Dirac notation#
Execute the following cells if you have problems running the code:
pip install wget
pip install opencv-python
Basis expansions#
Paul Dirac’s formalism for linear algebra is ingeniously tailored for the operations we perform in quantum theory, but may easily be applied to other problems. In this notebook we will use it to represent a photo of Dirac as a kid. By photo, we mean a grid of pixels assigned a numerical value given by the amount of light which at one point in time passed through a given regioun of the lens of the camera which was directed at the young Dirac.
Let’s begin by loading the image, which we shall refer to as \(\vert \Psi \rangle\):
import cv2, wget
import numpy as np
import matplotlib.pyplot as plt
dirac = 'https://1.bp.blogspot.com/-K4SHfqTCFH4/X6DuOKtxxkI/AAAAAAAANEo/RKb9SSr7NRsAggS8oWh3zRqRvwh1x7qUgCNcBGAsYHQ/w1200-h630-p-k-no-nu/dirac%2Bpaul%2Bchildhood.jpg'
filename = wget.download(dirac)
dirac = cv2.imread(filename)
dirac = cv2.resize(dirac, [140,75], interpolation = cv2.INTER_AREA)
psi = np.sum(dirac, axis = 2) #flatten out the color-channels
plt.figure()
plt.imshow(psi, cmap = "bone")
plt.axis("off")
plt.show()
Nx, Ny = psi.shape #get the shape of the image
The photo resides in a vectorspace \(\mathcal{V}\) which may be spanned by various bases. While the grid of pixels may seem like a natural choice of basis, it is actually seldomly the most compact and therefore typically not used on computers.
We shall construct an orthogonal and normalized basis, which we shall refer to as \(\{ \varphi_n \}\), spanning the space we are after. That the basis functions are mutually orthogonal and normalized means that
\[
\langle \varphi_m \vert \varphi_n \rangle = \delta_{m,n},
\]
where
\[\begin{split}
\delta_{mn} =
\begin{cases}
1, & \text{if } m=n,\\
0, & \text{if } m\neq n.
\end{cases}
\end{split}\]
When these two conditions are satisfied, we conveniently mash these two words into one by stating that the basis is orthonormal.
Note that this is a bit circular. A set of functions \(\{ \varphi_n \}\) must meet three criterions for it to be a basis for a vectorspace \(\mathcal{V}\):
Any vector \(\vert a \rangle \in \mathcal{V}\) can be expressed \(\vert a \rangle = \sum_{n} \vert \varphi_n \rangle c_n\).
The set \(\{ \varphi_n \}\) is linearly independent, meaning that no vector in the set can be expressed as a linear combination of the remaining vectors.
The basis must satisfy the completeness criterion, given by \(\sum_{n} \vert \varphi_n \rangle \langle \varphi_n \vert = \mathbb{1}\).
Inspired by Fourier-series, we shall construct a basis from simply cosine-functions:
\[
\varphi_{n}(x) = \cos{(n \pi x)} \hspace{1cm} x \in (0,1).
\]
We may extend this to two dimensions by means of a product:
\[
\varphi_{n_x, n_y}(x, y) := \varphi_{n_x}(x) \varphi_{n_y}(y) = \cos{(n_x \pi x)}\cos{(n_y \pi y)} .
\]
You would probably like to actually see these functions, so let’s construct the first few in a grid:
varphi = lambda x, y, nx, ny : np.sin(np.pi*x*nx)*np.sin(np.pi*y*ny)
fig, axs = plt.subplots(3, 3, figsize=(6, 6), sharey=True)
fig.suptitle('Various basis functions in our set')
t = np.linspace(0,1,20)
for nx in range(1,4):
for ny in range(1,4):
axs[nx-1,ny-1].contourf(t,t, varphi(t[None,:], t[:, None], nx,ny), cmap = "GnBu", levels = np.linspace(-1,1,200))
axs[nx-1,ny-1].text(.5,.5, "$\\varphi_{%i,%i}$" % (nx, ny), ha = "center", va = "center")
plt.show()
These are very different from the pixel-representation of the photo. Remember that the task we want to undertake is essentially to represent
\[
\vert \Psi \rangle = \sum_{n_x} \sum_{n_y} \varphi_{n_x, n_y} c_n.
\]
You should take a moment to think about (or discuss with someone) what this really means.
Discussion
What does the above mathematical expression mean in plain words. Explain it to somebody.
For a set of linearly dependent vectors, how can you tell which ones to remove in order to get an linearly independent set?
How is it a problem having a linear dependence in the first place?
Inner product space#
We have not yet defined the inner product for our vector space \(\mathcal{V}\). Recall that the inner product should be a mapping from two vectors in \(\mathcal{V}\) to a scalar:
\[
\langle \varphi_m \vert \varphi_n \rangle \in \mathbb{C}.
\]
For quantum mechanical systems you will typically use
\[
\langle \varphi_m \vert \varphi_n \rangle = \int_{\mathbb{R}^2} \big{(} \varphi_m(x,y)^*\varphi_n(x,y) \big{)}dxdy )
\]
In our case, we shall for simplicity rather use a numerical equivalent for real numbers:
def inner(psi_n, psi_m):
"""
Our simple inner product
"""
return np.sum(psi_n*psi_m)
By defining our inner product, our vector space \(\mathcal{V}\) has achieved the status of an inner product space, and we can check if our set of functions \(\{ \varphi_n \}\) meets the criterions (1-3) for being a basis of \(\mathcal{V}\):
t = np.linspace(0,1,100)
for nx in range(1,4):
for ny in range(1,4):
phi_m = varphi(t[None,:], t[:, None], nx,ny)
for nx_ in range(1,4):
for ny_ in range(1,4):
phi_n = varphi(t[None,:], t[:, None], nx_,ny_)
print("< phi_{%i %i} | phi_{%i %i} >" % (nx,ny,nx_, ny_), " = %.3f" % inner(phi_m, phi_n) )
< phi_{1 1} | phi_{1 1} > = 2450.250
< phi_{1 1} | phi_{1 2} > = 0.000
< phi_{1 1} | phi_{1 3} > = 0.000
< phi_{1 1} | phi_{2 1} > = -0.000
< phi_{1 1} | phi_{2 2} > = 0.000
< phi_{1 1} | phi_{2 3} > = -0.000
< phi_{1 1} | phi_{3 1} > = -0.000
< phi_{1 1} | phi_{3 2} > = 0.000
< phi_{1 1} | phi_{3 3} > = 0.000
< phi_{1 2} | phi_{1 1} > = 0.000
< phi_{1 2} | phi_{1 2} > = 2450.250
< phi_{1 2} | phi_{1 3} > = 0.000
< phi_{1 2} | phi_{2 1} > = 0.000
< phi_{1 2} | phi_{2 2} > = -0.000
< phi_{1 2} | phi_{2 3} > = 0.000
< phi_{1 2} | phi_{3 1} > = -0.000
< phi_{1 2} | phi_{3 2} > = -0.000
< phi_{1 2} | phi_{3 3} > = 0.000
< phi_{1 3} | phi_{1 1} > = 0.000
< phi_{1 3} | phi_{1 2} > = 0.000
< phi_{1 3} | phi_{1 3} > = 2450.250
< phi_{1 3} | phi_{2 1} > = -0.000
< phi_{1 3} | phi_{2 2} > = 0.000
< phi_{1 3} | phi_{2 3} > = -0.000
< phi_{1 3} | phi_{3 1} > = 0.000
< phi_{1 3} | phi_{3 2} > = 0.000
< phi_{1 3} | phi_{3 3} > = -0.000
< phi_{2 1} | phi_{1 1} > = -0.000
< phi_{2 1} | phi_{1 2} > = 0.000
< phi_{2 1} | phi_{1 3} > = -0.000
< phi_{2 1} | phi_{2 1} > = 2450.250
< phi_{2 1} | phi_{2 2} > = -0.000
< phi_{2 1} | phi_{2 3} > = -0.000
< phi_{2 1} | phi_{3 1} > = 0.000
< phi_{2 1} | phi_{3 2} > = -0.000
< phi_{2 1} | phi_{3 3} > = 0.000
< phi_{2 2} | phi_{1 1} > = 0.000
< phi_{2 2} | phi_{1 2} > = -0.000
< phi_{2 2} | phi_{1 3} > = 0.000
< phi_{2 2} | phi_{2 1} > = -0.000
< phi_{2 2} | phi_{2 2} > = 2450.250
< phi_{2 2} | phi_{2 3} > = 0.000
< phi_{2 2} | phi_{3 1} > = 0.000
< phi_{2 2} | phi_{3 2} > = 0.000
< phi_{2 2} | phi_{3 3} > = 0.000
< phi_{2 3} | phi_{1 1} > = -0.000
< phi_{2 3} | phi_{1 2} > = 0.000
< phi_{2 3} | phi_{1 3} > = -0.000
< phi_{2 3} | phi_{2 1} > = -0.000
< phi_{2 3} | phi_{2 2} > = 0.000
< phi_{2 3} | phi_{2 3} > = 2450.250
< phi_{2 3} | phi_{3 1} > = 0.000
< phi_{2 3} | phi_{3 2} > = -0.000
< phi_{2 3} | phi_{3 3} > = 0.000
< phi_{3 1} | phi_{1 1} > = -0.000
< phi_{3 1} | phi_{1 2} > = -0.000
< phi_{3 1} | phi_{1 3} > = 0.000
< phi_{3 1} | phi_{2 1} > = 0.000
< phi_{3 1} | phi_{2 2} > = 0.000
< phi_{3 1} | phi_{2 3} > = 0.000
< phi_{3 1} | phi_{3 1} > = 2450.250
< phi_{3 1} | phi_{3 2} > = -0.000
< phi_{3 1} | phi_{3 3} > = -0.000
< phi_{3 2} | phi_{1 1} > = 0.000
< phi_{3 2} | phi_{1 2} > = -0.000
< phi_{3 2} | phi_{1 3} > = 0.000
< phi_{3 2} | phi_{2 1} > = -0.000
< phi_{3 2} | phi_{2 2} > = 0.000
< phi_{3 2} | phi_{2 3} > = -0.000
< phi_{3 2} | phi_{3 1} > = -0.000
< phi_{3 2} | phi_{3 2} > = 2450.250
< phi_{3 2} | phi_{3 3} > = 0.000
< phi_{3 3} | phi_{1 1} > = 0.000
< phi_{3 3} | phi_{1 2} > = 0.000
< phi_{3 3} | phi_{1 3} > = -0.000
< phi_{3 3} | phi_{2 1} > = 0.000
< phi_{3 3} | phi_{2 2} > = 0.000
< phi_{3 3} | phi_{2 3} > = 0.000
< phi_{3 3} | phi_{3 1} > = -0.000
< phi_{3 3} | phi_{3 2} > = 0.000
< phi_{3 3} | phi_{3 3} > = 2450.250
Numerically we may consider anything below \(10^{-14}\) to be zero, but is this set orthonormal? The output above gives you this information, so see if you can figure it out before we move on.
A truncated basis#
We cannot construct the complete basis in the approach we are following here, but we can construct a basis which is quite large. From the above discussion, it was clear that our set was orthogonal, but not normalized. Let’s fix this by constructing a truncated set of basis functions in a list, whereby each function is normalized separately:
basis = []
# We should use a grid equal to the image dimensions for subsequent calculations
Nx, Ny = psi.shape
x = np.linspace(0,1,Nx)
y = np.linspace(0,1,Ny)
nc = 50
for nx in range(1,nc):
for ny in range(1,nc):
phi = varphi(x[:, None], y[None, :], nx,ny)
phi_normalized = phi*inner(phi, phi)**-.5 #normalize
print("< phi_{%i %i} | phi_{%i %i} >" %(nx,ny,nx,ny), " = %.2f" % inner(phi_normalized,phi_normalized))
basis.append(phi_normalized)
< phi_{1 1} | phi_{1 1} > = 1.00
< phi_{1 2} | phi_{1 2} > = 1.00
< phi_{1 3} | phi_{1 3} > = 1.00
< phi_{1 4} | phi_{1 4} > = 1.00
< phi_{1 5} | phi_{1 5} > = 1.00
< phi_{1 6} | phi_{1 6} > = 1.00
< phi_{1 7} | phi_{1 7} > = 1.00
< phi_{1 8} | phi_{1 8} > = 1.00
< phi_{1 9} | phi_{1 9} > = 1.00
< phi_{1 10} | phi_{1 10} > = 1.00
< phi_{1 11} | phi_{1 11} > = 1.00
< phi_{1 12} | phi_{1 12} > = 1.00
< phi_{1 13} | phi_{1 13} > = 1.00
< phi_{1 14} | phi_{1 14} > = 1.00
< phi_{1 15} | phi_{1 15} > = 1.00
< phi_{1 16} | phi_{1 16} > = 1.00
< phi_{1 17} | phi_{1 17} > = 1.00
< phi_{1 18} | phi_{1 18} > = 1.00
< phi_{1 19} | phi_{1 19} > = 1.00
< phi_{1 20} | phi_{1 20} > = 1.00
< phi_{1 21} | phi_{1 21} > = 1.00
< phi_{1 22} | phi_{1 22} > = 1.00
< phi_{1 23} | phi_{1 23} > = 1.00
< phi_{1 24} | phi_{1 24} > = 1.00
< phi_{1 25} | phi_{1 25} > = 1.00
< phi_{1 26} | phi_{1 26} > = 1.00
< phi_{1 27} | phi_{1 27} > = 1.00
< phi_{1 28} | phi_{1 28} > = 1.00
< phi_{1 29} | phi_{1 29} > = 1.00
< phi_{1 30} | phi_{1 30} > = 1.00
< phi_{1 31} | phi_{1 31} > = 1.00
< phi_{1 32} | phi_{1 32} > = 1.00
< phi_{1 33} | phi_{1 33} > = 1.00
< phi_{1 34} | phi_{1 34} > = 1.00
< phi_{1 35} | phi_{1 35} > = 1.00
< phi_{1 36} | phi_{1 36} > = 1.00
< phi_{1 37} | phi_{1 37} > = 1.00
< phi_{1 38} | phi_{1 38} > = 1.00
< phi_{1 39} | phi_{1 39} > = 1.00
< phi_{1 40} | phi_{1 40} > = 1.00
< phi_{1 41} | phi_{1 41} > = 1.00
< phi_{1 42} | phi_{1 42} > = 1.00
< phi_{1 43} | phi_{1 43} > = 1.00
< phi_{1 44} | phi_{1 44} > = 1.00
< phi_{1 45} | phi_{1 45} > = 1.00
< phi_{1 46} | phi_{1 46} > = 1.00
< phi_{1 47} | phi_{1 47} > = 1.00
< phi_{1 48} | phi_{1 48} > = 1.00
< phi_{1 49} | phi_{1 49} > = 1.00
< phi_{2 1} | phi_{2 1} > = 1.00
< phi_{2 2} | phi_{2 2} > = 1.00
< phi_{2 3} | phi_{2 3} > = 1.00
< phi_{2 4} | phi_{2 4} > = 1.00
< phi_{2 5} | phi_{2 5} > = 1.00
< phi_{2 6} | phi_{2 6} > = 1.00
< phi_{2 7} | phi_{2 7} > = 1.00
< phi_{2 8} | phi_{2 8} > = 1.00
< phi_{2 9} | phi_{2 9} > = 1.00
< phi_{2 10} | phi_{2 10} > = 1.00
< phi_{2 11} | phi_{2 11} > = 1.00
< phi_{2 12} | phi_{2 12} > = 1.00
< phi_{2 13} | phi_{2 13} > = 1.00
< phi_{2 14} | phi_{2 14} > = 1.00
< phi_{2 15} | phi_{2 15} > = 1.00
< phi_{2 16} | phi_{2 16} > = 1.00
< phi_{2 17} | phi_{2 17} > = 1.00
< phi_{2 18} | phi_{2 18} > = 1.00
< phi_{2 19} | phi_{2 19} > = 1.00
< phi_{2 20} | phi_{2 20} > = 1.00
< phi_{2 21} | phi_{2 21} > = 1.00
< phi_{2 22} | phi_{2 22} > = 1.00
< phi_{2 23} | phi_{2 23} > = 1.00
< phi_{2 24} | phi_{2 24} > = 1.00
< phi_{2 25} | phi_{2 25} > = 1.00
< phi_{2 26} | phi_{2 26} > = 1.00
< phi_{2 27} | phi_{2 27} > = 1.00
< phi_{2 28} | phi_{2 28} > = 1.00
< phi_{2 29} | phi_{2 29} > = 1.00
< phi_{2 30} | phi_{2 30} > = 1.00
< phi_{2 31} | phi_{2 31} > = 1.00
< phi_{2 32} | phi_{2 32} > = 1.00
< phi_{2 33} | phi_{2 33} > = 1.00
< phi_{2 34} | phi_{2 34} > = 1.00
< phi_{2 35} | phi_{2 35} > = 1.00
< phi_{2 36} | phi_{2 36} > = 1.00
< phi_{2 37} | phi_{2 37} > = 1.00
< phi_{2 38} | phi_{2 38} > = 1.00
< phi_{2 39} | phi_{2 39} > = 1.00
< phi_{2 40} | phi_{2 40} > = 1.00
< phi_{2 41} | phi_{2 41} > = 1.00
< phi_{2 42} | phi_{2 42} > = 1.00
< phi_{2 43} | phi_{2 43} > = 1.00
< phi_{2 44} | phi_{2 44} > = 1.00
< phi_{2 45} | phi_{2 45} > = 1.00
< phi_{2 46} | phi_{2 46} > = 1.00
< phi_{2 47} | phi_{2 47} > = 1.00
< phi_{2 48} | phi_{2 48} > = 1.00
< phi_{2 49} | phi_{2 49} > = 1.00
< phi_{3 1} | phi_{3 1} > = 1.00
< phi_{3 2} | phi_{3 2} > = 1.00
< phi_{3 3} | phi_{3 3} > = 1.00
< phi_{3 4} | phi_{3 4} > = 1.00
< phi_{3 5} | phi_{3 5} > = 1.00
< phi_{3 6} | phi_{3 6} > = 1.00
< phi_{3 7} | phi_{3 7} > = 1.00
< phi_{3 8} | phi_{3 8} > = 1.00
< phi_{3 9} | phi_{3 9} > = 1.00
< phi_{3 10} | phi_{3 10} > = 1.00
< phi_{3 11} | phi_{3 11} > = 1.00
< phi_{3 12} | phi_{3 12} > = 1.00
< phi_{3 13} | phi_{3 13} > = 1.00
< phi_{3 14} | phi_{3 14} > = 1.00
< phi_{3 15} | phi_{3 15} > = 1.00
< phi_{3 16} | phi_{3 16} > = 1.00
< phi_{3 17} | phi_{3 17} > = 1.00
< phi_{3 18} | phi_{3 18} > = 1.00
< phi_{3 19} | phi_{3 19} > = 1.00
< phi_{3 20} | phi_{3 20} > = 1.00
< phi_{3 21} | phi_{3 21} > = 1.00
< phi_{3 22} | phi_{3 22} > = 1.00
< phi_{3 23} | phi_{3 23} > = 1.00
< phi_{3 24} | phi_{3 24} > = 1.00
< phi_{3 25} | phi_{3 25} > = 1.00
< phi_{3 26} | phi_{3 26} > = 1.00
< phi_{3 27} | phi_{3 27} > = 1.00
< phi_{3 28} | phi_{3 28} > = 1.00
< phi_{3 29} | phi_{3 29} > = 1.00
< phi_{3 30} | phi_{3 30} > = 1.00
< phi_{3 31} | phi_{3 31} > = 1.00
< phi_{3 32} | phi_{3 32} > = 1.00
< phi_{3 33} | phi_{3 33} > = 1.00
< phi_{3 34} | phi_{3 34} > = 1.00
< phi_{3 35} | phi_{3 35} > = 1.00
< phi_{3 36} | phi_{3 36} > = 1.00
< phi_{3 37} | phi_{3 37} > = 1.00
< phi_{3 38} | phi_{3 38} > = 1.00
< phi_{3 39} | phi_{3 39} > = 1.00
< phi_{3 40} | phi_{3 40} > = 1.00
< phi_{3 41} | phi_{3 41} > = 1.00
< phi_{3 42} | phi_{3 42} > = 1.00
< phi_{3 43} | phi_{3 43} > = 1.00
< phi_{3 44} | phi_{3 44} > = 1.00
< phi_{3 45} | phi_{3 45} > = 1.00
< phi_{3 46} | phi_{3 46} > = 1.00
< phi_{3 47} | phi_{3 47} > = 1.00
< phi_{3 48} | phi_{3 48} > = 1.00
< phi_{3 49} | phi_{3 49} > = 1.00
< phi_{4 1} | phi_{4 1} > = 1.00
< phi_{4 2} | phi_{4 2} > = 1.00
< phi_{4 3} | phi_{4 3} > = 1.00
< phi_{4 4} | phi_{4 4} > = 1.00
< phi_{4 5} | phi_{4 5} > = 1.00
< phi_{4 6} | phi_{4 6} > = 1.00
< phi_{4 7} | phi_{4 7} > = 1.00
< phi_{4 8} | phi_{4 8} > = 1.00
< phi_{4 9} | phi_{4 9} > = 1.00
< phi_{4 10} | phi_{4 10} > = 1.00
< phi_{4 11} | phi_{4 11} > = 1.00
< phi_{4 12} | phi_{4 12} > = 1.00
< phi_{4 13} | phi_{4 13} > = 1.00
< phi_{4 14} | phi_{4 14} > = 1.00
< phi_{4 15} | phi_{4 15} > = 1.00
< phi_{4 16} | phi_{4 16} > = 1.00
< phi_{4 17} | phi_{4 17} > = 1.00
< phi_{4 18} | phi_{4 18} > = 1.00
< phi_{4 19} | phi_{4 19} > = 1.00
< phi_{4 20} | phi_{4 20} > = 1.00
< phi_{4 21} | phi_{4 21} > = 1.00
< phi_{4 22} | phi_{4 22} > = 1.00
< phi_{4 23} | phi_{4 23} > = 1.00
< phi_{4 24} | phi_{4 24} > = 1.00
< phi_{4 25} | phi_{4 25} > = 1.00
< phi_{4 26} | phi_{4 26} > = 1.00
< phi_{4 27} | phi_{4 27} > = 1.00
< phi_{4 28} | phi_{4 28} > = 1.00
< phi_{4 29} | phi_{4 29} > = 1.00
< phi_{4 30} | phi_{4 30} > = 1.00
< phi_{4 31} | phi_{4 31} > = 1.00
< phi_{4 32} | phi_{4 32} > = 1.00
< phi_{4 33} | phi_{4 33} > = 1.00
< phi_{4 34} | phi_{4 34} > = 1.00
< phi_{4 35} | phi_{4 35} > = 1.00
< phi_{4 36} | phi_{4 36} > = 1.00
< phi_{4 37} | phi_{4 37} > = 1.00
< phi_{4 38} | phi_{4 38} > = 1.00
< phi_{4 39} | phi_{4 39} > = 1.00
< phi_{4 40} | phi_{4 40} > = 1.00
< phi_{4 41} | phi_{4 41} > = 1.00
< phi_{4 42} | phi_{4 42} > = 1.00
< phi_{4 43} | phi_{4 43} > = 1.00
< phi_{4 44} | phi_{4 44} > = 1.00
< phi_{4 45} | phi_{4 45} > = 1.00
< phi_{4 46} | phi_{4 46} > = 1.00
< phi_{4 47} | phi_{4 47} > = 1.00
< phi_{4 48} | phi_{4 48} > = 1.00
< phi_{4 49} | phi_{4 49} > = 1.00
< phi_{5 1} | phi_{5 1} > = 1.00
< phi_{5 2} | phi_{5 2} > = 1.00
< phi_{5 3} | phi_{5 3} > = 1.00
< phi_{5 4} | phi_{5 4} > = 1.00
< phi_{5 5} | phi_{5 5} > = 1.00
< phi_{5 6} | phi_{5 6} > = 1.00
< phi_{5 7} | phi_{5 7} > = 1.00
< phi_{5 8} | phi_{5 8} > = 1.00
< phi_{5 9} | phi_{5 9} > = 1.00
< phi_{5 10} | phi_{5 10} > = 1.00
< phi_{5 11} | phi_{5 11} > = 1.00
< phi_{5 12} | phi_{5 12} > = 1.00
< phi_{5 13} | phi_{5 13} > = 1.00
< phi_{5 14} | phi_{5 14} > = 1.00
< phi_{5 15} | phi_{5 15} > = 1.00
< phi_{5 16} | phi_{5 16} > = 1.00
< phi_{5 17} | phi_{5 17} > = 1.00
< phi_{5 18} | phi_{5 18} > = 1.00
< phi_{5 19} | phi_{5 19} > = 1.00
< phi_{5 20} | phi_{5 20} > = 1.00
< phi_{5 21} | phi_{5 21} > = 1.00
< phi_{5 22} | phi_{5 22} > = 1.00
< phi_{5 23} | phi_{5 23} > = 1.00
< phi_{5 24} | phi_{5 24} > = 1.00
< phi_{5 25} | phi_{5 25} > = 1.00
< phi_{5 26} | phi_{5 26} > = 1.00
< phi_{5 27} | phi_{5 27} > = 1.00
< phi_{5 28} | phi_{5 28} > = 1.00
< phi_{5 29} | phi_{5 29} > = 1.00
< phi_{5 30} | phi_{5 30} > = 1.00
< phi_{5 31} | phi_{5 31} > = 1.00
< phi_{5 32} | phi_{5 32} > = 1.00
< phi_{5 33} | phi_{5 33} > = 1.00
< phi_{5 34} | phi_{5 34} > = 1.00
< phi_{5 35} | phi_{5 35} > = 1.00
< phi_{5 36} | phi_{5 36} > = 1.00
< phi_{5 37} | phi_{5 37} > = 1.00
< phi_{5 38} | phi_{5 38} > = 1.00
< phi_{5 39} | phi_{5 39} > = 1.00
< phi_{5 40} | phi_{5 40} > = 1.00
< phi_{5 41} | phi_{5 41} > = 1.00
< phi_{5 42} | phi_{5 42} > = 1.00
< phi_{5 43} | phi_{5 43} > = 1.00
< phi_{5 44} | phi_{5 44} > = 1.00
< phi_{5 45} | phi_{5 45} > = 1.00
< phi_{5 46} | phi_{5 46} > = 1.00
< phi_{5 47} | phi_{5 47} > = 1.00
< phi_{5 48} | phi_{5 48} > = 1.00
< phi_{5 49} | phi_{5 49} > = 1.00
< phi_{6 1} | phi_{6 1} > = 1.00
< phi_{6 2} | phi_{6 2} > = 1.00
< phi_{6 3} | phi_{6 3} > = 1.00
< phi_{6 4} | phi_{6 4} > = 1.00
< phi_{6 5} | phi_{6 5} > = 1.00
< phi_{6 6} | phi_{6 6} > = 1.00
< phi_{6 7} | phi_{6 7} > = 1.00
< phi_{6 8} | phi_{6 8} > = 1.00
< phi_{6 9} | phi_{6 9} > = 1.00
< phi_{6 10} | phi_{6 10} > = 1.00
< phi_{6 11} | phi_{6 11} > = 1.00
< phi_{6 12} | phi_{6 12} > = 1.00
< phi_{6 13} | phi_{6 13} > = 1.00
< phi_{6 14} | phi_{6 14} > = 1.00
< phi_{6 15} | phi_{6 15} > = 1.00
< phi_{6 16} | phi_{6 16} > = 1.00
< phi_{6 17} | phi_{6 17} > = 1.00
< phi_{6 18} | phi_{6 18} > = 1.00
< phi_{6 19} | phi_{6 19} > = 1.00
< phi_{6 20} | phi_{6 20} > = 1.00
< phi_{6 21} | phi_{6 21} > = 1.00
< phi_{6 22} | phi_{6 22} > = 1.00
< phi_{6 23} | phi_{6 23} > = 1.00
< phi_{6 24} | phi_{6 24} > = 1.00
< phi_{6 25} | phi_{6 25} > = 1.00
< phi_{6 26} | phi_{6 26} > = 1.00
< phi_{6 27} | phi_{6 27} > = 1.00
< phi_{6 28} | phi_{6 28} > = 1.00
< phi_{6 29} | phi_{6 29} > = 1.00
< phi_{6 30} | phi_{6 30} > = 1.00
< phi_{6 31} | phi_{6 31} > = 1.00
< phi_{6 32} | phi_{6 32} > = 1.00
< phi_{6 33} | phi_{6 33} > = 1.00
< phi_{6 34} | phi_{6 34} > = 1.00
< phi_{6 35} | phi_{6 35} > = 1.00
< phi_{6 36} | phi_{6 36} > = 1.00
< phi_{6 37} | phi_{6 37} > = 1.00
< phi_{6 38} | phi_{6 38} > = 1.00
< phi_{6 39} | phi_{6 39} > = 1.00
< phi_{6 40} | phi_{6 40} > = 1.00
< phi_{6 41} | phi_{6 41} > = 1.00
< phi_{6 42} | phi_{6 42} > = 1.00
< phi_{6 43} | phi_{6 43} > = 1.00
< phi_{6 44} | phi_{6 44} > = 1.00
< phi_{6 45} | phi_{6 45} > = 1.00
< phi_{6 46} | phi_{6 46} > = 1.00
< phi_{6 47} | phi_{6 47} > = 1.00
< phi_{6 48} | phi_{6 48} > = 1.00
< phi_{6 49} | phi_{6 49} > = 1.00
< phi_{7 1} | phi_{7 1} > = 1.00
< phi_{7 2} | phi_{7 2} > = 1.00
< phi_{7 3} | phi_{7 3} > = 1.00
< phi_{7 4} | phi_{7 4} > = 1.00
< phi_{7 5} | phi_{7 5} > = 1.00
< phi_{7 6} | phi_{7 6} > = 1.00
< phi_{7 7} | phi_{7 7} > = 1.00
< phi_{7 8} | phi_{7 8} > = 1.00
< phi_{7 9} | phi_{7 9} > = 1.00
< phi_{7 10} | phi_{7 10} > = 1.00
< phi_{7 11} | phi_{7 11} > = 1.00
< phi_{7 12} | phi_{7 12} > = 1.00
< phi_{7 13} | phi_{7 13} > = 1.00
< phi_{7 14} | phi_{7 14} > = 1.00
< phi_{7 15} | phi_{7 15} > = 1.00
< phi_{7 16} | phi_{7 16} > = 1.00
< phi_{7 17} | phi_{7 17} > = 1.00
< phi_{7 18} | phi_{7 18} > = 1.00
< phi_{7 19} | phi_{7 19} > = 1.00
< phi_{7 20} | phi_{7 20} > = 1.00
< phi_{7 21} | phi_{7 21} > = 1.00
< phi_{7 22} | phi_{7 22} > = 1.00
< phi_{7 23} | phi_{7 23} > = 1.00
< phi_{7 24} | phi_{7 24} > = 1.00
< phi_{7 25} | phi_{7 25} > = 1.00
< phi_{7 26} | phi_{7 26} > = 1.00
< phi_{7 27} | phi_{7 27} > = 1.00
< phi_{7 28} | phi_{7 28} > = 1.00
< phi_{7 29} | phi_{7 29} > = 1.00
< phi_{7 30} | phi_{7 30} > = 1.00
< phi_{7 31} | phi_{7 31} > = 1.00
< phi_{7 32} | phi_{7 32} > = 1.00
< phi_{7 33} | phi_{7 33} > = 1.00
< phi_{7 34} | phi_{7 34} > = 1.00
< phi_{7 35} | phi_{7 35} > = 1.00
< phi_{7 36} | phi_{7 36} > = 1.00
< phi_{7 37} | phi_{7 37} > = 1.00
< phi_{7 38} | phi_{7 38} > = 1.00
< phi_{7 39} | phi_{7 39} > = 1.00
< phi_{7 40} | phi_{7 40} > = 1.00
< phi_{7 41} | phi_{7 41} > = 1.00
< phi_{7 42} | phi_{7 42} > = 1.00
< phi_{7 43} | phi_{7 43} > = 1.00
< phi_{7 44} | phi_{7 44} > = 1.00
< phi_{7 45} | phi_{7 45} > = 1.00
< phi_{7 46} | phi_{7 46} > = 1.00
< phi_{7 47} | phi_{7 47} > = 1.00
< phi_{7 48} | phi_{7 48} > = 1.00
< phi_{7 49} | phi_{7 49} > = 1.00
< phi_{8 1} | phi_{8 1} > = 1.00
< phi_{8 2} | phi_{8 2} > = 1.00
< phi_{8 3} | phi_{8 3} > = 1.00
< phi_{8 4} | phi_{8 4} > = 1.00
< phi_{8 5} | phi_{8 5} > = 1.00
< phi_{8 6} | phi_{8 6} > = 1.00
< phi_{8 7} | phi_{8 7} > = 1.00
< phi_{8 8} | phi_{8 8} > = 1.00
< phi_{8 9} | phi_{8 9} > = 1.00
< phi_{8 10} | phi_{8 10} > = 1.00
< phi_{8 11} | phi_{8 11} > = 1.00
< phi_{8 12} | phi_{8 12} > = 1.00
< phi_{8 13} | phi_{8 13} > = 1.00
< phi_{8 14} | phi_{8 14} > = 1.00
< phi_{8 15} | phi_{8 15} > = 1.00
< phi_{8 16} | phi_{8 16} > = 1.00
< phi_{8 17} | phi_{8 17} > = 1.00
< phi_{8 18} | phi_{8 18} > = 1.00
< phi_{8 19} | phi_{8 19} > = 1.00
< phi_{8 20} | phi_{8 20} > = 1.00
< phi_{8 21} | phi_{8 21} > = 1.00
< phi_{8 22} | phi_{8 22} > = 1.00
< phi_{8 23} | phi_{8 23} > = 1.00
< phi_{8 24} | phi_{8 24} > = 1.00
< phi_{8 25} | phi_{8 25} > = 1.00
< phi_{8 26} | phi_{8 26} > = 1.00
< phi_{8 27} | phi_{8 27} > = 1.00
< phi_{8 28} | phi_{8 28} > = 1.00
< phi_{8 29} | phi_{8 29} > = 1.00
< phi_{8 30} | phi_{8 30} > = 1.00
< phi_{8 31} | phi_{8 31} > = 1.00
< phi_{8 32} | phi_{8 32} > = 1.00
< phi_{8 33} | phi_{8 33} > = 1.00
< phi_{8 34} | phi_{8 34} > = 1.00
< phi_{8 35} | phi_{8 35} > = 1.00
< phi_{8 36} | phi_{8 36} > = 1.00
< phi_{8 37} | phi_{8 37} > = 1.00
< phi_{8 38} | phi_{8 38} > = 1.00
< phi_{8 39} | phi_{8 39} > = 1.00
< phi_{8 40} | phi_{8 40} > = 1.00
< phi_{8 41} | phi_{8 41} > = 1.00
< phi_{8 42} | phi_{8 42} > = 1.00
< phi_{8 43} | phi_{8 43} > = 1.00
< phi_{8 44} | phi_{8 44} > = 1.00
< phi_{8 45} | phi_{8 45} > = 1.00
< phi_{8 46} | phi_{8 46} > = 1.00
< phi_{8 47} | phi_{8 47} > = 1.00
< phi_{8 48} | phi_{8 48} > = 1.00
< phi_{8 49} | phi_{8 49} > = 1.00
< phi_{9 1} | phi_{9 1} > = 1.00
< phi_{9 2} | phi_{9 2} > = 1.00
< phi_{9 3} | phi_{9 3} > = 1.00
< phi_{9 4} | phi_{9 4} > = 1.00
< phi_{9 5} | phi_{9 5} > = 1.00
< phi_{9 6} | phi_{9 6} > = 1.00
< phi_{9 7} | phi_{9 7} > = 1.00
< phi_{9 8} | phi_{9 8} > = 1.00
< phi_{9 9} | phi_{9 9} > = 1.00
< phi_{9 10} | phi_{9 10} > = 1.00
< phi_{9 11} | phi_{9 11} > = 1.00
< phi_{9 12} | phi_{9 12} > = 1.00
< phi_{9 13} | phi_{9 13} > = 1.00
< phi_{9 14} | phi_{9 14} > = 1.00
< phi_{9 15} | phi_{9 15} > = 1.00
< phi_{9 16} | phi_{9 16} > = 1.00
< phi_{9 17} | phi_{9 17} > = 1.00
< phi_{9 18} | phi_{9 18} > = 1.00
< phi_{9 19} | phi_{9 19} > = 1.00
< phi_{9 20} | phi_{9 20} > = 1.00
< phi_{9 21} | phi_{9 21} > = 1.00
< phi_{9 22} | phi_{9 22} > = 1.00
< phi_{9 23} | phi_{9 23} > = 1.00
< phi_{9 24} | phi_{9 24} > = 1.00
< phi_{9 25} | phi_{9 25} > = 1.00
< phi_{9 26} | phi_{9 26} > = 1.00
< phi_{9 27} | phi_{9 27} > = 1.00
< phi_{9 28} | phi_{9 28} > = 1.00
< phi_{9 29} | phi_{9 29} > = 1.00
< phi_{9 30} | phi_{9 30} > = 1.00
< phi_{9 31} | phi_{9 31} > = 1.00
< phi_{9 32} | phi_{9 32} > = 1.00
< phi_{9 33} | phi_{9 33} > = 1.00
< phi_{9 34} | phi_{9 34} > = 1.00
< phi_{9 35} | phi_{9 35} > = 1.00
< phi_{9 36} | phi_{9 36} > = 1.00
< phi_{9 37} | phi_{9 37} > = 1.00
< phi_{9 38} | phi_{9 38} > = 1.00
< phi_{9 39} | phi_{9 39} > = 1.00
< phi_{9 40} | phi_{9 40} > = 1.00
< phi_{9 41} | phi_{9 41} > = 1.00
< phi_{9 42} | phi_{9 42} > = 1.00
< phi_{9 43} | phi_{9 43} > = 1.00
< phi_{9 44} | phi_{9 44} > = 1.00
< phi_{9 45} | phi_{9 45} > = 1.00
< phi_{9 46} | phi_{9 46} > = 1.00
< phi_{9 47} | phi_{9 47} > = 1.00
< phi_{9 48} | phi_{9 48} > = 1.00
< phi_{9 49} | phi_{9 49} > = 1.00
< phi_{10 1} | phi_{10 1} > = 1.00
< phi_{10 2} | phi_{10 2} > = 1.00
< phi_{10 3} | phi_{10 3} > = 1.00
< phi_{10 4} | phi_{10 4} > = 1.00
< phi_{10 5} | phi_{10 5} > = 1.00
< phi_{10 6} | phi_{10 6} > = 1.00
< phi_{10 7} | phi_{10 7} > = 1.00
< phi_{10 8} | phi_{10 8} > = 1.00
< phi_{10 9} | phi_{10 9} > = 1.00
< phi_{10 10} | phi_{10 10} > = 1.00
< phi_{10 11} | phi_{10 11} > = 1.00
< phi_{10 12} | phi_{10 12} > = 1.00
< phi_{10 13} | phi_{10 13} > = 1.00
< phi_{10 14} | phi_{10 14} > = 1.00
< phi_{10 15} | phi_{10 15} > = 1.00
< phi_{10 16} | phi_{10 16} > = 1.00
< phi_{10 17} | phi_{10 17} > = 1.00
< phi_{10 18} | phi_{10 18} > = 1.00
< phi_{10 19} | phi_{10 19} > = 1.00
< phi_{10 20} | phi_{10 20} > = 1.00
< phi_{10 21} | phi_{10 21} > = 1.00
< phi_{10 22} | phi_{10 22} > = 1.00
< phi_{10 23} | phi_{10 23} > = 1.00
< phi_{10 24} | phi_{10 24} > = 1.00
< phi_{10 25} | phi_{10 25} > = 1.00
< phi_{10 26} | phi_{10 26} > = 1.00
< phi_{10 27} | phi_{10 27} > = 1.00
< phi_{10 28} | phi_{10 28} > = 1.00
< phi_{10 29} | phi_{10 29} > = 1.00
< phi_{10 30} | phi_{10 30} > = 1.00
< phi_{10 31} | phi_{10 31} > = 1.00
< phi_{10 32} | phi_{10 32} > = 1.00
< phi_{10 33} | phi_{10 33} > = 1.00
< phi_{10 34} | phi_{10 34} > = 1.00
< phi_{10 35} | phi_{10 35} > = 1.00
< phi_{10 36} | phi_{10 36} > = 1.00
< phi_{10 37} | phi_{10 37} > = 1.00
< phi_{10 38} | phi_{10 38} > = 1.00
< phi_{10 39} | phi_{10 39} > = 1.00
< phi_{10 40} | phi_{10 40} > = 1.00
< phi_{10 41} | phi_{10 41} > = 1.00
< phi_{10 42} | phi_{10 42} > = 1.00
< phi_{10 43} | phi_{10 43} > = 1.00
< phi_{10 44} | phi_{10 44} > = 1.00
< phi_{10 45} | phi_{10 45} > = 1.00
< phi_{10 46} | phi_{10 46} > = 1.00
< phi_{10 47} | phi_{10 47} > = 1.00
< phi_{10 48} | phi_{10 48} > = 1.00
< phi_{10 49} | phi_{10 49} > = 1.00
< phi_{11 1} | phi_{11 1} > = 1.00
< phi_{11 2} | phi_{11 2} > = 1.00
< phi_{11 3} | phi_{11 3} > = 1.00
< phi_{11 4} | phi_{11 4} > = 1.00
< phi_{11 5} | phi_{11 5} > = 1.00
< phi_{11 6} | phi_{11 6} > = 1.00
< phi_{11 7} | phi_{11 7} > = 1.00
< phi_{11 8} | phi_{11 8} > = 1.00
< phi_{11 9} | phi_{11 9} > = 1.00
< phi_{11 10} | phi_{11 10} > = 1.00
< phi_{11 11} | phi_{11 11} > = 1.00
< phi_{11 12} | phi_{11 12} > = 1.00
< phi_{11 13} | phi_{11 13} > = 1.00
< phi_{11 14} | phi_{11 14} > = 1.00
< phi_{11 15} | phi_{11 15} > = 1.00
< phi_{11 16} | phi_{11 16} > = 1.00
< phi_{11 17} | phi_{11 17} > = 1.00
< phi_{11 18} | phi_{11 18} > = 1.00
< phi_{11 19} | phi_{11 19} > = 1.00
< phi_{11 20} | phi_{11 20} > = 1.00
< phi_{11 21} | phi_{11 21} > = 1.00
< phi_{11 22} | phi_{11 22} > = 1.00
< phi_{11 23} | phi_{11 23} > = 1.00
< phi_{11 24} | phi_{11 24} > = 1.00
< phi_{11 25} | phi_{11 25} > = 1.00
< phi_{11 26} | phi_{11 26} > = 1.00
< phi_{11 27} | phi_{11 27} > = 1.00
< phi_{11 28} | phi_{11 28} > = 1.00
< phi_{11 29} | phi_{11 29} > = 1.00
< phi_{11 30} | phi_{11 30} > = 1.00
< phi_{11 31} | phi_{11 31} > = 1.00
< phi_{11 32} | phi_{11 32} > = 1.00
< phi_{11 33} | phi_{11 33} > = 1.00
< phi_{11 34} | phi_{11 34} > = 1.00
< phi_{11 35} | phi_{11 35} > = 1.00
< phi_{11 36} | phi_{11 36} > = 1.00
< phi_{11 37} | phi_{11 37} > = 1.00
< phi_{11 38} | phi_{11 38} > = 1.00
< phi_{11 39} | phi_{11 39} > = 1.00
< phi_{11 40} | phi_{11 40} > = 1.00
< phi_{11 41} | phi_{11 41} > = 1.00
< phi_{11 42} | phi_{11 42} > = 1.00
< phi_{11 43} | phi_{11 43} > = 1.00
< phi_{11 44} | phi_{11 44} > = 1.00
< phi_{11 45} | phi_{11 45} > = 1.00
< phi_{11 46} | phi_{11 46} > = 1.00
< phi_{11 47} | phi_{11 47} > = 1.00
< phi_{11 48} | phi_{11 48} > = 1.00
< phi_{11 49} | phi_{11 49} > = 1.00
< phi_{12 1} | phi_{12 1} > = 1.00
< phi_{12 2} | phi_{12 2} > = 1.00
< phi_{12 3} | phi_{12 3} > = 1.00
< phi_{12 4} | phi_{12 4} > = 1.00
< phi_{12 5} | phi_{12 5} > = 1.00
< phi_{12 6} | phi_{12 6} > = 1.00
< phi_{12 7} | phi_{12 7} > = 1.00
< phi_{12 8} | phi_{12 8} > = 1.00
< phi_{12 9} | phi_{12 9} > = 1.00
< phi_{12 10} | phi_{12 10} > = 1.00
< phi_{12 11} | phi_{12 11} > = 1.00
< phi_{12 12} | phi_{12 12} > = 1.00
< phi_{12 13} | phi_{12 13} > = 1.00
< phi_{12 14} | phi_{12 14} > = 1.00
< phi_{12 15} | phi_{12 15} > = 1.00
< phi_{12 16} | phi_{12 16} > = 1.00
< phi_{12 17} | phi_{12 17} > = 1.00
< phi_{12 18} | phi_{12 18} > = 1.00
< phi_{12 19} | phi_{12 19} > = 1.00
< phi_{12 20} | phi_{12 20} > = 1.00
< phi_{12 21} | phi_{12 21} > = 1.00
< phi_{12 22} | phi_{12 22} > = 1.00
< phi_{12 23} | phi_{12 23} > = 1.00
< phi_{12 24} | phi_{12 24} > = 1.00
< phi_{12 25} | phi_{12 25} > = 1.00
< phi_{12 26} | phi_{12 26} > = 1.00
< phi_{12 27} | phi_{12 27} > = 1.00
< phi_{12 28} | phi_{12 28} > = 1.00
< phi_{12 29} | phi_{12 29} > = 1.00
< phi_{12 30} | phi_{12 30} > = 1.00
< phi_{12 31} | phi_{12 31} > = 1.00
< phi_{12 32} | phi_{12 32} > = 1.00
< phi_{12 33} | phi_{12 33} > = 1.00
< phi_{12 34} | phi_{12 34} > = 1.00
< phi_{12 35} | phi_{12 35} > = 1.00
< phi_{12 36} | phi_{12 36} > = 1.00
< phi_{12 37} | phi_{12 37} > = 1.00
< phi_{12 38} | phi_{12 38} > = 1.00
< phi_{12 39} | phi_{12 39} > = 1.00
< phi_{12 40} | phi_{12 40} > = 1.00
< phi_{12 41} | phi_{12 41} > = 1.00
< phi_{12 42} | phi_{12 42} > = 1.00
< phi_{12 43} | phi_{12 43} > = 1.00
< phi_{12 44} | phi_{12 44} > = 1.00
< phi_{12 45} | phi_{12 45} > = 1.00
< phi_{12 46} | phi_{12 46} > = 1.00
< phi_{12 47} | phi_{12 47} > = 1.00
< phi_{12 48} | phi_{12 48} > = 1.00
< phi_{12 49} | phi_{12 49} > = 1.00
< phi_{13 1} | phi_{13 1} > = 1.00
< phi_{13 2} | phi_{13 2} > = 1.00
< phi_{13 3} | phi_{13 3} > = 1.00
< phi_{13 4} | phi_{13 4} > = 1.00
< phi_{13 5} | phi_{13 5} > = 1.00
< phi_{13 6} | phi_{13 6} > = 1.00
< phi_{13 7} | phi_{13 7} > = 1.00
< phi_{13 8} | phi_{13 8} > = 1.00
< phi_{13 9} | phi_{13 9} > = 1.00
< phi_{13 10} | phi_{13 10} > = 1.00
< phi_{13 11} | phi_{13 11} > = 1.00
< phi_{13 12} | phi_{13 12} > = 1.00
< phi_{13 13} | phi_{13 13} > = 1.00
< phi_{13 14} | phi_{13 14} > = 1.00
< phi_{13 15} | phi_{13 15} > = 1.00
< phi_{13 16} | phi_{13 16} > = 1.00
< phi_{13 17} | phi_{13 17} > = 1.00
< phi_{13 18} | phi_{13 18} > = 1.00
< phi_{13 19} | phi_{13 19} > = 1.00
< phi_{13 20} | phi_{13 20} > = 1.00
< phi_{13 21} | phi_{13 21} > = 1.00
< phi_{13 22} | phi_{13 22} > = 1.00
< phi_{13 23} | phi_{13 23} > = 1.00
< phi_{13 24} | phi_{13 24} > = 1.00
< phi_{13 25} | phi_{13 25} > = 1.00
< phi_{13 26} | phi_{13 26} > = 1.00
< phi_{13 27} | phi_{13 27} > = 1.00
< phi_{13 28} | phi_{13 28} > = 1.00
< phi_{13 29} | phi_{13 29} > = 1.00
< phi_{13 30} | phi_{13 30} > = 1.00
< phi_{13 31} | phi_{13 31} > = 1.00
< phi_{13 32} | phi_{13 32} > = 1.00
< phi_{13 33} | phi_{13 33} > = 1.00
< phi_{13 34} | phi_{13 34} > = 1.00
< phi_{13 35} | phi_{13 35} > = 1.00
< phi_{13 36} | phi_{13 36} > = 1.00
< phi_{13 37} | phi_{13 37} > = 1.00
< phi_{13 38} | phi_{13 38} > = 1.00
< phi_{13 39} | phi_{13 39} > = 1.00
< phi_{13 40} | phi_{13 40} > = 1.00
< phi_{13 41} | phi_{13 41} > = 1.00
< phi_{13 42} | phi_{13 42} > = 1.00
< phi_{13 43} | phi_{13 43} > = 1.00
< phi_{13 44} | phi_{13 44} > = 1.00
< phi_{13 45} | phi_{13 45} > = 1.00
< phi_{13 46} | phi_{13 46} > = 1.00
< phi_{13 47} | phi_{13 47} > = 1.00
< phi_{13 48} | phi_{13 48} > = 1.00
< phi_{13 49} | phi_{13 49} > = 1.00
< phi_{14 1} | phi_{14 1} > = 1.00
< phi_{14 2} | phi_{14 2} > = 1.00
< phi_{14 3} | phi_{14 3} > = 1.00
< phi_{14 4} | phi_{14 4} > = 1.00
< phi_{14 5} | phi_{14 5} > = 1.00
< phi_{14 6} | phi_{14 6} > = 1.00
< phi_{14 7} | phi_{14 7} > = 1.00
< phi_{14 8} | phi_{14 8} > = 1.00
< phi_{14 9} | phi_{14 9} > = 1.00
< phi_{14 10} | phi_{14 10} > = 1.00
< phi_{14 11} | phi_{14 11} > = 1.00
< phi_{14 12} | phi_{14 12} > = 1.00
< phi_{14 13} | phi_{14 13} > = 1.00
< phi_{14 14} | phi_{14 14} > = 1.00
< phi_{14 15} | phi_{14 15} > = 1.00
< phi_{14 16} | phi_{14 16} > = 1.00
< phi_{14 17} | phi_{14 17} > = 1.00
< phi_{14 18} | phi_{14 18} > = 1.00
< phi_{14 19} | phi_{14 19} > = 1.00
< phi_{14 20} | phi_{14 20} > = 1.00
< phi_{14 21} | phi_{14 21} > = 1.00
< phi_{14 22} | phi_{14 22} > = 1.00
< phi_{14 23} | phi_{14 23} > = 1.00
< phi_{14 24} | phi_{14 24} > = 1.00
< phi_{14 25} | phi_{14 25} > = 1.00
< phi_{14 26} | phi_{14 26} > = 1.00
< phi_{14 27} | phi_{14 27} > = 1.00
< phi_{14 28} | phi_{14 28} > = 1.00
< phi_{14 29} | phi_{14 29} > = 1.00
< phi_{14 30} | phi_{14 30} > = 1.00
< phi_{14 31} | phi_{14 31} > = 1.00
< phi_{14 32} | phi_{14 32} > = 1.00
< phi_{14 33} | phi_{14 33} > = 1.00
< phi_{14 34} | phi_{14 34} > = 1.00
< phi_{14 35} | phi_{14 35} > = 1.00
< phi_{14 36} | phi_{14 36} > = 1.00
< phi_{14 37} | phi_{14 37} > = 1.00
< phi_{14 38} | phi_{14 38} > = 1.00
< phi_{14 39} | phi_{14 39} > = 1.00
< phi_{14 40} | phi_{14 40} > = 1.00
< phi_{14 41} | phi_{14 41} > = 1.00
< phi_{14 42} | phi_{14 42} > = 1.00
< phi_{14 43} | phi_{14 43} > = 1.00
< phi_{14 44} | phi_{14 44} > = 1.00
< phi_{14 45} | phi_{14 45} > = 1.00
< phi_{14 46} | phi_{14 46} > = 1.00
< phi_{14 47} | phi_{14 47} > = 1.00
< phi_{14 48} | phi_{14 48} > = 1.00
< phi_{14 49} | phi_{14 49} > = 1.00
< phi_{15 1} | phi_{15 1} > = 1.00
< phi_{15 2} | phi_{15 2} > = 1.00
< phi_{15 3} | phi_{15 3} > = 1.00
< phi_{15 4} | phi_{15 4} > = 1.00
< phi_{15 5} | phi_{15 5} > = 1.00
< phi_{15 6} | phi_{15 6} > = 1.00
< phi_{15 7} | phi_{15 7} > = 1.00
< phi_{15 8} | phi_{15 8} > = 1.00
< phi_{15 9} | phi_{15 9} > = 1.00
< phi_{15 10} | phi_{15 10} > = 1.00
< phi_{15 11} | phi_{15 11} > = 1.00
< phi_{15 12} | phi_{15 12} > = 1.00
< phi_{15 13} | phi_{15 13} > = 1.00
< phi_{15 14} | phi_{15 14} > = 1.00
< phi_{15 15} | phi_{15 15} > = 1.00
< phi_{15 16} | phi_{15 16} > = 1.00
< phi_{15 17} | phi_{15 17} > = 1.00
< phi_{15 18} | phi_{15 18} > = 1.00
< phi_{15 19} | phi_{15 19} > = 1.00
< phi_{15 20} | phi_{15 20} > = 1.00
< phi_{15 21} | phi_{15 21} > = 1.00
< phi_{15 22} | phi_{15 22} > = 1.00
< phi_{15 23} | phi_{15 23} > = 1.00
< phi_{15 24} | phi_{15 24} > = 1.00
< phi_{15 25} | phi_{15 25} > = 1.00
< phi_{15 26} | phi_{15 26} > = 1.00
< phi_{15 27} | phi_{15 27} > = 1.00
< phi_{15 28} | phi_{15 28} > = 1.00
< phi_{15 29} | phi_{15 29} > = 1.00
< phi_{15 30} | phi_{15 30} > = 1.00
< phi_{15 31} | phi_{15 31} > = 1.00
< phi_{15 32} | phi_{15 32} > = 1.00
< phi_{15 33} | phi_{15 33} > = 1.00
< phi_{15 34} | phi_{15 34} > = 1.00
< phi_{15 35} | phi_{15 35} > = 1.00
< phi_{15 36} | phi_{15 36} > = 1.00
< phi_{15 37} | phi_{15 37} > = 1.00
< phi_{15 38} | phi_{15 38} > = 1.00
< phi_{15 39} | phi_{15 39} > = 1.00
< phi_{15 40} | phi_{15 40} > = 1.00
< phi_{15 41} | phi_{15 41} > = 1.00
< phi_{15 42} | phi_{15 42} > = 1.00
< phi_{15 43} | phi_{15 43} > = 1.00
< phi_{15 44} | phi_{15 44} > = 1.00
< phi_{15 45} | phi_{15 45} > = 1.00
< phi_{15 46} | phi_{15 46} > = 1.00
< phi_{15 47} | phi_{15 47} > = 1.00
< phi_{15 48} | phi_{15 48} > = 1.00
< phi_{15 49} | phi_{15 49} > = 1.00
< phi_{16 1} | phi_{16 1} > = 1.00
< phi_{16 2} | phi_{16 2} > = 1.00
< phi_{16 3} | phi_{16 3} > = 1.00
< phi_{16 4} | phi_{16 4} > = 1.00
< phi_{16 5} | phi_{16 5} > = 1.00
< phi_{16 6} | phi_{16 6} > = 1.00
< phi_{16 7} | phi_{16 7} > = 1.00
< phi_{16 8} | phi_{16 8} > = 1.00
< phi_{16 9} | phi_{16 9} > = 1.00
< phi_{16 10} | phi_{16 10} > = 1.00
< phi_{16 11} | phi_{16 11} > = 1.00
< phi_{16 12} | phi_{16 12} > = 1.00
< phi_{16 13} | phi_{16 13} > = 1.00
< phi_{16 14} | phi_{16 14} > = 1.00
< phi_{16 15} | phi_{16 15} > = 1.00
< phi_{16 16} | phi_{16 16} > = 1.00
< phi_{16 17} | phi_{16 17} > = 1.00
< phi_{16 18} | phi_{16 18} > = 1.00
< phi_{16 19} | phi_{16 19} > = 1.00
< phi_{16 20} | phi_{16 20} > = 1.00
< phi_{16 21} | phi_{16 21} > = 1.00
< phi_{16 22} | phi_{16 22} > = 1.00
< phi_{16 23} | phi_{16 23} > = 1.00
< phi_{16 24} | phi_{16 24} > = 1.00
< phi_{16 25} | phi_{16 25} > = 1.00
< phi_{16 26} | phi_{16 26} > = 1.00
< phi_{16 27} | phi_{16 27} > = 1.00
< phi_{16 28} | phi_{16 28} > = 1.00
< phi_{16 29} | phi_{16 29} > = 1.00
< phi_{16 30} | phi_{16 30} > = 1.00
< phi_{16 31} | phi_{16 31} > = 1.00
< phi_{16 32} | phi_{16 32} > = 1.00
< phi_{16 33} | phi_{16 33} > = 1.00
< phi_{16 34} | phi_{16 34} > = 1.00
< phi_{16 35} | phi_{16 35} > = 1.00
< phi_{16 36} | phi_{16 36} > = 1.00
< phi_{16 37} | phi_{16 37} > = 1.00
< phi_{16 38} | phi_{16 38} > = 1.00
< phi_{16 39} | phi_{16 39} > = 1.00
< phi_{16 40} | phi_{16 40} > = 1.00
< phi_{16 41} | phi_{16 41} > = 1.00
< phi_{16 42} | phi_{16 42} > = 1.00
< phi_{16 43} | phi_{16 43} > = 1.00
< phi_{16 44} | phi_{16 44} > = 1.00
< phi_{16 45} | phi_{16 45} > = 1.00
< phi_{16 46} | phi_{16 46} > = 1.00
< phi_{16 47} | phi_{16 47} > = 1.00
< phi_{16 48} | phi_{16 48} > = 1.00
< phi_{16 49} | phi_{16 49} > = 1.00
< phi_{17 1} | phi_{17 1} > = 1.00
< phi_{17 2} | phi_{17 2} > = 1.00
< phi_{17 3} | phi_{17 3} > = 1.00
< phi_{17 4} | phi_{17 4} > = 1.00
< phi_{17 5} | phi_{17 5} > = 1.00
< phi_{17 6} | phi_{17 6} > = 1.00
< phi_{17 7} | phi_{17 7} > = 1.00
< phi_{17 8} | phi_{17 8} > = 1.00
< phi_{17 9} | phi_{17 9} > = 1.00
< phi_{17 10} | phi_{17 10} > = 1.00
< phi_{17 11} | phi_{17 11} > = 1.00
< phi_{17 12} | phi_{17 12} > = 1.00
< phi_{17 13} | phi_{17 13} > = 1.00
< phi_{17 14} | phi_{17 14} > = 1.00
< phi_{17 15} | phi_{17 15} > = 1.00
< phi_{17 16} | phi_{17 16} > = 1.00
< phi_{17 17} | phi_{17 17} > = 1.00
< phi_{17 18} | phi_{17 18} > = 1.00
< phi_{17 19} | phi_{17 19} > = 1.00
< phi_{17 20} | phi_{17 20} > = 1.00
< phi_{17 21} | phi_{17 21} > = 1.00
< phi_{17 22} | phi_{17 22} > = 1.00
< phi_{17 23} | phi_{17 23} > = 1.00
< phi_{17 24} | phi_{17 24} > = 1.00
< phi_{17 25} | phi_{17 25} > = 1.00
< phi_{17 26} | phi_{17 26} > = 1.00
< phi_{17 27} | phi_{17 27} > = 1.00
< phi_{17 28} | phi_{17 28} > = 1.00
< phi_{17 29} | phi_{17 29} > = 1.00
< phi_{17 30} | phi_{17 30} > = 1.00
< phi_{17 31} | phi_{17 31} > = 1.00
< phi_{17 32} | phi_{17 32} > = 1.00
< phi_{17 33} | phi_{17 33} > = 1.00
< phi_{17 34} | phi_{17 34} > = 1.00
< phi_{17 35} | phi_{17 35} > = 1.00
< phi_{17 36} | phi_{17 36} > = 1.00
< phi_{17 37} | phi_{17 37} > = 1.00
< phi_{17 38} | phi_{17 38} > = 1.00
< phi_{17 39} | phi_{17 39} > = 1.00
< phi_{17 40} | phi_{17 40} > = 1.00
< phi_{17 41} | phi_{17 41} > = 1.00
< phi_{17 42} | phi_{17 42} > = 1.00
< phi_{17 43} | phi_{17 43} > = 1.00
< phi_{17 44} | phi_{17 44} > = 1.00
< phi_{17 45} | phi_{17 45} > = 1.00
< phi_{17 46} | phi_{17 46} > = 1.00
< phi_{17 47} | phi_{17 47} > = 1.00
< phi_{17 48} | phi_{17 48} > = 1.00
< phi_{17 49} | phi_{17 49} > = 1.00
< phi_{18 1} | phi_{18 1} > = 1.00
< phi_{18 2} | phi_{18 2} > = 1.00
< phi_{18 3} | phi_{18 3} > = 1.00
< phi_{18 4} | phi_{18 4} > = 1.00
< phi_{18 5} | phi_{18 5} > = 1.00
< phi_{18 6} | phi_{18 6} > = 1.00
< phi_{18 7} | phi_{18 7} > = 1.00
< phi_{18 8} | phi_{18 8} > = 1.00
< phi_{18 9} | phi_{18 9} > = 1.00
< phi_{18 10} | phi_{18 10} > = 1.00
< phi_{18 11} | phi_{18 11} > = 1.00
< phi_{18 12} | phi_{18 12} > = 1.00
< phi_{18 13} | phi_{18 13} > = 1.00
< phi_{18 14} | phi_{18 14} > = 1.00
< phi_{18 15} | phi_{18 15} > = 1.00
< phi_{18 16} | phi_{18 16} > = 1.00
< phi_{18 17} | phi_{18 17} > = 1.00
< phi_{18 18} | phi_{18 18} > = 1.00
< phi_{18 19} | phi_{18 19} > = 1.00
< phi_{18 20} | phi_{18 20} > = 1.00
< phi_{18 21} | phi_{18 21} > = 1.00
< phi_{18 22} | phi_{18 22} > = 1.00
< phi_{18 23} | phi_{18 23} > = 1.00
< phi_{18 24} | phi_{18 24} > = 1.00
< phi_{18 25} | phi_{18 25} > = 1.00
< phi_{18 26} | phi_{18 26} > = 1.00
< phi_{18 27} | phi_{18 27} > = 1.00
< phi_{18 28} | phi_{18 28} > = 1.00
< phi_{18 29} | phi_{18 29} > = 1.00
< phi_{18 30} | phi_{18 30} > = 1.00
< phi_{18 31} | phi_{18 31} > = 1.00
< phi_{18 32} | phi_{18 32} > = 1.00
< phi_{18 33} | phi_{18 33} > = 1.00
< phi_{18 34} | phi_{18 34} > = 1.00
< phi_{18 35} | phi_{18 35} > = 1.00
< phi_{18 36} | phi_{18 36} > = 1.00
< phi_{18 37} | phi_{18 37} > = 1.00
< phi_{18 38} | phi_{18 38} > = 1.00
< phi_{18 39} | phi_{18 39} > = 1.00
< phi_{18 40} | phi_{18 40} > = 1.00
< phi_{18 41} | phi_{18 41} > = 1.00
< phi_{18 42} | phi_{18 42} > = 1.00
< phi_{18 43} | phi_{18 43} > = 1.00
< phi_{18 44} | phi_{18 44} > = 1.00
< phi_{18 45} | phi_{18 45} > = 1.00
< phi_{18 46} | phi_{18 46} > = 1.00
< phi_{18 47} | phi_{18 47} > = 1.00
< phi_{18 48} | phi_{18 48} > = 1.00
< phi_{18 49} | phi_{18 49} > = 1.00
< phi_{19 1} | phi_{19 1} > = 1.00
< phi_{19 2} | phi_{19 2} > = 1.00
< phi_{19 3} | phi_{19 3} > = 1.00
< phi_{19 4} | phi_{19 4} > = 1.00
< phi_{19 5} | phi_{19 5} > = 1.00
< phi_{19 6} | phi_{19 6} > = 1.00
< phi_{19 7} | phi_{19 7} > = 1.00
< phi_{19 8} | phi_{19 8} > = 1.00
< phi_{19 9} | phi_{19 9} > = 1.00
< phi_{19 10} | phi_{19 10} > = 1.00
< phi_{19 11} | phi_{19 11} > = 1.00
< phi_{19 12} | phi_{19 12} > = 1.00
< phi_{19 13} | phi_{19 13} > = 1.00
< phi_{19 14} | phi_{19 14} > = 1.00
< phi_{19 15} | phi_{19 15} > = 1.00
< phi_{19 16} | phi_{19 16} > = 1.00
< phi_{19 17} | phi_{19 17} > = 1.00
< phi_{19 18} | phi_{19 18} > = 1.00
< phi_{19 19} | phi_{19 19} > = 1.00
< phi_{19 20} | phi_{19 20} > = 1.00
< phi_{19 21} | phi_{19 21} > = 1.00
< phi_{19 22} | phi_{19 22} > = 1.00
< phi_{19 23} | phi_{19 23} > = 1.00
< phi_{19 24} | phi_{19 24} > = 1.00
< phi_{19 25} | phi_{19 25} > = 1.00
< phi_{19 26} | phi_{19 26} > = 1.00
< phi_{19 27} | phi_{19 27} > = 1.00
< phi_{19 28} | phi_{19 28} > = 1.00
< phi_{19 29} | phi_{19 29} > = 1.00
< phi_{19 30} | phi_{19 30} > = 1.00
< phi_{19 31} | phi_{19 31} > = 1.00
< phi_{19 32} | phi_{19 32} > = 1.00
< phi_{19 33} | phi_{19 33} > = 1.00
< phi_{19 34} | phi_{19 34} > = 1.00
< phi_{19 35} | phi_{19 35} > = 1.00
< phi_{19 36} | phi_{19 36} > = 1.00
< phi_{19 37} | phi_{19 37} > = 1.00
< phi_{19 38} | phi_{19 38} > = 1.00
< phi_{19 39} | phi_{19 39} > = 1.00
< phi_{19 40} | phi_{19 40} > = 1.00
< phi_{19 41} | phi_{19 41} > = 1.00
< phi_{19 42} | phi_{19 42} > = 1.00
< phi_{19 43} | phi_{19 43} > = 1.00
< phi_{19 44} | phi_{19 44} > = 1.00
< phi_{19 45} | phi_{19 45} > = 1.00
< phi_{19 46} | phi_{19 46} > = 1.00
< phi_{19 47} | phi_{19 47} > = 1.00
< phi_{19 48} | phi_{19 48} > = 1.00
< phi_{19 49} | phi_{19 49} > = 1.00
< phi_{20 1} | phi_{20 1} > = 1.00
< phi_{20 2} | phi_{20 2} > = 1.00
< phi_{20 3} | phi_{20 3} > = 1.00
< phi_{20 4} | phi_{20 4} > = 1.00
< phi_{20 5} | phi_{20 5} > = 1.00
< phi_{20 6} | phi_{20 6} > = 1.00
< phi_{20 7} | phi_{20 7} > = 1.00
< phi_{20 8} | phi_{20 8} > = 1.00
< phi_{20 9} | phi_{20 9} > = 1.00
< phi_{20 10} | phi_{20 10} > = 1.00
< phi_{20 11} | phi_{20 11} > = 1.00
< phi_{20 12} | phi_{20 12} > = 1.00
< phi_{20 13} | phi_{20 13} > = 1.00
< phi_{20 14} | phi_{20 14} > = 1.00
< phi_{20 15} | phi_{20 15} > = 1.00
< phi_{20 16} | phi_{20 16} > = 1.00
< phi_{20 17} | phi_{20 17} > = 1.00
< phi_{20 18} | phi_{20 18} > = 1.00
< phi_{20 19} | phi_{20 19} > = 1.00
< phi_{20 20} | phi_{20 20} > = 1.00
< phi_{20 21} | phi_{20 21} > = 1.00
< phi_{20 22} | phi_{20 22} > = 1.00
< phi_{20 23} | phi_{20 23} > = 1.00
< phi_{20 24} | phi_{20 24} > = 1.00
< phi_{20 25} | phi_{20 25} > = 1.00
< phi_{20 26} | phi_{20 26} > = 1.00
< phi_{20 27} | phi_{20 27} > = 1.00
< phi_{20 28} | phi_{20 28} > = 1.00
< phi_{20 29} | phi_{20 29} > = 1.00
< phi_{20 30} | phi_{20 30} > = 1.00
< phi_{20 31} | phi_{20 31} > = 1.00
< phi_{20 32} | phi_{20 32} > = 1.00
< phi_{20 33} | phi_{20 33} > = 1.00
< phi_{20 34} | phi_{20 34} > = 1.00
< phi_{20 35} | phi_{20 35} > = 1.00
< phi_{20 36} | phi_{20 36} > = 1.00
< phi_{20 37} | phi_{20 37} > = 1.00
< phi_{20 38} | phi_{20 38} > = 1.00
< phi_{20 39} | phi_{20 39} > = 1.00
< phi_{20 40} | phi_{20 40} > = 1.00
< phi_{20 41} | phi_{20 41} > = 1.00
< phi_{20 42} | phi_{20 42} > = 1.00
< phi_{20 43} | phi_{20 43} > = 1.00
< phi_{20 44} | phi_{20 44} > = 1.00
< phi_{20 45} | phi_{20 45} > = 1.00
< phi_{20 46} | phi_{20 46} > = 1.00
< phi_{20 47} | phi_{20 47} > = 1.00
< phi_{20 48} | phi_{20 48} > = 1.00
< phi_{20 49} | phi_{20 49} > = 1.00
< phi_{21 1} | phi_{21 1} > = 1.00
< phi_{21 2} | phi_{21 2} > = 1.00
< phi_{21 3} | phi_{21 3} > = 1.00
< phi_{21 4} | phi_{21 4} > = 1.00
< phi_{21 5} | phi_{21 5} > = 1.00
< phi_{21 6} | phi_{21 6} > = 1.00
< phi_{21 7} | phi_{21 7} > = 1.00
< phi_{21 8} | phi_{21 8} > = 1.00
< phi_{21 9} | phi_{21 9} > = 1.00
< phi_{21 10} | phi_{21 10} > = 1.00
< phi_{21 11} | phi_{21 11} > = 1.00
< phi_{21 12} | phi_{21 12} > = 1.00
< phi_{21 13} | phi_{21 13} > = 1.00
< phi_{21 14} | phi_{21 14} > = 1.00
< phi_{21 15} | phi_{21 15} > = 1.00
< phi_{21 16} | phi_{21 16} > = 1.00
< phi_{21 17} | phi_{21 17} > = 1.00
< phi_{21 18} | phi_{21 18} > = 1.00
< phi_{21 19} | phi_{21 19} > = 1.00
< phi_{21 20} | phi_{21 20} > = 1.00
< phi_{21 21} | phi_{21 21} > = 1.00
< phi_{21 22} | phi_{21 22} > = 1.00
< phi_{21 23} | phi_{21 23} > = 1.00
< phi_{21 24} | phi_{21 24} > = 1.00
< phi_{21 25} | phi_{21 25} > = 1.00
< phi_{21 26} | phi_{21 26} > = 1.00
< phi_{21 27} | phi_{21 27} > = 1.00
< phi_{21 28} | phi_{21 28} > = 1.00
< phi_{21 29} | phi_{21 29} > = 1.00
< phi_{21 30} | phi_{21 30} > = 1.00
< phi_{21 31} | phi_{21 31} > = 1.00
< phi_{21 32} | phi_{21 32} > = 1.00
< phi_{21 33} | phi_{21 33} > = 1.00
< phi_{21 34} | phi_{21 34} > = 1.00
< phi_{21 35} | phi_{21 35} > = 1.00
< phi_{21 36} | phi_{21 36} > = 1.00
< phi_{21 37} | phi_{21 37} > = 1.00
< phi_{21 38} | phi_{21 38} > = 1.00
< phi_{21 39} | phi_{21 39} > = 1.00
< phi_{21 40} | phi_{21 40} > = 1.00
< phi_{21 41} | phi_{21 41} > = 1.00
< phi_{21 42} | phi_{21 42} > = 1.00
< phi_{21 43} | phi_{21 43} > = 1.00
< phi_{21 44} | phi_{21 44} > = 1.00
< phi_{21 45} | phi_{21 45} > = 1.00
< phi_{21 46} | phi_{21 46} > = 1.00
< phi_{21 47} | phi_{21 47} > = 1.00
< phi_{21 48} | phi_{21 48} > = 1.00
< phi_{21 49} | phi_{21 49} > = 1.00
< phi_{22 1} | phi_{22 1} > = 1.00
< phi_{22 2} | phi_{22 2} > = 1.00
< phi_{22 3} | phi_{22 3} > = 1.00
< phi_{22 4} | phi_{22 4} > = 1.00
< phi_{22 5} | phi_{22 5} > = 1.00
< phi_{22 6} | phi_{22 6} > = 1.00
< phi_{22 7} | phi_{22 7} > = 1.00
< phi_{22 8} | phi_{22 8} > = 1.00
< phi_{22 9} | phi_{22 9} > = 1.00
< phi_{22 10} | phi_{22 10} > = 1.00
< phi_{22 11} | phi_{22 11} > = 1.00
< phi_{22 12} | phi_{22 12} > = 1.00
< phi_{22 13} | phi_{22 13} > = 1.00
< phi_{22 14} | phi_{22 14} > = 1.00
< phi_{22 15} | phi_{22 15} > = 1.00
< phi_{22 16} | phi_{22 16} > = 1.00
< phi_{22 17} | phi_{22 17} > = 1.00
< phi_{22 18} | phi_{22 18} > = 1.00
< phi_{22 19} | phi_{22 19} > = 1.00
< phi_{22 20} | phi_{22 20} > = 1.00
< phi_{22 21} | phi_{22 21} > = 1.00
< phi_{22 22} | phi_{22 22} > = 1.00
< phi_{22 23} | phi_{22 23} > = 1.00
< phi_{22 24} | phi_{22 24} > = 1.00
< phi_{22 25} | phi_{22 25} > = 1.00
< phi_{22 26} | phi_{22 26} > = 1.00
< phi_{22 27} | phi_{22 27} > = 1.00
< phi_{22 28} | phi_{22 28} > = 1.00
< phi_{22 29} | phi_{22 29} > = 1.00
< phi_{22 30} | phi_{22 30} > = 1.00
< phi_{22 31} | phi_{22 31} > = 1.00
< phi_{22 32} | phi_{22 32} > = 1.00
< phi_{22 33} | phi_{22 33} > = 1.00
< phi_{22 34} | phi_{22 34} > = 1.00
< phi_{22 35} | phi_{22 35} > = 1.00
< phi_{22 36} | phi_{22 36} > = 1.00
< phi_{22 37} | phi_{22 37} > = 1.00
< phi_{22 38} | phi_{22 38} > = 1.00
< phi_{22 39} | phi_{22 39} > = 1.00
< phi_{22 40} | phi_{22 40} > = 1.00
< phi_{22 41} | phi_{22 41} > = 1.00
< phi_{22 42} | phi_{22 42} > = 1.00
< phi_{22 43} | phi_{22 43} > = 1.00
< phi_{22 44} | phi_{22 44} > = 1.00
< phi_{22 45} | phi_{22 45} > = 1.00
< phi_{22 46} | phi_{22 46} > = 1.00
< phi_{22 47} | phi_{22 47} > = 1.00
< phi_{22 48} | phi_{22 48} > = 1.00
< phi_{22 49} | phi_{22 49} > = 1.00
< phi_{23 1} | phi_{23 1} > = 1.00
< phi_{23 2} | phi_{23 2} > = 1.00
< phi_{23 3} | phi_{23 3} > = 1.00
< phi_{23 4} | phi_{23 4} > = 1.00
< phi_{23 5} | phi_{23 5} > = 1.00
< phi_{23 6} | phi_{23 6} > = 1.00
< phi_{23 7} | phi_{23 7} > = 1.00
< phi_{23 8} | phi_{23 8} > = 1.00
< phi_{23 9} | phi_{23 9} > = 1.00
< phi_{23 10} | phi_{23 10} > = 1.00
< phi_{23 11} | phi_{23 11} > = 1.00
< phi_{23 12} | phi_{23 12} > = 1.00
< phi_{23 13} | phi_{23 13} > = 1.00
< phi_{23 14} | phi_{23 14} > = 1.00
< phi_{23 15} | phi_{23 15} > = 1.00
< phi_{23 16} | phi_{23 16} > = 1.00
< phi_{23 17} | phi_{23 17} > = 1.00
< phi_{23 18} | phi_{23 18} > = 1.00
< phi_{23 19} | phi_{23 19} > = 1.00
< phi_{23 20} | phi_{23 20} > = 1.00
< phi_{23 21} | phi_{23 21} > = 1.00
< phi_{23 22} | phi_{23 22} > = 1.00
< phi_{23 23} | phi_{23 23} > = 1.00
< phi_{23 24} | phi_{23 24} > = 1.00
< phi_{23 25} | phi_{23 25} > = 1.00
< phi_{23 26} | phi_{23 26} > = 1.00
< phi_{23 27} | phi_{23 27} > = 1.00
< phi_{23 28} | phi_{23 28} > = 1.00
< phi_{23 29} | phi_{23 29} > = 1.00
< phi_{23 30} | phi_{23 30} > = 1.00
< phi_{23 31} | phi_{23 31} > = 1.00
< phi_{23 32} | phi_{23 32} > = 1.00
< phi_{23 33} | phi_{23 33} > = 1.00
< phi_{23 34} | phi_{23 34} > = 1.00
< phi_{23 35} | phi_{23 35} > = 1.00
< phi_{23 36} | phi_{23 36} > = 1.00
< phi_{23 37} | phi_{23 37} > = 1.00
< phi_{23 38} | phi_{23 38} > = 1.00
< phi_{23 39} | phi_{23 39} > = 1.00
< phi_{23 40} | phi_{23 40} > = 1.00
< phi_{23 41} | phi_{23 41} > = 1.00
< phi_{23 42} | phi_{23 42} > = 1.00
< phi_{23 43} | phi_{23 43} > = 1.00
< phi_{23 44} | phi_{23 44} > = 1.00
< phi_{23 45} | phi_{23 45} > = 1.00
< phi_{23 46} | phi_{23 46} > = 1.00
< phi_{23 47} | phi_{23 47} > = 1.00
< phi_{23 48} | phi_{23 48} > = 1.00
< phi_{23 49} | phi_{23 49} > = 1.00
< phi_{24 1} | phi_{24 1} > = 1.00
< phi_{24 2} | phi_{24 2} > = 1.00
< phi_{24 3} | phi_{24 3} > = 1.00
< phi_{24 4} | phi_{24 4} > = 1.00
< phi_{24 5} | phi_{24 5} > = 1.00
< phi_{24 6} | phi_{24 6} > = 1.00
< phi_{24 7} | phi_{24 7} > = 1.00
< phi_{24 8} | phi_{24 8} > = 1.00
< phi_{24 9} | phi_{24 9} > = 1.00
< phi_{24 10} | phi_{24 10} > = 1.00
< phi_{24 11} | phi_{24 11} > = 1.00
< phi_{24 12} | phi_{24 12} > = 1.00
< phi_{24 13} | phi_{24 13} > = 1.00
< phi_{24 14} | phi_{24 14} > = 1.00
< phi_{24 15} | phi_{24 15} > = 1.00
< phi_{24 16} | phi_{24 16} > = 1.00
< phi_{24 17} | phi_{24 17} > = 1.00
< phi_{24 18} | phi_{24 18} > = 1.00
< phi_{24 19} | phi_{24 19} > = 1.00
< phi_{24 20} | phi_{24 20} > = 1.00
< phi_{24 21} | phi_{24 21} > = 1.00
< phi_{24 22} | phi_{24 22} > = 1.00
< phi_{24 23} | phi_{24 23} > = 1.00
< phi_{24 24} | phi_{24 24} > = 1.00
< phi_{24 25} | phi_{24 25} > = 1.00
< phi_{24 26} | phi_{24 26} > = 1.00
< phi_{24 27} | phi_{24 27} > = 1.00
< phi_{24 28} | phi_{24 28} > = 1.00
< phi_{24 29} | phi_{24 29} > = 1.00
< phi_{24 30} | phi_{24 30} > = 1.00
< phi_{24 31} | phi_{24 31} > = 1.00
< phi_{24 32} | phi_{24 32} > = 1.00
< phi_{24 33} | phi_{24 33} > = 1.00
< phi_{24 34} | phi_{24 34} > = 1.00
< phi_{24 35} | phi_{24 35} > = 1.00
< phi_{24 36} | phi_{24 36} > = 1.00
< phi_{24 37} | phi_{24 37} > = 1.00
< phi_{24 38} | phi_{24 38} > = 1.00
< phi_{24 39} | phi_{24 39} > = 1.00
< phi_{24 40} | phi_{24 40} > = 1.00
< phi_{24 41} | phi_{24 41} > = 1.00
< phi_{24 42} | phi_{24 42} > = 1.00
< phi_{24 43} | phi_{24 43} > = 1.00
< phi_{24 44} | phi_{24 44} > = 1.00
< phi_{24 45} | phi_{24 45} > = 1.00
< phi_{24 46} | phi_{24 46} > = 1.00
< phi_{24 47} | phi_{24 47} > = 1.00
< phi_{24 48} | phi_{24 48} > = 1.00
< phi_{24 49} | phi_{24 49} > = 1.00
< phi_{25 1} | phi_{25 1} > = 1.00
< phi_{25 2} | phi_{25 2} > = 1.00
< phi_{25 3} | phi_{25 3} > = 1.00
< phi_{25 4} | phi_{25 4} > = 1.00
< phi_{25 5} | phi_{25 5} > = 1.00
< phi_{25 6} | phi_{25 6} > = 1.00
< phi_{25 7} | phi_{25 7} > = 1.00
< phi_{25 8} | phi_{25 8} > = 1.00
< phi_{25 9} | phi_{25 9} > = 1.00
< phi_{25 10} | phi_{25 10} > = 1.00
< phi_{25 11} | phi_{25 11} > = 1.00
< phi_{25 12} | phi_{25 12} > = 1.00
< phi_{25 13} | phi_{25 13} > = 1.00
< phi_{25 14} | phi_{25 14} > = 1.00
< phi_{25 15} | phi_{25 15} > = 1.00
< phi_{25 16} | phi_{25 16} > = 1.00
< phi_{25 17} | phi_{25 17} > = 1.00
< phi_{25 18} | phi_{25 18} > = 1.00
< phi_{25 19} | phi_{25 19} > = 1.00
< phi_{25 20} | phi_{25 20} > = 1.00
< phi_{25 21} | phi_{25 21} > = 1.00
< phi_{25 22} | phi_{25 22} > = 1.00
< phi_{25 23} | phi_{25 23} > = 1.00
< phi_{25 24} | phi_{25 24} > = 1.00
< phi_{25 25} | phi_{25 25} > = 1.00
< phi_{25 26} | phi_{25 26} > = 1.00
< phi_{25 27} | phi_{25 27} > = 1.00
< phi_{25 28} | phi_{25 28} > = 1.00
< phi_{25 29} | phi_{25 29} > = 1.00
< phi_{25 30} | phi_{25 30} > = 1.00
< phi_{25 31} | phi_{25 31} > = 1.00
< phi_{25 32} | phi_{25 32} > = 1.00
< phi_{25 33} | phi_{25 33} > = 1.00
< phi_{25 34} | phi_{25 34} > = 1.00
< phi_{25 35} | phi_{25 35} > = 1.00
< phi_{25 36} | phi_{25 36} > = 1.00
< phi_{25 37} | phi_{25 37} > = 1.00
< phi_{25 38} | phi_{25 38} > = 1.00
< phi_{25 39} | phi_{25 39} > = 1.00
< phi_{25 40} | phi_{25 40} > = 1.00
< phi_{25 41} | phi_{25 41} > = 1.00
< phi_{25 42} | phi_{25 42} > = 1.00
< phi_{25 43} | phi_{25 43} > = 1.00
< phi_{25 44} | phi_{25 44} > = 1.00
< phi_{25 45} | phi_{25 45} > = 1.00
< phi_{25 46} | phi_{25 46} > = 1.00
< phi_{25 47} | phi_{25 47} > = 1.00
< phi_{25 48} | phi_{25 48} > = 1.00
< phi_{25 49} | phi_{25 49} > = 1.00
< phi_{26 1} | phi_{26 1} > = 1.00
< phi_{26 2} | phi_{26 2} > = 1.00
< phi_{26 3} | phi_{26 3} > = 1.00
< phi_{26 4} | phi_{26 4} > = 1.00
< phi_{26 5} | phi_{26 5} > = 1.00
< phi_{26 6} | phi_{26 6} > = 1.00
< phi_{26 7} | phi_{26 7} > = 1.00
< phi_{26 8} | phi_{26 8} > = 1.00
< phi_{26 9} | phi_{26 9} > = 1.00
< phi_{26 10} | phi_{26 10} > = 1.00
< phi_{26 11} | phi_{26 11} > = 1.00
< phi_{26 12} | phi_{26 12} > = 1.00
< phi_{26 13} | phi_{26 13} > = 1.00
< phi_{26 14} | phi_{26 14} > = 1.00
< phi_{26 15} | phi_{26 15} > = 1.00
< phi_{26 16} | phi_{26 16} > = 1.00
< phi_{26 17} | phi_{26 17} > = 1.00
< phi_{26 18} | phi_{26 18} > = 1.00
< phi_{26 19} | phi_{26 19} > = 1.00
< phi_{26 20} | phi_{26 20} > = 1.00
< phi_{26 21} | phi_{26 21} > = 1.00
< phi_{26 22} | phi_{26 22} > = 1.00
< phi_{26 23} | phi_{26 23} > = 1.00
< phi_{26 24} | phi_{26 24} > = 1.00
< phi_{26 25} | phi_{26 25} > = 1.00
< phi_{26 26} | phi_{26 26} > = 1.00
< phi_{26 27} | phi_{26 27} > = 1.00
< phi_{26 28} | phi_{26 28} > = 1.00
< phi_{26 29} | phi_{26 29} > = 1.00
< phi_{26 30} | phi_{26 30} > = 1.00
< phi_{26 31} | phi_{26 31} > = 1.00
< phi_{26 32} | phi_{26 32} > = 1.00
< phi_{26 33} | phi_{26 33} > = 1.00
< phi_{26 34} | phi_{26 34} > = 1.00
< phi_{26 35} | phi_{26 35} > = 1.00
< phi_{26 36} | phi_{26 36} > = 1.00
< phi_{26 37} | phi_{26 37} > = 1.00
< phi_{26 38} | phi_{26 38} > = 1.00
< phi_{26 39} | phi_{26 39} > = 1.00
< phi_{26 40} | phi_{26 40} > = 1.00
< phi_{26 41} | phi_{26 41} > = 1.00
< phi_{26 42} | phi_{26 42} > = 1.00
< phi_{26 43} | phi_{26 43} > = 1.00
< phi_{26 44} | phi_{26 44} > = 1.00
< phi_{26 45} | phi_{26 45} > = 1.00
< phi_{26 46} | phi_{26 46} > = 1.00
< phi_{26 47} | phi_{26 47} > = 1.00
< phi_{26 48} | phi_{26 48} > = 1.00
< phi_{26 49} | phi_{26 49} > = 1.00
< phi_{27 1} | phi_{27 1} > = 1.00
< phi_{27 2} | phi_{27 2} > = 1.00
< phi_{27 3} | phi_{27 3} > = 1.00
< phi_{27 4} | phi_{27 4} > = 1.00
< phi_{27 5} | phi_{27 5} > = 1.00
< phi_{27 6} | phi_{27 6} > = 1.00
< phi_{27 7} | phi_{27 7} > = 1.00
< phi_{27 8} | phi_{27 8} > = 1.00
< phi_{27 9} | phi_{27 9} > = 1.00
< phi_{27 10} | phi_{27 10} > = 1.00
< phi_{27 11} | phi_{27 11} > = 1.00
< phi_{27 12} | phi_{27 12} > = 1.00
< phi_{27 13} | phi_{27 13} > = 1.00
< phi_{27 14} | phi_{27 14} > = 1.00
< phi_{27 15} | phi_{27 15} > = 1.00
< phi_{27 16} | phi_{27 16} > = 1.00
< phi_{27 17} | phi_{27 17} > = 1.00
< phi_{27 18} | phi_{27 18} > = 1.00
< phi_{27 19} | phi_{27 19} > = 1.00
< phi_{27 20} | phi_{27 20} > = 1.00
< phi_{27 21} | phi_{27 21} > = 1.00
< phi_{27 22} | phi_{27 22} > = 1.00
< phi_{27 23} | phi_{27 23} > = 1.00
< phi_{27 24} | phi_{27 24} > = 1.00
< phi_{27 25} | phi_{27 25} > = 1.00
< phi_{27 26} | phi_{27 26} > = 1.00
< phi_{27 27} | phi_{27 27} > = 1.00
< phi_{27 28} | phi_{27 28} > = 1.00
< phi_{27 29} | phi_{27 29} > = 1.00
< phi_{27 30} | phi_{27 30} > = 1.00
< phi_{27 31} | phi_{27 31} > = 1.00
< phi_{27 32} | phi_{27 32} > = 1.00
< phi_{27 33} | phi_{27 33} > = 1.00
< phi_{27 34} | phi_{27 34} > = 1.00
< phi_{27 35} | phi_{27 35} > = 1.00
< phi_{27 36} | phi_{27 36} > = 1.00
< phi_{27 37} | phi_{27 37} > = 1.00
< phi_{27 38} | phi_{27 38} > = 1.00
< phi_{27 39} | phi_{27 39} > = 1.00
< phi_{27 40} | phi_{27 40} > = 1.00
< phi_{27 41} | phi_{27 41} > = 1.00
< phi_{27 42} | phi_{27 42} > = 1.00
< phi_{27 43} | phi_{27 43} > = 1.00
< phi_{27 44} | phi_{27 44} > = 1.00
< phi_{27 45} | phi_{27 45} > = 1.00
< phi_{27 46} | phi_{27 46} > = 1.00
< phi_{27 47} | phi_{27 47} > = 1.00
< phi_{27 48} | phi_{27 48} > = 1.00
< phi_{27 49} | phi_{27 49} > = 1.00
< phi_{28 1} | phi_{28 1} > = 1.00
< phi_{28 2} | phi_{28 2} > = 1.00
< phi_{28 3} | phi_{28 3} > = 1.00
< phi_{28 4} | phi_{28 4} > = 1.00
< phi_{28 5} | phi_{28 5} > = 1.00
< phi_{28 6} | phi_{28 6} > = 1.00
< phi_{28 7} | phi_{28 7} > = 1.00
< phi_{28 8} | phi_{28 8} > = 1.00
< phi_{28 9} | phi_{28 9} > = 1.00
< phi_{28 10} | phi_{28 10} > = 1.00
< phi_{28 11} | phi_{28 11} > = 1.00
< phi_{28 12} | phi_{28 12} > = 1.00
< phi_{28 13} | phi_{28 13} > = 1.00
< phi_{28 14} | phi_{28 14} > = 1.00
< phi_{28 15} | phi_{28 15} > = 1.00
< phi_{28 16} | phi_{28 16} > = 1.00
< phi_{28 17} | phi_{28 17} > = 1.00
< phi_{28 18} | phi_{28 18} > = 1.00
< phi_{28 19} | phi_{28 19} > = 1.00
< phi_{28 20} | phi_{28 20} > = 1.00
< phi_{28 21} | phi_{28 21} > = 1.00
< phi_{28 22} | phi_{28 22} > = 1.00
< phi_{28 23} | phi_{28 23} > = 1.00
< phi_{28 24} | phi_{28 24} > = 1.00
< phi_{28 25} | phi_{28 25} > = 1.00
< phi_{28 26} | phi_{28 26} > = 1.00
< phi_{28 27} | phi_{28 27} > = 1.00
< phi_{28 28} | phi_{28 28} > = 1.00
< phi_{28 29} | phi_{28 29} > = 1.00
< phi_{28 30} | phi_{28 30} > = 1.00
< phi_{28 31} | phi_{28 31} > = 1.00
< phi_{28 32} | phi_{28 32} > = 1.00
< phi_{28 33} | phi_{28 33} > = 1.00
< phi_{28 34} | phi_{28 34} > = 1.00
< phi_{28 35} | phi_{28 35} > = 1.00
< phi_{28 36} | phi_{28 36} > = 1.00
< phi_{28 37} | phi_{28 37} > = 1.00
< phi_{28 38} | phi_{28 38} > = 1.00
< phi_{28 39} | phi_{28 39} > = 1.00
< phi_{28 40} | phi_{28 40} > = 1.00
< phi_{28 41} | phi_{28 41} > = 1.00
< phi_{28 42} | phi_{28 42} > = 1.00
< phi_{28 43} | phi_{28 43} > = 1.00
< phi_{28 44} | phi_{28 44} > = 1.00
< phi_{28 45} | phi_{28 45} > = 1.00
< phi_{28 46} | phi_{28 46} > = 1.00
< phi_{28 47} | phi_{28 47} > = 1.00
< phi_{28 48} | phi_{28 48} > = 1.00
< phi_{28 49} | phi_{28 49} > = 1.00
< phi_{29 1} | phi_{29 1} > = 1.00
< phi_{29 2} | phi_{29 2} > = 1.00
< phi_{29 3} | phi_{29 3} > = 1.00
< phi_{29 4} | phi_{29 4} > = 1.00
< phi_{29 5} | phi_{29 5} > = 1.00
< phi_{29 6} | phi_{29 6} > = 1.00
< phi_{29 7} | phi_{29 7} > = 1.00
< phi_{29 8} | phi_{29 8} > = 1.00
< phi_{29 9} | phi_{29 9} > = 1.00
< phi_{29 10} | phi_{29 10} > = 1.00
< phi_{29 11} | phi_{29 11} > = 1.00
< phi_{29 12} | phi_{29 12} > = 1.00
< phi_{29 13} | phi_{29 13} > = 1.00
< phi_{29 14} | phi_{29 14} > = 1.00
< phi_{29 15} | phi_{29 15} > = 1.00
< phi_{29 16} | phi_{29 16} > = 1.00
< phi_{29 17} | phi_{29 17} > = 1.00
< phi_{29 18} | phi_{29 18} > = 1.00
< phi_{29 19} | phi_{29 19} > = 1.00
< phi_{29 20} | phi_{29 20} > = 1.00
< phi_{29 21} | phi_{29 21} > = 1.00
< phi_{29 22} | phi_{29 22} > = 1.00
< phi_{29 23} | phi_{29 23} > = 1.00
< phi_{29 24} | phi_{29 24} > = 1.00
< phi_{29 25} | phi_{29 25} > = 1.00
< phi_{29 26} | phi_{29 26} > = 1.00
< phi_{29 27} | phi_{29 27} > = 1.00
< phi_{29 28} | phi_{29 28} > = 1.00
< phi_{29 29} | phi_{29 29} > = 1.00
< phi_{29 30} | phi_{29 30} > = 1.00
< phi_{29 31} | phi_{29 31} > = 1.00
< phi_{29 32} | phi_{29 32} > = 1.00
< phi_{29 33} | phi_{29 33} > = 1.00
< phi_{29 34} | phi_{29 34} > = 1.00
< phi_{29 35} | phi_{29 35} > = 1.00
< phi_{29 36} | phi_{29 36} > = 1.00
< phi_{29 37} | phi_{29 37} > = 1.00
< phi_{29 38} | phi_{29 38} > = 1.00
< phi_{29 39} | phi_{29 39} > = 1.00
< phi_{29 40} | phi_{29 40} > = 1.00
< phi_{29 41} | phi_{29 41} > = 1.00
< phi_{29 42} | phi_{29 42} > = 1.00
< phi_{29 43} | phi_{29 43} > = 1.00
< phi_{29 44} | phi_{29 44} > = 1.00
< phi_{29 45} | phi_{29 45} > = 1.00
< phi_{29 46} | phi_{29 46} > = 1.00
< phi_{29 47} | phi_{29 47} > = 1.00
< phi_{29 48} | phi_{29 48} > = 1.00
< phi_{29 49} | phi_{29 49} > = 1.00
< phi_{30 1} | phi_{30 1} > = 1.00
< phi_{30 2} | phi_{30 2} > = 1.00
< phi_{30 3} | phi_{30 3} > = 1.00
< phi_{30 4} | phi_{30 4} > = 1.00
< phi_{30 5} | phi_{30 5} > = 1.00
< phi_{30 6} | phi_{30 6} > = 1.00
< phi_{30 7} | phi_{30 7} > = 1.00
< phi_{30 8} | phi_{30 8} > = 1.00
< phi_{30 9} | phi_{30 9} > = 1.00
< phi_{30 10} | phi_{30 10} > = 1.00
< phi_{30 11} | phi_{30 11} > = 1.00
< phi_{30 12} | phi_{30 12} > = 1.00
< phi_{30 13} | phi_{30 13} > = 1.00
< phi_{30 14} | phi_{30 14} > = 1.00
< phi_{30 15} | phi_{30 15} > = 1.00
< phi_{30 16} | phi_{30 16} > = 1.00
< phi_{30 17} | phi_{30 17} > = 1.00
< phi_{30 18} | phi_{30 18} > = 1.00
< phi_{30 19} | phi_{30 19} > = 1.00
< phi_{30 20} | phi_{30 20} > = 1.00
< phi_{30 21} | phi_{30 21} > = 1.00
< phi_{30 22} | phi_{30 22} > = 1.00
< phi_{30 23} | phi_{30 23} > = 1.00
< phi_{30 24} | phi_{30 24} > = 1.00
< phi_{30 25} | phi_{30 25} > = 1.00
< phi_{30 26} | phi_{30 26} > = 1.00
< phi_{30 27} | phi_{30 27} > = 1.00
< phi_{30 28} | phi_{30 28} > = 1.00
< phi_{30 29} | phi_{30 29} > = 1.00
< phi_{30 30} | phi_{30 30} > = 1.00
< phi_{30 31} | phi_{30 31} > = 1.00
< phi_{30 32} | phi_{30 32} > = 1.00
< phi_{30 33} | phi_{30 33} > = 1.00
< phi_{30 34} | phi_{30 34} > = 1.00
< phi_{30 35} | phi_{30 35} > = 1.00
< phi_{30 36} | phi_{30 36} > = 1.00
< phi_{30 37} | phi_{30 37} > = 1.00
< phi_{30 38} | phi_{30 38} > = 1.00
< phi_{30 39} | phi_{30 39} > = 1.00
< phi_{30 40} | phi_{30 40} > = 1.00
< phi_{30 41} | phi_{30 41} > = 1.00
< phi_{30 42} | phi_{30 42} > = 1.00
< phi_{30 43} | phi_{30 43} > = 1.00
< phi_{30 44} | phi_{30 44} > = 1.00
< phi_{30 45} | phi_{30 45} > = 1.00
< phi_{30 46} | phi_{30 46} > = 1.00
< phi_{30 47} | phi_{30 47} > = 1.00
< phi_{30 48} | phi_{30 48} > = 1.00
< phi_{30 49} | phi_{30 49} > = 1.00
< phi_{31 1} | phi_{31 1} > = 1.00
< phi_{31 2} | phi_{31 2} > = 1.00
< phi_{31 3} | phi_{31 3} > = 1.00
< phi_{31 4} | phi_{31 4} > = 1.00
< phi_{31 5} | phi_{31 5} > = 1.00
< phi_{31 6} | phi_{31 6} > = 1.00
< phi_{31 7} | phi_{31 7} > = 1.00
< phi_{31 8} | phi_{31 8} > = 1.00
< phi_{31 9} | phi_{31 9} > = 1.00
< phi_{31 10} | phi_{31 10} > = 1.00
< phi_{31 11} | phi_{31 11} > = 1.00
< phi_{31 12} | phi_{31 12} > = 1.00
< phi_{31 13} | phi_{31 13} > = 1.00
< phi_{31 14} | phi_{31 14} > = 1.00
< phi_{31 15} | phi_{31 15} > = 1.00
< phi_{31 16} | phi_{31 16} > = 1.00
< phi_{31 17} | phi_{31 17} > = 1.00
< phi_{31 18} | phi_{31 18} > = 1.00
< phi_{31 19} | phi_{31 19} > = 1.00
< phi_{31 20} | phi_{31 20} > = 1.00
< phi_{31 21} | phi_{31 21} > = 1.00
< phi_{31 22} | phi_{31 22} > = 1.00
< phi_{31 23} | phi_{31 23} > = 1.00
< phi_{31 24} | phi_{31 24} > = 1.00
< phi_{31 25} | phi_{31 25} > = 1.00
< phi_{31 26} | phi_{31 26} > = 1.00
< phi_{31 27} | phi_{31 27} > = 1.00
< phi_{31 28} | phi_{31 28} > = 1.00
< phi_{31 29} | phi_{31 29} > = 1.00
< phi_{31 30} | phi_{31 30} > = 1.00
< phi_{31 31} | phi_{31 31} > = 1.00
< phi_{31 32} | phi_{31 32} > = 1.00
< phi_{31 33} | phi_{31 33} > = 1.00
< phi_{31 34} | phi_{31 34} > = 1.00
< phi_{31 35} | phi_{31 35} > = 1.00
< phi_{31 36} | phi_{31 36} > = 1.00
< phi_{31 37} | phi_{31 37} > = 1.00
< phi_{31 38} | phi_{31 38} > = 1.00
< phi_{31 39} | phi_{31 39} > = 1.00
< phi_{31 40} | phi_{31 40} > = 1.00
< phi_{31 41} | phi_{31 41} > = 1.00
< phi_{31 42} | phi_{31 42} > = 1.00
< phi_{31 43} | phi_{31 43} > = 1.00
< phi_{31 44} | phi_{31 44} > = 1.00
< phi_{31 45} | phi_{31 45} > = 1.00
< phi_{31 46} | phi_{31 46} > = 1.00
< phi_{31 47} | phi_{31 47} > = 1.00
< phi_{31 48} | phi_{31 48} > = 1.00
< phi_{31 49} | phi_{31 49} > = 1.00
< phi_{32 1} | phi_{32 1} > = 1.00
< phi_{32 2} | phi_{32 2} > = 1.00
< phi_{32 3} | phi_{32 3} > = 1.00
< phi_{32 4} | phi_{32 4} > = 1.00
< phi_{32 5} | phi_{32 5} > = 1.00
< phi_{32 6} | phi_{32 6} > = 1.00
< phi_{32 7} | phi_{32 7} > = 1.00
< phi_{32 8} | phi_{32 8} > = 1.00
< phi_{32 9} | phi_{32 9} > = 1.00
< phi_{32 10} | phi_{32 10} > = 1.00
< phi_{32 11} | phi_{32 11} > = 1.00
< phi_{32 12} | phi_{32 12} > = 1.00
< phi_{32 13} | phi_{32 13} > = 1.00
< phi_{32 14} | phi_{32 14} > = 1.00
< phi_{32 15} | phi_{32 15} > = 1.00
< phi_{32 16} | phi_{32 16} > = 1.00
< phi_{32 17} | phi_{32 17} > = 1.00
< phi_{32 18} | phi_{32 18} > = 1.00
< phi_{32 19} | phi_{32 19} > = 1.00
< phi_{32 20} | phi_{32 20} > = 1.00
< phi_{32 21} | phi_{32 21} > = 1.00
< phi_{32 22} | phi_{32 22} > = 1.00
< phi_{32 23} | phi_{32 23} > = 1.00
< phi_{32 24} | phi_{32 24} > = 1.00
< phi_{32 25} | phi_{32 25} > = 1.00
< phi_{32 26} | phi_{32 26} > = 1.00
< phi_{32 27} | phi_{32 27} > = 1.00
< phi_{32 28} | phi_{32 28} > = 1.00
< phi_{32 29} | phi_{32 29} > = 1.00
< phi_{32 30} | phi_{32 30} > = 1.00
< phi_{32 31} | phi_{32 31} > = 1.00
< phi_{32 32} | phi_{32 32} > = 1.00
< phi_{32 33} | phi_{32 33} > = 1.00
< phi_{32 34} | phi_{32 34} > = 1.00
< phi_{32 35} | phi_{32 35} > = 1.00
< phi_{32 36} | phi_{32 36} > = 1.00
< phi_{32 37} | phi_{32 37} > = 1.00
< phi_{32 38} | phi_{32 38} > = 1.00
< phi_{32 39} | phi_{32 39} > = 1.00
< phi_{32 40} | phi_{32 40} > = 1.00
< phi_{32 41} | phi_{32 41} > = 1.00
< phi_{32 42} | phi_{32 42} > = 1.00
< phi_{32 43} | phi_{32 43} > = 1.00
< phi_{32 44} | phi_{32 44} > = 1.00
< phi_{32 45} | phi_{32 45} > = 1.00
< phi_{32 46} | phi_{32 46} > = 1.00
< phi_{32 47} | phi_{32 47} > = 1.00
< phi_{32 48} | phi_{32 48} > = 1.00
< phi_{32 49} | phi_{32 49} > = 1.00
< phi_{33 1} | phi_{33 1} > = 1.00
< phi_{33 2} | phi_{33 2} > = 1.00
< phi_{33 3} | phi_{33 3} > = 1.00
< phi_{33 4} | phi_{33 4} > = 1.00
< phi_{33 5} | phi_{33 5} > = 1.00
< phi_{33 6} | phi_{33 6} > = 1.00
< phi_{33 7} | phi_{33 7} > = 1.00
< phi_{33 8} | phi_{33 8} > = 1.00
< phi_{33 9} | phi_{33 9} > = 1.00
< phi_{33 10} | phi_{33 10} > = 1.00
< phi_{33 11} | phi_{33 11} > = 1.00
< phi_{33 12} | phi_{33 12} > = 1.00
< phi_{33 13} | phi_{33 13} > = 1.00
< phi_{33 14} | phi_{33 14} > = 1.00
< phi_{33 15} | phi_{33 15} > = 1.00
< phi_{33 16} | phi_{33 16} > = 1.00
< phi_{33 17} | phi_{33 17} > = 1.00
< phi_{33 18} | phi_{33 18} > = 1.00
< phi_{33 19} | phi_{33 19} > = 1.00
< phi_{33 20} | phi_{33 20} > = 1.00
< phi_{33 21} | phi_{33 21} > = 1.00
< phi_{33 22} | phi_{33 22} > = 1.00
< phi_{33 23} | phi_{33 23} > = 1.00
< phi_{33 24} | phi_{33 24} > = 1.00
< phi_{33 25} | phi_{33 25} > = 1.00
< phi_{33 26} | phi_{33 26} > = 1.00
< phi_{33 27} | phi_{33 27} > = 1.00
< phi_{33 28} | phi_{33 28} > = 1.00
< phi_{33 29} | phi_{33 29} > = 1.00
< phi_{33 30} | phi_{33 30} > = 1.00
< phi_{33 31} | phi_{33 31} > = 1.00
< phi_{33 32} | phi_{33 32} > = 1.00
< phi_{33 33} | phi_{33 33} > = 1.00
< phi_{33 34} | phi_{33 34} > = 1.00
< phi_{33 35} | phi_{33 35} > = 1.00
< phi_{33 36} | phi_{33 36} > = 1.00
< phi_{33 37} | phi_{33 37} > = 1.00
< phi_{33 38} | phi_{33 38} > = 1.00
< phi_{33 39} | phi_{33 39} > = 1.00
< phi_{33 40} | phi_{33 40} > = 1.00
< phi_{33 41} | phi_{33 41} > = 1.00
< phi_{33 42} | phi_{33 42} > = 1.00
< phi_{33 43} | phi_{33 43} > = 1.00
< phi_{33 44} | phi_{33 44} > = 1.00
< phi_{33 45} | phi_{33 45} > = 1.00
< phi_{33 46} | phi_{33 46} > = 1.00
< phi_{33 47} | phi_{33 47} > = 1.00
< phi_{33 48} | phi_{33 48} > = 1.00
< phi_{33 49} | phi_{33 49} > = 1.00
< phi_{34 1} | phi_{34 1} > = 1.00
< phi_{34 2} | phi_{34 2} > = 1.00
< phi_{34 3} | phi_{34 3} > = 1.00
< phi_{34 4} | phi_{34 4} > = 1.00
< phi_{34 5} | phi_{34 5} > = 1.00
< phi_{34 6} | phi_{34 6} > = 1.00
< phi_{34 7} | phi_{34 7} > = 1.00
< phi_{34 8} | phi_{34 8} > = 1.00
< phi_{34 9} | phi_{34 9} > = 1.00
< phi_{34 10} | phi_{34 10} > = 1.00
< phi_{34 11} | phi_{34 11} > = 1.00
< phi_{34 12} | phi_{34 12} > = 1.00
< phi_{34 13} | phi_{34 13} > = 1.00
< phi_{34 14} | phi_{34 14} > = 1.00
< phi_{34 15} | phi_{34 15} > = 1.00
< phi_{34 16} | phi_{34 16} > = 1.00
< phi_{34 17} | phi_{34 17} > = 1.00
< phi_{34 18} | phi_{34 18} > = 1.00
< phi_{34 19} | phi_{34 19} > = 1.00
< phi_{34 20} | phi_{34 20} > = 1.00
< phi_{34 21} | phi_{34 21} > = 1.00
< phi_{34 22} | phi_{34 22} > = 1.00
< phi_{34 23} | phi_{34 23} > = 1.00
< phi_{34 24} | phi_{34 24} > = 1.00
< phi_{34 25} | phi_{34 25} > = 1.00
< phi_{34 26} | phi_{34 26} > = 1.00
< phi_{34 27} | phi_{34 27} > = 1.00
< phi_{34 28} | phi_{34 28} > = 1.00
< phi_{34 29} | phi_{34 29} > = 1.00
< phi_{34 30} | phi_{34 30} > = 1.00
< phi_{34 31} | phi_{34 31} > = 1.00
< phi_{34 32} | phi_{34 32} > = 1.00
< phi_{34 33} | phi_{34 33} > = 1.00
< phi_{34 34} | phi_{34 34} > = 1.00
< phi_{34 35} | phi_{34 35} > = 1.00
< phi_{34 36} | phi_{34 36} > = 1.00
< phi_{34 37} | phi_{34 37} > = 1.00
< phi_{34 38} | phi_{34 38} > = 1.00
< phi_{34 39} | phi_{34 39} > = 1.00
< phi_{34 40} | phi_{34 40} > = 1.00
< phi_{34 41} | phi_{34 41} > = 1.00
< phi_{34 42} | phi_{34 42} > = 1.00
< phi_{34 43} | phi_{34 43} > = 1.00
< phi_{34 44} | phi_{34 44} > = 1.00
< phi_{34 45} | phi_{34 45} > = 1.00
< phi_{34 46} | phi_{34 46} > = 1.00
< phi_{34 47} | phi_{34 47} > = 1.00
< phi_{34 48} | phi_{34 48} > = 1.00
< phi_{34 49} | phi_{34 49} > = 1.00
< phi_{35 1} | phi_{35 1} > = 1.00
< phi_{35 2} | phi_{35 2} > = 1.00
< phi_{35 3} | phi_{35 3} > = 1.00
< phi_{35 4} | phi_{35 4} > = 1.00
< phi_{35 5} | phi_{35 5} > = 1.00
< phi_{35 6} | phi_{35 6} > = 1.00
< phi_{35 7} | phi_{35 7} > = 1.00
< phi_{35 8} | phi_{35 8} > = 1.00
< phi_{35 9} | phi_{35 9} > = 1.00
< phi_{35 10} | phi_{35 10} > = 1.00
< phi_{35 11} | phi_{35 11} > = 1.00
< phi_{35 12} | phi_{35 12} > = 1.00
< phi_{35 13} | phi_{35 13} > = 1.00
< phi_{35 14} | phi_{35 14} > = 1.00
< phi_{35 15} | phi_{35 15} > = 1.00
< phi_{35 16} | phi_{35 16} > = 1.00
< phi_{35 17} | phi_{35 17} > = 1.00
< phi_{35 18} | phi_{35 18} > = 1.00
< phi_{35 19} | phi_{35 19} > = 1.00
< phi_{35 20} | phi_{35 20} > = 1.00
< phi_{35 21} | phi_{35 21} > = 1.00
< phi_{35 22} | phi_{35 22} > = 1.00
< phi_{35 23} | phi_{35 23} > = 1.00
< phi_{35 24} | phi_{35 24} > = 1.00
< phi_{35 25} | phi_{35 25} > = 1.00
< phi_{35 26} | phi_{35 26} > = 1.00
< phi_{35 27} | phi_{35 27} > = 1.00
< phi_{35 28} | phi_{35 28} > = 1.00
< phi_{35 29} | phi_{35 29} > = 1.00
< phi_{35 30} | phi_{35 30} > = 1.00
< phi_{35 31} | phi_{35 31} > = 1.00
< phi_{35 32} | phi_{35 32} > = 1.00
< phi_{35 33} | phi_{35 33} > = 1.00
< phi_{35 34} | phi_{35 34} > = 1.00
< phi_{35 35} | phi_{35 35} > = 1.00
< phi_{35 36} | phi_{35 36} > = 1.00
< phi_{35 37} | phi_{35 37} > = 1.00
< phi_{35 38} | phi_{35 38} > = 1.00
< phi_{35 39} | phi_{35 39} > = 1.00
< phi_{35 40} | phi_{35 40} > = 1.00
< phi_{35 41} | phi_{35 41} > = 1.00
< phi_{35 42} | phi_{35 42} > = 1.00
< phi_{35 43} | phi_{35 43} > = 1.00
< phi_{35 44} | phi_{35 44} > = 1.00
< phi_{35 45} | phi_{35 45} > = 1.00
< phi_{35 46} | phi_{35 46} > = 1.00
< phi_{35 47} | phi_{35 47} > = 1.00
< phi_{35 48} | phi_{35 48} > = 1.00
< phi_{35 49} | phi_{35 49} > = 1.00
< phi_{36 1} | phi_{36 1} > = 1.00
< phi_{36 2} | phi_{36 2} > = 1.00
< phi_{36 3} | phi_{36 3} > = 1.00
< phi_{36 4} | phi_{36 4} > = 1.00
< phi_{36 5} | phi_{36 5} > = 1.00
< phi_{36 6} | phi_{36 6} > = 1.00
< phi_{36 7} | phi_{36 7} > = 1.00
< phi_{36 8} | phi_{36 8} > = 1.00
< phi_{36 9} | phi_{36 9} > = 1.00
< phi_{36 10} | phi_{36 10} > = 1.00
< phi_{36 11} | phi_{36 11} > = 1.00
< phi_{36 12} | phi_{36 12} > = 1.00
< phi_{36 13} | phi_{36 13} > = 1.00
< phi_{36 14} | phi_{36 14} > = 1.00
< phi_{36 15} | phi_{36 15} > = 1.00
< phi_{36 16} | phi_{36 16} > = 1.00
< phi_{36 17} | phi_{36 17} > = 1.00
< phi_{36 18} | phi_{36 18} > = 1.00
< phi_{36 19} | phi_{36 19} > = 1.00
< phi_{36 20} | phi_{36 20} > = 1.00
< phi_{36 21} | phi_{36 21} > = 1.00
< phi_{36 22} | phi_{36 22} > = 1.00
< phi_{36 23} | phi_{36 23} > = 1.00
< phi_{36 24} | phi_{36 24} > = 1.00
< phi_{36 25} | phi_{36 25} > = 1.00
< phi_{36 26} | phi_{36 26} > = 1.00
< phi_{36 27} | phi_{36 27} > = 1.00
< phi_{36 28} | phi_{36 28} > = 1.00
< phi_{36 29} | phi_{36 29} > = 1.00
< phi_{36 30} | phi_{36 30} > = 1.00
< phi_{36 31} | phi_{36 31} > = 1.00
< phi_{36 32} | phi_{36 32} > = 1.00
< phi_{36 33} | phi_{36 33} > = 1.00
< phi_{36 34} | phi_{36 34} > = 1.00
< phi_{36 35} | phi_{36 35} > = 1.00
< phi_{36 36} | phi_{36 36} > = 1.00
< phi_{36 37} | phi_{36 37} > = 1.00
< phi_{36 38} | phi_{36 38} > = 1.00
< phi_{36 39} | phi_{36 39} > = 1.00
< phi_{36 40} | phi_{36 40} > = 1.00
< phi_{36 41} | phi_{36 41} > = 1.00
< phi_{36 42} | phi_{36 42} > = 1.00
< phi_{36 43} | phi_{36 43} > = 1.00
< phi_{36 44} | phi_{36 44} > = 1.00
< phi_{36 45} | phi_{36 45} > = 1.00
< phi_{36 46} | phi_{36 46} > = 1.00
< phi_{36 47} | phi_{36 47} > = 1.00
< phi_{36 48} | phi_{36 48} > = 1.00
< phi_{36 49} | phi_{36 49} > = 1.00
< phi_{37 1} | phi_{37 1} > = 1.00
< phi_{37 2} | phi_{37 2} > = 1.00
< phi_{37 3} | phi_{37 3} > = 1.00
< phi_{37 4} | phi_{37 4} > = 1.00
< phi_{37 5} | phi_{37 5} > = 1.00
< phi_{37 6} | phi_{37 6} > = 1.00
< phi_{37 7} | phi_{37 7} > = 1.00
< phi_{37 8} | phi_{37 8} > = 1.00
< phi_{37 9} | phi_{37 9} > = 1.00
< phi_{37 10} | phi_{37 10} > = 1.00
< phi_{37 11} | phi_{37 11} > = 1.00
< phi_{37 12} | phi_{37 12} > = 1.00
< phi_{37 13} | phi_{37 13} > = 1.00
< phi_{37 14} | phi_{37 14} > = 1.00
< phi_{37 15} | phi_{37 15} > = 1.00
< phi_{37 16} | phi_{37 16} > = 1.00
< phi_{37 17} | phi_{37 17} > = 1.00
< phi_{37 18} | phi_{37 18} > = 1.00
< phi_{37 19} | phi_{37 19} > = 1.00
< phi_{37 20} | phi_{37 20} > = 1.00
< phi_{37 21} | phi_{37 21} > = 1.00
< phi_{37 22} | phi_{37 22} > = 1.00
< phi_{37 23} | phi_{37 23} > = 1.00
< phi_{37 24} | phi_{37 24} > = 1.00
< phi_{37 25} | phi_{37 25} > = 1.00
< phi_{37 26} | phi_{37 26} > = 1.00
< phi_{37 27} | phi_{37 27} > = 1.00
< phi_{37 28} | phi_{37 28} > = 1.00
< phi_{37 29} | phi_{37 29} > = 1.00
< phi_{37 30} | phi_{37 30} > = 1.00
< phi_{37 31} | phi_{37 31} > = 1.00
< phi_{37 32} | phi_{37 32} > = 1.00
< phi_{37 33} | phi_{37 33} > = 1.00
< phi_{37 34} | phi_{37 34} > = 1.00
< phi_{37 35} | phi_{37 35} > = 1.00
< phi_{37 36} | phi_{37 36} > = 1.00
< phi_{37 37} | phi_{37 37} > = 1.00
< phi_{37 38} | phi_{37 38} > = 1.00
< phi_{37 39} | phi_{37 39} > = 1.00
< phi_{37 40} | phi_{37 40} > = 1.00
< phi_{37 41} | phi_{37 41} > = 1.00
< phi_{37 42} | phi_{37 42} > = 1.00
< phi_{37 43} | phi_{37 43} > = 1.00
< phi_{37 44} | phi_{37 44} > = 1.00
< phi_{37 45} | phi_{37 45} > = 1.00
< phi_{37 46} | phi_{37 46} > = 1.00
< phi_{37 47} | phi_{37 47} > = 1.00
< phi_{37 48} | phi_{37 48} > = 1.00
< phi_{37 49} | phi_{37 49} > = 1.00
< phi_{38 1} | phi_{38 1} > = 1.00
< phi_{38 2} | phi_{38 2} > = 1.00
< phi_{38 3} | phi_{38 3} > = 1.00
< phi_{38 4} | phi_{38 4} > = 1.00
< phi_{38 5} | phi_{38 5} > = 1.00
< phi_{38 6} | phi_{38 6} > = 1.00
< phi_{38 7} | phi_{38 7} > = 1.00
< phi_{38 8} | phi_{38 8} > = 1.00
< phi_{38 9} | phi_{38 9} > = 1.00
< phi_{38 10} | phi_{38 10} > = 1.00
< phi_{38 11} | phi_{38 11} > = 1.00
< phi_{38 12} | phi_{38 12} > = 1.00
< phi_{38 13} | phi_{38 13} > = 1.00
< phi_{38 14} | phi_{38 14} > = 1.00
< phi_{38 15} | phi_{38 15} > = 1.00
< phi_{38 16} | phi_{38 16} > = 1.00
< phi_{38 17} | phi_{38 17} > = 1.00
< phi_{38 18} | phi_{38 18} > = 1.00
< phi_{38 19} | phi_{38 19} > = 1.00
< phi_{38 20} | phi_{38 20} > = 1.00
< phi_{38 21} | phi_{38 21} > = 1.00
< phi_{38 22} | phi_{38 22} > = 1.00
< phi_{38 23} | phi_{38 23} > = 1.00
< phi_{38 24} | phi_{38 24} > = 1.00
< phi_{38 25} | phi_{38 25} > = 1.00
< phi_{38 26} | phi_{38 26} > = 1.00
< phi_{38 27} | phi_{38 27} > = 1.00
< phi_{38 28} | phi_{38 28} > = 1.00
< phi_{38 29} | phi_{38 29} > = 1.00
< phi_{38 30} | phi_{38 30} > = 1.00
< phi_{38 31} | phi_{38 31} > = 1.00
< phi_{38 32} | phi_{38 32} > = 1.00
< phi_{38 33} | phi_{38 33} > = 1.00
< phi_{38 34} | phi_{38 34} > = 1.00
< phi_{38 35} | phi_{38 35} > = 1.00
< phi_{38 36} | phi_{38 36} > = 1.00
< phi_{38 37} | phi_{38 37} > = 1.00
< phi_{38 38} | phi_{38 38} > = 1.00
< phi_{38 39} | phi_{38 39} > = 1.00
< phi_{38 40} | phi_{38 40} > = 1.00
< phi_{38 41} | phi_{38 41} > = 1.00
< phi_{38 42} | phi_{38 42} > = 1.00
< phi_{38 43} | phi_{38 43} > = 1.00
< phi_{38 44} | phi_{38 44} > = 1.00
< phi_{38 45} | phi_{38 45} > = 1.00
< phi_{38 46} | phi_{38 46} > = 1.00
< phi_{38 47} | phi_{38 47} > = 1.00
< phi_{38 48} | phi_{38 48} > = 1.00
< phi_{38 49} | phi_{38 49} > = 1.00
< phi_{39 1} | phi_{39 1} > = 1.00
< phi_{39 2} | phi_{39 2} > = 1.00
< phi_{39 3} | phi_{39 3} > = 1.00
< phi_{39 4} | phi_{39 4} > = 1.00
< phi_{39 5} | phi_{39 5} > = 1.00
< phi_{39 6} | phi_{39 6} > = 1.00
< phi_{39 7} | phi_{39 7} > = 1.00
< phi_{39 8} | phi_{39 8} > = 1.00
< phi_{39 9} | phi_{39 9} > = 1.00
< phi_{39 10} | phi_{39 10} > = 1.00
< phi_{39 11} | phi_{39 11} > = 1.00
< phi_{39 12} | phi_{39 12} > = 1.00
< phi_{39 13} | phi_{39 13} > = 1.00
< phi_{39 14} | phi_{39 14} > = 1.00
< phi_{39 15} | phi_{39 15} > = 1.00
< phi_{39 16} | phi_{39 16} > = 1.00
< phi_{39 17} | phi_{39 17} > = 1.00
< phi_{39 18} | phi_{39 18} > = 1.00
< phi_{39 19} | phi_{39 19} > = 1.00
< phi_{39 20} | phi_{39 20} > = 1.00
< phi_{39 21} | phi_{39 21} > = 1.00
< phi_{39 22} | phi_{39 22} > = 1.00
< phi_{39 23} | phi_{39 23} > = 1.00
< phi_{39 24} | phi_{39 24} > = 1.00
< phi_{39 25} | phi_{39 25} > = 1.00
< phi_{39 26} | phi_{39 26} > = 1.00
< phi_{39 27} | phi_{39 27} > = 1.00
< phi_{39 28} | phi_{39 28} > = 1.00
< phi_{39 29} | phi_{39 29} > = 1.00
< phi_{39 30} | phi_{39 30} > = 1.00
< phi_{39 31} | phi_{39 31} > = 1.00
< phi_{39 32} | phi_{39 32} > = 1.00
< phi_{39 33} | phi_{39 33} > = 1.00
< phi_{39 34} | phi_{39 34} > = 1.00
< phi_{39 35} | phi_{39 35} > = 1.00
< phi_{39 36} | phi_{39 36} > = 1.00
< phi_{39 37} | phi_{39 37} > = 1.00
< phi_{39 38} | phi_{39 38} > = 1.00
< phi_{39 39} | phi_{39 39} > = 1.00
< phi_{39 40} | phi_{39 40} > = 1.00
< phi_{39 41} | phi_{39 41} > = 1.00
< phi_{39 42} | phi_{39 42} > = 1.00
< phi_{39 43} | phi_{39 43} > = 1.00
< phi_{39 44} | phi_{39 44} > = 1.00
< phi_{39 45} | phi_{39 45} > = 1.00
< phi_{39 46} | phi_{39 46} > = 1.00
< phi_{39 47} | phi_{39 47} > = 1.00
< phi_{39 48} | phi_{39 48} > = 1.00
< phi_{39 49} | phi_{39 49} > = 1.00
< phi_{40 1} | phi_{40 1} > = 1.00
< phi_{40 2} | phi_{40 2} > = 1.00
< phi_{40 3} | phi_{40 3} > = 1.00
< phi_{40 4} | phi_{40 4} > = 1.00
< phi_{40 5} | phi_{40 5} > = 1.00
< phi_{40 6} | phi_{40 6} > = 1.00
< phi_{40 7} | phi_{40 7} > = 1.00
< phi_{40 8} | phi_{40 8} > = 1.00
< phi_{40 9} | phi_{40 9} > = 1.00
< phi_{40 10} | phi_{40 10} > = 1.00
< phi_{40 11} | phi_{40 11} > = 1.00
< phi_{40 12} | phi_{40 12} > = 1.00
< phi_{40 13} | phi_{40 13} > = 1.00
< phi_{40 14} | phi_{40 14} > = 1.00
< phi_{40 15} | phi_{40 15} > = 1.00
< phi_{40 16} | phi_{40 16} > = 1.00
< phi_{40 17} | phi_{40 17} > = 1.00
< phi_{40 18} | phi_{40 18} > = 1.00
< phi_{40 19} | phi_{40 19} > = 1.00
< phi_{40 20} | phi_{40 20} > = 1.00
< phi_{40 21} | phi_{40 21} > = 1.00
< phi_{40 22} | phi_{40 22} > = 1.00
< phi_{40 23} | phi_{40 23} > = 1.00
< phi_{40 24} | phi_{40 24} > = 1.00
< phi_{40 25} | phi_{40 25} > = 1.00
< phi_{40 26} | phi_{40 26} > = 1.00
< phi_{40 27} | phi_{40 27} > = 1.00
< phi_{40 28} | phi_{40 28} > = 1.00
< phi_{40 29} | phi_{40 29} > = 1.00
< phi_{40 30} | phi_{40 30} > = 1.00
< phi_{40 31} | phi_{40 31} > = 1.00
< phi_{40 32} | phi_{40 32} > = 1.00
< phi_{40 33} | phi_{40 33} > = 1.00
< phi_{40 34} | phi_{40 34} > = 1.00
< phi_{40 35} | phi_{40 35} > = 1.00
< phi_{40 36} | phi_{40 36} > = 1.00
< phi_{40 37} | phi_{40 37} > = 1.00
< phi_{40 38} | phi_{40 38} > = 1.00
< phi_{40 39} | phi_{40 39} > = 1.00
< phi_{40 40} | phi_{40 40} > = 1.00
< phi_{40 41} | phi_{40 41} > = 1.00
< phi_{40 42} | phi_{40 42} > = 1.00
< phi_{40 43} | phi_{40 43} > = 1.00
< phi_{40 44} | phi_{40 44} > = 1.00
< phi_{40 45} | phi_{40 45} > = 1.00
< phi_{40 46} | phi_{40 46} > = 1.00
< phi_{40 47} | phi_{40 47} > = 1.00
< phi_{40 48} | phi_{40 48} > = 1.00
< phi_{40 49} | phi_{40 49} > = 1.00
< phi_{41 1} | phi_{41 1} > = 1.00
< phi_{41 2} | phi_{41 2} > = 1.00
< phi_{41 3} | phi_{41 3} > = 1.00
< phi_{41 4} | phi_{41 4} > = 1.00
< phi_{41 5} | phi_{41 5} > = 1.00
< phi_{41 6} | phi_{41 6} > = 1.00
< phi_{41 7} | phi_{41 7} > = 1.00
< phi_{41 8} | phi_{41 8} > = 1.00
< phi_{41 9} | phi_{41 9} > = 1.00
< phi_{41 10} | phi_{41 10} > = 1.00
< phi_{41 11} | phi_{41 11} > = 1.00
< phi_{41 12} | phi_{41 12} > = 1.00
< phi_{41 13} | phi_{41 13} > = 1.00
< phi_{41 14} | phi_{41 14} > = 1.00
< phi_{41 15} | phi_{41 15} > = 1.00
< phi_{41 16} | phi_{41 16} > = 1.00
< phi_{41 17} | phi_{41 17} > = 1.00
< phi_{41 18} | phi_{41 18} > = 1.00
< phi_{41 19} | phi_{41 19} > = 1.00
< phi_{41 20} | phi_{41 20} > = 1.00
< phi_{41 21} | phi_{41 21} > = 1.00
< phi_{41 22} | phi_{41 22} > = 1.00
< phi_{41 23} | phi_{41 23} > = 1.00
< phi_{41 24} | phi_{41 24} > = 1.00
< phi_{41 25} | phi_{41 25} > = 1.00
< phi_{41 26} | phi_{41 26} > = 1.00
< phi_{41 27} | phi_{41 27} > = 1.00
< phi_{41 28} | phi_{41 28} > = 1.00
< phi_{41 29} | phi_{41 29} > = 1.00
< phi_{41 30} | phi_{41 30} > = 1.00
< phi_{41 31} | phi_{41 31} > = 1.00
< phi_{41 32} | phi_{41 32} > = 1.00
< phi_{41 33} | phi_{41 33} > = 1.00
< phi_{41 34} | phi_{41 34} > = 1.00
< phi_{41 35} | phi_{41 35} > = 1.00
< phi_{41 36} | phi_{41 36} > = 1.00
< phi_{41 37} | phi_{41 37} > = 1.00
< phi_{41 38} | phi_{41 38} > = 1.00
< phi_{41 39} | phi_{41 39} > = 1.00
< phi_{41 40} | phi_{41 40} > = 1.00
< phi_{41 41} | phi_{41 41} > = 1.00
< phi_{41 42} | phi_{41 42} > = 1.00
< phi_{41 43} | phi_{41 43} > = 1.00
< phi_{41 44} | phi_{41 44} > = 1.00
< phi_{41 45} | phi_{41 45} > = 1.00
< phi_{41 46} | phi_{41 46} > = 1.00
< phi_{41 47} | phi_{41 47} > = 1.00
< phi_{41 48} | phi_{41 48} > = 1.00
< phi_{41 49} | phi_{41 49} > = 1.00
< phi_{42 1} | phi_{42 1} > = 1.00
< phi_{42 2} | phi_{42 2} > = 1.00
< phi_{42 3} | phi_{42 3} > = 1.00
< phi_{42 4} | phi_{42 4} > = 1.00
< phi_{42 5} | phi_{42 5} > = 1.00
< phi_{42 6} | phi_{42 6} > = 1.00
< phi_{42 7} | phi_{42 7} > = 1.00
< phi_{42 8} | phi_{42 8} > = 1.00
< phi_{42 9} | phi_{42 9} > = 1.00
< phi_{42 10} | phi_{42 10} > = 1.00
< phi_{42 11} | phi_{42 11} > = 1.00
< phi_{42 12} | phi_{42 12} > = 1.00
< phi_{42 13} | phi_{42 13} > = 1.00
< phi_{42 14} | phi_{42 14} > = 1.00
< phi_{42 15} | phi_{42 15} > = 1.00
< phi_{42 16} | phi_{42 16} > = 1.00
< phi_{42 17} | phi_{42 17} > = 1.00
< phi_{42 18} | phi_{42 18} > = 1.00
< phi_{42 19} | phi_{42 19} > = 1.00
< phi_{42 20} | phi_{42 20} > = 1.00
< phi_{42 21} | phi_{42 21} > = 1.00
< phi_{42 22} | phi_{42 22} > = 1.00
< phi_{42 23} | phi_{42 23} > = 1.00
< phi_{42 24} | phi_{42 24} > = 1.00
< phi_{42 25} | phi_{42 25} > = 1.00
< phi_{42 26} | phi_{42 26} > = 1.00
< phi_{42 27} | phi_{42 27} > = 1.00
< phi_{42 28} | phi_{42 28} > = 1.00
< phi_{42 29} | phi_{42 29} > = 1.00
< phi_{42 30} | phi_{42 30} > = 1.00
< phi_{42 31} | phi_{42 31} > = 1.00
< phi_{42 32} | phi_{42 32} > = 1.00
< phi_{42 33} | phi_{42 33} > = 1.00
< phi_{42 34} | phi_{42 34} > = 1.00
< phi_{42 35} | phi_{42 35} > = 1.00
< phi_{42 36} | phi_{42 36} > = 1.00
< phi_{42 37} | phi_{42 37} > = 1.00
< phi_{42 38} | phi_{42 38} > = 1.00
< phi_{42 39} | phi_{42 39} > = 1.00
< phi_{42 40} | phi_{42 40} > = 1.00
< phi_{42 41} | phi_{42 41} > = 1.00
< phi_{42 42} | phi_{42 42} > = 1.00
< phi_{42 43} | phi_{42 43} > = 1.00
< phi_{42 44} | phi_{42 44} > = 1.00
< phi_{42 45} | phi_{42 45} > = 1.00
< phi_{42 46} | phi_{42 46} > = 1.00
< phi_{42 47} | phi_{42 47} > = 1.00
< phi_{42 48} | phi_{42 48} > = 1.00
< phi_{42 49} | phi_{42 49} > = 1.00
< phi_{43 1} | phi_{43 1} > = 1.00
< phi_{43 2} | phi_{43 2} > = 1.00
< phi_{43 3} | phi_{43 3} > = 1.00
< phi_{43 4} | phi_{43 4} > = 1.00
< phi_{43 5} | phi_{43 5} > = 1.00
< phi_{43 6} | phi_{43 6} > = 1.00
< phi_{43 7} | phi_{43 7} > = 1.00
< phi_{43 8} | phi_{43 8} > = 1.00
< phi_{43 9} | phi_{43 9} > = 1.00
< phi_{43 10} | phi_{43 10} > = 1.00
< phi_{43 11} | phi_{43 11} > = 1.00
< phi_{43 12} | phi_{43 12} > = 1.00
< phi_{43 13} | phi_{43 13} > = 1.00
< phi_{43 14} | phi_{43 14} > = 1.00
< phi_{43 15} | phi_{43 15} > = 1.00
< phi_{43 16} | phi_{43 16} > = 1.00
< phi_{43 17} | phi_{43 17} > = 1.00
< phi_{43 18} | phi_{43 18} > = 1.00
< phi_{43 19} | phi_{43 19} > = 1.00
< phi_{43 20} | phi_{43 20} > = 1.00
< phi_{43 21} | phi_{43 21} > = 1.00
< phi_{43 22} | phi_{43 22} > = 1.00
< phi_{43 23} | phi_{43 23} > = 1.00
< phi_{43 24} | phi_{43 24} > = 1.00
< phi_{43 25} | phi_{43 25} > = 1.00
< phi_{43 26} | phi_{43 26} > = 1.00
< phi_{43 27} | phi_{43 27} > = 1.00
< phi_{43 28} | phi_{43 28} > = 1.00
< phi_{43 29} | phi_{43 29} > = 1.00
< phi_{43 30} | phi_{43 30} > = 1.00
< phi_{43 31} | phi_{43 31} > = 1.00
< phi_{43 32} | phi_{43 32} > = 1.00
< phi_{43 33} | phi_{43 33} > = 1.00
< phi_{43 34} | phi_{43 34} > = 1.00
< phi_{43 35} | phi_{43 35} > = 1.00
< phi_{43 36} | phi_{43 36} > = 1.00
< phi_{43 37} | phi_{43 37} > = 1.00
< phi_{43 38} | phi_{43 38} > = 1.00
< phi_{43 39} | phi_{43 39} > = 1.00
< phi_{43 40} | phi_{43 40} > = 1.00
< phi_{43 41} | phi_{43 41} > = 1.00
< phi_{43 42} | phi_{43 42} > = 1.00
< phi_{43 43} | phi_{43 43} > = 1.00
< phi_{43 44} | phi_{43 44} > = 1.00
< phi_{43 45} | phi_{43 45} > = 1.00
< phi_{43 46} | phi_{43 46} > = 1.00
< phi_{43 47} | phi_{43 47} > = 1.00
< phi_{43 48} | phi_{43 48} > = 1.00
< phi_{43 49} | phi_{43 49} > = 1.00
< phi_{44 1} | phi_{44 1} > = 1.00
< phi_{44 2} | phi_{44 2} > = 1.00
< phi_{44 3} | phi_{44 3} > = 1.00
< phi_{44 4} | phi_{44 4} > = 1.00
< phi_{44 5} | phi_{44 5} > = 1.00
< phi_{44 6} | phi_{44 6} > = 1.00
< phi_{44 7} | phi_{44 7} > = 1.00
< phi_{44 8} | phi_{44 8} > = 1.00
< phi_{44 9} | phi_{44 9} > = 1.00
< phi_{44 10} | phi_{44 10} > = 1.00
< phi_{44 11} | phi_{44 11} > = 1.00
< phi_{44 12} | phi_{44 12} > = 1.00
< phi_{44 13} | phi_{44 13} > = 1.00
< phi_{44 14} | phi_{44 14} > = 1.00
< phi_{44 15} | phi_{44 15} > = 1.00
< phi_{44 16} | phi_{44 16} > = 1.00
< phi_{44 17} | phi_{44 17} > = 1.00
< phi_{44 18} | phi_{44 18} > = 1.00
< phi_{44 19} | phi_{44 19} > = 1.00
< phi_{44 20} | phi_{44 20} > = 1.00
< phi_{44 21} | phi_{44 21} > = 1.00
< phi_{44 22} | phi_{44 22} > = 1.00
< phi_{44 23} | phi_{44 23} > = 1.00
< phi_{44 24} | phi_{44 24} > = 1.00
< phi_{44 25} | phi_{44 25} > = 1.00
< phi_{44 26} | phi_{44 26} > = 1.00
< phi_{44 27} | phi_{44 27} > = 1.00
< phi_{44 28} | phi_{44 28} > = 1.00
< phi_{44 29} | phi_{44 29} > = 1.00
< phi_{44 30} | phi_{44 30} > = 1.00
< phi_{44 31} | phi_{44 31} > = 1.00
< phi_{44 32} | phi_{44 32} > = 1.00
< phi_{44 33} | phi_{44 33} > = 1.00
< phi_{44 34} | phi_{44 34} > = 1.00
< phi_{44 35} | phi_{44 35} > = 1.00
< phi_{44 36} | phi_{44 36} > = 1.00
< phi_{44 37} | phi_{44 37} > = 1.00
< phi_{44 38} | phi_{44 38} > = 1.00
< phi_{44 39} | phi_{44 39} > = 1.00
< phi_{44 40} | phi_{44 40} > = 1.00
< phi_{44 41} | phi_{44 41} > = 1.00
< phi_{44 42} | phi_{44 42} > = 1.00
< phi_{44 43} | phi_{44 43} > = 1.00
< phi_{44 44} | phi_{44 44} > = 1.00
< phi_{44 45} | phi_{44 45} > = 1.00
< phi_{44 46} | phi_{44 46} > = 1.00
< phi_{44 47} | phi_{44 47} > = 1.00
< phi_{44 48} | phi_{44 48} > = 1.00
< phi_{44 49} | phi_{44 49} > = 1.00
< phi_{45 1} | phi_{45 1} > = 1.00
< phi_{45 2} | phi_{45 2} > = 1.00
< phi_{45 3} | phi_{45 3} > = 1.00
< phi_{45 4} | phi_{45 4} > = 1.00
< phi_{45 5} | phi_{45 5} > = 1.00
< phi_{45 6} | phi_{45 6} > = 1.00
< phi_{45 7} | phi_{45 7} > = 1.00
< phi_{45 8} | phi_{45 8} > = 1.00
< phi_{45 9} | phi_{45 9} > = 1.00
< phi_{45 10} | phi_{45 10} > = 1.00
< phi_{45 11} | phi_{45 11} > = 1.00
< phi_{45 12} | phi_{45 12} > = 1.00
< phi_{45 13} | phi_{45 13} > = 1.00
< phi_{45 14} | phi_{45 14} > = 1.00
< phi_{45 15} | phi_{45 15} > = 1.00
< phi_{45 16} | phi_{45 16} > = 1.00
< phi_{45 17} | phi_{45 17} > = 1.00
< phi_{45 18} | phi_{45 18} > = 1.00
< phi_{45 19} | phi_{45 19} > = 1.00
< phi_{45 20} | phi_{45 20} > = 1.00
< phi_{45 21} | phi_{45 21} > = 1.00
< phi_{45 22} | phi_{45 22} > = 1.00
< phi_{45 23} | phi_{45 23} > = 1.00
< phi_{45 24} | phi_{45 24} > = 1.00
< phi_{45 25} | phi_{45 25} > = 1.00
< phi_{45 26} | phi_{45 26} > = 1.00
< phi_{45 27} | phi_{45 27} > = 1.00
< phi_{45 28} | phi_{45 28} > = 1.00
< phi_{45 29} | phi_{45 29} > = 1.00
< phi_{45 30} | phi_{45 30} > = 1.00
< phi_{45 31} | phi_{45 31} > = 1.00
< phi_{45 32} | phi_{45 32} > = 1.00
< phi_{45 33} | phi_{45 33} > = 1.00
< phi_{45 34} | phi_{45 34} > = 1.00
< phi_{45 35} | phi_{45 35} > = 1.00
< phi_{45 36} | phi_{45 36} > = 1.00
< phi_{45 37} | phi_{45 37} > = 1.00
< phi_{45 38} | phi_{45 38} > = 1.00
< phi_{45 39} | phi_{45 39} > = 1.00
< phi_{45 40} | phi_{45 40} > = 1.00
< phi_{45 41} | phi_{45 41} > = 1.00
< phi_{45 42} | phi_{45 42} > = 1.00
< phi_{45 43} | phi_{45 43} > = 1.00
< phi_{45 44} | phi_{45 44} > = 1.00
< phi_{45 45} | phi_{45 45} > = 1.00
< phi_{45 46} | phi_{45 46} > = 1.00
< phi_{45 47} | phi_{45 47} > = 1.00
< phi_{45 48} | phi_{45 48} > = 1.00
< phi_{45 49} | phi_{45 49} > = 1.00
< phi_{46 1} | phi_{46 1} > = 1.00
< phi_{46 2} | phi_{46 2} > = 1.00
< phi_{46 3} | phi_{46 3} > = 1.00
< phi_{46 4} | phi_{46 4} > = 1.00
< phi_{46 5} | phi_{46 5} > = 1.00
< phi_{46 6} | phi_{46 6} > = 1.00
< phi_{46 7} | phi_{46 7} > = 1.00
< phi_{46 8} | phi_{46 8} > = 1.00
< phi_{46 9} | phi_{46 9} > = 1.00
< phi_{46 10} | phi_{46 10} > = 1.00
< phi_{46 11} | phi_{46 11} > = 1.00
< phi_{46 12} | phi_{46 12} > = 1.00
< phi_{46 13} | phi_{46 13} > = 1.00
< phi_{46 14} | phi_{46 14} > = 1.00
< phi_{46 15} | phi_{46 15} > = 1.00
< phi_{46 16} | phi_{46 16} > = 1.00
< phi_{46 17} | phi_{46 17} > = 1.00
< phi_{46 18} | phi_{46 18} > = 1.00
< phi_{46 19} | phi_{46 19} > = 1.00
< phi_{46 20} | phi_{46 20} > = 1.00
< phi_{46 21} | phi_{46 21} > = 1.00
< phi_{46 22} | phi_{46 22} > = 1.00
< phi_{46 23} | phi_{46 23} > = 1.00
< phi_{46 24} | phi_{46 24} > = 1.00
< phi_{46 25} | phi_{46 25} > = 1.00
< phi_{46 26} | phi_{46 26} > = 1.00
< phi_{46 27} | phi_{46 27} > = 1.00
< phi_{46 28} | phi_{46 28} > = 1.00
< phi_{46 29} | phi_{46 29} > = 1.00
< phi_{46 30} | phi_{46 30} > = 1.00
< phi_{46 31} | phi_{46 31} > = 1.00
< phi_{46 32} | phi_{46 32} > = 1.00
< phi_{46 33} | phi_{46 33} > = 1.00
< phi_{46 34} | phi_{46 34} > = 1.00
< phi_{46 35} | phi_{46 35} > = 1.00
< phi_{46 36} | phi_{46 36} > = 1.00
< phi_{46 37} | phi_{46 37} > = 1.00
< phi_{46 38} | phi_{46 38} > = 1.00
< phi_{46 39} | phi_{46 39} > = 1.00
< phi_{46 40} | phi_{46 40} > = 1.00
< phi_{46 41} | phi_{46 41} > = 1.00
< phi_{46 42} | phi_{46 42} > = 1.00
< phi_{46 43} | phi_{46 43} > = 1.00
< phi_{46 44} | phi_{46 44} > = 1.00
< phi_{46 45} | phi_{46 45} > = 1.00
< phi_{46 46} | phi_{46 46} > = 1.00
< phi_{46 47} | phi_{46 47} > = 1.00
< phi_{46 48} | phi_{46 48} > = 1.00
< phi_{46 49} | phi_{46 49} > = 1.00
< phi_{47 1} | phi_{47 1} > = 1.00
< phi_{47 2} | phi_{47 2} > = 1.00
< phi_{47 3} | phi_{47 3} > = 1.00
< phi_{47 4} | phi_{47 4} > = 1.00
< phi_{47 5} | phi_{47 5} > = 1.00
< phi_{47 6} | phi_{47 6} > = 1.00
< phi_{47 7} | phi_{47 7} > = 1.00
< phi_{47 8} | phi_{47 8} > = 1.00
< phi_{47 9} | phi_{47 9} > = 1.00
< phi_{47 10} | phi_{47 10} > = 1.00
< phi_{47 11} | phi_{47 11} > = 1.00
< phi_{47 12} | phi_{47 12} > = 1.00
< phi_{47 13} | phi_{47 13} > = 1.00
< phi_{47 14} | phi_{47 14} > = 1.00
< phi_{47 15} | phi_{47 15} > = 1.00
< phi_{47 16} | phi_{47 16} > = 1.00
< phi_{47 17} | phi_{47 17} > = 1.00
< phi_{47 18} | phi_{47 18} > = 1.00
< phi_{47 19} | phi_{47 19} > = 1.00
< phi_{47 20} | phi_{47 20} > = 1.00
< phi_{47 21} | phi_{47 21} > = 1.00
< phi_{47 22} | phi_{47 22} > = 1.00
< phi_{47 23} | phi_{47 23} > = 1.00
< phi_{47 24} | phi_{47 24} > = 1.00
< phi_{47 25} | phi_{47 25} > = 1.00
< phi_{47 26} | phi_{47 26} > = 1.00
< phi_{47 27} | phi_{47 27} > = 1.00
< phi_{47 28} | phi_{47 28} > = 1.00
< phi_{47 29} | phi_{47 29} > = 1.00
< phi_{47 30} | phi_{47 30} > = 1.00
< phi_{47 31} | phi_{47 31} > = 1.00
< phi_{47 32} | phi_{47 32} > = 1.00
< phi_{47 33} | phi_{47 33} > = 1.00
< phi_{47 34} | phi_{47 34} > = 1.00
< phi_{47 35} | phi_{47 35} > = 1.00
< phi_{47 36} | phi_{47 36} > = 1.00
< phi_{47 37} | phi_{47 37} > = 1.00
< phi_{47 38} | phi_{47 38} > = 1.00
< phi_{47 39} | phi_{47 39} > = 1.00
< phi_{47 40} | phi_{47 40} > = 1.00
< phi_{47 41} | phi_{47 41} > = 1.00
< phi_{47 42} | phi_{47 42} > = 1.00
< phi_{47 43} | phi_{47 43} > = 1.00
< phi_{47 44} | phi_{47 44} > = 1.00
< phi_{47 45} | phi_{47 45} > = 1.00
< phi_{47 46} | phi_{47 46} > = 1.00
< phi_{47 47} | phi_{47 47} > = 1.00
< phi_{47 48} | phi_{47 48} > = 1.00
< phi_{47 49} | phi_{47 49} > = 1.00
< phi_{48 1} | phi_{48 1} > = 1.00
< phi_{48 2} | phi_{48 2} > = 1.00
< phi_{48 3} | phi_{48 3} > = 1.00
< phi_{48 4} | phi_{48 4} > = 1.00
< phi_{48 5} | phi_{48 5} > = 1.00
< phi_{48 6} | phi_{48 6} > = 1.00
< phi_{48 7} | phi_{48 7} > = 1.00
< phi_{48 8} | phi_{48 8} > = 1.00
< phi_{48 9} | phi_{48 9} > = 1.00
< phi_{48 10} | phi_{48 10} > = 1.00
< phi_{48 11} | phi_{48 11} > = 1.00
< phi_{48 12} | phi_{48 12} > = 1.00
< phi_{48 13} | phi_{48 13} > = 1.00
< phi_{48 14} | phi_{48 14} > = 1.00
< phi_{48 15} | phi_{48 15} > = 1.00
< phi_{48 16} | phi_{48 16} > = 1.00
< phi_{48 17} | phi_{48 17} > = 1.00
< phi_{48 18} | phi_{48 18} > = 1.00
< phi_{48 19} | phi_{48 19} > = 1.00
< phi_{48 20} | phi_{48 20} > = 1.00
< phi_{48 21} | phi_{48 21} > = 1.00
< phi_{48 22} | phi_{48 22} > = 1.00
< phi_{48 23} | phi_{48 23} > = 1.00
< phi_{48 24} | phi_{48 24} > = 1.00
< phi_{48 25} | phi_{48 25} > = 1.00
< phi_{48 26} | phi_{48 26} > = 1.00
< phi_{48 27} | phi_{48 27} > = 1.00
< phi_{48 28} | phi_{48 28} > = 1.00
< phi_{48 29} | phi_{48 29} > = 1.00
< phi_{48 30} | phi_{48 30} > = 1.00
< phi_{48 31} | phi_{48 31} > = 1.00
< phi_{48 32} | phi_{48 32} > = 1.00
< phi_{48 33} | phi_{48 33} > = 1.00
< phi_{48 34} | phi_{48 34} > = 1.00
< phi_{48 35} | phi_{48 35} > = 1.00
< phi_{48 36} | phi_{48 36} > = 1.00
< phi_{48 37} | phi_{48 37} > = 1.00
< phi_{48 38} | phi_{48 38} > = 1.00
< phi_{48 39} | phi_{48 39} > = 1.00
< phi_{48 40} | phi_{48 40} > = 1.00
< phi_{48 41} | phi_{48 41} > = 1.00
< phi_{48 42} | phi_{48 42} > = 1.00
< phi_{48 43} | phi_{48 43} > = 1.00
< phi_{48 44} | phi_{48 44} > = 1.00
< phi_{48 45} | phi_{48 45} > = 1.00
< phi_{48 46} | phi_{48 46} > = 1.00
< phi_{48 47} | phi_{48 47} > = 1.00
< phi_{48 48} | phi_{48 48} > = 1.00
< phi_{48 49} | phi_{48 49} > = 1.00
< phi_{49 1} | phi_{49 1} > = 1.00
< phi_{49 2} | phi_{49 2} > = 1.00
< phi_{49 3} | phi_{49 3} > = 1.00
< phi_{49 4} | phi_{49 4} > = 1.00
< phi_{49 5} | phi_{49 5} > = 1.00
< phi_{49 6} | phi_{49 6} > = 1.00
< phi_{49 7} | phi_{49 7} > = 1.00
< phi_{49 8} | phi_{49 8} > = 1.00
< phi_{49 9} | phi_{49 9} > = 1.00
< phi_{49 10} | phi_{49 10} > = 1.00
< phi_{49 11} | phi_{49 11} > = 1.00
< phi_{49 12} | phi_{49 12} > = 1.00
< phi_{49 13} | phi_{49 13} > = 1.00
< phi_{49 14} | phi_{49 14} > = 1.00
< phi_{49 15} | phi_{49 15} > = 1.00
< phi_{49 16} | phi_{49 16} > = 1.00
< phi_{49 17} | phi_{49 17} > = 1.00
< phi_{49 18} | phi_{49 18} > = 1.00
< phi_{49 19} | phi_{49 19} > = 1.00
< phi_{49 20} | phi_{49 20} > = 1.00
< phi_{49 21} | phi_{49 21} > = 1.00
< phi_{49 22} | phi_{49 22} > = 1.00
< phi_{49 23} | phi_{49 23} > = 1.00
< phi_{49 24} | phi_{49 24} > = 1.00
< phi_{49 25} | phi_{49 25} > = 1.00
< phi_{49 26} | phi_{49 26} > = 1.00
< phi_{49 27} | phi_{49 27} > = 1.00
< phi_{49 28} | phi_{49 28} > = 1.00
< phi_{49 29} | phi_{49 29} > = 1.00
< phi_{49 30} | phi_{49 30} > = 1.00
< phi_{49 31} | phi_{49 31} > = 1.00
< phi_{49 32} | phi_{49 32} > = 1.00
< phi_{49 33} | phi_{49 33} > = 1.00
< phi_{49 34} | phi_{49 34} > = 1.00
< phi_{49 35} | phi_{49 35} > = 1.00
< phi_{49 36} | phi_{49 36} > = 1.00
< phi_{49 37} | phi_{49 37} > = 1.00
< phi_{49 38} | phi_{49 38} > = 1.00
< phi_{49 39} | phi_{49 39} > = 1.00
< phi_{49 40} | phi_{49 40} > = 1.00
< phi_{49 41} | phi_{49 41} > = 1.00
< phi_{49 42} | phi_{49 42} > = 1.00
< phi_{49 43} | phi_{49 43} > = 1.00
< phi_{49 44} | phi_{49 44} > = 1.00
< phi_{49 45} | phi_{49 45} > = 1.00
< phi_{49 46} | phi_{49 46} > = 1.00
< phi_{49 47} | phi_{49 47} > = 1.00
< phi_{49 48} | phi_{49 48} > = 1.00
< phi_{49 49} | phi_{49 49} > = 1.00
You should now have a orthonormal set of functions spanning at least a subspace of \(\mathcal{V}\). The final criterion of completeness is a bit cumbersome to test for, so we leave it out for now. Suffice to say, what we will do in the following is to approximate \(\vert \Psi \rangle\) in a truncated basis such that
\[
\vert \Psi \rangle \approx \sum_{n_x}^{N_x} \sum_{n_y}^{N_y} \varphi_{n_x, n_y} c_n.
\]
Discussion
Mathematically speaking, does a truncated basis still formally qualify as a basis?
What is the vector space spanned by a truncated basis?
Projection#
Given a orthonormal trucanted basis for \(\mathcal{V}\), we can determine the expansion coefficients \(c\) by means of projection. In other words, we shall determine the components of \(\vert \Psi \rangle\) in the space spanned by \(\{ \varphi_n \}\):
\[
c_m = \langle \varphi_m \vert \Psi \rangle.
\]
With our numerical setup, this is now done in a (somewhat slow) breeze:
c = np.zeros(len(basis))
for m in range(len(basis)):
phi_m = basis[m]
c[m] = inner(phi_m, psi)
The coefficients by themselves are not of much interest, but you may have a look if you wish:
plt.figure()
plt.title("Coefficients of $\\varphi_{n_x,n_y}$")
plt.imshow(c.reshape(nc-1,nc-1))
plt.colorbar()
plt.xlabel("nx")
plt.ylabel("ny")
plt.show()
The linear combination
\[
\sum_{n_x}^{N_x} \sum_{n_y}^{N_y} \varphi_{n_x, n_y} c_n \approx \vert \Psi \rangle
\]
should however now be quite interesting. If we have done everything correctly, we expect this linear combination to be an approximate representation of the photo of the young Dirac. Let’s have a look, and notice that there is no direct reference to \(\vert \Psi \rangle\) in the following code:
z = 0
for m in range(len(basis)):
phi_m = basis[m]
z += c[m]*phi_m
plt.figure()
plt.imshow(z, cmap = "bone")
plt.axis("off")
plt.show()
For a side-by-side comparison, we include
plt.figure()
plt.imshow(psi, cmap = "bone")
plt.axis("off")
plt.show()
This is an approximate representation, but we managed to capture quite a lot of what goes on in the picture. This demonstration furthermore illuminates some concepts that is central in our quest for understanding the quantum molecular world using numerics. In the analytical case, the choice of basis is arbitrary as long as it is complete. When truncating, however, we would like to know how to refine our basis towards the exact result.
If you would like to pursue this latter part in more detail, you should have a look on he completeness relation. Can you measure how well our truncated set span \(\mathcal{V}\)?