doc/v628/math_2mlp_2src_2TNeuron_8cxx_source.html

// @(#)root/mlp:$Id$

// Author: Christophe.Delaere@cern.ch   20/07/03


/*************************************************************************

 * Copyright (C) 1995-2003, Rene Brun and Fons Rademakers.               *

 * All rights reserved.                                                  *

 *                                                                       *

 * For the licensing terms see $ROOTSYS/LICENSE.                         *

 * For the list of contributors see $ROOTSYS/README/CREDITS.             *

 *************************************************************************/


/** \class TNeuron


This class describes an elementary neuron, which is the basic

element for a Neural Network.

A network is built connecting neurons by synapses.

There are different types of neurons: linear (a+bx),

sigmoid (1/(1+exp(-x)), tanh or gaussian.

An external function can also be used, together with its derivative.

In a Multi Layer Perceptron, the input layer is made of

inactive neurons (returning the normalized input) and output neurons

are linear. Hidden neurons may be anything, the default being sigmoids.


This implementation contains several methods to compute the value,

the derivative, the DeDw, ...

Values are stored in local buffers. The SetNewEvent() method is

there to inform buffered values are outdated.


*/


#include "TSynapse.h"

#include "TNeuron.h"

#include "TTree.h"

#include "TTreeFormula.h"

#include "TFormula.h"

#include "TBranch.h"

#include "TROOT.h"

#include "TH1D.h"

#include "TRegexp.h"

#include "TMath.h"


ClassImp(TNeuron);


////////////////////////////////////////////////////////////////////////////////

/// Usual constructor


TNeuron::TNeuron(TNeuron::ENeuronType type /*= kSigmoid*/,

                 const char* name /*= ""*/, const char* title /*= ""*/,

                 const char* extF /*= ""*/, const char* extD  /*= ""*/ )

   :TNamed(name, title)

{

   fpre.SetOwner(false);

   fpost.SetOwner(false);

   flayer.SetOwner(false);

   fWeight = 0.;

   fNorm[0] = 1.;

   fNorm[1] = 0.;

   fType = type;

   fNewInput = true;

   fNewValue = true;

   fNewDeriv = true;

   fNewDeDw = true;

   fFormula = 0;

   fDeDw  = 0;

   fDEDw  = 0;

   fValue = 0;

   fExtF  = 0;

   fExtD  = 0;

   fIndex = 0;

   fDerivative = 0;

   fInput = 0;

   if(fType==kExternal) {

      fExtF = (TFormula*)gROOT->FindObject(extF);

      fExtD = (TFormula*)gROOT->FindObject(extD);

   }

}


////////////////////////////////////////////////////////////////////////////////

/// The Sigmoid.

/// Fast computation of the values of the sigmoid function.

/// Uses values of the function up  to the seventh order

/// tabulated at 700 points.

/// Values were computed in long double precision (16 bytes,

/// precision to about 37 digits) on a hp computer.

/// Some values were checked with Mathematica.

/// Result should be correct to ~ 15 digits (about double

/// precision)

///

/// From the mlpfit package (J.Schwindling   20-Jul-1999)


Double_t TNeuron::Sigmoid(Double_t x) const

{

   static Double_t sigval[7000] = {

   -3.500000e+01, 6.30511676014698530e-16, 6.30511676014698130e-16, 3.15255838007348670e-16, 1.05085279335782620e-16, 2.62713198339455210e-17, 5.25426396678905190e-18, 8.75710661131491060e-19, 1.25101523018779380e-19, 1.56376903773461590e-20,

   -3.490000e+01, 6.96823167838580650e-16, 6.96823167838580160e-16, 3.48411583919289640e-16, 1.16137194639762880e-16, 2.90342986599405540e-17, 5.80685973198804710e-18, 9.67809955331319670e-19, 1.38258565047325200e-19, 1.72823206309141090e-20,

   -3.480000e+01, 7.70108700136546340e-16, 7.70108700136545750e-16, 3.85054350068272280e-16, 1.28351450022757030e-16, 3.20878625056890590e-17, 6.41757250113773230e-18, 1.06959541685626250e-18, 1.52799345265172810e-19, 1.90999181581447200e-20,

   -3.470000e+01, 8.51101739147945470e-16, 8.51101739147944780e-16, 4.25550869573971650e-16, 1.41850289857990070e-16, 3.54625724644972780e-17, 7.09251449289935940e-18, 1.18208574881652770e-18, 1.68869392688066160e-19, 2.11086740860059710e-20,

   -3.460000e+01, 9.40612890429916560e-16, 9.40612890429915770e-16, 4.70306445214957000e-16, 1.56768815071651720e-16, 3.91922037679126390e-17, 7.83844075358240950e-18, 1.30640679226369560e-18, 1.86629541751945290e-19, 2.33286927189903510e-20,

   -3.450000e+01, 1.03953801167022100e-15, 1.03953801167021980e-15, 5.19769005835108810e-16, 1.73256335278368870e-16, 4.33140838195918600e-17, 8.66281676391822790e-18, 1.44380279398632340e-18, 2.06257541998032470e-19, 2.57821927497506280e-20,

   -3.440000e+01, 1.14886717873211280e-15, 1.14886717873211140e-15, 5.74433589366054410e-16, 1.91477863122017240e-16, 4.78694657805038730e-17, 9.57389315610059860e-18, 1.59564885935004120e-18, 2.27949837049989100e-19, 2.84937296312444480e-20,

   -3.430000e+01, 1.26969459466634980e-15, 1.26969459466634820e-15, 6.34847297333172530e-16, 2.11615765777723080e-16, 5.29039414444302330e-17, 1.05807882888858320e-17, 1.76346471481423380e-18, 2.51923530687727210e-19, 3.14904413359607800e-20,

   -3.420000e+01, 1.40322954086308920e-15, 1.40322954086308720e-15, 7.01614770431541630e-16, 2.33871590143845880e-16, 5.84678975359608160e-17, 1.16935795071919010e-17, 1.94892991786522940e-18, 2.78418559695007730e-19, 3.48023199618697190e-20,

   -3.410000e+01, 1.55080847994653150e-15, 1.55080847994652920e-15, 7.75404239973262210e-16, 2.58468079991085760e-16, 6.46170199977706390e-17, 1.29234039995538080e-17, 2.15390066659219480e-18, 3.07700095227425790e-19, 3.84625119034205930e-20,

   -3.400000e+01, 1.71390843154201000e-15, 1.71390843154200710e-15, 8.56954215771000580e-16, 2.85651405256998220e-16, 7.14128513142485820e-17, 1.42825702628493230e-17, 2.38042837714142370e-18, 3.40061196734451790e-19, 4.25076495917971450e-20,

   -3.390000e+01, 1.89416175478487890e-15, 1.89416175478487530e-15, 9.47080877392433920e-16, 3.15693625797475610e-16, 7.89234064493677060e-17, 1.57846812898730630e-17, 2.63078021497868450e-18, 3.75825744996909330e-19, 4.69782181246022790e-20,

   -3.380000e+01, 2.09337248551938710e-15, 2.09337248551938240e-15, 1.04668624275968680e-15, 3.48895414253226000e-16, 8.72238535633050470e-17, 1.74447707126604240e-17, 2.90746178544320960e-18, 4.15351683634688560e-19, 5.19189604543221620e-20,

   -3.370000e+01, 2.31353439169574760e-15, 2.31353439169574210e-15, 1.15676719584786570e-15, 3.85589065282618330e-16, 9.63972663206527960e-17, 1.92794532641298470e-17, 3.21324221068806990e-18, 4.59034601526799130e-19, 5.73793251908329070e-20,

   -3.360000e+01, 2.55685092766997700e-15, 2.55685092766997070e-15, 1.27842546383497880e-15, 4.26141821278321860e-16, 1.06535455319578300e-16, 2.13070910639147860e-17, 3.55118184398550770e-18, 5.07311691997846610e-19, 6.34139614997100740e-20,

   -3.350000e+01, 2.82575728711560320e-15, 2.82575728711559530e-15, 1.41287864355778950e-15, 4.70959547852591190e-16, 1.17739886963145140e-16, 2.35479773926279630e-17, 3.92466289877097270e-18, 5.60666128395751820e-19, 7.00832660494436280e-20,

   -3.340000e+01, 3.12294477526050570e-15, 3.12294477526049620e-15, 1.56147238763023820e-15, 5.20490795876739570e-16, 1.30122698969181640e-16, 2.60245397938350280e-17, 4.33742329897207160e-18, 6.19631899853029210e-19, 7.74539874815976920e-20,

   -3.330000e+01, 3.45138774437420440e-15, 3.45138774437419260e-15, 1.72569387218708450e-15, 5.75231290729020130e-16, 1.43807822682251060e-16, 2.87615645364486300e-17, 4.79359408940757550e-18, 6.84799155629502340e-19, 8.55998944536499720e-20,

   -3.320000e+01, 3.81437336208505550e-15, 3.81437336208504050e-15, 1.90718668104250570e-15, 6.35728893680825560e-16, 1.58932223420201530e-16, 3.17864446840383680e-17, 5.29774078067241470e-18, 7.56820111524445930e-19, 9.46025139405095430e-20,

   -3.310000e+01, 4.21553451045883940e-15, 4.21553451045882130e-15, 2.10776725522939290e-15, 7.02589085076452470e-16, 1.75647271269107180e-16, 3.51294542538190670e-17, 5.85490904230238850e-18, 8.36415577471544070e-19, 1.04551947183886600e-19,

   -3.300000e+01, 4.65888614510337560e-15, 4.65888614510335430e-15, 2.32944307255165550e-15, 7.76481024183870600e-16, 1.94120256045960400e-16, 3.88240512091891920e-17, 6.47067520153056710e-18, 9.24382171646948210e-19, 1.15547771455799630e-19,

   -3.290000e+01, 5.14886547819381740e-15, 5.14886547819379060e-15, 2.57443273909686890e-15, 8.58144246365605200e-16, 2.14536061591392470e-16, 4.29072123182749640e-17, 7.15120205304464960e-18, 1.02160029329175600e-18, 1.27700036661385360e-19,

   -3.280000e+01, 5.69037638758347510e-15, 5.69037638758344200e-15, 2.84518819379168870e-15, 9.48396064597207920e-16, 2.37099016149291180e-16, 4.74198032298539250e-17, 7.90330053830754850e-18, 1.12904293404352430e-18, 1.41130366755337750e-19,

   -3.270000e+01, 6.28883849646157640e-15, 6.28883849646153690e-15, 3.14441924823072900e-15, 1.04813974941021660e-15, 2.62034937352540980e-16, 5.24069874705029230e-17, 8.73449791174873020e-18, 1.24778541596360200e-18, 1.55973176995324680e-19,

   -3.260000e+01, 6.95024141476392120e-15, 6.95024141476387310e-15, 3.47512070738188800e-15, 1.15837356912726370e-15, 2.89593392281799860e-16, 5.79186784563535330e-17, 9.65311307605677590e-18, 1.37901615372178300e-18, 1.72377019215069530e-19,

   -3.250000e+01, 7.68120468520203540e-15, 7.68120468520197700e-15, 3.84060234260092930e-15, 1.28020078086693710e-15, 3.20050195216714590e-16, 6.40100390433350520e-17, 1.06683398405532210e-17, 1.52404854864971080e-18, 1.90506068581026560e-19,

   -3.240000e+01, 8.48904403387170610e-15, 8.48904403387163350e-15, 4.24452201693574420e-15, 1.41484067231186670e-15, 3.53710168077942670e-16, 7.07420336155789230e-17, 1.17903389359266190e-17, 1.68433413370288750e-18, 2.10541766712632160e-19,

   -3.230000e+01, 9.38184458849859670e-15, 9.38184458849850840e-15, 4.69092229424916660e-15, 1.56364076474966340e-15, 3.90910191187386470e-16, 7.81820382374655680e-17, 1.30303397062403500e-17, 1.86147710089036070e-18, 2.32684637611015680e-19,

   -3.220000e+01, 1.03685417971139710e-14, 1.03685417971138640e-14, 5.18427089855682470e-15, 1.72809029951886980e-15, 4.32022574879681600e-16, 8.64045149759219900e-17, 1.44007524959822210e-17, 2.05725035656752340e-18, 2.57156294570599160e-19,

   -3.210000e+01, 1.14590108570221770e-14, 1.14590108570220460e-14, 5.72950542851089130e-15, 1.90983514283687630e-15, 4.77458785709175300e-16, 9.54917571418175490e-17, 1.59152928569637550e-17, 2.27361326527886920e-18, 2.84201658159441780e-19,

   -3.200000e+01, 1.26641655490940160e-14, 1.26641655490938570e-14, 6.33208277454676750e-15, 2.11069425818214890e-15, 5.27673564545483790e-16, 1.05534712909075370e-16, 1.75891188181721000e-17, 2.51273125973683490e-18, 3.14091407466595250e-19,

   -3.190000e+01, 1.39960674665542220e-14, 1.39960674665540250e-14, 6.99803373327681690e-15, 2.33267791109214150e-15, 5.83169477772970090e-16, 1.16633895554567910e-16, 1.94389825924192790e-17, 2.77699751320026640e-18, 3.47124689149411470e-19,

   -3.180000e+01, 1.54680467314603800e-14, 1.54680467314601400e-14, 7.73402336572983000e-15, 2.57800778857645030e-15, 6.44501947144032790e-16, 1.28900389428774660e-16, 2.14833982381184800e-17, 3.06905689115674430e-18, 3.83632111393833500e-19,

   -3.170000e+01, 1.70948354070450830e-14, 1.70948354070447900e-14, 8.54741770352210300e-15, 2.84913923450717270e-15, 7.12284808626695750e-16, 1.42456961725300190e-16, 2.37428269542037130e-17, 3.39183242202539070e-18, 4.23979052752246120e-19,

   -3.160000e+01, 1.88927149411560280e-14, 1.88927149411556710e-14, 9.44635747057747730e-15, 3.14878582352558780e-15, 7.87196455881277930e-16, 1.57439291176208010e-16, 2.62398818626854730e-17, 3.74855455180767740e-18, 4.68569318974826550e-19,

   -3.150000e+01, 2.08796791164589010e-14, 2.08796791164584650e-14, 1.04398395582287960e-14, 3.47994651940930800e-15, 8.69986629852181640e-16, 1.73997325970378200e-16, 2.89995543283769920e-17, 4.14279347547689150e-18, 5.17849184433227460e-19,

   -3.140000e+01, 2.30756141382617880e-14, 2.30756141382612580e-14, 1.15378070691300960e-14, 3.84593568970967660e-15, 9.61483922427241660e-16, 1.92296784485377340e-16, 3.20494640808725600e-17, 4.57849486868931840e-18, 5.72311858584474310e-19,

   -3.130000e+01, 2.55024976623420620e-14, 2.55024976623414120e-14, 1.27512488311700560e-14, 4.25041627705625120e-15, 1.06260406926384610e-15, 2.12520813852682500e-16, 3.54201356420848460e-17, 5.06001937743243370e-18, 6.32502422176989520e-19,

   -3.120000e+01, 2.81846187547126010e-14, 2.81846187547118060e-14, 1.40923093773551080e-14, 4.69743645911783960e-15, 1.17435911477919500e-15, 2.34871822955733110e-16, 3.91453038259202140e-17, 5.59218626083565740e-18, 6.99023282601935360e-19,

   -3.110000e+01, 3.11488209847576830e-14, 3.11488209847567110e-14, 1.55744104923773830e-14, 5.19147016412514760e-15, 1.29786754103096350e-15, 2.59573508206063350e-16, 4.32622513676341070e-17, 6.18032162393540810e-18, 7.72540202988845880e-19,

   -3.100000e+01, 3.44247710846985810e-14, 3.44247710846973950e-14, 1.72123855423475110e-14, 5.73746184744838010e-15, 1.43436546186170000e-15, 2.86873092372182000e-16, 4.78121820619776690e-17, 6.83031172312461810e-18, 8.53788965386815150e-19,

   -3.090000e+01, 3.80452558642202530e-14, 3.80452558642188080e-14, 1.90226279321079550e-14, 6.34087597736835340e-15, 1.58521899434160580e-15, 3.17043798868128200e-16, 5.28406331446237000e-17, 7.54866187778500530e-18, 9.43582734718530590e-19,

   -3.080000e+01, 4.20465103518829610e-14, 4.20465103518811940e-14, 2.10232551759388270e-14, 7.00775172531176340e-15, 1.75193793132735160e-15, 3.50387586265234630e-16, 5.83979310441271980e-17, 8.34256157771000690e-18, 1.04282019720813850e-18,

   -3.070000e+01, 4.64685804474675720e-14, 4.64685804474654130e-14, 2.32342902237305450e-14, 7.74476340790874180e-15, 1.93619085197646560e-15, 3.87238170395005280e-16, 6.45396950657382470e-17, 9.21995643793518570e-18, 1.15249455473504320e-18,

   -3.060000e+01, 5.13557237147994640e-14, 5.13557237147968260e-14, 2.56778618573957750e-14, 8.55928728579683310e-15, 2.13982182144832910e-15, 4.27964364289314180e-16, 7.13273940481018150e-17, 1.01896277211239110e-17, 1.27370346513211610e-18,

   -3.050000e+01, 5.67568523263239960e-14, 5.67568523263207780e-14, 2.83784261631571670e-14, 9.45947538771690840e-15, 2.36486884692815310e-15, 4.72973769385201140e-16, 7.88289615640570200e-17, 1.12612802233958120e-17, 1.40766002791425000e-18,

   -3.040000e+01, 6.27260225925671670e-14, 6.27260225925632420e-14, 3.13630112962776830e-14, 1.04543370987566040e-14, 2.61358427468783960e-15, 5.22716854937043290e-16, 8.71194758226656970e-17, 1.24456394031879920e-17, 1.55570492538600840e-18,

   -3.030000e+01, 6.93229759758606750e-14, 6.93229759758558660e-14, 3.46614879879231310e-14, 1.15538293293045040e-14, 2.88845733232452430e-15, 5.77691466464264150e-16, 9.62819110771637780e-17, 1.37545587252480860e-17, 1.71931984064075470e-18,

   -3.020000e+01, 7.66137370029775430e-14, 7.66137370029716740e-14, 3.83068685014799680e-14, 1.27689561671560770e-14, 3.19223904178706240e-15, 6.38447808356629930e-16, 1.06407968059177450e-16, 1.52011382940936700e-17, 1.90014228674307500e-18,

   -3.010000e+01, 8.46712740607860540e-14, 8.46712740607788850e-14, 4.23356370303822730e-14, 1.41118790101226440e-14, 3.52796975252827130e-15, 7.05593950504698390e-16, 1.17598991750464440e-16, 1.67998559642610260e-17, 2.09998199550986870e-18,

   -3.000000e+01, 9.35762296883929890e-14, 9.35762296883842290e-14, 4.67881148441833550e-14, 1.55960382813886140e-14, 3.89900957034423470e-15, 7.79801914067679430e-16, 1.29966985677557410e-16, 1.85667122395398620e-17, 2.32083902991468430e-18,

   -2.990000e+01, 1.03417727674778080e-13, 1.03417727674767390e-13, 5.17088638373729960e-14, 1.72362879457838680e-14, 4.30907198644240230e-15, 8.61814397287054390e-16, 1.43635732880700410e-16, 2.05193904113928150e-17, 2.56492380139014880e-18,

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   3.000000e-01, 5.74442516811660030e-01, 2.44458311690745720e-01, -1.81980919777883710e-02, -1.90168142062321630e-02, 2.93216717606735060e-03, 1.70598204579083550e-03, -3.96619989543381990e-04, -1.47135961074908440e-04, 4.86790802182843600e-05,

   4.000000e-01, 5.98687660112451670e-01, 2.40260745741529220e-01, -2.37107708141042070e-02, -1.76817683206875460e-02, 3.72086991006114480e-03, 1.43997222858043440e-03, -4.85111608501311170e-04, -1.04626298216035220e-04, 5.67032531438075270e-05,

   5.000000e-01, 6.22459331201854590e-01, 2.35003712201594490e-01, -2.87783974261603720e-02, -1.60594593815974360e-02, 4.36483044084713490e-03, 1.13016810992858680e-03, -5.42105497383336100e-04, -5.78708906527865420e-05, 5.92762197634034040e-05,

   6.000000e-01, 6.45656306225795840e-01, 2.28784240456657210e-01, -3.33238673875909590e-02, -1.42115219385533400e-02, 4.84698674038245340e-03, 7.96055199473061600e-04, -5.66149170755055010e-04, -1.11785776363180860e-05, 5.66412336602477280e-05,

   7.000000e-01, 6.68187772168166720e-01, 2.21712873293108850e-01, -3.72893942201710100e-02, -1.22044526350346600e-02, 5.16008921756597530e-03, 4.57108356135250480e-04, -5.58678296160798530e-04, 3.15880914084643170e-05, 4.96436994272184320e-05,

   8.000000e-01, 6.89974481127613390e-01, 2.13909696520294070e-01, -4.06373836046081060e-02, -1.01057421786886320e-02, 5.30628176052315180e-03, 1.31183858107712160e-04, -5.23552542648549510e-04, 6.74201480805629090e-05, 3.95349355063020810e-05,

   9.000000e-01, 7.10949502625003670e-01, 2.05500307342263570e-01, -4.33501876231358880e-02, -7.98032509405418970e-03, 5.29596124463789070e-03, -1.66736205775554540e-04, -4.66365777962912890e-04, 9.43948827803063110e-05, 2.77403009365558620e-05,

   1.000000e+00, 7.31058578630004900e-01, 1.96611933241481850e-01, -4.54288738364742040e-02, -5.88759675270594200e-03, 5.14611922359971710e-03, -4.25349801037941650e-04, -3.93658206291141790e-04, 1.11724987283642060e-04, 1.56394991495607550e-05,

   1.100000e+00, 7.50260105595117910e-01, 1.87369879547520460e-01, -4.68912058409069810e-02, -3.87915850373224920e-03, 4.87839910350648060e-03, -6.37369522318305400e-04, -3.12151769446088590e-04, 1.19649447598686270e-04, 4.39535348760824660e-06,

   1.200000e+00, 7.68524783499018090e-01, 1.77894440646805430e-01, -4.77690661603623610e-02, -1.99735857190554190e-03, 4.51709579145437390e-03, -7.99430009776364570e-04, -2.28103804212773750e-04, 1.19213830328362910e-04, -5.14980858689474360e-06,

   1.300000e+00, 7.85834983042559390e-01, 1.68298362469059830e-01, -4.81055595824342180e-02, -2.74611731590405520e-04, 4.08729027151194960e-03, -9.11658508830296780e-04, -1.46836905411708300e-04, 1.11995839548817050e-04, -1.25083357559637600e-05,

   1.400000e+00, 8.02183888558581470e-01, 1.58684897495614790e-01, -4.79520193807447880e-02, 1.26658622274202650e-03, 3.61325966507915430e-03, -9.77022016894534080e-04, -7.24646867350922030e-05, 9.98277933086790470e-05, -1.75234957455372060e-05,

   1.500000e+00, 8.17574476193643650e-01, 1.49146452070332860e-01, -4.73651063923763370e-02, 2.61307784655404700e-03, 3.11724537099207850e-03, -1.00056620297502270e-03, -7.80102976522905780e-06, 8.45551079739369940e-05, -2.03066444225203900e-05,

   1.600000e+00, 8.32018385133924680e-01, 1.39763791933060880e-01, -4.64041484978087170e-02, 3.76004778666888090e-03, 2.61860738066120330e-03, -9.88646731697842430e-04, 4.55814033575266490e-05, 6.78538337828735700e-05, -2.11556871820008980e-05,

   1.700000e+00, 8.45534734916465690e-01, 1.30605746966207800e-01, -4.51288221565356030e-02, 4.70976335376686790e-03, 2.13334834774818110e-03, -9.48229364517820420e-04, 8.71882334678036630e-05, 5.11149154480668850e-05, -2.04723258355812330e-05,

   1.800000e+00, 8.58148935099512730e-01, 1.21729340287085030e-01, -4.35972335941857140e-02, 5.47019109445189610e-03, 1.67395968424669120e-03, -8.86307608006953510e-04, 1.17381772299137870e-04, 3.53908570690065840e-05, -1.86903606637618860e-05,

   1.900000e+00, 8.69891525637002010e-01, 1.13180259261931090e-01, -4.18644187703871160e-02, 6.05360545705724280e-03, 1.24952420608354210e-03, -8.09460731799582210e-04, 1.37140621784980930e-04, 2.13929590802673740e-05, -1.62216037519927020e-05,

   2.000000e+00, 8.80797077977882430e-01, 1.04993585403506520e-01, -3.99812505280765300e-02, 6.47527792470100220e-03, 8.66003964518882580e-04, -7.23553848759599000e-04, 1.47830679701737250e-04, 9.52409466015653990e-06, -1.34210561408648320e-05,

   2.100000e+00, 8.90903178804387190e-01, 9.71947048006252950e-02, -3.79937190695184560e-02, 6.75230682549018880e-03, 5.26645053446529490e-04, -6.33566815394946450e-04, 1.51007140072426080e-04, -6.78431444195273990e-08, -1.05695507215487880e-05,

   2.200000e+00, 9.00249510880315130e-01, 8.98003290400685160e-02, -3.59425377751787790e-02, 6.90262241097351280e-03, 2.32440237481248250e-04, -5.43529946386249270e-04, 1.48257384045381190e-04, -7.42839527943956290e-06, -7.87016077876311010e-06,

   2.300000e+00, 9.08877038985144270e-01, 8.28195669907408480e-02, -3.38630193212059100e-02, 6.94418048858966300e-03, -1.73976795857944340e-05, -4.56541019292191090e-04, 1.41086975496147570e-04, -1.27361870108446520e-05, -5.45406812893927270e-06,

   2.400000e+00, 9.16827303506077550e-01, 7.62549990518523320e-02, -3.17851656336421080e-02, 6.89434162824405490e-03, -2.24986027547160530e-04, -3.74838428925960460e-04, 1.30845663828534150e-04, -1.62496950231642210e-05, -3.39187260641409450e-06,

   2.500000e+00, 9.24141819978756440e-01, 7.01037165451081630e-02, -2.97339179227170370e-02, 6.76942168408115490e-03, -3.93368339730086620e-04, -2.99908237158971970e-04, 1.18687212286738230e-04, -1.82641271644429910e-05, -1.70710132276501460e-06,

   2.600000e+00, 9.30861579656653280e-01, 6.43582991757734310e-02, -2.77295184468892250e-02, 6.58439252316387910e-03, -5.26168559702410540e-04, -2.32607033498257950e-04, 1.05555593802384450e-04, -1.90791914477173410e-05, -3.89617153928184060e-07,

   2.700000e+00, 9.37026643943003720e-01, 5.90077124839150850e-02, -2.57879425535990910e-02, 6.35270861473479200e-03, -6.27307713045430010e-04, -1.73287043781767810e-04, 9.21901110565374300e-05, -1.89770546921191960e-05, 5.92484434840341820e-07,

   2.800000e+00, 9.42675824101131490e-01, 5.40381147563840990e-02, -2.39213669826538470e-02, 6.08623461297321240e-03, -7.00781674416260940e-04, -1.21914175348934030e-04, 7.91428101009795250e-05, -1.82089651359146990e-05, 1.28317708681261880e-06,

   2.900000e+00, 9.47846436921582210e-01, 4.94335689366433020e-02, -2.21386477125931100e-02, 5.79525041829335050e-03, -7.50494941518227080e-04, -7.81733147369432530e-05, 6.68027637707623900e-05, -1.69886858896900930e-05, 1.73116951598277200e-06,

   3.000000e+00, 9.52574126822433250e-01, 4.51766597309121370e-02, -2.04457873304717400e-02, 5.48851270404273740e-03, -7.80143233713328820e-04, -4.15580551386109330e-05, 5.54231098116953620e-05, -1.54908971165042420e-05, 1.98477178874566190e-06,

   3.100000e+00, 9.56892745058913970e-01, 4.12490195125302800e-02, -1.88463777560686640e-02, 5.17335497467660920e-03, -7.93136875871795610e-04, -1.14441252533540270e-05, 4.51479527965794610e-05, -1.38529346180267520e-05, 2.08862370841833540e-06,

   3.200000e+00, 9.60834277203235780e-01, 3.76317689545712720e-02, -1.73420090460590200e-02, 4.85581145777831070e-03, -7.92556942875540260e-04, 1.28527968678344200e-05, 3.60372788765845660e-05, -1.21785339929207800e-05, 2.08188494032338610e-06,

   3.300000e+00, 9.64428810727363970e-01, 3.43058797663663290e-02, -1.59326389408494530e-02, 4.54075324118333870e-03, -7.81136715871746850e-04, 3.20333477669136790e-05, 2.80888515200175560e-05, -1.05425695254940430e-05, 1.99749627553838900e-06,

   3.400000e+00, 9.67704535301549650e-01, 3.12524676583614820e-02, -1.46169208631806680e-02, 4.23202787498998340e-03, -7.61261892057005900e-04, 4.67828549658594210e-05, 2.12566585862236030e-05, -8.99607145360522770e-06, 1.86217080497491890e-06,

   3.500000e+00, 9.70687769248643640e-01, 2.84530238797355600e-02, -1.33924903383311200e-02, 3.93259607872179120e-03, -7.34984014121930130e-04, 5.77497348688372760e-05, 1.54658929379206620e-05, -7.57105242822983730e-06, 1.69683959383878260e-06,

   3.600000e+00, 9.73403006423134150e-01, 2.58895935095379770e-02, -1.22562114024881400e-02, 3.64466119950055150e-03, -7.04042619029962590e-04, 6.55318946370028460e-05, 1.06247064779465970e-05, -6.28486711652862430e-06, 1.51734380667807310e-06,

   3.700000e+00, 9.75872978582330910e-01, 2.35449082551804700e-02, -1.12043856218404410e-02, 3.36978867111854600e-03, -6.69892570298140370e-04, 7.06693116302657790e-05, 6.63311834132022210e-06, -5.14397050514005120e-06, 1.33522575415529580e-06,

   3.800000e+00, 9.78118729063869650e-01, 2.14024809183500400e-02, -1.02329269754952420e-02, 3.10901396359800210e-03, -6.33733890292697130e-04, 7.36412131670987950e-05, 3.38951570113992980e-06, -4.14703775227697050e-06, 1.15852126130838430e-06,

   3.900000e+00, 9.80159694265922640e-01, 1.94466680024557300e-02, -9.33750616255004350e-03, 2.86293843734488620e-03, -5.96542131231841840e-04, 7.48665453514710520e-05, 7.95188183514702470e-07, -3.28747035475217040e-06, 9.92494306357317580e-07,

   4.000000e+00, 9.82013790037908450e-01, 1.76627062132911140e-02, -8.51366796419456350e-03, 2.63181317810481970e-03, -5.59097914300470120e-04, 7.47066762395398010e-05, -1.24269413614214560e-06, -2.55534876234905550e-06, 8.40282944541781740e-07,

   4.100000e+00, 9.83697500628559100e-01, 1.60367278856850850e-02, -7.75692519656619260e-03, 2.41561133966800450e-03, -5.22014734440236390e-04, 7.34695105422522440e-05, -2.80929796912433010e-06, -1.93890813171395740e-06, 7.03444793457820960e-07,

   4.200000e+00, 9.85225968306726930e-01, 1.45557596807991810e-02, -7.06283258555579810e-03, 2.21408980691468420e-03, -4.85764488348582080e-04, 7.14143932084043720e-05, -3.98123376869768300e-06, -1.42561795102166160e-06, 5.82402709583479820e-07,

   4.300000e+00, 9.86613082172335230e-01, 1.32077082587400730e-02, -6.42704362421851400e-03, 2.02684115234202150e-03, -4.50700451530002570e-04, 6.87573457418927490e-05, -4.82630245069904450e-06, -1.00294258400730340e-06, 4.76798514972928770e-07,

   4.400000e+00, 9.87871565015725820e-01, 1.19813360491064070e-02, -5.84535316925687610e-03, 1.85333692799611760e-03, -4.17077623458163860e-04, 6.56763134025453160e-05, -5.40368325106174610e-06, -6.58851848354832670e-07, 3.85766258848206380e-07,

   4.500000e+00, 9.89013057369406810e-01, 1.08662297222252340e-02, -5.31372821854368160e-03, 1.69296333866136780e-03, -3.85070493374473810e-04, 6.23162067713295410e-05, -5.76440909701650410e-06, -3.82140937580884150e-07, 3.08137729042538020e-07,

   4.600000e+00, 9.90048198133095750e-01, 9.85276350650618640e-03, -4.82832900299487880e-03, 1.54505030236922430e-03, -3.54788366451459870e-04, 5.87936015930567060e-05, -5.95201382230377430e-06, -1.62608851827789640e-07, 2.42592671010626930e-07,

   4.700000e+00, 9.90986701347152170e-01, 8.93205910024237080e-03, -4.38552223386581410e-03, 1.40889483693683920e-03, -3.26288442377168090e-04, 5.52010205716216920e-05, -6.00326657261755740e-06, 8.86506405301201780e-09, 1.87765077032699150e-07,

   4.800000e+00, 9.91837428846840120e-01, 8.09594358532946330e-03, -3.98188807709751180e-03, 1.28377962835140660e-03, -2.99586865189515150e-04, 5.16107638858808760e-05, -5.94893341840661460e-06, 1.40315385838889720e-07, 1.42315417642172960e-07,

   4.900000e+00, 9.92608458655718120e-01, 7.33690646083770200e-03, -3.61422218297444010e-03, 1.16898754705786820e-03, -2.74667971829368530e-04, 4.80782851857429910e-05, -5.81452533962046400e-06, 2.38731847095225350e-07, 1.04977086195802830e-07,

   5.000000e+00, 9.93307149075715160e-01, 6.64805667079015460e-03, -3.27953388316128140e-03, 1.06381278763365480e-03, -2.51491963154407420e-04, 4.46451297657817080e-05, -5.62100625972984250e-06, 3.10129709169231030e-07, 7.45837869158400470e-08,

   5.100000e+00, 9.93940198508415860e-01, 6.02308029746670070e-03, -2.97504147776283090e-03, 9.67569219974718500e-04, -2.30001209438043020e-04, 4.13414640178132570e-05, -5.38544554286533600e-06, 3.59636242105717580e-07, 5.00832087848591070e-08,

   5.200000e+00, 9.94513701100549600e-01, 5.45619942383627960e-03, -2.69816537102396480e-03, 8.79596458486708520e-04, -2.10125385909201100e-04, 3.81882321625761050e-05, -5.12160710363574680e-06, 3.91584076958449200e-07, 3.05411323561951730e-08,

   5.300000e+00, 9.95033198349943080e-01, 4.94213253142593120e-03, -2.44651967370107920e-03, 7.99264081279476690e-04, -1.91785615006918260e-04, 3.51989792480763220e-05, -4.84047268317013990e-06, 4.09605096400368890e-07, 1.51391212973002660e-08,

   5.400000e+00, 9.95503726839058860e-01, 4.47605668860335490e-03, -2.21790277074585940e-03, 7.25974364620968290e-04, -1.74897772363819330e-04, 3.23813797045458010e-05, -4.55070047506629860e-06, 4.16720717412710390e-07, 3.16814392573476410e-09,

   5.500000e+00, 9.95929862284103850e-01, 4.05357169486976650e-03, -2.01028725239550500e-03, 6.59163838992845080e-04, -1.59375094194757470e-04, 2.97385092867708520e-05, -4.25902259388678110e-06, 4.15426030123352990e-07, -5.98016885505318570e-09,

   5.600000e+00, 9.96315760100564000e-01, 3.67066627579938630e-03, -1.82180952274887910e-03, 5.98303921724940090e-04, -1.45130205452988760e-04, 2.72698956944830560e-05, -3.97058622553927970e-06, 4.07766414969878050e-07, -1.28234186230422650e-08,

   5.700000e+00, 9.96665192692586690e-01, 3.32368636763575840e-03, -1.65075933023153730e-03, 5.42900836868885190e-04, -1.32076671237156660e-04, 2.49723800306181780e-05, -3.68924396212467030e-06, 3.95406070736085290e-07, -1.77986544427550980e-08,

   5.800000e+00, 9.96981583675291550e-01, 3.00930548759914500e-03, -1.49556940698976870e-03, 4.92494995082163160e-04, -1.20130158692274330e-04, 2.28408178788691450e-05, -3.41779901612000880e-06, 3.79688433955302940e-07, -2.12723568777360370e-08,

   5.900000e+00, 9.97268039236988920e-01, 2.72449715340041280e-03, -1.35480535737818120e-03, 4.46659974161181810e-04, -1.09209283108593270e-04, 2.08686453886228180e-05, -3.15821088901942300e-06, 3.61688823780909770e-07, -2.35498468733292700e-08,

   6.000000e+00, 9.97527376843365230e-01, 2.46650929136004800e-03, -1.22715589769015220e-03, 4.05001213808975830e-04, -9.92362000505793020e-05, 1.90483324974313430e-05, -2.91176675437529030e-06, 3.42259858984122120e-07, -2.48839237613873960e-08,

   6.100000e+00, 9.97762151478723710e-01, 2.23284055527215100e-03, -1.11142351870121400e-03, 3.67154515600090470e-04, -9.01369950517951440e-05, 1.73717423893457380e-05, -2.67922338831252450e-06, 3.22070306219285100e-07, -2.54826405262093900e-08,

   6.200000e+00, 9.97974679610950100e-01, 2.02121846637157500e-03, -1.00651561821512090e-03, 3.32784420306461000e-04, -8.18419135636989510e-05, 1.58304135300521570e-05, -2.46092400072710690e-06, 3.01638062064545770e-07, -2.55161950143962260e-08,

   6.300000e+00, 9.98167061057507190e-01, 1.82957927732589060e-03, -9.11436131557156830e-04, 3.01582519222294770e-04, -7.42854663041933490e-05, 1.44157781558078800e-05, -2.25689382743798350e-06, 2.81357968618219770e-07, -2.51229617521266020e-08,

   6.400000e+00, 9.98341198919825530e-01, 1.65604945915082470e-03, -8.25277672943750660e-04, 2.73265743380650350e-04, -6.74064387680514710e-05, 1.31193289221307530e-05, -2.06691786360688020e-06, 2.61525130420608030e-07, -2.44147172473251530e-08,

   6.500000e+00, 9.98498817743262990e-01, 1.49892870856904940e-03, -7.47214189103107150e-04, 2.47574664154802410e-04, -6.11478282924288020e-05, 1.19327435270117310e-05, -1.89060366781194860e-06, 2.42354351223451110e-07, -2.34811272785029050e-08,

   6.600000e+00, 9.98641480049571100e-01, 1.35667437397324320e-03, -6.76494117783343330e-04, 2.24271830305211500e-04, -5.54567275815383040e-05, 1.08479754917148960e-05, -1.72743175318997390e-06, 2.23996251086150210e-07, -2.23935715918401650e-08,

   6.700000e+00, 9.98770601378722530e-01, 1.22788720030741820e-03, -6.12434037322566940e-04, 2.03140159741224220e-04, -5.02841698614196030e-05, 9.85731788582393180e-06, -1.57679571105668350e-06, 2.06550563194937130e-07, -2.12083825151639430e-08,

   6.800000e+00, 9.98887463967139680e-01, 1.11129829643590400e-03, -5.54412788819910760e-04, 1.83981398835655990e-04, -4.55849477472547160e-05, 8.95344559655879560e-06, -1.43803388408028780e-06, 1.90077049463261540e-07, -1.99695713410904680e-08,

   6.900000e+00, 9.98993229179914400e-01, 1.00575723260145560e-03, -5.01866049266854600e-04, 1.66614657822645790e-04, -4.13174153633906250e-05, 8.12944074027207590e-06, -1.31045411900319600e-06, 1.74604416741991380e-07, -1.87111114252562830e-08,

   7.000000e+00, 9.99088948805599400e-01, 9.10221180121826540e-04, -4.54281331967594540e-04, 1.50875027423562060e-04, -3.74432811738753480e-05, 7.37880497244096900e-06, -1.19335288038025050e-06, 1.60137562702363960e-07, -1.74588408352964750e-08,

   7.100000e+00, 9.99175575313601680e-01, 8.23745010334750930e-04, -4.11193389445558120e-04, 1.36612279213740410e-04, -3.39273972842914250e-05, 6.69546174926586470e-06, -1.08602979344121380e-06, 1.46663432811572760e-07, -1.62320407865954220e-08,

   7.200000e+00, 9.99253971166163320e-01, 7.45472274815779240e-04, -3.72179993596051240e-04, 1.23689650223444190e-04, -3.07375495998706260e-05, 6.07375100916500350e-06, -9.87798502316527490e-07, 1.34155727489317400e-07, -1.50447394841792490e-08,

   7.300000e+00, 9.99324917269367120e-01, 6.74626993939636430e-04, -3.36858067936590810e-04, 1.11982710742320710e-04, -2.78442521156261930e-05, 5.50841825822966410e-06, -8.97994575796458760e-07, 1.22578661398167780e-07, -1.39067846545079820e-08,

   7.400000e+00, 9.99389120640565620e-01, 6.10506185842614760e-04, -3.04880147293569100e-04, 1.01378313170817010e-04, -2.52205477252674230e-05, 4.99459964447470730e-06, -8.15981062985799730e-07, 1.11889944579739760e-07, -1.28247221712007600e-08,

   7.500000e+00, 9.99447221363076400e-01, 5.52473072702160420e-04, -2.75931141039014920e-04, 9.17736189542991000e-05, -2.28418172279072060e-05, 4.52780427792291130e-06, -7.41152192379702000e-07, 1.02043127397168810e-07, -1.18025128443360290e-08,

   7.600000e+00, 9.99499798892920400e-01, 4.99950905932039760e-04, -2.49725376969387250e-04, 8.30752000803310330e-05, -2.06855976523322050e-05, 4.10389478553116230e-06, -6.72935617035874460e-07, 9.29894275301906520e-08, -1.08421146857547030e-08,

   7.700000e+00, 9.99547377776759500e-01, 4.52417356363562560e-04, -2.26003904032111420e-04, 7.51982112629214300e-05, -1.87314105805525660e-05, 3.71906687172526550e-06, -6.10793532989768880e-07, 8.46791371308547520e-08, -9.94395377704565340e-09,

   7.800000e+00, 9.99590432835013920e-01, 4.09399419723413860e-04, -2.04532033302023900e-04, 6.80656287356991040e-05, -1.69606008127532920e-05, 3.36982847838178880e-06, -5.54222935506773140e-07, 7.70626912387012800e-08, -9.10730322364054310e-09,

   7.900000e+00, 9.99629393859373660e-01, 3.70468791714924570e-04, -1.85097097848342280e-04, 6.16075514935193710e-05, -1.53561854558387080e-05, 3.05297899532582600e-06, -5.02755226147291380e-07, 7.00914642564754660e-08, -8.33058653549456410e-09,

   8.000000e+00, 9.99664649869533520e-01, 3.35237670756474240e-04, -1.67506413381611650e-04, 5.57605608301848110e-05, -1.39027133219421480e-05, 2.76558885777998050e-06, -4.55955341173887610e-07, 6.37183493199892450e-08, -7.61161908358632620e-09,

   8.100000e+00, 9.99696552969971060e-01, 3.03354949928885320e-04, -1.51585422805842160e-04, 5.04671340958345240e-05, -1.25861343788082970e-05, 2.50497977566681800e-06, -4.13420537045400910e-07, 5.78981654174098590e-08, -6.94779899154796610e-09,

   8.200000e+00, 9.99725421843898680e-01, 2.74502762937523960e-04, -1.37176009006269880e-04, 4.56751087227269870e-05, -1.13936788903748580e-05, 2.26870576703247800e-06, -3.74778940336349630e-07, 5.25879288228433850e-08, -6.33625688386961700e-09,

   8.300000e+00, 9.99751544918160650e-01, 2.48393351911641610e-04, -1.24134961365243270e-04, 4.13371927279997050e-05, -1.03137458146273360e-05, 2.05453511063052970e-06, -3.39687946303437860e-07, 4.77470185436928630e-08, -5.77397227994794290e-09,

   8.400000e+00, 9.99775183229766660e-01, 2.24766227653115970e-04, -1.12332582609199500e-04, 3.74105180850925840e-05, -9.33579997993102270e-06, 1.86043328799364710e-06, -3.07832531578974220e-07, 4.33372598136731630e-08, -5.25786305429553240e-09,

   8.500000e+00, 9.99796573021944800e-01, 2.03385595519805850e-04, -1.01651423642826370e-04, 3.38562335528360220e-05, -8.45027753490249690e-06, 1.68454695073643520e-06, -2.78923531334687870e-07, 3.93229449984878610e-08, -4.78485323932654510e-09,

   8.600000e+00, 9.99815928095036610e-01, 1.84038022497226820e-04, -9.19851350192266420e-05, 3.06391337558131090e-05, -7.64849915592080710e-06, 1.52518892241238460e-06, -2.52695919086895630e-07, 3.56708074528069760e-08, -4.35192349451369590e-09,

   8.700000e+00, 9.99833441935222610e-01, 1.66530323188393110e-04, -8.32374246258395520e-05, 2.77273215161909540e-05, -6.92259049692898490e-06, 1.38082422437826690e-06, -2.28907117570329520e-07, 3.23499607343890290e-08, -3.95614777483459150e-09,

   8.800000e+00, 9.99849289641940200e-01, 1.50687644447730390e-04, -7.53211120350152910e-05, 2.50919006417658550e-05, -6.26540937530153360e-06, 1.25005710047956180e-06, -2.07335361348965880e-07, 2.93318130250367760e-08, -3.59471907670550150e-09,

   8.900000e+00, 9.99863629672920530e-01, 1.36351730213388530e-04, -6.81572707766472030e-05, 2.27066965745659000e-05, -5.67047920292358180e-06, 1.13161900488518310e-06, -1.87778125690477490e-07, 2.65899645286942290e-08, -3.26496659905701230e-09,

   9.000000e+00, 9.99876605424013800e-01, 1.23379349764848930e-04, -6.16744505398747690e-05, 2.05480024968597550e-05, -5.13192819138484970e-06, 1.02435751019101220e-06, -1.70050631402633010e-07, 2.41000939307157270e-08, -2.96436621206719760e-09,

   9.100000e+00, 9.99888346659370430e-01, 1.11640874161088810e-04, -5.58079720039935180e-05, 1.85943486753980140e-05, -4.64443388288644270e-06, 9.27226088269874940e-07, -1.53984431565228430e-07, 2.18398386394125530e-08, -2.69054576040561850e-09,

   9.200000e+00, 9.99898970806092250e-01, 1.01018987009750880e-04, -5.04992876380484690e-05, 1.68262929992220030e-05, -4.20317258295546220e-06, 8.39274713695973640e-07, -1.39426083184529280e-07, 1.97886724333609890e-08, -2.44128642819715730e-09,

   9.300000e+00, 9.99908584126147800e-01, 9.14075169901689510e-05, -4.56954023970421620e-05, 1.52262308308658500e-05, -3.80377329648253310e-06, 7.59641238451180340e-07, -1.26235904580310470e-07, 1.79277832574711560e-08, -2.21452114796530720e-09,

   9.400000e+00, 9.99917282777148310e-01, 8.27103807127096620e-05, -4.13483487833612670e-05, 1.37782224450406340e-05, -3.44227579427705870e-06, 6.87543486658803350e-07, -1.14286817650953480e-07, 1.62399532076432020e-08, -2.00833083607346070e-09,

   9.500000e+00, 9.99925153772489360e-01, 7.48406255528386630e-05, -3.74147112379321680e-05, 1.24678364729066370e-05, -3.11509246276708830e-06, 6.22272018989971020e-07, -1.03463272937304910e-07, 1.47094421850544280e-08, -1.82093907471919660e-09,

   9.600000e+00, 9.99932275850380250e-01, 6.77195630593283900e-05, -3.38551952798433820e-05, 1.12820079040004520e-05, -2.81897361428864240e-06, 5.63183517913633550e-07, -9.36602545299373900e-08, 1.33218762596424920e-08, -1.65070572874812520e-09,

   9.700000e+00, 9.99938720260383440e-01, 6.12759844101147830e-05, -3.06342372286879860e-05, 1.02089093220870340e-05, -2.55097595934782470e-06, 5.09694746927039620e-07, -8.47823612630032110e-08, 1.20641414358960210e-08, -1.49611987895293270e-09,

   9.800000e+00, 9.99944551475277170e-01, 5.54454501839007800e-05, -2.77196507235351010e-05, 9.23783416603736810e-06, -2.30843396511461800e-06, 4.61277039162938400e-07, -7.67429602510730080e-08, 1.09242832443545460e-08, -1.35579236756069850e-09,

   9.900000e+00, 9.99949827835316270e-01, 5.01696474376548870e-05, -2.50823065990140750e-05, 8.35909091275179450e-06, -2.08893384610551040e-06, 4.17451273209463760e-07, -6.94634086049875410e-08, 9.89141237430900580e-09, -1.22844818252731630e-09,

   1.000000e+01, 9.99954602131297610e-01, 4.53958077359516730e-05, -2.26958429950565990e-05, 7.56390717663194530e-06, -1.89028995346304090e-06, 3.77783296510341030e-07, -6.28723390698916470e-08, 8.95561640484862610e-09, -1.11291885194540550e-09,

   1.010000e+01, 9.99958922132235250e-01, 4.10761803735431730e-05, -2.05364028648659190e-05, 6.84434280966311460e-06, -1.71052334841719230e-06, 3.41879759270231690e-07, -5.69050053322319550e-08, 8.10787757266656900e-09, -1.00813497577477500e-09,

   1.020000e+01, 9.99962831062897070e-01, 3.71675555730039750e-05, -1.85823963079666270e-05, 6.19321116831338960e-06, -1.54784236341642940e-06, 3.09384324322486770e-07, -5.15026828177809950e-08, 7.33999642781074730e-09, -9.13118987119022980e-10,

   1.030000e+01, 9.99966368035961280e-01, 3.36308329296659620e-05, -1.68142853938692990e-05, 5.60400778868745020e-06, -1.40062497106619520e-06, 2.79974220887243180e-07, -4.66121209299951520e-08, 6.64452116626694230e-09, -8.26978207671312410e-10,

   1.040000e+01, 9.99969568443099480e-01, 3.04306308209097750e-05, -1.52143893589815410e-05, 5.07084578019280360e-06, -1.26740279644937950e-06, 2.53357112530681430e-07, -4.21850428417584110e-08, 6.01468238557349960e-09, -7.48898240323380870e-10,

   1.050000e+01, 9.99972464308885420e-01, 2.75349329002983130e-05, -1.37667082567419530e-05, 4.58839731085322790e-06, -1.14684662267372210e-06, 2.29268251912926360e-07, -3.81776891415831150e-08, 5.44433298228359790e-09, -6.78136725116404050e-10,

   1.060000e+01, 9.99975084611060550e-01, 2.49147681628238800e-05, -1.24567633202728270e-05, 4.15184061479803880e-06, -1.03775325265255170e-06, 2.07467897071115020e-07, -3.45504018382091540e-08, 4.92789289455700780e-09, -6.14017471766445350e-10,

   1.070000e+01, 9.99977455570349560e-01, 2.25439213991371070e-05, -1.12714524597185250e-05, 3.75681200479746720e-06, -9.39033602238237710e-07, 1.87738966018924190e-07, -3.12672454379726200e-08, 4.46029838670065200e-09, -5.55924972150872550e-10,

   1.080000e+01, 9.99979600912720090e-01, 2.03986711571594440e-05, -1.01989194643063940e-05, 3.39936242040826270e-06, -8.49701910954555350e-07, 1.69884908351422640e-07, -2.82956620217398040e-08, 4.03695557286271950e-09, -5.03299288768600680e-10,

   1.090000e+01, 9.99981542106704310e-01, 1.84575526018420250e-05, -9.22843561338458930e-06, 3.07591808572562090e-06, -7.68865966779615540e-07, 1.53727774324813170e-07, -2.56061574585065820e-08, 3.65369788255584290e-09, -4.55631309778496850e-10,

   1.100000e+01, 9.99983298578151940e-01, 1.67011429106034340e-05, -8.35029252246862110e-06, 2.78324489025938510e-06, -6.95718250776955250e-07, 1.39106463536484480e-07, -2.31720160978619510e-08, 3.30674717983455920e-09, -4.12458357364119000e-10,

   1.110000e+01, 9.99984887904558970e-01, 1.51118670655464890e-05, -7.55570516079585820e-06, 2.51841614239820780e-06, -6.29527915921011750e-07, 1.25875136865743850e-07, -2.09690414812554580e-08, 2.99267825968001440e-09, -3.73360133536596960e-10,

   1.120000e+01, 9.99986325990915410e-01, 1.36738221060752420e-05, -6.83672407706992100e-06, 2.27878337760155160e-06, -5.69633522273675250e-07, 1.13901776754521030e-07, -1.89753208008990390e-08, 2.70838645858564190e-09, -3.37954985802325990e-10,

   1.130000e+01, 9.99987627228825620e-01, 1.23726180889609920e-05, -6.18615596090805290e-06, 2.06194993314845680e-06, -5.15436457797194670e-07, 1.03066882215768930e-07, -1.71710110142078850e-08, 2.45105813081807930e-09, -3.05896474172170790e-10,

   1.140000e+01, 9.99988804640494890e-01, 1.11952341690387850e-05, -5.59749174984812630e-06, 1.86574702823836450e-06, -4.66394980589778340e-07, 9.32622861614335840e-08, -1.55381446904247040e-08, 2.21814375683459170e-09, -2.76870220601440280e-10,

   1.150000e+01, 9.99989870009019180e-01, 1.01298883641566480e-05, -5.06484156640055810e-06, 1.68821211272117090e-06, -4.22018824253730030e-07, 8.43900837478793370e-08, -1.40604538242312510e-08, 2.00733346547603950e-09, -2.50591021986417530e-10,

   1.160000e+01, 9.99990833996280190e-01, 9.16591970422912340e-06, -4.58287583726045680e-06, 1.52756926995416270e-06, -3.81864313499765880e-07, 7.63616614509696120e-08, -1.27232099987598100e-08, 1.81653476653133770e-09, -2.26800208194065460e-10,

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   1.180000e+01, 9.99992495498402860e-01, 7.50444527956575040e-06, -3.75216632266128950e-06, 1.25068456322867110e-06, -3.12652368961592510e-07, 6.25229652442683430e-08, -1.04179914531162750e-08, 1.48756946140725130e-09, -1.85767439983336050e-10,

   1.190000e+01, 9.99993209641301890e-01, 6.79031258912383860e-06, -3.39511018590376710e-06, 1.13167265650891500e-06, -2.82902794965877070e-07, 5.65744114695242290e-08, -9.42701947414724110e-09, 1.34613163960855980e-09, -1.68120109240106090e-10,

   1.200000e+01, 9.99993855825397790e-01, 6.14413685133317550e-06, -3.07203067501699310e-06, 1.02398505813788140e-06, -2.55983681274537310e-07, 5.11917030553082150e-08, -8.53027282820451160e-09, 1.21813108896187020e-09, -1.52146565740089000e-10,

   1.210000e+01, 9.99994440517666390e-01, 5.55945142579066820e-06, -2.77969480522334770e-06, 9.26544330131622270e-07, -2.31625780190364130e-07, 4.63210351783787160e-08, -7.71879894849246740e-09, 1.10229312885685030e-09, -1.37688538516805890e-10,

   1.220000e+01, 9.99994969569698240e-01, 5.03040499652609140e-06, -2.51517719316132110e-06, 8.38375527779919400e-07, -2.09585447070190430e-07, 4.19137155214044240e-08, -6.98449465133022680e-09, 9.97463647539518500e-10, -1.24602634882611740e-10,

   1.230000e+01, 9.99995448276255190e-01, 4.55170302661081300e-06, -2.27583079521066120e-06, 7.58596453101359750e-07, -1.89642207361636460e-07, 3.79256791492816810e-08, -6.32002577174939780e-09, 9.02597761305668940e-10, -1.12758957765584690e-10,

   1.240000e+01, 9.99995881428255130e-01, 4.11855478219938940e-06, -2.05926042853633910e-06, 6.86408834539737520e-07, -1.71596554534475850e-07, 3.43170492981490410e-08, -5.71875436249462110e-09, 8.16749528846053340e-10, -1.02039848611428460e-10,

   1.250000e+01, 9.99996273360715840e-01, 3.72662539634620680e-06, -1.86329881038450400e-06, 6.21090344987523090e-07, -1.55267957048707560e-07, 3.10517397537616080e-08, -5.17467275194488770e-09, 7.39062624692496680e-10, -9.23387449901975160e-11,

   1.260000e+01, 9.99996627996136310e-01, 3.37199249328072390e-06, -1.68598487626864630e-06, 5.61987378546745830e-07, -1.40493054560707270e-07, 2.80970948990030250e-08, -4.68234382074757800e-09, 6.68761884064919670e-10, -8.35591428840212360e-11,

   1.270000e+01, 9.99996948883751350e-01, 3.05110693938728140e-06, -1.52554416041168150e-06, 5.08508513977657970e-07, -1.27124025435932610e-07, 2.54235638765753120e-08, -4.23684691561620810e-09, 6.05145639118406560e-10, -7.56136544244528810e-11,

   1.280000e+01, 9.99997239235049800e-01, 2.76075732836992650e-06, -1.38037104238289500e-06, 4.60118599613961530e-07, -1.15027109329103450e-07, 2.30044056455347370e-08, -3.83372887222818370e-09, 5.47578773672759970e-10, -6.84231525942881740e-11,

   1.290000e+01, 9.99997501955914410e-01, 2.49803784540252620e-06, -1.24901268249259760e-06, 4.16333400707343890e-07, -1.04081270126766200e-07, 2.08154220123400230e-08, -3.46895966789292030e-09, 4.95486430012472260e-10, -6.19159951078822260e-11,

   1.300000e+01, 9.99997739675702050e-01, 2.26031918883764270e-06, -1.13015448536443780e-06, 3.76714755763438350e-07, -9.41769859371668570e-08, 1.88347159911528980e-08, -3.13889226903028720e-09, 4.48348307309722370e-10, -5.60273203362117570e-11,

   1.310000e+01, 9.99997954773558460e-01, 2.04522225861253610e-06, -1.02260694636362590e-06, 3.40866193501335580e-07, -8.52151540718136390e-08, 1.70424730968043850e-08, -2.84022627887281730e-09, 4.05693496684508060e-10, -5.06984087491533260e-11,

   1.320000e+01, 9.99998149402227090e-01, 1.85059434815133000e-06, -9.25293749369885780e-07, 3.08428966659113580e-07, -7.71061001041075170e-08, 1.54207633994051250e-08, -2.56997502752137550e-09, 3.67095802910523550e-10, -4.58761039091408600e-11,

   1.330000e+01, 9.99998325509594440e-01, 1.67448760159332860e-06, -8.37240996883241340e-07, 2.79078463023493540e-07, -6.97686811239346070e-08, 1.39533623741242100e-08, -2.32543577985619090e-09, 3.32169507337571490e-10, -4.15122875693579500e-11,

   1.340000e+01, 9.99998484858183550e-01, 1.51513952083031450e-06, -7.57567464763911470e-07, 2.52520957823951480e-07, -6.31294742432537220e-08, 1.26255887651222860e-08, -2.10416276712682460e-09, 3.00565530764879660e-10, -3.75634039080735170e-11,

   1.350000e+01, 9.99998629042793130e-01, 1.37095532733418150e-06, -6.85475784146004530e-07, 2.28490675037187380e-07, -5.71220422554890060e-08, 1.14241578507341960e-08, -1.90394277558092690e-09, 2.71967958795808980e-10, -3.39900283708562110e-11,

   1.360000e+01, 9.99998759506458890e-01, 1.24049200230635130e-06, -6.20244462330858940e-07, 2.06747128230650730e-07, -5.16862691192765790e-08, 1.03370486493598750e-08, -1.72277305049099810e-09, 2.46090895663075560e-10, -3.07564769965723200e-11,

   1.370000e+01, 9.99998877554894690e-01, 1.12244384546689700e-06, -5.61220662851848130e-07, 1.87072714364296580e-07, -4.67677586323083690e-08, 9.35338374359172940e-09, -1.55884129662682110e-09, 2.22675615662537220e-10, -2.78304524736294260e-11,

   1.380000e+01, 9.99998984369560470e-01, 1.01562940799105980e-06, -5.07813672491387920e-07, 1.69270536495415590e-07, -4.23172902904494250e-08, 8.46332052519952860e-09, -1.41050757680551750e-09, 2.01487984198645400e-10, -2.51827235121774230e-11,

   1.390000e+01, 9.99999081019486650e-01, 9.18979668846808110e-07, -4.59488989898996230e-07, 1.53162433617502940e-07, -3.82903268972099070e-08, 7.65795277692489650e-09, -1.27628792882307610e-09, 1.82316123050208660e-10, -2.27868344282110090e-11,

   1.400000e+01, 9.99999168471972340e-01, 8.31527336225271330e-07, -4.15762976674349830e-07, 1.38587197933167670e-07, -3.46465690045819890e-08, 6.92922160969115450e-09, -1.15483953800280790e-09, 1.64968296833256300e-10, -2.06188421188755080e-11,

   1.410000e+01, 9.99999247602266880e-01, 7.52397167011296440e-07, -3.76198017403725340e-07, 1.25398961733719140e-07, -3.13495517333212480e-08, 6.26983486681250500e-09, -1.04494731794733730e-09, 1.49270999789335270e-10, -1.86570778668548890e-11,

   1.420000e+01, 9.99999319202329100e-01, 6.80797207426378850e-07, -3.40398140228036230e-07, 1.13465737752892160e-07, -2.83662799435664040e-08, 5.67319419099261900e-09, -9.45511765996212160e-10, 1.35067223981535910e-10, -1.68819316474784270e-11,

   1.430000e+01, 9.99999383988753320e-01, 6.16010867192104680e-07, -3.08005054126430060e-07, 1.02668098395962280e-07, -2.56668981094086800e-08, 5.13332902615417150e-09, -8.55537972502435670e-10, 1.22214891754338360e-10, -1.52756568269569580e-11,

   1.440000e+01, 9.99999442609941450e-01, 5.57389747901928650e-07, -2.78694563267460070e-07, 9.28979806336570320e-08, -2.32243915974626420e-08, 4.64483689518981040e-09, -7.74125674469692400e-10, 1.10585436923242510e-10, -1.38221933357031860e-11,

   1.450000e+01, 9.99999495652591830e-01, 5.04347153835143390e-07, -2.52173322551391810e-07, 8.40576046064723110e-08, -2.10143163630518180e-08, 4.20282935724158810e-09, -7.00460254446204730e-10, 1.00062520620668450e-10, -1.25070075785966340e-11,

   1.460000e+01, 9.99999543647571490e-01, 4.56352220275225500e-07, -2.28175901880168750e-07, 7.60584951218552990e-08, -1.90145543614346250e-08, 3.80288310471801340e-09, -6.33804594951415360e-10, 9.05408690493893990e-11, -1.13169475058356990e-11,

   1.470000e+01, 9.99999587075228960e-01, 4.12924600573522180e-07, -2.06462129779964910e-07, 6.88205962555279310e-08, -1.72050922283712700e-08, 3.44099571150165140e-09, -5.73491707208582470e-10, 8.19252215961030130e-11, -1.02401114150637630e-11,

   1.480000e+01, 9.99999626370201570e-01, 3.73629658790020030e-07, -1.86814689795835930e-07, 6.22714701992147370e-08, -1.55678210168108540e-08, 3.11354559018851020e-09, -5.18918060651933660e-10, 7.41293788468815700e-11, -9.26572918904046500e-12,

   1.490000e+01, 9.99999661925765950e-01, 3.38074119802057690e-07, -1.69036945606879720e-07, 5.63455723395658040e-08, -1.40863549868900440e-08, 2.81725575819483420e-09, -4.69537546646774780e-10, 6.70753410335421040e-11, -8.38405479444785790e-12,

   1.500000e+01, 9.99999694097773120e-01, 3.05902133349452300e-07, -1.52950973098582340e-07, 5.09835953154601910e-08, -1.27458676368528910e-08, 2.54916105057859740e-09, -4.24856016172213160e-10, 6.06925283347279390e-11, -7.58626897755046640e-12,

   1.510000e+01, 9.99999723208210730e-01, 2.76791712626669860e-07, -1.38395779699661530e-07, 4.61318754907927890e-08, -1.15329433348335780e-08, 2.30657845183041010e-09, -3.84426336931071180e-10, 5.49170752662939320e-11, -6.86439119237450490e-12,

   1.520000e+01, 9.99999749548425520e-01, 2.50451511780763260e-07, -1.25225693164406170e-07, 4.17418559041674510e-08, -1.04354430674030120e-08, 2.08708025003213170e-09, -3.47843920526066450e-10, 4.96911921302037290e-11, -6.21119988774924510e-12,

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   1.540000e+01, 9.99999794947584510e-01, 2.05052373468196750e-07, -1.02526144687613890e-07, 3.41753535315569260e-08, -8.54382436740518010e-09, 1.70875926729129500e-09, -2.84791342487242120e-10, 4.06839435767306050e-11, -5.08535946704138450e-12,

   1.550000e+01, 9.99999814460898140e-01, 1.85539067412074810e-07, -9.27694992812854920e-08, 3.09231434772669350e-08, -7.73077439440740950e-09, 1.54615028892062660e-09, -2.57690184834589790e-10, 3.68124464096959630e-11, -4.60144651691731410e-12,

   1.560000e+01, 9.99999832117275170e-01, 1.67882696630342710e-07, -8.39413201305668000e-08, 2.79804212537906240e-08, -6.99509591858538340e-09, 1.39901542577429730e-09, -2.33167984982521050e-10, 3.33093542418082680e-11, -4.16357980575916520e-12,

   1.570000e+01, 9.99999848093426350e-01, 1.51906550605678100e-07, -7.59532522272354270e-08, 2.53177353586795660e-08, -6.32942614780639910e-09, 1.26588215281746030e-09, -2.10979333222425560e-10, 3.01396117234032380e-11, -3.76737820988777190e-12,

   1.580000e+01, 9.99999862549246110e-01, 1.37450735006717020e-07, -6.87253486106513630e-08, 2.29084369417482830e-08, -5.72710293787126690e-09, 1.14541806854910020e-09, -1.90902171750383300e-10, 2.72714989147432330e-11, -3.40887738775178280e-12,

   1.590000e+01, 9.99999875629413060e-01, 1.24370571424198600e-07, -6.21852702440583400e-08, 2.07284131026607290e-08, -5.18209811965393330e-09, 1.03641756152715300e-09, -1.72735572787080440e-10, 2.46763139790698300e-11, -3.08449014268216460e-12,

   1.600000e+01, 9.99999887464837920e-01, 1.12535149390932300e-07, -5.62675620313048730e-08, 1.87558455676622010e-08, -4.68895717053024010e-09, 9.37789745552565470e-10, -1.56297728074587390e-10, 2.23280860534098520e-11, -2.79097055313068040e-12,

   1.610000e+01, 9.99999898173973390e-01, 1.01826016194119430e-07, -5.09129977285210830e-08, 1.69709923304823300e-08, -4.24274462644235940e-09, 8.48547542817657510e-10, -1.41424129646242390e-10, 2.02033154286029420e-11, -2.52538151268419670e-12,

   1.620000e+01, 9.99999907864000170e-01, 9.21359913675753000e-08, -4.60679871947459620e-08, 1.53559900722216440e-08, -3.83899468837582570e-09, 7.67797805803683330e-10, -1.27965923676962550e-10, 1.82807384424077860e-11, -2.28506535603968290e-12,

   1.630000e+01, 9.99999916631899020e-01, 8.33680939991463290e-08, -4.16840400493334860e-08, 1.38946753829519570e-08, -3.47366652899215460e-09, 6.94732379100357940e-10, -1.15788420950832340e-10, 1.65411147361098290e-11, -2.06761727781812690e-12,

   1.640000e+01, 9.99999924565422190e-01, 7.54345721176905650e-08, -3.77172803684701810e-08, 1.25724229959070900e-08, -3.14310385218560890e-09, 6.28620011720849680e-10, -1.04769749048147460e-10, 1.49670347482546070e-11, -1.87086127889144730e-12,

   1.650000e+01, 9.99999931743970950e-01, 6.82560244455773610e-08, -3.41280075639034880e-08, 1.13759994153780210e-08, -2.84399830088317200e-09, 5.68799038992244420e-10, -9.47996327706489370e-11, 1.35427455211542820e-11, -1.69282840006403590e-12,

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   1.690000e+01, 9.99999954246614360e-01, 4.57533835077131030e-08, -2.28766896604843540e-08, 7.62556182458008140e-09, -1.90638975835440750e-09, 3.81277672554679400e-10, -6.35461857204007500e-11, 9.07799994900577560e-12, -1.13474334800917420e-12,

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   1.710000e+01, 9.99999962540295880e-01, 3.74597027564935260e-08, -1.87298499750173800e-08, 6.24328238951959010e-09, -1.56082012963683560e-09, 3.12163838830165950e-10, -5.20272441059724400e-11, 7.43244562493773470e-12, -9.29051248425964030e-13,

   1.720000e+01, 9.99999966105057920e-01, 3.38949409642348850e-08, -1.69474693332503790e-08, 5.64915567850545770e-09, -1.41228853667072560e-09, 2.82457554151907220e-10, -4.70762079645806580e-11, 6.72515797759035930e-12, -8.40641100005626450e-13,

   1.730000e+01, 9.99999969330587990e-01, 3.06694110644097520e-08, -1.53347045915920700e-08, 5.11156757012218340e-09, -1.27789157899298040e-09, 2.55578190383583000e-10, -4.25963232589326220e-11, 6.08517709270804790e-12, -7.60644150518967430e-13,

   1.740000e+01, 9.99999972249168370e-01, 2.77508308821900330e-08, -1.38754146709863800e-08, 4.62513771025639040e-09, -1.15628417086124560e-09, 2.31256731491117960e-10, -3.85427543548140800e-11, 5.50609798582152590e-12, -6.88259803440484810e-13,

   1.750000e+01, 9.99999974890009020e-01, 2.51099902964165140e-08, -1.25549945176966280e-08, 4.18499775222447320e-09, -1.04624922788559510e-09, 2.09249761508916940e-10, -3.48749322287556890e-11, 4.98212516904363390e-12, -6.22763644507803410e-13,

   1.760000e+01, 9.99999977279540600e-01, 2.27204588952999930e-08, -1.13602289314307310e-08, 3.78674263299741260e-09, -9.46685486176279800e-10, 1.89337028406031900e-10, -3.15561484579332660e-11, 4.50801465311386740e-12, -5.63500192849079330e-13,

   1.770000e+01, 9.99999979441678180e-01, 2.05583214523152080e-08, -1.02791603035130130e-08, 3.42638648607461990e-09, -8.56596480637136030e-10, 1.71319239774823510e-10, -2.85531878449379760e-11, 4.07902146807789830e-12, -5.09876341781741150e-13,

   1.780000e+01, 9.99999981398061120e-01, 1.86019385748511750e-08, -9.30096894139346290e-09, 3.10032274977641010e-09, -7.75080572100068920e-10, 1.55016068282403210e-10, -2.58359960011984590e-11, 3.69085217754266420e-12, -4.61355423678786930e-13,

   1.790000e+01, 9.99999983168269550e-01, 1.68317301301231750e-08, -8.41586478175444280e-09, 2.80528807171338990e-09, -7.01321923492638810e-10, 1.40264346924246440e-10, -2.33773785626150360e-11, 3.33962191139516880e-12, -4.17451839537109420e-13,

   1.800000e+01, 9.99999984770020500e-01, 1.52299792808080730e-08, -7.61498940845176490e-09, 2.53832964818240970e-09, -6.34582334728182720e-10, 1.26916436018670270e-10, -2.11527290274570720e-11, 3.02181548706907280e-12, -3.77726199527563320e-13,

   1.810000e+01, 9.99999986219344610e-01, 1.37806551691327910e-08, -6.89032739465993630e-09, 2.29677567161567480e-09, -5.74193854601768850e-10, 1.14838745599494990e-10, -1.91397824929634930e-11, 2.73425223034198820e-12, -3.41780925915358260e-13,

   1.820000e+01, 9.99999987530747370e-01, 1.24692524747864200e-08, -6.23462608191095050e-09, 2.07820859031547940e-09, -5.19552095751452490e-10, 1.03910398419324440e-10, -1.73183928262324930e-11, 2.47405414365580530e-12, -3.09256274362693850e-13,

   1.830000e+01, 9.99999988717353630e-01, 1.12826462409003450e-08, -5.64132299315206480e-09, 1.88044091285195110e-09, -4.70110185780287060e-10, 9.40220201829777590e-11, -1.56703310394700660e-11, 2.23861710344074940e-12, -2.79826733809259210e-13,

   1.840000e+01, 9.99999989791039430e-01, 1.02089605151518090e-08, -5.10448015335302930e-09, 1.70149331496909350e-09, -4.25373294001316050e-10, 8.50746449038807820e-11, -1.41791028518528920e-11, 2.02558479822844680e-12, -2.53197768912388570e-13,

   1.850000e+01, 9.99999990762550420e-01, 9.23744949130964340e-09, -4.61872466032434790e-09, 1.53957482988780090e-09, -3.84893679028459880e-10, 7.69787244282962100e-11, -1.28297836122509570e-11, 1.83282514676019000e-12, -2.29102872454708450e-13,

   1.860000e+01, 9.99999991641610020e-01, 8.35838996164923970e-09, -4.17919491096193710e-09, 1.39306492374552380e-09, -3.48266207648820590e-10, 6.96532322147402270e-11, -1.16088689307822070e-11, 1.65840896010956230e-12, -2.07300898227456780e-13,

   1.870000e+01, 9.99999992437015980e-01, 7.56298400386765620e-09, -3.78149194473510020e-09, 1.26049727677921560e-09, -3.15124300128561930e-10, 6.30248523992157960e-11, -1.05041395243705370e-11, 1.50059063429142370e-12, -1.87573647703208950e-13,

   1.880000e+01, 9.99999993156729050e-01, 6.84327092855724760e-09, -3.42163541744826620e-09, 1.14054510792918420e-09, -2.85136261372177340e-10, 5.70272460303881300e-11, -9.50453892371564860e-12, 1.35779068014539740e-12, -1.69723686350405390e-13,

   1.890000e+01, 9.99999993807952350e-01, 6.19204760598108620e-09, -3.09602376464908920e-09, 1.03200789598872740e-09, -2.58001961216697570e-10, 5.16003871311458980e-11, -8.60006281779316590e-12, 1.22857991566633670e-12, -1.53572367739414650e-13,

   1.900000e+01, 9.99999994397203550e-01, 5.60279637475461250e-09, -2.80139815598597900e-09, 9.33799364401108190e-10, -2.33449830636501440e-10, 4.66899619417901430e-11, -7.78165892846167970e-12, 1.11166516258882510e-12, -1.38958045668612940e-13,

   1.910000e+01, 9.99999994930380160e-01, 5.06961981092019570e-09, -2.53480987975905280e-09, 8.44936609452320900e-10, -2.11234143796065330e-10, 4.22468253324071740e-11, -7.04113641313259240e-12, 1.00587630408506780e-12, -1.25734456420026820e-13,

   1.920000e+01, 9.99999995412818250e-01, 4.58718170456303600e-09, -2.29359083123928190e-09, 7.64530263051603250e-10, -1.91132558748822240e-10, 3.82265089441330630e-11, -6.37108388881173700e-12, 9.10154574055845760e-13, -1.13769254956240810e-13,

   1.930000e+01, 9.99999995849346290e-01, 4.15065365324235680e-09, -2.07532680939325240e-09, 6.91775591645800390e-10, -1.72943892168808220e-10, 3.45887761367049390e-11, -5.76479525709860340e-12, 8.23541960818220710e-13, -1.02942690410456670e-13,

   1.940000e+01, 9.99999996244333220e-01, 3.75566673772821010e-09, -1.87783335475907260e-09, 6.25944442183002370e-10, -1.56486105844073100e-10, 3.12972192881436440e-11, -5.21620258780029460e-12, 7.45171619145671900e-13, -9.31464076153326440e-14,

   1.950000e+01, 9.99999996601732220e-01, 3.39826779639862290e-09, -1.69913388665108740e-09, 5.66377954518213050e-10, -1.41594484780145320e-10, 2.83188954162658910e-11, -4.71981538945660100e-12, 6.74259194706837880e-13, -8.42823626773298690e-14,

   1.960000e+01, 9.99999996925120090e-01, 3.07487986067683370e-09, -1.53743992088353070e-09, 5.12479967324586100e-10, -1.28119988679517820e-10, 2.56239964752521010e-11, -4.27066565899153560e-12, 6.10094974079608410e-13, -7.62618417444422280e-14,

   1.970000e+01, 9.99999997217733580e-01, 2.78226635553385050e-09, -1.39113317002591930e-09, 4.63711051514635650e-10, -1.15927760298323590e-10, 2.31855510275305900e-11, -3.86425816054372880e-12, 5.52036781779190810e-13, -6.90045731477784620e-14,

   1.980000e+01, 9.99999997482501230e-01, 2.51749870676266970e-09, -1.25874934704353510e-09, 4.19583111455978510e-10, -1.04895775751394730e-10, 2.09791543052389950e-11, -3.49652543585985230e-12, 4.99503553214271660e-13, -6.24379240317863160e-14,

   1.990000e+01, 9.99999997722072930e-01, 2.27792703082745150e-09, -1.13896351022477420e-09, 3.79654499948956970e-10, -9.49136232575887370e-11, 1.89827239596575490e-11, -3.16378709598952840e-12, 4.51969519249915690e-13, -5.64961734333785040e-14,

   2.000000e+01, 9.99999997938846420e-01, 2.06115361394184920e-09, -1.03057680272257050e-09, 3.43525598075287350e-10, -8.58813981027037640e-11, 1.71762790540935310e-11, -2.86271298686651670e-12, 4.08958944176434980e-13, -5.11198545352164150e-14,

   2.010000e+01, 9.99999998134991070e-01, 1.86500891494625040e-09, -9.32504453994866920e-10, 3.10834815679450130e-10, -7.77087027604431210e-11, 1.55417400883208640e-11, -2.59028986013089150e-12, 3.70041364421770110e-13, -4.62551595106321980e-14,

   2.020000e+01, 9.99999998312470110e-01, 1.68752985181301180e-09, -8.43764923058748870e-10, 2.81254972454411600e-10, -7.03137421643505800e-11, 1.40627480531691870e-11, -2.34379121562788890e-12, 3.34827280356277340e-13, -4.18534010040367140e-14,

   2.030000e+01, 9.99999998473059870e-01, 1.52694015446351060e-09, -7.63470074900209110e-10, 2.54490023412372220e-10, -6.36225050759109730e-11, 1.27245007043093660e-11, -2.12075001376061900e-12, 3.02964258073152960e-13, -3.78705248574103820e-14,

   2.040000e+01, 9.99999998618367410e-01, 1.38163258726171380e-09, -6.90816291721948200e-10, 2.30272095968043680e-10, -5.75680233557080490e-11, 1.15136044166204650e-11, -1.91893398459636310e-12, 2.74133402130800350e-13, -3.42666692063229750e-14,

   2.050000e+01, 9.99999998749847130e-01, 1.25015286326097820e-09, -6.25076430067606910e-10, 2.08358808980614170e-10, -5.20897017241928200e-11, 1.04179401364542740e-11, -1.73632328661428310e-12, 2.48046163955918000e-13, -3.10057655329591960e-14,

   2.060000e+01, 9.99999998868814850e-01, 1.13118508921247310e-09, -5.65592543326656920e-10, 1.88530846922499150e-10, -4.71327113040982220e-11, 9.42654209020901760e-12, -1.57109029149796130e-12, 2.24441453965363630e-13, -2.80551776835127940e-14,

   2.070000e+01, 9.99999998976461410e-01, 1.02353859566414990e-09, -5.11769296784443690e-10, 1.70589764896393730e-10, -4.26474408748880140e-11, 8.52948803529343670e-12, -1.42158129265418420e-12, 2.03083028504486790e-13, -2.53853752372474360e-14,

   2.080000e+01, 9.99999999073863940e-01, 9.26136020341316250e-10, -4.63068009312930200e-10, 1.54356002532491450e-10, -3.85890003472135510e-11, 7.71779995507898760e-12, -1.28629995439192380e-12, 1.83757125449920370e-13, -2.29696379582943160e-14,

   2.090000e+01, 9.99999999161997440e-01, 8.38002525543446580e-10, -4.19001262069475020e-10, 1.39667086888326170e-10, -3.49167714879988000e-11, 6.98335420396666360e-12, -1.16389233611674490e-12, 1.66270324813525820e-13, -2.07837883723313160e-14,

   2.100000e+01, 9.99999999241743990e-01, 7.58256041641286250e-10, -3.79128020245690870e-10, 1.26376006365262140e-10, -3.15940013996647920e-11, 6.31880020327266280e-12, -1.05313334165867850e-12, 1.50447612935973550e-13, -1.88059497917515770e-14,

   2.110000e+01, 9.99999999313901600e-01, 6.86098439027881960e-10, -3.43049219043209910e-10, 1.14349739367249250e-10, -2.85874346849019580e-11, 5.71748687421624950e-12, -9.52914458114660960e-13, 1.36130630895985690e-13, -1.70163273676139010e-14,

   2.120000e+01, 9.99999999379192480e-01, 6.20807540169556160e-10, -3.10403769699376070e-10, 1.03467922976190680e-10, -2.58669806155803370e-11, 5.17339607172913470e-12, -8.62232661492544680e-13, 1.23176089604941330e-13, -1.53970099771192710e-14,

   2.130000e+01, 9.99999999438270120e-01, 5.61729891810647090e-10, -2.80864945589783040e-10, 9.36216483195673650e-11, -2.34054119747116840e-11, 4.68108235287027450e-12, -7.80180378121024880e-13, 1.11454335724711900e-13, -1.39317909638732220e-14,

   2.140000e+01, 9.99999999491725800e-01, 5.08274224993904350e-10, -2.54137112238609450e-10, 8.47123705739746900e-11, -2.11780925573794440e-11, 4.23561847703019730e-12, -7.05936401356469130e-13, 1.00848054056096410e-13, -1.26060059368765470e-14,

   2.150000e+01, 9.99999999540094440e-01, 4.59905537442205450e-10, -2.29952768509589620e-10, 7.66509226955211350e-11, -1.91627306033759160e-11, 3.83254609247343600e-12, -6.38757672678323810e-13, 9.12510934110227360e-14, -1.14063860049076810e-14,

   2.160000e+01, 9.99999999583860210e-01, 4.16139739076070330e-10, -2.08069869364862890e-10, 6.93566230061727730e-11, -1.73391556938190990e-11, 3.46783111567418200e-12, -5.77971844915817840e-13, 8.25674042175323160e-14, -1.03209249774382680e-14,

   2.170000e+01, 9.99999999623461200e-01, 3.76538807077571410e-10, -1.88269403397004230e-10, 6.27564677044804220e-11, -1.56891168788596160e-11, 3.13782335686772680e-12, -5.22970553176555670e-13, 7.47100772248225910e-14, -9.33875920300291470e-15,

   2.180000e+01, 9.99999999659293650e-01, 3.40706402010826230e-10, -1.70353200889332250e-10, 5.67844002190568430e-11, -1.41961000160705930e-11, 2.83921998773667190e-12, -4.73203326130296410e-13, 6.76004736874283440e-14, -8.45005884241790450e-15,

   2.190000e+01, 9.99999999691716050e-01, 3.08283901123787880e-10, -1.54141950466854970e-10, 5.13806500922590160e-11, -1.28451624913850980e-11, 2.56903248560515810e-12, -4.28172076710239100e-13, 6.11674383231901790e-14, -7.64592948868777890e-15,

   2.200000e+01, 9.99999999721053250e-01, 2.78946809131269810e-10, -1.39473404487823600e-10, 4.64911347774003090e-11, -1.16227836684129700e-11, 2.32455672330775130e-12, -3.87426117093010900e-13, 5.53465871680641350e-14, -6.91832314898794850e-15,

   2.210000e+01, 9.99999999747598460e-01, 2.52401510557107620e-10, -1.26200755214847310e-10, 4.20669183624780810e-11, -1.05167295693840130e-11, 2.10334590538259950e-12, -3.50557648065698950e-13, 5.00796632004138530e-14, -6.25995769780880440e-15,

   2.220000e+01, 9.99999999771617690e-01, 2.28382331131840030e-10, -1.14191165513761530e-10, 3.80637218031481840e-11, -9.51593043340088230e-12, 1.90318607972571140e-12, -3.17197677636130170e-13, 4.53139532856885770e-14, -5.66424399512856770e-15,

   2.230000e+01, 9.99999999793351080e-01, 2.06648878835349790e-10, -1.03324439374971130e-10, 3.44414797631878660e-11, -8.61036992656238030e-12, 1.72207397961864170e-12, -2.87012328038495440e-13, 4.10017606060865360e-14, -5.12521994019332860e-15,

   2.240000e+01, 9.99999999813016350e-01, 1.86983637972757640e-10, -9.34918189514159360e-11, 3.11639396271633880e-11, -7.79098489513655400e-12, 1.55819697436559350e-12, -2.59699494173693080e-13, 3.70999272951259230e-14, -4.63749080089746830e-15,

   2.250000e+01, 9.99999999830810230e-01, 1.69189792204262680e-10, -8.45948960735061490e-11, 2.81982986720852590e-11, -7.04957465847958610e-12, 1.40991492787922590e-12, -2.34985820040973830e-13, 3.35694024995018370e-14, -4.19617522156412460e-15,

   2.260000e+01, 9.99999999846910790e-01, 1.53089254741075000e-10, -7.65446273471011700e-11, 2.55148757667428430e-11, -6.37871893387360370e-12, 1.27574378364987830e-12, -2.12623962900032170e-13, 3.03748515452576770e-14, -3.79685636875619410e-15,

   2.270000e+01, 9.99999999861479140e-01, 1.38520885992999430e-10, -6.92604429773116690e-11, 2.30868143129785320e-11, -5.77170357184862140e-12, 1.15434071181131950e-12, -1.92390117782418320e-13, 2.74843022966878780e-14, -3.43553772617158530e-15,

   2.280000e+01, 9.99999999874661150e-01, 1.25338880829263350e-10, -6.26694403989218490e-11, 2.08898134558340590e-11, -5.22245335872190240e-12, 1.04449066964973590e-12, -1.74081777576741110e-13, 2.48688251686159030e-14, -3.10860309620449580e-15,

   2.290000e+01, 9.99999999886588720e-01, 1.13411309311772790e-10, -5.67056546430242640e-11, 1.89018848724333370e-11, -4.72547121382095930e-12, 9.45094241049241960e-13, -1.57515706269890320e-13, 2.25022435895129010e-14, -2.81278040785696970e-15,

   2.300000e+01, 9.99999999897381200e-01, 1.02618796295957670e-10, -5.13093981374482180e-11, 1.71031327054623260e-11, -4.27578317285537590e-12, 8.55156633166992920e-13, -1.42526105059804710e-13, 2.03608720176785480e-14, -2.54510896877928730e-15,

   2.310000e+01, 9.99999999907146720e-01, 9.28533266842058060e-11, -4.64266633334811670e-11, 1.54755544387458930e-11, -3.86888860681256030e-12, 7.73777720212946720e-13, -1.28962952985636000e-13, 1.84232788884655840e-14, -2.30290983368759400e-15,

   2.320000e+01, 9.99999999915982870e-01, 8.40171643744709210e-11, -4.20085821801765730e-11, 1.40028607220196020e-11, -3.50071517815193910e-12, 7.00143034689203340e-13, -1.16690505467805710e-13, 1.66700721200499090e-14, -2.08375899259708350e-15,

   2.330000e+01, 9.99999999923978140e-01, 7.60218740845145900e-11, -3.80109370364779650e-11, 1.26703123416397720e-11, -3.16757808348350120e-12, 6.33515615926123530e-13, -1.05585935730828360e-13, 1.50837050310157920e-14, -1.88546311052990970e-15,

   2.340000e+01, 9.99999999931212580e-01, 6.87874362618821850e-11, -3.43937181262093800e-11, 1.14645727055819860e-11, -2.86614317481825930e-12, 5.73228634332757030e-13, -9.55381055118278960e-14, 1.36483007273187600e-14, -1.70603757589353910e-15,

   2.350000e+01, 9.99999999937758570e-01, 6.22414462213298320e-11, -3.11207231067909190e-11, 1.03735743663476410e-11, -2.59339359029557740e-12, 5.18678717542582510e-13, -8.64464527515860870e-14, 1.23494932010329620e-14, -1.54368663783071520e-15,

   2.360000e+01, 9.99999999943681610e-01, 5.63183894943992020e-11, -2.81591947440278380e-11, 9.38639824589477160e-12, -2.34659956041643930e-12, 4.69319911660386450e-13, -7.82199851357639110e-14, 1.11742835505470860e-14, -1.39678543374930320e-15,

   2.370000e+01, 9.99999999949040990e-01, 5.09589861386018280e-11, -2.54794930667040940e-11, 8.49316435383681970e-12, -2.12329108759359880e-12, 4.24658217172477320e-13, -7.07763694133320710e-14, 1.01109098832148270e-14, -1.26386372715798570e-15,

   2.380000e+01, 9.99999999953890440e-01, 4.61095974438298670e-11, -2.30547987197888400e-11, 7.68493290517888300e-12, -1.92123322558602250e-12, 3.84246644833725180e-13, -6.40411073777944180e-14, 9.14872959840117060e-15, -1.14359119305063860e-15,

   2.390000e+01, 9.99999999958278260e-01, 4.17216890981185860e-11, -2.08608445473185910e-11, 6.95361484794573110e-12, -1.73840371140619950e-12, 3.47680742049146680e-13, -5.79467902641600380e-14, 8.27811287277588580e-15, -1.03476410357095610e-15,

   2.400000e+01, 9.99999999962248640e-01, 3.77513454399406490e-11, -1.88756727185451600e-11, 6.29189090523161070e-12, -1.57297272583284800e-12, 3.14594544976547720e-13, -5.24324240994173280e-14, 7.49034628181943890e-15, -9.36293280703099570e-16,

   2.410000e+01, 9.99999999965841210e-01, 3.41588299355048740e-11, -1.70794149665856120e-11, 5.69313832141732000e-12, -1.42328457996538810e-12, 2.84656915837500860e-13, -4.74428192543912290e-14, 6.77754559295334130e-15, -8.47193195414959260e-16,

   2.420000e+01, 9.99999999969091840e-01, 3.09081874821725750e-11, -1.54540937401309710e-11, 5.15136457940677950e-12, -1.28784114453325620e-12, 2.57568228779275750e-13, -4.29280380874208080e-14, 6.13257685750054600e-15, -7.66572104154818930e-16,

   2.430000e+01, 9.99999999972033150e-01, 2.79668845577048780e-11, -1.39834422780702910e-11, 4.66114742550199920e-12, -1.16528685611478420e-12, 2.33057371118670670e-13, -3.88428951516830370e-14, 5.54898501173698450e-15, -6.93623123984117890e-16,

   2.440000e+01, 9.99999999974694460e-01, 2.53054836138380930e-11, -1.26527418062786780e-11, 4.21758060166598080e-12, -1.05439515020303940e-12, 2.10879029955225560e-13, -3.51465049640768190e-14, 5.02092927245075130e-15, -6.27616157023431210e-16,

   2.450000e+01, 9.99999999977102650e-01, 2.28973484554069520e-11, -1.14486742271791870e-11, 3.81622474204353670e-12, -9.54056185336121260e-13, 1.90811236997319130e-13, -3.18018728095848100e-14, 4.54312468042591100e-15, -5.67890583388830820e-16,

   2.460000e+01, 9.99999999979281570e-01, 2.07183776563503520e-11, -1.03591888277459260e-11, 3.45306294229580770e-12, -8.63265735430868160e-13, 1.72653147028940160e-13, -2.87755244857455290e-14, 4.11078920679855240e-15, -5.13848649487116960e-16,

   2.470000e+01, 9.99999999981253220e-01, 1.87467633445398620e-11, -9.37338167191849080e-12, 3.12446055707186930e-12, -7.81115139150820290e-13, 1.56223027783305240e-13, -2.60371712815979360e-14, 3.71959589290838880e-15, -4.64949485497862530e-16,

   2.480000e+01, 9.99999999983037240e-01, 1.69627729412651200e-11, -8.48138647034482390e-12, 2.82712882325645110e-12, -7.06782205718200820e-13, 1.41356441105275410e-13, -2.35594068380909870e-14, 3.36562954464492610e-15, -4.20703692167169170e-16,

   2.490000e+01, 9.99999999984651500e-01, 1.53485516709541000e-11, -7.67427583524147330e-12, 2.55809194492343870e-12, -6.39522986152333650e-13, 1.27904597199056330e-13, -2.13174328560392550e-14, 3.04534754787128340e-15, -3.80668442736043620e-16,

   2.500000e+01, 9.99999999986112110e-01, 1.38879438645782700e-11, -6.94397193209626070e-12, 2.31465731057017010e-12, -5.78664327578250840e-13, 1.15732865489933500e-13, -1.92888109064166970e-14, 2.75554441275317920e-15, -3.44443050981845840e-16,

   2.510000e+01, 9.99999999987433720e-01, 1.25663312682865470e-11, -6.28316563398536010e-12, 2.09438854455651170e-12, -5.23597136086490280e-13, 1.04719427196243050e-13, -1.74532378590221670e-14, 2.49331969214078320e-15, -3.11664961016287790e-16,

   2.520000e+01, 9.99999999988629540e-01, 1.13704867390081220e-11, -5.68524336937477280e-12, 1.89508112303873240e-12, -4.73770280716587120e-13, 9.47540561260790210e-14, -1.57923426819337060e-14, 2.25604895292020590e-15, -2.82006118704587770e-16,

   2.530000e+01, 9.99999999989711560e-01, 1.02884418627584790e-11, -5.14422093127338680e-12, 1.71474031035389420e-12, -4.28685077553189540e-13, 8.57370154965243110e-14, -1.42895025780495160e-14, 2.04135750980577790e-15, -2.55169688389684050e-16,

   2.540000e+01, 9.99999999990690670e-01, 9.30936717072967560e-12, -4.65468358527817370e-12, 1.55156119503494810e-12, -3.87890298729848920e-13, 7.75780597344145440e-14, -1.29296766185506780e-14, 1.84709665869245460e-15, -2.30887082061432010e-16,

   2.550000e+01, 9.99999999991576520e-01, 8.42346375432673730e-12, -4.21173187709241450e-12, 1.40391062565016820e-12, -3.50977656388890460e-13, 7.01955312683174650e-14, -1.16992552082327010e-14, 1.67132217170365880e-15, -2.08915271237704210e-16,

   2.560000e+01, 9.99999999992378100e-01, 7.62186519439670540e-12, -3.81093259714025940e-12, 1.27031086567469130e-12, -3.17577716399308540e-13, 6.35155432721159960e-14, -1.05859238761040960e-14, 1.51227483870575570e-15, -1.89034354653797760e-16,

   2.570000e+01, 9.99999999993103410e-01, 6.89654882312605530e-12, -3.44827441151546520e-12, 1.14942480380678020e-12, -2.87356200935840890e-13, 5.74712401808265320e-14, -9.57854002802387150e-15, 1.36836286054230050e-15, -1.71045357416795870e-16,

   2.580000e+01, 9.99999999993759770e-01, 6.24025543048449800e-12, -3.12012771520330850e-12, 1.04004257170847540e-12, -2.60010642914138620e-13, 5.20021285776356180e-14, -8.66702142787523540e-15, 1.23814591777340460e-15, -1.54768239598054020e-16,

   2.590000e+01, 9.99999999994353630e-01, 5.64641661161116710e-12, -2.82320830577370160e-12, 9.41069435236645860e-13, -2.35267358798534080e-13, 4.70534717554558880e-14, -7.84224529115900320e-15, 1.12032075547500640e-15, -1.40040094333163040e-16,

   2.600000e+01, 9.99999999994890860e-01, 5.10908902801111980e-12, -2.55454451397945690e-12, 8.51514837975750460e-13, -2.12878709485236670e-13, 4.25757418935669650e-14, -7.09595698110103680e-15, 1.01370813982582700e-15, -1.26713517395362360e-16,

   2.610000e+01, 9.99999999995377140e-01, 4.62289492462592040e-12, -2.31144746229158880e-12, 7.70482487416282180e-13, -1.92620621846946820e-13, 3.85241243665398760e-14, -6.42068739347348420e-15, 9.17241055939117900e-16, -1.14655131924544790e-16,

   2.620000e+01, 9.99999999995817010e-01, 4.18296830745373390e-12, -2.09148415370936970e-12, 6.97161384558125010e-13, -1.74290346133698860e-13, 3.48580692244068100e-14, -5.80967820329014760e-15, 8.29954028819262650e-16, -1.03744253546861090e-16,

   2.630000e+01, 9.99999999996215140e-01, 3.78490624304569280e-12, -1.89245312150852060e-12, 6.30817707159956550e-13, -1.57704426785213970e-13, 3.15408853551327240e-14, -5.25681422521876490e-15, 7.50973460563626540e-16, -9.38716825249754870e-17,

   2.640000e+01, 9.99999999996575300e-01, 3.42472479246811050e-12, -1.71236239622232650e-12, 5.70787465399622950e-13, -1.42696866345996170e-13, 2.85393732676354040e-14, -4.75656221075129030e-15, 6.79508887101247850e-16, -8.49386108504218940e-17,

   2.650000e+01, 9.99999999996901150e-01, 3.09881913870262030e-12, -1.54940956934170750e-12, 5.16469856440834000e-13, -1.29117464107007590e-13, 2.58234928201211660e-14, -4.30391546959340840e-15, 6.14845066962833870e-16, -7.68556333398695290e-17,

   2.660000e+01, 9.99999999997196020e-01, 2.80392750842574440e-12, -1.40196375420501020e-12, 4.67321251396428690e-13, -1.16830312846486510e-13, 2.33660625682490340e-14, -3.89434376102541680e-15, 5.56334822903795940e-16, -6.95418528380157220e-17,

   2.670000e+01, 9.99999999997462920e-01, 2.53709852708530230e-12, -1.26854926353621420e-12, 4.22849754507780140e-13, -1.05712438624799420e-13, 2.11424877241016340e-14, -3.52374795373085620e-15, 5.03392564736955720e-16, -6.29240705716849610e-17,

   2.680000e+01, 9.99999999997704390e-01, 2.29566168055180610e-12, -1.14783084027063300e-12, 3.82610280086697580e-13, -9.56525700199177090e-14, 1.91305140032808680e-14, -3.18841900031258660e-15, 4.55488428549162340e-16, -5.69360535519149340e-17,

   2.690000e+01, 9.99999999997922770e-01, 2.07720058771549270e-12, -1.03860029385343170e-12, 3.46200097948267330e-13, -8.65500244856285820e-14, 1.73100048965504150e-14, -2.88500081589996880e-15, 4.12142973645204890e-16, -5.15178716919529540e-17,

   2.700000e+01, 9.99999999998120500e-01, 1.87952881653201790e-12, -9.39764408262476450e-13, 3.13254802751803660e-13, -7.83137006867733800e-14, 1.56627401368836600e-14, -2.61045668932360430e-15, 3.72922384144227540e-16, -4.66152980068137490e-17,

   2.710000e+01, 9.99999999998299360e-01, 1.70066800147561990e-12, -8.50334000734917720e-13, 2.83444666909711020e-13, -7.08611667264636660e-14, 1.41722333449070980e-14, -2.36203889068930450e-15, 3.37434127204601900e-16, -4.21792658913934270e-17,

   2.720000e+01, 9.99999999998461120e-01, 1.53882804339207140e-12, -7.69414021693667660e-13, 2.56471340562977240e-13, -6.41178351399549690e-14, 1.28235670276752620e-14, -2.13726117117396640e-15, 3.05323024423354020e-16, -3.81653780454018200e-17,

   2.730000e+01, 9.99999999998607560e-01, 1.39238919358461520e-12, -6.96194596790368790e-13, 2.32064865595497110e-13, -5.80162163982280180e-14, 1.16032432793871060e-14, -1.93387387981168440e-15, 2.76267697091335900e-16, -3.45334621302622340e-17,

   2.740000e+01, 9.99999999998740120e-01, 1.25988584282460730e-12, -6.29942921410716320e-13, 2.09980973802513880e-13, -5.24952434500993650e-14, 1.04990486898082330e-14, -1.74984144823082500e-15, 2.49977349727104320e-16, -3.12471687108489570e-17,

   2.750000e+01, 9.99999999998860020e-01, 1.13999185304175630e-12, -5.69995926519578510e-13, 1.89998642172326450e-13, -4.74996605426484150e-14, 9.49993210835640690e-15, -1.58332201800164190e-15, 2.26188859698017630e-16, -2.82736074581265470e-17,

   2.760000e+01, 9.99999999998968490e-01, 1.03150728488855420e-12, -5.15753642443213040e-13, 1.71917880813695000e-13, -4.29794702030690830e-14, 8.59589404047194890e-15, -1.43264900669803580e-15, 2.04664143800493900e-16, -2.55830179716839340e-17,

   2.770000e+01, 9.99999999999066640e-01, 9.33346388344024310e-13, -4.66673194171140950e-13, 1.55557731389799560e-13, -3.88894328471595120e-14, 7.77788656931575120e-15, -1.29631442818057490e-15, 1.85187775443305800e-16, -2.31484719276477160e-17,

   2.780000e+01, 9.99999999999155450e-01, 8.44526736162543640e-13, -4.22263368080558590e-13, 1.40754456026377370e-13, -3.51886140063566000e-14, 7.03772280117622370e-15, -1.17295380016433840e-15, 1.67564828585848670e-16, -2.09456035709668770e-17,

   2.790000e+01, 9.99999999999235830e-01, 7.64159391411773770e-13, -3.82079695705302950e-13, 1.27359898568045010e-13, -3.18399746418166060e-14, 6.36799492828546310e-15, -1.06133248802162440e-15, 1.51618926852816940e-16, -1.89523658547483410e-17,

   2.800000e+01, 9.99999999999308550e-01, 6.91440010693064080e-13, -3.45720005346053980e-13, 1.15240001781699250e-13, -2.88100004452654500e-14, 5.76200008898934550e-15, -9.60333348143642610e-16, 1.37190478300163660e-16, -1.71488097860027170e-17,

   2.810000e+01, 9.99999999999374390e-01, 6.25640794002349870e-13, -3.12820397000783510e-13, 1.04273465666666880e-13, -2.60683664165362450e-14, 5.21367328325505900e-15, -8.68945547191779780e-16, 1.24135078165283750e-16, -1.55168847694178470e-17,

   2.820000e+01, 9.99999999999433900e-01, 5.66103200663120480e-13, -2.83051600331239800e-13, 9.43505334435329370e-14, -2.35876333607764100e-14, 4.71752667211255270e-15, -7.86254445337848910e-16, 1.12322063615623210e-16, -1.40402579509355260e-17,

   2.830000e+01, 9.99999999999487740e-01, 5.12231358429965140e-13, -2.56115679214720190e-13, 8.53718930713984750e-14, -2.13429732677621560e-14, 4.26859465351744730e-15, -7.11432442241246580e-16, 1.01633206031131970e-16, -1.27041507530585410e-17,

   2.840000e+01, 9.99999999999536480e-01, 4.63486099798866320e-13, -2.31743049899218340e-13, 7.72476832995962260e-14, -1.93119208248274500e-14, 3.86238416493684800e-15, -6.43730694146593790e-16, 9.19615277324998190e-17, -1.14951909658805120e-17,

   2.850000e+01, 9.99999999999580670e-01, 4.19379565837602710e-13, -2.09689782918625460e-13, 6.98965943060912380e-14, -1.74741485764641810e-14, 3.49482971526938580e-15, -5.82471619203747550e-16, 8.32102313125876770e-17, -1.04012789135151130e-17,

   2.860000e+01, 9.99999999999620530e-01, 3.79470323529567900e-13, -1.89735161764639940e-13, 6.32450539214506480e-14, -1.58112634803146610e-14, 3.16225269604373280e-15, -5.27042116000888960e-16, 7.52917308554413040e-17, -9.41146635647302730e-18,

   2.870000e+01, 9.99999999999656610e-01, 3.43358947763788770e-13, -1.71679473881776470e-13, 5.72264912938468950e-14, -1.43066228234224260e-14, 2.86132456466876570e-15, -4.76887427439554530e-16, 6.81267753470107030e-17, -8.51584691800206660e-18,

   2.880000e+01, 9.99999999999689360e-01, 3.10684023754150380e-13, -1.55342011876978680e-13, 5.17806706255952050e-14, -1.29451676563666270e-14, 2.58903353126045530e-15, -4.31505588539119280e-16, 6.16436555043627530e-17, -7.70545693773891780e-18,

   2.890000e+01, 9.99999999999718890e-01, 2.81118529878744400e-13, -1.40559264939293190e-13, 4.68530883130450390e-14, -1.17132720782349170e-14, 2.34265441563644660e-15, -3.90442402602562120e-16, 5.57774860850767700e-17, -6.97218576038371540e-18,

   2.900000e+01, 9.99999999999745650e-01, 2.54366564737562880e-13, -1.27183282368716740e-13, 4.23944274561957760e-14, -1.05986068640273770e-14, 2.11972137279684820e-15, -3.53286895463265750e-16, 5.04695564939306290e-17, -6.30869456153592520e-18,

   2.910000e+01, 9.99999999999769850e-01, 2.30160385671822320e-13, -1.15080192835858200e-13, 3.83600642785840840e-14, -9.59001606962836320e-15, 1.91800321391860960e-15, -3.19667202317413840e-16, 4.56667431875292930e-17, -5.70834289827299170e-18,

   2.920000e+01, 9.99999999999791720e-01, 2.08257729105462710e-13, -1.04128864552687990e-13, 3.47096215175337460e-14, -8.67740537936897830e-15, 1.73548107586801300e-15, -2.89246845976074600e-16, 4.13209779960313320e-17, -5.16512224936623100e-18,

   2.930000e+01, 9.99999999999811600e-01, 1.88439385889827740e-13, -9.42196929448783500e-14, 3.14065643149357740e-14, -7.85164107872210740e-15, 1.57032821573968700e-15, -2.61721369288369650e-16, 3.73887670407447510e-17, -4.67359587998036610e-18,

   2.940000e+01, 9.99999999999829470e-01, 1.70507007384838220e-13, -8.52535036923900290e-14, 2.84178345641106270e-14, -7.10445864101796640e-15, 1.42089172819971680e-15, -2.36815288031994070e-16, 3.38307554327728270e-17, -4.22884442900430890e-18,

   2.950000e+01, 9.99999999999845680e-01, 1.54281120319141160e-13, -7.71405601595467770e-14, 2.57135200531663900e-14, -6.42838001328366320e-15, 1.28567600265355900e-15, -2.14279333774535300e-16, 3.06113333960599290e-17, -3.82641667443192610e-18,

   2.960000e+01, 9.99999999999860440e-01, 1.39599330561269830e-13, -6.97996652806154250e-14, 2.32665550935254810e-14, -5.81663877337487480e-15, 1.16332775467237650e-15, -1.93887959111196630e-16, 2.76982798727806240e-17, -3.46228498403571140e-18,

   2.970000e+01, 9.99999999999873660e-01, 1.26314697824611900e-13, -6.31573489122899990e-14, 2.10524496374193610e-14, -5.26311240934952190e-15, 1.05262248186777700e-15, -1.75437080310587040e-16, 2.50624400441669680e-17, -3.13280500547021870e-18,

   2.980000e+01, 9.99999999999885760e-01, 1.14294265039617650e-13, -5.71471325197957610e-14, 1.90490441732565420e-14, -4.76226104330978190e-15, 9.52452208660214540e-16, -1.58742034776121860e-16, 2.26774335392800970e-17, -2.83467919236854260e-18,

   2.990000e+01, 9.99999999999896530e-01, 1.03417727674766650e-13, -5.17088638373726360e-14, 1.72362879457837450e-14, -4.30907198644237150e-15, 8.61814397287048370e-16, -1.43635732880699370e-16, 2.05193904113926700e-17, -2.56492380139013070e-18,

   3.000000e+01, 9.99999999999906410e-01, 9.35762296883842290e-14, -4.67881148441833610e-14, 1.55960382813886140e-14, -3.89900957034423470e-15, 7.79801914067679530e-16, -1.29966985677557410e-16, 1.85667122395398650e-17, -2.32083902991468430e-18,

   3.010000e+01, 9.99999999999915290e-01, 8.46712740607782790e-14, -4.23356370303819700e-14, 1.41118790101225430e-14, -3.52796975252824600e-15, 7.05593950504693360e-16, -1.17598991750463600e-16, 1.67998559642609060e-17, -2.09998199550985370e-18,

   3.020000e+01, 9.99999999999923390e-01, 7.66137370029714090e-14, -3.83068685014798350e-14, 1.27689561671560310e-14, -3.19223904178705130e-15, 6.38447808356627660e-16, -1.06407968059177070e-16, 1.52011382940936180e-17, -1.90014228674306770e-18,

   3.030000e+01, 9.99999999999930720e-01, 6.93229759758561190e-14, -3.46614879879232510e-14, 1.15538293293045450e-14, -2.88845733232453450e-15, 5.77691466464266220e-16, -9.62819110771641100e-17, 1.37545587252481340e-17, -1.71931984064076160e-18,

   3.040000e+01, 9.99999999999937270e-01, 6.27260225925628000e-14, -3.13630112962774620e-14, 1.04543370987565300e-14, -2.61358427468782110e-15, 5.22716854937039650e-16, -8.71194758226650810e-17, 1.24456394031879060e-17, -1.55570492538599900e-18,

   3.050000e+01, 9.99999999999943270e-01, 5.67568523263207840e-14, -2.83784261631571700e-14, 9.45947538771690840e-15, -2.36486884692815350e-15, 4.72973769385201240e-16, -7.88289615640570320e-17, 1.12612802233958130e-17, -1.40766002791424940e-18,

   3.060000e+01, 9.99999999999948600e-01, 5.13557237147964600e-14, -2.56778618573955920e-14, 8.55928728579677160e-15, -2.13982182144831410e-15, 4.27964364289311180e-16, -7.13273940481013100e-17, 1.01896277211238390e-17, -1.27370346513210690e-18,

   3.070000e+01, 9.99999999999953480e-01, 4.64685804474652490e-14, -2.32342902237304630e-14, 7.74476340790871500e-15, -1.93619085197645890e-15, 3.87238170395003900e-16, -6.45396950657380130e-17, 9.21995643793515330e-18, -1.15249455473503900e-18,

   3.080000e+01, 9.99999999999957920e-01, 4.20465103518813390e-14, -2.10232551759388990e-14, 7.00775172531178780e-15, -1.75193793132735770e-15, 3.50387586265235810e-16, -5.83979310441273950e-17, 8.34256157771003620e-18, -1.04282019720814140e-18,

   3.090000e+01, 9.99999999999961920e-01, 3.80452558642185360e-14, -1.90226279321078230e-14, 6.34087597736830850e-15, -1.58521899434159470e-15, 3.17043798868125930e-16, -5.28406331446233300e-17, 7.54866187778495290e-18, -9.43582734718524040e-19,

   3.100000e+01, 9.99999999999965580e-01, 3.44247710846973950e-14, -1.72123855423475140e-14, 5.73746184744838090e-15, -1.43436546186170020e-15, 2.86873092372182050e-16, -4.78121820619776750e-17, 6.83031172312461890e-18, -8.53788965386815540e-19,

   3.110000e+01, 9.99999999999968800e-01, 3.11488209847564900e-14, -1.55744104923772730e-14, 5.19147016412511060e-15, -1.29786754103095420e-15, 2.59573508206061480e-16, -4.32622513676337930e-17, 6.18032162393536420e-18, -7.72540202988840200e-19,

   3.120000e+01, 9.99999999999971800e-01, 2.81846187547117050e-14, -1.40923093773550570e-14, 4.69743645911782230e-15, -1.17435911477919090e-15, 2.34871822955732270e-16, -3.91453038259200720e-17, 5.59218626083563660e-18, -6.99023282601933050e-19,

   3.130000e+01, 9.99999999999974460e-01, 2.55024976623415030e-14, -1.27512488311701020e-14, 4.25041627705626620e-15, -1.06260406926384980e-15, 2.12520813852683260e-16, -3.54201356420849750e-17, 5.06001937743245150e-18, -6.32502422176991450e-19,

   3.140000e+01, 9.99999999999976910e-01, 2.30756141382610940e-14, -1.15378070691300150e-14, 3.84593568970964980e-15, -9.61483922427234960e-16, 1.92296784485376010e-16, -3.20494640808723390e-17, 4.57849486868928600e-18, -5.72311858584469210e-19,

   3.150000e+01, 9.99999999999979130e-01, 2.08796791164584650e-14, -1.04398395582287960e-14, 3.47994651940930800e-15, -8.69986629852181640e-16, 1.73997325970378200e-16, -2.89995543283769920e-17, 4.14279347547689220e-18, -5.17849184433227650e-19,

   3.160000e+01, 9.99999999999981130e-01, 1.88927149411555350e-14, -9.44635747057741110e-15, 3.14878582352556530e-15, -7.87196455881272310e-16, 1.57439291176206870e-16, -2.62398818626852850e-17, 3.74855455180765200e-18, -4.68569318974822510e-19,

   3.170000e+01, 9.99999999999982900e-01, 1.70948354070447300e-14, -8.54741770352207300e-15, 2.84913923450716240e-15, -7.12284808626693180e-16, 1.42456961725299670e-16, -2.37428269542036270e-17, 3.39183242202537880e-18, -4.23979052752244240e-19,

   3.180000e+01, 9.99999999999984570e-01, 1.54680467314601930e-14, -7.73402336572985840e-15, 2.57800778857645970e-15, -6.44501947144035160e-16, 1.28900389428775130e-16, -2.14833982381185570e-17, 3.06905689115675550e-18, -3.83632111393834950e-19,

   3.190000e+01, 9.99999999999986010e-01, 1.39960674665539270e-14, -6.99803373327676720e-15, 2.33267791109212490e-15, -5.83169477772965950e-16, 1.16633895554567090e-16, -1.94389825924191410e-17, 2.77699751320024640e-18, -3.47124689149409350e-19,

   3.200000e+01, 9.99999999999987340e-01, 1.26641655490938550e-14, -6.33208277454676670e-15, 2.11069425818214850e-15, -5.27673564545483690e-16, 1.05534712909075360e-16, -1.75891188181721000e-17, 2.51273125973683490e-18, -3.14091407466594670e-19,

   3.210000e+01, 9.99999999999988560e-01, 1.14590108570219640e-14, -5.72950542851085020e-15, 1.90983514283686250e-15, -4.77458785709171850e-16, 9.54917571418168590e-17, -1.59152928569636410e-17, 2.27361326527885370e-18, -2.84201658159439420e-19,

   3.220000e+01, 9.99999999999989670e-01, 1.03685417971138640e-14, -5.18427089855682390e-15, 1.72809029951886960e-15, -4.32022574879681600e-16, 8.64045149759219900e-17, -1.44007524959822210e-17, 2.05725035656752380e-18, -2.57156294570599110e-19,

   3.230000e+01, 9.99999999999990560e-01, 9.38184458849850840e-15, -4.69092229424916660e-15, 1.56364076474966340e-15, -3.90910191187386520e-16, 7.81820382374655680e-17, -1.30303397062403490e-17, 1.86147710089036070e-18, -2.32684637611014280e-19,

   3.240000e+01, 9.99999999999991560e-01, 8.48904403387157360e-15, -4.24452201693571420e-15, 1.41484067231185670e-15, -3.53710168077940160e-16, 7.07420336155784300e-17, -1.17903389359265360e-17, 1.68433413370287570e-18, -2.10541766712631340e-19,

   3.250000e+01, 9.99999999999992340e-01, 7.68120468520197700e-15, -3.84060234260092930e-15, 1.28020078086693710e-15, -3.20050195216714640e-16, 6.40100390433350650e-17, -1.06683398405532220e-17, 1.52404854864971060e-18, -1.90506068581026700e-19,

   3.260000e+01, 9.99999999999993010e-01, 6.95024141476382340e-15, -3.47512070738186320e-15, 1.15837356912725540e-15, -2.89593392281797740e-16, 5.79186784563531140e-17, -9.65311307605670500e-18, 1.37901615372177360e-18, -1.72377019215068900e-19,

   3.270000e+01, 9.99999999999993670e-01, 6.28883849646153690e-15, -3.14441924823072860e-15, 1.04813974941021660e-15, -2.62034937352540930e-16, 5.24069874705029170e-17, -8.73449791174872870e-18, 1.24778541596360150e-18, -1.55973176995325000e-19,

   3.280000e+01, 9.99999999999994340e-01, 5.69037638758344200e-15, -2.84518819379168870e-15, 9.48396064597207920e-16, -2.37099016149291180e-16, 4.74198032298539190e-17, -7.90330053830754850e-18, 1.12904293404352410e-18, -1.41130366755338760e-19,

   3.290000e+01, 9.99999999999994890e-01, 5.14886547819375430e-15, -2.57443273909685070e-15, 8.58144246365599090e-16, -2.14536061591390950e-16, 4.29072123182746550e-17, -7.15120205304459720e-18, 1.02160029329174860e-18, -1.27700036661385190e-19,

   3.300000e+01, 9.99999999999995340e-01, 4.65888614510335430e-15, -2.32944307255165550e-15, 7.76481024183870600e-16, -1.94120256045960430e-16, 3.88240512091891920e-17, -6.47067520153056780e-18, 9.24382171646948020e-19, -1.15547771455798300e-19,

   3.310000e+01, 9.99999999999995780e-01, 4.21553451045879130e-15, -2.10776725522937790e-15, 7.02589085076447440e-16, -1.75647271269105920e-16, 3.51294542538188150e-17, -5.85490904230234690e-18, 8.36415577471538480e-19, -1.04551947183885770e-19,

   3.320000e+01, 9.99999999999996230e-01, 3.81437336208504050e-15, -1.90718668104250570e-15, 6.35728893680825560e-16, -1.58932223420201530e-16, 3.17864446840383680e-17, -5.29774078067241470e-18, 7.56820111524446220e-19, -9.46025139405087250e-20,

   3.330000e+01, 9.99999999999996560e-01, 3.45138774437419260e-15, -1.72569387218708430e-15, 5.75231290729020130e-16, -1.43807822682251060e-16, 2.87615645364486240e-17, -4.79359408940757470e-18, 6.84799155629502910e-19, -8.55998944536504290e-20,

   3.340000e+01, 9.99999999999996890e-01, 3.12294477526047450e-15, -1.56147238763022740e-15, 5.20490795876735930e-16, -1.30122698969180730e-16, 2.60245397938348490e-17, -4.33742329897204160e-18, 6.19631899853024490e-19, -7.74539874815976800e-20,

   3.350000e+01, 9.99999999999997220e-01, 2.82575728711559530e-15, -1.41287864355778950e-15, 4.70959547852591190e-16, -1.17739886963145140e-16, 2.35479773926279630e-17, -3.92466289877097200e-18, 5.60666128395752110e-19, -7.00832660494431820e-20,

   3.360000e+01, 9.99999999999997450e-01, 2.55685092766995250e-15, -1.27842546383496980e-15, 4.26141821278318850e-16, -1.06535455319577530e-16, 2.13070910639146380e-17, -3.55118184398548230e-18, 5.07311691997843240e-19, -6.34139614997088460e-20,

   3.370000e+01, 9.99999999999997670e-01, 2.31353439169574210e-15, -1.15676719584786570e-15, 3.85589065282618280e-16, -9.63972663206527840e-17, 1.92794532641298440e-17, -3.21324221068806990e-18, 4.59034601526799610e-19, -5.73793251908333040e-20,

   3.380000e+01, 9.99999999999997890e-01, 2.09337248551938240e-15, -1.04668624275968680e-15, 3.48895414253225950e-16, -8.72238535633050340e-17, 1.74447707126604210e-17, -2.90746178544320920e-18, 4.15351683634688900e-19, -5.19189604543224990e-20,

   3.390000e+01, 9.99999999999998110e-01, 1.89416175478486190e-15, -9.47080877392427420e-16, 3.15693625797473390e-16, -7.89234064493671520e-17, 1.57846812898729520e-17, -2.63078021497866600e-18, 3.75825744996906480e-19, -4.69782181246030610e-20,

   3.400000e+01, 9.99999999999998330e-01, 1.71390843154200710e-15, -8.56954215771000580e-16, 2.85651405256998220e-16, -7.14128513142485820e-17, 1.42825702628493230e-17, -2.38042837714142440e-18, 3.40061196734451400e-19, -4.25076495917978010e-20,

   3.410000e+01, 9.99999999999998450e-01, 1.55080847994651830e-15, -7.75404239973256690e-16, 2.58468079991083940e-16, -6.46170199977701830e-17, 1.29234039995537170e-17, -2.15390066659217940e-18, 3.07700095227423530e-19, -3.84625119034199790e-20,

   3.420000e+01, 9.99999999999998560e-01, 1.40322954086308700e-15, -7.01614770431541530e-16, 2.33871590143845830e-16, -5.84678975359608040e-17, 1.16935795071918990e-17, -1.94892991786522900e-18, 2.78418559695007630e-19, -3.48023199618701640e-20,

   3.430000e+01, 9.99999999999998780e-01, 1.26969459466634840e-15, -6.34847297333172530e-16, 2.11615765777723100e-16, -5.29039414444302390e-17, 1.05807882888858340e-17, -1.76346471481423380e-18, 2.51923530687728270e-19, -3.14904413359617250e-20,

   3.440000e+01, 9.99999999999998890e-01, 1.14886717873210330e-15, -5.74433589366050270e-16, 1.91477863122015880e-16, -4.78694657805035270e-17, 9.57389315610053080e-18, -1.59564885935003000e-18, 2.27949837049987270e-19, -2.84937296312450620e-20,

   3.450000e+01, 9.99999999999999000e-01, 1.03953801167021980e-15, -5.19769005835108810e-16, 1.73256335278368870e-16, -4.33140838195918600e-17, 8.66281676391822790e-18, -1.44380279398632340e-18, 2.06257541998031890e-19, -2.57821927497502700e-20,

   3.460000e+01, 9.99999999999999110e-01, 9.40612890429909060e-16, -4.70306445214953640e-16, 1.56768815071650610e-16, -3.91922037679123620e-17, 7.83844075358235410e-18, -1.30640679226368620e-18, 1.86629541751943390e-19, -2.33286927189902040e-20,

   3.470000e+01, 9.99999999999999110e-01, 8.51101739147944780e-16, -4.25550869573971700e-16, 1.41850289857990070e-16, -3.54625724644972780e-17, 7.09251449289935940e-18, -1.18208574881652830e-18, 1.68869392688066110e-19, -2.11086740860057180e-20,

   3.480000e+01, 9.99999999999999220e-01, 7.70108700136545650e-16, -3.85054350068272230e-16, 1.28351450022757000e-16, -3.20878625056890530e-17, 6.41757250113773230e-18, -1.06959541685626230e-18, 1.52799345265172830e-19, -1.90999181581443530e-20,

   3.490000e+01, 9.99999999999999330e-01, 6.96823167838575130e-16, -3.48411583919287070e-16, 1.16137194639762020e-16, -2.90342986599403450e-17, 5.80685973198800470e-18, -9.67809955331312550e-19, 1.38258565047323660e-19, -1.72823206309143410e-20 };


   Int_t i = (Int_t)(10*x+350.5);

   if(i<0)   return TMath::Exp(x);

   if(i>699) return 1;

   Double_t* basePoint = sigval+(10*i);

   Double_t res =  x - basePoint[0];

   res =        basePoint[1] + res * ( basePoint[2] + res * ( basePoint[3]

      + res * ( basePoint[4] + res * ( basePoint[5] + res * ( basePoint[6]

      + res * ( basePoint[7] + res * ( basePoint[8] )))))));

   /*

   if(x<-15) return TMath::Exp(x);

   if(x> 15) return 1;

   return (1/(1+TMath::Exp(-x)));

   */

   return res;

}


////////////////////////////////////////////////////////////////////////////////

/// The Derivative of the Sigmoid.


Double_t TNeuron::DSigmoid(Double_t x) const

{

   //if (x>2.1972246) return x/(1+TMath::Exp(x));

   //Double_t a = Sigmoid(x);

   //return a-a*a;

   if (TMath::Abs(x) > 5)

      return TMath::Exp(-TMath::Abs(x));

   Double_t expmx = TMath::Exp(-x);

   return expmx / ((1 + expmx) * (1 + expmx));

}


////////////////////////////////////////////////////////////////////////////////

/// Adds a synapse to the neuron as an input

/// This method is used by the TSynapse while

/// connecting two neurons.


void TNeuron::AddPre(TSynapse * pre)

{

   fpre.AddLast(pre);

   if (fpre.GetEntriesFast() == fpre.GetSize())

      fpre.Expand(2 * fpre.GetSize());

}


////////////////////////////////////////////////////////////////////////////////

/// Adds a synapse to the neuron as an output

/// This method is used by the TSynapse while

/// connecting two neurons.


void TNeuron::AddPost(TSynapse * post)

{

   fpost.AddLast(post);

   if (fpost.GetEntriesFast() == fpost.GetSize())

      fpost.Expand(2 * fpost.GetSize());

}


////////////////////////////////////////////////////////////////////////////////

/// Tells a neuron which neurons form its layer (including itself).

/// This is needed for self-normalizing functions, like Softmax.


void TNeuron::AddInLayer(TNeuron * nearP)

{

   flayer.AddLast(nearP);

   if (flayer.GetEntriesFast() == flayer.GetSize())

      flayer.Expand(2 * flayer.GetSize());

}


////////////////////////////////////////////////////////////////////////////////

/// Returns the neuron type.


TNeuron::ENeuronType TNeuron::GetType() const

{

   return fType;

}


////////////////////////////////////////////////////////////////////////////////

/// Sets a formula that can be used to make the neuron an input.

/// The formula is automatically normalized to mean=0, RMS=1.

/// This normalisation is used by GetValue() (input neurons)

/// and GetError() (output neurons)


TTreeFormula* TNeuron::UseBranch(TTree* input, const char* formula)

{

   if (fFormula) delete fFormula;

   // Set the formula

   // One checks for {}: defined as instance in TMultiLayerPerceptron

   // so that EvalInstance can be used. This allows to use arrays as

   // input, also in complex calculation, without detailed string parsing.

   TRegexp re("{[0-9]+}$");

   TString f(formula);

   Ssiz_t len = f.Length();

   Ssiz_t pos = re.Index(f,&len);

   if(pos==-1 || len<3)

      fFormula = new TTreeFormula(Form("NF%zu",(size_t)this),formula,input);

   else {

      TString newformula(formula,pos);

      TString val = f(pos+1,len-2);

      fFormula = new TTreeFormula(Form("NF%zu",(size_t)this),

                                  (const char*) newformula,input);

      fIndex = val.Atoi();

      f = newformula;

   }

   // Computes the default normalization

   TH1D tmp("tmpb", "tmpb", 1, -FLT_MAX, FLT_MAX);

   input->Draw(Form("%s>>tmpb",(const char*)f),"","goff");

   fNorm[0] = tmp.GetRMS();

   if(fNorm[0]<1e-15) fNorm[0]=1.;

   fNorm[1] = tmp.GetMean();

   // Check the dimensionality

   if(fFormula->GetNdata()>1 && fIndex==0)

      Warning("TNeuron::UseBranch()","all indices in arrays must be specified, otherwise the first element will be assumed.");

   return fFormula;

}


////////////////////////////////////////////////////////////////////////////////

/// Returns the formula value.


Double_t TNeuron::GetBranch() const

{

   Double_t branch = fFormula->EvalInstance(fIndex);

   if (TMath::IsNaN(branch))

      branch = 0.;

   return branch;

}


////////////////////////////////////////////////////////////////////////////////

/// Returns neuron input


Double_t TNeuron::GetInput() const

{

   if (!fNewInput) {

      return fInput;

   }

   ((TNeuron*)this)->fNewInput = false;

   Double_t input = 0.0;

   Int_t nEntries = fpre.GetEntriesFast();

   if (nEntries) {

      input = fWeight;

      for (Int_t i = 0; i < nEntries; i++) {

         TSynapse *preSynapse = (TSynapse*)fpre.UncheckedAt(i);

         input += preSynapse->GetValue();

      }

   }

   return (((TNeuron*)this)->fInput = input);

}


////////////////////////////////////////////////////////////////////////////////

/// Computes the output using the appropriate function and all

/// the weighted inputs, or uses the branch as input.

/// In that case, the branch normalisation is also used.


Double_t TNeuron::GetValue() const

{

   if (!fNewValue) {

      return fValue;

   }

   ((TNeuron*)this)->fNewValue = false;

   Int_t nentries = fpre.GetEntriesFast();

   if (!nentries) {

      Double_t branch = GetBranch();

      return (((TNeuron*)this)->fValue = (branch - fNorm[1]) / fNorm[0]);

   } else {

      Double_t input = GetInput();

      Double_t value = 0;

      switch (fType) {

      case TNeuron::kOff: {

         value = 0;

         break;

      }

      case TNeuron::kLinear: {

         value = input;

         break;

      }

      case TNeuron::kSigmoid: {

         value =  Sigmoid(input);

         break;

      }

      case TNeuron::kTanh: {

         value = TMath::TanH(input);

         break;

      }

      case TNeuron::kGauss: {

         value = TMath::Exp(-input * input);

         break;

      }

      case TNeuron::kSoftmax: {

         Double_t normalization = 0.0;

         for (Int_t i = 0; i < flayer.GetEntriesFast(); i++) {

            // this is not very efficient, as the same normalization

            // is calculated once per neuron instead of just once

            normalization += TMath::Exp(((TNeuron*) flayer.UncheckedAt(i))->GetInput());

         }

         if (normalization > 0.0) {

            // exp(a_k) / sum_k'[ exp(a_k') ]

            value = TMath::Exp(input) / normalization;

         } else {

            // all neurons have output = 0 ?

            value = 1.0 / flayer.GetEntriesFast();

         }

         break;

      }

      case TNeuron::kExternal: {

         value = fExtF->Eval(input);

         break;

      }

      }

      return (((TNeuron*)this)->fValue = value);

   }

}


////////////////////////////////////////////////////////////////////////////////

/// computes the derivative for the appropriate function

/// at the working point


Double_t TNeuron::GetDerivative() const

{

   if (!fNewDeriv)

      return fDerivative;

   ((TNeuron*)this)->fNewDeriv = false;

   Int_t nentries = fpre.GetEntriesFast();

   Double_t input = fWeight;

   for (Int_t i=0;i<nentries;i++) {

      TSynapse *preSynapse = (TSynapse*)fpre.UncheckedAt(i);

      input += preSynapse->GetValue();

   }

   Double_t derivative = 0;

   switch (fType) {

      case TNeuron::kOff: {

         derivative = 0;

         break;

      }

      case TNeuron::kLinear: {

         derivative = 1;

         break;

      }

      case TNeuron::kSigmoid: {

         derivative = DSigmoid(input);

         break;

      }

      case TNeuron::kTanh: {

         derivative = (1 - (TMath::TanH(input) * TMath::TanH(input)));

         break;

      }

      case TNeuron::kGauss: {

         derivative = (-2) * input * TMath::Exp(-input * input);

         break;

      }

      case TNeuron::kSoftmax: {

         // actually this is not the derivative, as the Softmax function needs

         // exp(activation) of all the neurons in the layer for the normalization.

         // it will be smartly taken care of in GetDeDw()

         derivative = GetValue();

         break;

      }

      case TNeuron::kExternal: {

         derivative = fExtD->Eval(input);

         break;

      }

   }

   return (((TNeuron*)this)->fDerivative = derivative);

}


////////////////////////////////////////////////////////////////////////////////

/// Computes the error for output neurons.

/// Returns 0 for other neurons.


Double_t TNeuron::GetError() const

{

   if (!fpost.GetEntriesFast())

      return (GetValue() - (GetBranch() - fNorm[1]) / fNorm[0]);

   return 0;

}


////////////////////////////////////////////////////////////////////////////////

/// Computes the normalized target pattern for output neurons.

/// Returns 0 for other neurons.


Double_t TNeuron::GetTarget() const

{

   if (!fpost.GetEntriesFast())

      return ((GetBranch() - fNorm[1]) / fNorm[0]);

   return 0;

}


////////////////////////////////////////////////////////////////////////////////

/// Computes the derivative of the error wrt the neuron weight.


Double_t TNeuron::GetDeDw() const

{

   if (!fNewDeDw)

      return fDeDw;

   ((TNeuron*)this)->fNewDeDw = false;

   // Output units DeDw is just the error for these cases:

   //  - linear output,  with sum-of-squares error

   //  - sigmoid output, with binary cross-entropy

   //  - softmax output, with 1-of-c cross entropy

   Int_t nEntries = fpost.GetEntriesFast();

   if (nEntries == 0) {

      // output neuron

      ((TNeuron*)this)->fDeDw = GetError();

   } else {

      // hidden nuron

      ((TNeuron*)this)->fDeDw = 0.0;

      if (fType != TNeuron::kSoftmax) {

         // non-softmax

         for (Int_t i = 0; i < nEntries; i++) {

            TSynapse *postSynapse = (TSynapse*)fpost.UncheckedAt(i);

            ((TNeuron*)this)->fDeDw +=

              postSynapse->GetWeight() *

              postSynapse->GetPost()->GetDeDw();

         }

      } else {

         // softmax derivative can be taken care of correcting the forward weight

         for (Int_t i = 0; i < nEntries; i++) {

            TSynapse *postSynapse = (TSynapse*)fpost.UncheckedAt(i);

            ((TNeuron*)this)->fDeDw +=

              (postSynapse->GetWeight() - postSynapse->GetPost()->GetInput()) *

              postSynapse->GetPost()->GetDeDw();

         }

      }

      ((TNeuron*)this)->fDeDw *= GetDerivative();

   }

   return fDeDw;

}


////////////////////////////////////////////////////////////////////////////////

/// Uses the branch type to force an external value.


void TNeuron::ForceExternalValue(Double_t value)

{

   fNewValue = false;

   fValue = (value - fNorm[1]) / fNorm[0];

}


////////////////////////////////////////////////////////////////////////////////

/// Sets the normalization variables.

/// Any input neuron will return (branch-mean)/RMS.

/// When UseBranch is called, mean and RMS are automatically set

/// to the actual branch mean and RMS.


void TNeuron::SetNormalisation(Double_t mean, Double_t RMS)

{

   fNorm[0] = RMS;

   fNorm[1] = mean;

}


////////////////////////////////////////////////////////////////////////////////

/// Sets the neuron weight to w.

/// The neuron weight corresponds to the bias in the

/// linear combination of the inputs.


void TNeuron::SetWeight(Double_t w)

{

   fWeight = w;

}


////////////////////////////////////////////////////////////////////////////////

/// Inform the neuron that inputs of the network have changed,

/// so that the buffered values have to be recomputed.


void TNeuron::SetNewEvent() const

{

   ((TNeuron*)this)->fNewInput = true;

   ((TNeuron*)this)->fNewValue = true;

   ((TNeuron*)this)->fNewDeriv = true;

   ((TNeuron*)this)->fNewDeDw = true;

}


////////////////////////////////////////////////////////////////////////////////

/// Sets the derivative of the total error wrt the neuron weight.


void TNeuron::SetDEDw(Double_t in)

{

   fDEDw = in;

}

f
#define f(i)
Definition RSha256.hxx:104

e
#define e(i)
Definition RSha256.hxx:103

Int_t
int Int_t
Definition RtypesCore.h:45

ClassImp
#define ClassImp(name)
Definition Rtypes.h:377

TBranch.h

w
winID w
Definition TGWin32VirtualGLProxy.cxx:39

input
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void input
Definition TGWin32VirtualXProxy.cxx:142

value
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void value
Definition TGWin32VirtualXProxy.cxx:142

len
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t Int_t Int_t UInt_t UInt_t Rectangle_t Int_t Int_t Window_t TString Int_t GCValues_t GetPrimarySelectionOwner GetDisplay GetScreen GetColormap GetNativeEvent const char const char dpyName wid window const char font_name cursor keysym reg const char only_if_exist regb h Point_t winding char text const char depth char const char Int_t count const char ColorStruct_t color const char Pixmap_t Pixmap_t PictureAttributes_t attr const char char ret_data h unsigned char height h Atom_t Int_t ULong_t ULong_t unsigned char prop_list Atom_t Atom_t Atom_t Time_t UChar_t len
Definition TGWin32VirtualXProxy.cxx:249

type
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t Int_t Int_t UInt_t UInt_t Rectangle_t Int_t Int_t Window_t TString Int_t GCValues_t GetPrimarySelectionOwner GetDisplay GetScreen GetColormap GetNativeEvent const char const char dpyName wid window const char font_name cursor keysym reg const char only_if_exist regb h Point_t winding char text const char depth char const char Int_t count const char ColorStruct_t color const char Pixmap_t Pixmap_t PictureAttributes_t attr const char char ret_data h unsigned char height h Atom_t Int_t ULong_t ULong_t unsigned char prop_list Atom_t Atom_t Atom_t Time_t type
Definition TGWin32VirtualXProxy.cxx:249

name
char name[80]
Definition TGX11.cxx:110

TH1D.h

nentries
int nentries
Definition THbookFile.cxx:91

TMath.h

TROOT.h

gROOT
#define gROOT
Definition TROOT.h:405

TRegexp.h

Form
char * Form(const char *fmt,...)
Formats a string in a circular formatting buffer.
Definition TString.cxx:2467

TTreeFormula.h

TTree.h

TCollection::SetOwner
virtual void SetOwner(Bool_t enable=kTRUE)
Set whether this collection is the owner (enable==true) of its content.
Definition TCollection.cxx:746

TCollection::GetSize
virtual Int_t GetSize() const
Return the capacity of the collection, i.e.
Definition TCollection.h:184

TFormula
The Formula class.
Definition TFormula.h:87

TFormula::Eval
Double_t Eval(Double_t x) const
Sets first variable (e.g. x) and evaluate formula.
Definition TFormula.cxx:3445

TH1D
1-D histogram with a double per channel (see TH1 documentation)}
Definition TH1.h:620

TH1::GetMean
virtual Double_t GetMean(Int_t axis=1) const
For axis = 1,2 or 3 returns the mean value of the histogram along X,Y or Z axis.
Definition TH1.cxx:7445

TH1::GetRMS
Double_t GetRMS(Int_t axis=1) const
This function returns the Standard Deviation (Sigma) of the distribution not the Root Mean Square (RM...
Definition TH1.h:317

TNamed
The TNamed class is the base class for all named ROOT classes.
Definition TNamed.h:29

TNeuron
This class describes an elementary neuron, which is the basic element for a Neural Network.
Definition TNeuron.h:25

TNeuron::GetDerivative
Double_t GetDerivative() const
computes the derivative for the appropriate function at the working point
Definition TNeuron.cxx:1007

TNeuron::fWeight
Double_t fWeight
weight used for computation
Definition TNeuron.h:70

TNeuron::fpost
TObjArray fpost
pointers to the next level in a network
Definition TNeuron.h:68

TNeuron::SetWeight
void SetWeight(Double_t w)
Sets the neuron weight to w.
Definition TNeuron.cxx:1144

TNeuron::TNeuron
TNeuron(ENeuronType type=kSigmoid, const char *name="", const char *title="", const char *extF="", const char *extD="")
Usual constructor.
Definition TNeuron.cxx:47

TNeuron::flayer
TObjArray flayer
pointers to the current level in a network (neurons, not synapses)
Definition TNeuron.h:69

TNeuron::fExtD
TFormula * fExtD
derivative (external mode)
Definition TNeuron.h:74

TNeuron::fDerivative
Double_t fDerivative
! buffer containing the last neuron derivative
Definition TNeuron.h:82

TNeuron::fNewInput
Bool_t fNewInput
! do we need to compute fInput again ?
Definition TNeuron.h:77

TNeuron::fFormula
TTreeFormula * fFormula
! formula to be used for inputs and outputs
Definition TNeuron.h:75

TNeuron::fIndex
Int_t fIndex
! index in the formula
Definition TNeuron.h:76

TNeuron::fDEDw
Double_t fDEDw
! buffer containing the sum over all examples of DeDw
Definition TNeuron.h:85

TNeuron::GetValue
Double_t GetValue() const
Computes the output using the appropriate function and all the weighted inputs, or uses the branch as...
Definition TNeuron.cxx:944

TNeuron::Sigmoid
Double_t Sigmoid(Double_t x) const
The Sigmoid.
Definition TNeuron.cxx:91

TNeuron::fDeDw
Double_t fDeDw
! buffer containing the last derivative of the error
Definition TNeuron.h:84

TNeuron::SetDEDw
void SetDEDw(Double_t in)
Sets the derivative of the total error wrt the neuron weight.
Definition TNeuron.cxx:1164

TNeuron::GetDeDw
Double_t GetDeDw() const
Computes the derivative of the error wrt the neuron weight.
Definition TNeuron.cxx:1080

TNeuron::GetBranch
Double_t GetBranch() const
Returns the formula value.
Definition TNeuron.cxx:910

TNeuron::GetError
Double_t GetError() const
Computes the error for output neurons.
Definition TNeuron.cxx:1059

TNeuron::fNewValue
Bool_t fNewValue
! do we need to compute fValue again ?
Definition TNeuron.h:79

TNeuron::AddPost
void AddPost(TSynapse *)
Adds a synapse to the neuron as an output This method is used by the TSynapse while connecting two ne...
Definition TNeuron.cxx:842

TNeuron::UseBranch
TTreeFormula * UseBranch(TTree *, const char *)
Sets a formula that can be used to make the neuron an input.
Definition TNeuron.cxx:874

TNeuron::fNewDeriv
Bool_t fNewDeriv
! do we need to compute fDerivative again ?
Definition TNeuron.h:81

TNeuron::ForceExternalValue
void ForceExternalValue(Double_t value)
Uses the branch type to force an external value.
Definition TNeuron.cxx:1121

TNeuron::fInput
Double_t fInput
! buffer containing the last neuron input
Definition TNeuron.h:78

TNeuron::GetTarget
Double_t GetTarget() const
Computes the normalized target pattern for output neurons.
Definition TNeuron.cxx:1070

TNeuron::fNorm
Double_t fNorm[2]
normalisation to mean=0, RMS=1.
Definition TNeuron.h:71

TNeuron::GetInput
Double_t GetInput() const
Returns neuron input.
Definition TNeuron.cxx:921

TNeuron::DSigmoid
Double_t DSigmoid(Double_t x) const
The Derivative of the Sigmoid.
Definition TNeuron.cxx:814

TNeuron::fType
ENeuronType fType
neuron type
Definition TNeuron.h:72

TNeuron::AddPre
void AddPre(TSynapse *)
Adds a synapse to the neuron as an input This method is used by the TSynapse while connecting two neu...
Definition TNeuron.cxx:830

TNeuron::fExtF
TFormula * fExtF
function (external mode)
Definition TNeuron.h:73

TNeuron::GetType
ENeuronType GetType() const
Returns the neuron type.
Definition TNeuron.cxx:863

TNeuron::fNewDeDw
Bool_t fNewDeDw
! do we need to compute fDeDw again ?
Definition TNeuron.h:83

TNeuron::fValue
Double_t fValue
! buffer containing the last neuron output
Definition TNeuron.h:80

TNeuron::SetNewEvent
void SetNewEvent() const
Inform the neuron that inputs of the network have changed, so that the buffered values have to be rec...
Definition TNeuron.cxx:1153

TNeuron::SetNormalisation
void SetNormalisation(Double_t mean, Double_t RMS)
Sets the normalization variables.
Definition TNeuron.cxx:1133

TNeuron::AddInLayer
void AddInLayer(TNeuron *)
Tells a neuron which neurons form its layer (including itself).
Definition TNeuron.cxx:853

TNeuron::ENeuronType
ENeuronType
Definition TNeuron.h:29

TNeuron::kLinear
@ kLinear
Definition TNeuron.h:29

TNeuron::kSigmoid
@ kSigmoid
Definition TNeuron.h:29

TNeuron::kExternal
@ kExternal
Definition TNeuron.h:29

TNeuron::kSoftmax
@ kSoftmax
Definition TNeuron.h:29

TNeuron::kGauss
@ kGauss
Definition TNeuron.h:29

TNeuron::kOff
@ kOff
Definition TNeuron.h:29

TNeuron::kTanh
@ kTanh
Definition TNeuron.h:29

TNeuron::fpre
TObjArray fpre
pointers to the previous level in a network
Definition TNeuron.h:67

TObjArray::GetEntriesFast
Int_t GetEntriesFast() const
Definition TObjArray.h:58

TObjArray::Expand
virtual void Expand(Int_t newSize)
Expand or shrink the array to newSize elements.
Definition TObjArray.cxx:387

TObjArray::AddLast
void AddLast(TObject *obj) override
Add object in the next empty slot in the array.
Definition TObjArray.cxx:178

TObjArray::UncheckedAt
TObject * UncheckedAt(Int_t i) const
Definition TObjArray.h:84

TObject::Warning
virtual void Warning(const char *method, const char *msgfmt,...) const
Issue warning message.
Definition TObject.cxx:956

TObject::FindObject
virtual TObject * FindObject(const char *name) const
Must be redefined in derived classes.
Definition TObject.cxx:403

TRegexp
Regular expression class.
Definition TRegexp.h:31

TRegexp::Index
Ssiz_t Index(const TString &str, Ssiz_t *len, Ssiz_t start=0) const
Find the first occurrence of the regexp in string and return the position, or -1 if there is no match...
Definition TRegexp.cxx:209

TString
Basic string class.
Definition TString.h:139

TString::Atoi
Int_t Atoi() const
Return integer value of string.
Definition TString.cxx:1966

TSynapse
This is a simple weighted bidirectional connection between two neurons.
Definition TSynapse.h:20

TSynapse::GetValue
Double_t GetValue() const
Returns the value: weighted input.
Definition TSynapse.cxx:79

TSynapse::GetPost
TNeuron * GetPost() const
Definition TSynapse.h:28

TSynapse::GetWeight
Double_t GetWeight() const
Definition TSynapse.h:30

TTreeFormula
Used to pass a selection expression to the Tree drawing routine.
Definition TTreeFormula.h:58

TTreeFormula::EvalInstance
T EvalInstance(Int_t i=0, const char *stringStack[]=nullptr)
Evaluate this treeformula.
Definition TTreeFormula.cxx:3936

TTreeFormula::GetNdata
virtual Int_t GetNdata()
Return number of available instances in the formula.
Definition TTreeFormula.cxx:4444

TTree
A TTree represents a columnar dataset.
Definition TTree.h:79

double

int

x
Double_t x[n]
Definition legend1.C:17

TMath::IsNaN
Bool_t IsNaN(Double_t x)
Definition TMath.h:890

TMath::Exp
Double_t Exp(Double_t x)
Returns the base-e exponential function of x, which is e raised to the power x.
Definition TMath.h:707

TMath::TanH
Double_t TanH(Double_t)
Returns the hyperbolic tangent of x.
Definition TMath.h:616

TMath::Abs
Short_t Abs(Short_t d)
Returns the absolute value of parameter Short_t d.
Definition TMathBase.h:123