FEDVR.jl
This is a Julia package for the Finite-Element Discrete Variable Representation method, used in the solution of partial differential equations. The main purpose for the package is for numerical solution of the Time-Dependent Schrödinger Equation ([i∂ₜ-Ĥ]|ψ⟩ = 0), however, its usefulness is not limited to this equation.
Usage
Grid setup
using FEDVRWe set up the basis for the calculations like so:
basis = FEDVR.Basis(range(0,stop=1,length=11),10)FEDVR Basis(FEDVR Grid with 10 elements of order 10 [dirichlet0,dirichlet0])
By default, Dirichlet0 boundary conditions at both boundaries are
assumed (by passing any other symbol than :dirichlet0, Dirichlet1
boundary conditions are applied; Neumann boundary conditions not yet
supported).
We can then plot the grid point locations:
plot(basis.grid)
as well as the basis functions:
plot(basis)
Expansion of scalar functions
A scalar function can be expanded by
f = x -> x*(x-1)^2
ϕ = project(f, basis)[2:end-1]
Note that the function expanded has to vanish at the boundaries of
the grid, since :dirichlet0 was chosen above. For non-vanishing
functions, pass :dirichlet1 to the Basis constructor.
Kinetic operator
The 1D kinetic operator is given by T̂ = -∂ₓ²/2, and can be retrieved by
T = kinop(basis)89×89 BlockBandedMatrices.BlockBandedMatrix{Float64}:
38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
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76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
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-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
-0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
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⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
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⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633 │ -50.0 │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267 │ 76.7633 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455 │ -93.5532 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825 │ 129.491 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899 │ -208.298 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111 │ 405.94 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09 │ -1037.72 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1 │ 4144.88 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7 │ -43683.7 │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ -50.0 │ 76.7633 -93.5532 129.491 -208.298 405.94 -1037.72 4144.88 -43683.7 │ 136500.0 │ -43683.7 4144.88 -1037.72 405.94 -208.298 129.491 -93.5532 76.7633
──────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────────┼───────────────┼──────────────────────────────────────────────────────────────────────────────────────────────
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -43683.7 │ 38845.7 -12242.1 2051.09 -703.111 339.899 -204.825 145.455 -118.267
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 4144.88 │ -12242.1 13209.7 -5878.71 1216.19 -489.409 270.205 -183.222 145.455
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -1037.72 │ 2051.09 -5878.71 7776.17 -4092.18 966.858 -437.805 270.205 -204.825
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 405.94 │ -703.111 1216.19 -4092.18 6168.51 -3660.71 966.858 -489.409 339.899
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -208.298 │ 339.899 -489.409 966.858 -3660.71 6168.51 -4092.18 1216.19 -703.111
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 129.491 │ -204.825 270.205 -437.805 966.858 -4092.18 7776.17 -5878.71 2051.09
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ -93.5532 │ 145.455 -183.222 270.205 -489.409 1216.19 -5878.71 13209.7 -12242.1
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ │ ⋅ │ -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 │ 76.7633 │ -118.267 145.455 -204.825 339.899 -703.111 2051.09 -12242.1 38845.7
which returns a BlockBandedMatrix.
In the special case of bases of polynomial order 2, the derivative operators reduce to tridiagonal matrices
derop(FEDVR.Basis(0.0:10, 2), 2)9×9 LinearAlgebra.Tridiagonal{Float64,Array{Float64,1}}:
-2.0 1.0 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
1.0 -2.0 1.0 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ 1.0 -2.0 1.0 ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ 1.0 -2.0 1.0 ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ 1.0 -2.0 1.0 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ 1.0 -2.0 1.0 ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ 1.0 -2.0 1.0 ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.0 -2.0 1.0
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 1.0 -2.0
which we recognize as the three-point stencil of the second derivative, arising from a finite-difference treatment.
Its eigenstates (also known as the eigenstates of a particle-in-a-box) can be computed using Julia’s builtin sparse diagonalization routine:
λ,ϕ = eigs(T,which=:SR)
If we plot the eigenvalues, we see the typical quadratic behaviour initially, but due to the division into finite elements, a series of steps occurs towards higher energies.
Wishes
- Efficiently calculate matrix elements for
- Local operators
- Derivative operators
- Two-body operators
- Allow different polynomial orders n in different finite elements
- Helper routines for different types of grids
- Cartesian Nd grids
- Spherical coordinates
- Radial grid
- Angular? [c.f. Schneider2016]
- Tensor product bases (multi-body problems)
- Laplacian operators
- Exterior Complex Scaling [c.f. Rescigno2000]
- Support for different quadratures [c.f. Baye2015]
References
- <<Rescigno2000>>Rescigno, T. N., & McCurdy, C. W. (2000). Numerical grid methods for quantum-mechanical scattering problems. Physical Review A, 62(3), 032706. DOI: 10.1103/physreva.62.032706
- <<McCurdy2001>>McCurdy, C. W., Horner, D. A., & Rescigno, T. N. (2001). Practical calculation of amplitudes for electron-impact ionization. Physical Review A, 63(2), 022711. DOI: 10.1103/physreva.63.022711
- <<McCurdy2004>>McCurdy, C. W., Baertschy, M., & Rescigno, T. N. (2004). Solving the three-body coulomb breakup problem using exterior complex scaling. Journal of Physics B: Atomic, Molecular and Optical Physics, 37(17), 137–187. DOI: 10.1088/0953-4075/37/17/r01
- <<Balzer2010>>Balzer, K., Bauch, S., & Bonitz, M. (2010). Finite elements and the discrete variable representation in nonequilibrium green’s function calculations. atomic and molecular models. Journal of Physics: Conference Series, 220(1), 012020. DOI: 10.1088/1742-6596/220/1/012020
- <<Baye2015>>Baye, D. (2015). The Lagrange-mesh method. Physics Reports, 565, 1–107. DOI: 10.1016/j.physrep.2014.11.006
- <<Schneider2016>>Schneider, B. I., Guan, X., & Bartschat, K. (2016). Time propagation of partial differential equations using the Short Iterative Lanczos method and finite-element discrete variable representation. Advances in Quantum Chemistry, 72, 95–127. DOI: 10.1016/bs.aiq.2015.12.002