1. Simple SIR model with gamma distributed lengths of stay
The SIR model uses 3 compartments: S (susceptible), I (infected), R (recovered) to describe clinical status of individuals. We use the most simple form of SIR model to demonstrate how to define the distribution of the lengths of stay distribution.
The model equations are:
\[S_{t+1} - S_{t} = -\lambda S_{t} = -\frac{\beta I_{t}}{N}S_{t}\] \[I_{t+1} - I_{t} = \frac{\beta I_{t}}{N}S_{t} - \gamma I_{t}\] \[R_{t+1} - R_{t} = \gamma I_{t}\]
- \(N\): total population size, \(N = S + I + R\)
- \(\beta\): the product of contact rates and transmission probability; usually we define \(\lambda =\frac{\beta I_{t}}{N}\) as the force of infection
- \(\gamma\): recovery rate
Usually to solve the model easier we make an assumption that the recovery rate \(\gamma\) is constant, this will leads to an exponentially distributed length of stay i.e most individuals recover after 1 day being infected.
A more realistic length of stay distribution can look like this, of which most patients recovered after 4 days. We defined this using a gamma distribution with shape = 3 and rate = 1/2.
The model now look like this:
Model specification
Model transition
We have two transitions S -> I and
I -> R in this case. The transitions are specified in a
list follow this format "transition" = equation", of which
equation is defined with one of our functions for waiting time
distribution.
Where timeStep is the duration of a time step used for
simulation.
Another option to define the transitions is by using denim’s DSL. Refer to the Model definition in denim article for more information.
transitions <- denim_dsl({
S -> I = beta * (I/N) * S * timeStep
I -> R = d_gamma(rate = 1/4, shape = 3)
})Initial state
Use a vector to define the compartments with their assigned names and
initial values in the format
compartment_name = initial_value:
initialValues <- c(
S = 999,
I = 1,
R = 0
)Model parameters
If we use a math expression, any symbols except the compartment names
are parameters, and would be defined by constant values. There are two
constant parameters in our example: beta and
N:
parameters <- c(
beta = 1.2,
N = 1000
)Note that we do not need to specify variable timeStep
since denim will automatically use the timeStep from the
simulation settings in the next step.
Model application
Time step specification
We run the model for 30 days and give output at 0.01 daily intervals. The default interval (time step) is 1 if not declared explicitly.
simulationDuration <- 30
timeStep <- 0.01
mod <- sim(transitions = transitions,
initialValues = initialValues,
parameters = parameters,
simulationDuration = simulationDuration,
timeStep = timeStep)
head(mod)
#> Time S I R
#> 1 0.00 999.0000 1.000000 0.000000e+00
#> 2 0.01 998.9880 1.011988 2.599289e-09
#> 3 0.02 998.9759 1.024120 2.078652e-08
#> 4 0.03 998.9636 1.036396 7.019852e-08
#> 5 0.04 998.9512 1.048820 1.665435e-07
#> 6 0.05 998.9386 1.061393 3.256027e-07
plot(mod)
2. How the algorithm work?
In the SIR model, all infected individuals are presented by a single compartment I and have the same recovery rate \(\gamma\).
We want the recovery rate of individuals who had been infected for 1 day differ from the recovery rate of 2-day infected patients. So rather than using one compartment for infected (I), we define multiple infected sub-compartments. The number of sub-compartments depends on the maximum day we expect all infected individuals would be recovered.
For example, if we expect a disease with a maximum 4 days of infection, we will end up with 4 sub-compartments. Each sub-compartment has its own recovery rate \(\gamma_{1}\), \(\gamma_{2}\), \(\gamma_{3}\), \(\gamma_{4}\). At day 4 it is certain that the patient will recover (because we assume that this disease has a maximum 4 days of infection), \(\gamma_{4} = 1\).
Let \(R_1 + R_2 + R_3 + R_4 = \Sigma R\). We have \(\frac{R_1}{\Sigma R} = p_1\), \(\frac{R_2}{\Sigma R} = p_2\), \(\frac{R_3}{\Sigma R} = p_3\), \(\frac{R_4}{\Sigma R} = p_4\). Our mission is to estimate \(\gamma_{1}\), \(\gamma_{2}\), \(\gamma_{3}\) to obtain \(p_1\), \(p_2\), \(p_3\), \(p_4\) that fit a pre-defined distribution at the equilibrium state. This can be obtained by setting:
\[\gamma_{i} = \frac{p_i}{1 - \sum_{j=1}^{i-1}p_j}\]
For a given length of stay distribution, we identify the maximum
length of stay using its cumulative distribution function. Because
cumulative distribution function is asymptotic to 1 and never equal to
1, we need to set a value that is acceptable to be rounded to 1. If we
want a cumulative probability of 0.999 to be rounded as 1, we set the
error tolerance threshold as 1 - 0.999 = 0.001 (specified
by the argument errorTolerance = 0.001). The time when
cumulative probability = 0.999 will be set as the maximum length of stay
of the compartment. Default errorTolerance of
denim is set at 0.001.
Initialize population in sub-compartments
By default, the initial population is always assigned to the first
sub-compartment (for example, if the initial value for I compartment is
I = 1, denim will initialize I1 = 1 while
I2 = I3 = I4 = 0).
User can also choose to distribute initial population across
sub-compartments based on the specified distribution, i.e. with initial
population I = n, then denim will initialize
I1 = n*p1, I2 = n*p2, I3 = n*p3,
I4 = n*p4. To set up the initial population in this way,
simply specify the parameter dist_init = TRUE (only
applicable for distribution transitions).
3. Waiting time distribution
denim offers 2 main ways to define a transition: either
by a waiting time distribution, or a mathematical expression.
Current available distributions in this package including:
d_exponential(rate): Discrete exponential distribution with parameterrated_gamma(rate, shape): Discrete gamma distribution with parametersrateandshaped_weibull(scale, shape): Discrete Weibull distribution with parametersscaleandshaped_lognormal(mu, sigma): Discrete log-normal distribution with parametersmuandsigmanonparametric(waitingTimes): A vector of values, could be numbers, percentages, density of the length of stay based on real data,denimwill convert it into a distribution
Mathematical expression: Transition can also be described using a
math expression such as beta * S * I / N. You will need to
define parameters that are not compartment names in the
parameters argument
4. Multiple transitions from a compartment
In denim, transitions between one compartment to
multiple compartments are modeled as either (i) multinomial transition
or (ii) competing risks.
Consider this example:
There are two scenarios in this example:
Susceptible individuals can be infected or vaccinated. The assumption here is they will be infected first (
S -> I), and then the rest of them who were not infected will get vaccinated (S -> V).Infected individuals can recover or die. If the mortality probability is known, we can implement it into the model, for example by defining
0.9 * I -> R(90% individuals will recover) and then0.1 * I -> D(10% of them die). By doing so, we ensure that the mortality probability is 10%, while also define the length of stay of individuals at the infected state before recover or die follows gamma or log-normal distribution, respectively.
We can define the model for this example as follows:
transitions <- denim_dsl({
S -> I = beta * S * I / N
S -> V = 5
0.9 * I -> R = d_gamma(1/3, 2)
0.1 * I -> D = d_lognormal(2, 0.5)
})
initialValues <- c(
S = 999,
I = 1,
R = 0,
V = 0,
D = 0
)
parameters <- c(
beta = 0.12,
N = 1000
)
simulationDuration <- 10
timeStep <- 0.01
mod <- sim(transitions = transitions,
initialValues = initialValues,
parameters = parameters,
simulationDuration = simulationDuration,
timeStep = timeStep)
head(mod)
#> Time S I V R D
#> 1 0.00 999.0000 1.000000 0 0.000000e+00 0.000000e+00
#> 2 0.01 993.8801 1.119875 5 4.988903e-06 0.000000e+00
#> 3 0.02 988.7466 1.253422 10 2.050940e-05 1.466074e-33
#> 4 0.03 983.5978 1.402113 15 4.775442e-05 1.651901e-29
#> 5 0.04 978.4323 1.567566 20 8.805255e-05 8.337600e-27
#> 6 0.05 973.2483 1.751562 25 1.428825e-04 8.315472e-25
plot(mod, ylim = c(0, 1000))
For a more detailed explanation for transitions to multiple states, refer to this article
5. Another example
transitions <- denim_dsl({
S -> I = beta * S * (I + IV) / N
S -> V = 2
0.1 * I -> D = d_lognormal(mu = d_mu, sigma = d_sigma)
0.9 * I -> R = d_gamma(rate = r_rate, shape = r_shape)
V -> IV = 0.1 * beta * V * (I + IV) / N
IV -> R = d_exponential(iv_r_rate)
})
initialValues <- c(
S = 999,
I = 1,
R = 0,
V = 0,
IV = 0,
D = 0
)
parameters <- c(
beta = 0.12,
N = 1000,
d_mu = 2,
d_sigma = 1/2,
r_rate = 1/3,
r_shape = 2,
iv_r_rate = 2
)
simulationDuration <- 10
timeStep <- 0.01
mod <- sim(transitions = transitions,
initialValues = initialValues,
parameters = parameters,
simulationDuration = simulationDuration,
timeStep = timeStep)
plot(mod)
mod
#> Time S I V IV D
#> 1 0.00 999.000000 1.000000 0.0000000 0.000000e+00 0.000000e+00
#> 2 0.01 996.880120 1.119875 2.0000000 0.000000e+00 0.000000e+00
#> 3 0.02 994.746154 1.253825 3.9999731 2.687700e-05 1.466074e-33
#> 4 0.03 992.596483 1.403470 5.9999129 8.652930e-05 1.651901e-29
#> 5 0.04 990.429303 1.570609 7.9998119 1.858705e-04 8.337600e-27
#> 6 0.05 988.242611 1.757246 9.9996611 3.329828e-04 8.315472e-25
#> 7 0.06 986.034182 1.965604 11.9994502 5.372916e-04 3.090351e-23
#> 8 0.07 983.801540 2.198157 13.9991671 8.097639e-04 5.936766e-22
#> 9 0.08 981.541938 2.457649 15.9987977 1.163134e-03 7.128608e-21
#> 10 0.09 979.252327 2.747129 17.9983256 1.612159e-03 6.029773e-20
#> 11 0.10 976.929321 3.069977 19.9977319 2.173909e-03 3.891737e-19
#> 12 0.11 974.569168 3.429946 21.9969947 2.868095e-03 2.026823e-18
#> 13 0.12 972.167707 3.831191 23.9960886 3.717442e-03 8.870316e-18
#> 14 0.13 969.720326 4.278322 25.9949843 4.748106e-03 3.362659e-17
#> 15 0.14 967.221920 4.776438 27.9936482 5.990147e-03 1.130145e-16
#> 16 0.15 964.666840 5.331185 29.9920417 7.478065e-03 3.429094e-16
#> 17 0.16 962.048836 5.948808 31.9901203 9.251399e-03 9.530053e-16
#> 18 0.17 959.361003 6.636207 33.9878331 1.135540e-02 2.454445e-15
#> 19 0.18 956.595713 7.401002 35.9851219 1.384178e-02 5.914335e-15
#> 20 0.19 953.744552 8.251602 37.9819200 1.676958e-02 1.343984e-14
#> 21 0.20 950.798243 9.197277 39.9781514 2.020611e-02 2.899338e-14
#> 22 0.21 947.746567 10.248235 41.9737294 2.422797e-02 5.971098e-14
#> 23 0.22 944.578284 11.415707 43.9685553 2.892231e-02 1.179600e-13
#> 24 0.23 941.281042 12.712037 45.9625169 3.438806e-02 2.244511e-13
#> 25 0.24 937.841286 14.150766 47.9554866 4.073742e-02 4.128151e-13
#> 26 0.25 934.244160 15.746737 49.9473199 4.809749e-02 7.361666e-13
#> 27 0.26 930.473412 17.516190 51.9378530 5.661201e-02 1.276310e-12
#> 28 0.27 926.511289 19.476861 53.9269006 6.644334e-02 2.156390e-12
#> 29 0.28 922.338438 21.648085 55.9142537 7.777460e-02 3.557965e-12
#> 30 0.29 917.933807 24.050895 57.8996763 9.081198e-02 5.743670e-12
#> 31 0.30 913.274548 26.708117 59.8829027 1.057873e-01 9.086844e-12
#> 32 0.31 908.335934 29.644455 61.8636344 1.229609e-01 1.410976e-11
#> 33 0.32 903.091276 32.886571 63.8415362 1.426244e-01 2.153229e-11
#> 34 0.33 897.511871 36.463140 65.8162325 1.651039e-01 3.233324e-11
#> 35 0.34 891.566957 40.404890 67.7873037 1.907634e-01 4.782678e-11
#> 36 0.35 885.223707 44.744614 69.7542813 2.200085e-01 6.975675e-11
#> 37 0.36 878.447257 49.517138 71.7166436 2.532897e-01 1.004122e-10
#> 38 0.37 871.200774 54.759252 73.6738112 2.911066e-01 1.427674e-10
#> 39 0.38 863.445584 60.509581 75.6251420 3.340116e-01 2.006508e-10
#> 40 0.39 855.141368 66.808394 77.5699263 3.826134e-01 2.789474e-10
#> 41 0.40 846.246431 73.697331 79.5073823 4.375811e-01 3.838386e-10
#> 42 0.41 836.718063 81.219038 81.4366510 4.996477e-01 5.230871e-10
#> 43 0.42 826.513003 89.416709 83.3567922 5.696128e-01 7.063707e-10
#> 44 0.43 815.588019 98.333503 85.2667806 6.483454e-01 9.456741e-10
#> 45 0.44 803.900610 108.011840 87.1655022 7.367856e-01 1.255745e-09
#> 46 0.45 791.409839 118.492572 89.0517527 8.359458e-01 1.654622e-09
#> 47 0.46 778.077308 129.814002 90.9242357 9.469100e-01 2.164250e-09
#> 48 0.47 763.868256 142.010789 92.7815637 1.070832e+00 2.811178e-09
#> 49 0.48 748.752795 155.112712 94.6222597 1.208932e+00 3.627376e-09
#> 50 0.49 732.707243 169.143336 96.4447616 1.362492e+00 4.651156e-09
#> 51 0.50 715.715540 184.118594 98.2474288 1.532845e+00 5.928228e-09
#> 52 0.51 697.770706 200.045333 100.0285515 1.721370e+00 7.512908e-09
#> 53 0.52 678.876278 216.919870 101.7863623 1.929474e+00 9.469482e-09
#> 54 0.53 659.047683 234.726631 103.5190518 2.158578e+00 1.187376e-08
#> 55 0.54 638.313445 253.436928 105.2247862 2.410101e+00 1.481481e-08
#> 56 0.55 616.716173 273.007985 106.9017288 2.685435e+00 1.839697e-08
#> 57 0.56 594.313222 293.382274 108.5480636 2.985925e+00 2.274206e-08
#> 58 0.57 571.176958 314.487244 110.1620213 3.312843e+00 2.799188e-08
#> 59 0.58 547.394547 336.235538 111.7419073 3.667358e+00 3.431106e-08
#> 60 0.59 523.067228 358.525726 113.2861305 4.050516e+00 4.189020e-08
#> 61 0.60 498.309018 381.243590 114.7932322 4.463209e+00 5.094942e-08
#> 62 0.61 473.244877 404.263967 116.2619138 4.906150e+00 6.174238e-08
#> 63 0.62 448.008358 427.453099 117.6910630 5.379852e+00 7.456065e-08
#> 64 0.63 422.738824 450.671417 119.0797762 5.884611e+00 8.973872e-08
#> 65 0.64 397.578349 473.776640 120.4273771 6.420487e+00 1.076595e-07
#> 66 0.65 372.668431 496.627068 121.7334305 6.987299e+00 1.287606e-07
#> 67 0.66 348.146690 519.084879 122.9977501 7.584622e+00 1.535411e-07
#> 68 0.67 324.143701 541.019303 124.2204001 8.211786e+00 1.825690e-07
#> 69 0.68 300.780125 562.309487 125.4016916 8.867891e+00 2.164904e-07
#> 70 0.69 278.164269 582.846942 126.5421723 9.551814e+00 2.560382e-07
#> 71 0.70 256.390169 602.537456 127.6426112 1.026224e+01 3.020430e-07
#> 72 0.71 235.536271 621.302418 128.7039790 1.099766e+01 3.554446e-07
#> 73 0.72 215.664718 639.079529 129.7274245 1.175645e+01 4.173050e-07
#> 74 0.73 196.821236 655.822918 130.7142492 1.253683e+01 4.888226e-07
#> 75 0.74 179.035549 671.502725 131.6658795 1.333695e+01 5.713483e-07
#> 76 0.75 162.322271 686.104214 132.5838393 1.415491e+01 6.664022e-07
#> 77 0.76 146.682153 699.626522 133.4697228 1.498874e+01 7.756939e-07
#> 78 0.77 132.103596 712.081149 134.3251688 1.583649e+01 9.011431e-07
#> 79 0.78 118.564332 723.490275 135.1518369 1.669624e+01 1.044903e-06
#> 80 0.79 106.033165 733.885015 135.9513861 1.756608e+01 1.209387e-06
#> 81 0.80 94.471717 743.303685 136.7254562 1.844418e+01 1.397297e-06
#> 82 0.81 83.836081 751.790133 137.4756523 1.932877e+01 1.611652e-06
#> 83 0.82 74.078371 759.392199 138.2035315 2.021815e+01 1.855826e-06
#> 84 0.83 65.148099 766.160333 138.9105926 2.111075e+01 2.133586e-06
#> 85 0.84 56.993393 772.146380 139.5982691 2.200505e+01 2.449129e-06
#> 86 0.85 49.562027 777.402546 140.2679231 2.289967e+01 2.807130e-06
#> 87 0.86 42.802275 781.980544 140.9208424 2.379330e+01 3.212791e-06
#> 88 0.87 36.663601 785.930906 141.5582384 2.468477e+01 3.671896e-06
#> 89 0.88 31.097190 789.302446 142.1812465 2.557297e+01 4.190866e-06
#> 90 0.89 26.056350 792.141866 142.7909265 2.645691e+01 4.776826e-06
#> 91 0.90 21.496786 794.493471 143.3882648 2.733569e+01 5.437674e-06
#> 92 0.91 17.376784 796.398996 143.9741769 2.820849e+01 6.182155e-06
#> 93 0.92 13.657301 797.897504 144.5495106 2.907459e+01 7.019942e-06
#> 94 0.93 10.301996 799.025363 145.1150497 2.993334e+01 7.961728e-06
#> 95 0.94 7.277204 799.816268 145.6715171 3.078415e+01 9.019315e-06
#> 96 0.95 4.551871 800.301308 146.2195792 3.162652e+01 1.020572e-05
#> 97 0.96 2.097451 800.509064 146.7598496 3.246001e+01 1.153530e-05
#> 98 0.97 0.000000 800.465722 147.1806904 3.328421e+01 1.302384e-05
#> 99 0.98 0.000000 800.206436 145.7081477 3.409768e+01 1.468869e-05
#> 100 0.99 0.000000 799.940904 144.2493688 3.488128e+01 1.654895e-05
#> 101 1.00 0.000000 799.669171 142.8042979 3.563566e+01 1.862553e-05
#> 102 1.01 0.000000 799.391280 141.3728765 3.636145e+01 2.094138e-05
#> 103 1.02 0.000000 799.107275 139.9550433 3.705927e+01 2.352163e-05
#> 104 1.03 0.000000 798.817200 138.5507346 3.772976e+01 2.639376e-05
#> 105 1.04 0.000000 798.521098 137.1598842 3.837351e+01 2.958779e-05
#> 106 1.05 0.000000 798.219014 135.7824238 3.899113e+01 3.313650e-05
#> 107 1.06 0.000000 797.910989 134.4182827 3.958319e+01 3.707562e-05
#> 108 1.07 0.000000 797.597067 133.0673884 4.015028e+01 4.144407e-05
#> 109 1.08 0.000000 797.277291 131.7296662 4.069298e+01 4.628419e-05
#> 110 1.09 0.000000 796.951702 130.4050396 4.121183e+01 5.164197e-05
#> 111 1.10 0.000000 796.620343 129.0934307 4.170739e+01 5.756735e-05
#> 112 1.11 0.000000 796.283256 127.7947594 4.218020e+01 6.411446e-05
#> 113 1.12 0.000000 795.940482 126.5089446 4.263079e+01 7.134194e-05
#> 114 1.13 0.000000 795.592064 125.2359034 4.305969e+01 7.931320e-05
#> 115 1.14 0.000000 795.238042 123.9755517 4.346740e+01 8.809679e-05
#> 116 1.15 0.000000 794.878457 122.7278040 4.385443e+01 9.776666e-05
#> 117 1.16 0.000000 794.513351 121.4925739 4.422129e+01 1.084026e-04
#> 118 1.17 0.000000 794.142764 120.2697735 4.456845e+01 1.200904e-04
#> 119 1.18 0.000000 793.766736 119.0593142 4.489639e+01 1.329225e-04
#> 120 1.19 0.000000 793.385308 117.8611064 4.520559e+01 1.469981e-04
#> 121 1.20 0.000000 792.998519 116.6750593 4.549651e+01 1.624237e-04
#> 122 1.21 0.000000 792.606410 115.5010819 4.576960e+01 1.793137e-04
#> 123 1.22 0.000000 792.209019 114.3390818 4.602530e+01 1.977902e-04
#> 124 1.23 0.000000 791.806387 113.1889665 4.626405e+01 2.179841e-04
#> 125 1.24 0.000000 791.398553 112.0506426 4.648628e+01 2.400351e-04
#> 126 1.25 0.000000 790.985554 110.9240162 4.669242e+01 2.640925e-04
#> 127 1.26 0.000000 790.567431 109.8089929 4.688287e+01 2.903155e-04
#> 128 1.27 0.000000 790.144221 108.7054780 4.705804e+01 3.188733e-04
#> 129 1.28 0.000000 789.715963 107.6133764 4.721833e+01 3.499464e-04
#> 130 1.29 0.000000 789.282695 106.5325925 4.736413e+01 3.837263e-04
#> 131 1.30 0.000000 788.844455 105.4630306 4.749582e+01 4.204164e-04
#> 132 1.31 0.000000 788.401280 104.4045948 4.761378e+01 4.602326e-04
#> 133 1.32 0.000000 787.953208 103.3571891 4.771837e+01 5.034036e-04
#> 134 1.33 0.000000 787.500277 102.3207171 4.780995e+01 5.501712e-04
#> 135 1.34 0.000000 787.042522 101.2950826 4.788889e+01 6.007914e-04
#> 136 1.35 0.000000 786.579981 100.2801892 4.795552e+01 6.555346e-04
#> 137 1.36 0.000000 786.112691 99.2759407 4.801018e+01 7.146860e-04
#> 138 1.37 0.000000 785.640688 98.2822407 4.805322e+01 7.785464e-04
#> 139 1.38 0.000000 785.164008 97.2989931 4.808495e+01 8.474327e-04
#> 140 1.39 0.000000 784.682687 96.3261016 4.810569e+01 9.216783e-04
#> 141 1.40 0.000000 784.196761 95.3634706 4.811577e+01 1.001634e-03
#> 142 1.41 0.000000 783.706266 94.4110040 4.811548e+01 1.087667e-03
#> 143 1.42 0.000000 783.211236 93.4686065 4.810512e+01 1.180165e-03
#> 144 1.43 0.000000 782.711708 92.5361827 4.808500e+01 1.279533e-03
#> 145 1.44 0.000000 782.207715 91.6136377 4.805540e+01 1.386195e-03
#> 146 1.45 0.000000 781.699293 90.7008766 4.801660e+01 1.500595e-03
#> 147 1.46 0.000000 781.186477 89.7978051 4.796888e+01 1.623198e-03
#> 148 1.47 0.000000 780.669300 88.9043291 4.791251e+01 1.754489e-03
#> 149 1.48 0.000000 780.147797 88.0203550 4.784775e+01 1.894976e-03
#> 150 1.49 0.000000 779.622001 87.1457894 4.777487e+01 2.045187e-03
#> 151 1.50 0.000000 779.091947 86.2805396 4.769411e+01 2.205672e-03
#> 152 1.51 0.000000 778.557668 85.4245130 4.760573e+01 2.377007e-03
#> 153 1.52 0.000000 778.019197 84.5776177 4.750997e+01 2.559788e-03
#> 154 1.53 0.000000 777.476567 83.7397622 4.740707e+01 2.754637e-03
#> 155 1.54 0.000000 776.929812 82.9108555 4.729725e+01 2.962198e-03
#> 156 1.55 0.000000 776.378964 82.0908071 4.718075e+01 3.183143e-03
#> 157 1.56 0.000000 775.824055 81.2795269 4.705779e+01 3.418166e-03
#> 158 1.57 0.000000 775.265118 80.4769255 4.692858e+01 3.667988e-03
#> 159 1.58 0.000000 774.702185 79.6829141 4.679335e+01 3.933356e-03
#> 160 1.59 0.000000 774.135288 78.8974042 4.665229e+01 4.215044e-03
#> 161 1.60 0.000000 773.564458 78.1203081 4.650561e+01 4.513851e-03
#> 162 1.61 0.000000 772.989727 77.3515386 4.635350e+01 4.830605e-03
#> 163 1.62 0.000000 772.411127 76.5910091 4.619617e+01 5.166159e-03
#> 164 1.63 0.000000 771.828688 75.8386336 4.603380e+01 5.521397e-03
#> 165 1.64 0.000000 771.242441 75.0943267 4.586658e+01 5.897229e-03
#> 166 1.65 0.000000 770.652418 74.3580037 4.569468e+01 6.294594e-03
#> 167 1.66 0.000000 770.058648 73.6295804 4.551829e+01 6.714460e-03
#> 168 1.67 0.000000 769.461161 72.9089733 4.533757e+01 7.157821e-03
#> 169 1.68 0.000000 768.859989 72.1960996 4.515270e+01 7.625706e-03
#> 170 1.69 0.000000 768.255161 71.4908771 4.496384e+01 8.119167e-03
#> 171 1.70 0.000000 767.646707 70.7932243 4.477115e+01 8.639291e-03
#> 172 1.71 0.000000 767.034656 70.1030601 4.457479e+01 9.187190e-03
#> 173 1.72 0.000000 766.419037 69.4203044 4.437490e+01 9.764010e-03
#> 174 1.73 0.000000 765.799880 68.7448777 4.417165e+01 1.037092e-02
#> 175 1.74 0.000000 765.177214 68.0767010 4.396517e+01 1.100914e-02
#> 176 1.75 0.000000 764.551067 67.4156960 4.375560e+01 1.167988e-02
#> 177 1.76 0.000000 763.921468 66.7617854 4.354310e+01 1.238443e-02
#> 178 1.77 0.000000 763.288445 66.1148921 4.332778e+01 1.312407e-02
#> 179 1.78 0.000000 762.652027 65.4749399 4.310978e+01 1.390013e-02
#> 180 1.79 0.000000 762.012242 64.8418534 4.288924e+01 1.471396e-02
#> 181 1.80 0.000000 761.369117 64.2155578 4.266627e+01 1.556696e-02
#> 182 1.81 0.000000 760.722680 63.5959788 4.244100e+01 1.646053e-02
#> 183 1.82 0.000000 760.072959 62.9830431 4.221355e+01 1.739613e-02
#> 184 1.83 0.000000 759.419980 62.3766777 4.198403e+01 1.837524e-02
#> 185 1.84 0.000000 758.763771 61.7768107 4.175256e+01 1.939936e-02
#> 186 1.85 0.000000 758.104358 61.1833705 4.151924e+01 2.047003e-02
#> 187 1.86 0.000000 757.441769 60.5962865 4.128419e+01 2.158881e-02
#> 188 1.87 0.000000 756.776030 60.0154886 4.104750e+01 2.275731e-02
#> 189 1.88 0.000000 756.107167 59.4409074 4.080929e+01 2.397716e-02
#> 190 1.89 0.000000 755.435206 58.8724741 4.056965e+01 2.525000e-02
#> 191 1.90 0.000000 754.760174 58.3101208 4.032867e+01 2.657753e-02
#> 192 1.91 0.000000 754.082096 57.7537801 4.008645e+01 2.796145e-02
#> 193 1.92 0.000000 753.400997 57.2033853 3.984308e+01 2.940352e-02
#> 194 1.93 0.000000 752.716904 56.6588703 3.959865e+01 3.090551e-02
#> 195 1.94 0.000000 752.029841 56.1201699 3.935324e+01 3.246922e-02
#> 196 1.95 0.000000 751.339833 55.5872193 3.910694e+01 3.409646e-02
#> 197 1.96 0.000000 750.646906 55.0599544 3.885984e+01 3.578911e-02
#> 198 1.97 0.000000 749.951084 54.5383119 3.861201e+01 3.754905e-02
#> 199 1.98 0.000000 749.252392 54.0222291 3.836352e+01 3.937817e-02
#> 200 1.99 0.000000 748.550854 53.5116439 3.811446e+01 4.127843e-02
#> 201 2.00 0.000000 747.846495 53.0064949 3.786489e+01 4.325178e-02
#> 202 2.01 0.000000 747.139337 52.5067212 3.761489e+01 4.530021e-02
#> 203 2.02 0.000000 746.429406 52.0122627 3.736452e+01 4.742574e-02
#> 204 2.03 0.000000 745.716725 51.5230600 3.711386e+01 4.963041e-02
#> 205 2.04 0.000000 745.001317 51.0390541 3.686296e+01 5.191627e-02
#> 206 2.05 0.000000 744.283207 50.5601867 3.661189e+01 5.428542e-02
#> 207 2.06 0.000000 743.562416 50.0864003 3.636071e+01 5.673997e-02
#> 208 2.07 0.000000 742.838969 49.6176378 3.610949e+01 5.928205e-02
#> 209 2.08 0.000000 742.112888 49.1538428 3.585826e+01 6.191382e-02
#> 210 2.09 0.000000 741.384195 48.6949595 3.560711e+01 6.463745e-02
#> 211 2.10 0.000000 740.652914 48.2409328 3.535607e+01 6.745516e-02
#> 212 2.11 0.000000 739.919067 47.7917081 3.510519e+01 7.036915e-02
#> 213 2.12 0.000000 739.182676 47.3472313 3.485454e+01 7.338168e-02
#> 214 2.13 0.000000 738.443763 46.9074490 3.460416e+01 7.649500e-02
#> 215 2.14 0.000000 737.702351 46.4723086 3.435409e+01 7.971140e-02
#> 216 2.15 0.000000 736.958460 46.0417576 3.410438e+01 8.303317e-02
#> 217 2.16 0.000000 736.212113 45.6157446 3.385508e+01 8.646265e-02
#> 218 2.17 0.000000 735.463331 45.1942183 3.360624e+01 9.000215e-02
#> 219 2.18 0.000000 734.712135 44.7771283 3.335788e+01 9.365404e-02
#> 220 2.19 0.000000 733.958547 44.3644247 3.311005e+01 9.742069e-02
#> 221 2.20 0.000000 733.202588 43.9560580 3.286279e+01 1.013045e-01
#> 222 2.21 0.000000 732.444279 43.5519794 3.261615e+01 1.053078e-01
#> 223 2.22 0.000000 731.683639 43.1521407 3.237014e+01 1.094331e-01
#> 224 2.23 0.000000 730.920691 42.7564940 3.212482e+01 1.136828e-01
#> 225 2.24 0.000000 730.155454 42.3649922 3.188020e+01 1.180593e-01
#> 226 2.25 0.000000 729.387949 41.9775886 3.163634e+01 1.225651e-01
#> 227 2.26 0.000000 728.618196 41.5942370 3.139325e+01 1.272027e-01
#> 228 2.27 0.000000 727.846215 41.2148918 3.115096e+01 1.319745e-01
#> 229 2.28 0.000000 727.072026 40.8395080 3.090952e+01 1.368831e-01
#> 230 2.29 0.000000 726.295648 40.4680409 3.066894e+01 1.419309e-01
#> 231 2.30 0.000000 725.517102 40.1004464 3.042924e+01 1.471205e-01
#> 232 2.31 0.000000 724.736407 39.7366810 3.019047e+01 1.524543e-01
#> 233 2.32 0.000000 723.953582 39.3767015 2.995264e+01 1.579349e-01
#> 234 2.33 0.000000 723.168647 39.0204654 2.971577e+01 1.635649e-01
#> 235 2.34 0.000000 722.381620 38.6679306 2.947990e+01 1.693467e-01
#> 236 2.35 0.000000 721.592521 38.3190555 2.924503e+01 1.752830e-01
#> 237 2.36 0.000000 720.801369 37.9737988 2.901120e+01 1.813762e-01
#> 238 2.37 0.000000 720.008181 37.6321201 2.877842e+01 1.876290e-01
#> 239 2.38 0.000000 719.212977 37.2939789 2.854671e+01 1.940440e-01
#> 240 2.39 0.000000 718.415776 36.9593357 2.831609e+01 2.006236e-01
#> 241 2.40 0.000000 717.616595 36.6281512 2.808657e+01 2.073705e-01
#> 242 2.41 0.000000 716.815454 36.3003864 2.785819e+01 2.142872e-01
#> 243 2.42 0.000000 716.012369 35.9760031 2.763094e+01 2.213763e-01
#> 244 2.43 0.000000 715.207359 35.6549634 2.740485e+01 2.286404e-01
#> 245 2.44 0.000000 714.400442 35.3372296 2.717993e+01 2.360821e-01
#> 246 2.45 0.000000 713.591636 35.0227649 2.695620e+01 2.437040e-01
#> 247 2.46 0.000000 712.780958 34.7115325 2.673366e+01 2.515086e-01
#> 248 2.47 0.000000 711.968426 34.4034963 2.651234e+01 2.594985e-01
#> 249 2.48 0.000000 711.154057 34.0986204 2.629223e+01 2.676763e-01
#> 250 2.49 0.000000 710.337869 33.7968696 2.607336e+01 2.760445e-01
#> 251 2.50 0.000000 709.519879 33.4982089 2.585574e+01 2.846058e-01
#> 252 2.51 0.000000 708.700103 33.2026037 2.563936e+01 2.933627e-01
#> 253 2.52 0.000000 707.878560 32.9100199 2.542426e+01 3.023178e-01
#> 254 2.53 0.000000 707.055265 32.6204238 2.521042e+01 3.114735e-01
#> 255 2.54 0.000000 706.230235 32.3337820 2.499786e+01 3.208326e-01
#> 256 2.55 0.000000 705.403488 32.0500615 2.478659e+01 3.303975e-01
#> 257 2.56 0.000000 704.575039 31.7692299 2.457661e+01 3.401708e-01
#> 258 2.57 0.000000 703.744906 31.4912548 2.436794e+01 3.501549e-01
#> 259 2.58 0.000000 702.913104 31.2161046 2.416057e+01 3.603525e-01
#> 260 2.59 0.000000 702.079649 30.9437477 2.395452e+01 3.707660e-01
#> 261 2.60 0.000000 701.244559 30.6741531 2.374978e+01 3.813980e-01
#> 262 2.61 0.000000 700.407849 30.4072900 2.354637e+01 3.922509e-01
#> 263 2.62 0.000000 699.569534 30.1431282 2.334428e+01 4.033273e-01
#> 264 2.63 0.000000 698.729631 29.8816376 2.314352e+01 4.146295e-01
#> 265 2.64 0.000000 697.888156 29.6227886 2.294410e+01 4.261602e-01
#> 266 2.65 0.000000 697.045124 29.3665518 2.274601e+01 4.379217e-01
#> 267 2.66 0.000000 696.200551 29.1128984 2.254926e+01 4.499165e-01
#> 268 2.67 0.000000 695.354452 28.8617998 2.235386e+01 4.621470e-01
#> 269 2.68 0.000000 694.506842 28.6132275 2.215979e+01 4.746157e-01
#> 270 2.69 0.000000 693.657738 28.3671538 2.196707e+01 4.873248e-01
#> 271 2.70 0.000000 692.807154 28.1235509 2.177570e+01 5.002769e-01
#> 272 2.71 0.000000 691.955104 27.8823916 2.158567e+01 5.134744e-01
#> 273 2.72 0.000000 691.101606 27.6436489 2.139699e+01 5.269194e-01
#> 274 2.73 0.000000 690.246672 27.4072962 2.120965e+01 5.406146e-01
#> 275 2.74 0.000000 689.390319 27.1733071 2.102366e+01 5.545620e-01
#> 276 2.75 0.000000 688.532560 26.9416555 2.083902e+01 5.687641e-01
#> 277 2.76 0.000000 687.673411 26.7123158 2.065572e+01 5.832232e-01
#> 278 2.77 0.000000 686.812886 26.4852624 2.047376e+01 5.979415e-01
#> 279 2.78 0.000000 685.950999 26.2604704 2.029314e+01 6.129212e-01
#> 280 2.79 0.000000 685.087766 26.0379147 2.011387e+01 6.281648e-01
#> 281 2.80 0.000000 684.223201 25.8175710 1.993593e+01 6.436743e-01
#> 282 2.81 0.000000 683.357317 25.5994148 1.975933e+01 6.594519e-01
#> 283 2.82 0.000000 682.490129 25.3834223 1.958406e+01 6.755000e-01
#> 284 2.83 0.000000 681.621651 25.1695698 1.941012e+01 6.918205e-01
#> 285 2.84 0.000000 680.751897 24.9578338 1.923751e+01 7.084158e-01
#> 286 2.85 0.000000 679.880881 24.7481911 1.906623e+01 7.252878e-01
#> 287 2.86 0.000000 679.008618 24.5406190 1.889626e+01 7.424388e-01
#> 288 2.87 0.000000 678.135120 24.3350948 1.872762e+01 7.598707e-01
#> 289 2.88 0.000000 677.260402 24.1315961 1.856028e+01 7.775857e-01
#> 290 2.89 0.000000 676.384477 23.9301010 1.839426e+01 7.955859e-01
#> 291 2.90 0.000000 675.507359 23.7305875 1.822954e+01 8.138731e-01
#> 292 2.91 0.000000 674.629061 23.5330341 1.806613e+01 8.324495e-01
#> 293 2.92 0.000000 673.749597 23.3374194 1.790401e+01 8.513170e-01
#> 294 2.93 0.000000 672.868980 23.1437225 1.774318e+01 8.704775e-01
#> 295 2.94 0.000000 671.987224 22.9519225 1.758364e+01 8.899330e-01
#> 296 2.95 0.000000 671.104342 22.7619987 1.742539e+01 9.096854e-01
#> 297 2.96 0.000000 670.220347 22.5739310 1.726841e+01 9.297366e-01
#> 298 2.97 0.000000 669.335252 22.3876991 1.711270e+01 9.500884e-01
#> 299 2.98 0.000000 668.449070 22.2032832 1.695827e+01 9.707427e-01
#> 300 2.99 0.000000 667.561814 22.0206637 1.680509e+01 9.917013e-01
#> 301 3.00 0.000000 666.673497 21.8398211 1.665317e+01 1.012966e+00
#> 302 3.01 0.000000 665.784132 21.6607364 1.650250e+01 1.034538e+00
#> 303 3.02 0.000000 664.893732 21.4833904 1.635307e+01 1.056420e+00
#> 304 3.03 0.000000 664.002310 21.3077645 1.620489e+01 1.078614e+00
#> 305 3.04 0.000000 663.109877 21.1338402 1.605793e+01 1.101120e+00
#> 306 3.05 0.000000 662.216448 20.9615991 1.591221e+01 1.123941e+00
#> 307 3.06 0.000000 661.322033 20.7910231 1.576770e+01 1.147078e+00
#> 308 3.07 0.000000 660.426646 20.6220945 1.562441e+01 1.170533e+00
#> 309 3.08 0.000000 659.530300 20.4547954 1.548232e+01 1.194307e+00
#> 310 3.09 0.000000 658.633006 20.2891085 1.534144e+01 1.218403e+00
#> 311 3.10 0.000000 657.734777 20.1250164 1.520175e+01 1.242821e+00
#> 312 3.11 0.000000 656.835625 19.9625021 1.506325e+01 1.267563e+00
#> 313 3.12 0.000000 655.935562 19.8015487 1.492593e+01 1.292630e+00
#> 314 3.13 0.000000 655.034601 19.6421395 1.478979e+01 1.318025e+00
#> 315 3.14 0.000000 654.132753 19.4842581 1.465481e+01 1.343747e+00
#> 316 3.15 0.000000 653.230031 19.3278882 1.452099e+01 1.369800e+00
#> 317 3.16 0.000000 652.326446 19.1730136 1.438833e+01 1.396184e+00
#> 318 3.17 0.000000 651.422010 19.0196184 1.425682e+01 1.422900e+00
#> 319 3.18 0.000000 650.516736 18.8676869 1.412645e+01 1.449950e+00
#> 320 3.19 0.000000 649.610635 18.7172035 1.399721e+01 1.477334e+00
#> 321 3.20 0.000000 648.703718 18.5681530 1.386910e+01 1.505056e+00
#> 322 3.21 0.000000 647.795998 18.4205199 1.374210e+01 1.533115e+00
#> 323 3.22 0.000000 646.887487 18.2742894 1.361622e+01 1.561512e+00
#> 324 3.23 0.000000 645.978194 18.1294466 1.349145e+01 1.590249e+00
#> 325 3.24 0.000000 645.068133 17.9859767 1.336777e+01 1.619328e+00
#> 326 3.25 0.000000 644.157315 17.8438654 1.324518e+01 1.648749e+00
#> 327 3.26 0.000000 643.245751 17.7030982 1.312367e+01 1.678513e+00
#> 328 3.27 0.000000 642.333452 17.5636609 1.300325e+01 1.708621e+00
#> 329 3.28 0.000000 641.420431 17.4255396 1.288389e+01 1.739074e+00
#> 330 3.29 0.000000 640.506697 17.2887203 1.276559e+01 1.769874e+00
#> 331 3.30 0.000000 639.592263 17.1531894 1.264834e+01 1.801022e+00
#> 332 3.31 0.000000 638.677139 17.0189333 1.253214e+01 1.832517e+00
#> 333 3.32 0.000000 637.761337 16.8859387 1.241699e+01 1.864362e+00
#> 334 3.33 0.000000 636.844867 16.7541922 1.230286e+01 1.896557e+00
#> 335 3.34 0.000000 635.927742 16.6236809 1.218976e+01 1.929103e+00
#> 336 3.35 0.000000 635.009971 16.4943917 1.207767e+01 1.962000e+00
#> 337 3.36 0.000000 634.091566 16.3663119 1.196660e+01 1.995250e+00
#> 338 3.37 0.000000 633.172538 16.2394288 1.185653e+01 2.028854e+00
#> 339 3.38 0.000000 632.252897 16.1137300 1.174745e+01 2.062812e+00
#> 340 3.39 0.000000 631.332654 15.9892030 1.163936e+01 2.097124e+00
#> 341 3.40 0.000000 630.411820 15.8658357 1.153226e+01 2.131792e+00
#> 342 3.41 0.000000 629.490406 15.7436159 1.142612e+01 2.166816e+00
#> 343 3.42 0.000000 628.568423 15.6225318 1.132095e+01 2.202198e+00
#> 344 3.43 0.000000 627.645880 15.5025715 1.121674e+01 2.237936e+00
#> 345 3.44 0.000000 626.722789 15.3837233 1.111349e+01 2.274033e+00
#> 346 3.45 0.000000 625.799160 15.2659758 1.101117e+01 2.310488e+00
#> 347 3.46 0.000000 624.875004 15.1493174 1.090979e+01 2.347302e+00
#> 348 3.47 0.000000 623.950331 15.0337369 1.080935e+01 2.384476e+00
#> 349 3.48 0.000000 623.025151 14.9192232 1.070982e+01 2.422011e+00
#> 350 3.49 0.000000 622.099475 14.8057652 1.061121e+01 2.459905e+00
#> 351 3.50 0.000000 621.173313 14.6933520 1.051351e+01 2.498161e+00
#> 352 3.51 0.000000 620.246676 14.5819728 1.041670e+01 2.536778e+00
#> 353 3.52 0.000000 619.319573 14.4716170 1.032080e+01 2.575757e+00
#> 354 3.53 0.000000 618.392015 14.3622741 1.022577e+01 2.615097e+00
#> 355 3.54 0.000000 617.464012 14.2539335 1.013163e+01 2.654801e+00
#> 356 3.55 0.000000 616.535574 14.1465850 1.003836e+01 2.694866e+00
#> 357 3.56 0.000000 615.606712 14.0402184 9.945950e+00 2.735295e+00
#> 358 3.57 0.000000 614.677434 13.9348237 9.854401e+00 2.776087e+00
#> 359 3.58 0.000000 613.747751 13.8303908 9.763703e+00 2.817242e+00
#> 360 3.59 0.000000 612.817674 13.7269099 9.673849e+00 2.858761e+00
#> 361 3.60 0.000000 611.887211 13.6243713 9.584831e+00 2.900644e+00
#> 362 3.61 0.000000 610.956373 13.5227653 9.496643e+00 2.942890e+00
#> 363 3.62 0.000000 610.025170 13.4220824 9.409278e+00 2.985500e+00
#> 364 3.63 0.000000 609.093611 13.3223132 9.322729e+00 3.028474e+00
#> 365 3.64 0.000000 608.161707 13.2234484 9.236988e+00 3.071812e+00
#> 366 3.65 0.000000 607.229466 13.1254787 9.152050e+00 3.115515e+00
#> 367 3.66 0.000000 606.296899 13.0283951 9.067907e+00 3.159581e+00
#> 368 3.67 0.000000 605.364014 12.9321885 8.984553e+00 3.204011e+00
#> 369 3.68 0.000000 604.430823 12.8368500 8.901980e+00 3.248806e+00
#> 370 3.69 0.000000 603.497334 12.7423709 8.820182e+00 3.293964e+00
#> 371 3.70 0.000000 602.563556 12.6487424 8.739153e+00 3.339486e+00
#> 372 3.71 0.000000 601.629500 12.5559558 8.658884e+00 3.385372e+00
#> 373 3.72 0.000000 600.695174 12.4640028 8.579371e+00 3.431621e+00
#> 374 3.73 0.000000 599.760588 12.3728748 8.500605e+00 3.478233e+00
#> 375 3.74 0.000000 598.825751 12.2825635 8.422580e+00 3.525209e+00
#> 376 3.75 0.000000 597.890674 12.1930607 8.345291e+00 3.572548e+00
#> 377 3.76 0.000000 596.955364 12.1043583 8.268729e+00 3.620249e+00
#> 378 3.77 0.000000 596.019831 12.0164481 8.192888e+00 3.668313e+00
#> 379 3.78 0.000000 595.084084 11.9293222 8.117762e+00 3.716739e+00
#> 380 3.79 0.000000 594.148133 11.8429727 8.043344e+00 3.765526e+00
#> 381 3.80 0.000000 593.211987 11.7573919 7.969627e+00 3.814675e+00
#> 382 3.81 0.000000 592.275654 11.6725719 7.896606e+00 3.864185e+00
#> 383 3.82 0.000000 591.339144 11.5885053 7.824272e+00 3.914056e+00
#> 384 3.83 0.000000 590.402466 11.5051844 7.752619e+00 3.964287e+00
#> 385 3.84 0.000000 589.465629 11.4226018 7.681642e+00 4.014878e+00
#> 386 3.85 0.000000 588.528641 11.3407501 7.611332e+00 4.065829e+00
#> 387 3.86 0.000000 587.591512 11.2596220 7.541684e+00 4.117138e+00
#> 388 3.87 0.000000 586.654250 11.1792103 7.472691e+00 4.168806e+00
#> 389 3.88 0.000000 585.716864 11.0995078 7.404345e+00 4.220832e+00
#> 390 3.89 0.000000 584.779364 11.0205076 7.336640e+00 4.273215e+00
#> 391 3.90 0.000000 583.841757 10.9422026 7.269570e+00 4.325955e+00
#> 392 3.91 0.000000 582.904053 10.8645859 7.203127e+00 4.379051e+00
#> 393 3.92 0.000000 581.966260 10.7876506 7.137305e+00 4.432503e+00
#> 394 3.93 0.000000 581.028386 10.7113901 7.072097e+00 4.486309e+00
#> 395 3.94 0.000000 580.090442 10.6357976 7.007495e+00 4.540471e+00
#> 396 3.95 0.000000 579.152434 10.5608665 6.943493e+00 4.594986e+00
#> 397 3.96 0.000000 578.214371 10.4865904 6.880084e+00 4.649853e+00
#> 398 3.97 0.000000 577.276263 10.4129626 6.817261e+00 4.705074e+00
#> 399 3.98 0.000000 576.338117 10.3399769 6.755016e+00 4.760645e+00
#> 400 3.99 0.000000 575.399943 10.2676269 6.693344e+00 4.816568e+00
#> 401 4.00 0.000000 574.461747 10.1959063 6.632237e+00 4.872841e+00
#> 402 4.01 0.000000 573.523539 10.1248089 6.571688e+00 4.929463e+00
#> 403 4.02 0.000000 572.585327 10.0543287 6.511691e+00 4.986434e+00
#> 404 4.03 0.000000 571.647120 9.9844595 6.452238e+00 5.043752e+00
#> 405 4.04 0.000000 570.708925 9.9151954 6.393325e+00 5.101417e+00
#> 406 4.05 0.000000 569.770751 9.8465304 6.334943e+00 5.159428e+00
#> 407 4.06 0.000000 568.832606 9.7784587 6.277088e+00 5.217784e+00
#> 408 4.07 0.000000 567.894497 9.7109744 6.219752e+00 5.276485e+00
#> 409 4.08 0.000000 566.956435 9.6440719 6.162932e+00 5.335529e+00
#> 410 4.09 0.000000 566.018425 9.5777455 6.106620e+00 5.394915e+00
#> 411 4.10 0.000000 565.080477 9.5119895 6.050812e+00 5.454643e+00
#> 412 4.11 0.000000 564.142598 9.4467983 5.995504e+00 5.514711e+00
#> 413 4.12 0.000000 563.204796 9.3821666 5.940690e+00 5.575118e+00
#> 414 4.13 0.000000 562.267080 9.3180888 5.886366e+00 5.635865e+00
#> 415 4.14 0.000000 561.329457 9.2545595 5.832529e+00 5.696948e+00
#> 416 4.15 0.000000 560.391934 9.1915735 5.779174e+00 5.758369e+00
#> 417 4.16 0.000000 559.454521 9.1291255 5.726298e+00 5.820124e+00
#> 418 4.17 0.000000 558.517225 9.0672102 5.673898e+00 5.882214e+00
#> 419 4.18 0.000000 557.580052 9.0058225 5.621970e+00 5.944638e+00
#> 420 4.19 0.000000 556.643013 8.9449573 5.570512e+00 6.007393e+00
#> 421 4.20 0.000000 555.706112 8.8846096 5.519521e+00 6.070480e+00
#> 422 4.21 0.000000 554.769360 8.8247744 5.468993e+00 6.133897e+00
#> 423 4.22 0.000000 553.832763 8.7654467 5.418927e+00 6.197642e+00
#> 424 4.23 0.000000 552.896328 8.7066216 5.369320e+00 6.261716e+00
#> 425 4.24 0.000000 551.960064 8.6482943 5.320168e+00 6.326116e+00
#> 426 4.25 0.000000 551.023977 8.5904600 5.271470e+00 6.390841e+00
#> 427 4.26 0.000000 550.088076 8.5331140 5.223223e+00 6.455890e+00
#> 428 4.27 0.000000 549.152368 8.4762516 5.175424e+00 6.521263e+00
#> 429 4.28 0.000000 548.216860 8.4198681 5.128071e+00 6.586957e+00
#> 430 4.29 0.000000 547.281560 8.3639590 5.081160e+00 6.652972e+00
#> 431 4.30 0.000000 546.346475 8.3085197 5.034689e+00 6.719306e+00
#> 432 4.31 0.000000 545.411612 8.2535458 4.988656e+00 6.785958e+00
#> 433 4.32 0.000000 544.476978 8.1990328 4.943056e+00 6.852927e+00
#> 434 4.33 0.000000 543.542582 8.1449762 4.897887e+00 6.920212e+00
#> 435 4.34 0.000000 542.608430 8.0913718 4.853147e+00 6.987810e+00
#> 436 4.35 0.000000 541.674529 8.0382152 4.808831e+00 7.055722e+00
#> 437 4.36 0.000000 540.740886 7.9855022 4.764937e+00 7.123945e+00
#> 438 4.37 0.000000 539.807509 7.9332285 4.721462e+00 7.192478e+00
#> 439 4.38 0.000000 538.874405 7.8813901 4.678402e+00 7.261320e+00
#> 440 4.39 0.000000 537.941581 7.8299827 4.635754e+00 7.330470e+00
#> 441 4.40 0.000000 537.009043 7.7790022 4.593514e+00 7.399926e+00
#> 442 4.41 0.000000 536.076799 7.7284447 4.551680e+00 7.469687e+00
#> 443 4.42 0.000000 535.144856 7.6783061 4.510247e+00 7.539751e+00
#> 444 4.43 0.000000 534.213220 7.6285824 4.469213e+00 7.610117e+00
#> 445 4.44 0.000000 533.281899 7.5792698 4.428575e+00 7.680784e+00
#> 446 4.45 0.000000 532.350900 7.5303644 4.388347e+00 7.751750e+00
#> 447 4.46 0.000000 531.420228 7.4818623 4.348527e+00 7.823014e+00
#> 448 4.47 0.000000 530.489892 7.4337597 4.309109e+00 7.894574e+00
#> 449 4.48 0.000000 529.559897 7.3860529 4.270089e+00 7.966429e+00
#> 450 4.49 0.000000 528.630251 7.3387381 4.231463e+00 8.038578e+00
#> 451 4.50 0.000000 527.700960 7.2918117 4.193227e+00 8.111018e+00
#> 452 4.51 0.000000 526.772032 7.2452701 4.155376e+00 8.183749e+00
#> 453 4.52 0.000000 525.843471 7.1991095 4.117908e+00 8.256769e+00
#> 454 4.53 0.000000 524.915286 7.1533265 4.080816e+00 8.330077e+00
#> 455 4.54 0.000000 523.987482 7.1079175 4.044098e+00 8.403670e+00
#> 456 4.55 0.000000 523.060067 7.0628791 4.007749e+00 8.477548e+00
#> 457 4.56 0.000000 522.133046 7.0182077 3.971766e+00 8.551709e+00
#> 458 4.57 0.000000 521.206426 6.9738999 3.936145e+00 8.626152e+00
#> 459 4.58 0.000000 520.280214 6.9299524 3.900882e+00 8.700874e+00
#> 460 4.59 0.000000 519.354416 6.8863618 3.865972e+00 8.775875e+00
#> 461 4.60 0.000000 518.429039 6.8431248 3.831413e+00 8.851153e+00
#> 462 4.61 0.000000 517.504088 6.8002381 3.797200e+00 8.926706e+00
#> 463 4.62 0.000000 516.579570 6.7576984 3.763330e+00 9.002533e+00
#> 464 4.63 0.000000 515.655491 6.7155026 3.729799e+00 9.078632e+00
#> 465 4.64 0.000000 514.731858 6.6736474 3.696603e+00 9.155001e+00
#> 466 4.65 0.000000 513.808676 6.6321297 3.663740e+00 9.231640e+00
#> 467 4.66 0.000000 512.885953 6.5909463 3.631204e+00 9.308546e+00
#> 468 4.67 0.000000 511.963693 6.5500943 3.598994e+00 9.385718e+00
#> 469 4.68 0.000000 511.041904 6.5095705 3.567105e+00 9.463154e+00
#> 470 4.69 0.000000 510.120591 6.4693719 3.535534e+00 9.540852e+00
#> 471 4.70 0.000000 509.199760 6.4294955 3.504278e+00 9.618812e+00
#> 472 4.71 0.000000 508.279417 6.3899384 3.473333e+00 9.697031e+00
#> 473 4.72 0.000000 507.359569 6.3506975 3.442696e+00 9.775508e+00
#> 474 4.73 0.000000 506.440221 6.3117701 3.412363e+00 9.854241e+00
#> 475 4.74 0.000000 505.521379 6.2731533 3.382332e+00 9.933229e+00
#> 476 4.75 0.000000 504.603049 6.2348441 3.352599e+00 1.001247e+01
#> 477 4.76 0.000000 503.685237 6.1968398 3.323160e+00 1.009196e+01
#> 478 4.77 0.000000 502.767948 6.1591376 3.294014e+00 1.017170e+01
#> 479 4.78 0.000000 501.851189 6.1217347 3.265156e+00 1.025169e+01
#> 480 4.79 0.000000 500.934966 6.0846285 3.236584e+00 1.033193e+01
#> 481 4.80 0.000000 500.019283 6.0478161 3.208295e+00 1.041241e+01
#> 482 4.81 0.000000 499.104147 6.0112950 3.180285e+00 1.049313e+01
#> 483 4.82 0.000000 498.189563 5.9750624 3.152552e+00 1.057409e+01
#> 484 4.83 0.000000 497.275537 5.9391158 3.125092e+00 1.065530e+01
#> 485 4.84 0.000000 496.362075 5.9034526 3.097903e+00 1.073674e+01
#> 486 4.85 0.000000 495.449182 5.8680701 3.070982e+00 1.081842e+01
#> 487 4.86 0.000000 494.536863 5.8329659 3.044326e+00 1.090033e+01
#> 488 4.87 0.000000 493.625125 5.7981374 3.017931e+00 1.098248e+01
#> 489 4.88 0.000000 492.713972 5.7635821 2.991797e+00 1.106485e+01
#> 490 4.89 0.000000 491.803411 5.7292977 2.965919e+00 1.114746e+01
#> 491 4.90 0.000000 490.893445 5.6952815 2.940294e+00 1.123029e+01
#> 492 4.91 0.000000 489.984082 5.6615312 2.914921e+00 1.131335e+01
#> 493 4.92 0.000000 489.075326 5.6280445 2.889797e+00 1.139664e+01
#> 494 4.93 0.000000 488.167183 5.5948188 2.864918e+00 1.148014e+01
#> 495 4.94 0.000000 487.259657 5.5618520 2.840282e+00 1.156387e+01
#> 496 4.95 0.000000 486.352754 5.5291417 2.815887e+00 1.164782e+01
#> 497 4.96 0.000000 485.446480 5.4966855 2.791731e+00 1.173199e+01
#> 498 4.97 0.000000 484.540839 5.4644812 2.767809e+00 1.181637e+01
#> 499 4.98 0.000000 483.635837 5.4325265 2.744121e+00 1.190096e+01
#> 500 4.99 0.000000 482.731478 5.4008192 2.720663e+00 1.198577e+01
#> 501 5.00 0.000000 481.827769 5.3693572 2.697434e+00 1.207079e+01
#> 502 5.01 0.000000 480.924713 5.3381381 2.674430e+00 1.215602e+01
#> 503 5.02 0.000000 480.022317 5.3071599 2.651650e+00 1.224145e+01
#> 504 5.03 0.000000 479.120584 5.2764203 2.629090e+00 1.232709e+01
#> 505 5.04 0.000000 478.219520 5.2459174 2.606749e+00 1.241294e+01
#> 506 5.05 0.000000 477.319131 5.2156489 2.584625e+00 1.249898e+01
#> 507 5.06 0.000000 476.419420 5.1856128 2.562714e+00 1.258523e+01
#> 508 5.07 0.000000 475.520393 5.1558070 2.541016e+00 1.267167e+01
#> 509 5.08 0.000000 474.622054 5.1262295 2.519526e+00 1.275832e+01
#> 510 5.09 0.000000 473.724409 5.0968782 2.498244e+00 1.284515e+01
#> 511 5.10 0.000000 472.827462 5.0677512 2.477168e+00 1.293219e+01
#> 512 5.11 0.000000 471.931218 5.0388465 2.456294e+00 1.301941e+01
#> 513 5.12 0.000000 471.035682 5.0101621 2.435621e+00 1.310682e+01
#> 514 5.13 0.000000 470.140858 4.9816961 2.415146e+00 1.319442e+01
#> 515 5.14 0.000000 469.246752 4.9534465 2.394869e+00 1.328221e+01
#> 516 5.15 0.000000 468.353367 4.9254115 2.374785e+00 1.337019e+01
#> 517 5.16 0.000000 467.460708 4.8975892 2.354895e+00 1.345834e+01
#> 518 5.17 0.000000 466.568780 4.8699776 2.335194e+00 1.354668e+01
#> 519 5.18 0.000000 465.677588 4.8425750 2.315683e+00 1.363520e+01
#> 520 5.19 0.000000 464.787136 4.8153795 2.296357e+00 1.372389e+01
#> 521 5.20 0.000000 463.897428 4.7883893 2.277217e+00 1.381277e+01
#> 522 5.21 0.000000 463.008470 4.7616026 2.258258e+00 1.390181e+01
#> 523 5.22 0.000000 462.120264 4.7350176 2.239481e+00 1.399103e+01
#> 524 5.23 0.000000 461.232817 4.7086325 2.220882e+00 1.408042e+01
#> 525 5.24 0.000000 460.346132 4.6824458 2.202460e+00 1.416999e+01
#> 526 5.25 0.000000 459.460213 4.6564554 2.184214e+00 1.425971e+01
#> 527 5.26 0.000000 458.575065 4.6306599 2.166140e+00 1.434961e+01
#> 528 5.27 0.000000 457.690692 4.6050575 2.148238e+00 1.443967e+01
#> 529 5.28 0.000000 456.807099 4.5796465 2.130506e+00 1.452989e+01
#> 530 5.29 0.000000 455.924290 4.5544252 2.112941e+00 1.462027e+01
#> 531 5.30 0.000000 455.042268 4.5293921 2.095543e+00 1.471081e+01
#> 532 5.31 0.000000 454.161038 4.5045454 2.078309e+00 1.480151e+01
#> 533 5.32 0.000000 453.280605 4.4798836 2.061237e+00 1.489237e+01
#> 534 5.33 0.000000 452.400971 4.4554050 2.044327e+00 1.498338e+01
#> 535 5.34 0.000000 451.522142 4.4311082 2.027576e+00 1.507454e+01
#> 536 5.35 0.000000 450.644122 4.4069914 2.010982e+00 1.516585e+01
#> 537 5.36 0.000000 449.766914 4.3830533 1.994545e+00 1.525731e+01
#> 538 5.37 0.000000 448.890523 4.3592921 1.978262e+00 1.534892e+01
#> 539 5.38 0.000000 448.014951 4.3357065 1.962131e+00 1.544067e+01
#> 540 5.39 0.000000 447.140205 4.3122949 1.946152e+00 1.553257e+01
#> 541 5.40 0.000000 446.266286 4.2890558 1.930323e+00 1.562461e+01
#> 542 5.41 0.000000 445.393200 4.2659877 1.914642e+00 1.571679e+01
#> 543 5.42 0.000000 444.520950 4.2430892 1.899107e+00 1.580911e+01
#> 544 5.43 0.000000 443.649540 4.2203588 1.883717e+00 1.590157e+01
#> 545 5.44 0.000000 442.778973 4.1977951 1.868471e+00 1.599417e+01
#> 546 5.45 0.000000 441.909254 4.1753966 1.853367e+00 1.608689e+01
#> 547 5.46 0.000000 441.040386 4.1531620 1.838403e+00 1.617975e+01
#> 548 5.47 0.000000 440.172373 4.1310898 1.823579e+00 1.627274e+01
#> 549 5.48 0.000000 439.305218 4.1091787 1.808892e+00 1.636586e+01
#> 550 5.49 0.000000 438.438926 4.0874273 1.794342e+00 1.645911e+01
#> 551 5.50 0.000000 437.573500 4.0658342 1.779927e+00 1.655248e+01
#> 552 5.51 0.000000 436.708943 4.0443982 1.765645e+00 1.664598e+01
#> 553 5.52 0.000000 435.845259 4.0231178 1.751495e+00 1.673960e+01
#> 554 5.53 0.000000 434.982452 4.0019918 1.737476e+00 1.683334e+01
#> 555 5.54 0.000000 434.120525 3.9810188 1.723587e+00 1.692719e+01
#> 556 5.55 0.000000 433.259482 3.9601975 1.709825e+00 1.702117e+01
#> 557 5.56 0.000000 432.399326 3.9395267 1.696191e+00 1.711526e+01
#> 558 5.57 0.000000 431.540060 3.9190052 1.682682e+00 1.720947e+01
#> 559 5.58 0.000000 430.681689 3.8986316 1.669297e+00 1.730379e+01
#> 560 5.59 0.000000 429.824215 3.8784046 1.656035e+00 1.739822e+01
#> 561 5.60 0.000000 428.967641 3.8583232 1.642895e+00 1.749276e+01
#> 562 5.61 0.000000 428.111972 3.8383860 1.629875e+00 1.758740e+01
#> 563 5.62 0.000000 427.257210 3.8185918 1.616975e+00 1.768216e+01
#> 564 5.63 0.000000 426.403359 3.7989394 1.604193e+00 1.777701e+01
#> 565 5.64 0.000000 425.550421 3.7794277 1.591527e+00 1.787198e+01
#> 566 5.65 0.000000 424.698401 3.7600555 1.578978e+00 1.796704e+01
#> 567 5.66 0.000000 423.847301 3.7408216 1.566542e+00 1.806220e+01
#> 568 5.67 0.000000 422.997125 3.7217248 1.554220e+00 1.815746e+01
#> 569 5.68 0.000000 422.147876 3.7027641 1.542010e+00 1.825282e+01
#> 570 5.69 0.000000 421.299556 3.6839382 1.529912e+00 1.834827e+01
#> 571 5.70 0.000000 420.452169 3.6652460 1.517923e+00 1.844381e+01
#> 572 5.71 0.000000 419.605718 3.6466865 1.506043e+00 1.853945e+01
#> 573 5.72 0.000000 418.760206 3.6282586 1.494270e+00 1.863518e+01
#> 574 5.73 0.000000 417.915636 3.6099611 1.482604e+00 1.873100e+01
#> 575 5.74 0.000000 417.072012 3.5917930 1.471044e+00 1.882690e+01
#> 576 5.75 0.000000 416.229335 3.5737531 1.459589e+00 1.892289e+01
#> 577 5.76 0.000000 415.387609 3.5558405 1.448236e+00 1.901896e+01
#> 578 5.77 0.000000 414.546837 3.5380541 1.436986e+00 1.911512e+01
#> 579 5.78 0.000000 413.707022 3.5203928 1.425838e+00 1.921136e+01
#> 580 5.79 0.000000 412.868166 3.5028556 1.414790e+00 1.930767e+01
#> 581 5.80 0.000000 412.030273 3.4854416 1.403841e+00 1.940407e+01
#> 582 5.81 0.000000 411.193345 3.4681496 1.392990e+00 1.950054e+01
#> 583 5.82 0.000000 410.357385 3.4509786 1.382237e+00 1.959709e+01
#> 584 5.83 0.000000 409.522396 3.4339278 1.371580e+00 1.969371e+01
#> 585 5.84 0.000000 408.688381 3.4169960 1.361019e+00 1.979040e+01
#> 586 5.85 0.000000 407.855341 3.4001824 1.350552e+00 1.988716e+01
#> 587 5.86 0.000000 407.023281 3.3834859 1.340179e+00 1.998399e+01
#> 588 5.87 0.000000 406.192203 3.3669056 1.329898e+00 2.008089e+01
#> 589 5.88 0.000000 405.362108 3.3504405 1.319709e+00 2.017786e+01
#> 590 5.89 0.000000 404.533001 3.3340897 1.309610e+00 2.027489e+01
#> 591 5.90 0.000000 403.704883 3.3178524 1.299602e+00 2.037198e+01
#> 592 5.91 0.000000 402.877757 3.3017274 1.289682e+00 2.046913e+01
#> 593 5.92 0.000000 402.051626 3.2857140 1.279851e+00 2.056635e+01
#> 594 5.93 0.000000 401.226491 3.2698112 1.270107e+00 2.066362e+01
#> 595 5.94 0.000000 400.402357 3.2540182 1.260449e+00 2.076095e+01
#> 596 5.95 0.000000 399.579224 3.2383339 1.250876e+00 2.085834e+01
#> 597 5.96 0.000000 398.757096 3.2227577 1.241388e+00 2.095578e+01
#> 598 5.97 0.000000 397.935975 3.2072885 1.231984e+00 2.105328e+01
#> 599 5.98 0.000000 397.115863 3.1919255 1.222663e+00 2.115082e+01
#> 600 5.99 0.000000 396.296763 3.1766679 1.213425e+00 2.124842e+01
#> 601 6.00 0.000000 395.478676 3.1615149 1.204267e+00 2.134606e+01
#> 602 6.01 0.000000 394.661607 3.1464654 1.195190e+00 2.144376e+01
#> 603 6.02 0.000000 393.845555 3.1315188 1.186193e+00 2.154149e+01
#> 604 6.03 0.000000 393.030525 3.1166742 1.177275e+00 2.163928e+01
#> 605 6.04 0.000000 392.216518 3.1019308 1.168435e+00 2.173710e+01
#> 606 6.05 0.000000 391.403537 3.0872878 1.159672e+00 2.183497e+01
#> 607 6.06 0.000000 390.591583 3.0727443 1.150986e+00 2.193288e+01
#> 608 6.07 0.000000 389.780659 3.0582996 1.142376e+00 2.203082e+01
#> 609 6.08 0.000000 388.970767 3.0439529 1.133842e+00 2.212881e+01
#> 610 6.09 0.000000 388.161909 3.0297034 1.125381e+00 2.222683e+01
#> 611 6.10 0.000000 387.354087 3.0155503 1.116995e+00 2.232489e+01
#> 612 6.11 0.000000 386.547303 3.0014928 1.108681e+00 2.242297e+01
#> 613 6.12 0.000000 385.741560 2.9875303 1.100440e+00 2.252110e+01
#> 614 6.13 0.000000 384.936860 2.9736619 1.092270e+00 2.261925e+01
#> 615 6.14 0.000000 384.133204 2.9598868 1.084171e+00 2.271743e+01
#> 616 6.15 0.000000 383.330594 2.9462044 1.076142e+00 2.281564e+01
#> 617 6.16 0.000000 382.529033 2.9326139 1.068183e+00 2.291388e+01
#> 618 6.17 0.000000 381.728522 2.9191146 1.060293e+00 2.301214e+01
#> 619 6.18 0.000000 380.929064 2.9057058 1.052471e+00 2.311043e+01
#> 620 6.19 0.000000 380.130660 2.8923867 1.044716e+00 2.320874e+01
#> 621 6.20 0.000000 379.333312 2.8791566 1.037028e+00 2.330707e+01
#> 622 6.21 0.000000 378.537022 2.8660148 1.029406e+00 2.340542e+01
#> 623 6.22 0.000000 377.741792 2.8529607 1.021850e+00 2.350379e+01
#> 624 6.23 0.000000 376.947624 2.8399935 1.014359e+00 2.360218e+01
#> 625 6.24 0.000000 376.154519 2.8271126 1.006932e+00 2.370058e+01
#> 626 6.25 0.000000 375.362480 2.8143173 9.995693e-01 2.379900e+01
#> 627 6.26 0.000000 374.571507 2.8016069 9.922693e-01 2.389744e+01
#> 628 6.27 0.000000 373.781604 2.7889807 9.850317e-01 2.399589e+01
#> 629 6.28 0.000000 372.992771 2.7764381 9.778560e-01 2.409434e+01
#> 630 6.29 0.000000 372.205010 2.7639784 9.707416e-01 2.419281e+01
#> 631 6.30 0.000000 371.418323 2.7516010 9.636879e-01 2.429129e+01
#> 632 6.31 0.000000 370.632711 2.7393052 9.566943e-01 2.438978e+01
#> 633 6.32 0.000000 369.848177 2.7270905 9.497602e-01 2.448827e+01
#> 634 6.33 0.000000 369.064722 2.7149561 9.428850e-01 2.458677e+01
#> 635 6.34 0.000000 368.282347 2.7029014 9.360683e-01 2.468527e+01
#> 636 6.35 0.000000 367.501054 2.6909259 9.293094e-01 2.478377e+01
#> 637 6.36 0.000000 366.720844 2.6790289 9.226077e-01 2.488228e+01
#> 638 6.37 0.000000 365.941720 2.6672097 9.159629e-01 2.498079e+01
#> 639 6.38 0.000000 365.163682 2.6554679 9.093742e-01 2.507929e+01
#> 640 6.39 0.000000 364.386732 2.6438028 9.028412e-01 2.517780e+01
#> 641 6.40 0.000000 363.610872 2.6322137 8.963633e-01 2.527630e+01
#> 642 6.41 0.000000 362.836102 2.6207002 8.899400e-01 2.537480e+01
#> 643 6.42 0.000000 362.062426 2.6092616 8.835709e-01 2.547329e+01
#> 644 6.43 0.000000 361.289842 2.5978973 8.772553e-01 2.557178e+01
#> 645 6.44 0.000000 360.518355 2.5866069 8.709928e-01 2.567025e+01
#> 646 6.45 0.000000 359.747963 2.5753896 8.647828e-01 2.576872e+01
#> 647 6.46 0.000000 358.978670 2.5642450 8.586250e-01 2.586718e+01
#> 648 6.47 0.000000 358.210476 2.5531724 8.525187e-01 2.596563e+01
#> 649 6.48 0.000000 357.443382 2.5421714 8.464635e-01 2.606407e+01
#> 650 6.49 0.000000 356.677391 2.5312414 8.404589e-01 2.616249e+01
#> 651 6.50 0.000000 355.912502 2.5203819 8.345045e-01 2.626090e+01
#> 652 6.51 0.000000 355.148718 2.5095922 8.285997e-01 2.635929e+01
#> 653 6.52 0.000000 354.386039 2.4988719 8.227441e-01 2.645767e+01
#> 654 6.53 0.000000 353.624468 2.4882204 8.169373e-01 2.655603e+01
#> 655 6.54 0.000000 352.864004 2.4776373 8.111787e-01 2.665437e+01
#> 656 6.55 0.000000 352.104650 2.4671220 8.054680e-01 2.675269e+01
#> 657 6.56 0.000000 351.346406 2.4566739 7.998046e-01 2.685099e+01
#> 658 6.57 0.000000 350.589273 2.4462926 7.941882e-01 2.694926e+01
#> 659 6.58 0.000000 349.833253 2.4359776 7.886182e-01 2.704752e+01
#> 660 6.59 0.000000 349.078347 2.4257283 7.830944e-01 2.714575e+01
#> 661 6.60 0.000000 348.324556 2.4155442 7.776161e-01 2.724395e+01
#> 662 6.61 0.000000 347.571880 2.4054250 7.721831e-01 2.734213e+01
#> 663 6.62 0.000000 346.820322 2.3953700 7.667948e-01 2.744028e+01
#> 664 6.63 0.000000 346.069881 2.3853788 7.614509e-01 2.753840e+01
#> 665 6.64 0.000000 345.320559 2.3754509 7.561510e-01 2.763650e+01
#> 666 6.65 0.000000 344.572358 2.3655859 7.508946e-01 2.773456e+01
#> 667 6.66 0.000000 343.825277 2.3557832 7.456814e-01 2.783259e+01
#> 668 6.67 0.000000 343.079318 2.3460423 7.405109e-01 2.793059e+01
#> 669 6.68 0.000000 342.334482 2.3363629 7.353827e-01 2.802855e+01
#> 670 6.69 0.000000 341.590770 2.3267445 7.302965e-01 2.812649e+01
#> 671 6.70 0.000000 340.848183 2.3171866 7.252519e-01 2.822438e+01
#> 672 6.71 0.000000 340.106721 2.3076887 7.202484e-01 2.832224e+01
#> 673 6.72 0.000000 339.366385 2.2982505 7.152858e-01 2.842006e+01
#> 674 6.73 0.000000 338.627177 2.2888713 7.103635e-01 2.851785e+01
#> 675 6.74 0.000000 337.889097 2.2795509 7.054813e-01 2.861559e+01
#> 676 6.75 0.000000 337.152145 2.2702888 7.006388e-01 2.871330e+01
#> 677 6.76 0.000000 336.416324 2.2610845 6.958357e-01 2.881096e+01
#> 678 6.77 0.000000 335.681633 2.2519377 6.910714e-01 2.890858e+01
#> 679 6.78 0.000000 334.948073 2.2428478 6.863458e-01 2.900616e+01
#> 680 6.79 0.000000 334.215645 2.2338145 6.816584e-01 2.910369e+01
#> 681 6.80 0.000000 333.484350 2.2248373 6.770090e-01 2.920118e+01
#> 682 6.81 0.000000 332.754188 2.2159158 6.723970e-01 2.929863e+01
#> 683 6.82 0.000000 332.025161 2.2070497 6.678223e-01 2.939602e+01
#> 684 6.83 0.000000 331.297268 2.1982384 6.632844e-01 2.949337e+01
#> 685 6.84 0.000000 330.570511 2.1894817 6.587831e-01 2.959067e+01
#> 686 6.85 0.000000 329.844890 2.1807791 6.543179e-01 2.968792e+01
#> 687 6.86 0.000000 329.120406 2.1721301 6.498887e-01 2.978512e+01
#> 688 6.87 0.000000 328.397060 2.1635345 6.454949e-01 2.988227e+01
#> 689 6.88 0.000000 327.674851 2.1549917 6.411364e-01 2.997937e+01
#> 690 6.89 0.000000 326.953781 2.1465015 6.368128e-01 3.007641e+01
#> 691 6.90 0.000000 326.233850 2.1380634 6.325237e-01 3.017340e+01
#> 692 6.91 0.000000 325.515058 2.1296771 6.282689e-01 3.027034e+01
#> 693 6.92 0.000000 324.797407 2.1213421 6.240481e-01 3.036722e+01
#> 694 6.93 0.000000 324.080897 2.1130582 6.198609e-01 3.046404e+01
#> 695 6.94 0.000000 323.365528 2.1048248 6.157070e-01 3.056080e+01
#> 696 6.95 0.000000 322.651300 2.0966417 6.115862e-01 3.065751e+01
#> 697 6.96 0.000000 321.938215 2.0885085 6.074982e-01 3.075416e+01
#> 698 6.97 0.000000 321.226273 2.0804249 6.034425e-01 3.085075e+01
#> 699 6.98 0.000000 320.515474 2.0723904 5.994191e-01 3.094728e+01
#> 700 6.99 0.000000 319.805818 2.0644046 5.954275e-01 3.104374e+01
#> 701 7.00 0.000000 319.097306 2.0564674 5.914675e-01 3.114015e+01
#> 702 7.01 0.000000 318.389939 2.0485782 5.875387e-01 3.123649e+01
#> 703 7.02 0.000000 317.683716 2.0407368 5.836410e-01 3.133277e+01
#> 704 7.03 0.000000 316.978639 2.0329428 5.797740e-01 3.142898e+01
#> 705 7.04 0.000000 316.274707 2.0251959 5.759375e-01 3.152513e+01
#> 706 7.05 0.000000 315.571920 2.0174957 5.721312e-01 3.162121e+01
#> 707 7.06 0.000000 314.870280 2.0098419 5.683548e-01 3.171722e+01
#> 708 7.07 0.000000 314.169786 2.0022341 5.646080e-01 3.181317e+01
#> 709 7.08 0.000000 313.470439 1.9946720 5.608906e-01 3.190904e+01
#> 710 7.09 0.000000 312.772240 1.9871553 5.572024e-01 3.200485e+01
#> 711 7.10 0.000000 312.075187 1.9796837 5.535430e-01 3.210059e+01
#> 712 7.11 0.000000 311.379282 1.9722568 5.499122e-01 3.219626e+01
#> 713 7.12 0.000000 310.684524 1.9648744 5.463097e-01 3.229185e+01
#> 714 7.13 0.000000 309.990915 1.9575360 5.427354e-01 3.238737e+01
#> 715 7.14 0.000000 309.298454 1.9502415 5.391889e-01 3.248282e+01
#> 716 7.15 0.000000 308.607141 1.9429904 5.356700e-01 3.257820e+01
#> 717 7.16 0.000000 307.916977 1.9357824 5.321785e-01 3.267350e+01
#> 718 7.17 0.000000 307.227961 1.9286173 5.287141e-01 3.276873e+01
#> 719 7.18 0.000000 306.540094 1.9214948 5.252765e-01 3.286388e+01
#> 720 7.19 0.000000 305.853377 1.9144145 5.218656e-01 3.295895e+01
#> 721 7.20 0.000000 305.167808 1.9073762 5.184811e-01 3.305395e+01
#> 722 7.21 0.000000 304.483389 1.9003795 5.151228e-01 3.314887e+01
#> 723 7.22 0.000000 303.800119 1.8934241 5.117904e-01 3.324371e+01
#> 724 7.23 0.000000 303.117999 1.8865098 5.084838e-01 3.333847e+01
#> 725 7.24 0.000000 302.437028 1.8796363 5.052026e-01 3.343315e+01
#> 726 7.25 0.000000 301.757207 1.8728032 5.019467e-01 3.352775e+01
#> 727 7.26 0.000000 301.078535 1.8660104 4.987158e-01 3.362227e+01
#> 728 7.27 0.000000 300.401013 1.8592574 4.955097e-01 3.371670e+01
#> 729 7.28 0.000000 299.724641 1.8525441 4.923282e-01 3.381106e+01
#> 730 7.29 0.000000 299.049418 1.8458701 4.891712e-01 3.390533e+01
#> 731 7.30 0.000000 298.375345 1.8392352 4.860383e-01 3.399951e+01
#> 732 7.31 0.000000 297.702422 1.8326391 4.829293e-01 3.409361e+01
#> 733 7.32 0.000000 297.030649 1.8260815 4.798441e-01 3.418763e+01
#> 734 7.33 0.000000 296.360025 1.8195621 4.767825e-01 3.428156e+01
#> 735 7.34 0.000000 295.690550 1.8130808 4.737442e-01 3.437540e+01
#> 736 7.35 0.000000 295.022225 1.8066371 4.707290e-01 3.446916e+01
#> 737 7.36 0.000000 294.355050 1.8002310 4.677368e-01 3.456283e+01
#> 738 7.37 0.000000 293.689023 1.7938620 4.647673e-01 3.465641e+01
#> 739 7.38 0.000000 293.024146 1.7875299 4.618203e-01 3.474990e+01
#> 740 7.39 0.000000 292.360418 1.7812345 4.588957e-01 3.484330e+01
#> 741 7.40 0.000000 291.697839 1.7749756 4.559933e-01 3.493661e+01
#> 742 7.41 0.000000 291.036409 1.7687528 4.531128e-01 3.502983e+01
#> 743 7.42 0.000000 290.376127 1.7625659 4.502540e-01 3.512296e+01
#> 744 7.43 0.000000 289.716994 1.7564147 4.474169e-01 3.521600e+01
#> 745 7.44 0.000000 289.059009 1.7502989 4.446011e-01 3.530894e+01
#> 746 7.45 0.000000 288.402172 1.7442183 4.418066e-01 3.540179e+01
#> 747 7.46 0.000000 287.746484 1.7381726 4.390331e-01 3.549455e+01
#> 748 7.47 0.000000 287.091942 1.7321616 4.362804e-01 3.558721e+01
#> 749 7.48 0.000000 286.438549 1.7261851 4.335484e-01 3.567978e+01
#> 750 7.49 0.000000 285.786302 1.7202427 4.308369e-01 3.577225e+01
#> 751 7.50 0.000000 285.135203 1.7143344 4.281457e-01 3.586463e+01
#> 752 7.51 0.000000 284.485250 1.7084598 4.254746e-01 3.595691e+01
#> 753 7.52 0.000000 283.836444 1.7026187 4.228235e-01 3.604910e+01
#> 754 7.53 0.000000 283.188784 1.6968108 4.201922e-01 3.614118e+01
#> 755 7.54 0.000000 282.542270 1.6910361 4.175805e-01 3.623317e+01
#> 756 7.55 0.000000 281.896902 1.6852941 4.149883e-01 3.632506e+01
#> 757 7.56 0.000000 281.252679 1.6795848 4.124153e-01 3.641685e+01
#> 758 7.57 0.000000 280.609600 1.6739078 4.098615e-01 3.650854e+01
#> 759 7.58 0.000000 279.967667 1.6682630 4.073267e-01 3.660014e+01
#> 760 7.59 0.000000 279.326878 1.6626501 4.048107e-01 3.669163e+01
#> 761 7.60 0.000000 278.687232 1.6570690 4.023133e-01 3.678302e+01
#> 762 7.61 0.000000 278.048730 1.6515194 3.998344e-01 3.687430e+01
#> 763 7.62 0.000000 277.411372 1.6460010 3.973738e-01 3.696549e+01
#> 764 7.63 0.000000 276.775156 1.6405137 3.949314e-01 3.705657e+01
#> 765 7.64 0.000000 276.140083 1.6350573 3.925070e-01 3.714756e+01
#> 766 7.65 0.000000 275.506151 1.6296315 3.901005e-01 3.723843e+01
#> 767 7.66 0.000000 274.873362 1.6242362 3.877117e-01 3.732921e+01
#> 768 7.67 0.000000 274.241713 1.6188712 3.853404e-01 3.741987e+01
#> 769 7.68 0.000000 273.611205 1.6135361 3.829866e-01 3.751044e+01
#> 770 7.69 0.000000 272.981837 1.6082309 3.806500e-01 3.760090e+01
#> 771 7.70 0.000000 272.353609 1.6029554 3.783306e-01 3.769125e+01
#> 772 7.71 0.000000 271.726521 1.5977092 3.760281e-01 3.778150e+01
#> 773 7.72 0.000000 271.100571 1.5924924 3.737425e-01 3.787164e+01
#> 774 7.73 0.000000 270.475760 1.5873045 3.714736e-01 3.796167e+01
#> 775 7.74 0.000000 269.852086 1.5821455 3.692212e-01 3.805160e+01
#> 776 7.75 0.000000 269.229550 1.5770152 3.669853e-01 3.814141e+01
#> 777 7.76 0.000000 268.608151 1.5719133 3.647656e-01 3.823112e+01
#> 778 7.77 0.000000 267.987888 1.5668396 3.625621e-01 3.832072e+01
#> 779 7.78 0.000000 267.368761 1.5617941 3.603746e-01 3.841021e+01
#> 780 7.79 0.000000 266.750769 1.5567764 3.582030e-01 3.849959e+01
#> 781 7.80 0.000000 266.133912 1.5517865 3.560471e-01 3.858887e+01
#> 782 7.81 0.000000 265.518189 1.5468241 3.539068e-01 3.867803e+01
#> 783 7.82 0.000000 264.903599 1.5418890 3.517820e-01 3.876708e+01
#> 784 7.83 0.000000 264.290143 1.5369810 3.496725e-01 3.885602e+01
#> 785 7.84 0.000000 263.677819 1.5321001 3.475783e-01 3.894484e+01
#> 786 7.85 0.000000 263.066626 1.5272459 3.454991e-01 3.903356e+01
#> 787 7.86 0.000000 262.456565 1.5224184 3.434350e-01 3.912216e+01
#> 788 7.87 0.000000 261.847634 1.5176173 3.413857e-01 3.921065e+01
#> 789 7.88 0.000000 261.239834 1.5128425 3.393511e-01 3.929903e+01
#> 790 7.89 0.000000 260.633162 1.5080937 3.373311e-01 3.938729e+01
#> 791 7.90 0.000000 260.027619 1.5033709 3.353256e-01 3.947544e+01
#> 792 7.91 0.000000 259.423205 1.4986738 3.333345e-01 3.956348e+01
#> 793 7.92 0.000000 258.819917 1.4940023 3.313576e-01 3.965140e+01
#> 794 7.93 0.000000 258.217756 1.4893563 3.293948e-01 3.973921e+01
#> 795 7.94 0.000000 257.616721 1.4847355 3.274460e-01 3.982690e+01
#> 796 7.95 0.000000 257.016812 1.4801397 3.255112e-01 3.991447e+01
#> 797 7.96 0.000000 256.418027 1.4755689 3.235901e-01 4.000193e+01
#> 798 7.97 0.000000 255.820366 1.4710228 3.216827e-01 4.008927e+01
#> 799 7.98 0.000000 255.223828 1.4665013 3.197888e-01 4.017650e+01
#> 800 7.99 0.000000 254.628412 1.4620042 3.179084e-01 4.026361e+01
#> 801 8.00 0.000000 254.034119 1.4575315 3.160414e-01 4.035060e+01
#> 802 8.01 0.000000 253.440946 1.4530828 3.141875e-01 4.043748e+01
#> 803 8.02 0.000000 252.848894 1.4486580 3.123468e-01 4.052423e+01
#> 804 8.03 0.000000 252.257961 1.4442571 3.105191e-01 4.061087e+01
#> 805 8.04 0.000000 251.668146 1.4398798 3.087043e-01 4.069739e+01
#> 806 8.05 0.000000 251.079450 1.4355260 3.069022e-01 4.078379e+01
#> 807 8.06 0.000000 250.491871 1.4311956 3.051129e-01 4.087007e+01
#> 808 8.07 0.000000 249.905409 1.4268883 3.033362e-01 4.095624e+01
#> 809 8.08 0.000000 249.320062 1.4226041 3.015719e-01 4.104228e+01
#> 810 8.09 0.000000 248.735829 1.4183427 2.998201e-01 4.112820e+01
#> 811 8.10 0.000000 248.152711 1.4141041 2.980805e-01 4.121400e+01
#> 812 8.11 0.000000 247.570706 1.4098881 2.963531e-01 4.129969e+01
#> 813 8.12 0.000000 246.989814 1.4056945 2.946379e-01 4.138525e+01
#> 814 8.13 0.000000 246.410033 1.4015232 2.929346e-01 4.147069e+01
#> 815 8.14 0.000000 245.831363 1.3973741 2.912431e-01 4.155601e+01
#> 816 8.15 0.000000 245.253803 1.3932470 2.895635e-01 4.164120e+01
#> 817 8.16 0.000000 244.677351 1.3891418 2.878956e-01 4.172628e+01
#> 818 8.17 0.000000 244.102008 1.3850583 2.862393e-01 4.181123e+01
#> 819 8.18 0.000000 243.527772 1.3809964 2.845946e-01 4.189606e+01
#> 820 8.19 0.000000 242.954643 1.3769559 2.829612e-01 4.198077e+01
#> 821 8.20 0.000000 242.382619 1.3729368 2.813392e-01 4.206535e+01
#> 822 8.21 0.000000 241.811700 1.3689388 2.797284e-01 4.214981e+01
#> 823 8.22 0.000000 241.241885 1.3649619 2.781288e-01 4.223415e+01
#> 824 8.23 0.000000 240.673173 1.3610059 2.765402e-01 4.231836e+01
#> 825 8.24 0.000000 240.105562 1.3570707 2.749626e-01 4.240245e+01
#> 826 8.25 0.000000 239.539053 1.3531562 2.733959e-01 4.248642e+01
#> 827 8.26 0.000000 238.973644 1.3492621 2.718400e-01 4.257026e+01
#> 828 8.27 0.000000 238.409334 1.3453885 2.702947e-01 4.265398e+01
#> 829 8.28 0.000000 237.846122 1.3415351 2.687602e-01 4.273757e+01
#> 830 8.29 0.000000 237.284008 1.3377018 2.672361e-01 4.282104e+01
#> 831 8.30 0.000000 236.722990 1.3338885 2.657225e-01 4.290438e+01
#> 832 8.31 0.000000 236.163068 1.3300951 2.642193e-01 4.298759e+01
#> 833 8.32 0.000000 235.604240 1.3263215 2.627264e-01 4.307068e+01
#> 834 8.33 0.000000 235.046506 1.3225675 2.612437e-01 4.315365e+01
#> 835 8.34 0.000000 234.489864 1.3188329 2.597711e-01 4.323649e+01
#> 836 8.35 0.000000 233.934314 1.3151178 2.583086e-01 4.331920e+01
#> 837 8.36 0.000000 233.379855 1.3114219 2.568560e-01 4.340179e+01
#> 838 8.37 0.000000 232.826485 1.3077451 2.554133e-01 4.348424e+01
#> 839 8.38 0.000000 232.274204 1.3040874 2.539805e-01 4.356658e+01
#> 840 8.39 0.000000 231.723011 1.3004486 2.525573e-01 4.364878e+01
#> 841 8.40 0.000000 231.172904 1.2968285 2.511439e-01 4.373086e+01
#> 842 8.41 0.000000 230.623883 1.2932271 2.497400e-01 4.381281e+01
#> 843 8.42 0.000000 230.075946 1.2896442 2.483456e-01 4.389463e+01
#> 844 8.43 0.000000 229.529093 1.2860798 2.469607e-01 4.397633e+01
#> 845 8.44 0.000000 228.983323 1.2825337 2.455851e-01 4.405789e+01
#> 846 8.45 0.000000 228.438634 1.2790057 2.442188e-01 4.413933e+01
#> 847 8.46 0.000000 227.895025 1.2754959 2.428617e-01 4.422064e+01
#> 848 8.47 0.000000 227.352497 1.2720040 2.415137e-01 4.430182e+01
#> 849 8.48 0.000000 226.811046 1.2685300 2.401748e-01 4.438288e+01
#> 850 8.49 0.000000 226.270673 1.2650738 2.388449e-01 4.446380e+01
#> 851 8.50 0.000000 225.731376 1.2616351 2.375240e-01 4.454460e+01
#> 852 8.51 0.000000 225.193154 1.2582141 2.362119e-01 4.462526e+01
#> 853 8.52 0.000000 224.656007 1.2548104 2.349085e-01 4.470580e+01
#> 854 8.53 0.000000 224.119932 1.2514241 2.336140e-01 4.478621e+01
#> 855 8.54 0.000000 223.584930 1.2480549 2.323280e-01 4.486649e+01
#> 856 8.55 0.000000 223.050998 1.2447029 2.310506e-01 4.494664e+01
#> 857 8.56 0.000000 222.518136 1.2413678 2.297818e-01 4.502666e+01
#> 858 8.57 0.000000 221.986343 1.2380497 2.285214e-01 4.510654e+01
#> 859 8.58 0.000000 221.455618 1.2347483 2.272694e-01 4.518630e+01
#> 860 8.59 0.000000 220.925959 1.2314637 2.260257e-01 4.526593e+01
#> 861 8.60 0.000000 220.397365 1.2281956 2.247903e-01 4.534543e+01
#> 862 8.61 0.000000 219.869836 1.2249440 2.235631e-01 4.542480e+01
#> 863 8.62 0.000000 219.343370 1.2217088 2.223440e-01 4.550404e+01
#> 864 8.63 0.000000 218.817965 1.2184898 2.211329e-01 4.558314e+01
#> 865 8.64 0.000000 218.293622 1.2152870 2.199299e-01 4.566212e+01
#> 866 8.65 0.000000 217.770338 1.2121004 2.187348e-01 4.574097e+01
#> 867 8.66 0.000000 217.248113 1.2089297 2.175476e-01 4.581968e+01
#> 868 8.67 0.000000 216.726946 1.2057749 2.163682e-01 4.589826e+01
#> 869 8.68 0.000000 216.206835 1.2026358 2.151966e-01 4.597671e+01
#> 870 8.69 0.000000 215.687779 1.1995125 2.140327e-01 4.605504e+01
#> 871 8.70 0.000000 215.169776 1.1964048 2.128764e-01 4.613322e+01
#> 872 8.71 0.000000 214.652827 1.1933126 2.117277e-01 4.621128e+01
#> 873 8.72 0.000000 214.136929 1.1902358 2.105865e-01 4.628921e+01
#> 874 8.73 0.000000 213.622082 1.1871743 2.094528e-01 4.636700e+01
#> 875 8.74 0.000000 213.108284 1.1841280 2.083266e-01 4.644467e+01
#> 876 8.75 0.000000 212.595535 1.1810969 2.072076e-01 4.652220e+01
#> 877 8.76 0.000000 212.083832 1.1780808 2.060960e-01 4.659960e+01
#> 878 8.77 0.000000 211.573175 1.1750797 2.049916e-01 4.667686e+01
#> 879 8.78 0.000000 211.063562 1.1720934 2.038944e-01 4.675400e+01
#> 880 8.79 0.000000 210.554993 1.1691219 2.028044e-01 4.683100e+01
#> 881 8.80 0.000000 210.047466 1.1661651 2.017214e-01 4.690787e+01
#> 882 8.81 0.000000 209.540980 1.1632228 2.006454e-01 4.698461e+01
#> 883 8.82 0.000000 209.035533 1.1602951 1.995765e-01 4.706121e+01
#> 884 8.83 0.000000 208.531126 1.1573818 1.985144e-01 4.713769e+01
#> 885 8.84 0.000000 208.027755 1.1544829 1.974592e-01 4.721403e+01
#> 886 8.85 0.000000 207.525420 1.1515982 1.964108e-01 4.729024e+01
#> 887 8.86 0.000000 207.024121 1.1487276 1.953692e-01 4.736631e+01
#> 888 8.87 0.000000 206.523855 1.1458712 1.943343e-01 4.744226e+01
#> 889 8.88 0.000000 206.024621 1.1430287 1.933061e-01 4.751807e+01
#> 890 8.89 0.000000 205.526419 1.1402001 1.922845e-01 4.759374e+01
#> 891 8.90 0.000000 205.029246 1.1373854 1.912695e-01 4.766929e+01
#> 892 8.91 0.000000 204.533102 1.1345844 1.902609e-01 4.774470e+01
#> 893 8.92 0.000000 204.037985 1.1317971 1.892588e-01 4.781998e+01
#> 894 8.93 0.000000 203.543895 1.1290234 1.882632e-01 4.789512e+01
#> 895 8.94 0.000000 203.050829 1.1262632 1.872739e-01 4.797014e+01
#> 896 8.95 0.000000 202.558788 1.1235164 1.862909e-01 4.804502e+01
#> 897 8.96 0.000000 202.067768 1.1207829 1.853143e-01 4.811976e+01
#> 898 8.97 0.000000 201.577770 1.1180628 1.843438e-01 4.819438e+01
#> 899 8.98 0.000000 201.088791 1.1153558 1.833795e-01 4.826886e+01
#> 900 8.99 0.000000 200.600831 1.1126619 1.824214e-01 4.834321e+01
#> 901 9.00 0.000000 200.113888 1.1099810 1.814693e-01 4.841742e+01
#> 902 9.01 0.000000 199.627962 1.1073131 1.805233e-01 4.849150e+01
#> 903 9.02 0.000000 199.143050 1.1046581 1.795833e-01 4.856545e+01
#> 904 9.03 0.000000 198.659151 1.1020159 1.786492e-01 4.863926e+01
#> 905 9.04 0.000000 198.176265 1.0993865 1.777211e-01 4.871295e+01
#> 906 9.05 0.000000 197.694389 1.0967697 1.767988e-01 4.878649e+01
#> 907 9.06 0.000000 197.213523 1.0941654 1.758823e-01 4.885991e+01
#> 908 9.07 0.000000 196.733666 1.0915737 1.749717e-01 4.893319e+01
#> 909 9.08 0.000000 196.254815 1.0889944 1.740667e-01 4.900634e+01
#> 910 9.09 0.000000 195.776970 1.0864275 1.731675e-01 4.907935e+01
#> 911 9.10 0.000000 195.300129 1.0838729 1.722739e-01 4.915223e+01
#> 912 9.11 0.000000 194.824292 1.0813305 1.713859e-01 4.922498e+01
#> 913 9.12 0.000000 194.349456 1.0788002 1.705035e-01 4.929760e+01
#> 914 9.13 0.000000 193.875620 1.0762820 1.696266e-01 4.937008e+01
#> 915 9.14 0.000000 193.402784 1.0737759 1.687552e-01 4.944243e+01
#> 916 9.15 0.000000 192.930946 1.0712816 1.678893e-01 4.951464e+01
#> 917 9.16 0.000000 192.460103 1.0687993 1.670287e-01 4.958672e+01
#> 918 9.17 0.000000 191.990256 1.0663287 1.661736e-01 4.965867e+01
#> 919 9.18 0.000000 191.521403 1.0638699 1.653237e-01 4.973048e+01
#> 920 9.19 0.000000 191.053542 1.0614227 1.644792e-01 4.980217e+01
#> 921 9.20 0.000000 190.586673 1.0589872 1.636399e-01 4.987371e+01
#> 922 9.21 0.000000 190.120793 1.0565632 1.628058e-01 4.994513e+01
#> 923 9.22 0.000000 189.655902 1.0541506 1.619769e-01 5.001641e+01
#> 924 9.23 0.000000 189.191997 1.0517494 1.611531e-01 5.008756e+01
#> 925 9.24 0.000000 188.729079 1.0493596 1.603345e-01 5.015857e+01
#> 926 9.25 0.000000 188.267145 1.0469811 1.595209e-01 5.022946e+01
#> 927 9.26 0.000000 187.806194 1.0446137 1.587123e-01 5.030020e+01
#> 928 9.27 0.000000 187.346224 1.0422575 1.579087e-01 5.037082e+01
#> 929 9.28 0.000000 186.887236 1.0399124 1.571101e-01 5.044130e+01
#> 930 9.29 0.000000 186.429226 1.0375782 1.563163e-01 5.051165e+01
#> 931 9.30 0.000000 185.972193 1.0352551 1.555275e-01 5.058187e+01
#> 932 9.31 0.000000 185.516137 1.0329428 1.547435e-01 5.065195e+01
#> 933 9.32 0.000000 185.061056 1.0306414 1.539644e-01 5.072190e+01
#> 934 9.33 0.000000 184.606949 1.0283507 1.531900e-01 5.079172e+01
#> 935 9.34 0.000000 184.153813 1.0260707 1.524203e-01 5.086140e+01
#> 936 9.35 0.000000 183.701649 1.0238014 1.516554e-01 5.093096e+01
#> 937 9.36 0.000000 183.250454 1.0215426 1.508951e-01 5.100037e+01
#> 938 9.37 0.000000 182.800227 1.0192944 1.501395e-01 5.106966e+01
#> 939 9.38 0.000000 182.350967 1.0170566 1.493885e-01 5.113881e+01
#> 940 9.39 0.000000 181.902672 1.0148293 1.486420e-01 5.120783e+01
#> 941 9.40 0.000000 181.455341 1.0126123 1.479001e-01 5.127672e+01
#> 942 9.41 0.000000 181.008972 1.0104055 1.471627e-01 5.134548e+01
#> 943 9.42 0.000000 180.563565 1.0082090 1.464298e-01 5.141410e+01
#> 944 9.43 0.000000 180.119118 1.0060227 1.457014e-01 5.148259e+01
#> 945 9.44 0.000000 179.675629 1.0038465 1.449773e-01 5.155095e+01
#> 946 9.45 0.000000 179.233097 1.0016804 1.442576e-01 5.161917e+01
#> 947 9.46 0.000000 178.791520 0.9995242 1.435423e-01 5.168727e+01
#> 948 9.47 0.000000 178.350898 0.9973780 1.428313e-01 5.175523e+01
#> 949 9.48 0.000000 177.911229 0.9952417 1.421246e-01 5.182306e+01
#> 950 9.49 0.000000 177.472511 0.9931152 1.414222e-01 5.189075e+01
#> 951 9.50 0.000000 177.034743 0.9909985 1.407240e-01 5.195832e+01
#> 952 9.51 0.000000 176.597924 0.9888916 1.400299e-01 5.202575e+01
#> 953 9.52 0.000000 176.162052 0.9867943 1.393401e-01 5.209305e+01
#> 954 9.53 0.000000 175.727125 0.9847066 1.386544e-01 5.216022e+01
#> 955 9.54 0.000000 175.293144 0.9826285 1.379728e-01 5.222725e+01
#> 956 9.55 0.000000 174.860105 0.9805599 1.372953e-01 5.229416e+01
#> 957 9.56 0.000000 174.428008 0.9785007 1.366218e-01 5.236093e+01
#> 958 9.57 0.000000 173.996851 0.9764510 1.359524e-01 5.242757e+01
#> 959 9.58 0.000000 173.566633 0.9744106 1.352869e-01 5.249408e+01
#> 960 9.59 0.000000 173.137352 0.9723795 1.346254e-01 5.256046e+01
#> 961 9.60 0.000000 172.709008 0.9703577 1.339679e-01 5.262671e+01
#> 962 9.61 0.000000 172.281598 0.9683451 1.333143e-01 5.269282e+01
#> 963 9.62 0.000000 171.855121 0.9663416 1.326645e-01 5.275881e+01
#> 964 9.63 0.000000 171.429575 0.9643472 1.320187e-01 5.282466e+01
#> 965 9.64 0.000000 171.004961 0.9623618 1.313766e-01 5.289038e+01
#> 966 9.65 0.000000 170.581275 0.9603855 1.307384e-01 5.295598e+01
#> 967 9.66 0.000000 170.158516 0.9584181 1.301039e-01 5.302144e+01
#> 968 9.67 0.000000 169.736683 0.9564596 1.294732e-01 5.308677e+01
#> 969 9.68 0.000000 169.315776 0.9545100 1.288462e-01 5.315196e+01
#> 970 9.69 0.000000 168.895791 0.9525691 1.282229e-01 5.321703e+01
#> 971 9.70 0.000000 168.476728 0.9506371 1.276033e-01 5.328197e+01
#> 972 9.71 0.000000 168.058585 0.9487137 1.269873e-01 5.334678e+01
#> 973 9.72 0.000000 167.641362 0.9467990 1.263749e-01 5.341145e+01
#> 974 9.73 0.000000 167.225056 0.9448928 1.257662e-01 5.347600e+01
#> 975 9.74 0.000000 166.809666 0.9429953 1.251610e-01 5.354042e+01
#> 976 9.75 0.000000 166.395190 0.9411063 1.245594e-01 5.360470e+01
#> 977 9.76 0.000000 165.981628 0.9392257 1.239612e-01 5.366886e+01
#> 978 9.77 0.000000 165.568977 0.9373536 1.233666e-01 5.373289e+01
#> 979 9.78 0.000000 165.157237 0.9354899 1.227755e-01 5.379678e+01
#> 980 9.79 0.000000 164.746406 0.9336344 1.221878e-01 5.386055e+01
#> 981 9.80 0.000000 164.336482 0.9317873 1.216035e-01 5.392419e+01
#> 982 9.81 0.000000 163.927464 0.9299484 1.210227e-01 5.398770e+01
#> 983 9.82 0.000000 163.519351 0.9281178 1.204452e-01 5.405108e+01
#> 984 9.83 0.000000 163.112141 0.9262952 1.198711e-01 5.411432e+01
#> 985 9.84 0.000000 162.705833 0.9244808 1.193003e-01 5.417745e+01
#> 986 9.85 0.000000 162.300425 0.9226745 1.187328e-01 5.424044e+01
#> 987 9.86 0.000000 161.895916 0.9208762 1.181686e-01 5.430330e+01
#> 988 9.87 0.000000 161.492304 0.9190858 1.176077e-01 5.436603e+01
#> 989 9.88 0.000000 161.089588 0.9173034 1.170500e-01 5.442864e+01
#> 990 9.89 0.000000 160.687767 0.9155289 1.164955e-01 5.449111e+01
#> 991 9.90 0.000000 160.286838 0.9137623 1.159442e-01 5.455346e+01
#> 992 9.91 0.000000 159.886801 0.9120034 1.153962e-01 5.461568e+01
#> 993 9.92 0.000000 159.487655 0.9102523 1.148512e-01 5.467777e+01
#> 994 9.93 0.000000 159.089397 0.9085090 1.143094e-01 5.473973e+01
#> 995 9.94 0.000000 158.692027 0.9067733 1.137707e-01 5.480157e+01
#> 996 9.95 0.000000 158.295542 0.9050453 1.132351e-01 5.486327e+01
#> 997 9.96 0.000000 157.899942 0.9033249 1.127026e-01 5.492485e+01
#> 998 9.97 0.000000 157.505224 0.9016121 1.121731e-01 5.498630e+01
#> 999 9.98 0.000000 157.111388 0.8999068 1.116467e-01 5.504763e+01
#> 1000 9.99 0.000000 156.718432 0.8982089 1.111232e-01 5.510882e+01
#> 1001 10.00 0.000000 156.326355 0.8965186 1.106028e-01 5.516989e+01
#> R
#> 1 0.000000e+00
#> 2 4.988903e-06
#> 3 2.050940e-05
#> 4 4.828863e-05
#> 5 9.031093e-05
#> 6 1.488540e-04
#> 7 2.265301e-04
#> 8 3.263324e-04
#> 9 4.516876e-04
#> 10 6.065156e-04
#> 11 7.952969e-04
#> 12 1.023148e-03
#> 13 1.295909e-03
#> 14 1.620238e-03
#> 15 2.003722e-03
#> 16 2.454999e-03
#> 17 2.983898e-03
#> 18 3.601592e-03
#> 19 4.320775e-03
#> 20 5.155859e-03
#> 21 6.123189e-03
#> 22 7.241297e-03
#> 23 8.531173e-03
#> 24 1.001658e-02
#> 25 1.172438e-02
#> 26 1.368494e-02
#> 27 1.593256e-02
#> 28 1.850592e-02
#> 29 2.144865e-02
#> 30 2.480987e-02
#> 31 2.864487e-02
#> 32 3.301580e-02
#> 33 3.799248e-02
#> 34 4.365323e-02
#> 35 5.008583e-02
#> 36 5.738853e-02
#> 37 6.567121e-02
#> 38 7.505652e-02
#> 39 8.568123e-02
#> 40 9.769760e-02
#> 41 1.112749e-01
#> 42 1.266009e-01
#> 43 1.438835e-01
#> 44 1.633528e-01
#> 45 1.852621e-01
#> 46 2.098907e-01
#> 47 2.375447e-01
#> 48 2.685594e-01
#> 49 3.033010e-01
#> 50 3.421677e-01
#> 51 3.855917e-01
#> 52 4.340398e-01
#> 53 4.880150e-01
#> 54 5.480564e-01
#> 55 6.147397e-01
#> 56 6.886769e-01
#> 57 7.705150e-01
#> 58 8.609349e-01
#> 59 9.606491e-01
#> 60 1.070399e+00
#> 61 1.190951e+00
#> 62 1.323092e+00
#> 63 1.467628e+00
#> 64 1.625372e+00
#> 65 1.797146e+00
#> 66 1.983771e+00
#> 67 2.186058e+00
#> 68 2.404810e+00
#> 69 2.640806e+00
#> 70 2.894803e+00
#> 71 3.167527e+00
#> 72 3.459669e+00
#> 73 3.771879e+00
#> 74 4.104766e+00
#> 75 4.458892e+00
#> 76 4.834770e+00
#> 77 5.232865e+00
#> 78 5.653592e+00
#> 79 6.097314e+00
#> 80 6.564347e+00
#> 81 7.054958e+00
#> 82 7.569365e+00
#> 83 8.107744e+00
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