Module:Interval extension
Jump to navigation
Jump to search
-- Calculated by http://www.mikebattagliamusic.com/HE-JS/HE.html.
-- Note: that the unit is Nat, not Bit.
local p = {}
local lookup_table = {
2.4653643754704344,2.4695266012463977,2.481977751440438,2.50260902420515,2.5312627678840913,2.567689182317395,2.6115996095425507,2.66261768398535,2.72031930048547,2.7842148507295414,2.853751443697008,2.928330669227051,3.0073152593561856,3.090020206534788,3.1757371885316212,3.263729017319167,3.3532651662074815,3.443602896054329,3.5340283335137124,3.6238375972460055,3.7123756557206176,3.799029665878395,3.8832456264756248,3.964531708752836,4.042466027995334,4.116686651526813,4.186926015620279,4.2529753983642005,4.314697132114772,4.372021272827121,4.424946710278236,4.473505640933111,4.51780131552448,4.557956968797875,4.59414579553084,4.626553202953188,4.655389023199273,4.680873080409855,4.703238521400898,4.722711831650773,4.739522827306652,4.7539002142927815,4.766048273628878,4.776184609009857,4.784506840117841,4.791190382176286,4.796413981077449,4.800338619146656,4.803105294696435,4.8048505651475795,4.805703216360352,4.805772050182217,4.805168088906504,4.803974599253207,4.8022837297257945,4.8001654243690615,4.797686296559008,4.794922951678031,4.791917578197595,4.788713474812101,4.785363932222346,4.781903367339263,4.778366197073783,4.774780176999239,4.771163070682565,4.767537082582425,4.76392552738042,4.760330625522416,4.756774581467077,4.753255174768539,4.749786838324933,4.74637290280506,4.743007817094253,4.739704903867711,4.736459722233702,4.733268941523425,4.7301336719598135,4.7270605748804675,4.724041878724853,4.721084244830571,4.718179901637087,4.715332179813202,4.712549961142381,4.70982103317236,4.70715649813247,4.70455635602271,4.702018386397216,4.699553691485319,4.697157830395287,4.694837464464719,4.692597034585348,4.690427658973706,4.68834377052793,4.686335377241617,4.684412471121167,4.682572831720714,4.680808687479725,4.679123369067,4.677513545813737,4.6759747768282045,4.67450262121867,4.6730981892080665,4.67174704789826,4.670446976843386,4.669190204482908,4.66797340014803,4.666789902501151,4.66562971953587,4.664495071698055,4.663368195420773,4.662253531595757,4.661143308662474,4.660036416397992,4.6589195321271095,4.657798206964495,4.656680212470681,4.655550005524599,4.654415357686785,4.653271828065505,4.652129408667159,4.650984768822946,4.649842349424599,4.648701040249186,4.647569723080173,4.646450618363426,4.645341505653079,4.6442512667325975,4.643178791379048,4.642124079592432,4.641102674493814,4.640093481847463,4.6391109345515105,4.638150591714223,4.6372180044502675,4.6362987398615125,4.635407230846089,4.634530154728798,4.633666401286707,4.6328148602968815,4.63196776019879,4.631129541884164,4.630294654238337,4.629449774586112,4.628610446048554,4.627758905058729,4.626898482285438,4.626024736836947,4.625146550496725,4.624246159697836,4.623342438230147,4.622420953195526,4.621488365931572,4.620551337775886,4.619597656276201,4.618643974776515,4.617684742162163,4.616715517541412,4.615755174704127,4.614793721643909,4.613841150367157,4.612894130205071,4.611960432718186,4.611031176123033,4.610124123986545,4.609223733187658,4.60833999573277,4.607474021844815,4.606623591077925,4.605783152317435,4.604963807792677,4.604151124605519,4.603350653870627,4.602562395588001,4.601781908865908,4.601008083481415,4.600240919434521,4.599479306502294,4.598719914015934,4.5979660726442395,4.597214451718412,4.5964606103467185,4.595714540535558,4.5949729116161295,4.594234613365502,4.593504086675407,4.592785772437578,4.592078560429083,4.591388001764585,4.590716316889954,4.590064616028122,4.589439560516689,4.588838929909787,4.588282708220217,4.587752021658112,4.587260192898671,4.5868083321648285,4.586399770125384,4.586031176111537,4.58570699101502,4.585422773944102,4.585181855567582,4.584975354101993,4.584808820662002,4.584676704132942,4.584571232954281,4.584492407126019,4.584438006202289,4.584399148399624,4.5843725030492255,4.584352519036426,4.584342527030027,4.584329204354828,4.584314771456695,4.584303669227363,4.584278134099897,4.584250378526565,4.584217071838567,4.584182654927635,4.584144907347905,4.584104939322306,4.584078293971908,4.584051648621509,4.584040546392176,4.584046097506842,4.5840649712967085,4.584114931328705,4.584185985596435,4.584287015883363,4.584409140406024,4.5845656818396145,4.584745537954806,4.584948708751595,4.58516742266945,4.585396128593704,4.585630385632625,4.585856871111012,4.586064482799535,4.586251000252325,4.586388667896051,4.586480816399512,4.586509682195778,4.586457501717914,4.586319834074188,4.586087797481134,4.585749179486485,4.585292877860909,4.584727774387873,4.584039436169243,4.583233414319687,4.582314149730935,4.581284973071791,4.580160317240385,4.578944623128451,4.577651213411188,4.576305623216061,4.574923395664135,4.573522294322346,4.572130074764022,4.57076561077903,4.569453327271902,4.568215428701304,4.567071899080033,4.56605604509609,4.565170087195339,4.564444001396979,4.563890000153276,4.563518075470631,4.563334888686641,4.563350431807707,4.563554712827429,4.563953282860473,4.5645417010151075,4.565296652609732,4.566210366083815,4.56726396764749,4.568429701727426,4.569690914979622,4.571010970047284,4.572366552248809,4.573722134450335,4.575055512193195,4.57631894589126,4.577491341308796,4.578539391757807,4.579438672333757,4.580159207017451,4.580674350458491,4.580971890204608,4.581026291128339,4.580832002115016,4.58036903915184,4.579645173799347,4.578658185611666,4.5774180665952,4.575924816749948,4.574196199642842,4.572259970847215,4.570128342815331,4.567834622235191,4.565407674903059,4.562885248398666,4.56030398007881,4.557689405070956,4.55509370385297,4.552552403558713,4.550103251767919,4.547779555168586,4.545630163569776,4.543680612098954,4.541968648335853,4.540519807407937,4.539360734665604,4.538511414121653,4.53799405023475,4.53781419411956,4.537982948005418,4.538508083452854,4.539381828901337,4.5405986332362,4.542150724896909,4.544021450539468,4.546187495482276,4.548638867718937,4.551333378777983,4.5542565957612835,4.557375211980841,4.560653700302791,4.564069856268467,4.567580381183473,4.571164180812075,4.5747857280204105,4.578411716120479,4.582014389538951,4.585571543817161,4.589045431375376,4.59243050109893,4.595687895185159,4.598800960290062,4.601765255521909,4.604545253746831,4.607143175410698,4.609526824048443,4.611698420105932,4.6136424204621,4.615352163779347,4.616806555821941,4.618007817035747,4.6189381838538335,4.619588774492734,4.619947376500183,4.620011769430313,4.6197675203849915,4.619202416911953,4.6183120181194655,4.617079670663527,4.615508705212939,4.613575807086104,4.611286527397687,4.608639755924755,4.605626610883842,4.602250422943751,4.598522294333811,4.594444445499891,4.590031309340124,4.585306200536109,4.580287992877711,4.574994449931865,4.569472201061767,4.563747891617818,4.557865930517347,4.551869616454752,4.545814460576698,4.539745982023448,4.5337174714958,4.5277966525926825,4.522036816014892,4.516496803577891,4.51123434687421,4.506306067273445,4.501765255476391,4.497669643075579,4.49406141854247,4.490983880571464,4.488465894958822,4.486545209284277,4.485245138229426,4.484575673800668,4.484545697781471,4.485148548834232,4.486383116736021,4.488222756136437,4.490657475029084,4.4936450849424965,4.497144507628144,4.501117995506298,4.50551891921376,4.510283996043335,4.515365486408893,4.520701217826171,4.5262323484797085,4.531888934324707,4.537624345997972,4.543365308785906,4.549062972879446,4.554660716908994,4.560100809282021,4.565344392195863,4.570350387401986,4.57508104732066,4.57950084481802,4.583587575435401,4.587322365382934,4.590688561316622,4.593687273459397,4.59630517913606,4.598555601021809,4.600441869785444,4.601980638770964,4.603187451099435,4.604082290783656,4.604695133842824,4.605047074512672,4.6051803012646655,4.605112577665736,4.604882761518548,4.6045208288423,4.604062306770857,4.603536061100484,4.602976508742112,4.602409184823209,4.601861844917104,4.601362244597129,4.600928147430219,4.60058952943557,4.600349721281982,4.600227596759321,4.600237588765721,4.600383027969981,4.600671685932633,4.601099121761943,4.601666445680848,4.602371437243478,4.603202994220501,4.604153345051385,4.605203615946265,4.606347145567539,4.607558398787743,4.608828493823412,4.610124123986545,4.611434187047812,4.61272426609628,4.613973266896217,4.615153433874291,4.6162292398966365,4.617178480504588,4.617966738787215,4.618564038725319,4.618930412293301,4.6190358834719625,4.6188504762421045,4.618328671463464,4.6174471544544415,4.616165957189439,4.614451772980459,4.61227018491657,4.60959010675564,4.606390444261937,4.60264677253093,4.598325784874621,4.5934241506242115,4.587926326658636,4.581821210748562,4.575119905123325,4.567819079114126,4.559948708740164,4.551518786007839,4.542573719834485,4.5331445964622334,4.52329358837535,4.513072876051699,4.50254685242141,4.4917998944274125,4.480911938120903,4.469975132005341,4.459081624584188,4.448329115475571,4.4378275167498815,4.427673417802313,4.417980061372055,4.408846257300167,4.400367484758907,4.392640333143467,4.3857613918490355,4.379801715143342,4.374829026625311,4.370912160116804,4.368098855203948,4.366412426568342,4.365888401343848,4.366533440868066,4.36833866335753,4.371276313238909,4.3753319576140735,4.380442313775828,4.3865618625839105,4.393623990662328,4.4015365495076235,4.4102262644062025,4.4195998766316755,4.429553025228317,4.4399824594633355,4.450782708158073,4.461856071694404,4.4730904175560715,4.4843880461249475,4.495651257782905,4.506783463134749,4.517704726129285,4.528327339154784,4.538589129726982,4.548425704915749,4.557781553574419,4.566608936116859,4.574877876523872,4.582557288553322,4.5896316290841455,4.596093126555804,4.601939560522433,4.607178702544563,4.61181943440566,4.615890621901986,4.619398926371144,4.622383205615795,4.624873435655138,4.626898482285438,4.628491652194692,4.629698464523167,4.630546674844192,4.631072920514566,4.631302736661755,4.631289413986556,4.631040724049501,4.630602185990856,4.629986012262886,4.629224399330657,4.6283251187547005,4.627314815885417,4.626210144066805,4.625004441961265,4.623726575365062,4.622362111380062,4.6209243726814675,4.6194155797151435,4.617831291589355,4.616172618527039,4.6144295685217935,4.612612133580019,4.610714762587049,4.608726353313551,4.606654677320057,4.604505285721234,4.602272627402416,4.599955592140669,4.5975697230570605,4.595121681489188,4.592615908328787,4.590073497811588,4.587505552166925,4.584925394069995,4.582364109762933,4.579832801475069,4.577349232773337,4.574950041014534,4.572645218205061,4.570469181255847,4.5684374732879585,4.566571188537128,4.564896972353754,4.563425926967169,4.562175815944306,4.561155521068629,4.5603850263529395,4.559856560236701,4.55958788628685,4.559571232942851,4.559801049090038,4.560268452944945,4.5609634525011735,4.561871614860589,4.5629807275709275,4.564259704390056,4.565697443088643,4.567267298316289,4.56894706561433,4.570710099632366,4.572527534574133,4.574386047764432,4.576249001846464,4.578104184367963,4.579927170424398,4.581703527117636,4.583416601103677,4.585050849261456,4.586602940922173,4.58804956140423,4.589400702714024,4.590644152399292,4.591792122912297,4.592832401800775,4.593778311739926,4.594636514067347,4.5954125598977065,4.596109779899804,4.5967514887552365,4.597337686464006,4.597886136593044,4.598405720925817,4.598898659908191,4.599397150005232,4.599900080994006,4.600409673320379,4.600954792780618,4.601527667814188,4.602143841542156,4.602806644633322,4.603526069094085,4.604302114924445,4.605146994576668,4.606058487604887,4.60703881445497,4.608095746687449,4.6092270638564585,4.6104349864078635,4.611718404118731,4.6130795374349285,4.6145172761335225,4.616032730437446,4.617618128786167,4.619280132517283,4.621007639401464,4.622798428992841,4.624652501291416,4.626563194959588,4.6285194077680245,4.630517809047927,4.632547296569961,4.634591216990128,4.636641798747895,4.638683498722197,4.640693002231434,4.642655876377473,4.644544365586984,4.6463318245095655,4.6479960486865535,4.649494849646483,4.650803802484821,4.651867396054905,4.652658985006334,4.653123058192445,4.653215206695908,4.65288102959299,4.652063905514096,4.650710543758425,4.648757661618784,4.646147527502641,4.642813528033999,4.638703482734996,4.6337518884525695,4.627902123817122,4.621096457236126,4.613288259346385,4.604437562122304,4.5945066179841545,4.5834587895751415,4.571286305334735,4.557986944817073,4.543555156907495,4.528017586956403,4.511415313212333,4.493790524146754,4.475220935365001,4.455787593141206,4.435590417539368,4.414751533082149,4.393401946075677,4.371694867284745,4.349789058588809,4.327862155657188,4.306096235050935,4.284684475560435,4.263822276421932,4.243708367540475,4.224544809489906,4.20651367883127,4.189814815692543,4.174619194405434,4.161091127964055,4.149386047579052,4.139616085766671,4.131904477272497,4.126338929708249,4.122970513328851,4.121850298389228,4.122983836004049,4.12636002394398,4.131935563514627,4.139646061785868,4.149411582706516,4.161108891530987,4.174618084182501,4.189787060119212,4.20644817567821,4.224432676973649,4.243542944323423,4.263595790943552,4.284388046037259,4.305719869476566,4.327402523362824,4.349235057345118,4.3710453868687935,4.392651435372799,4.413893330754743,4.434625633810367,4.45471289734181,4.4740285559346775,4.492486012200169,4.509985346074286,4.526466605518628,4.541882050947058,4.556187273442241,4.5693678401060405,4.5814093180403175,4.592331691257869,4.60213495975869,4.610861312014241,4.618546275158386,4.625228706993787,4.630960787998306,4.63580358043327,4.63981148522241,4.643043344181188,4.645566880908535,4.647436496328179,4.648724354930786,4.64947708607955,4.64976796448807,4.649639178627809,4.649159562320632,4.648361312031603,4.647304379799119,4.646020962088246,4.644559908708049,4.642953416123593,4.641234791022875,4.6394295685333615,4.637575496234784,4.635680345687676,4.633777423580034,4.631884493478793,4.630007106498618,4.628167467098176,4.62637778772973,4.624646950176749,4.622980505553898,4.621385115198778,4.619862999557254,4.618428591527459,4.617070788880061,4.6157973631755915,4.614606093968185,4.613498091480775,4.61246669437576,4.611504131092609,4.610614842523054,4.60978661621483,4.609017231722069,4.608294476592506,4.607610579265607,4.606954437512041,4.606320500217141,4.605698775374506,4.605079270977738,4.60444311323697,4.603792522598071,4.603107515048239,4.602380319026944,4.60160982431125,4.60077937755716,4.599882317427073,4.598917533698057,4.597883916147177,4.596769252322169,4.595587975121164,4.594324541423097,4.5929967147949,4.591603385013641,4.590150103193984,4.588652412456997,4.587122525254945,4.585570433594228,4.5840116805959115,4.582460699158128,4.580934142624876,4.579454215454823,4.5780386812149,4.576704193249106,4.575468515124373,4.574349410407634,4.573364642665821,4.5725230936824,4.571846967916038,4.571344036927265,4.57101985183075,4.570885514855823,4.57094546689422,4.57119637727714,4.571647127788048,4.572289946866413,4.573119283397568,4.574122924929246,4.575299761238515,4.576633138981376,4.578110845705563,4.579717338290009,4.58143707361365,4.583261169893018,4.585162981777716,4.587129186592545,4.589146461662304,4.591191492305396,4.593248735400754,4.595312639833712,4.597348788693338,4.599350520642034,4.601307843673399,4.603194112437035,4.605000445149475,4.6067057475749875,4.608306689044772,4.609772183316697,4.61109112816143,4.612245760012038,4.613213874409856,4.613983258902617,4.614521717025256,4.614819256771375,4.614842571452973,4.614578338394853,4.613989920240217,4.613059553422129,4.611765033481929,4.610079715069214,4.607979173279456,4.605447864991585,4.602464695969873,4.599011902647385,4.59508504413239,4.590670797749691,4.585770273722217,4.58038569249584,4.574527046076958,4.568208767363704,4.561455281260613,4.5543010046786145,4.546774803413976,4.538929968167496,4.530808687410638,4.522480905188199,4.513999912200975,4.505446754723097,4.496884715461761,4.488401502028693,4.480071499360422,4.4719790843998775,4.464211964758784,4.456847856042469,4.449964473856261,4.443641754251353,4.437951861718407,4.432955858518748,4.428715917136641,4.425276446489413,4.42268407594026,4.420971001954245,4.420143885868971,4.420226042366031,4.421209699884896,4.423087086865031,4.4258271170643075,4.429406475801127,4.4337707621517595,4.438871126307144,4.444659828681152,4.451052492330855,4.457984724326127,4.465384360176307,4.473153700263268,4.4812316823256815,4.489525047637155,4.4979549703694275,4.5064415144713035,4.514904743891587,4.523275824808418,4.5314925847375305,4.539480638742397,4.547198908574486,4.554588552418331,4.561615153363004,4.568245404720502,4.5744515509174954,4.580213607941182,4.585528245122764,4.590372147780639,4.594767520373474,4.598705481117801,4.602207124249352,4.605284662220394,4.607958079043724,4.610245138286273,4.612174705744308,4.613772316545293,4.615065726262562,4.61607824957771,4.616835421618206,4.617368328626179,4.617694734168563,4.617833512035222,4.617806866684824,4.6176325616842995,4.617327250377648,4.6168920429878035,4.616343592858764,4.615685230659331,4.614913625720702,4.614037659826347,4.613051781861597,4.611949330488853,4.610731415931048,4.609378054175384,4.607890355444794,4.6062561072870105,4.604476419924969,4.602537970683469,4.600435208447845,4.598161471880496,4.595718981427291,4.593107737088228,4.590333289977974,4.5873967503194635,4.584310330564962,4.581091794281401,4.577748913029316,4.574311662827903,4.570801137912895,4.567245093857624,4.563665735120756,4.560106360396688,4.5565880639211525,4.553158585280279,4.549846790270334,4.546692646916915,4.543727241462151,4.54099276237751,4.538506973229921,4.536312062490849,4.534429124396025,4.532883694072916,4.531687983973786,4.530865308780235,4.530414558269327,4.5303479448933315,4.530657697091713,4.531340484195673,4.532387424421745,4.533769651973664,4.53547717484503,4.537480017016647,4.539748202469315,4.542251755183837,4.544952927580481,4.547805090296051,4.550784928648947,4.55384137238424,4.556937784145132,4.560041967466558,4.5631028520935875,4.566089351784088,4.568968159850062,4.571710410495244,4.574279466362838,4.576656453662975,4.578823608828724,4.580749845617953,4.582445156037062,4.583881784512719,4.5850663923825214,4.585992318308872,4.586673995189902,4.587114753694412,4.587324585828801,4.587327916497601,4.587131407038411,4.586767253916298,4.586256551366992,4.5856203936262245,4.58489652827373,4.584094947315907,4.583260059670085,4.582418510686663,4.5815847332637745,4.580795364758218,4.580069278959857,4.579434231442025,4.578899103988187,4.578491652171675,4.57821853733009,4.578085310578097,4.5781141763743625,4.578297363158352,4.578642642490601,4.5791422428105735,4.579793943672405,4.580591083738495,4.581519230110712,4.582568390782655,4.583724132856194,4.5849698029873265,4.58628985805499,4.587668754938116,4.589079848286308,4.590520917653698,4.591961987021088,4.593391954159147,4.594795275946806,4.596156409263001,4.597467582547199,4.5987143629012674,4.599880096981207,4.6009781074622165,4.601987300108564,4.602908785143183,4.603739231897273,4.604483081262568,4.605137002570268,4.605704326489172,4.606192824579813,4.606605827510992,4.606947776174442,4.607227552353628,4.607447376494416,4.607615020157341,4.607738254902935,4.607825962514663,4.607881473661327,4.607910339457592,4.607919221241058,4.607913670126392,4.60789590655946,4.607871481654928,4.607843726081596,4.60781486028533,4.607788214934932,4.6077637900304,4.607747136686401,4.6077371446800015,4.607733814011201,4.607734924234134,4.607751577578134,4.607774892259733,4.607812639839464,4.607854828310929,4.607915890572259,4.607988055062922,4.608070211559984,4.608171241846912,4.608286705031973,4.6084143806693,4.608560930096492,4.60872968398235,4.6089084298746075,4.609104939333798,4.609330314589253,4.609566792074041,4.6098343558009605,4.610120793317746,4.610431655739063,4.610763612396113,4.6111222144035615,4.611505241315542,4.611922685138454,4.612364553865898,4.612837508835474,4.613338219378383,4.613870016163422,4.614446221865793,4.615054624033229,4.61570188400333,4.616390222221962,4.617116308020325,4.6178879129589525,4.618705037037845,4.619566570034069,4.62047473239349,4.621440626345442,4.622449818991791,4.6235111921160055,4.624628076386884,4.625797141135625,4.627021717031032,4.628299583627236,4.629634071593037,4.631022960482569,4.6324695809646315,4.633975043262159,4.635534906483416,4.637163603526537,4.6388444810475225,4.640593082167439,4.642404965994552,4.644281242751796,4.646229683999703,4.648248069292408,4.65033639862991,4.652500223126875,4.654742873452103,4.657065459828529,4.659469092479085,4.66195710207257,4.66453059883192,4.667188472534199,4.669936274294075,4.672761791659282,4.675676126859152,4.6786670674414195,4.681733503183151,4.684864331855014,4.688060663679942,4.691302514645136,4.694582113190063,4.697886136639522,4.701192380534851,4.70448530175498,4.707736034503645,4.710925704990981,4.714016565637255,4.716977530200335,4.71976752043169,4.722341017191053,4.724654721784028,4.72664646172635,4.7282585054254875,4.7294275701742405,4.730073719921416,4.730123679953414,4.729485301766773,4.728061995966295,4.725756062933852,4.722455370153183,4.718053336222692,4.712413403721587,4.705414558350141,4.696923573356363,4.686803891319463,4.674921175264519,4.661132206433141,4.645302647850414,4.627302603433152,4.607007728212839,4.5843014487814955,4.559089396189812,4.5312838628260765,4.5008293375436494,4.467688072762822,4.431845635585492,4.3933353326996825,4.352208234360356,4.308574252637935,4.262552181386308,4.214330758504159,4.164122036571766,4.112186917978465,4.058825162916252,4.004385381386177,3.949227285618616,3.893764988767663,3.8384270368855353,3.7836664009289698,3.7299460438610925,3.677747802434885,3.6275446316198514,3.5798094863854892,3.534999778580225,3.4935507155938135,3.4558753003573455,3.422346567776315,3.393318678966352,3.369073630552434,3.3498701044779486,3.3359023897561637,3.327310374476634,3.3241928684803934,3.3265687455573003,3.3344158012486957,3.347656319949274,3.3661404215630815,3.3896760375227144,3.418017808559984,3.450875966489379,3.487915223985132,3.528756995027083,3.5729960482446748,3.620209388700416,3.669930722762415,3.7217026385822423,3.775046630075725,3.8294941831650835,3.8845812246642604,3.939857004062384,3.994886313969641,4.0492650332383375,4.1026190167399665,4.154608536256946,4.2049271702596815,4.253309575467105,4.299531486846672,4.3434119380602345,4.384811041018172,4.423619993872994,4.459781065032142,4.4932620580305205,4.524061862645171,4.552217116232866,4.577779999271447,4.60082711714329,4.6214628308041075,4.6397915012096105,4.655939693774181,4.6700350841351375,4.682210899044463,4.692615908375213,4.701376677541776,4.708638645748407,4.714540590861767,4.719200196512778,4.722751799676371,4.725308643091736,4.726982859275137,4.727884360296969,4.728096412877227,4.727720047302842,4.726837420070876,4.7255151445573285,4.723829826144594,4.721839196425207,4.71959876654583,4.717155165869661,4.714563905543366,4.711841638910944,4.709043877119058,4.7061894939575755,4.703306244999828,4.7004174449274165,4.697535306192604,4.694682033254058,4.691863177226446,4.689098722122565,4.686384227050682,4.683737455577731,4.681150636143176,4.678625989192887,4.676183498739663,4.673794298987235,4.671473933056673,4.669217960056241,4.66701971864834,4.6648792088329705,4.662793099941332,4.660759171527559,4.6587685418081834,4.6568189903373405,4.654906076223296,4.65303313013485,4.651192380511469,4.649381606907288,4.647599699099372,4.645842216195988,4.6441180399806035,4.642420509115618,4.640746292932231,4.63910094254511,4.637484457954255,4.635897949382598,4.634338086161341,4.632815970519815,4.63132827178922,4.629874989969558,4.628459455729628,4.627082779292362,4.625751621995361,4.624463763392758,4.623216983038687,4.622016832047813,4.620859979751338,4.619750867040993,4.61869282458558,4.617679191047497,4.616708856203812,4.615782930277459,4.614900303045503,4.614057643839146,4.6132571731042535,4.612493339726158,4.611759482367263,4.611065593033965,4.610395018382266,4.609753309526831,4.60913269490713,4.608532064300228,4.607952527929057,4.607387424456019,4.606838974326981,4.606293854866742,4.605764278527569,4.605240253303062,4.604723999639089,4.604209966420982,4.603703704763409,4.603200773774635,4.602700063231727,4.602210454918152,4.601718626158711,4.601232348513936,4.600756062875561,4.600273115899586,4.599802381375877,4.599337197966835,4.5988731247807255,4.598417933378083,4.597960521529574,4.597507550572797,4.597052359170154,4.596602718882178,4.596149747925401,4.5956945565227585,4.5952371446742495,4.594777512379873,4.594311218747897,4.593840484224189,4.593366419031681,4.59288791294744,4.5924116273090645,4.5919286803330905,4.591449064025916,4.5909772192792735,4.5905109256472985,4.590061285359322,4.589619416631879,4.589207523923634,4.588810064113522,4.588450351883141,4.588115064557292,4.587814194142375,4.5875466304154555,4.587321255160001,4.587128076369612,4.586963763375487,4.5868338672922935,4.586721734776033,4.586635137387238,4.586554091113109,4.5864741550619135,4.5863864474501845,4.586275425156857,4.586128875729664,4.585934586716341,4.585679235441689,4.585347278784639,4.584929834961729,4.584409140406024,4.583785195117524,4.5830357946375635,4.582164269634943,4.581167289440864,4.580034862048925,4.57877808968846,4.577399192805335,4.575899281622482,4.574298340152703,4.572608580848262,4.5708510979448915,4.569035883448992,4.567197354271493,4.565354384202262,4.563539169706363,4.561773915242461,4.560097478613222,4.558533174500242,4.557104317585123,4.555847545224661,4.554786172100454,4.553935741333569,4.553335110726669,4.5529865007256225,4.552908785120294,4.553118617254682,4.553615997128786,4.554400924742609,4.555486722771348,4.556847856087538,4.558489875805845,4.560389467244672,4.5625321975058855,4.564898082576687,4.567461587329612,4.570194956191328,4.573080425594903,4.576074696845939,4.579148904148173,4.582271961259471,4.585415002383569,4.588533618603137,4.591607825905374,4.594593215372949,4.597474243884799,4.600198730963057,4.602758905047191,4.605109246996936,4.607236434137094,4.609103829110865,4.61069477857425,4.611985967845651,4.612957412912269,4.613598011544769,4.6138744570551555,4.6137934107810255,4.613328227371983,4.612472245490426,4.611222134467557,4.60957678408044,4.607522871653878,4.605073719863071,4.602232659376818,4.599004131086852,4.595404788337174,4.591449064025916,4.58716138305761,4.582567280559722,4.577693401882652,4.5725808252749305,4.567261747201623,4.561783907248861,4.556182832550508,4.550519585367896,4.544845235955954,4.539210854569613,4.533675283024336,4.528296252912653,4.5231226140436265,4.518219869570321,4.513646861308197,4.509438006168186,4.505648815296952,4.50232924872649,4.499512613144797,4.497229994794006,4.4955080390245135,4.494370060517918,4.4938193899430185,4.493868239752083,4.494511058830442,4.495733414279965,4.4975197629795876,4.49984012891011,4.502671197389935,4.505968559501732,4.509687806328171,4.513784528951922,4.518203216226322,4.522886136558841,4.527777778802816,4.532822631811586,4.537965184438485,4.543139933530452,4.548289147494956,4.553365086745868,4.5583233423658545,4.563105072539454,4.567676970578667,4.571989076451496,4.57601696525341,4.579741763194541,4.583126832918092,4.586168843755263,4.588852252584986,4.59117594918433,4.593137713107427,4.594748646583608,4.596018741619275,4.596961320889625,4.597599699076259,4.597954970414907,4.598049339364236,4.597918333058109,4.597588596846927,4.597087886304019,4.596455059232052,4.595716760981424,4.594907408463066,4.5940492061356455,4.5931765709100905,4.59232502992027,4.591509016064312,4.590760725807285,4.590090151155588,4.589528378351351,4.589079848286308,4.588763434750324,4.5885924604185995,4.5885680355140686,4.588702372488994,4.588993250897512,4.589446221854288,4.590049072907056,4.590804024501683,4.591709966415235,4.592746914634914,4.593918199829519,4.595206058432118,4.596604939328044,4.598095968727433,4.599669154623885,4.601306733450466,4.6029953825319785,4.604718448524423,4.606457057637933,4.608189005413845,4.609899858954024,4.611558532016339,4.613152812148526,4.614652723331383,4.61603050999158,4.617258416555785,4.618313128342399,4.619154677325823,4.619756418155659,4.62008171347511,4.620091705481509,4.619753087486859,4.619022560796763,4.617869039169087,4.616250334132369,4.6141298083298095,4.611463052844077,4.608222312101843,4.604372058969241,4.599884537872939,4.594727552347876,4.588890000164718,4.582351897310667,4.5751099131169255,4.567168488475228,4.558520962047977,4.549195089408505,4.539219736353079,4.5286248789009,4.517462697529833,4.50579758517001,4.493686163191027,4.481212808535816,4.468467449261972,4.455540013427089,4.442541523324494,4.429581891024581,4.416775469489473,4.404245493464763,4.392116307918971,4.380500045368357,4.369528822341974,4.3593203224707455,4.349980016933327,4.341620038245974,4.334331424689211,4.328205214543561,4.3233091314079495,4.31970978865837,4.317443823651619,4.316542322629824,4.317026379828719,4.318879341904304,4.322098988410713,4.326640910430618,4.3324484865944255,4.339470646647208,4.347621903423109,4.356812328864537,4.366942002907502,4.377905454373349,4.389580558739422,4.401850742597734,4.41459832231736,4.4276845200316455,4.440999423670199,4.454413137149831,4.467816858623081,4.4810929044590235,4.4941413545936655,4.5068689503006105,4.519183543076396,4.531015188876226,4.5422950538782345,4.55296540648989,4.562989609354394,4.5723265842232115,4.580959677752342,4.588864465037252,4.596049827861407,4.60250799466427,4.608254508566908,4.613312684250917,4.617700285283229,4.621450618351842,4.624589218584219,4.6271593846747585,4.6291910926426585,4.630739853634583,4.631830092555062,4.632515100104896,4.632828182972081,4.632807088736349,4.632495116092096,4.631932233064925,4.63114508500523,4.630174750161544,4.6290489841071985,4.627795542415527,4.6264432908827935,4.625015544190598,4.623538947689338,4.622031264945946,4.620521361756688,4.61901478923623,4.617538192734971,4.61609823359051,4.614713785592713,4.613393730525046,4.612152501285642,4.610991208097435,4.609924283858556,4.608955059237806,4.60808575468105,4.607319700857089,4.606654677320057,4.606089573847019,4.605613288208644,4.605226930627863,4.604921619321212,4.604676260052958,4.604486411931369,4.604323209160176,4.6041755495100505,4.604030110305792,4.603842482630068,4.603610446037013,4.6033040245074295,4.602884360238651,4.6023436816701455,4.6016386901075155,4.6007582833214276,4.599669154623885,4.59835576089382,4.596797007895501,4.5949729116161295,4.59288458227864,4.590499823417966,4.587837508823974,4.584887646490265,4.581654677308571,4.57815414439996,4.5743993704396315,4.5704214416697155,4.5662347909883465,4.561879386421122,4.557390755101907,4.552803313941633,4.5481692434181635,4.543534062671763,4.538949952180295,4.534462431084023,4.530128120752544,4.525992540326123,4.522108980505554,4.518524070654036,4.5152844401347645,4.512424505858672,4.50998312562842,4.507990275463208,4.506473710936368,4.505445644500164,4.50492050905273,4.504906076154597,4.505391243576434,4.506377121541174,4.507840395367218,4.509757750372967,4.512110312768557,4.514852563413724,4.517952305843403,4.5213673515861315,4.525051071278712,4.528951284443281,4.533016920824908,4.537204681729197,4.541461276455349,4.545732304079636,4.549967804570061,4.5541255894551576,4.558161249817597,4.562027046071247,4.5656907817510435,4.56912026039192,4.57228883664348,4.575166534486523,4.577737810799983,4.579990453131594,4.581916689920824,4.583498757600739,4.584754419738271,4.585677014995822,4.5862720944880575,4.5865618626736415,4.586559642227775,4.58628319671739,4.585750289709418,4.584986456331325,4.5840294441628435,4.5828870247645055,4.58160693772244,4.58020916704945,4.578721468318863,4.577188250448013,4.575622836112098,4.57405964222205,4.572534195911733,4.571065370971014,4.569682033196156,4.568397505262361,4.567240652965891,4.566230350096613,4.565373257992127,4.564686029996432,4.564170886555394,4.563843370790079,4.563696821362887,4.563741230280218,4.563961054421006,4.564360734676984,4.564922507481219,4.565641931941979,4.566505685384064,4.567497114463476,4.568599565836216,4.5698074883876165,4.571089795875546,4.572435386070672,4.573834266966595,4.5752597932129175,4.576705303472039,4.578148593285293,4.579579670646283,4.58099631510914,4.582376322215199,4.583717471518594,4.585009771012925,4.586259882035791,4.587447820574394,4.588589129749801,4.589672707332676,4.590707435106488,4.591687761956569,4.592628120781053,4.593524070688206,4.594384493461495,4.59521716066145,4.5960209620651415,4.596806999901901,4.597574163948794,4.598333556435153,4.599087397806848,4.599835688063876,4.600583978320904,4.6013389299155305,4.602092771287225,4.602852163773586,4.6036215482663465,4.6043964838737725,4.605176970595866,4.605966339101426,4.606760148498718,4.607558398787743,4.608363310414369,4.6091737731556615,4.609989787011619,4.610811351982244,4.611641798736335,4.61247335571336,4.61332045581145,4.614176437693007,4.615043521803896,4.615926149035851,4.616826539834739,4.617743583977627,4.618689493916779,4.619659828760464,4.620655698731614,4.621685985613697,4.62274735873791,4.623850920333589,4.624987788617266,4.626173506710007,4.62739697238248,4.628664846972285,4.629979350925287,4.631342704687353,4.6327526878126175,4.634213741192814,4.635720313713273,4.637275736042798,4.6388800081813875,4.640530909683175,4.64223177121696,4.6439848132286095,4.645782264157591,4.64763633645617,4.649530376780348,4.651471046467723,4.65345945574123,4.655495604600868,4.657578382823705,4.659703349518007,4.6618638433461745,4.664062084754074,4.66629252262704,4.6685440547357375,4.670813350411368,4.6730804256411345,4.675333067972767,4.677560175176935,4.679737322349105,4.681837864138879,4.6838384858646585,4.685699219500844,4.687380097021838,4.688850032185509,4.690045742284656,4.690921708179019,4.691405765377931,4.69143907206593,4.6909539046440845,4.689854783940131,4.688071765909275,4.68550493048752,4.682059908725537,4.677646772565731,4.672151169045976,4.665475398548143,4.657508438778909,4.648152590120146,4.637295720055597,4.624843459635939,4.610702550134783,4.5947886146092065,4.577032819237354,4.557370771089109,4.535748069240748,4.512156942131754,4.486581846641075,4.459043877004457,4.429575229686981,4.398262502077459,4.3651956222335,4.3305067066841785,4.294351186640165,4.256916689777193,4.218426370904855,4.17911226661621,4.139261924650973,4.099165113194719,4.059134915114619,4.019496625730103,3.980609957271524,3.942806866395903,3.9064526164482487,3.8718913765378358,3.8394695362198017,3.809516831705282,3.782327472071549,3.758210099294004,3.737402301080326,3.720137224246461,3.7065980555763653,3.696941336503602,3.6912703177609436,3.6896394002721102,3.6920730089416294,3.6985533802025725,3.708996137112027,3.7232935880454865,3.7412847506776563,3.7627853280016486,3.7875477403033853,3.8153277385375888,3.845831113626989,3.878737011143917,3.9137279073295015,3.9504529717368726,3.9885602636962214,4.027703393652403,4.067529310712665,4.107699396882384,4.147887246619197,4.187779777055932,4.227077228000613,4.265524248178586,4.302875478321599,4.338922196518184,4.373465672863279,4.4063637988214115,4.437492229424038,4.466756595721817,4.494076961663536,4.519425571675848,4.54278577241474,4.564162004771928,4.583580914097801,4.6010924604243435,4.616759926458744,4.630645484685254,4.642842393830264,4.653446133066031,4.662553291787743,4.670262679836461,4.6766864297284405,4.681916689967143,4.686072254406428,4.689255263556158,4.691545653467526,4.693050005542128,4.693860468283427,4.694054757296752,4.693717249525033,4.692918999236,4.691721068690985,4.690193401934784,4.688382628330595,4.68633648746455,4.684111600706247,4.681737944074884,4.679247714035527,4.676675327499107,4.674040768478425,4.671370682323877,4.668685053048264,4.66598832154332,4.6633093536053085,4.660643708342497,4.658004708430085,4.655396794759807,4.652835510452726,4.650315304394177,4.647837286807094,4.645410339474942,4.6430300215059885,4.6407052146837,4.638427037224609,4.63620992202685,4.634038325969355,4.631932233064925,4.629873879746625,4.62787769891259,4.625943690562818,4.624066303582644,4.622249978863802,4.620496936852155,4.618809397993573,4.617185141842188,4.615625278620933,4.614127587883942,4.612696510522949,4.611336487429684,4.610030865260151,4.608791856466614,4.607613909934408,4.606494805217665,4.605430101424653,4.604419798555371,4.6034627863868876,4.602554624027468,4.60168753991658,4.600859313608356,4.60006772465693,4.599307221947637,4.598574474811675,4.597862821911445,4.597175593915748,4.5964961374805835,4.595830003720618,4.595163869960653,4.594508838430021,4.593843814892989,4.593185452693557,4.592514878041859,4.591833201160829,4.591141532273398,4.590432099819036,4.589712675358274,4.5889799282223125,4.588220535735953,4.587452261466128,4.586670664521103,4.585870193786212,4.585058620821989,4.5842414967430996,4.583419931772476,4.582597256578921,4.581775691608298,4.580966339089941,4.580175860361451,4.579404255422826,4.578669287841,4.57797428828477,4.577315926085339,4.576720846593105,4.576185719139267,4.575717205061426,4.575319745251314,4.575012213498797,4.574784617797477,4.574638068370285,4.574586998115354,4.574619194580419,4.574733547542546,4.574936718339335,4.575208722957987,4.575537348946236,4.575928147418748,4.576353362802191,4.576808554204833,4.577265966053342,4.577707834780784,4.578126388826629,4.578491652171675,4.578775869242594,4.5789757093705825,4.579053424975911,4.578993472937515,4.578783640803127,4.57840172411408,4.5778332899722445,4.577063905479486,4.5760935706358055,4.574908962766004,4.573511192093013,4.571900258616834,4.5700872645668005,4.568082201949311,4.565890621879032,4.563552492381563,4.561065593011034,4.558477663353579,4.555802026084397,4.55308753101255,4.550353051927905,4.547648548862459,4.545002887612478,4.542453815757692,4.540043521769564,4.537804202113161,4.535774714591146,4.5339928067832505,4.532478462702272,4.531263878813278,4.530362377791464,4.5298061561018965,4.529601875082175,4.529755085846967,4.530276890625602,4.531157297411684,4.532399636874011,4.533982814776851,4.535897949336739,4.538126166763809,4.5406408217076635,4.543416379040836,4.54642286274413,4.54963473769008,4.553018697190687,4.556539214112089,4.560161871543351,4.563854473019412,4.567597034527471,4.571340706258465,4.575064393976661,4.578748113669262,4.582365219985866,4.585891288021944,4.589317435994029,4.592617018551721,4.595793366363821,4.598823164748729,4.601710854598179,4.6044486643516365,4.607042145123771,4.609480194685245,4.6117750254883285,4.613929968201819,4.615943912602784,4.617825740474689,4.619578782486335,4.6212074795294535,4.622711831604045,4.62409850004771,4.625360823522847,4.626501022475324,4.627514656013408,4.628386181016031,4.629122258820795,4.6296929134085,4.630097034556214,4.630300205353004,4.630292433792471,4.630052625638883,4.629554135541841,4.62876809770508,4.627670087224066,4.626224576964938,4.624413803360761,4.62220890061527,4.6195832233780685,4.616509016075822,4.612970735587467,4.608950618346072,4.6044320110076375,4.59941713401803,4.593893774924986,4.587867484843172,4.581357137562454,4.574376055758032,4.56695199500324,4.559117151763143,4.550919265623873,4.542406076171561,4.533629763884072,4.524664713697935,4.515574208320347,4.506435963356637,4.497335465972666,4.48834932155083,4.479569678594587,4.471083134492735,4.462980727525798,4.455343503967902,4.448255840761976,4.441797673959211,4.436042278273203,4.4310551568570125,4.426887379965567,4.423590017853797,4.421205258993163,4.419759748734064,4.419265699528765,4.4197175602626,4.421121992273169,4.423457901324738,4.426685319391715,4.430774270454899,4.435669243367629,4.441309175868578,4.447637446588151,4.4545663479146205,4.462025935803194,4.4699296128650765,4.478197443049076,4.4867361676287985,4.495462519884249,4.504295453541302,4.513146150765294,4.521941336842631,4.530608847282649,4.539076517594688,4.547278844625681,4.555161427451899,4.562697620722943,4.569817480394016,4.576497691783517,4.582718270878647,4.588450351883141,4.593690604128197,4.598429035607415,4.602672307658395,4.606422640727002,4.609691137042568,4.612492229503225,4.614849232790573,4.616778800248609,4.618305356781866,4.6194499966260745,4.620252687806834,4.620730083668144,4.620902168222802,4.620802248158807,4.620449197266025,4.619875212009521,4.619088063949826,4.618109957545609,4.616960876809666,4.615653034194265,4.614193091037006,4.6126032517965525,4.610872414243574,4.609022782836735,4.607053247353103,4.60497157935321,4.60277222772239,4.600461853798243,4.598044898472502,4.595523582191034,4.592897904953839,4.590177858767316,4.587368994746132,4.5844768640049525,4.581509238104313,4.578477219273543,4.575405232417176,4.572304379764545,4.569185763544984,4.5660771393318225,4.562999601360793,4.559978684759361,4.5570354837632605,4.55419775394582,4.551489920211574,4.548947509694385,4.546584955292388,4.544427792133044,4.5425037757896884,4.540831780052185,4.539428458264534,4.538307133101933,4.537483347685447,4.536959322460944,4.536741718766024,4.536829426377752,4.537213563512663,4.537887468833157,4.538831158326436,4.540039080877832,4.541482370691082,4.543137713084586,4.544977352485013,4.546972423096099,4.549100720459177,4.551323386771584,4.553603784676521,4.555925260829989,4.558252288098125,4.560554890461729,4.562809753239203,4.564992451526016,4.567092993315765,4.56907252080579,4.570937695333687,4.572671863555459,4.574266143687638,4.575729417513692,4.577047252135487,4.578239631565823,4.579295453575365,4.580236922622781,4.581070700045669,4.581810108519229,4.5824740218333275,4.583070211548495,4.583621992346332,4.584142686902037,4.584638956553211,4.585133005758518,4.585630385632625,4.586152190411263,4.586703971209101,4.58729349958667,4.587921885766902,4.588606893316733,4.58934519156736,4.590127898735318,4.590973888610474,4.591863177180026,4.592804646227444,4.593790524192192,4.5948141497366715,4.595873302415016,4.596961320889625,4.598068213154101,4.599197309877242,4.6003352883838495,4.601475487336324,4.602617906734665,4.603759215910072,4.6048983046396135,4.606020740025156,4.607137624296032,4.608243406337575,4.6093325350351195,4.610418333063864,4.61149413908621,4.612556622433355,4.613621326226368,4.614686030019381,4.615750733812393,4.6168209887200735,4.617906786748819,4.619007017675697,4.620125012169508,4.621275203128383,4.622449818991791,4.623655521097332,4.624902301451403,4.626190160054007,4.62752575824274,4.628911316463472,4.630344614270335,4.631832313000929,4.6333799637699205,4.634985346131442,4.636646239639629,4.638365974963279,4.640147882771193,4.641984191502839,4.643874901158215,4.6458177912914564,4.647805090342029,4.649830136972334,4.651890710736503,4.653972378736406,4.656062928519775,4.658154588526079,4.660218492959051,4.662239098697625,4.6641964217290015,4.66606270647985,4.667804646262171,4.669390044610899,4.670776713054571,4.671925793790519,4.67278510634088,4.673295808890191,4.673414602744053,4.673061551851268,4.6721755939505085,4.670687895219908,4.668519629831205,4.665594192402005,4.661830536658176,4.65713318342746,4.6514321886650585,4.644637624313379,4.636665113429494,4.627440271076877,4.616885381650204,4.604931611327611,4.591522338739511,4.57661093452271,4.560151879536952,4.54213407155291,4.522546408341261,4.501403322800147,4.478731460279975,4.454589662596219,4.429052314685418,4.402214895719841,4.374197309776291,4.3451427756131675,4.315227818676863,4.284634515528439,4.2535782494169485,4.222279954706109,4.1909894315559,4.15997091302443,4.129478640163404,4.099801270935454,4.0712108099592115,4.043984812967971,4.018398615249157,3.9947075680773945,3.973164802281442,3.9540023544543246,3.937426726061604,3.923617773218447,3.9127298169125555,3.9048938634500376,3.90019428977381,3.898697709259859,3.9004163343604494,3.9053324015086517,3.913399281341275,3.9245303764695376,3.9386024521478653,3.955465628280287,3.9749367180828385,3.996813660981691,4.020858869269152,4.046828093899932,4.074465983599405,4.1034872110737455,4.133623102373127,4.164578338197321,4.1960886854882276,4.2278721476208085,4.259666711982822,4.29122923975189,4.322326584112028,4.3527433618141815,4.3822786225074255,4.4107791554269635,4.438081757801598,4.464069856223325,4.488644640851078,4.51172395518778,4.533256728978494,4.5532140964269425,4.571582734857919,4.588363754494345,4.603584910909548,4.617276180122717,4.629488632388777,4.640283329969054,4.649725776016605,4.657894796359692,4.6648625554889716,4.670703438340975,4.675518475202626,4.679385381679254,4.68237521203859,4.684581225007027,4.686073364629362,4.6869249056191915,4.687210232913046,4.686994849663989,4.686340928356283,4.685299539244862,4.683927303699322,4.68226418974526,4.680367928975211,4.67826516673957,4.675988099503404,4.673580025961111,4.671058709679625,4.668456347124009,4.665787371192396,4.663073986343453,4.660335066367045,4.657585044161305,4.654828360617966,4.652089440641561,4.649371614900888,4.646683765179415,4.644035883483541,4.641427969813265,4.638873346843788,4.636376455466842,4.633936185459493,4.6315591981593425,4.629246603789322,4.627001733018233,4.62483346762954,4.6227251542792445,4.620697887203079,4.618738343725844,4.616848744293406,4.6150290889057635,4.613287149123452,4.611610712494204,4.610009771024418,4.608469891815964,4.607012169104571,4.605614398431577,4.604283241134579,4.603027578997044,4.601835199566705,4.600709433512363,4.599660272840418,4.5986799459903365,4.597765122293317,4.596914691526428,4.596141976364868,4.595431433687573,4.5947974963926725,4.5942157395756364,4.593707257472197,4.59325095584662,4.592856826705308,4.592515988264792,4.592218448518675,4.591957546129355,4.591731060650967,4.591521228516578,4.591332490617922,4.591139311827532,4.590945022814209,4.590732970233954,4.590493162080366,4.5902122756782475,4.589883649689998,4.589497292109219,4.589034329146044,4.588501422138072,4.587887468855971,4.587189138630942,4.58639865990245,4.585518253116364,4.584551248941482,4.583499867823672,4.582376322215199,4.581185053007796,4.579936052207864,4.578643752713534,4.577321477200005,4.575991430125945,4.574674705727083,4.573385736901553,4.572143397439221,4.570976553136352,4.569899636891077,4.568935963384997,4.56810551663091,4.567431611310414,4.566925349652842,4.566602274779259,4.5664834809254,4.566572298760061,4.566878720289645,4.567407186405882,4.56816324822344,4.569138023958853,4.570330403389187,4.571741496737377,4.573351319990621,4.57514877091959,4.57712274729495,4.579253265103901,4.581518119887779,4.583903988971383,4.586380896335518,4.588926637521515,4.591520118293645,4.594130252409775,4.596734835411238,4.599312773062303,4.601829648452038,4.604261036675913,4.606583623052327,4.608769652007948,4.610800249752911,4.612646550490951,4.614277467979934,4.6156818999905305,4.616826539834739,4.61768363193923,4.618248735412268,4.61848632311999,4.6183819621642614,4.617910117417619,4.617063017319528,4.615815126742524,4.614154233234341,4.612068124342714,4.609554579621775,4.606596945727526,4.603193002214102,4.5993571819796335,4.595081713463591,4.590382139787039,4.585280665408643,4.5797839516660055,4.57393751769939,4.567762457744529,4.561298739827022,4.5545907728641986,4.547689627110991,4.540648593268196,4.533519851813678,4.526384449021566,4.519282352917457,4.512307932450678,4.5055089272073605,4.498963052792831,4.492745804366553,4.486911582852254,4.481531442517663,4.476658674063575,4.4723532295283865,4.46865729738356,4.465617506992292,4.463260503704979,4.461617373763754,4.46070366028968,4.46051603261396,4.461062262297124,4.462325695995174,4.464291900809978,4.466922018938873,4.47018607436266,4.474040768386944,4.478421708081595,4.4832844845292845,4.488569145691615,4.494209078192594,4.500131007318625,4.50627387080838,4.512566614394129,4.518951506483344,4.52535638258536,4.531712408878318,4.537977396890751,4.544086953692531,4.5499900090287255,4.555653256211338,4.561031176100103,4.566089351784088,4.570810019696361,4.575160983371856,4.579131140581241,4.582713829986914,4.585896839136611,4.5886812782532616,4.591078249566202,4.59307443040023,4.594693135436945,4.595951018020346,4.596852519042164,4.597419842961068,4.597670753343989,4.59762745464959,4.597309930890674,4.596731504742437,4.595931034007546,4.594914069800666,4.593719469924463,4.592360557054134,4.590868417431813,4.589259704401498,4.587567724651188,4.5858146826395485,4.584015011264711,4.582198686545875,4.58039235383344,4.578611556248469,4.576881828918429,4.575220935410253,4.573644418845006,4.572177814350153,4.57083000370916,4.56961875048896,4.568557377364751,4.567658096788801,4.566923129206975,4.566353584842207,4.565967227261428,4.5657607257958395,4.565717427101442,4.5658495436305016,4.5661470833766185,4.566600054333393,4.567200684940293,4.56793232185332,4.568782752620206,4.56974753634922,4.5707989174670285,4.5719313448589665,4.573120393620501,4.5743582921911,4.575621725889165,4.576906253822961,4.578196332871425,4.579464207461223,4.580720979821688,4.581947776162956,4.583130163586892,4.584268142093498,4.585356160568106,4.586393108787784,4.587372325414932,4.5883026922330155,4.589174217235636,4.589993561760393,4.590768497367818,4.591503464949646,4.592205125843475,4.592872369826374,4.593517409350606,4.594154677314306,4.5947786226028065,4.59541033945184,4.596045386969673,4.596705969614972,4.59737987493547,4.598093748281566,4.598852030544994,4.599653611502818,4.600507372938507,4.601421086412594,4.602400303039743,4.603452794380488,4.60457189909723,4.605775380756902,4.6070576882448355,4.608428813567433,4.6098876465017575,4.611428635933146,4.61306288409093,4.61478372963751,4.616596723687551,4.618498535572256,4.620475842616423,4.622536416380587,4.624671375081282,4.62687183693504,4.629134471273061,4.631450396311881,4.6338062893763,4.636181056230584,4.638573586651802,4.640960565958355,4.643318679468642,4.645625722723999,4.647858381042826,4.649994449966459,4.651993961469299,4.653825829309213,4.655448975237671,4.656830092566674,4.657917000818357,4.658653078623122,4.659005019292973,4.658903989006044,4.658292256169807,4.657108758522928,4.655287992912345,4.652766676630862,4.649469314519017,4.6453315136466795,4.64028555041492,4.634254819441344,4.627173817572891,4.618990364331697,4.609635625895904,4.5990663035711155,4.587234657771206,4.57410738180818,4.559668932560979,4.543900436239742,4.526811884850874,4.508417711292515,4.488766765373737,4.467911227572408,4.445924372602133,4.4229061205269105,4.398963052748342,4.374242828916555,4.348887557567011,4.323072653923168,4.296987966106615,4.270832224022402,4.244824141588377,4.2191890940599865,4.194153566915607,4.169961809200543,4.146839196170233,4.125029976869978,4.10475064477175,4.086217693347516,4.069633183171111,4.055170309020107,4.04300337589501,4.03326339010193,4.026061373934182,4.021488365672283,4.019587664010626,4.020395906306003,4.023897549437352,4.030054845824946,4.038806733207463,4.050047740406254,4.063663514459206,4.0794919628180795,4.097382095163968,4.117127410031301,4.138522516177446,4.161352030353364,4.185385026188956,4.21039168753705,4.236128875575275,4.26236455371059,4.288864464904086,4.315422107690181,4.341807665921693,4.367831291477035,4.393313128241018,4.4180877529965805,4.442004175424797,4.464941381225936,4.486789458329595,4.507462919569907,4.526891820902069,4.545029532962877,4.561840528618458,4.577319256754139,4.591466827592847,4.604302114924445,4.615841772092923,4.626137979576142,4.6352284849538306,4.643181011824915,4.65004552022139,4.655904166640316,4.660815792897156,4.664854783928438,4.668089973556024,4.670593526270578,4.672444267900362,4.67369437892324,4.674417134052808,4.674676926219195,4.674530376792003,4.674023004911493,4.673215872838995,4.672154499714775,4.6708677513351,4.669411138846632,4.667809087153905,4.666091572276115,4.664291900901263,4.662430057042149,4.660527134934503,4.658595347030592,4.6566602284578815,4.654725109885171,4.652817746885793,4.650922596338682,4.649068524040103,4.647249978875388,4.645480283519739,4.6437561073043545,4.642081891120967,4.640454304300778,4.638886669518987,4.637366774323327,4.635904610720198,4.6344901867032,4.6331190613806,4.631801226758798,4.6305255806084595,4.6292876820378535,4.628088641269913,4.626918466298237,4.62577826734576,4.624664713743682,4.623561152148003,4.622474243896324,4.621393996982245,4.620311529622298,4.619227952039419,4.61813438245014,4.617028600408596,4.615907275245986,4.61476374562471,4.613596901321836,4.612406742337363,4.611192158448358,4.609955370100688,4.608693046625552,4.607409628914684,4.606122880535017,4.604818368588417,4.603518297533552,4.602220446924552,4.6009425803283515,4.599689138636683,4.598472334301813,4.597303269553074,4.596199707957399,4.59516275973772,4.594217960021503,4.593366419031681,4.592621459443453,4.5919897425944205,4.591486811605646,4.591106005139533,4.590866196985946,4.590759615584352,4.590790701826483,4.5909516841518085,4.591241452337393,4.591652234822704,4.592171819155477,4.592792433775178,4.593488543554341,4.594254597378301,4.595053957890259,4.5958799637526155,4.5966981980544395,4.597483125668265,4.59821698302716,4.598859802105527,4.599398260228165,4.599783507586012,4.600002221503867,4.600017764624933,4.599812373382277,4.599353851310834,4.598619993951939,4.5975874866239925,4.596243006651796,4.5945676802454845,4.592551515398657,4.590184520104915,4.587465584141326,4.584392487062024,4.580973000427541,4.577224887804811,4.573150369639699,4.568782752620206,4.564135359421529,4.559257039852736,4.5541688881495554,4.548914203006388,4.543542944455229,4.5380950805216775,4.5326294530211975,4.5271938015399185,4.52184585767037,4.51663891211335,4.51163180668432,4.5068778320840766,4.502439160796883,4.498347989287803,4.4946720411557655,4.491436851528235,4.488694600883075,4.4864663834560154,4.484788836603855,4.483668621664193,4.483132383987427,4.4831701315671575,4.483794076855651,4.48498090517131,4.486717293838933,4.48898547929159,4.491742162834883,4.4949595888954805,4.498601120116588,4.502605694236872,4.506936673899539,4.511531886620325,4.516342482590168,4.521317391554135,4.526384449021566,4.531497025629264,4.536599610230565,4.541644463239338,4.546570522394255,4.5513478116761155,4.555917489269457,4.560255130269746,4.564324097320186,4.56809219395571,4.571543877055254,4.574656942160151,4.577423617709866,4.579826140137469,4.581870060557626,4.583559819862069,4.584902079388397,4.585912382257676,4.5865973898075065,4.586989298502952,4.587102541242146,4.586959322483754,4.586589618246974,4.5860256249968705,4.585300649421442,4.584435785756422,4.583471002027407,4.5824384946994625,4.581363798900054,4.580279111094246,4.579216627747103,4.578199663540224,4.577253753601076,4.576399992165388,4.575661693914762,4.575057732639062,4.574603651459353,4.57430389126737,4.57417177473831,4.574217293878575,4.574440448688162,4.574841239167074,4.575413003977709,4.576162404457668,4.577079448600552,4.57815414439996,4.579372058957761,4.5807331922739545,4.5822175603357405,4.583815171136722,4.585510481555831,4.587296830255469,4.58916200478337,4.591089351795534,4.593064438393831,4.595089485024124,4.597147838342416,4.599225065450574,4.601324497017399,4.603432810367689,4.605553336170247,4.607670531304005,4.609803269558829,4.611927126030188,4.614053202947413,4.616178169641706,4.618307577227732,4.620442535928425,4.622583045743785,4.624733547565545,4.6268940413937045,4.629065637451197,4.631246115292158,4.633446577145917,4.635663692343676,4.637886358656102,4.640125678312527,4.64237387975242,4.644619860746446,4.646869172409273,4.649098500059301,4.651311174365331,4.653491652206295,4.655618839346463,4.657676082441834,4.659654499708942,4.661515233345124,4.663248291343979,4.6648081545652405,4.666161516320912,4.667297274381661,4.668156586932022,4.668693934831731,4.668878231838656,4.668650636137333,4.66796340814163,4.6667599264819515,4.664986900457499,4.662581047361075,4.659486856046017,4.655649925588595,4.650996981275212,4.645484724411472,4.639046541621379,4.631634693318805,4.623199219471754,4.6136968213858305,4.60309419237304,4.591372458643519,4.578501644178075,4.564487300091377,4.54933608772103,4.533056888850505,4.515704104403539,4.4973232535204,4.477976508685357,4.457759349070675,4.436768364071554,4.41512012709599,4.392950085341844,4.370407008682175,4.3476607612257725,4.324886758196091,4.302258194370715,4.279982681438162,4.258254508411744,4.237266854081841,4.217238432366297,4.198350209603219,4.1808009156976516,4.1647737374335705,4.150438538919749,4.137940759360435,4.127423617514007,4.11899813567378,4.112750911228542,4.108752998446011,4.107058798249916,4.107660539079722,4.110563772050095,4.115730749581308,4.123092637851505,4.132568390586565,4.144042544601438,4.157384093590012,4.17244759834804,4.189070966327279,4.2070621289602865,4.226251222138286,4.246420642166371,4.2673872022605615,4.288939960063547,4.31088351633908,4.333025802519714,4.355175860260928,4.377153833447538,4.398807621537687,4.419968470645516,4.4405098153566325,4.46030842092544,4.4792499343898085,4.497259970813204,4.5142641452590935,4.530205836357873,4.545045076083943,4.55875965997863,4.5713340449208655,4.582788214923443,4.59312216998636,4.602368106574678,4.61055600070759,4.61772804085656,4.623939738168251,4.629239942451722,4.633691936414172,4.637337908527062,4.640255574395722,4.642499334943881,4.6441280319870035,4.645203838009352,4.645785594826391,4.6459243726930515,4.645675682755996,4.645085044155491,4.6442079680382,4.643073320200387,4.641729950451118,4.640213385924257,4.638551382193137,4.636771694831089,4.63490652030318,4.632974732399274,4.6309852129028375,4.628975709393602,4.626942891202769,4.6249067423431365,4.622875034375237,4.620853318413738,4.618849366019171,4.616868728306204,4.614906964383103,4.612971845810401,4.611071144148631,4.6091904264996595,4.607343015538688,4.605522249928114,4.603722578553274,4.601952883197632,4.600209833192389,4.598500089875145,4.596811440793633,4.595158318845987,4.593535172917539,4.591958656352288,4.59041655669797,4.588923306852716,4.587483347708259,4.586101120156333,4.584788836649203,4.583548717632736,4.582395196005065,4.581328271766189,4.58036237781424,4.579505285709754,4.578759215898594,4.578134160387162,4.577634560067188,4.577260414938675,4.577013945447489,4.5768940413706956,4.576897372039495,4.577028378345622,4.577259304715742,4.577595702264524,4.578020917647967,4.57851718729914,4.579071188542844,4.579650724914012,4.580251355520914,4.580834222560882,4.581387113581652,4.58186784011176,4.582265299921872,4.582541745432257,4.58267830285305,4.582642775719185,4.582418510686663,4.581983303296821,4.58131494909099,4.580393464056373,4.579216627747103,4.577771117487981,4.576051382164342,4.574064083113782,4.5718092203363065,4.56930344717591,4.566557865861928,4.563593570630093,4.560441647722535,4.557124301597922,4.553680390058917,4.550148770908184,4.546564971279588,4.542982281873928,4.5394328991562665,4.535971224050335,4.532643885919329,4.529488632342982,4.526556533576223,4.5238831167529145,4.52151945212799,4.519485523714245,4.517820189314345,4.5165412124952224,4.515675238607274,4.515232259656901,4.515227818765168,4.515651923925676,4.516509016030157,4.51777800084288,4.51944666591158,4.521495027223458,4.523893108759315,4.526604273162353,4.529595213744575,4.532827072703319,4.536259882012985,4.53983146918931,4.543514078658964,4.547259970835816,4.551016965242001,4.5547473142977895,4.5584032784170505,4.561954881580585,4.565361045539862,4.568596235167416,4.571626033552317,4.574431566904696,4.57699396143469,4.579302114912965,4.581353806893654,4.583137935147425,4.584660050788943,4.585930145824609,4.586958212260821,4.587757572772778,4.588343770481547,4.588739009845793,4.588966605547114,4.589054313158842,4.589022116693777,4.58889777172525,4.588716805387127,4.588491430131672,4.588248291309285,4.588024026276764,4.587825296371708,4.587677636721582,4.587605472230919,4.587612133568519,4.58772093541598,4.587938539110901,4.588278267328484,4.5887434507375255,4.589336309783894,4.590055734244656,4.59091171612621,4.591900924759758,4.593004486355433,4.5942335031425685,4.595584644452364,4.597040146717888,4.598604450830873,4.600259793224387,4.602013945458962,4.603848033744734,4.605757617189969,4.607740475348801,4.60978661621483,4.611890488673389,4.614048762055679,4.616251444355302,4.618499645795189,4.620777823254275,4.623088197178427,4.625410783554845,4.6277600152816625,4.63011257767728,4.632457368512365,4.6347866162263855,4.637092549258807,4.639354073373898,4.641548984112993,4.643675061030224,4.645690115654129,4.64757527419484,4.649309442416625,4.650852652293885,4.652178258476224,4.653240741823374,4.654000134309738,4.654418688355586,4.654442003037184,4.654030110328937,4.653126388861246,4.65167643771038,4.6496336275131425,4.64693911645407,4.643536283163565,4.639377388055498,4.634410250652004,4.628594902927488,4.621872503066487,4.614216405718604,4.605602185979311,4.59598987582301,4.585381695695571,4.573763212698866,4.561145529062229,4.547551959467265,4.533006928818509,4.517569278931426,4.501287859615087,4.484252598927089,4.466542322695697,4.448266942991308,4.429545253667784,4.410513812145916,4.391308065623563,4.372084555534316,4.353007594872294,4.334248157969217,4.31597277826507,4.298369083435568,4.281603606920693,4.265848433275092,4.251268985715815,4.238022915899375,4.226256773252953,4.216096012967999,4.207661649344232,4.201046941108038,4.196327383418872,4.193564038538061,4.1927846620389335,4.1939892539214885,4.19718225507746,4.202317036143654,4.209333645081679,4.218155476509147,4.228680389916203,4.240791811894864,4.25436095658488,4.269227951883871,4.285245138141721,4.302244871695517,4.320050627098876,4.338486989128352,4.35738409367516,4.376558753955315,4.3958599796499,4.415109024866657,4.434159340178399,4.4528765886101995,4.471123102518333,4.488784528940669,4.505758727367345,4.5219613208554295,4.537319034691323,4.5517685861678245,4.565271117482267,4.577796652615446,4.589325207554562,4.599857892522541,4.609389156404717,4.61794453432855,4.625547340975638,4.63223199325691,4.638028467191562,4.642983392142791,4.647144507696727,4.650562884108299,4.653290701855371,4.655373480078207,4.656866729923472,4.65783373409836,4.658304468622072,4.65834110597887,4.6579802835255535,4.657277512408786,4.6562605482018995,4.654974910045159,4.653453904626564,4.651728618188244,4.649835688086999,4.647789547220963,4.645619061386399,4.643350875933707,4.64099609309222,4.638575807097669,4.636107781516988,4.6336008981336425,4.631070700068699,4.628527179328557,4.625982548365483,4.623451240077609,4.620929923796134,4.618437473310926,4.615977219290783,4.613558043519171,4.611187717556625,4.608869572071943,4.606620260409125,4.604428680338837,4.602312595428014,4.600273115899586,4.598316903091155,4.596441736556852,4.594654277634279,4.59294564453997,4.591321388388589,4.589782619403071,4.588316014908215,4.58691713401229,4.58558486649236,4.584303669227363,4.5830613297650284,4.581847856098961,4.580646594885159,4.579438672333757,4.57822186799889,4.576958434300825,4.575652812131296,4.5742672539105715,4.572799539192785,4.571230794188071,4.56954103488363,4.567720269273065,4.565768497356372,4.563669065789555,4.561419754126748,4.559018341922082,4.556477041627825,4.55379030212931,4.55098254833107,4.548053780233103,4.545041745415142,4.541954215437721,4.5388300481035015,4.535692558094085,4.532569500982801,4.529503065241115,4.526533218894624,4.52367772551026,4.520990986011754,4.518504086641237,4.516250334086706,4.514258594144427,4.512565504171196,4.511196599294479,4.510162981743608,4.5094924070919165,4.509198198014602,4.509288126072195,4.509756640150034,4.510602630025182,4.511820544582974,4.513399281594078,4.515311085485163,4.517537082466362,4.520048406741411,4.522819523182845,4.525807133096267,4.5289768195707465,4.5322974963641505,4.535723644336215,4.539215295461346,4.542735812382742,4.5462596599729395,4.5497368781999405,4.553143042159213,4.55644484516276,4.559628964535381,4.5626554322514785,4.565518697196387,4.568208767363704,4.5707023280718335,4.5730115917730405,4.575124346015058,4.577049472581353,4.578793632809526,4.580351275584908,4.581754597372566,4.5830102595100985,4.584131584672705,4.585140777319051,4.586050049901402,4.586882717101358,4.587657652708783,4.5883915100676775,4.589103162967906,4.589808154530536,4.590525358545431,4.591269207910725,4.592051915078684,4.592882361832773,4.593771650402326,4.594727552347876,4.595763390344621,4.5968747235008305,4.598072654045834,4.599351630864968,4.600709433512363,4.602157164217355,4.603685941196476,4.60529021333506,4.606965539741374,4.608703038631952,4.610498269115061,4.612340128961367,4.614217515941538,4.616120438049175,4.618026690825612,4.619928502710318,4.6217981181299574,4.623619993963467,4.625374146198046,4.627022827253965,4.6285549349018895,4.629926060224489,4.631101786310832,4.632052137141718,4.632740475360351,4.633116840934733,4.633141265839265,4.632776002494216,4.63195776819239,4.630656586914586,4.628810286176544,4.626375567283864,4.623314682656815,4.619561018919403,4.61508904094416,4.609863221597226,4.603831380400735,4.5969801946794915,4.589289680420697,4.580737633165687,4.571319612022733,4.561046719221168,4.549933387659129,4.5380073729099495,4.52530531233043,4.511881606844304,4.497798428935837,4.48314015554796,4.46799005340067,4.452446932335028,4.4366251453131635,4.420650147526535,4.404648504389534,4.388758993768816,4.373129275314504,4.357902567784987,4.343223200161583,4.329242162763212,4.316113776577592,4.303967937687909,4.292936762623215,4.283145706574963,4.274699130498874,4.267698064681868,4.2622246656210026,4.258337775131737,4.256087353246064,4.255500045314381,4.256578071782555,4.259320322427652,4.263681278109411,4.269623191248104,4.277071676907207,4.28594013769793,4.296135314893885,4.307541745310019,4.320036194200744,4.333480993922344,4.347740697276967,4.362655432162225,4.378096412717868,4.393905987287375,4.4099331655518235,4.426043610536293,4.442087442144792,4.457949197192263,4.473496759149645,4.488624656838279,4.503227419079501,4.5172306609367805,4.530538903237853,4.5430999655048545,4.554863887705783,4.565788481369172,4.575847101144619,4.585030865248657,4.59332201011435,4.6007405197544955,4.607291945283757,4.6130018218296,4.617896794742419,4.62201572182488,4.6254019017713786,4.628086420824046,4.630124790129546,4.631574741280408,4.632471801410498,4.632878143004078,4.63284483631608,4.632416290263834,4.631644685325205,4.630585532646857,4.629266587802121,4.627747802829396,4.626062484416679,4.624243939251969,4.622336576252597,4.620365930546029,4.618367529266129,4.616353584865164,4.614360734699931,4.612400080999763,4.610492718000394,4.608649747931154,4.606886713913111,4.605201395500398,4.603614886928747,4.6021227473064235,4.600730527748095,4.5994282362473635,4.598225864810626,4.597106760093884,4.596074252765939,4.595115020151589,4.594220180467369,4.593387513267413,4.592588152755455,4.591828760269095,4.591080470012068,4.590347722876107,4.589594991727346,4.588828937903387,4.58802957739143,4.587186918185075,4.586277645602723,4.585309531204909,4.584261480755898,4.583136824924492,4.58192557170429,4.5806188393118275,4.579226619753502,4.577745582360516,4.5761823884704675,4.574543699420956,4.57283173565785,4.571075362977413,4.569269030264979,4.567443823762679,4.565609735476914,4.563784528974615,4.561995959829115,4.56025624049268,4.558599787876239,4.557036593986194,4.555591083727075,4.554284351334616,4.553140821713347,4.552172707315536,4.551397771708113,4.550821566005745,4.550468515112966,4.550335288360973,4.550426326641501,4.55074829129215,4.551293410752385,4.552065015691008,4.553042011872286,4.5542310606338186,4.555607737071075,4.557152057171254,4.558860690265558,4.560696998997188,4.562653211805612,4.564702683340432,4.566825429588848,4.569002576760994,4.571209699952338,4.5734323662647505,4.575636158787297,4.577822187742911,4.579967138449995,4.58205435756455,4.584079404194841,4.58602229432807,4.587893019970638,4.58966715621801,4.591354695076587,4.592956746769302,4.59446442951269,4.595891065981949,4.597239986845878,4.598512302327411,4.5997268862164145,4.6008903998504875,4.601998402337896,4.603076428806108,4.604132250815653,4.605175860372933,4.606213918815546,4.607256418149893,4.6083189014970385,4.609401368856983,4.610516032681993,4.6116595623032675,4.6128419497272075,4.614062084730879,4.615314416199616,4.616603385025151,4.617916778755219,4.6192468258292845,4.620577983126285,4.6219046995315525,4.623199219471754,4.624447110048759,4.625619505466301,4.626689760373981,4.627634560090201,4.628415046812297,4.628994583183468,4.629329870509318,4.629384271433049,4.629118928151995,4.628482770411227,4.6274324995163445,4.62591704521242,4.62389532925092,4.621316281376915,4.618139933564807,4.614325207566066,4.609828804686295,4.604619638683361,4.59866773353807,4.591950884791755,4.584456879992154,4.576176837355801,4.567109646659765,4.5572797328085795,4.546695977585714,4.535398349016768,4.523440137802541,4.510866863083299,4.497761791579039,4.484192646888693,4.470257128630389,4.456064038651588,4.441715517462151,4.427338130476469,4.413060663554802,4.399007461665672,4.385328404905068,4.3721445075727114,4.359595657758192,4.347817302659361,4.336942669028206,4.327083889380983,4.318351986011012,4.310860201657483,4.304680700811051,4.299897860414642,4.296562750723183,4.294719780654002,4.294388934219895,4.295576872758464,4.2982713838174424,4.302435830040034,4.308028022954779,4.314986900300349,4.3232247544650235,4.3326538778370765,4.343169909460787,4.354645173698835,4.366976419818433,4.380019318838259,4.393642864452193,4.4077171605770475,4.422093437339767,4.436658452001161,4.451263434688174,4.465800693776279,4.480138112736419,4.494183543065129,4.507825962469085,4.520988765565888,4.533583134520875,4.545554668410313,4.556844525418738,4.567409406851748,4.577223777581878,4.586260992258724,4.594513279321754,4.601979528548031,4.6086708421668865,4.614596101961785,4.619783063506058,4.624258372150102,4.628056444804848,4.631210588158293,4.6337685417965675,4.635771383968204,4.637253531584133,4.638276046905683,4.638873346843788,4.639085399424045,4.638971046461917,4.638556933307804,4.637896350662501,4.637023715436944,4.635964562758595,4.634766632213586,4.6334510180376505,4.632048806472919,4.6305788713092575,4.629068968119998,4.62753241958034,4.625989209703083,4.624450440717559,4.622927214853101,4.621420642332643,4.619938494716717,4.61848965378879,4.617064127542461,4.615671907984131,4.614301892884467,4.612948531128802,4.611611822717137,4.6102851063118715,4.608961720575405,4.607636114393073,4.606292744643809,4.604941603334011,4.603562706450883,4.602162715332022,4.600733858416896,4.599279466374305,4.597792877866649,4.5962840849003275,4.594755307921208,4.5932120980439555,4.591662226829104,4.590113465837186,4.588585799081001,4.587085887898147,4.585633716301424,4.584233725182567,4.582913670114904,4.581686873773636,4.580576650840363,4.579594103544416,4.578752554560994,4.578070877679965,4.577554624015993,4.577223777581878,4.577093881498684,4.577148282422415,4.577414735926401,4.577885470450108,4.578552714433005,4.5794231292126915,4.580488943228634,4.581737944028567,4.58315680893729,4.584731105056673,4.586451950603247,4.588301582010082,4.590254464149712,4.592296164124004,4.5944100285889595,4.596573853085912,4.598764322933265,4.600975887016349,4.603177459093035,4.605371259609189,4.607522871653878,4.609635625895904,4.611690648545399,4.613681278264765,4.615607515054001,4.617458256683775,4.619231282708219,4.620928813573201,4.62254751860992,4.624099610270643,4.62557176588017,4.626983969451301,4.628329559646434,4.629617418249038,4.630848655482044,4.632031042905986,4.633164580520864,4.634245937657878,4.635276224539962,4.6362621025047135,4.637186918208136,4.638047340981427,4.638835599264056,4.6395350397120225,4.6401367805418605,4.640613066180238,4.640950573951955,4.641115997169013,4.641092682487415,4.640837331212761,4.640328849109318,4.639525047705623,4.638391510090744,4.636882717124418,4.634968692787443,4.6326028077166255,4.629749534778098,4.626370016169197,4.622426504310193,4.617875700506687,4.612705392306414,4.606878942352578,4.600366374625981,4.593174350464224,4.58528288585451,4.576693091019773,4.567411627297615,4.5574640298155025,4.546880274592637,4.535691447871151,4.523954171020644,4.51173061652538,4.499084067092557,4.4861022303339055,4.472875034307019,4.459500178630027,4.446087575373322,4.432753797944896,4.419606537969275,4.406779022198448,4.394397816046806,4.382582823591136,4.37145394890823,4.3611388676354075,4.351745271397191,4.343377521149304,4.3361366471786695,4.330101475313544,4.325349721159254,4.321931344747792,4.319897416334088,4.319277911937339,4.320072831557542,4.322286616086431,4.325891509950678,4.330849765570552,4.337106982022327,4.344606537936409,4.3532485132488095,4.362951861685403,4.373608891621669,4.38511413187895,4.397338796596992,4.410172973705406,4.423471223999938,4.437131406970729,4.451010303859391,4.4649902310349985,4.478959055981294,4.492797984844416,4.506399325999839,4.519675371835834,4.532539524963603,4.5449029675484836,4.556715739558478,4.56790900717172,4.578438361470878,4.588274936659684,4.5973931976106694,4.605769829642235,4.613407053200246,4.620310419399365,4.626479928239592,4.631933343287858,4.636699530340426,4.640798473410095,4.644261258738997,4.647125633906861,4.649420464709952,4.651193490734403,4.652475798222343,4.653306244976437,4.653724799022284,4.6537714283854825,4.6534694477476295,4.652864376248991,4.6519817490170325,4.650852652293885,4.649505951875815,4.647958301106821,4.646239676006103,4.644363399248859,4.642351675293755,4.640212275701324,4.637964074261432,4.635615952757545,4.633174572527263,4.630655476691653,4.628055334581914,4.625385248427379,4.622651879565648,4.619854117773788,4.6169975141664645,4.614096501641811,4.611141088193428,4.60814681694238,4.605115908334535,4.602066125936827,4.598994139080453,4.5959154908864805,4.592842393807175,4.5897803989572035,4.5867550414640315,4.583770762219391,4.580851986127814,4.578006484749835,4.575247580760651,4.572605250179463,4.570089485012667,4.567715828381331,4.565499823406521,4.563458123432234,4.561604051133671,4.559949818963097,4.558504308703978,4.557277512362713,4.556276091276903,4.55549782500068,4.55495492598631,4.5546418431191285,4.554556355953267,4.554690692928193,4.555044854043906,4.555598855287608,4.556353806882232,4.557295275929645,4.558407719308783,4.559673373452712,4.561092238361432,4.56263544823868,4.564291900855121,4.566053824650223,4.5678934640506546,4.56980859861055,4.571784795431774,4.573806511393263,4.5758659749344845,4.577949863380238,4.580045964278258,4.582153167405611,4.584255929641231,4.586339818086987,4.588411494080477,4.590452083831835,4.592451595334662,4.594406697920159,4.596295187129661,4.598114842517298,4.599847900516142,4.601483258896857,4.602992051863178,4.604365397631641,4.605578871297712,4.60660138661926,4.607415180029351,4.607985834617055,4.608284484586107,4.608277823248507,4.607933654139191,4.607208678563762,4.60607625117182,4.604504175498301,4.602436940396541,4.599866774306007,4.596737055857104,4.593040013489298,4.588735679176993,4.583798517792723,4.578235190674089,4.572012391133095,4.565144552067873,4.557633893924293,4.549490408708754,4.540744072440457,4.531415979355136,4.521566081491187,4.511238787765944,4.500494050217803,4.4894073640062295,4.478055334513619,4.466536771581031,4.45493383170553,4.443358647403373,4.431913359184421,4.42071676090253,4.409865441952895,4.399490408641637,4.389689360586882,4.380579981419551,4.372261080980703,4.364823697550862,4.358362200079352,4.352953193948565,4.348657741419829,4.345528022971004,4.343615108857019,4.342938983090671,4.3435063070095605,4.34532152150542,4.348357981227852,4.3525879306035264,4.357966960715115,4.364427347963692,4.371908030087929,4.380315748361437,4.389563905395424,4.399561462909365,4.410187406603539,4.421346257305686,4.432919221161951,4.444791945210209,4.456860068494735,4.46900812783047,4.481135092930487,4.493137713061995,4.504926060167396,4.5164102061890965,4.527521317305232,4.5381905596939385,4.54834798931042,4.557958079020808,4.566976419907772,4.575369705283311,4.583122392026358,4.590225598353447,4.596670442481107,4.602465806192806,4.607619461049074,4.61214806039391,4.616082690469444,4.619445555734342,4.622258860647268,4.62456590390262,4.6264077637489285,4.62779665263846,4.6287936328325445,4.629423129235714,4.629718448535966,4.629715117867166,4.629454215477845,4.62895461515787,4.628249623595238,4.627373657700882,4.626334489035332,4.625165424286591,4.623885337244521,4.622501999469656,4.621044276758261,4.619522161116738,4.617942313882684,4.616324719068898,4.614674927790048,4.613007372944266,4.611330936315017,4.609652279239903,4.607981393725322,4.606336043338206,4.604718448524423,4.603143042182104,4.601614265202984,4.600157652714525,4.598775425162597,4.597484235891198,4.59629185646086,4.5952104993238505,4.594263479161767,4.59345079597461,4.592789103106378,4.592282841448805,4.591951995014688,4.591798784249897,4.591819878485629,4.592037482180551,4.592438272659463,4.593034462374632,4.593816059319657,4.594785283940406,4.595938805568079,4.597258860635743,4.5987498900351325,4.600394130199313,4.602178258453088,4.604093393012988,4.606121770312084,4.608255618789841,4.610467182872928,4.6127453603320125,4.615080159160694,4.617444934008575,4.619830803092189,4.622212231284069,4.624582557246619,4.626921796967037,4.629208856209591,4.631438183859615,4.6335831345667104,4.635633716324478,4.637573275788917,4.639376277832564,4.641033840671951,4.642528200740146,4.643829382017951,4.644926282276032,4.645794476609857,4.646413981006628,4.646749268332479,4.646782575020477,4.646489476166091,4.645833334412522,4.644787504409372,4.6433308919209075,4.641413536915133,4.639028778054447,4.636133316644454,4.632704948226486,4.628710366112548,4.624135137404508,4.6189570576437,4.613162804154925,4.606737944040052,4.599680256853217,4.591991963040287,4.583680834161796,4.574763523561745,4.5652611254758675,4.555214718152696,4.544664269617831,4.533655299011537,4.522253309486879,4.51052713486572,4.498558931645123,4.486421974538684,4.474218404056265,4.462035927809593,4.449988898760793,4.438180567642657,4.426713074965046,4.415698553244216,4.405240253212957,4.395449197164596,4.386415313156721,4.378237411030391,4.370998757505597,4.364770406850066,4.359624523554455,4.355604406313162,4.352754464043514,4.3510969012041745,4.350649481362075,4.351402212510817,4.353338441306402,4.3564237508379,4.360619283302647,4.365871747999849,4.372104539547114,4.379232170778584,4.3871824772035986,4.3958499876434995,4.4051392229260316,4.414946932318402,4.4251609833043535,4.435681455819895,4.446392886679968,4.4572020171581785,4.468007816967602,4.478708145598376,4.489229728336907,4.4994793064567995,4.509393597250856,4.518904877120146,4.527960965586806,4.536515233287637,4.544533263311705,4.551985079639812,4.558855139150891,4.565133449838541,4.570813350365161,4.575897061176616,4.580399015171039,4.584326983908961,4.587712053632513,4.590568657239829,4.592933432087704,4.594821921297204,4.596276313339795,4.59732547401174,4.597994938440505,4.598329115543421,4.59834576888742,4.598087086943966,4.5975786048405265,4.596851408819231,4.595928813561679,4.594841905310004,4.593613998745801,4.592263967658939,4.590820677845683,4.589303003095895,4.587732037645313,4.586124434837932,4.584500178686552,4.582874812312239,4.5812605481672595,4.579689582716677,4.578165246629293,4.57670197280324,4.575323075920114,4.574027445756985,4.572842837887183,4.571777023871241,4.570839995715559,4.5700439658724035,4.569401146794038,4.5689115384804655,4.56859068405275,4.568438583510892,4.56846522886129,4.568662848543412,4.569038103894859,4.569589884692695,4.570317080713988,4.571213030621139,4.572262191293081,4.573471224067416,4.574824585823075,4.576310064107794,4.57791322602344,4.579626300009481,4.58143041227605,4.583310019702083,4.585254020058245,4.587240208885872,4.589255263509765,4.591280310140058,4.593297585209818,4.595280443368647,4.597221113056012,4.599090728475648,4.600871526060621,4.602537970683469,4.604075629446056,4.605451195660385,4.606648015982457,4.607632783724273,4.608384404650101,4.608877343632476,4.6090771837604665,4.608959500129539,4.608489875828763,4.60764166550774,4.606383782924337,4.604694023619891,4.602532419568803,4.59988120720414,4.596718182067239,4.593021139699433,4.588764544973258,4.583949508111648,4.578559375770605,4.572601919510663,4.566071588217156,4.558986145457017,4.551372236580647,4.5432487353779125,4.534648948536812,4.525630607649878,4.516242562526173,4.506544765204096,4.496603829059644,4.486500800366946,4.476317835623064,4.46614819355439,4.456082912441453,4.446211920341846,4.43664401910303,4.427462475444994,4.418786083221598,4.410703660267502,4.403296252856831,4.396657119715975,4.390862866227329,4.385986767104486,4.382083223271173,4.37919664364472,4.377371437142455,4.376634249114777,4.376986189784617,4.378436140935443,4.38095856743979,4.384534595507793,4.38911537533039,4.39465538776732,4.401089129665523,4.408343326311403,4.416346923437237,4.425002221424898,4.434222622885595,4.443904877086536,4.453957945747194,4.464277467911846,4.474763523516497,4.4853272947264875,4.495872192146624,4.506307177496378,4.516552314724555,4.526532108671691,4.536186607299389,4.5454369847793865,4.554246603754884,4.562568834862684,4.570367040745985,4.57761124538559,4.5842925669980295,4.590392131793438,4.595904388657147,4.600834888703824,4.605196954608665,4.608989476148737,4.612251311126704,4.614982459542566,4.61721955875312,4.618993695000498,4.620320411405764,4.621245227109185,4.621790346569425,4.621990186697414,4.621874723512354,4.621475043256373,4.620826673063339,4.619955148060716,4.618897105605303,4.617671419486964,4.616312506616632,4.614845902121773,4.613296030906918,4.611690648545399,4.610049739050017,4.608392176210634,4.606751266715252,4.605140333239068,4.603573808680215,4.602076117943226,4.600661693926233,4.599352741087901,4.598154810542897,4.597082335189353,4.596145307033669,4.595357048751043,4.594720891010276,4.594249046263634,4.593940404288184,4.593793854860992,4.593813838873791,4.594001466549514,4.594340084544163,4.594838574641203,4.5954825039425025,4.596264100887528,4.597166712132282,4.598185896785028,4.5992961197183035,4.600488499148642,4.60174194084031,4.603042011895177,4.604358736294041,4.605677681138774,4.606975531747773,4.608224532547709,4.609401368856983,4.610474954433461,4.611425305264346,4.612218004438706,4.612827516829075,4.613224976639188,4.613375966958114,4.613241629983188,4.612814194153876,4.612033707431782,4.610892398256373,4.609351408824986,4.607380763118419,4.604952705563344,4.602051693038694,4.598648859748204,4.594727552347876,4.590275558385445,4.585285106300376,4.579750644978007,4.57367661531007,4.567071899080033,4.559953149631896,4.552342571424325,4.544275691591187,4.535793588381012,4.526940670711133,4.517769119059414,4.508345546801853,4.498743228652045,4.489035439323586,4.479312106874071,4.469648726462962,4.460134115924919,4.450879297553267,4.441956435838668,4.4334687815139135,4.4255073728595296,4.418153256149643,4.411494138995979,4.405604406335065,4.40055289198876,4.396398437772527,4.393186562826626,4.390960565845456,4.389741541064744,4.389550582720225,4.390384360143098,4.392229550658163,4.395073941813156,4.398869794021949,4.403584910819476,4.409152678829745,4.415514256237295,4.422593037659733,4.430306866599998,4.438578027452764,4.44730993082284,4.456411538429697,4.465797363107479,4.475356382562858,4.485015322082241,4.494675371824565,4.5042621468533035,4.513691270225528,4.5228872467817745,4.531792344929514,4.540337730846881,4.548478995616546,4.5561761712129085,4.563387069164505,4.570083933898001,4.576253442738197,4.581882273009892,4.586959322483754,4.591490142274447,4.595481393719569,4.598946399494322,4.601904033388568,4.604363177185775,4.606367129580338,4.607926992801591,4.609086065543932,4.609862111374293,4.610296208541204,4.610418333063864,4.610266232522005,4.609867662488958,4.609260370544456,4.608483214491163,4.607556178341877,4.606515899453397,4.605393464067855,4.6042199584273815,4.603023138105311,4.601821876891505,4.600651701919833,4.599525935865492,4.598472334301813,4.597500889235198,4.596644907353642,4.595896617096615,4.595285994483313,4.594818590628404,4.594496625977754,4.5943300925377635,4.594326761868964,4.594481082856689,4.594793055500939,4.595261569578781,4.595876633083816,4.596628254009643,4.597509771018664,4.598502310321012,4.599591439018555,4.600773826442494,4.6019995125608295,4.603275158711164,4.604563017313764,4.605837553241165,4.6070843335952345,4.608263390350374,4.609350298602052,4.610318412999869,4.611128875741161,4.611750600583797,4.612156942177376,4.6123123733880345,4.612179146636041,4.611735057462731,4.610940137842505,4.609771073093763,4.608191225859711,4.606182832573414,4.603717027438608,4.6007760468883605,4.5973421273557395,4.593399725719679,4.588944401088448,4.583975043239113,4.578491652171675,4.572511991453068,4.566047163312623,4.559124923323676,4.551773027059558,4.544043654998133,4.535966783158602,4.527606804471094,4.51902145052814,4.510280665374535,4.50146216461561,4.492638112742026,4.483889556027912,4.475304202084995,4.466970868747936,4.458973932959662,4.451401102331898,4.4443356435846395,4.437860823437879,4.432045475713478,4.426962875125029,4.4226652021503945,4.419214629273836,4.416648904075082,4.415002443465065,4.414289680341915,4.414520606712032,4.415702994135949,4.417807976817401,4.4208255627499895,4.4247035714558525,4.42940425535526,4.43487210330155,4.441044942810462,4.4478517196142695,4.455212497661778,4.463054002239392,4.471281864397789,4.479817258308706,4.488575807029215,4.4974675825017245,4.506410428229172,4.515331069497962,4.524141798696366,4.5327871046777215,4.541184830944966,4.549291678803699,4.557056577998993,4.5644273480529804,4.57137290272353,4.57786215576851,4.5838795640668515,4.589401812936957,4.594425571710025,4.598954171054855,4.602976508742112,4.6065203403451305,4.609591216978573,4.61220912265524,4.614392931164995,4.616185941202239,4.6175959243275,4.61866284856638,4.61941780016101,4.619897416468185,4.620133893952974,4.620163869972172,4.620015100099113,4.6197331034740605,4.619343415224479,4.618873790923703,4.618361978151463,4.617840173372822,4.617326140154715,4.6168554056310045,4.616446843591559,4.616118217603309,4.615887291233187,4.615771828048126,4.615782930277459,4.615931700150518,4.61621702744437,4.616650014388348,4.617225109867786,4.617945644551484,4.618793854872507,4.619764189716192,4.620843326407338,4.6220201627166135,4.623265832847752,4.624567014125553,4.625894840753754,4.6272215571590225,4.628518297545091,4.629750645001031,4.630891954176442,4.631907808160392,4.632758238927284,4.633407719343253,4.633819612051499,4.633961720586959,4.6337962973699,4.633282264151792,4.632395196028102,4.631102896533765,4.629375389649583,4.6271860300251575,4.62451150297889,4.62134181650438,4.617652545697098,4.613444800779977,4.608714140861284,4.603460565941021,4.597700729363187,4.5914523946947154,4.5847333255025395,4.577575718251725,4.570022871636671,4.562113643460043,4.553903544868503,4.545453638123385,4.536821654817219,4.528076428771866,4.5192901244779895,4.5105471188785184,4.501915135572381,4.493480771948374,4.485329515172354,4.477531309289119,4.470168310795728,4.463309353514043,4.457026601934724,4.451386669433766,4.446442846711965,4.442236212017849,4.438821166275147,4.436217693496658,4.43444577769518,4.433519851768843,4.433433254380049,4.434179324191198,4.435735856743625,4.438072876018132,4.441147083320322,4.444907408395268,4.449308332102705,4.454281020620773,4.4597510890129435,4.465657475017889,4.471919132361481,4.478461676107192,4.4852051702038285,4.492083001275394,4.499007461710162,4.505919709692669,4.5127464705093185,4.519424461452915,4.525910383829061,4.532137624261759,4.538067324948346,4.543670620092555,4.548905321222922,4.553761436333045,4.558205658734928,4.562243539543235,4.5658661969745005,4.569071410582857,4.57187139282057,4.574275025471104,4.576307843661927,4.577980949622369,4.579322098925764,4.580357936922508,4.5811217703006,4.581635803518706,4.5819455557170885,4.582067680239748,4.582044365558151,4.581904477468558,4.581683543104837,4.5814104282632515,4.581102896510734,4.580807577210484,4.580528911254232,4.5803113075593105,4.580153655902786,4.580084822080923,4.580114798100121,4.580255796412647,4.580510037464366,4.580887513261679,4.581386003358719,4.581995515749086,4.582720491324514,4.58353983584927,4.584449108431621,4.585430545504635,4.586454171049114,4.587507772612791,4.588563594622335,4.589590550835614,4.590558665233429,4.591450174248849,4.592211787181075,4.592826850686109,4.593246514954887,4.593451906197544,4.593399725719679,4.593059997502097,4.592407186417332,4.591410206223251,4.590039080900657,4.588276046882617,4.586101120156333,4.583503198492472,4.580468959215835,4.5769995125493566,4.573094858493036,4.56876720949914,4.564026557574069,4.558896217399422,4.553401724102665,4.547586376378197,4.541482370691082,4.535141887519184,4.528615997117433,4.521966871970096,4.5152577947843655,4.508546497152774,4.501915135572381,4.495426992750385,4.489165335406778,4.483189005357024,4.477579048875249,4.472399858891583,4.467714718113221,4.463590239916157,4.460075274109456,4.457217560279244,4.455057066451121,4.4536215481984165,4.452945422432062,4.453025358483257,4.4538680176896,4.455468959159361,4.457811529548538,4.4608701937296695,4.464603873454225,4.468979262034205,4.473935297208284,4.479423129167397,4.485373924089685,4.4917299503826165,4.4984079413261995,4.5053423937673704,4.512461143215469,4.519694245625699,4.526965095615665,4.534208190032305,4.541362466614288,4.548352430202153,4.555134782101501,4.561658452057401,4.567873480037856,4.5737510002466,4.579253265103901,4.584353629259359,4.589038770037777,4.593298695432751,4.597122303214951,4.600516254721973,4.603482770399687,4.606038503592088,4.608193446305578,4.609978684782287,4.611408651920347,4.612512213516024,4.61331379447385,4.613856693488223,4.614158674126074,4.614263035081802,4.614194201259939,4.613985479348483,4.613673506704232,4.613277157117053,4.612834178166675,4.612364553865898,4.611891598896322,4.6114308563790125,4.611012302333167,4.610639267427586,4.610317302776936,4.610070833285748,4.609884315832958,4.609768852647897,4.609707790386567,4.609707790386567,4.6097466481892315,4.609812151342295,4.609879874941225,4.609939826979622,4.609962031438287,4.609919842966823,4.609785505991896,4.609531264940176,4.6091204824548635,4.608534284746094,4.607732703788268,4.606693535122721,4.605372369832122,4.603769207916471,4.601838530235505,4.599567014114023,4.5969446675456265,4.593950396294583,4.590587531029694,4.586847189967493,4.582740475337313,4.578269607585021,4.573463452506882,4.568336443001031,4.56292410620133,4.557260859018714,4.551390000147579,4.545362599842858,4.539229728359479,4.533042455952373,4.52687516755807,4.5207833743232335,4.514840350961458,4.509114931294606,4.503662626469341,4.498563372536856,4.4938715704208825,4.489651613051548,4.48596123202138,4.482851497585312,4.480359047100137,4.4785293997061215,4.477392531422461,4.476962875147288,4.4772515331099365,4.478266276870938,4.480001555315627,4.4824407151000045,4.48555600065074,4.4893207666174355,4.493691714305694,4.498626655244053,4.504064527171183,4.5099542598321545,4.516230350073907,4.522829515189245,4.529685141802171,4.536726175644957,4.543888223787476,4.551100231961996,4.558303358353056,4.5654365406993245,4.572437606516538,4.579257705995634,4.585847989327546,4.592167378263745,4.598181455893295,4.603862466642867,4.609185985607927,4.614135359444476,4.618701706369046,4.622877254821104,4.62666533546945,4.630078160766348,4.633113510265933,4.635801359987403,4.638143930376623,4.640177858790392,4.641908696343376,4.6433841826217055,4.644612089185913,4.6456323840615985,4.646456169478093,4.647117862346328,4.647637446679104,4.648037126935084,4.64834021779587,4.64855671126786,4.648707701586786,4.648797629644382,4.6488375976699805,4.648826495440647,4.64876987407105,4.6486599620006555,4.64849231833773,4.648254730630008,4.647936096648156,4.647513101710576,4.646973533365001,4.646289636038101,4.645440315494141,4.644400036605656,4.6431454846910505,4.641642242839389,4.639879208821339,4.637807532827839,4.6354227739671545,4.632692735774221,4.629601875127972,4.626129097792676,4.622265521984867,4.617996714806414,4.613319345588517,4.608234524554109,4.602753353932525,4.596886935953096,4.590638601284625,4.5840560895132425,4.577148282422415,4.569960699152407,4.562539969066418,4.554928280635912,4.54717670411582,4.539349632436272,4.531498135852197,4.523688827739593,4.5159905419203215,4.508467671324513,4.5011868293281605,4.494217959976061,4.487619905083676,4.481461498472867,4.475788259283897,4.470662360001029,4.466122658426925,4.462210232810115,4.458962830730329,4.456398215754499,4.454537482118356,4.4533795195989665,4.45292432819633,4.453167467018714,4.454073408932254,4.4556332721534835,4.457802647765073,4.460537126849691,4.463791190267077,4.467512657539367,4.4716493481886985,4.476126877278542,4.480898615445703,4.485889067530719,4.491038281495193,4.496288525746598,4.5015787380236025,4.506848966287811,4.512051470953094,4.5171340715415855,4.522061240919424,4.526785239500476,4.531282752603143,4.53553157576876,4.539500622755196,4.543185452670716,4.546580514400654,4.549675815938611,4.552482459513918,4.555000445126575,4.557251977235248,4.559243717177536,4.561001200080904,4.562535528174686,4.563874457032211,4.56503463999748,4.566054934873156,4.566935341659241,4.567712497712531,4.568393064370627,4.56900812787566,4.569559908673496,4.570075052114534,4.570541345746509,4.570978773582218,4.571380674284063,4.571754819412575,4.572087886292557,4.572372103363475,4.572601919510663,4.572744028046121,4.572796208523985,4.572736256485588,4.5725397470264,4.572182255241885,4.571640466450448,4.5708866250787565,4.569908518674544,4.568676171218612,4.567170708921095,4.565376588660928,4.563273826425311,4.560855760876646,4.5581146204544,4.555053735827372,4.551674217218497,4.547977174850708,4.543998135857869,4.539735990017049,4.535236256468512,4.530521139670921,4.52562838720401,4.520609069322711,4.515509815390217,4.510379475215595,4.505269119053775,4.5002464705036855,4.495367040711989,4.490688561271216,4.486273204665627,4.482175371818955,4.47844724320906,4.475154321989005,4.472332135292654,4.470028422706137,4.4682720500257185,4.467096323939395,4.466526779574632,4.466568968046095,4.467231771137253,4.4685151888481025,4.47039701671998,4.472878364975819,4.47591482469829,4.47948197098286,4.483540946026868,4.488031797791916,4.492918999144142,4.498137046930482,4.503635981118943,4.509349188333525,4.515222267650501,4.521187495470943,4.527194911762852,4.533176792927299,4.539082068709353,4.544858558631153,4.550458523106566,4.5558431043329275,4.560973444507573,4.565817347165436,4.570355938516653,4.574559242542023,4.5784217081268785,4.581931122818956,4.585086376395321,4.587890799524771,4.59035216376784,4.592477130462128,4.594283463174566,4.595784484580354,4.597002399138157,4.597951639746107,4.598659961977537,4.599149570291111,4.59943045669323,4.599528156311358,4.599457102043629,4.599238388125773,4.5988820065641915,4.598391288027685,4.59777622452265,4.597047918278421,4.596193046619799,4.595221601553184,4.594115819511642,4.592873480049307,4.591485701382713,4.589931389276129,4.588193890385555,4.586265433150458,4.5841260335580385,4.581750156480833,4.579133361027107,4.576257883629929,4.5731070709453014,4.569678702527357,4.5659550148091625,4.561947110020052,4.557646106376559,4.5530653265538845,4.548220313673093,4.54312216996352,4.537799761221428,4.5322808430201516,4.526600942493554,4.520802248113099,4.514926948350253,4.509031664574611,4.503158585257638,4.49737432377533,4.491735501497283,4.486288747786693,4.481113998694756,4.476247891578268,4.471763701150825,4.467712497667354,4.464135359376388,4.461084466755788,4.458593126493553,4.456696865723545,4.455422329796164,4.454776180049007,4.45478062094074,4.455432321802562,4.456727951965677,4.458648637640216,4.4611732845904495,4.46427191679718,4.467903456011875,4.472039036438273,4.476614265146244,4.481583622995526,4.486893819285322,4.492486012200169,4.498302470147539,4.504281020643169,4.510361711648663,4.516491252463225,4.522611911494324,4.528672618487031,4.534625633855214,4.540428769127409,4.546047607392684,4.551442180625443,4.556586953698219,4.561459722152346,4.566051604204357,4.57034483628732,4.574331646840702,4.578016476756234,4.581397105588052,4.58447908445082,4.587281287134403,4.589802603415869,4.592063017308016,4.59408140260071,4.5958610899627494,4.597417622515202,4.598774314939664,4.599934497904937,4.600909273640353,4.601707523929378,4.602332579440813,4.602796652626922,4.60308753103544,4.6032129862269,4.603166356863703,4.602928769155982,4.602506884441337,4.6018851595987025,4.60104027994648,4.599975576153469,4.5986710642068696,4.59712563388375,4.595305978496112,4.5932220900503555,4.590866196985946,4.588227197073553,4.585311751650775,4.582123191386413,4.578664846949266,4.574956702352134,4.571020962053683,4.566872058952045,4.562547740626951,4.558071321760002,4.553488321491461,4.548845369184525,4.544180212418926,4.539541701003727,4.534993117646126,4.5305755405946515,4.526342260550102,4.522352119327939,4.518660628074827,4.515304424147563,4.512347900476276,4.50981326151963,4.507762679761889,4.506209477878251,4.505182521664981,4.50470956669541,4.504792833415404,4.505441203608431,4.506652456828624,4.508423262407182,4.510725864770774,4.513534728791937,4.516830980680805,4.520560219513647,4.524694689717133,4.5291855414821995,4.5339761534392515,4.5390221166709575,4.544260148470121,4.549639178581812,4.555103695859369,4.560601519824927,4.566074918885955,4.571471712564591,4.576754153281103,4.581871170780559,4.586791678820829,4.591472378707514,4.595892176204882,4.6000199850708,4.603845813298868,4.607345235984555,4.610519363350792,4.6133537624994485,4.615843992538789,4.618001155698147,4.619826362200456,4.621325163160381,4.622503109692589,4.623382406255745,4.623957501735183,4.624249490366635,4.624259482373035,4.623998579983715,4.623483436542673,4.6227085009352455,4.621684875390763,4.62041033946336,4.618892664713569,4.617121859134992,4.61509903295056,4.612827516829075,4.610292877872404,4.60749622630348,4.604427570115904,4.60109801153901,4.597487566559998,4.593600676070602,4.589436229847888,4.585006440344125,4.580313528005177,4.5753652643915785,4.570186074407862,4.564789280729227,4.559205969597805,4.553455014803462,4.547583045709397,4.541620038334806,4.535613732265823,4.529609646642709,4.523658851720395,4.517812417753812,4.512124745666689,4.50665467727449,4.501444401048678,4.496558309919381,4.492055245702063,4.48796851508472,4.484350298545216,4.4812405641091475,4.478673728687445,4.47667754785344,4.475274226065797,4.474474865553849,4.474296119661594,4.474718004376233,4.475753842372967,4.477371437186729,4.479557466142322,4.482277512328815,4.48549826905821,4.48917976830491,4.493275380705719,4.4977373666745075,4.502514655956345,4.507549516958702,4.512793099872515,4.518189893551122,4.523683276624927,4.529227729953664,4.5347710730594715,4.540265566356219,4.545674572487106,4.550949241643072,4.556066259142515,4.560986767182771,4.565691891973977,4.570146106382264,4.5743538512993664,4.57828626092902,4.581933343264823,4.585297318752643,4.588361534048479,4.591131540266999,4.593611778299935,4.5957911459179535,4.597679635127455,4.599279466374305,4.6005906396585035,4.601618706094716,4.602358114568278,4.602817746862654,4.603002043869578,4.602896572690917,4.602513545778937,4.601846301796038,4.600899281633954,4.599663603509218,4.598145928759431,4.596344036938724,4.594263479161767,4.591902034982692,4.589270806630831,4.586375345220851,4.58322453253622,4.579842793481469,4.576237899617131,4.572437606516538,4.568466339084223,4.564351852893518,4.560136336415886,4.555841994109994,4.551521006453705,4.547212231249685,4.5429600774152625,4.538813394759503,4.534821033091469,4.531028511551424,4.527483569725501,4.524236167645694,4.521326273337601,4.518796075272686,4.51668332103068,4.515017986630781,4.513832268538053,4.513140599650628,4.512969625318905,4.513319345542883,4.514195311437231,4.5155986332248785,4.517507106447163,4.5199096288747524,4.522788436940713,4.52610356261945,4.529835021898162,4.533926193407255,4.538354872688063,4.54306776903979,4.548012701984573,4.55314526260508,4.558422152206916,4.563783418751682,4.56918798399085,4.574591439007087,4.579948264660129,4.585210721363847,4.5903532739907735,4.595329293177711,4.600109913128395,4.604675149830025,4.60899058637167,4.6130362387405315,4.616802114930207,4.620276002488433,4.623434586733609,4.626274536996935,4.628792522609611,4.630984102679904,4.632839285201413,4.634363621288806,4.635548229158615,4.6363953292567075,4.636907142028949,4.637078116360675,4.636913803366549,4.636417533715373,4.6355815358466135,4.634413581320803,4.63291589058381,4.631088463635632,4.628937961813871,4.626467715787326,4.6236877175623965,4.620604628476683,4.617237322320053,4.613589129761303,4.609690026819635,4.605557777061979,4.601212364501137,4.596685985602173,4.592007506161353,4.587208012420807,4.582336354189602,4.577423617709866,4.5725108812301345,4.567648104782402,4.5628763666152,4.558244516537592,4.55379696346691,4.5495792265434165,4.545630163569776,4.542000844800918,4.538724576924841,4.535835776852476,4.533366641048888,4.531334933081006,4.529773959636832,4.528690382053963,4.528095302561731,4.527989831383071,4.528370637849182,4.529233281068331,4.530556666804786,4.532325251937482,4.534513501338954,4.53708366742947,4.540006884412767,4.543245404709113,4.54676925229931,4.550520695590829,4.554460876781006,4.558546497175442,4.562739809194407,4.566991963028838,4.57126077020727,4.575512924041703,4.57969735427721,4.583792966678057,4.587757572772778,4.591567857879776,4.595189405088118,4.59860334060794,4.601784129311775,4.604718448524423,4.607384093787219,4.609777734431363,4.611879386444056,4.613684608933565,4.615187850785222,4.616376899546762,4.617257306332851,4.61781907913709,4.618063328182411,4.6179856125770815,4.617601475442167,4.616898704325403,4.615886181010254,4.614569456611386,4.6129563026893345,4.611051160135832,4.608878453855409,4.606430412287535,4.60374145234314,4.600808243353425,4.5976751942357215,4.594346745881762,4.59085398453368,4.5872302168794725,4.583498757600739,4.579691803162544,4.575855982928085,4.572020162693628,4.56822764115357,4.564520606779375,4.5609368071507745,4.5575139898475,4.554302114901548,4.551338929892649,4.548657741508802,4.54629407688387,4.5442901244893195,4.542661427446213,4.541443512888417,4.540655254605795,4.540314416165282,4.540432099796209,4.541002754383909,4.542034151488916,4.54352962178003,4.545459189238052,4.547819523194184,4.550579537406292,4.553723688753314,4.557217560324316,4.561021184093703,4.565101253373476,4.569423351252704,4.5739419585911225,4.578611556248469,4.583393286422077,4.588244960640485,4.593123280209293,4.597989387325838,4.6027933219581225,4.607505108086946,4.612089218578446,4.616511236521689,4.620737855228676,4.624745760017811,4.628511636207492,4.632006618001454,4.635212941832765,4.638113954357425,4.640697443123167,4.642951195677726,4.644864109791768,4.6464372956882265,4.647651879577237,4.648514522796395,4.649021894676905,4.6491828770022305,4.64898969821184,4.648453460535065,4.647580825309507,4.646381784541563,4.6448707711293675,4.643055556633454,4.640956125066621,4.638593570664601,4.635984546771394,4.633154588514465,4.630131451467146,4.626945111648635,4.6236177735176005,4.62019051532257,4.616698864197413,4.61317501660719,4.609663381469236,4.606186163242214,4.602807754856255,4.5995514709929575,4.5964517285632525,4.59356625915967,4.5909072752344775,4.5885225163738035,4.586443068819781,4.5846889165852085,4.583286705020483,4.582250867023739,4.581604717276574,4.5813482557789875,4.581492584760314,4.582029932660018,4.582953638140501,4.584263701201764,4.585924594709942,4.587922995989835,4.590236700582779,4.592829071131976,4.595665690726493,4.598713252678334,4.601932899184833,4.605273559991061,4.608705259077818,4.612178036413108,4.6156552546401315,4.619086953726892,4.622435386093659,4.625663914383632,4.628730350125347,4.631593615070274,4.634241496766145,4.63662292495803,4.638719025856062,4.640504264332776,4.641955325706574,4.643057777079321,4.643790524215286,4.644142464885136,4.644110268420071,4.643677281476092,4.642849055167864,4.64160893615139,4.639971357324802,4.6379363186881,4.635494938457818,4.6326727517614215,4.629467538153045,4.62589373053082,4.621967982238749,4.617705836397895,4.613125056575194,4.608261169904508,4.603120837723439,4.597744028057584,4.592151835142678,4.586387557673118,4.580480061445168,4.574473755376161,4.568399725708227,4.562314593810965,4.556252776595304,4.550257572755644,4.544378942323981,4.538669065778177,4.533159029360366,4.527906564663076,4.5229494192660376,4.518326450971914,4.514076517583371,4.510222933782005,4.506808998262214,4.503852474590929,4.501372236558016,4.499383827284539,4.4978861365475655,4.496899148359893,4.496398437816992,4.496384004918859,4.496839196321497,4.497748468903841,4.499079626200825,4.500801581970317,4.502886580638989,4.505289103066574,4.507969181227476,4.510890177764898,4.514006573538575,4.5172650778477115,4.5206346044501755,4.524058531976371,4.527502443515367,4.530913048366365,4.534258150064302,4.5374911192459795,4.540580869669267,4.543499645760831,4.546196377265743,4.5486677335152015,4.5508748567065425,4.552798873049899,4.5544231292012745,4.5557354127084,4.556719070227278,4.557367440420308,4.5576838539562905,4.5576583188288255,4.557294165706712,4.5565958354816845,4.555576650828942,4.554243273086085,4.552606804482444,4.550698331260152,4.548533396540276,4.546133094558546,4.543525180888297,4.540732970211125,4.5378064225590276,4.534761081053072,4.531648015948188,4.528497203263574,4.525350831470694,4.522244427703413,4.519227951993726,4.516333600806701,4.513606893282599,4.51107447477182,4.508791856421026,4.506780132465949,4.505065948256988,4.503697043380272,4.502673417835802,4.502029488534508,4.501775247482791,4.501925127578781,4.502478018599548,4.503436140990955,4.504797274307138,4.506550316318763,4.5086730625671665,4.5111488597083484,4.513955503283645,4.51706412749679,4.520432543876321,4.5240496501929055,4.527853273962279,4.531815659611111,4.53588795733034,4.540046852438365,4.544227952005056,4.5484046106800164,4.552530199100048,4.556564749239554,4.5604771748564,4.564221956810325,4.567772449750928,4.571099787881945,4.574170664515377,4.576960654746692,4.57944644389429,4.581619150174706,4.5834576793522075,4.584948708751595,4.586085577035267,4.5868693944261585,4.5872912791408025,4.587359002739732,4.5870814470064145,4.5864563914949805,4.585503820218231,4.584248158080698,4.582694956197049,4.58087752125528,4.578818057714058,4.576537659809115,4.574072964897249,4.571461720558192,4.568726131250609,4.565918377452364,4.563065104513856,4.560214052021215,4.557400747108306,4.554658496463127,4.55204170100941,4.54957367542875,4.547304379753147,4.5452526877724635,4.543464118626967,4.541959766552387,4.540769607567922,4.539910295017572,4.539404033360002,4.53925748393281,4.539480638742397,4.540076828457562,4.541036061071907,4.54236166725423,4.544033662991734,4.546034284717486,4.5483435484186865,4.550929257630273,4.553770318116511,4.556828982297672,4.56006639237109,4.563450351871701,4.566932010990441,4.570479173262246,4.574048539992717,4.577590151149858,4.581072920491536,4.5844524391004216,4.587689849173848,4.590747403132086,4.593587353395402,4.596185275059266,4.598514522773278,4.600540679626506,4.602250422943751,4.6036215482663465,4.60463296135856,4.605284662220394,4.605565548622512,4.605472289896118,4.605002665595341,4.604167777949518,4.602973178073313,4.6014277477501935,4.59955591188469,4.597370993152004,4.594891865342,4.592158496480278,4.589186429687902,4.586013412544604,4.582669421069584,4.5791955335113705,4.575626166780897,4.572004619572562,4.568364198574362,4.564750422926562,4.561205481100626,4.5577626797845525,4.554469758564472,4.551357803682515,4.548469003610146,4.545827783251897,4.5434652288499,4.541415757315085,4.5396960219914515,4.538321566000064,4.537314593799589,4.53668287695056,4.536426415452975,4.5365374377463015,4.53702593583694,4.537876366603824,4.539070966480021,4.5405886412297995,4.542407186394494,4.544501066846641,4.546842527012906,4.549388268198894,4.552106093939539,4.5549660282156434,4.557921441664011,4.560931256036108,4.563963274866873,4.566967538124306,4.569915180012144,4.572761791613054,4.575476286684906,4.578027578985567,4.580374590266507,4.582503997852525,4.584379164386825,4.585981216079539,4.587303491593069,4.588317125131148,4.589025447362578,4.589417356058023,4.589493961440419,4.589255263509765,4.588705703157794,4.587865264397306,4.586745049457631,4.585361711682772,4.58373301463966,4.581898926353891,4.579868328608934,4.577688960990919,4.575384138181444,4.572992717983174,4.570555778644642,4.56810551663091,4.565683010190511,4.563326006903175,4.561075585017433,4.558958389883685,4.557027712202728,4.5553002053185585,4.553810286142109,4.552597922698977,4.551666445657964,4.551052492375866,4.550761613967349,4.550811573999346,4.55120681336359
}
-- Get from the table with Linear Interpolation
function p.harmonic_entropy_with_lookup_table(c)
if c < 0 then c = -c end
if c == 0 then return 2.4653643754704344 end
if c >= #lookup_table then return 4.805772050182217 end
if c == math.floor(c) then return lookup_table[math.floor(c)] end
b = c - math.floor(c)
return lookup_table[math.floor(c)] * (1 - b) + lookup_table[math.floor(c) + 1] * b
end
return p