
2030   0.9520016573 -0.1483299604
2031  -0.4171599780  0.2856004972
2032   1.0419690711 -0.1251479934
2033  -0.6451273565  0.3125907213
2034   0.7299256927 -0.1935382070
2035   0.0605536694  0.2189777078
2036   1.2138442622  0.0181661008
2037  -1.0446189492  0.3641532787
2038  -0.1635669701 -0.3133856848
2039   0.6491585001 -0.0490700910
2040   0.3609604475  0.1947475500
2041   1.0123381275  0.1082881343
2042  -0.3264717439  0.3037014382
2043   1.1544841189 -0.0979415232
2044  -0.9639085362  0.3463452357
2045   0.0455777030 -0.2891725609
2046   0.7079191813  0.0136733109
2047   0.3120639167  0.2123757544
2048   1.0760383110  0.0936191750
2049  -0.5273826505  0.3228114933
2050   0.9334260492 -0.1582147952
2051  -0.3780126603  0.2800278148
2052   1.0799768149 -0.1134037981
2053  -0.7462936871  0.3239930445
2054   0.5442570700 -0.2238881061
2055   0.3614098323  0.1632771210
2056   0.9804132274  0.1084229497
2057  -0.2372711854  0.2941239682
2058   1.2153073066 -0.0711813556
2059  -1.1389419450  0.3645921920
2060  -0.4514720636 -0.3416825835
2061   0.3729595826 -0.1354416191
2062   0.6698199906  0.1118878748
2063   0.4837655271  0.2009459972
2064   0.8733052779  0.1451296581
2065   0.0774027063  0.2619915834
2066   1.2536039329  0.0232208119
2067  -1.1769111368  0.3760811799
2068  -0.5630865738 -0.3530733411
2069   0.2030335736 -0.1689259721
2070   0.7733623431  0.0609100721
2071   0.2235850329  0.2320087029
2072   1.1620223292  0.0670755099
2073  -0.8233387411  0.3486066988
2074   0.3995653431 -0.2470016223
2075   0.5294849289  0.1198696029
2076   0.7273735970  0.1588454787
2077   0.4181441892  0.2182120791
2078   0.9734296910  0.1254432568
2079  -0.2011482519  0.2920289073
2080   1.2353840404 -0.0603444756
2081  -1.1969876936  0.3706152121
2082  -0.6352761421 -0.3590963081
2083   0.0758976045 -0.1905828426
2084   0.8013525325  0.0227692814
2085   0.1237370476  0.2404057597
2086   1.2189705600  0.0371211143
2087  -1.0431238024  0.3656911680
2088  -0.1576590059 -0.3129371407
2089   0.6522639523 -0.0472977018
2090   0.3570747294  0.1956791857
2091   1.0171758783  0.1071224188
2092  -0.3413830557  0.3051527635
2093   1.1419934165 -0.1024149167
2094  -0.9282234655  0.3425980250
2095   0.1363597023 -0.2784670396
2096   0.6955014046  0.0409079107
2097   0.3636968254  0.2086504214
2098   1.0234648882  0.1091090476
2099  -0.3573634807  0.3070394665
2100   1.1282473462 -0.1072090442
2101  -0.8893279481  0.3384742039
2102   0.2312083249 -0.2667983844
2103   0.6583614103  0.0693624975
2104   0.4625468523  0.1975084231
2105   0.8979789963  0.1387640557
2106   0.0098512669  0.2693936989
2107   1.2692578324  0.0029553801
2108  -1.2524662432  0.3807773497
2109  -0.8153630167 -0.3757398730
2110  -0.3064834617 -0.2446089050
2111   0.6238861378 -0.0919450385
2112   0.3631274834  0.1871658413
2113   1.0025596445  0.1089382450
2114  -0.2982379319  0.3007678933
2115   1.1762436837 -0.0894713796
2116  -1.0264402643  0.3528731051
2117  -0.1221383576 -0.3079320793
2118   0.6711830309 -0.0366415073
2119   0.3326771673  0.2013549093
2120   1.0464111726  0.0998031502
2121  -0.4331637288  0.3139233518
2122   1.0512402094 -0.1299491186
2123  -0.6770974877  0.3153720628
2124   0.6735266518 -0.2031292463
2125   0.1617773427  0.2020579955
2126   1.1654173235  0.0485332028
2127  -0.8529433502  0.3496251970
2128   0.3311078950 -0.2558830051
2129   0.5906315816  0.0993323685
2130   0.6109484372  0.1771894745
2131   0.6546282843  0.1832845312
2132   0.5833310643  0.1963884853
2133   0.7200033025  0.1749993193
2134   0.4492326614  0.2160009908
2135   0.9334670130  0.1347697984
2136  -0.0851351317  0.2800401039
2137   1.2698929170 -0.0255405395
2138  -1.2832197684  0.3809678751
2139  -0.9243462885 -0.3849659305
2140  -0.5811484160 -0.2773038865
2141   0.2498692395 -0.1743445248
2142   0.7382469836  0.0749607718
2143   0.3119487195  0.2214740951
2144   1.0852372901  0.0935846158
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2148   1.1541736892 -0.0856108157
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2150   0.0812235211 -0.2851723448
2151   0.7055914907  0.0243670563
2152   0.3273639639  0.2116774472
2153   1.0616434164  0.0982091892
2154  -0.4797122519  0.3184930249
2155   0.9963196424 -0.1439136756
2156  -0.5336276374  0.2988958927
2157   0.9002340552 -0.1600882912
2158  -0.2946781869  0.2700702166
2159   1.1485008891 -0.0884034561
2160  -0.9350794654  0.3445502667
2161   0.1204272175 -0.2805238396
2162   0.6991723598  0.0361281652
2163   0.3517493811  0.2097517079
2164   1.0365330300  0.1055248143
2165  -0.3986361969  0.3109599090
2166   1.0884847645 -0.1195908591
2167  -0.7783095747  0.3265454294
2168   0.4784733177 -0.2334928724
2169   0.4459957256  0.1435419953
2170   0.8650649332  0.1337987177
2171   0.0861264437  0.2595194799
2172   1.2491346099  0.0258379331
2173  -1.1586342501  0.3747403830
2174  -0.5046662727 -0.3475902750
2175   0.2958464595 -0.1513998818
2176   0.7260649396  0.0887539378
2177   0.3507155228  0.2178194819
2178   1.0456175528  0.1052146568
2179  -0.4254278365  0.3136852658
2180   1.0603008841 -0.1276283510
2181  -0.7015615017  0.3180902652
2182   0.6290263083 -0.2104684505
2183   0.2355878143  0.1887078925
2184   1.1110056270  0.0706763443
2185  -0.6573905601  0.3333016881
2186   0.7282744001 -0.1972171680
2187   0.0602457893  0.2184823200
2188   1.2134009429  0.0180737368
2189  -1.0432048506  0.3640202829
2190  -0.1595666216 -0.3129614552
2191   0.6513924354 -0.0478699865
2192   0.3580930667  0.1954177306
2193   1.0158948284  0.1074279200
2194  -0.3374313035  0.3047684485
2195   1.1453646102 -0.1012293910
2196  -0.9378335173  0.3436093831
2197   0.1122649943 -0.2813500552
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