Note
Go to the end to download the full example code.
Spectrum RaF#
Calculating the optical spectrum of \(^{226}\text{RaF}\) using spectroscopic constants.
Radium monofluoride is of particular interest due to its applications in precision measurements with a heavy nucleus.
from MoleCool.spectra import Molecule, ElectronicStateConstants, cm2THz
from MoleCool import pi, np, plt
from copy import deepcopy
Spectroscopic constants#
Literature:
[a] Garcia Ruiz 2020: “Spectroscopy of short-lived radioactive molecules”. see Extended Data Table 2 in https://doi.org/10.1038/s41586-020-2299-4 using the relations \(\omega_e \chi_e\approx\omega_e^2/(4D_e)\) and \(A_e\approx A_{00}\).
[b] Udrescu 2023: “Precision spectroscopy and laser cooling scheme of a radium-containing molecule” https://doi.org/10.1038/s41567-023-02296-w using the relations \(B_e\approx 3/2\,B_0 - 1/2\, B_1\) and \(\alpha_e \approx B_0-B_1\).
[c] Petrov, Skripnikov 2020: “Energy levels of radium monofluoride RaF in external electric and magnetic fields to search for P- and T,P-violation effects” https://doi.org/10.1103/PhysRevA.102.062801 where the hyperfine tensor components are converted into Frosch and Foley parameters.
[2] Skripnikov 2020: “Nuclear magnetization distribution effect in molecules: Ra+and RaF hyperfine structure”
[5] Nuclear magnetic moments: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.59.771
X_cts = ElectronicStateConstants(
const = {
'w_e' : 441.8, # [a]
'w_e x_e' : 1.6711, # [a]
'B_e' : 192.5175e-3, # [b]
'D_e' : 1.4e-7, # [a]
'alpha_e' : 1.0650e-3, # [b]
'gamma' : 5.8500e-3, # [b]
'b_F' : 3.2133e-3, # [c]
'c' : 0.6338e-3, # [c]
},
unit = '1/cm',
)
A_cts = ElectronicStateConstants(
const = {
'T_e' : 14321.377, # [b]
'w_e' : 435.5, # [a]
'w_e x_e' : 1.635, # [a]
'A_e' : 2067.6000, # [a]
'p' : -0.4107, # [b]
'B_e' : 191.5375e-3, # [b]
'D_e' : 1.4e-7, # [a]
'alpha_e' : 1.0450e-3, # [b]
},
unit = '1/cm',
)
export all constants as dictionary:
X_cts.to_dict(exclude_default=False)
# Or as a nice format using pandas.DataFrame:
df = X_cts.show(
formatting = 'non-zero',
createHTML = 'cts_A', # to create a html file with nice format
)
# which is the same as:
X_cts
| value (1/cm) | value (MHz) | ||
|---|---|---|---|
| vibration | w_e | 4.418000e+02 | 1.324483e+07 |
| w_e x_e | 1.671100e+00 | 5.009832e+04 | |
| rotation | B_e | 1.925175e-01 | 5.771529e+03 |
| D_e | 1.400000e-07 | 4.197094e-03 | |
| alpha_e | 1.065000e-03 | 3.192790e+01 | |
| spin-rotation | gamma | 5.850000e-03 | 1.753786e+02 |
| hyperfine | b_F | 3.213300e-03 | 9.633231e+01 |
| c | 6.338000e-04 | 1.900085e+01 | |
| Zeeman (no unit) | g_S | 2.002000e+00 | 2.002000e+00 |
| g'_L | 1.000000e+00 | 1.000000e+00 |
Setting up a molecule#
The diatomic molecule \(^{226}\text{RaF}\) has a single non-zero nuclear spin 1/2. We also set the temperature to 4 K which will affect the Boltzmann distribution of the calculated spectrum below.
We also add two electronic states – the ground state X and first excited state A with respective Hund’s cases b and a_p (meaning well-defined parity eigenstates due to lambda doubling). The vibrational states \(\nu\) are set to 0.
mol = Molecule(
I1 = 0.5, # nuclear spin 1/2
label = '226 RaF', # label
mass = 226+19, #
temp = 4,
)
mol.add_electronicstate(
'X', 2, 'Sigma',
const = X_cts,
nu = 0,
Hcase = 'b',
)
mol.add_electronicstate(
'A', 2, 'Pi',
const = A_cts,
nu = 0,
Hcase = 'a_p',
Gamma = 1/50e-9/(2*pi)*1e-6, # 50ns to in MHz [a]
)
mol.build_states(Fmax = 4)
print(mol)
Molecule 226 RaF: with the nuclear spins I1 = 0.5, I2 = 0 and mass 245 u
magnetic field strength: 0.00e+00G, temperature: 4.00K
Including the following defined electronic states:
* ground state X(^2)Sigma:
- Hunds case b
- open shell electronic state
--> includes 18 states
* excited state A(^2)Pi:
- Hunds case a_p
- open shell electronic state
- linewidth: 2 pi * 3.18 MHz
--> includes 32 states
or just a single electonic state:
print(mol.X)
ground state X(^2)Sigma:
- Hunds case b
- open shell electronic state
--> includes 18 states
The constants object X_cts (which is displayed above) is now also stored
as the attribute const inside the ElectronicState object:
print(type(mol.A.const)) # mol.A.const is the same as A_cts
mol.A.const
<class 'MoleCool.spectra.ElectronicStateConstants'>
| value (1/cm) | value (MHz) | ||
|---|---|---|---|
| electronic energy offset | T_e | 1.432138e+04 | 4.293441e+08 |
| vibration | w_e | 4.355000e+02 | 1.305596e+07 |
| w_e x_e | 1.635000e+00 | 4.901607e+04 | |
| rotation | B_e | 1.915375e-01 | 5.742150e+03 |
| D_e | 1.400000e-07 | 4.197094e-03 | |
| alpha_e | 1.045000e-03 | 3.132831e+01 | |
| spin-orbit | A_e | 2.067600e+03 | 6.198509e+07 |
| Lambda-doubling | p | -4.107000e-01 | -1.231248e+04 |
| Zeeman (no unit) | g_S | 2.002000e+00 | 2.002000e+00 |
| g'_L | 1.000000e+00 | 1.000000e+00 |
Electronic state#
mol.X.get_eigenstates(
mixed_states = False, # transform basis to good Hund's case basis
rounded = None, # better overview in table entries
createHTML = False, # to export html file
)
Calc Hamiltonian for X electronic state ..diagonalize it
| eigenvalue | ||||
|---|---|---|---|---|
| L | N | J | F | |
| 0 | 0.0 | 0.5 | 0.0 | -0.002410 |
| 1.0 | 0.000803 | |||
| 1.0 | 0.5 | 1.0 | 0.377616 | |
| 0.0 | 0.378712 | |||
| 1.5 | 1.0 | 0.385898 | ||
| 2.0 | 0.387677 | |||
| 2.0 | 1.5 | 2.0 | 1.142530 | |
| 1.0 | 1.143833 | |||
| 2.5 | 2.0 | 1.156864 | ||
| 3.0 | 1.158533 | |||
| 3.0 | 2.5 | 3.0 | 2.291473 | |
| 2.0 | 2.292839 | |||
| 3.5 | 3.0 | 2.311741 | ||
| 4.0 | 2.313363 | |||
| 4.0 | 3.5 | 4.0 | 3.824405 | |
| 3.0 | 3.825803 | |||
| 4.5 | 4.0 | 3.850569 | ||
| 5.0 | 4.5 | 4.0 | 5.742733 |
Zeeman splitting plot#
mol.X.plot_Zeeman(np.linspace(0,70e-4,5))
plt.ylim(0.375,0.391)
# mol.X.get_gfactors()
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for X electronic state ..diagonalize it
(0.375, 0.391)
Optical spectra#
mol.build_states(Fmax = 11)
mol.get_branratios(normalize = True)
Calculating linestrengths in pure basis
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for A electronic state ..diagonalize it
| P | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Om | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | ... | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| J | 0.5 | 1.5 | 0.5 | 2.5 | 1.5 | 3.5 | 2.5 | 4.5 | 3.5 | 5.5 | 4.5 | 6.5 | 5.5 | 7.5 | 6.5 | 8.5 | 7.5 | 9.5 | 8.5 | 10.5 | ... | 1.5 | 2.5 | 2.5 | 3.5 | 3.5 | 4.5 | 4.5 | 5.5 | 5.5 | 6.5 | 6.5 | 7.5 | 7.5 | 8.5 | 8.5 | 9.5 | 9.5 | 10.5 | 10.5 | 11.5 | 11.5 | ||||||||||||||||||||||||||||||||||||||||||
| F | 0.0 | 1.0 | 2.0 | 1.0 | 1.0 | 0.0 | 2.0 | 3.0 | 2.0 | 1.0 | 3.0 | 4.0 | 2.0 | 3.0 | 5.0 | 4.0 | 3.0 | 4.0 | 5.0 | 6.0 | 4.0 | 5.0 | 6.0 | 7.0 | 6.0 | 5.0 | 7.0 | 8.0 | 6.0 | 7.0 | 8.0 | 9.0 | 7.0 | 8.0 | 10.0 | 9.0 | 8.0 | 9.0 | 11.0 | 10.0 | ... | 1.0 | 2.0 | 3.0 | 2.0 | 3.0 | 2.0 | 4.0 | 3.0 | 4.0 | 3.0 | 5.0 | 4.0 | 5.0 | 4.0 | 5.0 | 6.0 | 5.0 | 6.0 | 6.0 | 7.0 | 7.0 | 6.0 | 8.0 | 7.0 | 8.0 | 7.0 | 8.0 | 9.0 | 9.0 | 8.0 | 9.0 | 10.0 | 9.0 | 10.0 | 10.0 | 11.0 | 10.0 | 11.0 | 11.0 | 11.0 | |||
| L | N | J | F | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 0 | 0.0 | 0.5 | 0.0 | 0.000000e+00 | 2.222222e-01 | 0.000000e+00 | 8.180280e-27 | 5.807241e-25 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.111727e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 3.332717e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| 1.0 | 6.665434e-01 | 4.444855e-01 | 1.158603e-28 | 6.011897e-26 | 1.394918e-24 | 6.586482e-32 | 3.072336e-09 | 0.000000e+00 | 1.667837e-01 | 5.554529e-02 | 0.000000e+00 | 0.000000e+00 | 7.598170e-33 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 1.666975e-01 | 4.998706e-01 | 0.000000e+00 | 6.151487e-09 | 0.000000e+00 | 1.072076e-20 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 1.0 | 0.5 | 1.0 | 1.701527e-32 | 1.525003e-24 | 1.979928e-01 | 1.058413e-02 | 4.893990e-01 | 4.762190e-01 | 1.341394e-31 | 0.000000e+00 | 1.361989e-28 | 1.418268e-26 | 0.000000e+00 | 0.000000e+00 | 6.675008e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 3.058791e-11 | 5.423055e-12 | 0.000000e+00 | 2.324046e-14 | 0.000000e+00 | 1.333522e-02 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 0.0 | 0.000000e+00 | 5.008218e-25 | 0.000000e+00 | 1.110495e-01 | 2.222222e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.815770e-28 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 3.893687e-11 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 1.5 | 1.0 | 1.061288e-31 | 1.531425e-27 | 2.192962e-02 | 4.895083e-01 | 1.060099e-02 | 5.237810e-01 | 4.360231e-30 | 0.000000e+00 | 1.371186e-29 | 1.020418e-26 | 0.000000e+00 | 0.000000e+00 | 1.734581e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 2.779582e-11 | 1.394314e-12 | 0.000000e+00 | 6.039313e-13 | 0.000000e+00 | 3.465317e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 2.0 | 0.000000e+00 | 9.972735e-25 | 4.801490e-01 | 8.888691e-02 | 2.777778e-01 | 0.000000e+00 | 5.525872e-31 | 5.181086e-30 | 3.235843e-28 | 1.597233e-26 | 1.353925e-09 | 0.000000e+00 | 1.999882e-02 | 2.001593e-01 | 0.000000e+00 | 0.000000e+00 | 3.253860e-34 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 7.784612e-12 | 4.542480e-12 | 6.968310e-13 | 6.972286e-14 | 3.998369e-01 | 4.000651e-02 | 0.000000e+00 | 2.259880e-09 | 0.000000e+00 | 2.808029e-24 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 2.0 | 1.5 | 2.0 | 0.000000e+00 | 2.741569e-01 | 3.517947e-28 | 4.025007e-26 | 8.731406e-25 | 0.000000e+00 | 3.760739e-03 | 2.134407e-01 | 4.960982e-01 | 5.457443e-02 | 3.542807e-31 | 0.000000e+00 | 1.378812e-31 | 6.109832e-30 | 0.000000e+00 | 0.000000e+00 | 2.662691e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 8.564528e-02 | 3.444133e-01 | 3.740491e-01 | 7.468456e-02 | 6.518883e-13 | 1.301594e-13 | 0.000000e+00 | 5.506243e-18 | 0.000000e+00 | 4.431260e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 1.0 | 3.334566e-01 | 5.551449e-02 | 3.565747e-29 | 1.424008e-27 | 9.496249e-26 | 2.547179e-32 | 1.798670e-01 | 0.000000e+00 | 5.329390e-02 | 4.443623e-01 | 0.000000e+00 | 0.000000e+00 | 4.504572e-30 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 3.333949e-01 | 4.005176e-02 | 0.000000e+00 | 3.601330e-01 | 0.000000e+00 | 6.276355e-13 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 2.5 | 2.0 | 0.000000e+00 | 3.620871e-03 | 1.966823e-30 | 1.313639e-26 | 3.524827e-26 | 0.000000e+00 | 4.964610e-01 | 1.091335e-02 | 3.772443e-03 | 3.343453e-01 | 2.621188e-29 | 0.000000e+00 | 1.187188e-29 | 1.450845e-31 | 0.000000e+00 | 0.000000e+00 | 2.016076e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 8.099059e-02 | 2.238280e-02 | 4.785531e-02 | 3.917604e-01 | 8.340167e-14 | 6.827554e-13 | 0.000000e+00 | 4.169092e-16 | 0.000000e+00 | 3.355161e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 3.0 | 0.000000e+00 | 0.000000e+00 | 1.879918e-28 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.429097e-02 | 4.900455e-01 | 2.800517e-01 | 0.000000e+00 | 1.738628e-30 | 7.098268e-28 | 5.660333e-31 | 1.028684e-29 | 0.000000e+00 | 7.460488e-10 | 1.020520e-02 | 2.144903e-01 | 0.000000e+00 | 0.000000e+00 | 8.277905e-33 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 9.328158e-02 | 4.351273e-01 | 3.046706e-02 | 7.583347e-13 | 5.309763e-14 | 9.127728e-13 | 2.113369e-17 | 3.569367e-01 | 1.700776e-02 | 0.000000e+00 | 1.121142e-09 | 0.000000e+00 | 4.335198e-21 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 3.0 | 2.5 | 3.0 | 0.000000e+00 | 0.000000e+00 | 2.780978e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.565523e-31 | 1.183359e-29 | 1.864954e-28 | 0.000000e+00 | 1.910992e-03 | 2.216763e-01 | 1.989217e-02 | 4.978427e-01 | 0.000000e+00 | 2.222585e-30 | 3.814545e-31 | 7.389385e-28 | 0.000000e+00 | 0.000000e+00 | 1.429684e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 1.171003e-12 | 7.409155e-13 | 7.307116e-14 | 4.251323e-01 | 4.192774e-02 | 3.439280e-01 | 3.425720e-02 | 8.795064e-13 | 4.256768e-17 | 0.000000e+00 | 8.277012e-15 | 0.000000e+00 | 2.140565e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 2.0 | 0.000000e+00 | 2.868909e-26 | 1.998034e-02 | 2.999712e-01 | 1.844546e-09 | 0.000000e+00 | 1.166987e-29 | 4.912145e-31 | 1.248853e-29 | 8.265199e-27 | 2.038931e-01 | 0.000000e+00 | 4.797793e-01 | 2.446632e-02 | 0.000000e+00 | 0.000000e+00 | 2.619854e-29 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 1.168382e-11 | 8.430043e-14 | 3.798580e-14 | 7.439649e-13 | 2.179599e-02 | 4.268820e-01 | 0.000000e+00 | 3.403245e-01 | 0.000000e+00 | 4.228841e-16 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 3.5 | 3.0 | 0.000000e+00 | 0.000000e+00 | 1.850475e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 6.389894e-30 | 8.927908e-32 | 1.065233e-30 | 0.000000e+00 | 4.984189e-01 | 6.530625e-03 | 3.001966e-01 | 1.919644e-03 | 0.000000e+00 | 2.760830e-28 | 6.757364e-29 | 2.139061e-29 | 0.000000e+00 | 0.000000e+00 | 2.148594e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 7.791903e-15 | 2.715541e-14 | 2.288575e-13 | 1.558159e-02 | 1.313169e-01 | 2.663055e-02 | 4.416034e-01 | 6.810070e-14 | 5.487323e-16 | 0.000000e+00 | 1.243907e-12 | 0.000000e+00 | 3.216938e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 4.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 6.336713e-30 | 0.000000e+00 | 0.000000e+00 | 1.814664e-02 | 4.941743e-01 | 0.000000e+00 | 2.756121e-01 | 2.438607e-28 | 6.950858e-30 | 2.671511e-30 | 1.648633e-27 | 4.698697e-10 | 0.000000e+00 | 6.174618e-03 | 2.224729e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 8.388611e-33 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 2.399004e-13 | 0.000000e+00 | 1.376533e-01 | 0.000000e+00 | 4.626171e-01 | 1.699913e-02 | 1.183023e-12 | 2.112296e-17 | 3.232988e-13 | 3.580022e-14 | 3.330818e-01 | 9.258497e-03 | 6.592772e-10 | 0.000000e+00 | 6.132033e-22 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 4.0 | 3.5 | 4.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.743099e-01 | 0.000000e+00 | 0.000000e+00 | 1.618399e-30 | 1.657237e-27 | 0.000000e+00 | 6.375248e-30 | 2.268211e-01 | 1.153655e-03 | 1.021632e-02 | 4.985006e-01 | 2.488633e-29 | 0.000000e+00 | 1.358343e-30 | 2.478755e-28 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 8.912055e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 1.373070e-01 | 0.000000e+00 | 2.392971e-13 | 0.000000e+00 | 1.166747e-12 | 3.022789e-17 | 4.562525e-01 | 2.432650e-02 | 3.254513e-01 | 1.946962e-02 | 3.158924e-13 | 7.528399e-14 | 1.157925e-15 | 0.000000e+00 | 1.244922e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 3.0 | 0.000000e+00 | 0.000000e+00 | 3.205560e-33 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.856203e-01 | 1.019200e-02 | 9.681309e-10 | 0.000000e+00 | 6.662237e-29 | 4.728503e-29 | 5.976319e-30 | 2.910068e-31 | 0.000000e+00 | 2.158100e-01 | 4.894647e-01 | 1.409310e-02 | 0.000000e+00 | 0.000000e+00 | 2.715430e-28 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 3.224717e-10 | 5.111356e-03 | 1.429550e-01 | 8.908010e-15 | 2.491402e-13 | 3.387162e-14 | 5.709864e-16 | 1.324538e-02 | 4.595129e-01 | 0.000000e+00 | 3.243135e-01 | 0.000000e+00 | 1.254037e-12 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 4.5 | 4.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.098537e-03 | 0.000000e+00 | 0.000000e+00 | 3.903984e-29 | 5.162505e-30 | 0.000000e+00 | 2.498169e-34 | 4.345692e-03 | 4.992773e-01 | 2.858435e-01 | 1.160476e-03 | 6.143065e-27 | 0.000000e+00 | 6.225017e-28 | 4.033044e-30 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.225381e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 5.498778e-04 | 0.000000e+00 | 9.583204e-16 | 0.000000e+00 | 2.749818e-14 | 1.978273e-16 | 1.075307e-02 | 1.592055e-01 | 1.693557e-02 | 4.634327e-01 | 1.643815e-14 | 1.791975e-12 | 2.891392e-13 | 0.000000e+00 | 3.108629e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 5.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 8.968545e-28 | 0.000000e+00 | 0.000000e+00 | 4.963108e-01 | 1.122913e-02 | 0.000000e+00 | 2.717556e-01 | 1.123099e-28 | 4.513607e-28 | 1.389258e-29 | 5.494511e-28 | 3.223891e-10 | 0.000000e+00 | 2.275698e-01 | 4.134173e-03 | 0.000000e+00 | 0.000000e+00 | 3.291081e-33 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 4.163502e-13 | 0.000000e+00 | 1.628123e-01 | 0.000000e+00 | 4.755907e-01 | 1.076779e-02 | 4.616221e-13 | 4.163628e-14 | 5.379572e-15 | 1.000601e-14 | 5.783752e-03 | 3.178842e-01 | 4.309651e-10 | 0.000000e+00 | 0.000000e+00 | 4.900658e-23 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 5.0 | 4.5 | 5.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.707305e-01 | 0.000000e+00 | 0.000000e+00 | 5.476266e-28 | 7.038661e-30 | 0.000000e+00 | 8.986497e-28 | 7.712215e-04 | 2.303411e-01 | 6.205220e-03 | 4.987861e-01 | 2.787713e-30 | 0.000000e+00 | 4.593874e-28 | 1.924878e-29 | 0.000000e+00 | 0.000000e+00 | 6.084294e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.626785e-01 | 0.000000e+00 | 4.160080e-13 | 0.000000e+00 | 4.576272e-13 | 6.111292e-14 | 4.714750e-01 | 1.580476e-02 | 1.250590e-02 | 3.130343e-01 | 1.163196e-14 | 9.853349e-15 | 9.201218e-17 | 0.000000e+00 | 0.000000e+00 | 8.091417e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 4.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.981005e-32 | 0.000000e+00 | 0.000000e+00 | 2.776303e-01 | 6.164349e-03 | 0.000000e+00 | 5.811109e-10 | 9.329529e-30 | 6.263722e-28 | 3.874125e-29 | 2.188723e-29 | 2.228520e-01 | 0.000000e+00 | 4.933940e-01 | 9.170438e-03 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 6.130689e-27 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 5.058197e-22 | 0.000000e+00 | 2.902333e-10 | 0.000000e+00 | 3.710929e-03 | 1.668157e-01 | 9.489737e-15 | 2.072837e-16 | 8.569252e-15 | 1.834794e-12 | 8.828556e-03 | 4.745063e-01 | 3.126852e-01 | 0.000000e+00 | 2.908341e-13 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 5.5 | 5.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 7.239206e-04 | 0.000000e+00 | 0.000000e+00 | 7.976208e-31 | 3.666191e-28 | 0.000000e+00 | 2.412027e-30 | 4.997577e-01 | 3.099866e-03 | 2.779371e-01 | 7.768394e-04 | 1.168546e-27 | 0.000000e+00 | 6.720143e-30 | 1.387103e-26 | 0.000000e+00 | 0.000000e+00 | 2.275393e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 4.349947e-04 | 0.000000e+00 | 1.112386e-15 | 0.000000e+00 | 7.522312e-15 | 6.828517e-13 | 7.749936e-03 | 1.765961e-01 | 4.748440e-01 | 1.171012e-02 | 4.416610e-13 | 3.685982e-16 | 3.441054e-14 | 0.000000e+00 | 0.000000e+00 | 3.026013e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 6.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.847146e-28 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 7.634063e-03 | 4.975794e-01 | 0.000000e+00 | 2.687937e-01 | 1.475032e-29 | 2.854604e-27 | 1.015563e-27 | 2.125826e-28 | 2.346771e-10 | 0.000000e+00 | 2.960512e-03 | 2.311128e-01 | 0.000000e+00 | 0.000000e+00 | 1.005121e-33 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.736113e-13 | 0.000000e+00 | 1.788647e-01 | 0.000000e+00 | 7.411016e-03 | 4.826972e-01 | 6.893120e-15 | 1.519381e-14 | 4.484031e-16 | 2.083583e-14 | 3.073484e-01 | 3.943192e-03 | 0.000000e+00 | 3.026205e-10 | 0.000000e+00 | 9.771800e-24 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 6.0 | 5.5 | 6.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.678845e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.190923e-28 | 1.026678e-27 | 0.000000e+00 | 2.812216e-28 | 5.515826e-04 | 2.328982e-01 | 4.989102e-01 | 4.165006e-03 | 1.752915e-30 | 0.000000e+00 | 2.566452e-30 | 2.863826e-27 | 0.000000e+00 | 0.000000e+00 | 4.416969e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.789198e-01 | 0.000000e+00 | 1.736647e-13 | 0.000000e+00 | 1.029941e-14 | 1.511089e-14 | 1.107323e-02 | 4.800630e-01 | 8.694096e-03 | 3.041397e-01 | 2.061830e-14 | 9.886559e-16 | 0.000000e+00 | 1.828396e-17 | 0.000000e+00 | 5.662181e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 5.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.373350e-32 | 0.000000e+00 | 0.000000e+00 | 4.125770e-03 | 2.725299e-01 | 0.000000e+00 | 3.851473e-10 | 1.377965e-26 | 1.372574e-29 | 3.545487e-28 | 3.941452e-30 | 2.274741e-01 | 0.000000e+00 | 6.445237e-03 | 4.953363e-01 | 0.000000e+00 | 0.000000e+00 | 1.167703e-27 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 5.900718e-22 | 0.000000e+00 | 2.307468e-10 | 0.000000e+00 | 2.760602e-03 | 1.820164e-01 | 2.679520e-15 | 7.038104e-13 | 4.488978e-13 | 1.978670e-16 | 4.826246e-01 | 6.286104e-03 | 3.040841e-01 | 0.000000e+00 | 0.000000e+00 | 3.457916e-14 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 6.5 | 6.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 5.121040e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 7.614798e-27 | 8.960998e-31 | 0.000000e+00 | 5.102286e-31 | 5.000735e-01 | 2.322557e-03 | 5.563545e-04 | 2.729352e-01 | 9.836584e-28 | 0.000000e+00 | 2.560424e-27 | 2.951514e-29 | 0.000000e+00 | 0.000000e+00 | 2.310541e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.420338e-04 | 0.000000e+00 | 3.319879e-16 | 0.000000e+00 | 1.752441e-13 | 1.831445e-16 | 1.884106e-01 | 5.818380e-03 | 4.815233e-01 | 8.576105e-03 | 5.813930e-16 | 5.475680e-14 | 0.000000e+00 | 9.564443e-15 | 0.000000e+00 | 2.961919e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 7.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 5.663900e-28 | 0.000000e+00 | 0.000000e+00 | 5.527553e-03 | 4.984100e-01 | 2.665184e-01 | 0.000000e+00 | 1.442118e-29 | 3.756857e-28 | 2.257132e-29 | 6.051526e-27 | 1.783699e-10 | 0.000000e+00 | 2.224082e-03 | 2.337234e-01 | 0.000000e+00 | 0.000000e+00 | 2.185958e-31 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 5.978981e-15 | 0.000000e+00 | 1.899483e-01 | 5.404801e-03 | 4.869871e-01 | 3.301393e-14 | 6.146111e-16 | 9.610496e-16 | 9.220846e-17 | 2.996097e-01 | 2.855514e-03 | 2.237047e-10 | 0.000000e+00 | 0.000000e+00 | 4.478348e-26 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 7.0 | 6.5 | 7.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.656452e-01 | 0.000000e+00 | 0.000000e+00 | 1.149271e-29 | 6.060683e-27 | 5.685230e-28 | 0.000000e+00 | 4.139165e-04 | 2.348368e-01 | 2.987589e-03 | 4.989532e-01 | 2.795058e-32 | 0.000000e+00 | 3.922456e-30 | 3.742933e-28 | 0.000000e+00 | 0.000000e+00 | 3.351960e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.901675e-01 | 0.000000e+00 | 5.985883e-15 | 9.305599e-16 | 3.290614e-14 | 4.853971e-01 | 8.183209e-03 | 2.974656e-01 | 6.387624e-03 | 9.541718e-16 | 2.062651e-16 | 8.318821e-20 | 0.000000e+00 | 0.000000e+00 | 4.176024e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 6.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.002116e-32 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.689850e-01 | 2.953402e-03 | 0.000000e+00 | 2.733954e-10 | 2.520535e-27 | 6.126854e-29 | 4.986511e-30 | 7.492890e-27 | 2.307271e-01 | 0.000000e+00 | 4.964136e-01 | 4.778135e-03 | 0.000000e+00 | 0.000000e+00 | 9.858763e-28 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.765784e-22 | 0.000000e+00 | 1.819269e-10 | 0.000000e+00 | 1.925539e-01 | 2.118043e-03 | 1.790979e-13 | 6.666940e-17 | 5.543931e-14 | 3.184293e-16 | 4.697138e-03 | 4.875252e-01 | 0.000000e+00 | 2.975269e-01 | 0.000000e+00 | 9.607552e-15 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 7.5 | 7.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.810788e-04 | 0.000000e+00 | 0.000000e+00 | 1.376808e-27 | 8.888677e-30 | 1.946623e-30 | 0.000000e+00 | 5.003062e-01 | 1.805065e-03 | 2.694906e-01 | 4.180620e-04 | 4.072421e-29 | 0.000000e+00 | 2.123674e-27 | 1.371833e-30 | 0.000000e+00 | 0.000000e+00 | 2.336609e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.728030e-04 | 0.000000e+00 | 8.586989e-18 | 2.239495e-14 | 3.062461e-16 | 4.517423e-03 | 1.969379e-01 | 6.550019e-03 | 4.857494e-01 | 2.101031e-17 | 1.568551e-14 | 5.798927e-17 | 0.000000e+00 | 0.000000e+00 | 2.911054e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 8.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.283950e-27 | 0.000000e+00 | 0.000000e+00 | 4.187464e-03 | 4.989959e-01 | 0.000000e+00 | 2.647378e-01 | 1.866400e-31 | 1.481851e-27 | 1.700149e-29 | 7.507063e-28 | 0.000000e+00 | 1.401071e-10 | 1.731871e-03 | 2.357307e-01 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.342556e-14 | 1.980399e-01 | 0.000000e+00 | 4.897586e-01 | 4.112986e-03 | 1.570985e-15 | 1.328140e-16 | 4.304836e-19 | 9.064099e-16 | 2.936810e-01 | 2.161023e-03 | 1.718756e-10 | 0.000000e+00 | 7.263227e-26 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 8.0 | 7.5 | 8.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.638569e-01 | 0.000000e+00 | 0.000000e+00 | 8.884808e-30 | 7.536745e-28 | 0.000000e+00 | 3.278972e-27 | 3.219823e-04 | 2.363543e-01 | 2.247011e-03 | 4.989509e-01 | 0.000000e+00 | 1.407692e-31 | 1.149456e-32 | 1.484140e-27 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.984049e-01 | 1.345031e-14 | 0.000000e+00 | 1.568389e-15 | 2.031592e-16 | 4.889495e-01 | 6.291440e-03 | 4.888356e-03 | 2.922789e-01 | 9.020825e-16 | 9.737784e-19 | 1.354520e-19 | 0.000000e+00 | 3.203191e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 7.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.527303e-31 | 0.000000e+00 | 0.000000e+00 | 2.663733e-01 | 2.217920e-03 | 2.039132e-10 | 0.000000e+00 | 2.111564e-27 | 3.624890e-30 | 1.368668e-27 | 3.508807e-29 | 2.331328e-01 | 0.000000e+00 | 4.970546e-01 | 3.683889e-03 | 0.000000e+00 | 0.000000e+00 | 3.949270e-29 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 4.572701e-24 | 0.000000e+00 | 1.453294e-10 | 2.002937e-01 | 1.670707e-03 | 1.132609e-16 | 2.277655e-14 | 1.167728e-17 | 1.584612e-14 | 3.640421e-03 | 4.907229e-01 | 2.923862e-01 | 0.000000e+00 | 0.000000e+00 | 5.824442e-17 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 8.5 | 8.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.945083e-04 | 0.000000e+00 | 0.000000e+00 | 1.122781e-27 | 6.761853e-31 | 0.000000e+00 | 3.993808e-30 | 5.004926e-01 | 1.443229e-03 | 2.669785e-01 | 3.256459e-04 | 0.000000e+00 | 7.574338e-29 | 8.119488e-29 | 9.569886e-30 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.214530e-04 | 1.501279e-17 | 0.000000e+00 | 1.156074e-17 | 6.567161e-15 | 3.604093e-03 | 2.033720e-01 | 4.885781e-01 | 5.165191e-03 | 1.594172e-17 | 9.732657e-17 | 1.213547e-16 | 0.000000e+00 | 2.869814e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 9.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 4.063662e-28 | 0.000000e+00 | 0.000000e+00 | 3.282188e-03 | 4.994344e-01 | 0.000000e+00 | 2.633162e-01 | 2.141383e-29 | 7.874354e-31 | 8.198269e-31 | 3.154014e-27 | 0.000000e+00 | 1.129371e-10 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 6.549946e-16 | 0.000000e+00 | 2.041963e-01 | 0.000000e+00 | 3.233382e-03 | 4.916399e-01 | 1.517385e-15 | 6.441020e-19 | 7.151829e-19 | 4.096199e-17 | 1.691274e-03 | 2.889906e-01 | 1.360761e-10 | 0.000000e+00 | 4.318185e-25 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 9.0 | 8.5 | 9.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.624015e-01 | 0.000000e+00 | 0.000000e+00 | 4.267515e-31 | 3.113142e-27 | 0.000000e+00 | 3.933599e-28 | 2.375721e-01 | 2.575605e-04 | 1.751120e-03 | 4.989214e-01 | 0.000000e+00 | 2.100356e-30 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.046938e-01 | 0.000000e+00 | 6.565906e-16 | 0.000000e+00 | 9.933477e-19 | 1.516784e-15 | 4.914450e-01 | 4.986591e-03 | 3.859945e-03 | 2.881362e-01 | 1.632241e-18 | 4.084090e-17 | 8.033565e-19 | 0.000000e+00 | 2.532787e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |
| 8.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 5.019993e-33 | 0.000000e+00 | 0.000000e+00 | 2.643653e-01 | 1.726434e-03 | 0.000000e+00 | 1.578510e-10 | 8.306502e-29 | 1.891787e-29 | 1.112323e-27 | 2.890324e-30 | 0.000000e+00 | 2.349789e-01 | 4.974521e-01 | 2.926924e-03 | 0.000000e+00 | 0.000000e+00 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 8.005386e-24 | 1.180821e-10 | 0.000000e+00 | 1.349128e-03 | 2.062231e-01 | 4.327558e-18 | 6.659228e-15 | 9.819470e-17 | 8.959957e-18 | 2.903067e-03 | 4.929361e-01 | 2.882590e-01 | 0.000000e+00 | 1.218950e-16 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 9.5 | 9.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.343678e-04 | 0.000000e+00 | 0.000000e+00 | 6.197872e-29 | 1.229855e-30 | 0.000000e+00 | 6.091054e-31 | 1.180320e-03 | 5.006510e-01 | 2.650688e-01 | 2.608420e-04 | 0.000000e+00 | 1.923116e-27 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.828254e-04 | 0.000000e+00 | 5.864440e-19 | 0.000000e+00 | 4.151272e-17 | 9.074060e-18 | 2.940038e-03 | 2.083934e-01 | 4.905532e-01 | 4.177068e-03 | 2.074383e-16 | 5.920639e-19 | 8.994489e-16 | 0.000000e+00 | 2.835743e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | ||
| 10.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.648660e-27 | 0.000000e+00 | 0.000000e+00 | 4.997789e-01 | 2.641956e-03 | 0.000000e+00 | 2.621602e-01 | 6.557662e-27 | 7.546280e-30 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 6.451482e-16 | 2.090310e-01 | 0.000000e+00 | 2.607907e-03 | 4.929649e-01 | 1.102796e-18 | 6.987364e-17 | 4.310685e-18 | 1.315404e-21 | 1.359054e-03 | 3.638130e-01 | 1.418920e-10 | 1.143614e-24 | |||
| 10.0 | 9.5 | 10.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.611952e-01 | 0.000000e+00 | 0.000000e+00 | 4.547938e-29 | 6.579992e-31 | 0.000000e+00 | 1.646603e-27 | 3.221486e-01 | 2.106776e-04 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.096517e-01 | 6.470641e-16 | 0.000000e+00 | 1.712193e-18 | 6.991746e-17 | 4.049017e-03 | 4.932741e-01 | 3.124358e-03 | 3.637096e-01 | 9.909925e-18 | 1.311814e-21 | 2.130525e-18 | 2.634777e-04 | |
| 9.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.720355e-32 | 0.000000e+00 | 0.000000e+00 | 2.627704e-01 | 1.381847e-03 | 0.000000e+00 | 1.257765e-10 | 2.782721e-31 | 2.123921e-28 | 6.397462e-29 | 7.727371e-30 | 0.000000e+00 | 2.364366e-01 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.130572e-25 | 0.000000e+00 | 9.753711e-11 | 0.000000e+00 | 2.109139e-01 | 1.111101e-03 | 3.429273e-18 | 4.201482e-17 | 2.091245e-16 | 3.357239e-19 | 4.945407e-01 | 2.368565e-03 | 2.848786e-01 | 0.000000e+00 | 9.035858e-16 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | |||
| 10.5 | 10.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.909100e-04 | 0.000000e+00 | 0.000000e+00 | 2.343906e-31 | 9.294005e-29 | 0.000000e+00 | 1.856125e-30 | 1.327775e-03 | 5.007914e-01 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.532364e-04 | 4.729448e-19 | 0.000000e+00 | 8.982410e-17 | 3.462533e-19 | 2.124173e-01 | 2.442852e-03 | 4.919774e-01 | 4.403345e-03 | 1.560468e-15 | 1.588458e-23 | 2.914897e-15 | 3.604793e-01 | ||
| 11.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.489634e-29 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 6.752507e-01 | 2.172492e-03 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 3.018017e-17 | 0.000000e+00 | 2.129240e-01 | 2.147471e-03 | 6.308779e-01 | 6.811413e-18 | 2.275580e-21 | 1.158433e-17 | 1.432611e-03 | |||
| 11.0 | 10.5 | 11.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.601791e-01 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.329548e-26 | 4.908978e-30 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.136612e-01 | 0.000000e+00 | 3.028468e-17 | 1.063477e-17 | 2.281772e-21 | 3.352882e-03 | 6.310456e-01 | 3.317953e-03 | 2.675728e-17 | |
| 10.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 4.670567e-32 | 0.000000e+00 | 0.000000e+00 | 1.130962e-03 | 2.614706e-01 | 0.000000e+00 | 1.025595e-10 | 5.711138e-29 | 4.157098e-27 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 2.521941e-25 | 8.177484e-11 | 0.000000e+00 | 2.147200e-01 | 9.303748e-04 | 9.079782e-17 | 1.318726e-19 | 1.572431e-15 | 9.083464e-24 | 4.957492e-01 | 2.511801e-03 | 3.627011e-01 | 2.924966e-15 | |||
| 11.5 | 11.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.584952e-04 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.480909e-29 | 2.153343e-27 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.301576e-04 | 0.000000e+00 | 1.844849e-20 | 6.841990e-16 | 9.518015e-24 | 2.157113e-01 | 2.629619e-03 | 6.339810e-01 | 5.112675e-15 | ||
| 12.0 | 11.5 | 11.0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 9.484776e-31 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 1.272896e-03 | 2.603888e-01 | ... | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 9.672021e-27 | 0.000000e+00 | 6.946730e-11 | 2.178721e-01 | 1.009186e-03 | 6.910528e-16 | 3.645936e-24 | 5.157559e-15 | 6.378246e-01 | |
46 rows × 88 columns
filtering transitions#
the index filter argument internally utilizes the filter function
multiindex_filter()
index_filter = (
dict(N = 1),
dict(P = +1, Om = 0.5, J = 0.5),
)
mol.get_branratios(normalize = False,
index_filter = index_filter)
Calculating linestrengths in pure basis
| P | 1 | ||||
|---|---|---|---|---|---|
| Om | 0.5 | ||||
| J | 0.5 | ||||
| F | 1.0 | 0.0 | |||
| L | N | J | F | ||
| 0 | 1.0 | 0.5 | 1.0 | 1.468197 | 0.476219 |
| 0.0 | 0.666667 | 0.000000 | |||
| 1.5 | 1.0 | 0.031803 | 0.523781 | ||
| 2.0 | 0.833333 | 0.000000 | |||
similarly the eigeneneries can be extracted:
df2 = mol.get_E(index_filter = index_filter, recalc_branratios = False)
f0 = df2.mean().mean()
print(f"Mean frequency of cooling transition: {f0*cm2THz:.6f} THz")
df2
# mol.X.nu = 1
# f0_repump = mol.get_E(index_filter = index_filter).mean().mean()
# print(f"Mean frequency of repumping transition: {f0*cm2THz:.6f} THz")
Mean frequency of cooling transition: 398.257789 THz
| P | 1 | ||||
|---|---|---|---|---|---|
| Om | 0.5 | ||||
| J | 0.5 | ||||
| F | 1.0 | 0.0 | |||
| L | N | J | F | ||
| 0 | 1.0 | 0.5 | 1.0 | 13284.454774 | 13284.454774 |
| 0.0 | 13284.453678 | 13284.453678 | |||
| 1.5 | 1.0 | 13284.446492 | 13284.446492 | ||
| 2.0 | 13284.444713 | 13284.444713 | |||
Checking rotational leakage#
Branching ratios for the state A(Om = 1/2, J = 1/2^+) decaying in any ground state (in percent). They reveal a vanishing probability of population leakage in any other ground state than X(N=1).
mol.get_branratios(
index_filter = (dict(), dict(P = +1, Om = 0.5, J = 0.5)),
recalc_branratios = False,
).round(6)*1e2
| P | 1 | ||||
|---|---|---|---|---|---|
| Om | 0.5 | ||||
| J | 0.5 | ||||
| F | 1.0 | 0.0 | |||
| L | N | J | F | ||
| 0 | 0.0 | 0.5 | 0.0 | 0.0000 | 0.0000 |
| 1.0 | 0.0000 | 0.0000 | |||
| 1.0 | 0.5 | 1.0 | 48.9399 | 47.6219 | |
| 0.0 | 22.2222 | 0.0000 | |||
| 1.5 | 1.0 | 1.0601 | 52.3781 | ||
| 2.0 | 27.7778 | 0.0000 | |||
| 2.0 | 1.5 | 2.0 | 0.0000 | 0.0000 | |
| 1.0 | 0.0000 | 0.0000 | |||
| 2.5 | 2.0 | 0.0000 | 0.0000 | ||
| 3.0 | 0.0000 | 0.0000 | |||
| 3.0 | 2.5 | 3.0 | 0.0000 | 0.0000 | |
| 2.0 | 0.0000 | 0.0000 | |||
| 3.5 | 3.0 | 0.0000 | 0.0000 | ||
| 4.0 | 0.0000 | 0.0000 | |||
| 4.0 | 3.5 | 4.0 | 0.0000 | 0.0000 | |
| 3.0 | 0.0000 | 0.0000 | |||
| 4.5 | 4.0 | 0.0000 | 0.0000 | ||
| 5.0 | 0.0000 | 0.0000 | |||
| 5.0 | 4.5 | 5.0 | 0.0000 | 0.0000 | |
| 4.0 | 0.0000 | 0.0000 | |||
| 5.5 | 5.0 | 0.0000 | 0.0000 | ||
| 6.0 | 0.0000 | 0.0000 | |||
| 6.0 | 5.5 | 6.0 | 0.0000 | 0.0000 | |
| 5.0 | 0.0000 | 0.0000 | |||
| 6.5 | 6.0 | 0.0000 | 0.0000 | ||
| 7.0 | 0.0000 | 0.0000 | |||
| 7.0 | 6.5 | 7.0 | 0.0000 | 0.0000 | |
| 6.0 | 0.0000 | 0.0000 | |||
| 7.5 | 7.0 | 0.0000 | 0.0000 | ||
| 8.0 | 0.0000 | 0.0000 | |||
| 8.0 | 7.5 | 8.0 | 0.0000 | 0.0000 | |
| 7.0 | 0.0000 | 0.0000 | |||
| 8.5 | 8.0 | 0.0000 | 0.0000 | ||
| 9.0 | 0.0000 | 0.0000 | |||
| 9.0 | 8.5 | 9.0 | 0.0000 | 0.0000 | |
| 8.0 | 0.0000 | 0.0000 | |||
| 9.5 | 9.0 | 0.0000 | 0.0000 | ||
| 10.0 | 0.0000 | 0.0000 | |||
| 10.0 | 9.5 | 10.0 | 0.0000 | 0.0000 | |
| 9.0 | 0.0000 | 0.0000 | |||
| 10.5 | 10.0 | 0.0000 | 0.0000 | ||
| 11.0 | 0.0000 | 0.0000 | |||
| 11.0 | 10.5 | 11.0 | 0.0000 | 0.0000 | |
| 10.0 | 0.0000 | 0.0000 | |||
| 11.5 | 11.0 | 0.0000 | 0.0000 | ||
| 12.0 | 11.5 | 11.0 | 0.0000 | 0.0000 | |
Plotting a simple spectrum#
mol.calc_branratios(threshold=0.0)
E, I = mol.calc_spectrum(
limits = (f0-0.15,f0+0.1)
)
plt.figure()
plt.plot(mol.Eplt, mol.I)
plt.xlabel('Frequency (cm$^{-1}$)')
plt.ylabel('Intensity (arb. u.)')
Calculating linestrengths in pure basis
Text(38.347222222222214, 0.5, 'Intensity (arb. u.)')
Nice spectrum with fortrat diagram#
# function to convert the xaxis units from cm^-1 to GHz with an offset
def xconv(x):
return (x * cm2THz - 398.258) * 1e3
# x-axis limits (always in units of cm^-1)
limits = np.array([398.250, 398.260])/cm2THz
fig, axs = plt.subplots(2,1, sharex=True)
ax = axs[0]
### Plotting normal spectra
mol.calc_branratios(threshold=0.0) # calculate branching ratios with Boltzmann
for sigma, linewidth, color in zip([0, None], [0.8, 1.5], ['C0', 'k']):
# calculate spectrum in a specific frequency range with Doppler broadening sigma
E, I = mol.calc_spectrum(
limits = limits,
sigma = sigma,
)
# plotting the spectrum
ax.plot(
xconv(E), I/I.max(),
lw = linewidth, color = color,
)
### Plotting fortrat diagram
ax = axs[1]
# make a deep copy of the molecule as we modify the constants
molf = deepcopy(mol)
for const in [*ElectronicStateConstants.const_HFS, *ElectronicStateConstants.const_eq0Q]:
molf.X.const[const] = 0
molf.X.eigenst_already_calc = False
molf.calc_branratios(threshold=0.0) # calculate branching ratios with Boltzmann
molf.plot_fortrat(
["N","J"],
ax = ax,
limits = limits,
limits_unit = 'cm-1',
branratio_TH = 1e-2,
legend = True,
xaxis_func = xconv,
)
# residual annotations and labels:
ax.set_ylim(top=11.9,bottom=-0.8)
ax.grid(True, axis='y')
ax.text(-0.1,6, "P$_1$", va='center', ha='right')
ax.text(1.3,7.8, "$^\\text{P}$Q$_{12}$", va='center', ha='right')
ax.text(-4.6,7.3, "$^\\text{Q}$R$_{12}$", va='bottom', ha='center')
ax.text(-5,5.2, "Q$_1$", va='top', ha='center')
ax.set_xlabel('Frequency (GHz)')
ax.set_ylabel('Intensity (arb. u.)')
Calculating linestrengths in pure basis
Calculating linestrengths in pure basis
Calc Hamiltonian for X electronic state ..diagonalize it
Calculating linestrengths in pure basis
Calculating linestrengths in pure basis
Text(33.972222222222214, 0.5, 'Intensity (arb. u.)')
Export properties for OBEs#
mol.X.Fmax = 4
mol.A.Fmax = 4
vibr_values = {
"vibrbranch": [
[0.996, 0.004],
[0.004, 0.988],
[1e-5, 0.008],
[1e-6, 3e-5]], #[4]
"vibrfreq": [
[752.760, 729.040],
[778.453, 753.113],
[805.745, 778.628],
[834.787, 805.715]],
}
mol.export_OBE_properties(
index_filter = (dict(N=1), dict(P=+1,Om=0.5,J=0.5)),
fname = 'test_226RaF.json',
HFfreq_offsets = [0,0],
QuNrs_const = (['N'],['J']), # ([],[]),
QuNrs_var = ([],[]), # (['J','F'],['F'])
include_mF = False,
vibr_values = vibr_values,
rounded = 6,
)
Calculating linestrengths in pure basis
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for A electronic state ..diagonalize it
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for X electronic state ..diagonalize it
Calc Hamiltonian for A electronic state ..diagonalize it
Calc Hamiltonian for A electronic state ..diagonalize it
Calc Hamiltonian for A electronic state ..diagonalize it
/home/docs/checkouts/readthedocs.org/user_builds/molecool-py/checkouts/v3.7.1/MoleCool/spectra.py:1314: UserWarning: Hcasebasis doesn't seem to be a good choice as the eigenstates are not diagonal (<75%).
warnings.warn("Hcasebasis doesn't seem to be a good choice as the eigenstates are not diagonal (<75%).")
{'mass': 245, 'level-specific': {'gs=X': {'v=0': {'N=1': {'gfac': [-0.468649, 0.0, 0.969165, 0.500492], 'HFfreq': [0.0, 32.867088, 248.303786, 301.634845], 'QuNrs': {'J': [0.5, 0.5, 1.5, 1.5], 'F': [1, 0, 1, 2]}}}}, 'exs=A': {'v=0': {'J=0.5': {'gfac': [-0.000333, -0.0], 'HFfreq': [0.0, 0.0], 'QuNrs': {'F': [1, 0]}}}, 'Gamma': 3.1830988618379066}}, 'transition-specific': {'gs=X <- exs=A': {'v=0 <- v=0': {'N=1 <- J=0.5': {'dMat_red': [[-1.211692, -0.690086], [-0.816497, 0.0], [-0.178334, 0.723727], [-0.912871, 0.0]], 'QuNrs_rows': {'J': [0.5, 0.5, 1.5, 1.5], 'F': [1, 0, 1, 2]}, 'QuNrs_cols': {'F': [1, 0]}}}, 'vibrbranch': [[0.996, 0.004], [0.004, 0.988], [1e-05, 0.008], [1e-06, 3e-05]], 'vibrfreq': [[752.76, 729.04], [778.453, 753.113], [805.745, 778.628], [834.787, 805.715]], 'QuNrs_rows': {'v': [0, 1, 2, 3]}, 'QuNrs_cols': {'v': [0, 1]}}}}
Total running time of the script: (0 minutes 24.519 seconds)