This example demonstrates how to generate a tripolar grid using the OrthogonalSphericalShellGrids package and how to visualize the grid using the GLMakie package. The example is structured into several key sections, each performing a specific task in the process of creating and visualizing the grid.
We begin by importing the required Julia packages. OrthogonalSphericalShellGrids is used for generating the tripolar grid, a type of grid used in geophysical and oceanographic modeling due to its ability to handle polar singularities effectively. GLMakie is used for visualization purposes, allowing the creation of figures and plots to visualize the grid.
using OrthogonalSphericalShellGrids
+using OrthogonalSphericalShellGrids: Face, Center
+using OrthogonalSphericalShellGrids: get_cartesian_nodes_and_vertices
+using GLMakie
The grid is generated via OrthogonalSphericalShellGrids.TripolarGrid
method by specifying the grid size and the latitude of the "north" singularities. Here, we use a lateral resolution of 6 degrees (60 x 30 grid points in the horizontal) and we configure the North hemisphere singularities to be at 60 degrees latitude. This setup creates a grid that covers the globe with a specific focus on handling the complexities near the North pole.
grid = OrthogonalSphericalShellGrids.TripolarGrid(size = (60, 30, 1),
+ north_poles_latitude = 60)
60×30×1 OrthogonalSphericalShellGrid{Float64, Oceananigans.Grids.Periodic, Oceananigans.Grids.RightConnected, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 4×4×4 halo and with precomputed metrics
+├── centered at (λ, φ) = (0.0, 2.6549)
+├── longitude: Oceananigans.Grids.Periodic extent 359.895 degrees variably spaced with min(Δλ)=0.286186, max(Δλ)=6.22702
+├── latitude: Oceananigans.Grids.RightConnected extent 175.667 degrees variably spaced with min(Δφ)=0.517693, max(Δφ)=5.86207
+└── z: Bounded z ∈ [0.0, 1.0] regularly spaced with Δz=1.0
The lines retrieve Cartesian coordinates for two types of grid nodes: Face
–Face
nodes and Center
–Center
nodes. This is done using the
getcartesiannodesandverticesmethod, which converts the grid's spherical coordinates into Cartesian coordinates for easier manipulation and visualization. The coordinates are stored in variables
xF,
yF,
zFfor Face-Face nodes, and
xC,
yC,
zC` for Center-Center nodes.
cartesian_nodes, _ = get_cartesian_nodes_and_vertices(grid, Face(), Face(), Center())
+xF, yF, zF = cartesian_nodes
+
+cartesian_nodes, _ = get_cartesian_nodes_and_vertices(grid, Center(), Center(), Center())
+xC, yC, zC = cartesian_nodes
([-0.17336355171244128 -0.2727661612221198 -0.3691804382656139 -0.46156893266041793 -0.5489548863764049 -0.6304360970395362 -0.7051971605582505 -0.7725199187561228 -0.831792020854692 -0.8825135943858438 -0.9243021090235471 -0.9568956045855725 -0.980154542555809 -0.9940626318436183 -0.9987270802885146 -0.9943788441072318 -0.9813736042939756 -0.9601944156240868 -0.9314572827484517 -0.8959213577496584 -0.8545060554586461 -0.8083181192606373 -0.7586923057247961 -0.7072490567710032 -0.6559689624224248 -0.60727156743142 -0.5640556679962432 -0.5296033894808341 -0.5072013179848617 -0.4994063993194244; -0.17146617556136307 -0.269785681663328 -0.3651558021402381 -0.45655221586958394 -0.543010169794805 -0.6236381146444054 -0.6976297671398487 -0.7642744283803597 -0.822965468244785 -0.8732069696573536 -0.9146186119779641 -0.9469389583825696 -0.9700273984370961 -0.9838650870572909 -0.9885553207724362 -0.9843239119995201 -0.971520277894516 -0.9506201756767245 -0.9222313231026021 -0.8871035793942776 -0.8461459590255302 -0.8004534809641265 -0.7513474860536971 -0.700432758521141 -0.6496712550958073 -0.6014601097765037 -0.558671460107434 -0.5245573017254965 -0.5023740264948067 -0.49465505628677464; -0.16769201261744424 -0.2638565952000316 -0.3571486553990876 -0.44656981895509407 -0.5311790914579109 -0.6101060482082731 -0.6825625414014365 -0.7478527617672691 -0.8053815666096745 -0.8546610649816523 -0.8953155313504988 -0.9270848005394264 -0.9498263796206178 -0.9635165996829284 -0.9682512279485149 -0.9642460786151682 -0.9518383146367378 -0.9314893452281541 -0.9037905264078262 -0.8694733018728965 -0.8294260088169972 -0.7847202909280058 -0.7366506797833241 -0.6867906150258034 -0.6370647077160735 -0.5898251449703025 -0.5478905828069446 -0.5144525693737039 -0.4927069237644645 -0.48513988041191547; -0.16208203542874697 -0.25504237413571823 -0.3452429786027916 -0.43172363516006884 -0.5135783715271196 -0.5899680014232159 -0.660131313505385 -0.7233947525234397 -0.7791805080152763 -0.8270129974166376 -0.8665238043555417 -0.8974552084102788 -0.9196625205143991 -0.9331155213741272 -0.9378993944685136 -0.9342156600862237 -0.9223837673863762 -0.9028442096010617 -0.8761643233143916 -0.8430483524463561 -0.8043539299181591 -0.761117828512808 -0.7145944346205472 -0.6663101165473879 -0.6181332932542383 -0.5723484480635673 -0.5316936398318083 -0.49926931510035233 -0.4781800121231977 -0.47084086525108615; -0.15469718776463942 -0.24343754004120294 -0.32956405115455945 -0.4121660204163524 -0.4903830563619681 -0.5634168029216329 -0.630541463326553 -0.6911129831937729 -0.7445768129218288 -0.7904742324124834 -0.8284472868856299 -0.858242450764751 -0.8797132082248105 -0.8928218168678842 -0.8976406106275676 -0.8943533085714631 -0.883256941976044 -0.8647652137425413 -0.83941439054679 -0.807873233549663 -0.7709590253933968 -0.7296624238834079 -0.685184452268136 -0.6389886658135293 -0.5928683027578014 -0.5490171282087735 -0.5100651370790651 -0.4789906138327752 -0.45877571017234986 -0.45174024820601283; -0.14561776776220567 -0.2291668279955748 -0.31027758059442584 -0.388099121736715 -0.4618263150292622 -0.5307105577423562 -0.5940695135273377 -0.6512956887380131 -0.7018637787691403 -0.7453367642890204 -0.7813707940074347 -0.8097189506060883 -0.8302340607769572 -0.8428707817810065 -0.8476872807812087 -0.8448469280299713 -0.8346205641098647 -0.8173900943911004 -0.7936544375767083 -0.7640392420625269 -0.7293123094797721 -0.6904073045568316 -0.6484588812521129 -0.6048520996464982 -0.5612859449667114 -0.5198402400185187 -0.4830091413550897 -0.45361734874558135 -0.43449316857043135 -0.42783663522419724; -0.1349426079870381 -0.21238405523755866 -0.2875884787109599 -0.35977384046653393 -0.4281989130925496 -0.4921729791951939 -0.5510646703713034 -0.6043098397742089 -0.651418402315299 -0.6919801204953274 -0.7256693613799884 -0.7522489015507369 -0.7715729132295085 -0.7835893289509845 -0.7883418590516897 -0.7859720338502042 -0.7767217730091854 -0.7609371662736897 -0.7390744074612711 -0.7117091872379969 -0.6795513435029952 -0.6434671677877949 -0.6045122820014774 -0.5639777620410878 -0.5234493244821024 -0.4848695695081972 -0.45056890530423765 -0.4231868512567027 -0.4053662445083691 -0.3991627394042668; -0.1227880555527912 -0.19327068375933204 -0.2617392407514014 -0.32748832895145624 -0.38984817720709664 -0.44819320169023447 -0.5019498735735962 -0.5506038050115969 -0.5937059961374697 -0.6308782207046707 -0.6618175665528635 -0.6863001897448312 -0.7041843893568944 -0.7154131661712062 -0.7200164974745102 -0.7181136491233174 -0.7099159661887166 -0.6957307512852973 -0.6759670777615957 -0.6511447205785094 -0.6219078423635591 -0.5890456241077764 -0.5535225047206889 -0.516520476286537 -0.47949325829920103 -0.4442231643608505 -0.4128491276556795 -0.3877940742722299 -0.37148393651458 -0.3658055534215391; -0.1092867573213308 -0.17203406842726854 -0.23300788483838825 -0.29158591663674227 -0.3471762551119962 -0.39922475577075944 -0.44722188177466476 -0.49070893631682244 -0.5292836359021946 -0.5626050032824361 -0.5903975890792549 -0.6124550655645447 -0.6286432760457655 -0.6389028713417393 -0.6432517250854888 -0.6417873986226402 -0.6346900340880439 -0.6222262054952569 -0.6047544725423578 -0.5827336846363088 -0.5567354923853237 -0.5274630207858869 -0.49577808564326276 -0.4627391404511073 -0.4296497870738666 -0.3981095999442589 -0.3700389663063305 -0.3476135201656748 -0.33301157009143917 -0.3279272705270966; -0.09458625762739656 -0.14890538669793285 -0.2017054158117732 -0.25245237160435124 -0.3006374880403946 -0.34578339995577 -0.3874499316818515 -0.4252394250616683 -0.45880156813823625 -0.48783770561088646 -0.5121046351521785 -0.5314179205955734 -0.5456547852024315 -0.5547566879924491 -0.5587317371683395 -0.5576571627352767 -0.5516821642164534 -0.5410315816261994 -0.5260110260907815 -0.5070143717835632 -0.4845348695906277 -0.45918157774358653 -0.4317031784656438 -0.4030210808213127 -0.37427165698474485 -0.34685040874639284 -0.3224333785206566 -0.3029196214982052 -0.29021051552664434 -0.285784764955385; -0.07884741888633923 -0.12413725278791794 -0.16817279092527154 -0.21051242598080885 -0.25073474671355467 -0.28844355151004214 -0.32327257009149973 -0.3548898517629575 -0.3830017903708746 -0.40735677023168265 -0.42774843411524655 -0.4440185946548549 -0.45605983555413815 -0.46381788068215263 -0.46729385074969226 -0.46654658360310425 -0.4616952725700714 -0.4529227884063621 -0.44048020887016903 -0.42469330340656597 -0.40597202253539016 -0.3848244075447356 -0.3618766507344438 -0.33790089518518224 -0.31385063960353254 -0.29089769496140605 -0.2704499645991024 -0.2541028844491066 -0.24345383915847799 -0.23974506555510222; -0.06224267873718799 -0.09800102788100669 -0.13277738333377656 -0.16622552717415318 -0.19801463616365902 -0.22783313807679847 -0.25539236775100005 -0.28042999332746543 -0.30271319094705557 -0.32204155573233284 -0.33824974863148494 -0.35120989328464763 -0.3608337555534154 -0.36707476238395237 -0.3699299488047028 -0.36944196597896406 -0.3657013451606751 -0.3588493005988227 -0.34908148051000965 -0.33665325313422245 -0.3218873553995251 -0.30518502303145156 -0.2870419713829763 -0.2680704843969711 -0.24902750038347965 -0.2308438824310934 -0.21463840709096027 -0.20167901463762905 -0.1932351963195468 -0.19029416264369178; -0.04495416087944619 -0.07078384802364276 -0.09590896171917541 -0.12008081895723474 -0.14306154462335027 -0.16462679868626828 -0.184568375531133 -0.20269665603523843 -0.21884289779731572 -0.23286135498785662 -0.24463122692155528 -0.2540584441832702 -0.2610773137687472 -0.2656520614624619 -0.26777833244533894 -0.2674847427447304 -0.264834618841731 -0.2599281266775273 -0.25290508286556096 -0.24394887021821865 -0.23329205453363458 -0.22122451133261328 -0.2081050532903382 -0.19437746811585607 -0.18059088333188733 -0.16742096282299748 -0.1556799827500877 -0.14628860377433242 -0.14016861600480945 -0.13803682405467774; -0.027171660274957276 -0.042785402007248514 -0.05797522885488518 -0.07259140337793961 -0.08649059153582489 -0.09953748679757311 -0.11160636387130848 -0.12258255113920791 -0.13236381346601114 -0.1408616403650565 -0.1480024387736359 -0.1537286352393712 -0.1579996996531805 -0.16079311254216697 -0.16210531150766008 -0.1619526713906703 -0.16037259974172546 -0.15742486789108182 -0.15319335345834398 -0.1477884486249885 -0.14135049463430394 -0.13405473152813957 -0.1261183626608485 -0.11781028449293914 -0.109463429787166 -0.10148760334298632 -0.09437556065527847 -0.08868584426734653 -0.08497768393585112 -0.08368594162069272; -0.009090526679840314 -0.014314501900697699 -0.019396986229065785 -0.024287981965398407 -0.028939611707291882 -0.03330665755483169 -0.03734707793599557 -0.04102249854077091 -0.04429867466181113 -0.04714592329128039 -0.04953952469293119 -0.05146009496928062 -0.05289393354592282 -0.05383335275603944 -0.054277001215150215 -0.05423019901076182 -0.05370531175719615 -0.05272220353159404 -0.051308827321937964 -0.04950203793082796 -0.047348747867600786 -0.044907589862633095 -0.04225128670077994 -0.03946991265030333 -0.03667502888888604 -0.034003981940970575 -0.031621935363869695 -0.029716109950188363 -0.028473957254269537 -0.028041239967729517; 0.009090526679840142 0.014314501900697699 0.019396986229065785 0.024287981965398865 0.028939611707292427 0.033306657554831066 0.03734707793599557 0.04102249854077014 0.044298674661811956 0.04714592329128039 0.04953952469293119 0.05146009496928062 0.05289393354592282 0.05383335275603944 0.054277001215150215 0.05423019901076182 0.053705311757197116 0.05272220353159404 0.051308827321937964 0.04950203793082796 0.0473487478676 0.04490758986263382 0.04225128670077994 0.03946991265030333 0.03667502888888604 0.034003981940970186 0.031621935363869993 0.029716109950188568 0.028473957254269537 0.028041239967729517; 0.027171660274957276 0.04278540200724878 0.057975228854884826 0.07259140337794005 0.08649059153582489 0.09953748679757311 0.11160636387130778 0.12258255113920866 0.13236381346601114 0.1408616403650565 0.148002438773635 0.15372863523937025 0.15799969965318147 0.160793112542166 0.16210531150766008 0.1619526713906703 0.16037259974172546 0.15742486789108182 0.15319335345834398 0.1477884486249885 0.14135049463430394 0.13405473152814026 0.1261183626608485 0.11781028449293858 0.109463429787166 0.10148760334298632 0.09437556065527876 0.08868584426734653 0.08497768393585112 0.08368594162069272; 0.04495416087944619 0.07078384802364276 0.09590896171917579 0.12008081895723517 0.14306154462335027 0.16462679868626828 0.184568375531133 0.20269665603523843 0.21884289779731572 0.23286135498785662 0.24463122692155528 0.2540584441832702 0.2610773137687472 0.26565206146246284 0.26777833244533894 0.2674847427447304 0.2648346188417301 0.2599281266775273 0.2529050828655601 0.24394887021821948 0.23329205453363383 0.22122451133261398 0.2081050532903382 0.19437746811585607 0.18059088333188686 0.16742096282299784 0.155679982750088 0.14628860377433242 0.14016861600480954 0.13803682405467774; 0.06224267873718799 0.09800102788100695 0.13277738333377623 0.16622552717415318 0.19801463616365902 0.22783313807679847 0.25539236775100005 0.2804299933274647 0.3027131909470564 0.322041555732332 0.33824974863148494 0.35120989328464763 0.36083375555341446 0.36707476238395237 0.36992994880470187 0.3694419659789632 0.36570134516067415 0.3588493005988227 0.34908148051000965 0.33665325313422245 0.3218873553995259 0.30518502303145156 0.2870419713829763 0.2680704843969706 0.24902750038347965 0.2308438824310934 0.21463840709096027 0.20167901463762905 0.1932351963195468 0.19029416264369178; 0.07884741888633923 0.12413725278791794 0.16817279092527154 0.21051242598080885 0.25073474671355467 0.28844355151004214 0.32327257009149973 0.3548898517629575 0.3830017903708746 0.40735677023168265 0.4277484341152474 0.44401859465485405 0.45605983555413815 0.46381788068215263 0.46729385074969226 0.46654658360310425 0.46169527257007065 0.4529227884063621 0.44048020887016903 0.42469330340656597 0.40597202253539016 0.3848244075447356 0.3618766507344443 0.33790089518518224 0.31385063960353254 0.29089769496140605 0.2704499645991024 0.2541028844491066 0.24345383915847799 0.23974506555510222; 0.09458625762739656 0.14890538669793285 0.2017054158117732 0.25245237160435124 0.3006374880403946 0.34578339995577 0.3874499316818515 0.4252394250616689 0.45880156813823564 0.48783770561088646 0.5121046351521785 0.5314179205955734 0.5456547852024315 0.5547566879924491 0.5587317371683395 0.5576571627352759 0.5516821642164534 0.5410315816261994 0.5260110260907815 0.5070143717835632 0.4845348695906283 0.45918157774358653 0.4317031784656438 0.4030210808213132 0.3742716569847445 0.34685040874639284 0.3224333785206569 0.3029196214982052 0.29021051552664434 0.285784764955385; 0.1092867573213308 0.17203406842726854 0.23300788483838825 0.29158591663674227 0.3471762551119962 0.39922475577075944 0.44722188177466476 0.4907089363168219 0.5292836359021946 0.5626050032824361 0.5903975890792549 0.6124550655645447 0.6286432760457663 0.6389028713417393 0.6432517250854888 0.6417873986226394 0.6346900340880439 0.6222262054952569 0.6047544725423578 0.5827336846363088 0.5567354923853237 0.5274630207858869 0.49577808564326276 0.4627391404511073 0.4296497870738666 0.3981095999442589 0.37003896630633076 0.3476135201656748 0.33301157009143917 0.3279272705270966; 0.1227880555527912 0.19327068375933204 0.2617392407514014 0.32748832895145624 0.38984817720709664 0.44819320169023447 0.5019498735735962 0.5506038050115969 0.5937059961374703 0.6308782207046707 0.6618175665528635 0.6863001897448312 0.7041843893568944 0.7154131661712055 0.7200164974745102 0.7181136491233181 0.709915966188716 0.6957307512852966 0.6759670777615957 0.6511447205785094 0.6219078423635586 0.5890456241077768 0.5535225047206889 0.5165204762865374 0.4794932582992007 0.4442231643608505 0.4128491276556795 0.3877940742722299 0.37148393651458 0.3658055534215391; 0.13494260798703822 0.21238405523755846 0.2875884787109599 0.35977384046653393 0.4281989130925496 0.49217297919519437 0.5510646703713034 0.6043098397742089 0.651418402315299 0.6919801204953279 0.7256693613799884 0.7522489015507369 0.7715729132295085 0.7835893289509851 0.7883418590516897 0.7859720338502042 0.7767217730091854 0.7609371662736902 0.7390744074612711 0.7117091872379965 0.6795513435029952 0.6434671677877944 0.6045122820014774 0.5639777620410878 0.5234493244821027 0.4848695695081972 0.45056890530423765 0.4231868512567027 0.4053662445083691 0.3991627394042668; 0.14561776776220559 0.22916682799557495 0.3102775805944257 0.38809912173671524 0.4618263150292622 0.5307105577423562 0.5940695135273377 0.6512956887380131 0.7018637787691403 0.7453367642890204 0.7813707940074347 0.8097189506060889 0.8302340607769567 0.8428707817810065 0.8476872807812081 0.8448469280299713 0.8346205641098647 0.8173900943911004 0.7936544375767083 0.7640392420625269 0.7293123094797717 0.6904073045568316 0.6484588812521129 0.6048520996464982 0.5612859449667114 0.5198402400185187 0.4830091413550897 0.45361734874558135 0.43449316857043135 0.42783663522419724; 0.15469718776463942 0.24343754004120294 0.32956405115455945 0.4121660204163524 0.4903830563619681 0.5634168029216329 0.630541463326553 0.6911129831937729 0.7445768129218288 0.7904742324124834 0.8284472868856299 0.858242450764751 0.8797132082248105 0.8928218168678842 0.8976406106275676 0.8943533085714631 0.883256941976044 0.8647652137425413 0.83941439054679 0.807873233549663 0.7709590253933968 0.7296624238834079 0.685184452268136 0.6389886658135293 0.5928683027578014 0.5490171282087735 0.5100651370790651 0.4789906138327752 0.45877571017234986 0.45174024820601283; 0.16208203542874697 0.25504237413571823 0.3452429786027916 0.43172363516006884 0.5135783715271196 0.5899680014232159 0.660131313505385 0.7233947525234397 0.7791805080152763 0.8270129974166376 0.8665238043555417 0.8974552084102788 0.9196625205143991 0.9331155213741272 0.9378993944685136 0.9342156600862237 0.9223837673863762 0.9028442096010617 0.8761643233143916 0.8430483524463561 0.8043539299181591 0.761117828512808 0.7145944346205472 0.6663101165473879 0.6181332932542383 0.5723484480635673 0.5316936398318083 0.49926931510035233 0.4781800121231977 0.47084086525108615; 0.16769201261744424 0.2638565952000316 0.3571486553990876 0.44656981895509407 0.5311790914579109 0.6101060482082731 0.6825625414014365 0.7478527617672691 0.8053815666096745 0.8546610649816523 0.8953155313504988 0.9270848005394264 0.9498263796206178 0.9635165996829284 0.9682512279485149 0.9642460786151682 0.9518383146367378 0.9314893452281541 0.9037905264078262 0.8694733018728965 0.8294260088169972 0.7847202909280058 0.7366506797833241 0.6867906150258034 0.6370647077160735 0.5898251449703025 0.5478905828069446 0.5144525693737039 0.4927069237644645 0.48513988041191547; 0.17146617556136307 0.269785681663328 0.3651558021402381 0.45655221586958394 0.543010169794805 0.6236381146444054 0.6976297671398487 0.7642744283803597 0.822965468244785 0.8732069696573536 0.9146186119779641 0.9469389583825696 0.9700273984370961 0.9838650870572909 0.9885553207724362 0.9843239119995201 0.971520277894516 0.9506201756767245 0.9222313231026021 0.8871035793942776 0.8461459590255302 0.8004534809641265 0.7513474860536971 0.700432758521141 0.6496712550958073 0.6014601097765037 0.558671460107434 0.5245573017254965 0.5023740264948067 0.49465505628677464; 0.17336355171244128 0.2727661612221198 0.3691804382656139 0.46156893266041793 0.5489548863764049 0.6304360970395362 0.7051971605582505 0.7725199187561228 0.831792020854692 0.8825135943858438 0.9243021090235471 0.9568956045855725 0.980154542555809 0.9940626318436183 0.9987270802885146 0.9943788441072318 0.9813736042939756 0.9601944156240868 0.9314572827484517 0.8959213577496584 0.8545060554586461 0.8083181192606373 0.7586923057247961 0.7072490567710032 0.6559689624224248 0.60727156743142 0.5640556679962432 0.5296033894808341 0.5072013179848617 0.4994063993194244; 0.17336355171244128 0.2727661612221198 0.3691804382656139 0.46156893266041793 0.5489548863764049 0.6304360970395362 0.7051971605582505 0.7725199187561228 0.8317920208546918 0.8825135943858436 0.9243021090235471 0.9568956045855725 0.980154542555809 0.9940626318436183 0.9987270802885146 0.9943788441072318 0.9813736042939756 0.9601944156240869 0.9314572827484517 0.8959213577496584 0.8545060554586461 0.8083181192606372 0.7586923057247961 0.7072490567710031 0.6559689624224248 0.6072715674314199 0.5640556679962432 0.529603389480834 0.5072013179848617 0.4994063993194244; 0.17146617556136304 0.269785681663328 0.36515580214023813 0.45655221586958394 0.543010169794805 0.6236381146444054 0.6976297671398489 0.7642744283803597 0.822965468244785 0.8732069696573534 0.9146186119779641 0.9469389583825696 0.9700273984370961 0.9838650870572909 0.9885553207724364 0.9843239119995201 0.9715202778945161 0.9506201756767245 0.9222313231026021 0.8871035793942776 0.8461459590255302 0.8004534809641265 0.7513474860536971 0.700432758521141 0.6496712550958073 0.6014601097765035 0.558671460107434 0.5245573017254965 0.5023740264948067 0.49465505628677464; 0.16769201261744424 0.2638565952000316 0.3571486553990874 0.44656981895509407 0.5311790914579108 0.610106048208273 0.6825625414014365 0.7478527617672691 0.8053815666096745 0.8546610649816523 0.8953155313504988 0.9270848005394264 0.9498263796206181 0.963516599682928 0.9682512279485153 0.9642460786151682 0.9518383146367378 0.9314893452281541 0.9037905264078262 0.8694733018728967 0.8294260088169972 0.7847202909280058 0.7366506797833242 0.6867906150258035 0.6370647077160733 0.5898251449703025 0.5478905828069446 0.5144525693737039 0.4927069237644645 0.48513988041191547; 0.16208203542874697 0.25504237413571823 0.3452429786027914 0.43172363516006884 0.5135783715271196 0.5899680014232159 0.660131313505385 0.7233947525234393 0.7791805080152763 0.8270129974166379 0.8665238043555417 0.8974552084102788 0.9196625205143991 0.9331155213741272 0.9378993944685136 0.9342156600862237 0.9223837673863762 0.9028442096010617 0.8761643233143913 0.8430483524463561 0.8043539299181591 0.7611178285128082 0.7145944346205472 0.6663101165473879 0.6181332932542383 0.5723484480635673 0.5316936398318082 0.49926931510035233 0.4781800121231977 0.47084086525108615; 0.15469718776463937 0.24343754004120294 0.32956405115455945 0.4121660204163524 0.49038305636196783 0.5634168029216332 0.6305414633265527 0.6911129831937729 0.7445768129218284 0.7904742324124834 0.8284472868856299 0.858242450764751 0.8797132082248105 0.8928218168678838 0.8976406106275672 0.8943533085714631 0.883256941976044 0.8647652137425413 0.83941439054679 0.807873233549663 0.7709590253933968 0.7296624238834082 0.6851844522681362 0.6389886658135293 0.5928683027578014 0.5490171282087735 0.510065137079065 0.47899061383277514 0.45877571017234986 0.45174024820601283; 0.14561776776220559 0.22916682799557495 0.3102775805944257 0.38809912173671524 0.4618263150292622 0.5307105577423562 0.5940695135273377 0.6512956887380131 0.7018637787691403 0.7453367642890204 0.7813707940074347 0.8097189506060889 0.8302340607769567 0.8428707817810059 0.8476872807812081 0.8448469280299713 0.8346205641098647 0.8173900943911004 0.7936544375767083 0.7640392420625269 0.7293123094797717 0.6904073045568316 0.6484588812521126 0.6048520996464979 0.5612859449667116 0.5198402400185187 0.4830091413550897 0.45361734874558135 0.43449316857043135 0.42783663522419724; 0.13494260798703822 0.21238405523755846 0.28758847871095966 0.35977384046653393 0.4281989130925496 0.49217297919519437 0.5510646703713034 0.6043098397742089 0.651418402315299 0.6919801204953279 0.7256693613799884 0.7522489015507369 0.7715729132295085 0.7835893289509851 0.7883418590516897 0.7859720338502048 0.7767217730091848 0.7609371662736902 0.7390744074612711 0.7117091872379965 0.6795513435029952 0.6434671677877944 0.6045122820014774 0.5639777620410878 0.5234493244821027 0.4848695695081975 0.45056890530423765 0.4231868512567027 0.4053662445083691 0.3991627394042668; 0.1227880555527912 0.19327068375933204 0.2617392407514014 0.32748832895145624 0.38984817720709664 0.44819320169023447 0.5019498735735962 0.5506038050115973 0.5937059961374703 0.6308782207046707 0.6618175665528635 0.6863001897448312 0.7041843893568951 0.7154131661712055 0.7200164974745109 0.7181136491233181 0.709915966188716 0.6957307512852966 0.6759670777615957 0.6511447205785094 0.6219078423635586 0.5890456241077768 0.5535225047206889 0.5165204762865374 0.4794932582992007 0.4442231643608505 0.4128491276556793 0.3877940742722299 0.37148393651458 0.3658055534215391; 0.1092867573213308 0.17203406842726854 0.23300788483838825 0.29158591663674227 0.3471762551119962 0.39922475577075944 0.44722188177466476 0.4907089363168219 0.5292836359021946 0.5626050032824361 0.5903975890792549 0.6124550655645447 0.6286432760457663 0.6389028713417393 0.6432517250854888 0.6417873986226394 0.6346900340880447 0.6222262054952569 0.6047544725423578 0.5827336846363088 0.5567354923853237 0.5274630207858869 0.49577808564326276 0.4627391404511073 0.4296497870738666 0.3981095999442589 0.37003896630633076 0.3476135201656748 0.33301157009143917 0.3279272705270966; 0.09458625762739656 0.14890538669793285 0.2017054158117732 0.25245237160435124 0.3006374880403951 0.34578339995577 0.3874499316818515 0.4252394250616689 0.45880156813823564 0.48783770561088646 0.5121046351521785 0.5314179205955734 0.5456547852024315 0.5547566879924491 0.5587317371683395 0.5576571627352759 0.5516821642164527 0.5410315816261994 0.5260110260907815 0.5070143717835632 0.4845348695906283 0.45918157774358653 0.4317031784656438 0.4030210808213132 0.3742716569847445 0.34685040874639284 0.3224333785206569 0.3029196214982052 0.29021051552664423 0.285784764955385; 0.07884741888633923 0.12413725278791818 0.16817279092527154 0.21051242598080885 0.25073474671355467 0.28844355151004214 0.32327257009149973 0.3548898517629575 0.3830017903708746 0.40735677023168265 0.4277484341152474 0.44401859465485405 0.45605983555413904 0.46381788068215263 0.46729385074969226 0.46654658360310425 0.46169527257007065 0.45292278840636124 0.4404802088701682 0.42469330340656597 0.40597202253539016 0.3848244075447356 0.3618766507344443 0.33790089518518224 0.31385063960353254 0.29089769496140605 0.2704499645991024 0.2541028844491066 0.2434538391584779 0.23974506555510222; 0.06224267873718799 0.09800102788100695 0.13277738333377623 0.16622552717415318 0.19801463616365902 0.22783313807679847 0.25539236775100005 0.2804299933274647 0.3027131909470564 0.322041555732332 0.33824974863148494 0.35120989328464763 0.36083375555341446 0.36707476238395237 0.36992994880470187 0.3694419659789632 0.36570134516067415 0.3588493005988227 0.34908148051000965 0.33665325313422245 0.3218873553995259 0.30518502303145156 0.2870419713829763 0.2680704843969706 0.24902750038347965 0.2308438824310934 0.21463840709096027 0.20167901463762883 0.1932351963195468 0.19029416264369178; 0.04495416087944619 0.07078384802364276 0.09590896171917579 0.12008081895723517 0.14306154462335027 0.16462679868626828 0.184568375531133 0.20269665603523843 0.21884289779731572 0.23286135498785662 0.24463122692155528 0.2540584441832702 0.2610773137687472 0.26565206146246284 0.26777833244533894 0.2674847427447304 0.2648346188417301 0.2599281266775273 0.2529050828655601 0.24394887021821948 0.23329205453363383 0.22122451133261398 0.2081050532903382 0.19437746811585607 0.18059088333188686 0.16742096282299784 0.155679982750088 0.14628860377433223 0.14016861600480954 0.13803682405467774; 0.027171660274957276 0.04278540200724878 0.057975228854884826 0.07259140337794005 0.08649059153582489 0.09953748679757311 0.11160636387130778 0.12258255113920866 0.13236381346601114 0.1408616403650565 0.148002438773635 0.15372863523937025 0.15799969965318147 0.160793112542166 0.16210531150766008 0.1619526713906703 0.16037259974172546 0.15742486789108182 0.15319335345834398 0.1477884486249885 0.14135049463430394 0.13405473152814026 0.1261183626608485 0.11781028449293858 0.109463429787166 0.10148760334298632 0.09437556065527876 0.08868584426734653 0.08497768393585112 0.08368594162069272; 0.009090526679840142 0.014314501900697699 0.019396986229065785 0.024287981965398865 0.028939611707292427 0.033306657554831066 0.03734707793599557 0.04102249854077014 0.044298674661811956 0.04714592329128039 0.04953952469293119 0.05146009496928062 0.05289393354592282 0.05383335275603944 0.054277001215150215 0.05423019901076182 0.053705311757197116 0.05272220353159404 0.051308827321937964 0.04950203793082796 0.0473487478676 0.04490758986263382 0.04225128670077994 0.03946991265030333 0.03667502888888604 0.034003981940970186 0.031621935363869993 0.029716109950188568 0.028473957254269537 0.028041239967729517; -0.009090526679840142 -0.014314501900697699 -0.019396986229065785 -0.024287981965398865 -0.028939611707292427 -0.033306657554831066 -0.03734707793599557 -0.04102249854077014 -0.044298674661811956 -0.04714592329128039 -0.04953952469293119 -0.05146009496928062 -0.05289393354592282 -0.05383335275603944 -0.054277001215150215 -0.05423019901076182 -0.053705311757197116 -0.05272220353159404 -0.051308827321937964 -0.04950203793082796 -0.0473487478676 -0.04490758986263382 -0.04225128670077994 -0.03946991265030333 -0.03667502888888604 -0.034003981940970186 -0.031621935363869993 -0.029716109950188568 -0.028473957254269537 -0.028041239967729517; -0.027171660274957276 -0.04278540200724878 -0.057975228854884826 -0.07259140337794005 -0.08649059153582489 -0.09953748679757311 -0.11160636387130778 -0.12258255113920866 -0.13236381346601114 -0.1408616403650565 -0.148002438773635 -0.15372863523937025 -0.15799969965318147 -0.160793112542166 -0.16210531150766008 -0.1619526713906703 -0.16037259974172546 -0.15742486789108182 -0.15319335345834398 -0.1477884486249885 -0.14135049463430394 -0.13405473152814026 -0.1261183626608485 -0.11781028449293858 -0.109463429787166 -0.10148760334298632 -0.09437556065527876 -0.08868584426734653 -0.08497768393585112 -0.08368594162069272; -0.04495416087944619 -0.07078384802364276 -0.09590896171917579 -0.12008081895723517 -0.14306154462335027 -0.16462679868626828 -0.184568375531133 -0.20269665603523843 -0.21884289779731572 -0.23286135498785662 -0.24463122692155528 -0.2540584441832702 -0.2610773137687472 -0.26565206146246284 -0.26777833244533894 -0.2674847427447304 -0.2648346188417301 -0.2599281266775273 -0.2529050828655601 -0.24394887021821948 -0.23329205453363383 -0.22122451133261398 -0.2081050532903382 -0.19437746811585607 -0.18059088333188686 -0.16742096282299784 -0.155679982750088 -0.14628860377433242 -0.14016861600480954 -0.13803682405467774; -0.06224267873718799 -0.09800102788100695 -0.13277738333377623 -0.16622552717415318 -0.19801463616365902 -0.22783313807679847 -0.25539236775100005 -0.2804299933274647 -0.3027131909470564 -0.322041555732332 -0.33824974863148494 -0.35120989328464763 -0.36083375555341446 -0.36707476238395237 -0.36992994880470187 -0.3694419659789632 -0.36570134516067415 -0.3588493005988227 -0.34908148051000965 -0.33665325313422245 -0.3218873553995259 -0.30518502303145156 -0.2870419713829763 -0.2680704843969706 -0.24902750038347965 -0.2308438824310934 -0.21463840709096027 -0.20167901463762905 -0.1932351963195468 -0.19029416264369178; -0.07884741888633923 -0.12413725278791794 -0.16817279092527154 -0.21051242598080885 -0.25073474671355467 -0.28844355151004214 -0.32327257009149973 -0.3548898517629575 -0.3830017903708746 -0.40735677023168265 -0.4277484341152474 -0.44401859465485405 -0.45605983555413815 -0.46381788068215263 -0.46729385074969226 -0.46654658360310425 -0.46169527257007065 -0.4529227884063621 -0.44048020887016903 -0.42469330340656597 -0.40597202253539016 -0.3848244075447356 -0.3618766507344443 -0.33790089518518224 -0.31385063960353254 -0.29089769496140605 -0.2704499645991024 -0.2541028844491066 -0.24345383915847799 -0.23974506555510222; -0.09458625762739656 -0.14890538669793285 -0.2017054158117732 -0.25245237160435124 -0.3006374880403946 -0.34578339995577 -0.3874499316818515 -0.4252394250616689 -0.45880156813823564 -0.48783770561088646 -0.5121046351521785 -0.5314179205955734 -0.5456547852024315 -0.5547566879924491 -0.5587317371683395 -0.5576571627352759 -0.5516821642164534 -0.5410315816261994 -0.5260110260907815 -0.5070143717835632 -0.4845348695906283 -0.45918157774358653 -0.4317031784656438 -0.4030210808213132 -0.3742716569847445 -0.34685040874639284 -0.3224333785206569 -0.3029196214982052 -0.29021051552664434 -0.285784764955385; -0.1092867573213308 -0.17203406842726854 -0.23300788483838825 -0.29158591663674227 -0.3471762551119962 -0.39922475577075944 -0.44722188177466476 -0.4907089363168219 -0.5292836359021946 -0.5626050032824361 -0.5903975890792549 -0.6124550655645447 -0.6286432760457663 -0.6389028713417393 -0.6432517250854888 -0.6417873986226394 -0.6346900340880439 -0.6222262054952569 -0.6047544725423578 -0.5827336846363088 -0.5567354923853237 -0.5274630207858869 -0.49577808564326276 -0.4627391404511073 -0.4296497870738666 -0.3981095999442589 -0.37003896630633076 -0.3476135201656748 -0.33301157009143917 -0.3279272705270966; -0.1227880555527912 -0.19327068375933204 -0.2617392407514014 -0.32748832895145624 -0.38984817720709664 -0.44819320169023447 -0.5019498735735962 -0.5506038050115969 -0.5937059961374703 -0.6308782207046707 -0.6618175665528635 -0.6863001897448312 -0.7041843893568944 -0.7154131661712055 -0.7200164974745102 -0.7181136491233181 -0.709915966188716 -0.6957307512852966 -0.6759670777615957 -0.6511447205785094 -0.6219078423635586 -0.5890456241077768 -0.5535225047206889 -0.5165204762865374 -0.4794932582992007 -0.4442231643608505 -0.4128491276556795 -0.3877940742722299 -0.37148393651458 -0.3658055534215391; -0.13494260798703822 -0.21238405523755846 -0.2875884787109599 -0.35977384046653393 -0.4281989130925496 -0.49217297919519437 -0.5510646703713034 -0.6043098397742089 -0.651418402315299 -0.6919801204953279 -0.7256693613799884 -0.7522489015507369 -0.7715729132295085 -0.7835893289509851 -0.7883418590516897 -0.7859720338502042 -0.7767217730091854 -0.7609371662736902 -0.7390744074612711 -0.7117091872379965 -0.6795513435029952 -0.6434671677877944 -0.6045122820014774 -0.5639777620410878 -0.5234493244821027 -0.4848695695081972 -0.45056890530423765 -0.4231868512567027 -0.4053662445083691 -0.3991627394042668; -0.14561776776220559 -0.22916682799557495 -0.3102775805944257 -0.38809912173671524 -0.4618263150292622 -0.5307105577423562 -0.5940695135273377 -0.6512956887380131 -0.7018637787691403 -0.7453367642890204 -0.7813707940074347 -0.8097189506060889 -0.8302340607769567 -0.8428707817810065 -0.8476872807812081 -0.8448469280299713 -0.8346205641098647 -0.8173900943911004 -0.7936544375767083 -0.7640392420625269 -0.7293123094797717 -0.6904073045568316 -0.6484588812521129 -0.6048520996464982 -0.5612859449667114 -0.5198402400185187 -0.4830091413550897 -0.45361734874558135 -0.43449316857043135 -0.42783663522419724; -0.15469718776463942 -0.24343754004120294 -0.32956405115455945 -0.4121660204163524 -0.4903830563619681 -0.5634168029216329 -0.630541463326553 -0.6911129831937729 -0.7445768129218288 -0.7904742324124834 -0.8284472868856299 -0.858242450764751 -0.8797132082248105 -0.8928218168678842 -0.8976406106275676 -0.8943533085714631 -0.883256941976044 -0.8647652137425413 -0.83941439054679 -0.807873233549663 -0.7709590253933968 -0.7296624238834079 -0.685184452268136 -0.6389886658135293 -0.5928683027578014 -0.5490171282087735 -0.5100651370790651 -0.4789906138327752 -0.45877571017234986 -0.45174024820601283; -0.16208203542874697 -0.25504237413571823 -0.3452429786027916 -0.43172363516006884 -0.5135783715271196 -0.5899680014232159 -0.660131313505385 -0.7233947525234397 -0.7791805080152763 -0.8270129974166376 -0.8665238043555417 -0.8974552084102788 -0.9196625205143991 -0.9331155213741272 -0.9378993944685136 -0.9342156600862237 -0.9223837673863762 -0.9028442096010617 -0.8761643233143916 -0.8430483524463561 -0.8043539299181591 -0.761117828512808 -0.7145944346205472 -0.6663101165473879 -0.6181332932542383 -0.5723484480635673 -0.5316936398318083 -0.49926931510035233 -0.4781800121231977 -0.47084086525108615; -0.16769201261744424 -0.2638565952000316 -0.3571486553990876 -0.44656981895509407 -0.5311790914579109 -0.6101060482082731 -0.6825625414014365 -0.7478527617672691 -0.8053815666096745 -0.8546610649816523 -0.8953155313504988 -0.9270848005394264 -0.9498263796206178 -0.9635165996829284 -0.9682512279485149 -0.9642460786151682 -0.9518383146367378 -0.9314893452281541 -0.9037905264078262 -0.8694733018728965 -0.8294260088169972 -0.7847202909280058 -0.7366506797833241 -0.6867906150258034 -0.6370647077160735 -0.5898251449703025 -0.5478905828069446 -0.5144525693737039 -0.4927069237644645 -0.48513988041191547; -0.17146617556136307 -0.269785681663328 -0.3651558021402381 -0.45655221586958394 -0.543010169794805 -0.6236381146444054 -0.6976297671398487 -0.7642744283803597 -0.822965468244785 -0.8732069696573536 -0.9146186119779641 -0.9469389583825696 -0.9700273984370961 -0.9838650870572909 -0.9885553207724362 -0.9843239119995201 -0.971520277894516 -0.9506201756767245 -0.9222313231026021 -0.8871035793942776 -0.8461459590255302 -0.8004534809641265 -0.7513474860536971 -0.700432758521141 -0.6496712550958073 -0.6014601097765037 -0.558671460107434 -0.5245573017254965 -0.5023740264948067 -0.49465505628677464; -0.17336355171244128 -0.2727661612221198 -0.3691804382656139 -0.46156893266041793 -0.5489548863764049 -0.6304360970395362 -0.7051971605582505 -0.7725199187561228 -0.831792020854692 -0.8825135943858438 -0.9243021090235471 -0.9568956045855725 -0.980154542555809 -0.9940626318436183 -0.9987270802885146 -0.9943788441072318 -0.9813736042939756 -0.9601944156240868 -0.9314572827484517 -0.8959213577496584 -0.8545060554586461 -0.8083181192606373 -0.7586923057247961 -0.7072490567710032 -0.6559689624224248 -0.60727156743142 -0.5640556679962432 -0.5296033894808341 -0.5072013179848617 -0.4994063993194244], [-0.009083103279740998 -0.01428511942685134 -0.01932240443160082 -0.024137636545694972 -0.02867671357503927 -0.03288947992301452 -0.03673036136657844 -0.04015889658480063 -0.04314015850682612 -0.04564506261266228 -0.047650563187460165 -0.04913974201221967 -0.050101796927525435 -0.05053194003690302 -0.05043121697644118 -0.04980625966628017 -0.04866898531566895 -0.04703625424384296 -0.044929498392808666 -0.04237433134421172 -0.0394001493133432 -0.036039731077160034 -0.03232884318935258 -0.028305855220852535 -0.024011368202566014 -0.019487857987643936 -0.014779333930466381 -0.009931012123682185 -0.004989001459909738 -0.0; -0.027150115081063988 -0.04270011428358324 -0.057758705288458785 -0.07215482635514493 -0.08572696402193652 -0.09832531382770597 -0.10981367006458886 -0.1200710120433018 -0.12899276613783248 -0.13649173473699158 -0.1424986945351325 -0.14696267680186426 -0.14985095096122678 -0.15114873970251896 -0.1508586987967492 -0.14900019779435325 -0.14560843893422656 -0.14073345109168692 -0.1344389936854343 -0.12680140243623358 -0.11790840501879192 -0.10785793025859365 -0.09675692985892959 -0.08472022692682367 -0.07186940098852561 -0.05833171489404686 -0.04423908511737579 -0.029727093542737816 -0.014934035939544038 -0.0; -0.04492059796027981 -0.07065095439536485 -0.09557145578758167 -0.11939997541821289 -0.14186994169558806 -0.16273387270728362 -0.18176647793115938 -0.19876727430138635 -0.21356268232675013 -0.22600758664212328 -0.2359863632583629 -0.24341339201319906 -0.24823308665062502 -0.2504194861123892 -0.2499754587712232 -0.24693157643310357 -0.2413447171232131 -0.23329645522463674 -0.22289129483793432 -0.21025479770837657 -0.19553165118307045 -0.1788837148593802 -0.16048807728244902 -0.1405351466078245 -0.11922679187124913 -0.0967745446478989 -0.07339786462605602 -0.049322467102568074 -0.02477870572316178 -0.0; -0.06220037531629606 -0.09783345547802876 -0.13235154290982576 -0.1653657884750015 -0.1965083983920291 -0.22543744735199436 -0.2518411228489047 -0.2754413296613309 -0.2959966070960882 -0.31330433562984816 -0.3272022327264119 -0.33756915878619703 -0.34432527253805745 -0.3474315901030258 -0.346889013100562 -0.34273689843942096 -0.33505124596970803 -0.3239425802843336 -0.3095536000945941 -0.2920566632972881 -0.2716511686686468 -0.24856088663061013 -0.22303128227153504 -0.19532686424583182 -0.16572858373656016 -0.13453129868059222 -0.10204131019450899 -0.06857397080267193 -0.03445135780198533 -0.0; -0.07880050463392396 -0.12395129201500019 -0.16769976077878868 -0.20955618450542476 -0.24905674214401238 -0.28576948536646013 -0.31929963336127665 -0.34929410844851994 -0.3754452528775987 -0.3974936947291789 -0.4152303576030567 -0.4284976335152897 -0.43718976015396327 -0.44125246162618204 -0.44068192562615677 -0.4355231994007274 -0.4258680920704409 -0.41185267207724424 -0.3936544462302411 -0.3714893015727173 -0.3456082837185835 -0.3162942760395855 -0.2838586337383658 -0.24863781597961723 -0.21099004836783447 -0.1712920375756696 -0.1299357501841936 -0.08732525906462077 -0.04387365311373985 -0.0; -0.09453931054294616 -0.1487190978491784 -0.20123081596123554 -0.2514909948459919 -0.29894617695630576 -0.3430798935962077 -0.38341889998978623 -0.41953857008711304 -0.45106738048345896 -0.4776904420033748 -0.49915206610490176 -0.5152573800256991 -0.5258730284648329 -0.5309270197686902 -0.5304077905416922 -0.5243625740841839 -0.5128951650793325 -0.49616317573872093 -0.4743748775793123 -0.44778571867721684 -0.4166945992388685 -0.38143997929400836 -0.3423958818886774 -0.2999678439466862 -0.25458885552516275 -0.20671531699541829 -0.1568230331411229 -0.1054032536142764 -0.05295876088860178 -0.0; -0.1092443557637722 -0.17186551538440756 -0.23257735243991082 -0.290710828040331 -0.34563024243045937 -0.3967410635326953 -0.4434969799057054 -0.4854060702974861 -0.5220360098715797 -0.5530182621600436 -0.5780512345173306 -0.5969024020952023 -0.609409430083387 -0.6154803453381643 -0.6150928259725481 -0.6082926906825328 -0.5951916784511634 -0.575964613940223 -0.5508460546623364 -0.5201265133780645 -0.48414834363139964 -0.4433013685260977 -0.3980183233734477 -0.34877017231502794 -0.29606134800943434 -0.24042495248333112 -0.18241794673431524 -0.1226163470173401 -0.061610437261598615 -0.0; -0.12275433026684825 -0.1931361676542032 -0.2613939718307689 -0.32678208830126587 -0.38859076387494956 -0.4461546685266955 -0.4988606381606837 -0.5461545251031258 -0.5875470691240401 -0.6226187290287768 -0.6510234421916031 -0.6724913057242213 -0.6868301973106677 -0.6939263753003531 -0.6937441158393913 -0.6863244592573579 -0.671783148444792 -0.6503078485843587 -0.6221547405355011 -0.587644579757757 -0.5471583093357457 -0.5011323099532774 -0.4500533621060475 -0.39445338700133725 -0.3349040230120407 -0.2720110847404387 -0.20640894216517733 -0.138754848398411 -0.06972323661344877 -0.0; -0.1349208379744406 -0.2122965209577826 -0.2873612060303612 -0.35930209652792744 -0.4273441575601024 -0.4907591792994364 -0.5488740823760155 -0.6010783500703358 -0.646830494996501 -0.6856634923498305 -0.7171891365816065 -0.7411013026254206 -0.757178115689253 -0.765283054425606 -0.7653650304313316 -0.7574575021087522 -0.7416766927105995 -0.718218990827775 -0.6873576167456422 -0.6494386402049243 -0.6048764344754651 -0.5541486486807161 -0.49779077544505146 -0.43639038464857854 -0.3705810868431504 -0.30103628217287276 -0.2284627428873973 -0.1535940701312627 -0.0771840589834026 -0.0; -0.14561005955421447 -0.22913459948959441 -0.3101893812336625 -0.38790422440415984 -0.4614479678440339 -0.5300379369759524 -0.592948691629146 -0.6495199395582633 -0.6991635203313463 -0.7413693851335008 -0.7757105195555061 -0.8018467778717494 -0.8195276179701331 -0.8285937453704048 -0.8289776921524546 -0.8207033717271729 -0.8038846629603755 -0.7787230870724758 -0.7455046479707458 -0.7045959113238324 -0.6564393999499889 -0.601548383227324 -0.5405011365689621 -0.47393474389865564 -0.40253851189271567 -0.32704705990440125 -0.24823314432743135 -0.16690027103237884 -0.08387514473509504 -0.0; -0.15470426948819188 -0.24346350819144622 -0.329622296160263 -0.4122629171608063 -0.4905074496773781 -0.5635275209057068 -0.6305533886330141 -0.6908822386420445 -0.7438856010843903 -0.7890158064415617 -0.8258114196800785 -0.8539016094608556 -0.8730094272592505 -0.8829539885121807 -0.8836515640174675 -0.8751156044283995 -0.8574557335585165 -0.8308757571702822 -0.795670742886837 -0.7522232338410063 -0.7009986637377845 -0.642540044297764 -0.5774619977640705 -0.5064442075284556 -0.4302243592237119 -0.349590643113037 -0.26537388655710187 -0.17843938302069107 -0.08967848173749446 -0.0; -0.1621031858215124 -0.25512371666703554 -0.34544062526665625 -0.43209845299430233 -0.5141819583355557 -0.5908260627964805 -0.6612251733221225 -0.7246417722813079 -0.7804141785216053 -0.827963396712097 -0.8667989868025158 -0.8965239005586522 -0.9168382474165633 -0.9275419669829891 -0.9285364000801603 -0.9198247640149808 -0.9015115505195137 -0.873800876389447 -0.8369938271225634 -0.7914848427680177 -0.7377572027291042 -0.6763776724542383 -0.6079903798810069 -0.5333099932779639 -0.45311427489519673 -0.36823608674123665 -0.27955492601261445 -0.18798806837506427 -0.09448139758640571 -0.0; -0.16772513193719168 -0.2639850560105428 -0.3574649513033959 -0.44718127029496646 -0.5321908743838923 -0.6116010996152267 -0.6845792418557338 -0.7503613560005965 -0.8082602734770314 -0.8576727531431322 -0.8980856924348853 -0.9290813380522378 -0.9503414483551212 -0.9616503727263066 -0.9628970262252827 -0.9540757506989864 -0.9352860659466241 -0.9067313263985689 -0.8687163099334942 -0.8216437758234271 -0.7660100382926455 -0.7023996107612742 -0.6314789835018362 -0.5539896041740379 -0.4707401365456435 -0.38259807769669213 -0.290480818191948 -0.19534623314980348 -0.09818289489364355 -0.0; -0.17150799144525702 -0.26994838220353407 -0.3655583319134056 -0.4573356902543544 -0.5443187807215241 -0.625596533880287 -0.7003180718474857 -0.7677016414272496 -0.8270428010589652 -0.8777217755149587 -0.9192099019823009 -0.9510751016338955 -0.9729863218881927 -0.9847169061208959 -0.9861468594716336 -0.9772639914321832 -0.9581639279642516 -0.9290489978352466 -0.8902260095509346 -0.8421029465861574 -0.7851846194628447 -0.7200673235048076 -0.647432560730361 -0.5680398932581251 -0.48271900374158594 -0.3923610456680835 -0.29790937282151825 -0.200349742787213 -0.1007000940512347 -0.0; -0.17340993983187863 -0.2729468644655802 -0.36962831254590145 -0.46244287334374506 -0.5504196228008855 -0.6326382866634336 -0.7082388716890223 -0.7764306639334978 -0.8365004998451111 -0.887820223609184 -0.92985325280855 -0.9621601839000541 -0.9844033791517097 -0.9963504874284316 -0.9978768624404454 -0.9889668536569505 -0.9697139569147938 -0.9403198236925779 -0.9010921399492995 -0.8524413972188651 -0.7948765901856594 -0.7289998861232156 -0.655500322244305 -0.5751465970784148 -0.48877903136052425 -0.3973007824897617 -0.3016684043129392 -0.20288185073015816 -0.10197402734156831 -0.0; -0.17340993983187863 -0.2729468644655802 -0.36962831254590145 -0.46244287334374506 -0.5504196228008855 -0.6326382866634336 -0.7082388716890223 -0.7764306639334979 -0.8365004998451111 -0.887820223609184 -0.92985325280855 -0.9621601839000541 -0.9844033791517097 -0.9963504874284316 -0.9978768624404454 -0.9889668536569505 -0.9697139569147937 -0.9403198236925779 -0.9010921399492995 -0.8524413972188651 -0.7948765901856594 -0.7289998861232155 -0.655500322244305 -0.5751465970784148 -0.48877903136052425 -0.3973007824897617 -0.3016684043129392 -0.20288185073015816 -0.10197402734156831 0.0; -0.17150799144525702 -0.26994838220353407 -0.36555833191340564 -0.4573356902543543 -0.5443187807215241 -0.625596533880287 -0.700318071847486 -0.7677016414272495 -0.8270428010589652 -0.8777217755149587 -0.9192099019823011 -0.9510751016338956 -0.9729863218881925 -0.984716906120896 -0.9861468594716336 -0.9772639914321832 -0.9581639279642516 -0.9290489978352466 -0.8902260095509346 -0.8421029465861574 -0.7851846194628447 -0.7200673235048076 -0.647432560730361 -0.5680398932581252 -0.48271900374158594 -0.3923610456680835 -0.2979093728215182 -0.200349742787213 -0.1007000940512347 0.0; -0.16772513193719168 -0.2639850560105428 -0.35746495130339584 -0.44718127029496635 -0.5321908743838923 -0.6116010996152267 -0.6845792418557338 -0.7503613560005965 -0.8082602734770314 -0.8576727531431322 -0.8980856924348853 -0.9290813380522378 -0.9503414483551212 -0.9616503727263064 -0.9628970262252827 -0.9540757506989864 -0.9352860659466244 -0.9067313263985689 -0.8687163099334946 -0.8216437758234268 -0.7660100382926458 -0.7023996107612739 -0.6314789835018362 -0.5539896041740379 -0.4707401365456437 -0.382598077696692 -0.2904808181919479 -0.19534623314980348 -0.09818289489364342 0.0; -0.1621031858215124 -0.2551237166670354 -0.34544062526665636 -0.43209845299430233 -0.5141819583355557 -0.5908260627964805 -0.6612251733221225 -0.7246417722813082 -0.780414178521605 -0.8279633967120973 -0.8667989868025158 -0.8965239005586522 -0.9168382474165636 -0.9275419669829891 -0.9285364000801606 -0.9198247640149813 -0.9015115505195139 -0.873800876389447 -0.8369938271225634 -0.7914848427680177 -0.7377572027291038 -0.6763776724542383 -0.6079903798810069 -0.5333099932779641 -0.45311427489519673 -0.36823608674123665 -0.27955492601261445 -0.18798806837506427 -0.09448139758640571 0.0; -0.15470426948819188 -0.24346350819144622 -0.329622296160263 -0.4122629171608063 -0.4905074496773781 -0.5635275209057068 -0.6305533886330141 -0.6908822386420445 -0.7438856010843903 -0.7890158064415617 -0.8258114196800781 -0.8539016094608561 -0.8730094272592505 -0.8829539885121807 -0.8836515640174675 -0.8751156044283995 -0.857455733558517 -0.8308757571702822 -0.795670742886837 -0.7522232338410063 -0.7009986637377845 -0.642540044297764 -0.5774619977640701 -0.5064442075284556 -0.4302243592237119 -0.349590643113037 -0.26537388655710187 -0.17843938302069107 -0.08967848173749446 0.0; -0.14561005955421447 -0.22913459948959441 -0.3101893812336625 -0.38790422440415984 -0.4614479678440339 -0.5300379369759524 -0.592948691629146 -0.6495199395582628 -0.6991635203313468 -0.7413693851335008 -0.7757105195555061 -0.8018467778717494 -0.8195276179701331 -0.8285937453704048 -0.8289776921524546 -0.8207033717271734 -0.8038846629603755 -0.7787230870724758 -0.7455046479707458 -0.7045959113238324 -0.6564393999499885 -0.601548383227324 -0.5405011365689621 -0.47393474389865525 -0.402538511892716 -0.32704705990440125 -0.24823314432743102 -0.16690027103237884 -0.08387514473509504 0.0; -0.1349208379744406 -0.2122965209577826 -0.2873612060303612 -0.35930209652792744 -0.4273441575601024 -0.4907591792994364 -0.5488740823760155 -0.6010783500703362 -0.646830494996501 -0.6856634923498305 -0.7171891365816065 -0.7411013026254206 -0.7571781156892524 -0.765283054425606 -0.7653650304313316 -0.7574575021087528 -0.7416766927105995 -0.718218990827775 -0.6873576167456422 -0.6494386402049243 -0.6048764344754651 -0.5541486486807161 -0.49779077544505146 -0.43639038464857854 -0.3705810868431504 -0.30103628217287276 -0.22846274288739696 -0.1535940701312627 -0.0771840589834026 0.0; -0.12275433026684825 -0.1931361676542032 -0.2613939718307689 -0.32678208830126587 -0.38859076387494956 -0.4461546685266955 -0.4988606381606837 -0.5461545251031258 -0.5875470691240395 -0.6226187290287768 -0.6510234421916031 -0.6724913057242213 -0.6868301973106677 -0.6939263753003537 -0.6937441158393913 -0.6863244592573572 -0.6717831484447928 -0.6503078485843595 -0.6221547405355011 -0.587644579757757 -0.5471583093357463 -0.5011323099532768 -0.4500533621060475 -0.39445338700133675 -0.3349040230120412 -0.2720110847404387 -0.20640894216517733 -0.138754848398411 -0.06972323661344877 0.0; -0.10924435576377206 -0.17186551538440775 -0.23257735243991082 -0.290710828040331 -0.34563024243045937 -0.3967410635326948 -0.4434969799057054 -0.4854060702974861 -0.5220360098715797 -0.5530182621600429 -0.5780512345173306 -0.5969024020952023 -0.609409430083387 -0.6154803453381635 -0.6150928259725481 -0.6082926906825328 -0.5951916784511634 -0.5759646139402222 -0.5508460546623364 -0.5201265133780653 -0.48414834363139964 -0.4433013685260983 -0.3980183233734477 -0.34877017231502794 -0.29606134800943384 -0.24042495248333112 -0.18241794673431524 -0.1226163470173401 -0.061610437261598615 0.0; -0.09453931054294631 -0.14871909784917817 -0.20123081596123588 -0.2514909948459916 -0.29894617695630576 -0.3430798935962077 -0.38341889998978623 -0.41953857008711304 -0.45106738048345896 -0.4776904420033748 -0.49915206610490176 -0.5152573800256982 -0.5258730284648337 -0.5309270197686902 -0.530407790541693 -0.5243625740841839 -0.5128951650793325 -0.49616317573872093 -0.4743748775793123 -0.44778571867721684 -0.4166945992388692 -0.38143997929400836 -0.3423958818886774 -0.2999678439466862 -0.25458885552516275 -0.20671531699541829 -0.1568230331411229 -0.1054032536142764 -0.05295876088860178 0.0; -0.07880050463392396 -0.12395129201500019 -0.16769976077878868 -0.20955618450542476 -0.24905674214401238 -0.28576948536646013 -0.31929963336127665 -0.34929410844851994 -0.3754452528775987 -0.3974936947291789 -0.4152303576030567 -0.4284976335152897 -0.43718976015396327 -0.44125246162618204 -0.44068192562615677 -0.4355231994007274 -0.4258680920704409 -0.41185267207724424 -0.3936544462302411 -0.3714893015727173 -0.3456082837185835 -0.3162942760395855 -0.2838586337383658 -0.24863781597961723 -0.21099004836783447 -0.1712920375756696 -0.1299357501841936 -0.08732525906462077 -0.04387365311373985 0.0; -0.06220037531629606 -0.09783345547802876 -0.13235154290982576 -0.1653657884750015 -0.1965083983920291 -0.22543744735199436 -0.2518411228489047 -0.2754413296613309 -0.2959966070960882 -0.31330433562984816 -0.3272022327264119 -0.33756915878619703 -0.34432527253805745 -0.3474315901030258 -0.346889013100562 -0.34273689843942096 -0.33505124596970803 -0.3239425802843336 -0.3095536000945941 -0.2920566632972881 -0.2716511686686468 -0.24856088663061013 -0.22303128227153504 -0.19532686424583182 -0.16572858373656016 -0.13453129868059222 -0.10204131019450899 -0.06857397080267193 -0.03445135780198533 0.0; -0.04492059796027981 -0.07065095439536485 -0.09557145578758167 -0.11939997541821289 -0.14186994169558806 -0.16273387270728362 -0.18176647793115938 -0.19876727430138635 -0.21356268232675013 -0.22600758664212328 -0.2359863632583629 -0.24341339201319906 -0.24823308665062502 -0.2504194861123892 -0.2499754587712232 -0.24693157643310357 -0.2413447171232131 -0.23329645522463674 -0.22289129483793432 -0.21025479770837657 -0.19553165118307045 -0.1788837148593802 -0.16048807728244902 -0.1405351466078245 -0.11922679187124913 -0.0967745446478989 -0.07339786462605602 -0.049322467102568074 -0.02477870572316178 0.0; -0.027150115081063988 -0.04270011428358324 -0.057758705288458785 -0.07215482635514493 -0.08572696402193652 -0.09832531382770597 -0.10981367006458886 -0.1200710120433018 -0.12899276613783248 -0.13649173473699158 -0.1424986945351325 -0.14696267680186426 -0.14985095096122678 -0.15114873970251896 -0.1508586987967492 -0.14900019779435325 -0.14560843893422656 -0.14073345109168692 -0.1344389936854343 -0.12680140243623358 -0.11790840501879192 -0.10785793025859365 -0.09675692985892959 -0.08472022692682367 -0.07186940098852561 -0.05833171489404686 -0.04423908511737579 -0.029727093542737816 -0.014934035939544038 0.0; -0.009083103279740998 -0.01428511942685134 -0.01932240443160082 -0.024137636545694972 -0.02867671357503927 -0.03288947992301452 -0.03673036136657844 -0.04015889658480063 -0.04314015850682612 -0.04564506261266228 -0.047650563187460165 -0.04913974201221967 -0.050101796927525435 -0.05053194003690302 -0.05043121697644118 -0.04980625966628017 -0.04866898531566895 -0.04703625424384296 -0.044929498392808666 -0.04237433134421172 -0.0394001493133432 -0.036039731077160034 -0.03232884318935258 -0.028305855220852535 -0.024011368202566014 -0.019487857987643936 -0.014779333930466381 -0.009931012123682185 -0.004989001459909738 0.0; 0.009083103279740998 0.01428511942685134 0.01932240443160082 0.024137636545694972 0.02867671357503927 0.03288947992301452 0.03673036136657844 0.04015889658480063 0.043140158506826946 0.045645062612663156 0.047650563187460165 0.04913974201222062 0.050101796927525435 0.05053194003690302 0.05043121697644019 0.04980625966628017 0.04866898531566895 0.04703625424384201 0.044929498392807736 0.04237433134421261 0.0394001493133432 0.03603973107716084 0.03232884318935258 0.02830585522085324 0.024011368202566014 0.01948785798764454 0.014779333930465825 0.009931012123682711 0.004989001459909738 0.0; 0.027150115081064158 0.04270011428358324 0.057758705288458424 0.07215482635514493 0.08572696402193652 0.09832531382770597 0.10981367006458817 0.1200710120433018 0.12899276613783248 0.13649173473699244 0.1424986945351325 0.14696267680186426 0.14985095096122678 0.15114873970251896 0.15085869879674824 0.14900019779435325 0.1456084389342256 0.14073345109168692 0.1344389936854343 0.12680140243623358 0.11790840501879192 0.10785793025859365 0.09675692985892884 0.08472022692682367 0.07186940098852496 0.058331714894047454 0.04423908511737579 0.029727093542738336 0.014934035939544038 0.0; 0.04492059796027981 0.07065095439536485 0.09557145578758201 0.11939997541821289 0.1418699416955886 0.16273387270728423 0.18176647793115938 0.19876727430138635 0.21356268232675013 0.22600758664212328 0.2359863632583629 0.24341339201319906 0.2482330866506241 0.2504194861123901 0.24997545877122224 0.24693157643310357 0.2413447171232131 0.23329645522463674 0.22289129483793432 0.2102547977083757 0.19553165118307045 0.1788837148593802 0.1604880772824483 0.14053514660782382 0.11922679187124975 0.0967745446478989 0.07339786462605602 0.04932246710256756 0.02477870572316178 0.0; 0.06220037531629606 0.09783345547802876 0.13235154290982612 0.1653657884750015 0.1965083983920291 0.22543744735199436 0.2518411228489047 0.2754413296613316 0.2959966070960882 0.31330433562984733 0.3272022327264119 0.33756915878619703 0.34432527253805745 0.3474315901030258 0.346889013100562 0.34273689843942096 0.33505124596970803 0.3239425802843336 0.309553600094595 0.2920566632972881 0.2716511686686468 0.24856088663060938 0.22303128227153504 0.19532686424583182 0.16572858373656016 0.13453129868059222 0.10204131019450952 0.06857397080267193 0.03445135780198533 0.0; 0.0788005046339241 0.12395129201500019 0.16769976077878868 0.20955618450542476 0.24905674214401288 0.2857694853664596 0.3192996333612773 0.34929410844851994 0.37544525287759944 0.3974936947291789 0.4152303576030567 0.4284976335152897 0.43718976015396327 0.4412524616261829 0.44068192562615766 0.4355231994007274 0.4258680920704409 0.41185267207724424 0.3936544462302411 0.3714893015727173 0.3456082837185835 0.31629427603958477 0.28385863373836506 0.24863781597961723 0.21099004836783447 0.1712920375756696 0.1299357501841941 0.08732525906462124 0.04387365311373985 0.0; 0.09453931054294631 0.14871909784917817 0.20123081596123588 0.2514909948459916 0.29894617695630576 0.3430798935962077 0.38341889998978623 0.41953857008711304 0.45106738048345896 0.4776904420033748 0.49915206610490176 0.5152573800256982 0.5258730284648337 0.530927019768691 0.530407790541693 0.5243625740841839 0.5128951650793325 0.49616317573872093 0.4743748775793123 0.44778571867721684 0.4166945992388692 0.38143997929400836 0.3423958818886781 0.29996784394668674 0.2545888555251622 0.20671531699541829 0.1568230331411229 0.1054032536142764 0.05295876088860178 0.0; 0.10924435576377206 0.17186551538440775 0.2325773524399111 0.290710828040331 0.34563024243045937 0.3967410635326948 0.4434969799057054 0.4854060702974861 0.5220360098715797 0.5530182621600429 0.5780512345173306 0.5969024020952023 0.609409430083387 0.6154803453381635 0.6150928259725481 0.608292690682532 0.5951916784511642 0.5759646139402222 0.5508460546623364 0.5201265133780653 0.48414834363139964 0.4433013685260983 0.3980183233734477 0.34877017231502794 0.29606134800943384 0.24042495248333065 0.18241794673431524 0.1226163470173401 0.061610437261598615 0.0; 0.12275433026684825 0.1931361676542032 0.2613939718307689 0.32678208830126587 0.38859076387494956 0.4461546685266955 0.4988606381606837 0.5461545251031251 0.5875470691240395 0.6226187290287768 0.6510234421916031 0.6724913057242213 0.6868301973106671 0.6939263753003537 0.6937441158393907 0.6863244592573572 0.6717831484447928 0.6503078485843595 0.6221547405355011 0.587644579757757 0.5471583093357463 0.5011323099532768 0.4500533621060475 0.39445338700133675 0.3349040230120412 0.2720110847404387 0.20640894216517772 0.138754848398411 0.06972323661344877 0.0; 0.1349208379744406 0.2122965209577826 0.2873612060303612 0.35930209652792744 0.4273441575601024 0.4907591792994364 0.5488740823760155 0.6010783500703362 0.646830494996501 0.6856634923498305 0.7171891365816065 0.7411013026254206 0.7571781156892524 0.765283054425606 0.7653650304313316 0.7574575021087528 0.7416766927105989 0.718218990827775 0.6873576167456422 0.6494386402049243 0.6048764344754651 0.5541486486807161 0.49779077544505146 0.43639038464857854 0.3705810868431504 0.30103628217287276 0.22846274288739696 0.1535940701312627 0.0771840589834026 0.0; 0.14561005955421447 0.22913459948959441 0.3101893812336625 0.38790422440415984 0.4614479678440336 0.5300379369759524 0.592948691629146 0.6495199395582628 0.6991635203313468 0.7413693851335008 0.7757105195555061 0.8018467778717494 0.8195276179701331 0.8285937453704048 0.8289776921524546 0.8207033717271734 0.8038846629603761 0.7787230870724758 0.7455046479707458 0.7045959113238324 0.6564393999499885 0.601548383227324 0.5405011365689621 0.47393474389865525 0.402538511892716 0.32704705990440125 0.24823314432743102 0.16690027103237884 0.08387514473509532 0.0; 0.15470426948819188 0.24346350819144608 0.329622296160263 0.4122629171608063 0.4905074496773781 0.5635275209057068 0.6305533886330141 0.6908822386420445 0.7438856010843903 0.7890158064415617 0.8258114196800781 0.8539016094608561 0.8730094272592499 0.8829539885121807 0.8836515640174675 0.8751156044283995 0.857455733558517 0.8308757571702826 0.7956707428868375 0.7522232338410063 0.7009986637377845 0.642540044297764 0.5774619977640701 0.5064442075284556 0.4302243592237119 0.349590643113037 0.26537388655710187 0.17843938302069107 0.08967848173749471 0.0; 0.1621031858215124 0.2551237166670354 0.34544062526665636 0.43209845299430233 0.5141819583355557 0.5908260627964805 0.6612251733221225 0.7246417722813082 0.780414178521605 0.8279633967120973 0.8667989868025158 0.8965239005586522 0.9168382474165636 0.9275419669829891 0.9285364000801606 0.9198247640149813 0.9015115505195139 0.873800876389447 0.8369938271225634 0.7914848427680177 0.7377572027291038 0.6763776724542383 0.6079903798810069 0.5333099932779641 0.45311427489519673 0.36823608674123665 0.27955492601261445 0.18798806837506446 0.09448139758640571 0.0; 0.16772513193719168 0.2639850560105428 0.35746495130339584 0.44718127029496635 0.5321908743838923 0.6116010996152267 0.6845792418557338 0.7503613560005965 0.8082602734770314 0.8576727531431322 0.8980856924348853 0.9290813380522378 0.9503414483551212 0.9616503727263064 0.9628970262252827 0.9540757506989864 0.9352860659466244 0.9067313263985689 0.8687163099334946 0.8216437758234268 0.7660100382926458 0.7023996107612739 0.6314789835018362 0.5539896041740379 0.4707401365456437 0.382598077696692 0.2904808181919479 0.19534623314980362 0.09818289489364342 0.0; 0.17150799144525702 0.26994838220353407 0.36555833191340564 0.4573356902543543 0.5443187807215241 0.625596533880287 0.700318071847486 0.7677016414272495 0.8270428010589652 0.8777217755149587 0.9192099019823011 0.9510751016338956 0.9729863218881925 0.984716906120896 0.9861468594716336 0.9772639914321832 0.9581639279642516 0.9290489978352466 0.8902260095509346 0.8421029465861574 0.7851846194628447 0.7200673235048076 0.647432560730361 0.5680398932581252 0.48271900374158594 0.3923610456680835 0.2979093728215182 0.200349742787213 0.1007000940512347 0.0; 0.17340993983187863 0.2729468644655802 0.36962831254590145 0.46244287334374506 0.5504196228008855 0.6326382866634336 0.7082388716890223 0.7764306639334979 0.8365004998451111 0.887820223609184 0.92985325280855 0.9621601839000541 0.9844033791517097 0.9963504874284316 0.9978768624404454 0.9889668536569505 0.9697139569147937 0.9403198236925779 0.9010921399492995 0.8524413972188651 0.7948765901856594 0.7289998861232155 0.655500322244305 0.5751465970784148 0.48877903136052425 0.3973007824897617 0.3016684043129392 0.20288185073015816 0.10197402734156831 0.0; 0.17340993983187863 0.2729468644655802 0.36962831254590145 0.46244287334374506 0.5504196228008855 0.6326382866634336 0.7082388716890223 0.7764306639334979 0.8365004998451111 0.887820223609184 0.92985325280855 0.9621601839000541 0.9844033791517097 0.9963504874284316 0.9978768624404454 0.9889668536569505 0.9697139569147937 0.9403198236925779 0.9010921399492995 0.8524413972188651 0.7948765901856594 0.7289998861232155 0.655500322244305 0.5751465970784148 0.48877903136052425 0.3973007824897617 0.3016684043129392 0.20288185073015816 0.10197402734156831 -0.0; 0.17150799144525702 0.26994838220353407 0.36555833191340564 0.4573356902543543 0.5443187807215241 0.625596533880287 0.700318071847486 0.7677016414272495 0.8270428010589652 0.8777217755149587 0.9192099019823011 0.9510751016338956 0.9729863218881925 0.984716906120896 0.9861468594716336 0.9772639914321832 0.9581639279642516 0.9290489978352466 0.8902260095509346 0.8421029465861574 0.7851846194628447 0.7200673235048076 0.647432560730361 0.5680398932581252 0.48271900374158594 0.3923610456680835 0.2979093728215182 0.200349742787213 0.1007000940512347 -0.0; 0.16772513193719168 0.2639850560105428 0.35746495130339584 0.44718127029496635 0.5321908743838923 0.6116010996152267 0.6845792418557338 0.7503613560005965 0.8082602734770314 0.8576727531431322 0.8980856924348853 0.9290813380522378 0.9503414483551212 0.9616503727263064 0.9628970262252827 0.9540757506989864 0.9352860659466244 0.9067313263985689 0.8687163099334946 0.8216437758234268 0.7660100382926458 0.7023996107612739 0.6314789835018362 0.5539896041740379 0.4707401365456437 0.382598077696692 0.2904808181919479 0.19534623314980348 0.09818289489364342 -0.0; 0.1621031858215124 0.2551237166670354 0.34544062526665636 0.43209845299430233 0.5141819583355557 0.5908260627964805 0.6612251733221225 0.7246417722813082 0.780414178521605 0.8279633967120973 0.8667989868025158 0.8965239005586522 0.9168382474165636 0.9275419669829891 0.9285364000801606 0.9198247640149813 0.9015115505195139 0.873800876389447 0.8369938271225634 0.7914848427680177 0.7377572027291038 0.6763776724542383 0.6079903798810069 0.5333099932779641 0.45311427489519673 0.36823608674123665 0.27955492601261445 0.18798806837506427 0.09448139758640571 -0.0; 0.15470426948819188 0.24346350819144622 0.329622296160263 0.4122629171608063 0.4905074496773781 0.5635275209057068 0.6305533886330141 0.6908822386420445 0.7438856010843903 0.7890158064415617 0.8258114196800781 0.8539016094608561 0.8730094272592505 0.8829539885121807 0.8836515640174675 0.8751156044283995 0.857455733558517 0.8308757571702822 0.795670742886837 0.7522232338410063 0.7009986637377845 0.642540044297764 0.5774619977640701 0.5064442075284556 0.4302243592237119 0.349590643113037 0.26537388655710187 0.17843938302069107 0.08967848173749446 -0.0; 0.14561005955421447 0.22913459948959441 0.3101893812336625 0.38790422440415984 0.4614479678440339 0.5300379369759524 0.592948691629146 0.6495199395582628 0.6991635203313468 0.7413693851335008 0.7757105195555061 0.8018467778717494 0.8195276179701331 0.8285937453704048 0.8289776921524546 0.8207033717271734 0.8038846629603755 0.7787230870724758 0.7455046479707458 0.7045959113238324 0.6564393999499885 0.601548383227324 0.5405011365689621 0.47393474389865525 0.402538511892716 0.32704705990440125 0.24823314432743102 0.16690027103237884 0.08387514473509504 -0.0; 0.1349208379744406 0.2122965209577826 0.2873612060303612 0.35930209652792744 0.4273441575601024 0.4907591792994364 0.5488740823760155 0.6010783500703362 0.646830494996501 0.6856634923498305 0.7171891365816065 0.7411013026254206 0.7571781156892524 0.765283054425606 0.7653650304313316 0.7574575021087528 0.7416766927105995 0.718218990827775 0.6873576167456422 0.6494386402049243 0.6048764344754651 0.5541486486807161 0.49779077544505146 0.43639038464857854 0.3705810868431504 0.30103628217287276 0.22846274288739696 0.1535940701312627 0.0771840589834026 -0.0; 0.12275433026684825 0.1931361676542032 0.2613939718307689 0.32678208830126587 0.38859076387494956 0.4461546685266955 0.4988606381606837 0.5461545251031258 0.5875470691240395 0.6226187290287768 0.6510234421916031 0.6724913057242213 0.6868301973106677 0.6939263753003537 0.6937441158393913 0.6863244592573572 0.6717831484447928 0.6503078485843595 0.6221547405355011 0.587644579757757 0.5471583093357463 0.5011323099532768 0.4500533621060475 0.39445338700133675 0.3349040230120412 0.2720110847404387 0.20640894216517733 0.138754848398411 0.06972323661344877 -0.0; 0.10924435576377206 0.17186551538440775 0.23257735243991082 0.290710828040331 0.34563024243045937 0.3967410635326948 0.4434969799057054 0.4854060702974861 0.5220360098715797 0.5530182621600429 0.5780512345173306 0.5969024020952023 0.609409430083387 0.6154803453381635 0.6150928259725481 0.6082926906825328 0.5951916784511634 0.5759646139402222 0.5508460546623364 0.5201265133780653 0.48414834363139964 0.4433013685260983 0.3980183233734477 0.34877017231502794 0.29606134800943384 0.24042495248333112 0.18241794673431524 0.1226163470173401 0.061610437261598615 -0.0; 0.09453931054294631 0.14871909784917817 0.20123081596123588 0.2514909948459916 0.29894617695630576 0.3430798935962077 0.38341889998978623 0.41953857008711304 0.45106738048345896 0.4776904420033748 0.49915206610490176 0.5152573800256982 0.5258730284648337 0.5309270197686902 0.530407790541693 0.5243625740841839 0.5128951650793325 0.49616317573872093 0.4743748775793123 0.44778571867721684 0.4166945992388692 0.38143997929400836 0.3423958818886774 0.2999678439466862 0.25458885552516275 0.20671531699541829 0.1568230331411229 0.1054032536142764 0.05295876088860178 -0.0; 0.07880050463392396 0.12395129201500019 0.16769976077878868 0.20955618450542476 0.24905674214401238 0.28576948536646013 0.31929963336127665 0.34929410844851994 0.3754452528775987 0.3974936947291789 0.4152303576030567 0.4284976335152897 0.43718976015396327 0.44125246162618204 0.44068192562615677 0.4355231994007274 0.4258680920704409 0.41185267207724424 0.3936544462302411 0.3714893015727173 0.3456082837185835 0.3162942760395855 0.2838586337383658 0.24863781597961723 0.21099004836783447 0.1712920375756696 0.1299357501841936 0.08732525906462077 0.04387365311373985 -0.0; 0.06220037531629606 0.09783345547802876 0.13235154290982576 0.1653657884750015 0.1965083983920291 0.22543744735199436 0.2518411228489047 0.2754413296613309 0.2959966070960882 0.31330433562984816 0.3272022327264119 0.33756915878619703 0.34432527253805745 0.3474315901030258 0.346889013100562 0.34273689843942096 0.33505124596970803 0.3239425802843336 0.3095536000945941 0.2920566632972881 0.2716511686686468 0.24856088663061013 0.22303128227153504 0.19532686424583182 0.16572858373656016 0.13453129868059222 0.10204131019450899 0.06857397080267193 0.03445135780198533 -0.0; 0.04492059796027981 0.07065095439536485 0.09557145578758167 0.11939997541821289 0.14186994169558806 0.16273387270728362 0.18176647793115938 0.19876727430138635 0.21356268232675013 0.22600758664212328 0.2359863632583629 0.24341339201319906 0.24823308665062502 0.2504194861123892 0.2499754587712232 0.24693157643310357 0.2413447171232131 0.23329645522463674 0.22289129483793432 0.21025479770837657 0.19553165118307045 0.1788837148593802 0.16048807728244902 0.1405351466078245 0.11922679187124913 0.0967745446478989 0.07339786462605602 0.049322467102568074 0.02477870572316178 -0.0; 0.027150115081063988 0.04270011428358324 0.057758705288458785 0.07215482635514493 0.08572696402193652 0.09832531382770597 0.10981367006458886 0.1200710120433018 0.12899276613783248 0.13649173473699158 0.1424986945351325 0.14696267680186426 0.14985095096122678 0.15114873970251896 0.1508586987967492 0.14900019779435325 0.14560843893422656 0.14073345109168692 0.1344389936854343 0.12680140243623358 0.11790840501879192 0.10785793025859365 0.09675692985892959 0.08472022692682367 0.07186940098852561 0.05833171489404686 0.04423908511737579 0.029727093542737816 0.014934035939544038 -0.0; 0.009083103279740998 0.01428511942685134 0.01932240443160082 0.024137636545694972 0.02867671357503927 0.03288947992301452 0.03673036136657844 0.04015889658480063 0.04314015850682612 0.04564506261266228 0.047650563187460165 0.04913974201221967 0.050101796927525435 0.05053194003690302 0.05043121697644118 0.04980625966628017 0.04866898531566895 0.04703625424384296 0.044929498392808666 0.04237433134421172 0.0394001493133432 0.036039731077160034 0.03232884318935258 0.028305855220852535 0.024011368202566014 0.019487857987643936 0.014779333930466381 0.009931012123682185 0.004989001459909738 -0.0], [-0.9848160113302673 -0.9619743014525436 -0.9291568482710499 -0.8867758989196258 -0.8353599097526787 -0.7755440733188218 -0.7080592103026847 -0.6337193686089488 -0.5534084935799899 -0.46806653798713777 -0.37867536899373416 -0.2862448037603199 -0.1917990684332063 -0.09636393001660877 -0.0009547002953969572 0.09343474134400287 0.18584181085911342 0.27534392128940677 0.36106601970974983 0.4421869929918105 0.5179450061720757 0.587641860199588 0.650646471697212 0.706397586530944 0.7544058420608156 0.7942552906845757 0.8256044904734249 0.848187258126772 0.861813165888554 0.8663678481562018; -0.9848158314575598 -0.961973173331576 -0.9291529325825325 -0.8867658965128461 -0.8353387595095769 -0.7755047611868381 -0.7079927018461037 -0.6336146701196017 -0.5532528394511432 -0.46784569517129065 -0.37837404334769753 -0.28584712824264114 -0.19128914965929264 -0.09572642767851314 -0.0001754133907157318 0.0943683067730085 0.18693991588448958 0.2766141307673509 0.36251281862200635 0.44381149575699924 0.5197447681802003 0.5896107967911927 0.6527748859484896 0.7086723036354197 0.7568104448960711 0.7967704483633639 0.8282083693186187 0.8508560025738595 0.8645214352888838 0.8690893943029842; -0.9848154795611216 -0.9619709662003686 -0.9291452710880393 -0.8867463237412065 -0.8352973676728779 -0.7754278152177506 -0.7078625040049189 -0.6334096757895837 -0.5529480200550048 -0.4674131307362162 -0.3777837154757548 -0.2850678747200403 -0.19028973505865565 -0.09447668024785139 0.0013526227520249971 0.09619925382004384 0.18909402504101153 0.2791063662943643 0.3653520973813252 0.4470001089159294 0.5232780038216095 0.5934767742413968 0.6569546049956185 0.7131399047034152 0.7615336698286713 0.8017112858560452 0.8333238642567496 0.8560992045923828 0.8698424587344786 0.8744365594106369; -0.9848149709979973 -0.9619677761673958 -0.9291341963434889 -0.8867180266839153 -0.8352375145196433 -0.7753165254450037 -0.7076741466041119 -0.6331130277730428 -0.5525067823263891 -0.4667867772114886 -0.37692863433818624 -0.28393874679874603 -0.18884108412285416 -0.0926645237897102 0.0035690959238661338 0.09885605139690522 0.19222083195185063 0.2827251985030024 0.36947617950215744 0.4516330156898841 0.5284130940714581 0.5990969343581661 0.6630323077630949 0.7196375787092393 0.7684043650990955 0.8088996128534982 0.840767176081578 0.8637289861568729 0.8775858818095572 0.8822181587394404; -0.9848143279660135 -0.9619637421995175 -0.9291201894380146 -0.8866822300856577 -0.8351617790737946 -0.7751756622978784 -0.7074356558453663 -0.632737283763299 -0.5519476712070157 -0.46599275803647605 -0.3758441737963707 -0.282506059717505 -0.18700209862814693 -0.0903629815442419 0.0063854975209461685 0.10223356704640398 0.1961977130534644 0.2873299524999975 0.37472611052090216 0.45753309971085826 0.5349552274625969 0.6062595798147725 0.6707805471405703 0.727923568396251 0.777168176828428 0.8180704314400848 0.8502648156666165 0.8734656781977171 0.8874682813026679 0.8921495099761978; -0.9848135785386068 -0.9619590401266433 -0.9291038594732265 -0.88664048588961 -0.8350734327169688 -0.7750112841183745 -0.7071572386874185 -0.6322984374807022 -0.5512943445344726 -0.4650644572721009 -0.37457562277248985 -0.2808292245447886 -0.184848484600304 -0.08766609891749323 0.009687607260863826 0.10619585254674166 0.20086578504856265 0.29273799997980304 0.38089514204884717 0.4644695756852625 0.542650132411704 0.6146879663786795 0.6799015659571119 0.7376809812860836 0.7874913349524639 0.828875685840146 0.8614573150445919 0.8849414980915711 0.8991168200577557 0.9038560801145485; -0.9848127554430918 -0.9619538750389759 -0.9290859174719834 -0.886594607572179 -0.8349763028636328 -0.7748304892407585 -0.706850873864555 -0.6318152930013817 -0.5505746720675981 -0.4640412854011565 -0.3731765644133479 -0.27897869540287 -0.18247023345184546 -0.08468593777339857 0.013338991867098008 0.11058012691066157 0.2060343496506209 0.29872963105801387 0.38773398651486446 0.47216357640356776 0.5511899426715318 0.6240463930206173 0.6900335609000158 0.7485241818581895 0.7989671350650583 0.8408908031298259 0.873905804009893 0.8977071462161592 0.9120758531139916 0.9168800943805473; -0.9848118946348599 -0.9619484723949864 -0.9290671457658026 -0.8865465927778677 -0.8348746115192313 -0.7746411205910072 -0.7065298211069128 -0.6313087078570441 -0.5498196356207782 -0.4629671574778273 -0.3717068553565327 -0.2770333793634632 -0.17996840236065567 -0.0815486807459428 0.017185607430628805 0.11520209879984014 0.21148693202168173 0.3050547881702212 0.3949582112219621 0.480296159410071 0.5602217597804916 0.6339492571494761 0.7007601644106047 0.7600086335430027 0.8111260756602306 0.853625064078816 0.8871025568603649 0.9112424748689442 0.9258176684357328 0.9306913006394556; -0.9848110337290414 -0.9619430682164011 -0.9290483641188529 -0.8864985373082951 -0.8347727947685265 -0.7744514331532488 -0.7062080643534274 -0.6308007267715657 -0.5490620579759036 -0.4618887155367665 -0.37023023806644023 -0.2750775379983507 -0.17745121189701585 -0.0783898437317994 0.0210615376311803 0.11986270257404513 0.21698904147256942 0.3114418571889576 0.40225804484405964 0.4885190942010046 0.5693593685316151 0.6439736305694228 0.7116238006683839 0.7716449443110712 0.8234504955014178 0.8665367293125876 0.9004865010244792 0.9249722710538628 0.9397584345054217 0.944702971967723; -0.9848102103576414 -0.9619378987902921 -0.9290303940141449 -0.8864525439981239 -0.8346753103796548 -0.774269737030516 -0.7058997092611757 -0.6303136358111348 -0.5483352012334921 -0.4608533473580082 -0.36881164909284114 -0.2731972519747779 -0.17502953684989278 -0.07534867126030427 0.02479580195193733 0.12435620002915478 0.22229763458600643 0.31760853474578793 0.4093106647583686 0.4964685574642738 0.5781983001912855 0.6536756239125818 0.7221432593816275 0.7829175352100223 0.8353942022908056 0.8790534765077419 0.9134642973171264 0.938287803629943 0.9532800306171456 0.9582938318278978; -0.9848094605237538 -0.9619331903252856 -0.9290140226425222 -0.8864106303749615 -0.8345864416592711 -0.7741040309765489 -0.7056183596745902 -0.6298689748230367 -0.5476712892529787 -0.4599070764097725 -0.36751432113310617 -0.2714765716611434 -0.1728119391442847 -0.07256188896347948 0.028220036516772674 0.1284794310938075 0.22717204994029036 0.3232745333132753 0.41579472640667436 0.5037815047333489 0.5863340262652043 0.6626103431366512 0.7318353167151405 0.7933077900121284 0.8464069805660868 0.8905980649619412 0.9254369330116032 0.9505740953244197 0.9657577326184118 0.9708358787879544; -0.9848088170249774 -0.9619291490168412 -0.9289999681864456 -0.8863746392105347 -0.83451010634215 -0.7739616429219782 -0.705376501352056 -0.6294865532379248 -0.5471000219238704 -0.45909241998367334 -0.3663968122526033 -0.26999353063746995 -0.1708994702371631 -0.07015709733229003 0.031176701293217556 0.13204180125393097 0.2313859339449468 0.3281755747778466 0.42140651789414 0.5101140370766438 0.593382541245719 0.6703546419043277 0.7402395589515084 0.8023208002196075 0.8559630587466704 0.9006182800530089 0.9358308594738352 0.9612419368730264 0.9765927628307849 0.981727116699817; -0.9848083080154617 -0.9619259519641189 -0.9289888479694525 -0.8863461560902377 -0.834449679532858 -0.773848894877906 -0.7051849235300108 -0.629183519374974 -0.5466471589631725 -0.45844633041294935 -0.36551012552131423 -0.26881624620219585 -0.1693805413073931 -0.06824619312533124 0.03352732556140982 0.13487540297233894 0.23473942896122485 0.33207780818567695 0.42587673324131814 0.515160610266232 0.5990020354943508 0.6765312279474296 0.7469448307542621 0.8095140013341104 0.8635917187551057 0.9086192448711486 0.9441316842652135 0.9697625965152188 0.9852476228023085 0.9904270973700678; -0.9848079557702182 -0.9619237393477577 -0.9289811509432858 -0.8863264379308532 -0.8344078394464043 -0.7737708094255003 -0.7050522092634309 -0.628973535139683 -0.5463332555329905 -0.45799834394955385 -0.3648951002887607 -0.2679993614908732 -0.1683262080841577 -0.06691927793015072 0.03516019816836442 0.1368445222851954 0.23707069915996937 0.33479153303331793 0.42898653635656964 0.5186725381239404 0.6029138835900409 0.6808321221678227 0.751615086268147 0.8145252706546253 0.8689074294572241 0.9141953162262125 0.9499175012263389 0.9757022094838597 0.991281132823061 0.9964921791840907; -0.9848077757066033 -0.9619226082246654 -0.9289772158076316 -0.8863163559506444 -0.8343864438675656 -0.7737308736311874 -0.7049843235124474 -0.6288661055560716 -0.5461726294699198 -0.45776906019034436 -0.3645802569182225 -0.2675810889116921 -0.16778622979474442 -0.06623953752986675 0.03599686854579166 0.137853719148687 0.23826577860388587 0.3361829835454676 0.4305814203613991 0.5204740267758265 0.6049209059457192 0.6830391455876217 0.7540120398970701 0.8170976183201717 0.8716363925159774 0.9170582410322592 0.952888360220193 0.9787522196417917 0.9943794705775171 0.9996067671144849; -0.9848077757066033 -0.9619226082246654 -0.9289772158076316 -0.8863163559506444 -0.8343864438675656 -0.7737308736311874 -0.7049843235124474 -0.6288661055560716 -0.5461726294699198 -0.45776906019034436 -0.3645802569182225 -0.2675810889116921 -0.16778622979474442 -0.06623953752986675 0.03599686854579166 0.137853719148687 0.23826577860388587 0.3361829835454676 0.4305814203613991 0.5204740267758265 0.6049209059457192 0.6830391455876217 0.7540120398970701 0.8170976183201717 0.8716363925159774 0.9170582410322592 0.952888360220193 0.9787522196417917 0.9943794705775171 0.9996067671144849; -0.9848079557702182 -0.9619237393477577 -0.9289811509432858 -0.8863264379308532 -0.8344078394464043 -0.7737708094255003 -0.7050522092634309 -0.628973535139683 -0.5463332555329905 -0.45799834394955385 -0.3648951002887607 -0.2679993614908732 -0.1683262080841577 -0.06691927793015072 0.03516019816836442 0.1368445222851954 0.23707069915996937 0.33479153303331793 0.42898653635656964 0.5186725381239404 0.6029138835900409 0.6808321221678227 0.751615086268147 0.8145252706546253 0.8689074294572241 0.9141953162262125 0.9499175012263389 0.9757022094838597 0.991281132823061 0.9964921791840907; -0.9848083080154617 -0.9619259519641189 -0.9289888479694525 -0.8863461560902377 -0.834449679532858 -0.773848894877906 -0.7051849235300108 -0.629183519374974 -0.5466471589631725 -0.45844633041294935 -0.36551012552131423 -0.26881624620219585 -0.1693805413073931 -0.06824619312533124 0.03352732556140982 0.13487540297233894 0.23473942896122485 0.33207780818567695 0.42587673324131814 0.515160610266232 0.5990020354943508 0.6765312279474296 0.7469448307542621 0.8095140013341104 0.8635917187551057 0.9086192448711486 0.9441316842652135 0.9697625965152188 0.9852476228023085 0.9904270973700678; -0.9848088170249774 -0.9619291490168412 -0.9289999681864456 -0.8863746392105347 -0.83451010634215 -0.7739616429219782 -0.705376501352056 -0.6294865532379248 -0.5471000219238704 -0.45909241998367334 -0.3663968122526033 -0.26999353063746995 -0.1708994702371631 -0.07015709733229003 0.031176701293217556 0.13204180125393097 0.2313859339449468 0.3281755747778466 0.42140651789414 0.5101140370766438 0.593382541245719 0.6703546419043277 0.7402395589515084 0.8023208002196075 0.8559630587466704 0.9006182800530089 0.9358308594738352 0.9612419368730264 0.9765927628307849 0.981727116699817; -0.9848094605237538 -0.9619331903252856 -0.9290140226425222 -0.8864106303749615 -0.8345864416592711 -0.7741040309765489 -0.7056183596745902 -0.6298689748230367 -0.5476712892529787 -0.4599070764097725 -0.36751432113310617 -0.2714765716611434 -0.1728119391442847 -0.07256188896347948 0.028220036516772674 0.1284794310938075 0.22717204994029036 0.3232745333132753 0.41579472640667436 0.5037815047333489 0.5863340262652043 0.6626103431366512 0.7318353167151405 0.7933077900121284 0.8464069805660868 0.8905980649619412 0.9254369330116032 0.9505740953244197 0.9657577326184118 0.9708358787879544; -0.9848102103576414 -0.9619378987902921 -0.9290303940141449 -0.8864525439981239 -0.8346753103796548 -0.774269737030516 -0.7058997092611757 -0.6303136358111348 -0.5483352012334921 -0.4608533473580082 -0.36881164909284114 -0.2731972519747779 -0.17502953684989278 -0.07534867126030427 0.02479580195193733 0.12435620002915478 0.22229763458600643 0.31760853474578793 0.4093106647583686 0.4964685574642738 0.5781983001912855 0.6536756239125818 0.7221432593816275 0.7829175352100223 0.8353942022908056 0.8790534765077419 0.9134642973171264 0.938287803629943 0.9532800306171456 0.9582938318278978; -0.9848110337290414 -0.9619430682164011 -0.9290483641188529 -0.8864985373082951 -0.8347727947685265 -0.7744514331532488 -0.7062080643534274 -0.6308007267715657 -0.5490620579759036 -0.4618887155367665 -0.37023023806644023 -0.2750775379983507 -0.17745121189701585 -0.0783898437317994 0.0210615376311803 0.11986270257404513 0.21698904147256942 0.3114418571889576 0.40225804484405964 0.4885190942010046 0.5693593685316151 0.6439736305694228 0.7116238006683839 0.7716449443110712 0.8234504955014178 0.8665367293125876 0.9004865010244792 0.9249722710538628 0.9397584345054217 0.944702971967723; -0.9848118946348599 -0.9619484723949864 -0.9290671457658026 -0.8865465927778677 -0.8348746115192313 -0.7746411205910072 -0.7065298211069128 -0.6313087078570441 -0.5498196356207782 -0.4629671574778273 -0.3717068553565327 -0.2770333793634632 -0.17996840236065567 -0.0815486807459428 0.017185607430628805 0.11520209879984014 0.21148693202168173 0.3050547881702212 0.3949582112219621 0.480296159410071 0.5602217597804916 0.6339492571494761 0.7007601644106047 0.7600086335430027 0.8111260756602306 0.853625064078816 0.8871025568603649 0.9112424748689442 0.9258176684357328 0.9306913006394556; -0.9848127554430918 -0.9619538750389759 -0.9290859174719834 -0.886594607572179 -0.8349763028636328 -0.7748304892407585 -0.706850873864555 -0.6318152930013817 -0.5505746720675981 -0.4640412854011565 -0.3731765644133479 -0.27897869540287 -0.18247023345184546 -0.08468593777339857 0.013338991867098008 0.11058012691066157 0.2060343496506209 0.29872963105801387 0.38773398651486446 0.47216357640356776 0.5511899426715318 0.6240463930206173 0.6900335609000158 0.7485241818581895 0.7989671350650583 0.8408908031298259 0.873905804009893 0.8977071462161592 0.9120758531139916 0.9168800943805473; -0.9848135785386068 -0.9619590401266433 -0.9291038594732265 -0.88664048588961 -0.8350734327169688 -0.7750112841183745 -0.7071572386874185 -0.6322984374807022 -0.5512943445344726 -0.4650644572721009 -0.37457562277248985 -0.2808292245447886 -0.184848484600304 -0.08766609891749323 0.009687607260863826 0.10619585254674166 0.20086578504856265 0.29273799997980304 0.38089514204884717 0.4644695756852625 0.542650132411704 0.6146879663786795 0.6799015659571119 0.7376809812860836 0.7874913349524639 0.828875685840146 0.8614573150445919 0.8849414980915711 0.8991168200577557 0.9038560801145485; -0.9848143279660135 -0.9619637421995175 -0.9291201894380146 -0.8866822300856577 -0.8351617790737946 -0.7751756622978784 -0.7074356558453663 -0.632737283763299 -0.5519476712070157 -0.46599275803647605 -0.3758441737963707 -0.282506059717505 -0.18700209862814693 -0.0903629815442419 0.0063854975209461685 0.10223356704640398 0.1961977130534644 0.2873299524999975 0.37472611052090216 0.45753309971085826 0.5349552274625969 0.6062595798147725 0.6707805471405703 0.727923568396251 0.777168176828428 0.8180704314400848 0.8502648156666165 0.8734656781977171 0.8874682813026679 0.8921495099761978; -0.9848149709979973 -0.9619677761673958 -0.9291341963434889 -0.8867180266839153 -0.8352375145196433 -0.7753165254450037 -0.7076741466041119 -0.6331130277730428 -0.5525067823263891 -0.4667867772114886 -0.37692863433818624 -0.28393874679874603 -0.18884108412285416 -0.0926645237897102 0.0035690959238661338 0.09885605139690522 0.19222083195185063 0.2827251985030024 0.36947617950215744 0.4516330156898841 0.5284130940714581 0.5990969343581661 0.6630323077630949 0.7196375787092393 0.7684043650990955 0.8088996128534982 0.840767176081578 0.8637289861568729 0.8775858818095572 0.8822181587394404; -0.9848154795611216 -0.9619709662003686 -0.9291452710880393 -0.8867463237412065 -0.8352973676728779 -0.7754278152177506 -0.7078625040049189 -0.6334096757895837 -0.5529480200550048 -0.4674131307362162 -0.3777837154757548 -0.2850678747200403 -0.19028973505865565 -0.09447668024785139 0.0013526227520249971 0.09619925382004384 0.18909402504101153 0.2791063662943643 0.3653520973813252 0.4470001089159294 0.5232780038216095 0.5934767742413968 0.6569546049956185 0.7131399047034152 0.7615336698286713 0.8017112858560452 0.8333238642567496 0.8560992045923828 0.8698424587344786 0.8744365594106369; -0.9848158314575598 -0.961973173331576 -0.9291529325825325 -0.8867658965128461 -0.8353387595095769 -0.7755047611868381 -0.7079927018461037 -0.6336146701196017 -0.5532528394511432 -0.46784569517129065 -0.37837404334769753 -0.28584712824264114 -0.19128914965929264 -0.09572642767851314 -0.0001754133907157318 0.0943683067730085 0.18693991588448958 0.2766141307673509 0.36251281862200635 0.44381149575699924 0.5197447681802003 0.5896107967911927 0.6527748859484896 0.7086723036354197 0.7568104448960711 0.7967704483633639 0.8282083693186187 0.8508560025738595 0.8645214352888838 0.8690893943029842; -0.9848160113302673 -0.9619743014525436 -0.9291568482710499 -0.8867758989196258 -0.8353599097526787 -0.7755440733188218 -0.7080592103026847 -0.6337193686089488 -0.5534084935799899 -0.46806653798713777 -0.37867536899373416 -0.2862448037603199 -0.1917990684332063 -0.09636393001660877 -0.0009547002953969572 0.09343474134400287 0.18584181085911342 0.27534392128940677 0.36106601970974983 0.4421869929918105 0.5179450061720757 0.587641860199588 0.650646471697212 0.706397586530944 0.7544058420608156 0.7942552906845757 0.8256044904734249 0.848187258126772 0.861813165888554 0.8663678481562018; -0.9848160113302673 -0.9619743014525436 -0.9291568482710499 -0.8867758989196258 -0.8353599097526787 -0.7755440733188218 -0.7080592103026847 -0.6337193686089488 -0.5534084935799899 -0.46806653798713777 -0.37867536899373416 -0.2862448037603199 -0.1917990684332063 -0.09636393001660877 -0.0009547002953969572 0.09343474134400287 0.18584181085911342 0.27534392128940677 0.36106601970974983 0.4421869929918105 0.5179450061720757 0.587641860199588 0.650646471697212 0.706397586530944 0.7544058420608156 0.7942552906845757 0.8256044904734249 0.848187258126772 0.861813165888554 0.8663678481562018; -0.9848158314575598 -0.961973173331576 -0.9291529325825325 -0.8867658965128461 -0.8353387595095769 -0.7755047611868381 -0.7079927018461037 -0.6336146701196017 -0.5532528394511432 -0.46784569517129065 -0.37837404334769753 -0.28584712824264114 -0.19128914965929264 -0.09572642767851314 -0.0001754133907157318 0.0943683067730085 0.18693991588448958 0.2766141307673509 0.36251281862200635 0.44381149575699924 0.5197447681802003 0.5896107967911927 0.6527748859484896 0.7086723036354197 0.7568104448960711 0.7967704483633639 0.8282083693186187 0.8508560025738595 0.8645214352888838 0.8690893943029842; -0.9848154795611216 -0.9619709662003686 -0.9291452710880393 -0.8867463237412065 -0.8352973676728779 -0.7754278152177506 -0.7078625040049189 -0.6334096757895837 -0.5529480200550048 -0.4674131307362162 -0.3777837154757548 -0.2850678747200403 -0.19028973505865565 -0.09447668024785139 0.0013526227520249971 0.09619925382004384 0.18909402504101153 0.2791063662943643 0.3653520973813252 0.4470001089159294 0.5232780038216095 0.5934767742413968 0.6569546049956185 0.7131399047034152 0.7615336698286713 0.8017112858560452 0.8333238642567496 0.8560992045923828 0.8698424587344786 0.8744365594106369; -0.9848149709979973 -0.9619677761673958 -0.9291341963434889 -0.8867180266839153 -0.8352375145196433 -0.7753165254450037 -0.7076741466041119 -0.6331130277730428 -0.5525067823263891 -0.4667867772114886 -0.37692863433818624 -0.28393874679874603 -0.18884108412285416 -0.0926645237897102 0.0035690959238661338 0.09885605139690522 0.19222083195185063 0.2827251985030024 0.36947617950215744 0.4516330156898841 0.5284130940714581 0.5990969343581661 0.6630323077630949 0.7196375787092393 0.7684043650990955 0.8088996128534982 0.840767176081578 0.8637289861568729 0.8775858818095572 0.8822181587394404; -0.9848143279660135 -0.9619637421995175 -0.9291201894380146 -0.8866822300856577 -0.8351617790737946 -0.7751756622978784 -0.7074356558453663 -0.632737283763299 -0.5519476712070157 -0.46599275803647605 -0.3758441737963707 -0.282506059717505 -0.18700209862814693 -0.0903629815442419 0.0063854975209461685 0.10223356704640398 0.1961977130534644 0.2873299524999975 0.37472611052090216 0.45753309971085826 0.5349552274625969 0.6062595798147725 0.6707805471405703 0.727923568396251 0.777168176828428 0.8180704314400848 0.8502648156666165 0.8734656781977171 0.8874682813026679 0.8921495099761978; -0.9848135785386068 -0.9619590401266433 -0.9291038594732265 -0.88664048588961 -0.8350734327169688 -0.7750112841183745 -0.7071572386874185 -0.6322984374807022 -0.5512943445344726 -0.4650644572721009 -0.37457562277248985 -0.2808292245447886 -0.184848484600304 -0.08766609891749323 0.009687607260863826 0.10619585254674166 0.20086578504856265 0.29273799997980304 0.38089514204884717 0.4644695756852625 0.542650132411704 0.6146879663786795 0.6799015659571119 0.7376809812860836 0.7874913349524639 0.828875685840146 0.8614573150445919 0.8849414980915711 0.8991168200577557 0.9038560801145485; -0.9848127554430918 -0.9619538750389759 -0.9290859174719834 -0.886594607572179 -0.8349763028636328 -0.7748304892407585 -0.706850873864555 -0.6318152930013817 -0.5505746720675981 -0.4640412854011565 -0.3731765644133479 -0.27897869540287 -0.18247023345184546 -0.08468593777339857 0.013338991867098008 0.11058012691066157 0.2060343496506209 0.29872963105801387 0.38773398651486446 0.47216357640356776 0.5511899426715318 0.6240463930206173 0.6900335609000158 0.7485241818581895 0.7989671350650583 0.8408908031298259 0.873905804009893 0.8977071462161592 0.9120758531139916 0.9168800943805473; -0.9848118946348599 -0.9619484723949864 -0.9290671457658026 -0.8865465927778677 -0.8348746115192313 -0.7746411205910072 -0.7065298211069128 -0.6313087078570441 -0.5498196356207782 -0.4629671574778273 -0.3717068553565327 -0.2770333793634632 -0.17996840236065567 -0.0815486807459428 0.017185607430628805 0.11520209879984014 0.21148693202168173 0.3050547881702212 0.3949582112219621 0.480296159410071 0.5602217597804916 0.6339492571494761 0.7007601644106047 0.7600086335430027 0.8111260756602306 0.853625064078816 0.8871025568603649 0.9112424748689442 0.9258176684357328 0.9306913006394556; -0.9848110337290414 -0.9619430682164011 -0.9290483641188529 -0.8864985373082951 -0.8347727947685265 -0.7744514331532488 -0.7062080643534274 -0.6308007267715657 -0.5490620579759036 -0.4618887155367665 -0.37023023806644023 -0.2750775379983507 -0.17745121189701585 -0.0783898437317994 0.0210615376311803 0.11986270257404513 0.21698904147256942 0.3114418571889576 0.40225804484405964 0.4885190942010046 0.5693593685316151 0.6439736305694228 0.7116238006683839 0.7716449443110712 0.8234504955014178 0.8665367293125876 0.9004865010244792 0.9249722710538628 0.9397584345054217 0.944702971967723; -0.9848102103576414 -0.9619378987902921 -0.9290303940141449 -0.8864525439981239 -0.8346753103796548 -0.774269737030516 -0.7058997092611757 -0.6303136358111348 -0.5483352012334921 -0.4608533473580082 -0.36881164909284114 -0.2731972519747779 -0.17502953684989278 -0.07534867126030427 0.02479580195193733 0.12435620002915478 0.22229763458600643 0.31760853474578793 0.4093106647583686 0.4964685574642738 0.5781983001912855 0.6536756239125818 0.7221432593816275 0.7829175352100223 0.8353942022908056 0.8790534765077419 0.9134642973171264 0.938287803629943 0.9532800306171456 0.9582938318278978; -0.9848094605237538 -0.9619331903252856 -0.9290140226425222 -0.8864106303749615 -0.8345864416592711 -0.7741040309765489 -0.7056183596745902 -0.6298689748230367 -0.5476712892529787 -0.4599070764097725 -0.36751432113310617 -0.2714765716611434 -0.1728119391442847 -0.07256188896347948 0.028220036516772674 0.1284794310938075 0.22717204994029036 0.3232745333132753 0.41579472640667436 0.5037815047333489 0.5863340262652043 0.6626103431366512 0.7318353167151405 0.7933077900121284 0.8464069805660868 0.8905980649619412 0.9254369330116032 0.9505740953244197 0.9657577326184118 0.9708358787879544; -0.9848088170249774 -0.9619291490168412 -0.9289999681864456 -0.8863746392105347 -0.83451010634215 -0.7739616429219782 -0.705376501352056 -0.6294865532379248 -0.5471000219238704 -0.45909241998367334 -0.3663968122526033 -0.26999353063746995 -0.1708994702371631 -0.07015709733229003 0.031176701293217556 0.13204180125393097 0.2313859339449468 0.3281755747778466 0.42140651789414 0.5101140370766438 0.593382541245719 0.6703546419043277 0.7402395589515084 0.8023208002196075 0.8559630587466704 0.9006182800530089 0.9358308594738352 0.9612419368730264 0.9765927628307849 0.981727116699817; -0.9848083080154617 -0.9619259519641189 -0.9289888479694525 -0.8863461560902377 -0.834449679532858 -0.773848894877906 -0.7051849235300108 -0.629183519374974 -0.5466471589631725 -0.45844633041294935 -0.36551012552131423 -0.26881624620219585 -0.1693805413073931 -0.06824619312533124 0.03352732556140982 0.13487540297233894 0.23473942896122485 0.33207780818567695 0.42587673324131814 0.515160610266232 0.5990020354943508 0.6765312279474296 0.7469448307542621 0.8095140013341104 0.8635917187551057 0.9086192448711486 0.9441316842652135 0.9697625965152188 0.9852476228023085 0.9904270973700678; -0.9848079557702182 -0.9619237393477577 -0.9289811509432858 -0.8863264379308532 -0.8344078394464043 -0.7737708094255003 -0.7050522092634309 -0.628973535139683 -0.5463332555329905 -0.45799834394955385 -0.3648951002887607 -0.2679993614908732 -0.1683262080841577 -0.06691927793015072 0.03516019816836442 0.1368445222851954 0.23707069915996937 0.33479153303331793 0.42898653635656964 0.5186725381239404 0.6029138835900409 0.6808321221678227 0.751615086268147 0.8145252706546253 0.8689074294572241 0.9141953162262125 0.9499175012263389 0.9757022094838597 0.991281132823061 0.9964921791840907; -0.9848077757066033 -0.9619226082246654 -0.9289772158076316 -0.8863163559506444 -0.8343864438675656 -0.7737308736311874 -0.7049843235124474 -0.6288661055560716 -0.5461726294699198 -0.45776906019034436 -0.3645802569182225 -0.2675810889116921 -0.16778622979474442 -0.06623953752986675 0.03599686854579166 0.137853719148687 0.23826577860388587 0.3361829835454676 0.4305814203613991 0.5204740267758265 0.6049209059457192 0.6830391455876217 0.7540120398970701 0.8170976183201717 0.8716363925159774 0.9170582410322592 0.952888360220193 0.9787522196417917 0.9943794705775171 0.9996067671144849; -0.9848077757066033 -0.9619226082246654 -0.9289772158076316 -0.8863163559506444 -0.8343864438675656 -0.7737308736311874 -0.7049843235124474 -0.6288661055560716 -0.5461726294699198 -0.45776906019034436 -0.3645802569182225 -0.2675810889116921 -0.16778622979474442 -0.06623953752986675 0.03599686854579166 0.137853719148687 0.23826577860388587 0.3361829835454676 0.4305814203613991 0.5204740267758265 0.6049209059457192 0.6830391455876217 0.7540120398970701 0.8170976183201717 0.8716363925159774 0.9170582410322592 0.952888360220193 0.9787522196417917 0.9943794705775171 0.9996067671144849; -0.9848079557702182 -0.9619237393477577 -0.9289811509432858 -0.8863264379308532 -0.8344078394464043 -0.7737708094255003 -0.7050522092634309 -0.628973535139683 -0.5463332555329905 -0.45799834394955385 -0.3648951002887607 -0.2679993614908732 -0.1683262080841577 -0.06691927793015072 0.03516019816836442 0.1368445222851954 0.23707069915996937 0.33479153303331793 0.42898653635656964 0.5186725381239404 0.6029138835900409 0.6808321221678227 0.751615086268147 0.8145252706546253 0.8689074294572241 0.9141953162262125 0.9499175012263389 0.9757022094838597 0.991281132823061 0.9964921791840907; -0.9848083080154617 -0.9619259519641189 -0.9289888479694525 -0.8863461560902377 -0.834449679532858 -0.773848894877906 -0.7051849235300108 -0.629183519374974 -0.5466471589631725 -0.45844633041294935 -0.36551012552131423 -0.26881624620219585 -0.1693805413073931 -0.06824619312533124 0.03352732556140982 0.13487540297233894 0.23473942896122485 0.33207780818567695 0.42587673324131814 0.515160610266232 0.5990020354943508 0.6765312279474296 0.7469448307542621 0.8095140013341104 0.8635917187551057 0.9086192448711486 0.9441316842652135 0.9697625965152188 0.9852476228023085 0.9904270973700678; -0.9848088170249774 -0.9619291490168412 -0.9289999681864456 -0.8863746392105347 -0.83451010634215 -0.7739616429219782 -0.705376501352056 -0.6294865532379248 -0.5471000219238704 -0.45909241998367334 -0.3663968122526033 -0.26999353063746995 -0.1708994702371631 -0.07015709733229003 0.031176701293217556 0.13204180125393097 0.2313859339449468 0.3281755747778466 0.42140651789414 0.5101140370766438 0.593382541245719 0.6703546419043277 0.7402395589515084 0.8023208002196075 0.8559630587466704 0.9006182800530089 0.9358308594738352 0.9612419368730264 0.9765927628307849 0.981727116699817; -0.9848094605237538 -0.9619331903252856 -0.9290140226425222 -0.8864106303749615 -0.8345864416592711 -0.7741040309765489 -0.7056183596745902 -0.6298689748230367 -0.5476712892529787 -0.4599070764097725 -0.36751432113310617 -0.2714765716611434 -0.1728119391442847 -0.07256188896347948 0.028220036516772674 0.1284794310938075 0.22717204994029036 0.3232745333132753 0.41579472640667436 0.5037815047333489 0.5863340262652043 0.6626103431366512 0.7318353167151405 0.7933077900121284 0.8464069805660868 0.8905980649619412 0.9254369330116032 0.9505740953244197 0.9657577326184118 0.9708358787879544; -0.9848102103576414 -0.9619378987902921 -0.9290303940141449 -0.8864525439981239 -0.8346753103796548 -0.774269737030516 -0.7058997092611757 -0.6303136358111348 -0.5483352012334921 -0.4608533473580082 -0.36881164909284114 -0.2731972519747779 -0.17502953684989278 -0.07534867126030427 0.02479580195193733 0.12435620002915478 0.22229763458600643 0.31760853474578793 0.4093106647583686 0.4964685574642738 0.5781983001912855 0.6536756239125818 0.7221432593816275 0.7829175352100223 0.8353942022908056 0.8790534765077419 0.9134642973171264 0.938287803629943 0.9532800306171456 0.9582938318278978; -0.9848110337290414 -0.9619430682164011 -0.9290483641188529 -0.8864985373082951 -0.8347727947685265 -0.7744514331532488 -0.7062080643534274 -0.6308007267715657 -0.5490620579759036 -0.4618887155367665 -0.37023023806644023 -0.2750775379983507 -0.17745121189701585 -0.0783898437317994 0.0210615376311803 0.11986270257404513 0.21698904147256942 0.3114418571889576 0.40225804484405964 0.4885190942010046 0.5693593685316151 0.6439736305694228 0.7116238006683839 0.7716449443110712 0.8234504955014178 0.8665367293125876 0.9004865010244792 0.9249722710538628 0.9397584345054217 0.944702971967723; -0.9848118946348599 -0.9619484723949864 -0.9290671457658026 -0.8865465927778677 -0.8348746115192313 -0.7746411205910072 -0.7065298211069128 -0.6313087078570441 -0.5498196356207782 -0.4629671574778273 -0.3717068553565327 -0.2770333793634632 -0.17996840236065567 -0.0815486807459428 0.017185607430628805 0.11520209879984014 0.21148693202168173 0.3050547881702212 0.3949582112219621 0.480296159410071 0.5602217597804916 0.6339492571494761 0.7007601644106047 0.7600086335430027 0.8111260756602306 0.853625064078816 0.8871025568603649 0.9112424748689442 0.9258176684357328 0.9306913006394556; -0.9848127554430918 -0.9619538750389759 -0.9290859174719834 -0.886594607572179 -0.8349763028636328 -0.7748304892407585 -0.706850873864555 -0.6318152930013817 -0.5505746720675981 -0.4640412854011565 -0.3731765644133479 -0.27897869540287 -0.18247023345184546 -0.08468593777339857 0.013338991867098008 0.11058012691066157 0.2060343496506209 0.29872963105801387 0.38773398651486446 0.47216357640356776 0.5511899426715318 0.6240463930206173 0.6900335609000158 0.7485241818581895 0.7989671350650583 0.8408908031298259 0.873905804009893 0.8977071462161592 0.9120758531139916 0.9168800943805473; -0.9848135785386068 -0.9619590401266433 -0.9291038594732265 -0.88664048588961 -0.8350734327169688 -0.7750112841183745 -0.7071572386874185 -0.6322984374807022 -0.5512943445344726 -0.4650644572721009 -0.37457562277248985 -0.2808292245447886 -0.184848484600304 -0.08766609891749323 0.009687607260863826 0.10619585254674166 0.20086578504856265 0.29273799997980304 0.38089514204884717 0.4644695756852625 0.542650132411704 0.6146879663786795 0.6799015659571119 0.7376809812860836 0.7874913349524639 0.828875685840146 0.8614573150445919 0.8849414980915711 0.8991168200577557 0.9038560801145485; -0.9848143279660135 -0.9619637421995175 -0.9291201894380146 -0.8866822300856577 -0.8351617790737946 -0.7751756622978784 -0.7074356558453663 -0.632737283763299 -0.5519476712070157 -0.46599275803647605 -0.3758441737963707 -0.282506059717505 -0.18700209862814693 -0.0903629815442419 0.0063854975209461685 0.10223356704640398 0.1961977130534644 0.2873299524999975 0.37472611052090216 0.45753309971085826 0.5349552274625969 0.6062595798147725 0.6707805471405703 0.727923568396251 0.777168176828428 0.8180704314400848 0.8502648156666165 0.8734656781977171 0.8874682813026679 0.8921495099761978; -0.9848149709979973 -0.9619677761673958 -0.9291341963434889 -0.8867180266839153 -0.8352375145196433 -0.7753165254450037 -0.7076741466041119 -0.6331130277730428 -0.5525067823263891 -0.4667867772114886 -0.37692863433818624 -0.28393874679874603 -0.18884108412285416 -0.0926645237897102 0.0035690959238661338 0.09885605139690522 0.19222083195185063 0.2827251985030024 0.36947617950215744 0.4516330156898841 0.5284130940714581 0.5990969343581661 0.6630323077630949 0.7196375787092393 0.7684043650990955 0.8088996128534982 0.840767176081578 0.8637289861568729 0.8775858818095572 0.8822181587394404; -0.9848154795611216 -0.9619709662003686 -0.9291452710880393 -0.8867463237412065 -0.8352973676728779 -0.7754278152177506 -0.7078625040049189 -0.6334096757895837 -0.5529480200550048 -0.4674131307362162 -0.3777837154757548 -0.2850678747200403 -0.19028973505865565 -0.09447668024785139 0.0013526227520249971 0.09619925382004384 0.18909402504101153 0.2791063662943643 0.3653520973813252 0.4470001089159294 0.5232780038216095 0.5934767742413968 0.6569546049956185 0.7131399047034152 0.7615336698286713 0.8017112858560452 0.8333238642567496 0.8560992045923828 0.8698424587344786 0.8744365594106369; -0.9848158314575598 -0.961973173331576 -0.9291529325825325 -0.8867658965128461 -0.8353387595095769 -0.7755047611868381 -0.7079927018461037 -0.6336146701196017 -0.5532528394511432 -0.46784569517129065 -0.37837404334769753 -0.28584712824264114 -0.19128914965929264 -0.09572642767851314 -0.0001754133907157318 0.0943683067730085 0.18693991588448958 0.2766141307673509 0.36251281862200635 0.44381149575699924 0.5197447681802003 0.5896107967911927 0.6527748859484896 0.7086723036354197 0.7568104448960711 0.7967704483633639 0.8282083693186187 0.8508560025738595 0.8645214352888838 0.8690893943029842; -0.9848160113302673 -0.9619743014525436 -0.9291568482710499 -0.8867758989196258 -0.8353599097526787 -0.7755440733188218 -0.7080592103026847 -0.6337193686089488 -0.5534084935799899 -0.46806653798713777 -0.37867536899373416 -0.2862448037603199 -0.1917990684332063 -0.09636393001660877 -0.0009547002953969572 0.09343474134400287 0.18584181085911342 0.27534392128940677 0.36106601970974983 0.4421869929918105 0.5179450061720757 0.587641860199588 0.650646471697212 0.706397586530944 0.7544058420608156 0.7942552906845757 0.8256044904734249 0.848187258126772 0.861813165888554 0.8663678481562018])
Finally, we can visualize the grid using two types of visual elements: surfaces and wireframes. Surfaces are plotted slightly smaller (at a scale of 0.99 instead of 1) than the wireframes to create a layered effect, enhancing the visual distinction between the grid's structure and its outline. The Face-Face nodes are visualized with blue surfaces and black wireframes, while the Center-Center nodes are visualized with blue surfaces and wireframes.
fig = Figure(size=(1200, 600))
+axN = Axis3(fig[1, 1]; aspect=(1, 1, 1), elevation = +0.9, azimuth = 7, height=1500)
+axS = Axis3(fig[1, 2]; aspect=(1, 1, 1), elevation = -0.9, azimuth = 7, height=1500)
+
+for ax in (axN, axS)
+ scale_factor = 0.99
+
+ surface!(ax, xF .* scale_factor, yF .* scale_factor, zF .* scale_factor, color = :blue)
+ wireframe!(ax, xF, yF, zF, color = :black)
+
+ surface!(ax, xC .* scale_factor, yC .* scale_factor, zC .* scale_factor, color = :blue)
+ wireframe!(ax, xC, yC, zC, color = :blue)
+
+ scatter!(ax, 0, 0, +1, color=:red, markersize=15)
+ scatter!(ax, 0, 0, -1, color=:red, markersize=15)
+
+ hidedecorations!(ax)
+ hidespines!(ax)
+end
+
+save("tripolar_grid_nodes.png", fig, px_per_unit = 2)
Above there are two views of the grid: northern hemisphere on the left, southern hemisphere on the right. The actual North and South poles are the red dots. On the left we see how the North hemisphere has does not have a gridline convergence singularity at the actual North Pole but the singularity has moved to the two fictitious poles shifted at latitude 60; on the right we see that the Southern hemisphere has its pole at the usual South Pole.
This tripolar configuration is typically used in ocean modeling so that the pole singularity in the Arctic ocean is moved away into the land mases of Russia and Canada; the South pole singularity is already within the land mass of Antarctica so things are all good down there!
This page was generated using Literate.jl.