GLxw2048.inc

From Citizendium
Jump to navigation Jump to search

// GLxw2048.inc

s text file, containing nodes and weights of the Gauss-Legendre (or Legenrde-Gauss) quadrature formula [1][2][3] with 2048 nodes.

Below, the file is provided and its generator. The update do another number of points is straightforward. For moderate number of nodes (maximum 32), the Efunda online service can be used [4].

GLxw2048.inc can be included "as is" to the C++ code for the numerical implementation of integration. This file is used in the generators of figures for the Cauchi integral implementation of the tetration to complex base and to base $b>\exp(1/\mathrm{e})$, and, in particular to $b=\mathrm e\approx 2.71$ described in Mathematics of Computation [5].

GLxw2048.inc

// The content of this section should be saved as GLxw2048.inc
// or (preferably) generated with the code from the next section

int NPO=2048;
DB GLx[2048]={
 -0.99999931092710532960
,-0.99999636931774495781
,-0.99999107714397238839
,-0.99998343324279355729
,-0.99997343748820805167
,-0.99996108986934204845
,-0.99994639040378036792
,-0.99992933912141495684
,-0.99990993606015263391
,-0.99988818126448765630
,-0.99986407478494651125
,-0.99983761667784529502
,-0.99980880700517365482
,-0.99977764583453508705
,-0.99974413323911432344
,-0.99970826929765858047
,-0.99967005409446628531
,-0.99962948771938001796
,-0.99958657026778192163
,-0.99954130184059060692
,-0.99949368254425898503
,-0.99944371249077269256
,-0.99939139179764890100
,-0.99933672058793537982
,-0.99927969899020972929
,-0.99922032713857872734
,-0.99915860517267775335
,-0.99909453323767026328
,-0.99902811148424729875
,-0.99895934006862701791
,-0.99888821915255423839
,-0.99881474890329998741
,-0.99873892949366105279
,-0.99866076110195953290
,-0.99858024391204238172
,-0.99849737811328094831
,-0.99841216390057050805
,-0.99832460147432978558
,-0.99823469104050046777
,-0.99814243281054670676
,-0.99804782700145461152
,-0.99795087383573172923
,-0.99785157354140651396
,-0.99774992635202778440
,-0.99764593250666416916
,-0.99753959224990354000
,-0.99743090583185243283
,-0.99731987350813545599
,-0.99720649553989468641
,-0.99709077219378905302
,-0.99697270374199370722
,-0.99685229046219938129
,-0.99672953263761173348
,-0.99660443055695068052
,-0.99647698451444971751
,-0.99634719480985522490
,-0.99621506174842576221
,-0.99608058564093134984
,-0.99594376680365273694
,-0.99580460555838065716
,-0.99566310223241507124
,-0.99551925715856439650
,-0.99537307067514472407
,-0.99522454312597902237
,-0.99507367486039632838
,-0.99492046623323092565
,-0.99476491760482150937
,-0.99460702934101033874
,-0.99444680181314237626
,-0.99428423539806441407
,-0.99411933047812418770
,-0.99395208744116947625
,-0.99378250668054719032
,-0.99361058859510244674
,-0.99343633358917763021
,-0.99325974207261144236
,-0.99308081446073793758
,-0.99289955117438554632
,-0.99271595263987608490
,-0.99253001928902375312
,-0.99234175155913411829
,-0.99215114989300308673
,-0.99195821473891586238
,-0.99176294655064589233
,-0.99156534578745379938
,-0.99136541291408630209
,-0.99116314840077512151
,-0.99095855272323587532
,-0.99075162636266695868
,-0.99054236980574841278
,-0.99033078354464077977
,-0.99011686807698394565
,-0.98990062390589596953
,-0.98968205153997190017
,-0.98946115149328258017
,-0.98923792428537343655
,-0.98901237044126325898
,-0.98878449049144296484
,-0.98855428497187435147
,-0.98832175442398883576
,-0.98808689939468618066
,-0.98784972043633320870
,-0.98761021810676250313
,-0.98736839296927109578
,-0.98712424559261914217
,-0.98687777655102858383
,-0.98662898642418179779
,-0.98637787579722023312
,-0.98612444526074303477
,-0.98586869541080565454
,-0.98561062684891844897
,-0.98535024018204526482
,-0.98508753602260201151
,-0.98482251498845522060
,-0.98455517770292059278
,-0.98428552479476153164
,-0.98401355689818766504
,-0.98373927465285335343
,-0.98346267870385618523
,-0.98318376970173545999
,-0.98290254830247065782
,-0.98261901516747989714
,-0.98233317096361837855
,-0.98204501636317681663
,-0.98175455204387985885
,-0.98146177868888449141
,-0.98116669698677843258
,-0.98086930763157851318
,-0.98056961132272904417
,-0.98026760876510017178
,-0.97996330066898621960
,-0.97965668775010401789
,-0.97934777072959122046
,-0.97903655033400460841
,-0.97872302729531838143
,-0.97840720235092243617
,-0.97808907624362063194
,-0.97776864972162904369
,-0.97744592353857420215
,-0.97712089845349132152
,-0.97679357523082251423
,-0.97646395464041499271
,-0.97613203745751925917
,-0.97579782446278728197
,-0.97546131644227065965
,-0.97512251418741877225
,-0.97478141849507691976
,-0.97443803016748444798
,-0.97409235001227286165
,-0.97374437884246392528
,-0.97339411747646775036
,-0.97304156673808087113
,-0.97268672745648430657
,-0.97232960046624161048
,-0.97197018660729690861
,-0.97160848672497292298
,-0.97124450166996898392
,-0.97087823229835902919
,-0.97050967947158959051
,-0.97013884405647776742
,-0.96976572692520918888
,-0.96939032895533596156
,-0.96901265102977460604
,-0.96863269403680398026
,-0.96825045887006319032
,-0.96786594642854948870
,-0.96747915761661615970
,-0.96709009334397039279
,-0.96669875452567114268
,-0.96630514208212697736
,-0.96590925693909391317
,-0.96551110002767323771
,-0.96511067228430931974
,-0.96470797465078740677
,-0.96430300807423141005
,-0.96389577350710167698
,-0.96348627190719275096
,-0.96307450423763111863
,-0.96266047146687294488
,-0.96224417456870179482
,-0.96182561452222634362
,-0.96140479231187807367
,-0.96098170892740895931
,-0.96055636536388913893
,-0.96012876262170457461
,-0.95969890170655469924
,-0.95926678362945005132
,-0.95883240940670989687
,-0.95839578005995983926
,-0.95795689661612941639
,-0.95751576010744968544
,-0.95707237157145079497
,-0.95662673205095954482
,-0.95617884259409693346
,-0.95572870425427569266
,-0.95527631809019781031
,-0.95482168516585203997
,-0.95436480655051139866
,-0.95390568331873065201
,-0.95344431655034378686
,-0.95298070733046147157
,-0.95251485674946850400
,-0.95204676590302124672
,-0.95157643589204505045
,-0.95110386782273166438
,-0.95062906280653663478
,-0.95015202196017669065
,-0.94967274640562711742
,-0.94919123727011911815
,-0.94870749568613716210
,-0.94822152279141632151
,-0.94773331972893959548
,-0.94724288764693522185
,-0.94675022769887397651
,-0.94625534104346646061
,-0.94575822884466037533
,-0.94525889227163778419
,-0.94475733249881236340
,-0.94425355070582663952
,-0.94374754807754921516
,-0.94323932580407198216
,-0.94272888508070732240
,-0.94221622710798529684
,-0.94170135309165082155
,-0.94118426424266083216
,-0.94066496177718143557
,-0.94014344691658504976
,-0.93961972088744753089
,-0.93909378492154528886
,-0.93856564025585238986
,-0.93803528813253764728
,-0.93750272979896170016
,-0.93696796650767407956
,-0.93643099951641026228
,-0.93589183008808871312
,-0.93535045949080791445
,-0.93480688899784338360
,-0.93426111988764467826
,-0.93371315344383238959
,-0.93316299095519512333
,-0.93261063371568646844
,-0.93205608302442195405
,-0.93149934018567599373
,-0.93094040650887881807
,-0.93037928330861339494
,-0.92981597190461233768
,-0.92925047362175480108
,-0.92868278979006336539
,-0.92811292174470090815
,-0.92754087082596746401
,-0.92696663837929707238
,-0.92639022575525461302
,-0.92581163430953262951
,-0.92523086540294814098
,-0.92464792040143944127
,-0.92406280067606288644
,-0.92347550760298967011
,-0.92288604256350258680
,-0.92229440694399278307
,-0.92170060213595649711
,-0.92110462953599178562
,-0.92050649054579523943
,-0.91990618657215868654
,-0.91930371902696588366
,-0.91869908932718919521
,-0.91809229889488626103
,-0.91748334915719665142
,-0.91687224154633851088
,-0.91625897749960518948
,-0.91564355845936186244
,-0.91502598587304213770
,-0.91440626119314465168
,-0.91378438587722965312
,-0.91316036138791557494
,-0.91253418919287559421
,-0.91190587076483418033
,-0.91127540758156363109
,-0.91064280112588059728
,-0.91000805288564259497
,-0.90937116435374450624
,-0.90873213702811506798
,-0.90809097241171334887
,-0.90744767201252521426
,-0.90680223734355977976
,-0.90615466992284585270
,-0.90550497127342836152
,-0.90485314292336477401
,-0.90419918640572150313
,-0.90354310325857030146
,-0.90288489502498464368
,-0.90222456325303609730
,-0.90156210949579068187
,-0.90089753531130521594
,-0.90023084226262365293
,-0.89956203191777340459
,-0.89889110584976165340
,-0.89821806563657165267
,-0.89754291286115901543
,-0.89686564911144799121
,-0.89618627598032773150
,-0.89550479506564854316
,-0.89482120797021813064
,-0.89413551630179782592
,-0.89344772167309880742
,-0.89275782570177830672
,-0.89206583001043580423
,-0.89137173622660921275
,-0.89067554598277104953
,-0.88997726091632459682
,-0.88927688266960005082
,-0.88857441288985065914
,-0.88786985322924884620
,-0.88716320534488232768
,-0.88645447089875021305
,-0.88574365155775909667
,-0.88503074899371913733
,-0.88431576488334012601
,-0.88359870090822754279
,-0.88287955875487860130
,-0.88215834011467828251
,-0.88143504668389535673
,-0.88070968016367839361
,-0.87998224226005176171
,-0.87925273468391161558
,-0.87852115915102187214
,-0.87778751738201017500
,-0.87705181110236384788
,-0.87631404204242583614
,-0.87557421193739063732
,-0.87483232252730021988
,-0.87408837555703993089
,-0.87334237277633439183
,-0.87259431593974338368
,-0.87184420680665772015
,-0.87109204714129510958
,-0.87033783871269600587
,-0.86958158329471944739
,-0.86882328266603888530
,-0.86806293861013800005
,-0.86730055291530650668
,-0.86653612737463594909
,-0.86576966378601548239
,-0.86500116395212764479
,-0.86423062968044411742
,-0.86345806278322147345
,-0.86268346507749691575
,-0.86190683838508400322
,-0.86112818453256836606
,-0.86034750535130340973
,-0.85956480267740600763
,-0.85878007835175218277
,-0.85799333421997277797
,-0.85720457213244911519
,-0.85641379394430864334
,-0.85562100151542057542
,-0.85482619671039151391
,-0.85402938139856106531
,-0.85323055745399744388
,-0.85242972675549306358
,-0.85162689118656011936
,-0.85082205263542615733
,-0.85001521299502963360
,-0.84920637416301546224
,-0.84839553804173055228
,-0.84758270653821933321
,-0.84676788156421926981
,-0.84595106503615636608
,-0.84513225887514065746
,-0.84431146500696169281
,-0.84348868536208400511
,-0.84266392187564257072
,-0.84183717648743825850
,-0.84100845114193326709
,-0.84017774778824655201
,-0.83934506838014924117
,-0.83851041487606003971
,-0.83767378923904062417
,-0.83683519343679102509
,-0.83599462944164499933
,-0.83515209923056539130
,-0.83430760478513948291
,-0.83346114809157433338
,-0.83261273114069210750
,-0.83176235592792539353
,-0.83091002445331250986
,-0.83005573872149280104
,-0.82919950074170192312
,-0.82834131252776711807
,-0.82748117609810247695
,-0.82661909347570419320
,-0.82575506668814580447
,-0.82488909776757342372
,-0.82402118875070095991
,-0.82315134167880532780
,-0.82227955859772164674
,-0.82140584155783842916
,-0.82053019261409275805
,-0.81965261382596545401
,-0.81877310725747623130
,-0.81789167497717884338
,-0.81700831905815621796
,-0.81612304157801558095
,-0.81523584461888357028
,-0.81434673026740133869
,-0.81345570061471964609
,-0.81256275775649394136
,-0.81166790379287943337
,-0.81077114082852615157
,-0.80987247097257399596
,-0.80897189633864777659
,-0.80806941904485224220
,-0.80716504121376709879
,-0.80625876497244201732
,-0.80535059245239163094
,-0.80444052578959052190
,-0.80352856712446819773
,-0.80261471860190405713
,-0.80169898237122234539
,-0.80078136058618709913
,-0.79986185540499708091
,-0.79894046899028070308
,-0.79801720350909094166
,-0.79709206113290023921
,-0.79616504403759539801
,-0.79523615440347246214
,-0.79430539441523158973
,-0.79337276626197191469
,-0.79243827213718639790
,-0.79150191423875666835
,-0.79056369476894785387
,-0.78962361593440340128
,-0.78868167994613988693
,-0.78773788901954181591
,-0.78679224537435641219
,-0.78584475123468839741
,-0.78489540882899476015
,-0.78394422039007951458
,-0.78299118815508844926
,-0.78203631436550386522
,-0.78107960126713930416
,-0.78012105111013426654
,-0.77916066614894891935
,-0.77819844864235879353
,-0.77723440085344947176
,-0.77626852504961126549
,-0.77530082350253388252
,-0.77433129848820108363
,-0.77335995228688533002
,-0.77238678718314241996
,-0.77141180546580611586
,-0.77043500942798276074
,-0.76945640136704588529
,-0.76847598358463080435
,-0.76749375838662920363
,-0.76650972808318371642
,-0.76552389498868249020
,-0.76453626142175374345
,-0.76354682970526031215
,-0.76255560216629418666
,-0.76156258113617103847
,-0.76056776895042473718
,-0.75957116794880185723
,-0.75857278047525617513
,-0.75757260887794315653
,-0.75657065550921443348
,-0.75556692272561227179
,-0.75456141288786402876
,-0.75355412836087660045
,-0.75254507151373085998
,-0.75153424471967608542
,-0.75052165035612437795
,-0.74950729080464507031
,-0.74849116845095912563
,-0.74747328568493352628
,-0.74645364490057565282
,-0.74543224849602765373
,-0.74440909887356080499
,-0.74338419843956985984
,-0.74235754960456738950
,-0.74132915478317811339
,-0.74029901639413322014
,-0.73926713686026467915
,-0.73823351860849954168
,-0.73719816406985423342
,-0.73616107567942883641
,-0.73512225587640136207
,-0.73408170710402201428
,-0.73303943180960744305
,-0.73199543244453498843
,-0.73094971146423691515
,-0.72990227132819463749
,-0.72885311449993293474
,-0.72780224344701415694
,-0.72674966064103242177
,-0.72569536855760780086
,-0.72463936967638049776
,-0.72358166648100501574
,-0.72252226145914431643
,-0.72146115710246396880
,-0.72039835590662628913
,-0.71933386037128447128
,-0.71826767300007670752
,-0.71719979630062030018
,-0.71613023278450576382
,-0.71505898496729091828
,-0.71398605536849497194
,-0.71291144651159259611
,-0.71183516092400799002
,-0.71075720113710893621
,-0.70967756968620084707
,-0.70859626911052080189
,-0.70751330195323157478
,-0.70642867076141565305
,-0.70534237808606924694
,-0.70425442648209628943
,-0.70316481850830242760
,-0.70207355672738900427
,-0.70098064370594703059
,-0.69988608201445114972
,-0.69878987422725359114
,-0.69769202292257811575
,-0.69659253068251395240
,-0.69549140009300972455
,-0.69438863374386736844
,-0.69328423422873604207
,-0.69217820414510602490
,-0.69107054609430260887
,-0.68996126268147998006
,-0.68885035651561509157
,-0.68773783020950152742
,-0.68662368637974335720
,-0.68550792764674898220
,-0.68439055663472497218
,-0.68327157597166989330
,-0.68215098828936812750
,-0.68102879622338368228
,-0.67990500241305399244
,-0.67877960950148371212
,-0.67765262013553849847
,-0.67652403696583878644
,-0.67539386264675355456
,-0.67426209983639408220
,-0.67312875119660769746
,-0.67199381939297151697
,-0.67085730709478617645
,-0.66971921697506955272
,-0.66857955171055047681
,-0.66743831398166243859
,-0.66629550647253728231
,-0.66515113187099889384
,-0.66400519286855687892
,-0.66285769216040023300
,-0.66170863244539100228
,-0.66055801642605793596
,-0.65940584680859013026
,-0.65825212630283066334
,-0.65709685762227022223
,-0.65594004348404072056
,-0.65478168660890890808
,-0.65362178972126997161
,-0.65246035554914112741
,-0.65129738682415520492
,-0.65013288628155422222
,-0.64896685666018295277
,-0.64779930070248248401
,-0.64663022115448376691
,-0.64545962076580115782
,-0.64428750228962595130
,-0.64311386848271990483
,-0.64193872210540875504
,-0.64076206592157572558
,-0.63958390269865502651
,-0.63840423520762534565
,-0.63722306622300333117
,-0.63604039852283706622
,-0.63485623488869953504
,-0.63367057810568208073
,-0.63248343096238785513
,-0.63129479625092525992
,-0.63010467676690137985
,-0.62891307530941540765
,-0.62771999468105206055
,-0.62652543768787498889
,-0.62532940713942017629
,-0.62413190584868933193
,-0.62293293663214327423
,-0.62173250230969530702
,-0.62053060570470458703
,-0.61932724964396948357
,-0.61812243695772093005
,-0.61691617047961576733
,-0.61570845304673007923
,-0.61449928749955251989
,-0.61328867668197763300
,-0.61207662344129916301
,-0.61086313062820335869
,-0.60964820109676226838
,-0.60843183770442702717
,-0.60721404331202113660
,-0.60599482078373373601
,-0.60477417298711286605
,-0.60355210279305872458
,-0.60232861307581691418
,-0.60110370671297168235
,-0.59987738658543915328
,-0.59864965557746055240
,-0.59742051657659542258
,-0.59618997247371483282
,-0.59495802616299457905
,-0.59372468054190837721
,-0.59248993851122104846
,-0.59125380297498169685
,-0.59001627684051687902
,-0.58877736301842376651
,-0.58753706442256329993
,-0.58629538397005333592
,-0.58505232458126178610
,-0.58380788917979974865
,-0.58256208069251463205
,-0.58131490204948327126
,-0.58006635618400503640
,-0.57881644603259493372
,-0.57756517453497669914
,-0.57631254463407588403
,-0.57505855927601293387
,-0.57380322141009625883
,-0.57254653398881529729
,-0.57128849996783357182
,-0.57002912230598173741
,-0.56876840396525062262
,-0.56750634791078426313
,-0.56624295711087292774
,-0.56497823453694613724
,-0.56371218316356567563
,-0.56244480596841859432
,-0.56117610593231020852
,-0.55990608603915708664
,-0.55863474927598003245
,-0.55736209863289705940
,-0.55608813710311635827
,-0.55481286768292925734
,-0.55353629337170317506
,-0.55225841717187456589
,-0.55097924208894185851
,-0.54969877113145838740
,-0.54841700731102531642
,-0.54713395364228455608
,-0.54584961314291167300
,-0.54456398883360879263
,-0.54327708373809749468
,-0.54198890088311170140
,-0.54069944329839055908
,-0.53940871401667131202
,-0.53811671607368216983
,-0.53682345250813516741
,-0.53552892636171901824
,-0.53423314067909196052
,-0.53293609850787459597
,-0.53163780289864272227
,-0.53033825690492015820
,-0.52903746358317156200
,-0.52773542599279524241
,-0.52643214719611596344
,-0.52512763025837774192
,-0.52382187824773663795
,-0.52251489423525353912
,-0.52120668129488693720
,-0.51989724250348569849
,-0.51858658094078182729
,-0.51727469968938322251
,-0.51596160183476642749
,-0.51464729046526937293
,-0.51333176867208411381
,-0.51201503954924955847
,-0.51069710619364419194
,-0.50937797170497879228
,-0.50805763918578913989
,-0.50673611174142872086
,-0.50541339248006142312
,-0.50408948451265422642
,-0.50276439095296988517
,-0.50143811491755960533
,-0.50011065952575571429
,-0.49878202789966432441
,-0.49745222316415799001
,-0.49612124844686835779
,-0.49478910687817881077
,-0.49345580159121710592
,-0.49212133572184800506
,-0.49078571240866589957
,-0.48944893479298742848
,-0.48811100601884409040
,-0.48677192923297484881
,-0.48543170758481873111
,-0.48409034422650742131
,-0.48274784231285784641
,-0.48140420500136475642
,-0.48005943545219329803
,-0.47871353682817158220
,-0.47736651229478324520
,-0.47601836502016000373
,-0.47466909817507420342
,-0.47331871493293136154
,-0.47196721846976270323
,-0.47061461196421769163
,-0.46926089859755655185
,-0.46790608155364278887
,-0.46655016401893569924
,-0.46519314918248287665
,-0.46383504023591271150
,-0.46247584037342688432
,-0.46111555279179285320
,-0.45975418069033633517
,-0.45839172727093378153
,-0.45702819573800484721
,-0.45566358929850485411
,-0.45429791116191724858
,-0.45293116454024605282
,-0.45156335264800831041
,-0.45019447870222652601
,-0.44882454592242109899
,-0.44745355753060275133
,-0.44608151675126494966
,-0.44470842681137632134
,-0.44333429094037306482
,-0.44195911237015135425
,-0.44058289433505973812
,-0.43920564007189153233
,-0.43782735281987720730
,-0.43644803582067676962
,-0.43506769231837213777
,-0.43368632555945951210
,-0.43230393879284173943
,-0.43092053526982067169
,-0.42953611824408951901
,-0.42815069097172519730
,-0.42676425671118066996
,-0.42537681872327728439
,-0.42398838027119710250
,-0.42259894462047522601
,-0.42120851503899211604
,-0.41981709479696590714
,-0.41842468716694471612
,-0.41703129542379894492
,-0.41563692284471357851
,-0.41424157270918047697
,-0.41284524829899066242
,-0.41144795289822660032
,-0.41004968979325447548
,-0.40865046227271646276
,-0.40725027362752299235
,-0.40584912715084500964
,-0.40444702613810622996
,-0.40304397388697538781
,-0.40163997369735848097
,-0.40023502887139100935
,-0.39882914271343020843
,-0.39742231853004727761
,-0.39601455963001960339
,-0.39460586932432297722
,-0.39319625092612380833
,-0.39178570775077133125
,-0.39037424311578980838
,-0.38896186034087072724
,-0.38754856274786499281
,-0.38613435366077511468
,-0.38471923640574738916
,-0.38330321431106407636
,-0.38188629070713557225
,-0.38046846892649257570
,-0.37904975230377825062
,-0.37763014417574038284
,-0.37620964788122353251
,-0.37478826676116118116
,-0.37336600415856787397
,-0.37194286341853135736
,-0.37051884788820471127
,-0.36909396091679847702
,-0.36766820585557278005
,-0.36624158605782944798
,-0.36481410487890412371
,-0.36338576567615837404
,-0.36195657180897179315
,-0.36052652663873410157
,-0.35909563352883724043
,-0.35766389584466746080
,-0.35623131695359740867
,-0.35479790022497820486
,-0.35336364903013152059
,-0.35192856674234164835
,-0.35049265673684756799
,-0.34905592239083500843
,-0.34761836708342850461
,-0.34617999419568345009
,-0.34474080711057814486
,-0.34330080921300583881
,-0.34186000388976677062
,-0.34041839452956020222
,-0.33897598452297644865
,-0.33753277726248890367
,-0.33608877614244606080
,-0.33464398455906353000
,-0.33319840591041604988
,-0.33175204359642949576
,-0.33030490101887288303
,-0.32885698158135036651
,-0.32740828868929323524
,-0.32595882574995190320
,-0.32450859617238789556
,-0.32305760336746583073
,-0.32160585074784539821
,-0.32015334172797333228
,-0.31870007972407538119
,-0.31724606815414827259
,-0.31579131043795167442
,-0.31433580999700015194
,-0.31287957025455512039
,-0.31142259463561679375
,-0.30996488656691612926
,-0.30850644947690676793
,-0.30704728679575697109
,-0.30558740195534155260
,-0.30412679838923380754
,-0.30266547953269743633
,-0.30120344882267846546
,-0.29974070969779716372
,-0.29827726559833995487
,-0.29681311996625132631
,-0.29534827624512573362
,-0.29388273788019950167
,-0.29241650831834272131
,-0.29094959100805114279
,-0.28948198939943806487
,-0.28801370694422622040
,-0.28654474709573965813
,-0.28507511330889562050
,-0.28360480904019641805
,-0.28213383774772129973
,-0.28066220289111831979
,-0.27918990793159620086
,-0.27771695633191619324
,-0.27624335155638393092
,-0.27476909707084128340
,-0.27329419634265820444
,-0.27181865284072457696
,-0.27034247003544205430
,-0.26886565139871589799
,-0.26738820040394681223
,-0.26591012052602277434
,-0.26443141524131086225
,-0.26295208802764907810
,-0.26147214236433816864
,-0.25999158173213344204
,-0.25851040961323658136
,-0.25702862949128745459
,-0.25554624485135592137
,-0.25406325917993363611
,-0.25257967596492584812
,-0.25109549869564319824
,-0.24961073086279351198
,-0.24812537595847358976
,-0.24663943747616099356
,-0.24515291891070583051
,-0.24366582375832253311
,-0.24217815551658163638
,-0.24068991768440155173
,-0.23920111376204033772
,-0.23771174725108746755
,-0.23622182165445559360
,-0.23473134047637230870
,-0.23324030722237190438
,-0.23174872539928712608
,-0.23025659851524092518
,-0.22876393007963820814
,-0.22727072360315758255
,-0.22577698259774310021
,-0.22428271057659599715
,-0.22278791105416643086
,-0.22129258754614521441
,-0.21979674356945554777
,-0.21830038264224474618
,-0.21680350828387596562
,-0.21530612401491992554
,-0.21380823335714662853
,-0.21230983983351707740
,-0.21081094696817498932
,-0.20931155828643850725
,-0.20781167731479190851
,-0.20631130758087731071
,-0.20481045261348637499
,-0.20330911594255200630
,-0.20180730109914005142
,-0.20030501161544099385
,-0.19880225102476164644
,-0.19729902286151684119
,-0.19579533066122111643
,-0.19429117796048040159
,-0.19278656829698369916
,-0.19128150520949476432
,-0.18977599223784378193
,-0.18827003292291904098
,-0.18676363080665860672
,-0.18525678943204199009
,-0.18374951234308181486
,-0.18224180308481548230
,-0.18073366520329683347
,-0.17922510224558780899
,-0.17771611775975010664
,-0.17620671529483683646
,-0.17469689840088417351
,-0.17318667062890300848
,-0.17167603553087059580
,-0.17016499665972219960
,-0.16865355756934273744
,-0.16714172181455842170
,-0.16562949295112839881
,-0.16411687453573638632
,-0.16260387012598230777
,-0.16109048328037392540
,-0.15957671755831847064
,-0.15806257652011427272
,-0.15654806372694238490
,-0.15503318274085820886
,-0.15351793712478311679
,-0.15200233044249607176
,-0.15048636625862524579
,-0.14897004813863963602
,-0.14745337964884067899
,-0.14593636435635386279
,-0.14441900582912033743
,-0.14290130763588852324
,-0.14138327334620571729
,-0.13986490653040969807
,-0.13834621075962032817
,-0.13682718960573115529
,-0.13530784664140101124
,-0.13378818544004560928
,-0.13226820957582913960
,-0.13074792262365586311
,-0.12922732815916170342
,-0.12770642975870583717
,-0.12618523099936228252
,-0.12466373545891148623
,-0.12314194671583190873
,-0.12161986834929160780
,-0.12009750393913982061
,-0.11857485706589854396
,-0.11705193131075411325
,-0.11552873025554877956
,-0.11400525748277228543
,-0.11248151657555343902
,-0.11095751111765168675
,-0.10943324469344868452
,-0.10790872088793986739
,-0.10638394328672601791
,-0.10485891547600483291
,-0.10333364104256248900
,-0.10180812357376520660
,-0.10028236665755081268
,-0.09875637388242030208
,-0.09723014883742939757
,-0.09570369511218010853
,-0.09417701629681228847
,-0.09265011598199519114
,-0.09112299775891902548
,-0.08959566521928650936
,-0.08806812195530442203
,-0.08654037155967515547
,-0.08501241762558826455
,-0.08348426374671201597
,-0.08195591351718493625
,-0.08042737053160735839
,-0.07889863838503296762
,-0.07736972067296034602
,-0.07584062099132451606
,-0.07431134293648848319
,-0.07278189010523477733
,-0.07125226609475699349
,-0.06972247450265133129
,-0.06819251892690813364
,-0.06666240296590342447
,-0.06513213021839044547
,-0.06360170428349119208
,-0.06207112876068794852
,-0.06054040724981482196
,-0.05900954335104927594
,-0.05747854066490366294
,-0.05594740279221675611
,-0.05441613333414528037
,-0.05288473589215544258
,-0.05135321406801446116
,-0.04982157146378209488
,-0.04828981168180217099
,-0.04675793832469411274
,-0.04522595499534446617
,-0.04369386529689842631
,-0.04216167283275136280
,-0.04062938120654034485
,-0.03909699402213566569
,-0.03756451488363236648
,-0.03603194739534175961
,-0.03449929516178295161
,-0.03296656178767436546
,-0.03143375087792526251
,-0.02990086603762726389
,-0.02836791087204587156
,-0.02683488898661198886
,-0.02530180398691344081
,-0.02376865947868649386
,-0.02223545906780737542
,-0.02070220636028379308
,-0.01916890496224645337
,-0.01763555847994058041
,-0.01610217051971743416
,-0.01456874468802582851
,-0.01303528459140364904
,-0.01150179383646937070
,-0.00996827602991357518
,-0.00843473477849046818
,-0.00690117368900939651
,-0.00536759636832636507
,-0.00383400642333555369
,-0.00230040746096083394
,-0.00076680308814728577
, 0.00076680308814728577
, 0.00230040746096083394
, 0.00383400642333555369
, 0.00536759636832636507
, 0.00690117368900939651
, 0.00843473477849046818
, 0.00996827602991357518
, 0.01150179383646937070
, 0.01303528459140364904
, 0.01456874468802582851
, 0.01610217051971743416
, 0.01763555847994058041
, 0.01916890496224645337
, 0.02070220636028379308
, 0.02223545906780737542
, 0.02376865947868649386
, 0.02530180398691344081
, 0.02683488898661198886
, 0.02836791087204587156
, 0.02990086603762726389
, 0.03143375087792526251
, 0.03296656178767436546
, 0.03449929516178295161
, 0.03603194739534175961
, 0.03756451488363236648
, 0.03909699402213566569
, 0.04062938120654034485
, 0.04216167283275136280
, 0.04369386529689842631
, 0.04522595499534446617
, 0.04675793832469411274
, 0.04828981168180217099
, 0.04982157146378209488
, 0.05135321406801446116
, 0.05288473589215544258
, 0.05441613333414528037
, 0.05594740279221675611
, 0.05747854066490366294
, 0.05900954335104927594
, 0.06054040724981482196
, 0.06207112876068794852
, 0.06360170428349119208
, 0.06513213021839044547
, 0.06666240296590342447
, 0.06819251892690813364
, 0.06972247450265133129
, 0.07125226609475699349
, 0.07278189010523477733
, 0.07431134293648848319
, 0.07584062099132451606
, 0.07736972067296034602
, 0.07889863838503296762
, 0.08042737053160735839
, 0.08195591351718493625
, 0.08348426374671201597
, 0.08501241762558826455
, 0.08654037155967515547
, 0.08806812195530442203
, 0.08959566521928650936
, 0.09112299775891902548
, 0.09265011598199519114
, 0.09417701629681228847
, 0.09570369511218010853
, 0.09723014883742939757
, 0.09875637388242030208
, 0.10028236665755081268
, 0.10180812357376520660
, 0.10333364104256248900
, 0.10485891547600483291
, 0.10638394328672601791
, 0.10790872088793986739
, 0.10943324469344868452
, 0.11095751111765168675
, 0.11248151657555343902
, 0.11400525748277228543
, 0.11552873025554877956
, 0.11705193131075411325
, 0.11857485706589854396
, 0.12009750393913982061
, 0.12161986834929160780
, 0.12314194671583190873
, 0.12466373545891148623
, 0.12618523099936228252
, 0.12770642975870583717
, 0.12922732815916170342
, 0.13074792262365586311
, 0.13226820957582913960
, 0.13378818544004560928
, 0.13530784664140101124
, 0.13682718960573115529
, 0.13834621075962032817
, 0.13986490653040969807
, 0.14138327334620571729
, 0.14290130763588852324
, 0.14441900582912033743
, 0.14593636435635386279
, 0.14745337964884067899
, 0.14897004813863963602
, 0.15048636625862524579
, 0.15200233044249607176
, 0.15351793712478311679
, 0.15503318274085820886
, 0.15654806372694238490
, 0.15806257652011427272
, 0.15957671755831847064
, 0.16109048328037392540
, 0.16260387012598230777
, 0.16411687453573638632
, 0.16562949295112839881
, 0.16714172181455842170
, 0.16865355756934273744
, 0.17016499665972219960
, 0.17167603553087059580
, 0.17318667062890300848
, 0.17469689840088417351
, 0.17620671529483683646
, 0.17771611775975010664
, 0.17922510224558780899
, 0.18073366520329683347
, 0.18224180308481548230
, 0.18374951234308181486
, 0.18525678943204199009
, 0.18676363080665860672
, 0.18827003292291904098
, 0.18977599223784378193
, 0.19128150520949476432
, 0.19278656829698369916
, 0.19429117796048040159
, 0.19579533066122111643
, 0.19729902286151684119
, 0.19880225102476164644
, 0.20030501161544099385
, 0.20180730109914005142
, 0.20330911594255200630
, 0.20481045261348637499
, 0.20631130758087731071
, 0.20781167731479190851
, 0.20931155828643850725
, 0.21081094696817498932
, 0.21230983983351707740
, 0.21380823335714662853
, 0.21530612401491992554
, 0.21680350828387596562
, 0.21830038264224474618
, 0.21979674356945554777
, 0.22129258754614521441
, 0.22278791105416643086
, 0.22428271057659599715
, 0.22577698259774310021
, 0.22727072360315758255
, 0.22876393007963820814
, 0.23025659851524092518
, 0.23174872539928712608
, 0.23324030722237190438
, 0.23473134047637230870
, 0.23622182165445559360
, 0.23771174725108746755
, 0.23920111376204033772
, 0.24068991768440155173
, 0.24217815551658163638
, 0.24366582375832253311
, 0.24515291891070583051
, 0.24663943747616099356
, 0.24812537595847358976
, 0.24961073086279351198
, 0.25109549869564319824
, 0.25257967596492584812
, 0.25406325917993363611
, 0.25554624485135592137
, 0.25702862949128745459
, 0.25851040961323658136
, 0.25999158173213344204
, 0.26147214236433816864
, 0.26295208802764907810
, 0.26443141524131086225
, 0.26591012052602277434
, 0.26738820040394681223
, 0.26886565139871589799
, 0.27034247003544205430
, 0.27181865284072457696
, 0.27329419634265820444
, 0.27476909707084128340
, 0.27624335155638393092
, 0.27771695633191619324
, 0.27918990793159620086
, 0.28066220289111831979
, 0.28213383774772129973
, 0.28360480904019641805
, 0.28507511330889562050
, 0.28654474709573965813
, 0.28801370694422622040
, 0.28948198939943806487
, 0.29094959100805114279
, 0.29241650831834272131
, 0.29388273788019950167
, 0.29534827624512573362
, 0.29681311996625132631
, 0.29827726559833995487
, 0.29974070969779716372
, 0.30120344882267846546
, 0.30266547953269743633
, 0.30412679838923380754
, 0.30558740195534155260
, 0.30704728679575697109
, 0.30850644947690676793
, 0.30996488656691612926
, 0.31142259463561679375
, 0.31287957025455512039
, 0.31433580999700015194
, 0.31579131043795167442
, 0.31724606815414827259
, 0.31870007972407538119
, 0.32015334172797333228
, 0.32160585074784539821
, 0.32305760336746583073
, 0.32450859617238789556
, 0.32595882574995190320
, 0.32740828868929323524
, 0.32885698158135036651
, 0.33030490101887288303
, 0.33175204359642949576
, 0.33319840591041604988
, 0.33464398455906353000
, 0.33608877614244606080
, 0.33753277726248890367
, 0.33897598452297644865
, 0.34041839452956020222
, 0.34186000388976677062
, 0.34330080921300583881
, 0.34474080711057814486
, 0.34617999419568345009
, 0.34761836708342850461
, 0.34905592239083500843
, 0.35049265673684756799
, 0.35192856674234164835
, 0.35336364903013152059
, 0.35479790022497820486
, 0.35623131695359740867
, 0.35766389584466746080
, 0.35909563352883724043
, 0.36052652663873410157
, 0.36195657180897179315
, 0.36338576567615837404
, 0.36481410487890412371
, 0.36624158605782944798
, 0.36766820585557278005
, 0.36909396091679847702
, 0.37051884788820471127
, 0.37194286341853135736
, 0.37336600415856787397
, 0.37478826676116118116
, 0.37620964788122353251
, 0.37763014417574038284
, 0.37904975230377825062
, 0.38046846892649257570
, 0.38188629070713557225
, 0.38330321431106407636
, 0.38471923640574738916
, 0.38613435366077511468
, 0.38754856274786499281
, 0.38896186034087072724
, 0.39037424311578980838
, 0.39178570775077133125
, 0.39319625092612380833
, 0.39460586932432297722
, 0.39601455963001960339
, 0.39742231853004727761
, 0.39882914271343020843
, 0.40023502887139100935
, 0.40163997369735848097
, 0.40304397388697538781
, 0.40444702613810622996
, 0.40584912715084500964
, 0.40725027362752299235
, 0.40865046227271646276
, 0.41004968979325447548
, 0.41144795289822660032
, 0.41284524829899066242
, 0.41424157270918047697
, 0.41563692284471357851
, 0.41703129542379894492
, 0.41842468716694471612
, 0.41981709479696590714
, 0.42120851503899211604
, 0.42259894462047522601
, 0.42398838027119710250
, 0.42537681872327728439
, 0.42676425671118066996
, 0.42815069097172519730
, 0.42953611824408951901
, 0.43092053526982067169
, 0.43230393879284173943
, 0.43368632555945951210
, 0.43506769231837213777
, 0.43644803582067676962
, 0.43782735281987720730
, 0.43920564007189153233
, 0.44058289433505973812
, 0.44195911237015135425
, 0.44333429094037306482
, 0.44470842681137632134
, 0.44608151675126494966
, 0.44745355753060275133
, 0.44882454592242109899
, 0.45019447870222652601
, 0.45156335264800831041
, 0.45293116454024605282
, 0.45429791116191724858
, 0.45566358929850485411
, 0.45702819573800484721
, 0.45839172727093378153
, 0.45975418069033633517
, 0.46111555279179285320
, 0.46247584037342688432
, 0.46383504023591271150
, 0.46519314918248287665
, 0.46655016401893569924
, 0.46790608155364278887
, 0.46926089859755655185
, 0.47061461196421769163
, 0.47196721846976270323
, 0.47331871493293136154
, 0.47466909817507420342
, 0.47601836502016000373
, 0.47736651229478324520
, 0.47871353682817158220
, 0.48005943545219329803
, 0.48140420500136475642
, 0.48274784231285784641
, 0.48409034422650742131
, 0.48543170758481873111
, 0.48677192923297484881
, 0.48811100601884409040
, 0.48944893479298742848
, 0.49078571240866589957
, 0.49212133572184800506
, 0.49345580159121710592
, 0.49478910687817881077
, 0.49612124844686835779
, 0.49745222316415799001
, 0.49878202789966432441
, 0.50011065952575571429
, 0.50143811491755960533
, 0.50276439095296988517
, 0.50408948451265422642
, 0.50541339248006142312
, 0.50673611174142872086
, 0.50805763918578913989
, 0.50937797170497879228
, 0.51069710619364419194
, 0.51201503954924955847
, 0.51333176867208411381
, 0.51464729046526937293
, 0.51596160183476642749
, 0.51727469968938322251
, 0.51858658094078182729
, 0.51989724250348569849
, 0.52120668129488693720
, 0.52251489423525353912
, 0.52382187824773663795
, 0.52512763025837774192
, 0.52643214719611596344
, 0.52773542599279524241
, 0.52903746358317156200
, 0.53033825690492015820
, 0.53163780289864272227
, 0.53293609850787459597
, 0.53423314067909196052
, 0.53552892636171901824
, 0.53682345250813516741
, 0.53811671607368216983
, 0.53940871401667131202
, 0.54069944329839055908
, 0.54198890088311170140
, 0.54327708373809749468
, 0.54456398883360879263
, 0.54584961314291167300
, 0.54713395364228455608
, 0.54841700731102531642
, 0.54969877113145838740
, 0.55097924208894185851
, 0.55225841717187456589
, 0.55353629337170317506
, 0.55481286768292925734
, 0.55608813710311635827
, 0.55736209863289705940
, 0.55863474927598003245
, 0.55990608603915708664
, 0.56117610593231020852
, 0.56244480596841859432
, 0.56371218316356567563
, 0.56497823453694613724
, 0.56624295711087292774
, 0.56750634791078426313
, 0.56876840396525062262
, 0.57002912230598173741
, 0.57128849996783357182
, 0.57254653398881529729
, 0.57380322141009625883
, 0.57505855927601293387
, 0.57631254463407588403
, 0.57756517453497669914
, 0.57881644603259493372
, 0.58006635618400503640
, 0.58131490204948327126
, 0.58256208069251463205
, 0.58380788917979974865
, 0.58505232458126178610
, 0.58629538397005333592
, 0.58753706442256329993
, 0.58877736301842376651
, 0.59001627684051687902
, 0.59125380297498169685
, 0.59248993851122104846
, 0.59372468054190837721
, 0.59495802616299457905
, 0.59618997247371483282
, 0.59742051657659542258
, 0.59864965557746055240
, 0.59987738658543915328
, 0.60110370671297168235
, 0.60232861307581691418
, 0.60355210279305872458
, 0.60477417298711286605
, 0.60599482078373373601
, 0.60721404331202113660
, 0.60843183770442702717
, 0.60964820109676226838
, 0.61086313062820335869
, 0.61207662344129916301
, 0.61328867668197763300
, 0.61449928749955251989
, 0.61570845304673007923
, 0.61691617047961576733
, 0.61812243695772093005
, 0.61932724964396948357
, 0.62053060570470458703
, 0.62173250230969530702
, 0.62293293663214327423
, 0.62413190584868933193
, 0.62532940713942017629
, 0.62652543768787498889
, 0.62771999468105206055
, 0.62891307530941540765
, 0.63010467676690137985
, 0.63129479625092525992
, 0.63248343096238785513
, 0.63367057810568208073
, 0.63485623488869953504
, 0.63604039852283706622
, 0.63722306622300333117
, 0.63840423520762534565
, 0.63958390269865502651
, 0.64076206592157572558
, 0.64193872210540875504
, 0.64311386848271990483
, 0.64428750228962595130
, 0.64545962076580115782
, 0.64663022115448376691
, 0.64779930070248248401
, 0.64896685666018295277
, 0.65013288628155422222
, 0.65129738682415520492
, 0.65246035554914112741
, 0.65362178972126997161
, 0.65478168660890890808
, 0.65594004348404072056
, 0.65709685762227022223
, 0.65825212630283066334
, 0.65940584680859013026
, 0.66055801642605793596
, 0.66170863244539100228
, 0.66285769216040023300
, 0.66400519286855687892
, 0.66515113187099889384
, 0.66629550647253728231
, 0.66743831398166243859
, 0.66857955171055047681
, 0.66971921697506955272
, 0.67085730709478617645
, 0.67199381939297151697
, 0.67312875119660769746
, 0.67426209983639408220
, 0.67539386264675355456
, 0.67652403696583878644
, 0.67765262013553849847
, 0.67877960950148371212
, 0.67990500241305399244
, 0.68102879622338368228
, 0.68215098828936812750
, 0.68327157597166989330
, 0.68439055663472497218
, 0.68550792764674898220
, 0.68662368637974335720
, 0.68773783020950152742
, 0.68885035651561509157
, 0.68996126268147998006
, 0.69107054609430260887
, 0.69217820414510602490
, 0.69328423422873604207
, 0.69438863374386736844
, 0.69549140009300972455
, 0.69659253068251395240
, 0.69769202292257811575
, 0.69878987422725359114
, 0.69988608201445114972
, 0.70098064370594703059
, 0.70207355672738900427
, 0.70316481850830242760
, 0.70425442648209628943
, 0.70534237808606924694
, 0.70642867076141565305
, 0.70751330195323157478
, 0.70859626911052080189
, 0.70967756968620084707
, 0.71075720113710893621
, 0.71183516092400799002
, 0.71291144651159259611
, 0.71398605536849497194
, 0.71505898496729091828
, 0.71613023278450576382
, 0.71719979630062030018
, 0.71826767300007670752
, 0.71933386037128447128
, 0.72039835590662628913
, 0.72146115710246396880
, 0.72252226145914431643
, 0.72358166648100501574
, 0.72463936967638049776
, 0.72569536855760780086
, 0.72674966064103242177
, 0.72780224344701415694
, 0.72885311449993293474
, 0.72990227132819463749
, 0.73094971146423691515
, 0.73199543244453498843
, 0.73303943180960744305
, 0.73408170710402201428
, 0.73512225587640136207
, 0.73616107567942883641
, 0.73719816406985423342
, 0.73823351860849954168
, 0.73926713686026467915
, 0.74029901639413322014
, 0.74132915478317811339
, 0.74235754960456738950
, 0.74338419843956985984
, 0.74440909887356080499
, 0.74543224849602765373
, 0.74645364490057565282
, 0.74747328568493352628
, 0.74849116845095912563
, 0.74950729080464507031
, 0.75052165035612437795
, 0.75153424471967608542
, 0.75254507151373085998
, 0.75355412836087660045
, 0.75456141288786402876
, 0.75556692272561227179
, 0.75657065550921443348
, 0.75757260887794315653
, 0.75857278047525617513
, 0.75957116794880185723
, 0.76056776895042473718
, 0.76156258113617103847
, 0.76255560216629418666
, 0.76354682970526031215
, 0.76453626142175374345
, 0.76552389498868249020
, 0.76650972808318371642
, 0.76749375838662920363
, 0.76847598358463080435
, 0.76945640136704588529
, 0.77043500942798276074
, 0.77141180546580611586
, 0.77238678718314241996
, 0.77335995228688533002
, 0.77433129848820108363
, 0.77530082350253388252
, 0.77626852504961126549
, 0.77723440085344947176
, 0.77819844864235879353
, 0.77916066614894891935
, 0.78012105111013426654
, 0.78107960126713930416
, 0.78203631436550386522
, 0.78299118815508844926
, 0.78394422039007951458
, 0.78489540882899476015
, 0.78584475123468839741
, 0.78679224537435641219
, 0.78773788901954181591
, 0.78868167994613988693
, 0.78962361593440340128
, 0.79056369476894785387
, 0.79150191423875666835
, 0.79243827213718639790
, 0.79337276626197191469
, 0.79430539441523158973
, 0.79523615440347246214
, 0.79616504403759539801
, 0.79709206113290023921
, 0.79801720350909094166
, 0.79894046899028070308
, 0.79986185540499708091
, 0.80078136058618709913
, 0.80169898237122234539
, 0.80261471860190405713
, 0.80352856712446819773
, 0.80444052578959052190
, 0.80535059245239163094
, 0.80625876497244201732
, 0.80716504121376709879
, 0.80806941904485224220
, 0.80897189633864777659
, 0.80987247097257399596
, 0.81077114082852615157
, 0.81166790379287943337
, 0.81256275775649394136
, 0.81345570061471964609
, 0.81434673026740133869
, 0.81523584461888357028
, 0.81612304157801558095
, 0.81700831905815621796
, 0.81789167497717884338
, 0.81877310725747623130
, 0.81965261382596545401
, 0.82053019261409275805
, 0.82140584155783842916
, 0.82227955859772164674
, 0.82315134167880532780
, 0.82402118875070095991
, 0.82488909776757342372
, 0.82575506668814580447
, 0.82661909347570419320
, 0.82748117609810247695
, 0.82834131252776711807
, 0.82919950074170192312
, 0.83005573872149280104
, 0.83091002445331250986
, 0.83176235592792539353
, 0.83261273114069210750
, 0.83346114809157433338
, 0.83430760478513948291
, 0.83515209923056539130
, 0.83599462944164499933
, 0.83683519343679102509
, 0.83767378923904062417
, 0.83851041487606003971
, 0.83934506838014924117
, 0.84017774778824655201
, 0.84100845114193326709
, 0.84183717648743825850
, 0.84266392187564257072
, 0.84348868536208400511
, 0.84431146500696169281
, 0.84513225887514065746
, 0.84595106503615636608
, 0.84676788156421926981
, 0.84758270653821933321
, 0.84839553804173055228
, 0.84920637416301546224
, 0.85001521299502963360
, 0.85082205263542615733
, 0.85162689118656011936
, 0.85242972675549306358
, 0.85323055745399744388
, 0.85402938139856106531
, 0.85482619671039151391
, 0.85562100151542057542
, 0.85641379394430864334
, 0.85720457213244911519
, 0.85799333421997277797
, 0.85878007835175218277
, 0.85956480267740600763
, 0.86034750535130340973
, 0.86112818453256836606
, 0.86190683838508400322
, 0.86268346507749691575
, 0.86345806278322147345
, 0.86423062968044411742
, 0.86500116395212764479
, 0.86576966378601548239
, 0.86653612737463594909
, 0.86730055291530650668
, 0.86806293861013800005
, 0.86882328266603888530
, 0.86958158329471944739
, 0.87033783871269600587
, 0.87109204714129510958
, 0.87184420680665772015
, 0.87259431593974338368
, 0.87334237277633439183
, 0.87408837555703993089
, 0.87483232252730021988
, 0.87557421193739063732
, 0.87631404204242583614
, 0.87705181110236384788
, 0.87778751738201017500
, 0.87852115915102187214
, 0.87925273468391161558
, 0.87998224226005176171
, 0.88070968016367839361
, 0.88143504668389535673
, 0.88215834011467828251
, 0.88287955875487860130
, 0.88359870090822754279
, 0.88431576488334012601
, 0.88503074899371913733
, 0.88574365155775909667
, 0.88645447089875021305
, 0.88716320534488232768
, 0.88786985322924884620
, 0.88857441288985065914
, 0.88927688266960005082
, 0.88997726091632459682
, 0.89067554598277104953
, 0.89137173622660921275
, 0.89206583001043580423
, 0.89275782570177830672
, 0.89344772167309880742
, 0.89413551630179782592
, 0.89482120797021813064
, 0.89550479506564854316
, 0.89618627598032773150
, 0.89686564911144799121
, 0.89754291286115901543
, 0.89821806563657165267
, 0.89889110584976165340
, 0.89956203191777340459
, 0.90023084226262365293
, 0.90089753531130521594
, 0.90156210949579068187
, 0.90222456325303609730
, 0.90288489502498464368
, 0.90354310325857030146
, 0.90419918640572150313
, 0.90485314292336477401
, 0.90550497127342836152
, 0.90615466992284585270
, 0.90680223734355977976
, 0.90744767201252521426
, 0.90809097241171334887
, 0.90873213702811506798
, 0.90937116435374450624
, 0.91000805288564259497
, 0.91064280112588059728
, 0.91127540758156363109
, 0.91190587076483418033
, 0.91253418919287559421
, 0.91316036138791557494
, 0.91378438587722965312
, 0.91440626119314465168
, 0.91502598587304213770
, 0.91564355845936186244
, 0.91625897749960518948
, 0.91687224154633851088
, 0.91748334915719665142
, 0.91809229889488626103
, 0.91869908932718919521
, 0.91930371902696588366
, 0.91990618657215868654
, 0.92050649054579523943
, 0.92110462953599178562
, 0.92170060213595649711
, 0.92229440694399278307
, 0.92288604256350258680
, 0.92347550760298967011
, 0.92406280067606288644
, 0.92464792040143944127
, 0.92523086540294814098
, 0.92581163430953262951
, 0.92639022575525461302
, 0.92696663837929707238
, 0.92754087082596746401
, 0.92811292174470090815
, 0.92868278979006336539
, 0.92925047362175480108
, 0.92981597190461233768
, 0.93037928330861339494
, 0.93094040650887881807
, 0.93149934018567599373
, 0.93205608302442195405
, 0.93261063371568646844
, 0.93316299095519512333
, 0.93371315344383238959
, 0.93426111988764467826
, 0.93480688899784338360
, 0.93535045949080791445
, 0.93589183008808871312
, 0.93643099951641026228
, 0.93696796650767407956
, 0.93750272979896170016
, 0.93803528813253764728
, 0.93856564025585238986
, 0.93909378492154528886
, 0.93961972088744753089
, 0.94014344691658504976
, 0.94066496177718143557
, 0.94118426424266083216
, 0.94170135309165082155
, 0.94221622710798529684
, 0.94272888508070732240
, 0.94323932580407198216
, 0.94374754807754921516
, 0.94425355070582663952
, 0.94475733249881236340
, 0.94525889227163778419
, 0.94575822884466037533
, 0.94625534104346646061
, 0.94675022769887397651
, 0.94724288764693522185
, 0.94773331972893959548
, 0.94822152279141632151
, 0.94870749568613716210
, 0.94919123727011911815
, 0.94967274640562711742
, 0.95015202196017669065
, 0.95062906280653663478
, 0.95110386782273166438
, 0.95157643589204505045
, 0.95204676590302124672
, 0.95251485674946850400
, 0.95298070733046147157
, 0.95344431655034378686
, 0.95390568331873065201
, 0.95436480655051139866
, 0.95482168516585203997
, 0.95527631809019781031
, 0.95572870425427569266
, 0.95617884259409693346
, 0.95662673205095954482
, 0.95707237157145079497
, 0.95751576010744968544
, 0.95795689661612941639
, 0.95839578005995983926
, 0.95883240940670989687
, 0.95926678362945005132
, 0.95969890170655469924
, 0.96012876262170457461
, 0.96055636536388913893
, 0.96098170892740895931
, 0.96140479231187807367
, 0.96182561452222634362
, 0.96224417456870179482
, 0.96266047146687294488
, 0.96307450423763111863
, 0.96348627190719275096
, 0.96389577350710167698
, 0.96430300807423141005
, 0.96470797465078740677
, 0.96511067228430931974
, 0.96551110002767323771
, 0.96590925693909391317
, 0.96630514208212697736
, 0.96669875452567114268
, 0.96709009334397039279
, 0.96747915761661615970
, 0.96786594642854948870
, 0.96825045887006319032
, 0.96863269403680398026
, 0.96901265102977460604
, 0.96939032895533596156
, 0.96976572692520918888
, 0.97013884405647776742
, 0.97050967947158959051
, 0.97087823229835902919
, 0.97124450166996898392
, 0.97160848672497292298
, 0.97197018660729690861
, 0.97232960046624161048
, 0.97268672745648430657
, 0.97304156673808087113
, 0.97339411747646775036
, 0.97374437884246392528
, 0.97409235001227286165
, 0.97443803016748444798
, 0.97478141849507691976
, 0.97512251418741877225
, 0.97546131644227065965
, 0.97579782446278728197
, 0.97613203745751925917
, 0.97646395464041499271
, 0.97679357523082251423
, 0.97712089845349132152
, 0.97744592353857420215
, 0.97776864972162904369
, 0.97808907624362063194
, 0.97840720235092243617
, 0.97872302729531838143
, 0.97903655033400460841
, 0.97934777072959122046
, 0.97965668775010401789
, 0.97996330066898621960
, 0.98026760876510017178
, 0.98056961132272904417
, 0.98086930763157851318
, 0.98116669698677843258
, 0.98146177868888449141
, 0.98175455204387985885
, 0.98204501636317681663
, 0.98233317096361837855
, 0.98261901516747989714
, 0.98290254830247065782
, 0.98318376970173545999
, 0.98346267870385618523
, 0.98373927465285335343
, 0.98401355689818766504
, 0.98428552479476153164
, 0.98455517770292059278
, 0.98482251498845522060
, 0.98508753602260201151
, 0.98535024018204526482
, 0.98561062684891844897
, 0.98586869541080565454
, 0.98612444526074303477
, 0.98637787579722023312
, 0.98662898642418179779
, 0.98687777655102858383
, 0.98712424559261914217
, 0.98736839296927109578
, 0.98761021810676250313
, 0.98784972043633320870
, 0.98808689939468618066
, 0.98832175442398883576
, 0.98855428497187435147
, 0.98878449049144296484
, 0.98901237044126325898
, 0.98923792428537343655
, 0.98946115149328258017
, 0.98968205153997190017
, 0.98990062390589596953
, 0.99011686807698394565
, 0.99033078354464077977
, 0.99054236980574841278
, 0.99075162636266695868
, 0.99095855272323587532
, 0.99116314840077512151
, 0.99136541291408630209
, 0.99156534578745379938
, 0.99176294655064589233
, 0.99195821473891586238
, 0.99215114989300308673
, 0.99234175155913411829
, 0.99253001928902375312
, 0.99271595263987608490
, 0.99289955117438554632
, 0.99308081446073793758
, 0.99325974207261144236
, 0.99343633358917763021
, 0.99361058859510244674
, 0.99378250668054719032
, 0.99395208744116947625
, 0.99411933047812418770
, 0.99428423539806441407
, 0.99444680181314237626
, 0.99460702934101033874
, 0.99476491760482150937
, 0.99492046623323092565
, 0.99507367486039632838
, 0.99522454312597902237
, 0.99537307067514472407
, 0.99551925715856439650
, 0.99566310223241507124
, 0.99580460555838065716
, 0.99594376680365273694
, 0.99608058564093134984
, 0.99621506174842576221
, 0.99634719480985522490
, 0.99647698451444971751
, 0.99660443055695068052
, 0.99672953263761173348
, 0.99685229046219938129
, 0.99697270374199370722
, 0.99709077219378905302
, 0.99720649553989468641
, 0.99731987350813545599
, 0.99743090583185243283
, 0.99753959224990354000
, 0.99764593250666416916
, 0.99774992635202778440
, 0.99785157354140651396
, 0.99795087383573172923
, 0.99804782700145461152
, 0.99814243281054670676
, 0.99823469104050046777
, 0.99832460147432978558
, 0.99841216390057050805
, 0.99849737811328094831
, 0.99858024391204238172
, 0.99866076110195953290
, 0.99873892949366105279
, 0.99881474890329998741
, 0.99888821915255423839
, 0.99895934006862701791
, 0.99902811148424729875
, 0.99909453323767026328
, 0.99915860517267775335
, 0.99922032713857872734
, 0.99927969899020972929
, 0.99933672058793537982
, 0.99939139179764890100
, 0.99944371249077269256
, 0.99949368254425898503
, 0.99954130184059060692
, 0.99958657026778192163
, 0.99962948771938001796
, 0.99967005409446628531
, 0.99970826929765858047
, 0.99974413323911432344
, 0.99977764583453508705
, 0.99980880700517365482
, 0.99983761667784529502
, 0.99986407478494651125
, 0.99988818126448765630
, 0.99990993606015263391
, 0.99992933912141495684
, 0.99994639040378036792
, 0.99996108986934204845
, 0.99997343748820805167
, 0.99998343324279355729
, 0.99999107714397238839
, 0.99999636931774495781
, 0.99999931092710532960
};
DB GLw[2048]={
 0.000001768383366665995
,0.000004116455830582231
,0.000006467995475736767
,0.000008819821897850314
,0.000011171688205646537
,0.000013523546398357259
,0.000015875379685302326
,0.000018227178707393919
,0.000020578936393340612
,0.000022930646511857619
,0.000025282303182626151
,0.000027633900687265033
,0.000029985433388250774
,0.000032336895691130890
,0.000034688282025679520
,0.000037039586835954831
,0.000039390804574797830
,0.000041741929700662707
,0.000044092956675726209
,0.000046443879964725560
,0.000048794694034225887
,0.000051145393352148338
,0.000053495972387460550
,0.000055846425609970998
,0.000058196747490190880
,0.000060546932499241067
,0.000062896975108789436
,0.000065246869791009321
,0.000067596611018552416
,0.000069946193264532207
,0.000072295611002514791
,0.000074644858706515042
,0.000076993930850996860
,0.000079342821910876271
,0.000081691526361526759
,0.000084040038678786248
,0.000086388353338965392
,0.000088736464818856788
,0.000091084367595744955
,0.000093432056147416970
,0.000095779524952173406
,0.000098126768488839803
,0.000100473781236778381
,0.000102820557675899872
,0.000105167092286675675
,0.000107513379550150122
,0.000109859413947952814
,0.000112205189962311112
,0.000114550702076062706
,0.000116895944772668195
,0.000119240912536223753
,0.000121585599851473924
,0.000123930001203824281
,0.000126274111079354244
,0.000128617923964829893
,0.000130961434347716812
,0.000133304636716192900
,0.000135647525559161239
,0.000137990095366262988
,0.000140332340627890276
,0.000142674255835199034
,0.000145015835480121958
,0.000147357074055381366
,0.000149697966054502139
,0.000152038505971824638
,0.000154378688302517523
,0.000156718507542590848
,0.000159057958188908796
,0.000161397034739202716
,0.000163735731692084014
,0.000166074043547057034
,0.000168411964804532019
,0.000170749489965838030
,0.000173086613533235835
,0.000175423330009930885
,0.000177759633900086164
,0.000180095519708835125
,0.000182430981942294658
,0.000184766015107577911
,0.000187100613712807289
,0.000189434772267127312
,0.000191768485280717554
,0.000194101747264805500
,0.000196434552731679532
,0.000198766896194701736
,0.000201098772168320877
,0.000203430175168085297
,0.000205761099710655715
,0.000208091540313818265
,0.000210421491496497273
,0.000212750947778768182
,0.000215079903681870466
,0.000217408353728220475
,0.000219736292441424321
,0.000222063714346290807
,0.000224390613968844195
,0.000226716985836337230
,0.000229042824477263845
,0.000231368124421372171
,0.000233692880199677299
,0.000236017086344474215
,0.000238340737389350614
,0.000240663827869199771
,0.000242986352320233376
,0.000245308305279994427
,0.000247629681287370032
,0.000249950474882604282
,0.000252270680607311064
,0.000254590293004486941
,0.000256909306618523908
,0.000259227715995222332
,0.000261545515681803692
,0.000263862700226923428
,0.000266179264180683798
,0.000268495202094646612
,0.000270810508521846156
,0.000273125178016801894
,0.000275439205135531350
,0.000277752584435562904
,0.000280065310475948544
,0.000282377377817276719
,0.000284688781021685099
,0.000286999514652873355
,0.000289309573276115996
,0.000291618951458275091
,0.000293927643767813085
,0.000296235644774805566
,0.000298542949050954024
,0.000300849551169598638
,0.000303155445705731005
,0.000305460627236006953
,0.000307765090338759231
,0.000310068829594010309
,0.000312371839583485129
,0.000314674114890623800
,0.000316975650100594392
,0.000319276439800305610
,0.000321576478578419612
,0.000323875761025364651
,0.000326174281733347848
,0.000328472035296367889
,0.000330769016310227729
,0.000333065219372547368
,0.000335360639082776464
,0.000337655270042207095
,0.000339949106853986446
,0.000342242144123129480
,0.000344534376456531668
,0.000346825798462981638
,0.000349116404753173848
,0.000351406189939721299
,0.000353695148637168194
,0.000355983275462002574
,0.000358270565032669010
,0.000360557011969581261
,0.000362842610895134912
,0.000365127356433720004
,0.000367411243211733759
,0.000369694265857593085
,0.000371976419001747343
,0.000374257697276690894
,0.000376538095316975740
,0.000378817607759224163
,0.000381096229242141336
,0.000383373954406527881
,0.000385650777895292562
,0.000387926694353464806
,0.000390201698428207361
,0.000392475784768828804
,0.000394748948026796219
,0.000397021182855747712
,0.000399292483911505035
,0.000401562845852086079
,0.000403832263337717519
,0.000406100731030847332
,0.000408368243596157351
,0.000410634795700575842
,0.000412900382013289990
,0.000415164997205758497
,0.000417428635951724091
,0.000419691292927226030
,0.000421952962810612673
,0.000424213640282553955
,0.000426473320026053904
,0.000428731996726463172
,0.000430989665071491477
,0.000433246319751220218
,0.000435501955458114781
,0.000437756566887037193
,0.000440010148735258507
,0.000442262695702471294
,0.000444514202490802133
,0.000446764663804824007
,0.000449014074351568839
,0.000451262428840539885
,0.000453509721983724209
,0.000455755948495605085
,0.000458001103093174456
,0.000460245180495945358
,0.000462488175425964333
,0.000464730082607823838
,0.000466970896768674643
,0.000469210612638238285
,0.000471449224948819397
,0.000473686728435318110
,0.000475923117835242497
,0.000478158387888720879
,0.000480392533338514196
,0.000482625548930028454
,0.000484857429411326985
,0.000487088169533142857
,0.000489317764048891203
,0.000491546207714681549
,0.000493773495289330186
,0.000495999621534372446
,0.000498224581214075063
,0.000500448369095448477
,0.000502670979948259109
,0.000504892408545041722
,0.000507112649661111679
,0.000509331698074577205
,0.000511549548566351735
,0.000513766195920166149
,0.000515981634922581016
,0.000518195860362998927
,0.000520408867033676678
,0.000522620649729737547
,0.000524831203249183561
,0.000527040522392907684
,0.000529248601964706080
,0.000531455436771290322
,0.000533661021622299589
,0.000535865351330312914
,0.000538068420710861335
,0.000540270224582440149
,0.000542470757766521043
,0.000544670015087564281
,0.000546867991373030930
,0.000549064681453394941
,0.000551260080162155387
,0.000553454182335848569
,0.000555646982814060177
,0.000557838476439437385
,0.000560028658057701067
,0.000562217522517657859
,0.000564405064671212258
,0.000566591279373378771
,0.000568776161482294021
,0.000570959705859228794
,0.000573141907368600156
,0.000575322760877983557
,0.000577502261258124829
,0.000579680403382952311
,0.000581857182129588911
,0.000584032592378364105
,0.000586206629012825994
,0.000588379286919753405
,0.000590550560989167794
,0.000592720446114345376
,0.000594888937191829054
,0.000597056029121440495
,0.000599221716806292065
,0.000601385995152798857
,0.000603548859070690645
,0.000605710303473023862
,0.000607870323276193572
,0.000610028913399945425
,0.000612186068767387599
,0.000614341784305002763
,0.000616496054942659954
,0.000618648875613626556
,0.000620800241254580221
,0.000622950146805620722
,0.000625098587210281909
,0.000627245557415543571
,0.000629391052371843339
,0.000631535067033088544
,0.000633677596356668093
,0.000635818635303464339
,0.000637958178837864897
,0.000640096221927774562
,0.000642232759544627061
,0.000644367786663396924
,0.000646501298262611297
,0.000648633289324361745
,0.000650763754834316054
,0.000652892689781730045
,0.000655020089159459329
,0.000657145947963971091
,0.000659270261195355886
,0.000661393023857339359
,0.000663514230957294015
,0.000665633877506250972
,0.000667751958518911664
,0.000669868469013659607
,0.000671983404012572071
,0.000674096758541431831
,0.000676208527629738838
,0.000678318706310721898
,0.000680427289621350408
,0.000682534272602345960
,0.000684639650298194068
,0.000686743417757155767
,0.000688845570031279299
,0.000690946102176411730
,0.000693045009252210601
,0.000695142286322155506
,0.000697237928453559750
,0.000699331930717581920
,0.000701424288189237493
,0.000703514995947410389
,0.000705604049074864607
,0.000707691442658255711
,0.000709777171788142455
,0.000711861231558998281
,0.000713943617069222898
,0.000716024323421153770
,0.000718103345721077678
,0.000720180679079242172
,0.000722256318609867132
,0.000724330259431156208
,0.000726402496665308365
,0.000728473025438529279
,0.000730541840881042850
,0.000732608938127102656
,0.000734674312315003369
,0.000736737958587092194
,0.000738799872089780329
,0.000740860047973554349
,0.000742918481392987601
,0.000744975167506751638
,0.000747030101477627562
,0.000749083278472517464
,0.000751134693662455710
,0.000753184342222620364
,0.000755232219332344497
,0.000757278320175127553
,0.000759322639938646658
,0.000761365173814767928
,0.000763405916999557823
,0.000765444864693294395
,0.000767482012100478603
,0.000769517354429845587
,0.000771550886894375947
,0.000773582604711306960
,0.000775612503102143897
,0.000777640577292671189
,0.000779666822512963735
,0.000781691233997398038
,0.000783713806984663472
,0.000785734536717773450
,0.000787753418444076635
,0.000789770447415268085
,0.000791785618887400472
,0.000793798928120895191
,0.000795810370380553523
,0.000797819940935567781
,0.000799827635059532428
,0.000801833448030455195
,0.000803837375130768203
,0.000805839411647339001
,0.000807839552871481749
,0.000809837794098968174
,0.000811834130630038752
,0.000813828557769413684
,0.000815821070826303944
,0.000817811665114422366
,0.000819800335951994590
,0.000821787078661770140
,0.000823771888571033379
,0.000825754761011614524
,0.000827735691319900623
,0.000829714674836846506
,0.000831691706907985759
,0.000833666782883441674
,0.000835639898117938167
,0.000837611047970810730
,0.000839580227806017317
,0.000841547432992149268
,0.000843512658902442192
,0.000845475900914786847
,0.000847437154411740038
,0.000849396414780535414
,0.000851353677413094415
,0.000853308937706036987
,0.000855262191060692535
,0.000857213432883110636
,0.000859162658584071907
,0.000861109863579098782
,0.000863055043288466260
,0.000864998193137212747
,0.000866939308555150753
,0.000868878384976877657
,0.000870815417841786476
,0.000872750402594076547
,0.000874683334682764260
,0.000876614209561693777
,0.000878543022689547698
,0.000880469769529857759
,0.000882394445551015507
,0.000884317046226282920
,0.000886237567033803132
,0.000888156003456610961
,0.000890072350982643604
,0.000891986605104751279
,0.000893898761320707725
,0.000895808815133220873
,0.000897716762049943392
,0.000899622597583483270
,0.000901526317251414350
,0.000903427916576286874
,0.000905327391085638045
,0.000907224736312002496
,0.000909119947792922833
,0.000911013021070960124
,0.000912903951693704368
,0.000914792735213784987
,0.000916679367188881283
,0.000918563843181732865
,0.000920446158760150107
,0.000922326309497024578
,0.000924204290970339409
,0.000926080098763179765
,0.000927953728463743176
,0.000929825175665349911
,0.000931694435966453413
,0.000933561504970650555
,0.000935426378286692048
,0.000937289051528492750
,0.000939149520315141965
,0.000941007780270913768
,0.000942863827025277301
,0.000944717656212907013
,0.000946569263473692987
,0.000948418644452751151
,0.000950265794800433517
,0.000952110710172338441
,0.000953953386229320833
,0.000955793818637502318
,0.000957632003068281514
,0.000959467935198344158
,0.000961301610709673236
,0.000963133025289559229
,0.000964962174630610198
,0.000966789054430761934
,0.000968613660393288057
,0.000970435988226810143
,0.000972256033645307812
,0.000974073792368128797
,0.000975889260119999030
,0.000977702432631032679
,0.000979513305636742203
,0.000981321874878048377
,0.000983128136101290322
,0.000984932085058235472
,0.000986733717506089611
,0.000988533029207506832
,0.000990330015930599492
,0.000992124673448948190
,0.000993916997541611678
,0.000995706983993136808
,0.000997494628593568469
,0.000999279927138459423
,0.001001062875428880230
,0.001002843469271429188
,0.001004621704478242055
,0.001006397576867002018
,0.001008171082260949527
,0.001009942216488891992
,0.001011710975385213748
,0.001013477354789885762
,0.001015241350548475452
,0.001017002958512156457
,0.001018762174537718356
,0.001020518994487576456
,0.001022273414229781525
,0.001024025429638029473
,0.001025775036591671093
,0.001027522230975721721
,0.001029267008680870960
,0.001031009365603492285
,0.001032749297645652740
,0.001034486800715122573
,0.001036221870725384828
,0.001037954503595644999
,0.001039684695250840585
,0.001041412441621650707
,0.001043137738644505671
,0.001044860582261596521
,0.001046580968420884574
,0.001048298893076110977
,0.001050014352186806183
,0.001051727341718299509
,0.001053437857641728566
,0.001055145895934048779
,0.001056851452578042821
,0.001058554523562330088
,0.001060255104881376097
,0.001061953192535501951
,0.001063648782530893716
,0.001065341870879611802
,0.001067032453599600391
,0.001068720526714696757
,0.001070406086254640656
,0.001072089128255083611
,0.001073769648757598260
,0.001075447643809687739
,0.001077123109464794824
,0.001078796041782311376
,0.001080466436827587485
,0.001082134290671940796
,0.001083799599392665726
,0.001085462359073042677
,0.001087122565802347270
,0.001088780215675859556
,0.001090435304794873139
,0.001092087829266704407
,0.001093737785204701657
,0.001095385168728254257
,0.001097029975962801743
,0.001098672203039842958
,0.001100311846096945149
,0.001101948901277753014
,0.001103583364731997850
,0.001105215232615506509
,0.001106844501090210526
,0.001108471166324155096
,0.001110095224491508097
,0.001111716671772569119
,0.001113335504353778373
,0.001114951718427725762
,0.001116565310193159731
,0.001118176275854996304
,0.001119784611624327942
,0.001121390313718432457
,0.001122993378360781980
,0.001124593801781051739
,0.001126191580215129004
,0.001127786709905121917
,0.001129379187099368329
,0.001130969008052444601
,0.001132556169025174462
,0.001134140666284637777
,0.001135722496104179294
,0.001137301654763417478
,0.001138878138548253204
,0.001140451943750878519
,0.001142023066669785350
,0.001143591503609774226
,0.001145157250881962956
,0.001146720304803795305
,0.001148280661699049644
,0.001149838317897847657
,0.001151393269736662861
,0.001152945513558329335
,0.001154495045712050257
,0.001156041862553406510
,0.001157585960444365245
,0.001159127335753288457
,0.001160665984854941500
,0.001162201904130501609
,0.001163735089967566477
,0.001165265538760162653
,0.001166793246908754109
,0.001168318210820250641
,0.001169840426908016361
,0.001171359891591878125
,0.001172876601298133937
,0.001174390552459561360
,0.001175901741515425946
,0.001177410164911489534
,0.001178915819100018665
,0.001180418700539792921
,0.001181918805696113246
,0.001183416131040810233
,0.001184910673052252496
,0.001186402428215354844
,0.001187891393021586645
,0.001189377563968980051
,0.001190860937562138196
,0.001192341510312243465
,0.001193819278737065670
,0.001195294239360970249
,0.001196766388714926470
,0.001198235723336515510
,0.001199702239769938707
,0.001201165934566025581
,0.001202626804282242026
,0.001204084845482698377
,0.001205540054738157481
,0.001206992428626042773
,0.001208441963730446342
,0.001209888656642136901
,0.001211332503958567928
,0.001212773502283885522
,0.001214211648228936486
,0.001215646938411276311
,0.001217079369455177035
,0.001218508937991635265
,0.001219935640658380083
,0.001221359474099880947
,0.001222780434967355573
,0.001224198519918777823
,0.001225613725618885586
,0.001227026048739188568
,0.001228435485957976172
,0.001229842033960325297
,0.001231245689438108111
,0.001232646449089999853
,0.001234044309621486618
,0.001235439267744873049
,0.001236831320179290124
,0.001238220463650702821
,0.001239606694891917897
,0.001240990010642591488
,0.001242370407649236813
,0.001243747882665231834
,0.001245122432450826882
,0.001246494053773152282
,0.001247862743406225948
,0.001249228498130960960
,0.001250591314735173189
,0.001251951190013588762
,0.001253308120767851694
,0.001254662103806531347
,0.001256013135945129964
,0.001257361214006090146
,0.001258706334818802340
,0.001260048495219612269
,0.001261387692051828413
,0.001262723922165729409
,0.001264057182418571441
,0.001265387469674595657
,0.001266714780805035572
,0.001268039112688124363
,0.001269360462209102228
,0.001270678826260223763
,0.001271994201740765212
,0.001273306585557031786
,0.001274615974622364934
,0.001275922365857149610
,0.001277225756188821508
,0.001278526142551874267
,0.001279823521887866751
,0.001281117891145430144
,0.001282409247280275207
,0.001283697587255199427
,0.001284982908040094090
,0.001286265206611951513
,0.001287544479954872051
,0.001288820725060071305
,0.001290093938925887062
,0.001291364118557786473
,0.001292631260968373046
,0.001293895363177393647
,0.001295156422211745579
,0.001296414435105483496
,0.001297669398899826451
,0.001298921310643164780
,0.001300170167391067122
,0.001301415966206287291
,0.001302658704158771191
,0.001303898378325663739
,0.001305134985791315697
,0.001306368523647290547
,0.001307598988992371350
,0.001308826378932567539
,0.001310050690581121756
,0.001311271921058516600
,0.001312490067492481446
,0.001313705127017999163
,0.001314917096777312889
,0.001316125973919932710
,0.001317331755602642401
,0.001318534438989506090
,0.001319734021251874939
,0.001320930499568393776
,0.001322123871125007787
,0.001323314133114969064
,0.001324501282738843248
,0.001325685317204516099
,0.001326866233727200083
,0.001328044029529440891
,0.001329218701841123963
,0.001330390247899481101
,0.001331558664949096803
,0.001332723950241914900
,0.001333886101037244912
,0.001335045114601768557
,0.001336200988209546144
,0.001337353719142023012
,0.001338503304688035874
,0.001339649742143819284
,0.001340793028813011897
,0.001341933162006662860
,0.001343070139043238153
,0.001344203957248626848
,0.001345334613956147436
,0.001346462106506554101
,0.001347586432248042916
,0.001348707588536258168
,0.001349825572734298518
,0.001350940382212723215
,0.001352052014349558293
,0.001353160466530302708
,0.001354265736147934541
,0.001355367820602917058
,0.001356466717303204891
,0.001357562423664250104
,0.001358654937109008242
,0.001359744255067944462
,0.001360830374979039515
,0.001361913294287795806
,0.001362993010447243375
,0.001364069520917945921
,0.001365142823168006740
,0.001366212914673074712
,0.001367279792916350213
,0.001368343455388591045
,0.001369403899588118331
,0.001370461123020822424
,0.001371515123200168721
,0.001372565897647203575
,0.001373613443890560086
,0.001374657759466463895
,0.001375698841918739039
,0.001376736688798813680
,0.001377771297665725877
,0.001378802666086129331
,0.001379830791634299104
,0.001380855671892137322
,0.001381877304449178860
,0.001382895686902597033
,0.001383910816857209213
,0.001384922691925482506
,0.001385931309727539317
,0.001386936667891162957
,0.001387938764051803282
,0.001388937595852582193
,0.001389933160944299171
,0.001390925456985436855
,0.001391914481642166510
,0.001392900232588353534
,0.001393882707505562907
,0.001394861904083064689
,0.001395837820017839362
,0.001396810453014583409
,0.001397779800785714523
,0.001398745861051377101
,0.001399708631539447628
,0.001400668109985539892
,0.001401624294133010463
,0.001402577181732963902
,0.001403526770544258090
,0.001404473058333509474
,0.001405416042875098324
,0.001406355721951174014
,0.001407292093351660176
,0.001408225154874259913
,0.001409154904324461006
,0.001410081339515541068
,0.001411004458268572636
,0.001411924258412428394
,0.001412840737783786172
,0.001413753894227134123
,0.001414663725594775719
,0.001415570229746834857
,0.001416473404551260877
,0.001417373247883833560
,0.001418269757628168145
,0.001419162931675720277
,0.001420052767925791024
,0.001420939264285531744
,0.001421822418669949068
,0.001422702229001909753
,0.001423578693212145614
,0.001424451809239258379
,0.001425321575029724509
,0.001426187988537900052
,0.001427051047726025447
,0.001427910750564230335
,0.001428767095030538293
,0.001429620079110871642
,0.001430469700799056151
,0.001431315958096825717
,0.001432158849013827177
,0.001432998371567624882
,0.001433834523783705398
,0.001434667303695482150
,0.001435496709344300055
,0.001436322738779440136
,0.001437145390058124057
,0.001437964661245518767
,0.001438780550414740987
,0.001439593055646861799
,0.001440402175030911094
,0.001441207906663882128
,0.001442010248650735959
,0.001442809199104405922
,0.001443604756145802062
,0.001444396917903815546
,0.001445185682515323086
,0.001445971048125191283
,0.001446753012886281043
,0.001447531574959451865
,0.001448306732513566205
,0.001449078483725493772
,0.001449846826780115812
,0.001450611759870329378
,0.001451373281197051596
,0.001452131388969223850
,0.001452886081403816069
,0.001453637356725830844
,0.001454385213168307659
,0.001455129648972327001
,0.001455870662387014568
,0.001456608251669545274
,0.001457342415085147473
,0.001458073150907106949
,0.001458800457416771008
,0.001459524332903552533
,0.001460244775664933982
,0.001460961784006471428
,0.001461675356241798485
,0.001462385490692630344
,0.001463092185688767660
,0.001463795439568100528
,0.001464495250676612364
,0.001465191617368383800
,0.001465884538005596547
,0.001466574010958537271
,0.001467260034605601412
,0.001467942607333297001
,0.001468621727536248439
,0.001469297393617200290
,0.001469969603987021034
,0.001470638357064706824
,0.001471303651277385153
,0.001471965485060318607
,0.001472623856856908497
,0.001473278765118698585
,0.001473930208305378658
,0.001474578184884788173
,0.001475222693332919904
,0.001475863732133923459
,0.001476501299780108882
,0.001477135394771950190
,0.001477766015618088916
,0.001478393160835337593
,0.001479016828948683243
,0.001479637018491290882
,0.001480253728004506919
,0.001480866956037862611
,0.001481476701149077512
,0.001482082961904062777
,0.001482685736876924623
,0.001483285024649967618
,0.001483880823813698073
,0.001484473132966827287
,0.001485061950716274929
,0.001485647275677172239
,0.001486229106472865310
,0.001486807441734918341
,0.001487382280103116861
,0.001487953620225470868
,0.001488521460758218110
,0.001489085800365827128
,0.001489646637721000505
,0.001490203971504677904
,0.001490757800406039230
,0.001491308123122507690
,0.001491854938359752841
,0.001492398244831693654
,0.001492938041260501535
,0.001493474326376603333
,0.001494007098918684301
,0.001494536357633691130
,0.001495062101276834803
,0.001495584328611593580
,0.001496103038409715920
,0.001496618229451223311
,0.001497129900524413207
,0.001497638050425861813
,0.001498142677960426971
,0.001498643781941250940
,0.001499141361189763182
,0.001499635414535683171
,0.001500125940817023099
,0.001500612938880090635
,0.001501096407579491639
,0.001501576345778132847
,0.001502052752347224561
,0.001502525626166283266
,0.001502994966123134323
,0.001503460771113914545
,0.001503923040043074762
,0.001504381771823382507
,0.001504836965375924445
,0.001505288619630108995
,0.001505736733523668829
,0.001506181306002663336
,0.001506622336021481142
,0.001507059822542842570
,0.001507493764537802050
,0.001507924160985750551
,0.001508351010874417981
,0.001508774313199875597
,0.001509194066966538306
,0.001509610271187167063
,0.001510022924882871176
,0.001510432027083110582
,0.001510837576825698161
,0.001511239573156801983
,0.001511638015130947581
,0.001512032901811020125
,0.001512424232268266652
,0.001512812005582298275
,0.001513196220841092286
,0.001513576877140994372
,0.001513953973586720693
,0.001514327509291360000
,0.001514697483376375721
,0.001515063894971608033
,0.001515426743215275892
,0.001515786027253979094
,0.001516141746242700235
,0.001516493899344806744
,0.001516842485732052818
,0.001517187504584581396
,0.001517528955090926036
,0.001517866836448012913
,0.001518201147861162620
,0.001518531888544092082
,0.001518859057718916400
,0.001519182654616150671
,0.001519502678474711805
,0.001519819128541920315
,0.001520132004073502096
,0.001520441304333590126
,0.001520747028594726289
,0.001521049176137862992
,0.001521347746252364915
,0.001521642738236010667
,0.001521934151394994418
,0.001522221985043927570
,0.001522506238505840332
,0.001522786911112183333
,0.001523064002202829180
,0.001523337511126074020
,0.001523607437238639092
,0.001523873779905672186
,0.001524136538500749195
,0.001524395712405875558
,0.001524651301011487715
,0.001524903303716454544
,0.001525151719928078756
,0.001525396549062098363
,0.001525637790542687947
,0.001525875443802460071
,0.001526109508282466641
,0.001526339983432200122
,0.001526566868709594964
,0.001526790163581028779
,0.001527009867521323624
,0.001527225980013747254
,0.001527438500550014303
,0.001527647428630287524
,0.001527852763763178932
,0.001528054505465750941
,0.001528252653263517565
,0.001528447206690445471
,0.001528638165288955120
,0.001528825528609921794
,0.001529009296212676702
,0.001529189467665007993
,0.001529366042543161775
,0.001529539020431843097
,0.001529708400924216962
,0.001529874183621909253
,0.001530036368135007665
,0.001530194954082062663
,0.001530349941090088336
,0.001530501328794563299
,0.001530649116839431520
,0.001530793304877103216
,0.001530933892568455602
,0.001531070879582833730
,0.001531204265598051270
,0.001531334050300391237
,0.001531460233384606744
,0.001531582814553921762
,0.001531701793520031723
,0.001531817170003104291
,0.001531928943731779971
,0.001532037114443172763
,0.001532141681882870764
,0.001532242645804936802
,0.001532340005971908971
,0.001532433762154801217
,0.001532523914133103858
,0.001532610461694784151
,0.001532693404636286706
,0.001532772742762534053
,0.001532848475886927016
,0.001532920603831345242
,0.001532989126426147540
,0.001533054043510172332
,0.001533115354930738017
,0.001533173060543643305
,0.001533227160213167610
,0.001533277653812071300
,0.001533324541221596068
,0.001533367822331465162
,0.001533407497039883647
,0.001533443565253538685
,0.001533476026887599711
,0.001533504881865718642
,0.001533530130120030068
,0.001533551771591151419
,0.001533569806228183061
,0.001533584233988708468
,0.001533595054838794301
,0.001533602268752990493
,0.001533605875714330282
,0.001533605875714330282
,0.001533602268752990493
,0.001533595054838794301
,0.001533584233988708468
,0.001533569806228183061
,0.001533551771591151419
,0.001533530130120030068
,0.001533504881865718642
,0.001533476026887599711
,0.001533443565253538685
,0.001533407497039883647
,0.001533367822331465162
,0.001533324541221596068
,0.001533277653812071300
,0.001533227160213167610
,0.001533173060543643305
,0.001533115354930738017
,0.001533054043510172332
,0.001532989126426147540
,0.001532920603831345242
,0.001532848475886927016
,0.001532772742762534053
,0.001532693404636286706
,0.001532610461694784151
,0.001532523914133103858
,0.001532433762154801217
,0.001532340005971908971
,0.001532242645804936802
,0.001532141681882870764
,0.001532037114443172763
,0.001531928943731779971
,0.001531817170003104291
,0.001531701793520031723
,0.001531582814553921762
,0.001531460233384606744
,0.001531334050300391237
,0.001531204265598051270
,0.001531070879582833730
,0.001530933892568455602
,0.001530793304877103216
,0.001530649116839431520
,0.001530501328794563299
,0.001530349941090088336
,0.001530194954082062663
,0.001530036368135007665
,0.001529874183621909253
,0.001529708400924216962
,0.001529539020431843097
,0.001529366042543161775
,0.001529189467665007993
,0.001529009296212676702
,0.001528825528609921794
,0.001528638165288955120
,0.001528447206690445471
,0.001528252653263517565
,0.001528054505465750941
,0.001527852763763178932
,0.001527647428630287524
,0.001527438500550014303
,0.001527225980013747254
,0.001527009867521323624
,0.001526790163581028779
,0.001526566868709594964
,0.001526339983432200122
,0.001526109508282466641
,0.001525875443802460071
,0.001525637790542687947
,0.001525396549062098363
,0.001525151719928078756
,0.001524903303716454544
,0.001524651301011487715
,0.001524395712405875558
,0.001524136538500749195
,0.001523873779905672186
,0.001523607437238639092
,0.001523337511126074020
,0.001523064002202829180
,0.001522786911112183333
,0.001522506238505840332
,0.001522221985043927570
,0.001521934151394994418
,0.001521642738236010667
,0.001521347746252364915
,0.001521049176137862992
,0.001520747028594726289
,0.001520441304333590126
,0.001520132004073502096
,0.001519819128541920315
,0.001519502678474711805
,0.001519182654616150671
,0.001518859057718916400
,0.001518531888544092082
,0.001518201147861162620
,0.001517866836448012913
,0.001517528955090926036
,0.001517187504584581396
,0.001516842485732052818
,0.001516493899344806744
,0.001516141746242700235
,0.001515786027253979094
,0.001515426743215275892
,0.001515063894971608033
,0.001514697483376375721
,0.001514327509291360000
,0.001513953973586720693
,0.001513576877140994372
,0.001513196220841092286
,0.001512812005582298275
,0.001512424232268266652
,0.001512032901811020125
,0.001511638015130947581
,0.001511239573156801983
,0.001510837576825698161
,0.001510432027083110582
,0.001510022924882871176
,0.001509610271187167063
,0.001509194066966538306
,0.001508774313199875597
,0.001508351010874417981
,0.001507924160985750551
,0.001507493764537802050
,0.001507059822542842570
,0.001506622336021481142
,0.001506181306002663336
,0.001505736733523668829
,0.001505288619630108995
,0.001504836965375924445
,0.001504381771823382507
,0.001503923040043074762
,0.001503460771113914545
,0.001502994966123134323
,0.001502525626166283266
,0.001502052752347224561
,0.001501576345778132847
,0.001501096407579491639
,0.001500612938880090635
,0.001500125940817023099
,0.001499635414535683171
,0.001499141361189763182
,0.001498643781941250940
,0.001498142677960426971
,0.001497638050425861813
,0.001497129900524413207
,0.001496618229451223311
,0.001496103038409715920
,0.001495584328611593580
,0.001495062101276834803
,0.001494536357633691130
,0.001494007098918684301
,0.001493474326376603333
,0.001492938041260501535
,0.001492398244831693654
,0.001491854938359752841
,0.001491308123122507690
,0.001490757800406039230
,0.001490203971504677904
,0.001489646637721000505
,0.001489085800365827128
,0.001488521460758218110
,0.001487953620225470868
,0.001487382280103116861
,0.001486807441734918341
,0.001486229106472865310
,0.001485647275677172239
,0.001485061950716274929
,0.001484473132966827287
,0.001483880823813698073
,0.001483285024649967618
,0.001482685736876924623
,0.001482082961904062777
,0.001481476701149077512
,0.001480866956037862611
,0.001480253728004506919
,0.001479637018491290882
,0.001479016828948683243
,0.001478393160835337593
,0.001477766015618088916
,0.001477135394771950190
,0.001476501299780108882
,0.001475863732133923459
,0.001475222693332919904
,0.001474578184884788173
,0.001473930208305378658
,0.001473278765118698585
,0.001472623856856908497
,0.001471965485060318607
,0.001471303651277385153
,0.001470638357064706824
,0.001469969603987021034
,0.001469297393617200290
,0.001468621727536248439
,0.001467942607333297001
,0.001467260034605601412
,0.001466574010958537271
,0.001465884538005596547
,0.001465191617368383800
,0.001464495250676612364
,0.001463795439568100528
,0.001463092185688767660
,0.001462385490692630344
,0.001461675356241798485
,0.001460961784006471428
,0.001460244775664933982
,0.001459524332903552533
,0.001458800457416771008
,0.001458073150907106949
,0.001457342415085147473
,0.001456608251669545274
,0.001455870662387014568
,0.001455129648972327001
,0.001454385213168307659
,0.001453637356725830844
,0.001452886081403816069
,0.001452131388969223850
,0.001451373281197051596
,0.001450611759870329378
,0.001449846826780115812
,0.001449078483725493772
,0.001448306732513566205
,0.001447531574959451865
,0.001446753012886281043
,0.001445971048125191283
,0.001445185682515323086
,0.001444396917903815546
,0.001443604756145802062
,0.001442809199104405922
,0.001442010248650735959
,0.001441207906663882128
,0.001440402175030911094
,0.001439593055646861799
,0.001438780550414740987
,0.001437964661245518767
,0.001437145390058124057
,0.001436322738779440136
,0.001435496709344300055
,0.001434667303695482150
,0.001433834523783705398
,0.001432998371567624882
,0.001432158849013827177
,0.001431315958096825717
,0.001430469700799056151
,0.001429620079110871642
,0.001428767095030538293
,0.001427910750564230335
,0.001427051047726025447
,0.001426187988537900052
,0.001425321575029724509
,0.001424451809239258379
,0.001423578693212145614
,0.001422702229001909753
,0.001421822418669949068
,0.001420939264285531744
,0.001420052767925791024
,0.001419162931675720277
,0.001418269757628168145
,0.001417373247883833560
,0.001416473404551260877
,0.001415570229746834857
,0.001414663725594775719
,0.001413753894227134123
,0.001412840737783786172
,0.001411924258412428394
,0.001411004458268572636
,0.001410081339515541068
,0.001409154904324461006
,0.001408225154874259913
,0.001407292093351660176
,0.001406355721951174014
,0.001405416042875098324
,0.001404473058333509474
,0.001403526770544258090
,0.001402577181732963902
,0.001401624294133010463
,0.001400668109985539892
,0.001399708631539447628
,0.001398745861051377101
,0.001397779800785714523
,0.001396810453014583409
,0.001395837820017839362
,0.001394861904083064689
,0.001393882707505562907
,0.001392900232588353534
,0.001391914481642166510
,0.001390925456985436855
,0.001389933160944299171
,0.001388937595852582193
,0.001387938764051803282
,0.001386936667891162957
,0.001385931309727539317
,0.001384922691925482506
,0.001383910816857209213
,0.001382895686902597033
,0.001381877304449178860
,0.001380855671892137322
,0.001379830791634299104
,0.001378802666086129331
,0.001377771297665725877
,0.001376736688798813680
,0.001375698841918739039
,0.001374657759466463895
,0.001373613443890560086
,0.001372565897647203575
,0.001371515123200168721
,0.001370461123020822424
,0.001369403899588118331
,0.001368343455388591045
,0.001367279792916350213
,0.001366212914673074712
,0.001365142823168006740
,0.001364069520917945921
,0.001362993010447243375
,0.001361913294287795806
,0.001360830374979039515
,0.001359744255067944462
,0.001358654937109008242
,0.001357562423664250104
,0.001356466717303204891
,0.001355367820602917058
,0.001354265736147934541
,0.001353160466530302708
,0.001352052014349558293
,0.001350940382212723215
,0.001349825572734298518
,0.001348707588536258168
,0.001347586432248042916
,0.001346462106506554101
,0.001345334613956147436
,0.001344203957248626848
,0.001343070139043238153
,0.001341933162006662860
,0.001340793028813011897
,0.001339649742143819284
,0.001338503304688035874
,0.001337353719142023012
,0.001336200988209546144
,0.001335045114601768557
,0.001333886101037244912
,0.001332723950241914900
,0.001331558664949096803
,0.001330390247899481101
,0.001329218701841123963
,0.001328044029529440891
,0.001326866233727200083
,0.001325685317204516099
,0.001324501282738843248
,0.001323314133114969064
,0.001322123871125007787
,0.001320930499568393776
,0.001319734021251874939
,0.001318534438989506090
,0.001317331755602642401
,0.001316125973919932710
,0.001314917096777312889
,0.001313705127017999163
,0.001312490067492481446
,0.001311271921058516600
,0.001310050690581121756
,0.001308826378932567539
,0.001307598988992371350
,0.001306368523647290547
,0.001305134985791315697
,0.001303898378325663739
,0.001302658704158771191
,0.001301415966206287291
,0.001300170167391067122
,0.001298921310643164780
,0.001297669398899826451
,0.001296414435105483496
,0.001295156422211745579
,0.001293895363177393647
,0.001292631260968373046
,0.001291364118557786473
,0.001290093938925887062
,0.001288820725060071305
,0.001287544479954872051
,0.001286265206611951513
,0.001284982908040094090
,0.001283697587255199427
,0.001282409247280275207
,0.001281117891145430144
,0.001279823521887866751
,0.001278526142551874267
,0.001277225756188821508
,0.001275922365857149610
,0.001274615974622364934
,0.001273306585557031786
,0.001271994201740765212
,0.001270678826260223763
,0.001269360462209102228
,0.001268039112688124363
,0.001266714780805035572
,0.001265387469674595657
,0.001264057182418571441
,0.001262723922165729409
,0.001261387692051828413
,0.001260048495219612269
,0.001258706334818802340
,0.001257361214006090146
,0.001256013135945129964
,0.001254662103806531347
,0.001253308120767851694
,0.001251951190013588762
,0.001250591314735173189
,0.001249228498130960960
,0.001247862743406225948
,0.001246494053773152282
,0.001245122432450826882
,0.001243747882665231834
,0.001242370407649236813
,0.001240990010642591488
,0.001239606694891917897
,0.001238220463650702821
,0.001236831320179290124
,0.001235439267744873049
,0.001234044309621486618
,0.001232646449089999853
,0.001231245689438108111
,0.001229842033960325297
,0.001228435485957976172
,0.001227026048739188568
,0.001225613725618885586
,0.001224198519918777823
,0.001222780434967355573
,0.001221359474099880947
,0.001219935640658380083
,0.001218508937991635265
,0.001217079369455177035
,0.001215646938411276311
,0.001214211648228936486
,0.001212773502283885522
,0.001211332503958567928
,0.001209888656642136901
,0.001208441963730446342
,0.001206992428626042773
,0.001205540054738157481
,0.001204084845482698377
,0.001202626804282242026
,0.001201165934566025581
,0.001199702239769938707
,0.001198235723336515510
,0.001196766388714926470
,0.001195294239360970249
,0.001193819278737065670
,0.001192341510312243465
,0.001190860937562138196
,0.001189377563968980051
,0.001187891393021586645
,0.001186402428215354844
,0.001184910673052252496
,0.001183416131040810233
,0.001181918805696113246
,0.001180418700539792921
,0.001178915819100018665
,0.001177410164911489534
,0.001175901741515425946
,0.001174390552459561360
,0.001172876601298133937
,0.001171359891591878125
,0.001169840426908016361
,0.001168318210820250641
,0.001166793246908754109
,0.001165265538760162653
,0.001163735089967566477
,0.001162201904130501609
,0.001160665984854941500
,0.001159127335753288457
,0.001157585960444365245
,0.001156041862553406510
,0.001154495045712050257
,0.001152945513558329335
,0.001151393269736662861
,0.001149838317897847657
,0.001148280661699049644
,0.001146720304803795305
,0.001145157250881962956
,0.001143591503609774226
,0.001142023066669785350
,0.001140451943750878519
,0.001138878138548253204
,0.001137301654763417478
,0.001135722496104179294
,0.001134140666284637777
,0.001132556169025174462
,0.001130969008052444601
,0.001129379187099368329
,0.001127786709905121917
,0.001126191580215129004
,0.001124593801781051739
,0.001122993378360781980
,0.001121390313718432457
,0.001119784611624327942
,0.001118176275854996304
,0.001116565310193159731
,0.001114951718427725762
,0.001113335504353778373
,0.001111716671772569119
,0.001110095224491508097
,0.001108471166324155096
,0.001106844501090210526
,0.001105215232615506509
,0.001103583364731997850
,0.001101948901277753014
,0.001100311846096945149
,0.001098672203039842958
,0.001097029975962801743
,0.001095385168728254257
,0.001093737785204701657
,0.001092087829266704407
,0.001090435304794873139
,0.001088780215675859556
,0.001087122565802347270
,0.001085462359073042677
,0.001083799599392665726
,0.001082134290671940796
,0.001080466436827587485
,0.001078796041782311376
,0.001077123109464794824
,0.001075447643809687739
,0.001073769648757598260
,0.001072089128255083611
,0.001070406086254640656
,0.001068720526714696757
,0.001067032453599600391
,0.001065341870879611802
,0.001063648782530893716
,0.001061953192535501951
,0.001060255104881376097
,0.001058554523562330088
,0.001056851452578042821
,0.001055145895934048779
,0.001053437857641728566
,0.001051727341718299509
,0.001050014352186806183
,0.001048298893076110977
,0.001046580968420884574
,0.001044860582261596521
,0.001043137738644505671
,0.001041412441621650707
,0.001039684695250840585
,0.001037954503595644999
,0.001036221870725384828
,0.001034486800715122573
,0.001032749297645652740
,0.001031009365603492285
,0.001029267008680870960
,0.001027522230975721721
,0.001025775036591671093
,0.001024025429638029473
,0.001022273414229781525
,0.001020518994487576456
,0.001018762174537718356
,0.001017002958512156457
,0.001015241350548475452
,0.001013477354789885762
,0.001011710975385213748
,0.001009942216488891992
,0.001008171082260949527
,0.001006397576867002018
,0.001004621704478242055
,0.001002843469271429188
,0.001001062875428880230
,0.000999279927138459423
,0.000997494628593568469
,0.000995706983993136808
,0.000993916997541611678
,0.000992124673448948190
,0.000990330015930599492
,0.000988533029207506832
,0.000986733717506089611
,0.000984932085058235472
,0.000983128136101290322
,0.000981321874878048377
,0.000979513305636742203
,0.000977702432631032679
,0.000975889260119999030
,0.000974073792368128797
,0.000972256033645307812
,0.000970435988226810143
,0.000968613660393288057
,0.000966789054430761934
,0.000964962174630610198
,0.000963133025289559229
,0.000961301610709673236
,0.000959467935198344158
,0.000957632003068281514
,0.000955793818637502318
,0.000953953386229320833
,0.000952110710172338441
,0.000950265794800433517
,0.000948418644452751151
,0.000946569263473692987
,0.000944717656212907013
,0.000942863827025277301
,0.000941007780270913768
,0.000939149520315141965
,0.000937289051528492750
,0.000935426378286692048
,0.000933561504970650555
,0.000931694435966453413
,0.000929825175665349911
,0.000927953728463743176
,0.000926080098763179765
,0.000924204290970339409
,0.000922326309497024578
,0.000920446158760150107
,0.000918563843181732865
,0.000916679367188881283
,0.000914792735213784987
,0.000912903951693704368
,0.000911013021070960124
,0.000909119947792922833
,0.000907224736312002496
,0.000905327391085638045
,0.000903427916576286874
,0.000901526317251414350
,0.000899622597583483270
,0.000897716762049943392
,0.000895808815133220873
,0.000893898761320707725
,0.000891986605104751279
,0.000890072350982643604
,0.000888156003456610961
,0.000886237567033803132
,0.000884317046226282920
,0.000882394445551015507
,0.000880469769529857759
,0.000878543022689547698
,0.000876614209561693777
,0.000874683334682764260
,0.000872750402594076547
,0.000870815417841786476
,0.000868878384976877657
,0.000866939308555150753
,0.000864998193137212747
,0.000863055043288466260
,0.000861109863579098782
,0.000859162658584071907
,0.000857213432883110636
,0.000855262191060692535
,0.000853308937706036987
,0.000851353677413094415
,0.000849396414780535414
,0.000847437154411740038
,0.000845475900914786847
,0.000843512658902442192
,0.000841547432992149268
,0.000839580227806017317
,0.000837611047970810730
,0.000835639898117938167
,0.000833666782883441674
,0.000831691706907985759
,0.000829714674836846506
,0.000827735691319900623
,0.000825754761011614524
,0.000823771888571033379
,0.000821787078661770140
,0.000819800335951994590
,0.000817811665114422366
,0.000815821070826303944
,0.000813828557769413684
,0.000811834130630038752
,0.000809837794098968174
,0.000807839552871481749
,0.000805839411647339001
,0.000803837375130768203
,0.000801833448030455195
,0.000799827635059532428
,0.000797819940935567781
,0.000795810370380553523
,0.000793798928120895191
,0.000791785618887400472
,0.000789770447415268085
,0.000787753418444076635
,0.000785734536717773450
,0.000783713806984663472
,0.000781691233997398038
,0.000779666822512963735
,0.000777640577292671189
,0.000775612503102143897
,0.000773582604711306960
,0.000771550886894375947
,0.000769517354429845587
,0.000767482012100478603
,0.000765444864693294395
,0.000763405916999557823
,0.000761365173814767928
,0.000759322639938646658
,0.000757278320175127553
,0.000755232219332344497
,0.000753184342222620364
,0.000751134693662455710
,0.000749083278472517464
,0.000747030101477627562
,0.000744975167506751638
,0.000742918481392987601
,0.000740860047973554349
,0.000738799872089780329
,0.000736737958587092194
,0.000734674312315003369
,0.000732608938127102656
,0.000730541840881042850
,0.000728473025438529279
,0.000726402496665308365
,0.000724330259431156208
,0.000722256318609867132
,0.000720180679079242172
,0.000718103345721077678
,0.000716024323421153770
,0.000713943617069222898
,0.000711861231558998281
,0.000709777171788142455
,0.000707691442658255711
,0.000705604049074864607
,0.000703514995947410389
,0.000701424288189237493
,0.000699331930717581920
,0.000697237928453559750
,0.000695142286322155506
,0.000693045009252210601
,0.000690946102176411730
,0.000688845570031279299
,0.000686743417757155767
,0.000684639650298194068
,0.000682534272602345960
,0.000680427289621350408
,0.000678318706310721898
,0.000676208527629738838
,0.000674096758541431831
,0.000671983404012572071
,0.000669868469013659607
,0.000667751958518911664
,0.000665633877506250972
,0.000663514230957294015
,0.000661393023857339359
,0.000659270261195355886
,0.000657145947963971091
,0.000655020089159459329
,0.000652892689781730045
,0.000650763754834316054
,0.000648633289324361745
,0.000646501298262611297
,0.000644367786663396924
,0.000642232759544627061
,0.000640096221927774562
,0.000637958178837864897
,0.000635818635303464339
,0.000633677596356668093
,0.000631535067033088544
,0.000629391052371843339
,0.000627245557415543571
,0.000625098587210281909
,0.000622950146805620722
,0.000620800241254580221
,0.000618648875613626556
,0.000616496054942659954
,0.000614341784305002763
,0.000612186068767387599
,0.000610028913399945425
,0.000607870323276193572
,0.000605710303473023862
,0.000603548859070690645
,0.000601385995152798857
,0.000599221716806292065
,0.000597056029121440495
,0.000594888937191829054
,0.000592720446114345376
,0.000590550560989167794
,0.000588379286919753405
,0.000586206629012825994
,0.000584032592378364105
,0.000581857182129588911
,0.000579680403382952311
,0.000577502261258124829
,0.000575322760877983557
,0.000573141907368600156
,0.000570959705859228794
,0.000568776161482294021
,0.000566591279373378771
,0.000564405064671212258
,0.000562217522517657859
,0.000560028658057701067
,0.000557838476439437385
,0.000555646982814060177
,0.000553454182335848569
,0.000551260080162155387
,0.000549064681453394941
,0.000546867991373030930
,0.000544670015087564281
,0.000542470757766521043
,0.000540270224582440149
,0.000538068420710861335
,0.000535865351330312914
,0.000533661021622299589
,0.000531455436771290322
,0.000529248601964706080
,0.000527040522392907684
,0.000524831203249183561
,0.000522620649729737547
,0.000520408867033676678
,0.000518195860362998927
,0.000515981634922581016
,0.000513766195920166149
,0.000511549548566351735
,0.000509331698074577205
,0.000507112649661111679
,0.000504892408545041722
,0.000502670979948259109
,0.000500448369095448477
,0.000498224581214075063
,0.000495999621534372446
,0.000493773495289330186
,0.000491546207714681549
,0.000489317764048891203
,0.000487088169533142857
,0.000484857429411326985
,0.000482625548930028454
,0.000480392533338514196
,0.000478158387888720879
,0.000475923117835242497
,0.000473686728435318110
,0.000471449224948819397
,0.000469210612638238285
,0.000466970896768674643
,0.000464730082607823838
,0.000462488175425964333
,0.000460245180495945358
,0.000458001103093174456
,0.000455755948495605085
,0.000453509721983724209
,0.000451262428840539885
,0.000449014074351568839
,0.000446764663804824007
,0.000444514202490802133
,0.000442262695702471294
,0.000440010148735258507
,0.000437756566887037193
,0.000435501955458114781
,0.000433246319751220218
,0.000430989665071491477
,0.000428731996726463172
,0.000426473320026053904
,0.000424213640282553955
,0.000421952962810612673
,0.000419691292927226030
,0.000417428635951724091
,0.000415164997205758497
,0.000412900382013289990
,0.000410634795700575842
,0.000408368243596157351
,0.000406100731030847332
,0.000403832263337717519
,0.000401562845852086079
,0.000399292483911505035
,0.000397021182855747712
,0.000394748948026796219
,0.000392475784768828804
,0.000390201698428207361
,0.000387926694353464806
,0.000385650777895292562
,0.000383373954406527881
,0.000381096229242141336
,0.000378817607759224163
,0.000376538095316975740
,0.000374257697276690894
,0.000371976419001747343
,0.000369694265857593085
,0.000367411243211733759
,0.000365127356433720004
,0.000362842610895134912
,0.000360557011969581261
,0.000358270565032669010
,0.000355983275462002574
,0.000353695148637168194
,0.000351406189939721299
,0.000349116404753173848
,0.000346825798462981638
,0.000344534376456531668
,0.000342242144123129480
,0.000339949106853986446
,0.000337655270042207095
,0.000335360639082776464
,0.000333065219372547368
,0.000330769016310227729
,0.000328472035296367889
,0.000326174281733347848
,0.000323875761025364651
,0.000321576478578419612
,0.000319276439800305610
,0.000316975650100594392
,0.000314674114890623800
,0.000312371839583485129
,0.000310068829594010309
,0.000307765090338759231
,0.000305460627236006953
,0.000303155445705731005
,0.000300849551169598638
,0.000298542949050954024
,0.000296235644774805566
,0.000293927643767813085
,0.000291618951458275091
,0.000289309573276115996
,0.000286999514652873355
,0.000284688781021685099
,0.000282377377817276719
,0.000280065310475948544
,0.000277752584435562904
,0.000275439205135531350
,0.000273125178016801894
,0.000270810508521846156
,0.000268495202094646612
,0.000266179264180683798
,0.000263862700226923428
,0.000261545515681803692
,0.000259227715995222332
,0.000256909306618523908
,0.000254590293004486941
,0.000252270680607311064
,0.000249950474882604282
,0.000247629681287370032
,0.000245308305279994427
,0.000242986352320233376
,0.000240663827869199771
,0.000238340737389350614
,0.000236017086344474215
,0.000233692880199677299
,0.000231368124421372171
,0.000229042824477263845
,0.000226716985836337230
,0.000224390613968844195
,0.000222063714346290807
,0.000219736292441424321
,0.000217408353728220475
,0.000215079903681870466
,0.000212750947778768182
,0.000210421491496497273
,0.000208091540313818265
,0.000205761099710655715
,0.000203430175168085297
,0.000201098772168320877
,0.000198766896194701736
,0.000196434552731679532
,0.000194101747264805500
,0.000191768485280717554
,0.000189434772267127312
,0.000187100613712807289
,0.000184766015107577911
,0.000182430981942294658
,0.000180095519708835125
,0.000177759633900086164
,0.000175423330009930885
,0.000173086613533235835
,0.000170749489965838030
,0.000168411964804532019
,0.000166074043547057034
,0.000163735731692084014
,0.000161397034739202716
,0.000159057958188908796
,0.000156718507542590848
,0.000154378688302517523
,0.000152038505971824638
,0.000149697966054502139
,0.000147357074055381366
,0.000145015835480121958
,0.000142674255835199034
,0.000140332340627890276
,0.000137990095366262988
,0.000135647525559161239
,0.000133304636716192900
,0.000130961434347716812
,0.000128617923964829893
,0.000126274111079354244
,0.000123930001203824281
,0.000121585599851473924
,0.000119240912536223753
,0.000116895944772668195
,0.000114550702076062706
,0.000112205189962311112
,0.000109859413947952814
,0.000107513379550150122
,0.000105167092286675675
,0.000102820557675899872
,0.000100473781236778381
,0.000098126768488839803
,0.000095779524952173406
,0.000093432056147416970
,0.000091084367595744955
,0.000088736464818856788
,0.000086388353338965392
,0.000084040038678786248
,0.000081691526361526759
,0.000079342821910876271
,0.000076993930850996860
,0.000074644858706515042
,0.000072295611002514791
,0.000069946193264532207
,0.000067596611018552416
,0.000065246869791009321
,0.000062896975108789436
,0.000060546932499241067
,0.000058196747490190880
,0.000055846425609970998
,0.000053495972387460550
,0.000051145393352148338
,0.000048794694034225887
,0.000046443879964725560
,0.000044092956675726209
,0.000041741929700662707
,0.000039390804574797830
,0.000037039586835954831
,0.000034688282025679520
,0.000032336895691130890
,0.000029985433388250774
,0.000027633900687265033
,0.000025282303182626151
,0.000022930646511857619
,0.000020578936393340612
,0.000018227178707393919
,0.000015875379685302326
,0.000013523546398357259
,0.000011171688205646537
,0.000008819821897850314
,0.000006467995475736767
,0.000004116455830582231
,0.000001768383366665995
};

GLxw2048.cc

// The code below generates the text in the previous section.
// If you plan to use some codes from TORI, the generation of the nodes and weights // with the code below is better, than copypast from the previous section.

#include <stdio.h>
#include <math.h>
#include<stdlib.h>
#define DB double
#define EPS 1.0e-18
// Be careful: numeration begins with UNITY !!!!
void gauleg(long double x1, long double x2, long double x[], long double w[],  int n)
{ int m,j,i; long double z1,z,xm,xl,pp,p3,p2,p1;
 m=(n+1)/2;
 xm=0.5*(x2+x1);
 xl=0.5*(x2-x1);
 for(i=1;i<=m;i++)
 { z=cos(M_PI*(i-0.25)/(n+0.5));
   do{	p1=1.0;
	p2=0.0;
	for(j=1;j<=n;j++) 
	{ p3=p2; p2=p1;
	  p1=((2.*j-1.)*z*p2-(j-1.)*p3)/j;
	}
	pp=n*(z*p1-p2)/(z*z-1.0);
	z1=z;
	z=z1-p1/pp;
      } while (fabs(z-z1) > EPS);
    x[i]=xm-xl*z;
    x[n+1-i]=xm+xl*z;
    w[i]=2.0*xl/((1.0-z*z)*pp*pp);
    w[n+1-i]=w[i];
  }
}
#undef EPS
//#include "gauleg.cin"
#define NPOINT 2048
#define X1 -1.0
#define X2 1.0
int main(void){ int i; long double xx=0.0; long double *x,*w;
x=(long double *)malloc((size_t)(NPOINT+1)*sizeof(long double));
w=(long double *)malloc((size_t)(NPOINT+1)*sizeof(long double));
gauleg(X1,X2,x,w,NPOINT);
printf("\n%2s %10s %12s\n","#","x[i]","w[i]");
for (i=1;i<=NPOINT;i++) {	printf("%4d ",i);
				printf("%18.16Lf ", x[i]);
				printf("%18.16Lf\n",w[i]);
			}
FILE *o; o=fopen("GLxw2048.inc","w");
fprintf(o,"int NPO=%3d;\n",NPOINT);
fprintf(o,"DB GLx[%3d]={\n",NPOINT);
for (i=1;i<=NPOINT;i++)
{	if(i>1)	fprintf(o,","); else fprintf(o," ");
	fprintf(o,"%24.21Lf\n",x[i]);}
fprintf(o,"};\n");
fprintf(o,"DB GLw[%3d]={\n",NPOINT);
for (i=1;i<=NPOINT;i++)
{	if(i>1)	fprintf(o,","); else fprintf(o," ");
	fprintf(o,"%24.22Lf\n",w[i]);}
fprintf(o,"};\n");
fclose(o);
//small test:
	for (i=1;i<=NPOINT;i++)
		xx += (w[i]*cos(x[i]));
	printf("from GAULEG: %32.30Lf\n",xx);
	printf("should be  : %32.30f\n",	2*sin(1.));
	printf("diff       : % 9.3Le\n",	xx-2*sin(1.));
	printf("failure in last diguits? Why are not they different?\n");
       free((char*)(w));
       free((char*)(x));
	return 0;
}

Keywords

Integration, Tetration, C++

References