Welcome to part 2 of the alanine tutorial. Here we take the computed dataset we used previously and solve for site specific delta values. We begin by importing.

```python
import sys; sys.path.insert(0, '..')
```

```python
import alanineTest
import readInput as ri
import fragmentAndSimulate as fas
import solveSystem as ss
import basicDeltaOperations as op

import copy
from tqdm import tqdm
import solveSystem as ss
import numpy as np
import sympy as sy
from datetime import date

today = date.today()
```

Here, we have imported the alanineTest.py file which we discussed before, allowing us to predict what the dataset should look like for a given standard. We standardize by defining and computing a forward model, without experimental fractionation and with all peaks observed, giving us theoretical values for each peak. To do so, we need to specify some hypothesized standard structure, which will often be wrong; it turns out that sample standard comparisons are robust to reasonable natural abundance errors in our hypothesized standard, so this does not need to be perfect.

```python
deltas = [-30,-30,0,0,0,0]
fragSubset = ['full','44']
df, expandedFrags, fragSubgeometryKeys, fragmentationDictionary = alanineTest.initializeAlanine(deltas, fragSubset)

forbiddenPeaks = {}
```

    Delta 18O
    0.0

```python
predictedMeasurement, MNDictStd, FF = alanineTest.simulateMeasurement(df, fragmentationDictionary, expandedFrags,
                                                                      fragSubgeometryKeys,
                                                                       abundanceThreshold = 0,
                                                                       massThreshold = 1,
                                                                         unresolvedDict = {},
                                                                        outputFull = False)
```

    Calculating Isotopologue Concentrations

    100%|███████████████████████████████████████████████████████████████████████████| 1512/1512 [00:00<00:00, 58239.78it/s]

    Compiling Isotopologue Dictionary

    100%|███████████████████████████████████████████████████████████████████████████| 1512/1512 [00:00<00:00, 52218.56it/s]

    Simulating Measurement

Next, we read in our sample and standard files. We have specific functions in the readInput.py for doing so; note that different functions are used for importing experimental data. The error option allows us to specify an error for each observed peak of sample and standard, e.g. a 1 per mil error on each observed peak. Likely experimental results will have different errors for different beams, but this is a basic way to understand how error will propagate. We can set error again for the molecular average measurement, from ri.SampleUValues

```python
standardJSON = ri.readJSON(str(today) + " TUTORIAL Standard Stochastic.json")
processStandard = ri.readComputedData(standardJSON, error = 0, theory = predictedMeasurement)

sampleJSON = ri.readJSON(str(today) + " TUTORIAL Sample Stochastic.json")
processSample = ri.readComputedData(sampleJSON, error = 0)
UValuesSmp = ri.readComputedUValues(sampleJSON, error = 0)
```

```python
processStandard
```

    {'M1': {'full': {'Subs': ['D', '15N', '17O', '13C'],
       'Predicted Abundance': [0.03246510641983099,
        0.09577373138104994,
        0.019795669505800258,
        0.8519654926933189],
       'Observed Abundance': [0.03246510641983099,
        0.09577373138104994,
        0.019795669505800258,
        0.8519654926933189],
       'Error': [0.0, 0.0, 0.0, 0.0]},
      '44': {'Subs': ['Unsub', 'D', '15N', '13C'],
       'Predicted Abundance': [0.3119004436751976,
        0.024348829814873244,
        0.09577373138104994,
        0.5679769951288792],
       'Observed Abundance': [0.3119004436751976,
        0.024348829814873244,
        0.09577373138104994,
        0.5679769951288792],
       'Error': [0.0, 0.0, 0.0, 0.0]}}}

Now, we set up the matrix inversion problem to find site-specific information. At this point, it would be useful to review the theory paper's description of this process. Computationally, we first determine which isotopologues were introduced via this experiment and track where they appear in the different fragments. We include a "precise identity" specifying in words which isotopologue these correspond to.

```python
MNKey = "M1"
isotopologuesDict = fas.isotopologueDataFrame(MNDictStd, df)
Isotopologues = isotopologuesDict[MNKey]
Isotopologues
```

      Number
      Full
      Stochastic
      Mass
      Composition
      Stochastic U
      full_01 Identity
      full_01 Subs
      44_01 Identity
      44_01 Subs
      Precise Identity

      00100000000000
      1
      (0, 0)1(0, 0)0(0, 0, 0, 0, 0, 0)(0, 0)
      0.01045
      1
      13C
      0.0109
      00100000000000
      13C
      00xxx0000000xx
      Unsub
      13C Ccarboxyl

      01000000000000
      2
      (0, 1)0(0, 0)0(0, 0, 0, 0, 0, 0)(0, 0)
      0.020899
      1
      13C
      0.0218
      01000000000000
      13C
      01xxx0000000xx
      13C
      13C Calphabeta

      00000100000000
      1
      (0, 0)0(0, 0)1(0, 0, 0, 0, 0, 0)(0, 0)
      0.003524
      1
      15N
      0.003676
      00000100000000
      15N
      00xxx1000000xx
      15N
      15N Namine

      00001000000000
      2
      (0, 0)0(0, 1)0(0, 0, 0, 0, 0, 0)(0, 0)
      0.000728
      1
      17O
      0.00076
      00001000000000
      17O
      00xxx0000000xx
      Unsub
      17O Ocarboxyl

      00000000000001
      2
      (0, 0)0(0, 0)0(0, 0, 0, 0, 0, 0)(0, 1)
      0.000299
      1
      D
      0.000312
      00000000000001
      D
      00xxx0000000xx
      Unsub
      D Hlost

      00000000000100
      6
      (0, 0)0(0, 0)0(0, 0, 0, 0, 0, 1)(0, 0)
      0.000896
      1
      D
      0.000935
      00000000000100
      D
      00xxx0000001xx
      D
      D Hretained

Next, we define "O value correction factors". We don't discuss these in detail here; briefly, they correct for instances when we do not see all of the M+N relative abundance associated with a fragment, e.g. because we do not observe certain low abundance ion beams. See the Appendix for a detailed discussion.

```python
OCorrection = ss.OValueCorrectTheoretical(predictedMeasurement, processSample, massThreshold = 1)
```

```python
OCorrection
```

    {'M1': {'full': 1.0, '44': 1.0}}

To solve and propagate error, we perform a monte carlo routine. We will go through the steps of this routine now (compare cf. solveSystem.M1MonteCarlo)

First, we perturb our O factors (again, see Appendix). We then perturb our standard based on their observed errors. Following perturbation, we calculate correction factors by taking the ratio between the perturbed and predicted abundance.

```python
variableOCorrect = copy.deepcopy(OCorrection)
```

```python
variableOCorrect = ss.modifyOValueCorrection(OCorrection, variableOCorrect, MNKey, amount = 0)
std = ss.perturbStandard(processStandard, theory = True)
```

```python
std
```

    {'M1': {'full': {'Subs': ['D', '15N', '17O', '13C'],
       'Predicted Abundance': [0.03246510641983099,
        0.09577373138104994,
        0.019795669505800258,
        0.8519654926933189],
       'Observed Abundance': [0.03246510641983099,
        0.09577373138104994,
        0.019795669505800258,
        0.8519654926933189],
       'Error': [0.0, 0.0, 0.0, 0.0],
       'Perturbed': array([0.03246511, 0.09577373, 0.01979567, 0.85196549]),
       'Correction Factor': array([1., 1., 1., 1.])},
      '44': {'Subs': ['Unsub', 'D', '15N', '13C'],
       'Predicted Abundance': [0.3119004436751976,
        0.024348829814873244,
        0.09577373138104994,
        0.5679769951288792],
       'Observed Abundance': [0.3119004436751976,
        0.024348829814873244,
        0.09577373138104994,
        0.5679769951288792],
       'Error': [0.0, 0.0, 0.0, 0.0],
       'Perturbed': array([0.31190044, 0.02434883, 0.09577373, 0.567977  ]),
       'Correction Factor': array([1., 1., 1., 1.])}}}

Next, we perturb our sample. This process has a few subroutines; we first discuss those, then show how they are run in a single function. Our first subroutine perturbs based on experimental error, as is done with the standard. See solveSystem.perturbSample

```python
perturbSample = ss.perturbSampleError(processSample)
perturbSample
```

    {'M1': {'full': {'Observed Abundance': array([0.03349737, 0.09509673, 0.01985428, 0.85155163]),
       'Subs': ['D', '15N', '17O', '13C']},
      '44': {'Observed Abundance': array([0.31608592, 0.02503145, 0.09509673, 0.5637859 ]),
       'Subs': ['Unsub', 'D', '15N', '13C']}}}

Next, we apply correction factors calculated from the standard to the sample. Renormalize should be set to be True, to remove the "W" factor discussed in the Appendix.

```python
correctedSample = ss.perturbSampleCorrectionFactors(perturbSample, std, renormalize = True)
correctedSample
```

    {'M1': {'full': {'Observed Abundance': array([0.03349737, 0.09509673, 0.01985428, 0.85155163]),
       'Subs': ['D', '15N', '17O', '13C']},
      '44': {'Observed Abundance': array([0.31608592, 0.02503145, 0.09509673, 0.5637859 ]),
       'Subs': ['Unsub', 'D', '15N', '13C']}}}

Finally, we apply our U Value correction factors, scaling our observations based on the hypothesized abundances of unobserved peaks. The output of this function gives the data we will use for the matrix routine.

```python
OCorrectedSample = ss.perturbSampleOCorrection(correctedSample, variableOCorrect)
OCorrectedSample
```

    {'M1': {'full': {'Observed Abundance': array([0.03349737, 0.09509673, 0.01985428, 0.85155163]),
       'Subs': ['D', '15N', '17O', '13C']},
      '44': {'Observed Abundance': array([0.31608592, 0.02503145, 0.09509673, 0.5637859 ]),
       'Subs': ['Unsub', 'D', '15N', '13C']}}}

Rather than run these functions individually each time, we have a parent function which deals with all of the sample perturbation. This function additionally processes the UValueCorrectedSample variables to give dataframes, and allows us to procedurally turn on or off different correction factors. Advanced users can go into more detail with these by reading the relevant sections of the paper and looking at the function description.

The M1 entry includes a corrected, standardized relative abundance for each observed ion beam.

```python
smp = ss.perturbSample(processSample, std, variableOCorrect, experimentalOCorrectList = [])['M1']
smp
```

      full
      44

      D
      0.033497
      0.025031

      15N
      0.095097
      0.095097

      17O
      0.019854
      0.000000

      13C
      0.851552
      0.563786

      Unsub
      0.000000
      0.316086

Next, we use knowledge of which isotopologues fragment to yield which substitutions and the corrected, standardized relative abundances to set up the matrix problem we hope to invert. The "comp" variable gives the composition matrix, specifying how each isotopologue is sampled in each observation. The columns of this matrix correspond to the Isotopologues in the Isotopologues dataframe; the first column is 13C Ccarboxyl, the second is 13C Calphabeta, and so forth. The rows refer to different observations; the first gives closure, then the second gives the full.D observation, the third gives full.15N, the fourth full.17O, and the fifth full.13C; the pattern repeats for the 44 peak. The rows of the "meas" vector are given in the same way.

```python
comp, meas = ss.constructMatrix(Isotopologues, smp, MNKey, fragmentationDictionary)
```

```python
sy.Matrix(comp)
```

$\displaystyle \left[\begin{matrix}1.0 & 1.0 & 1.0 & 1.0 & 1.0 & 1.0\\0 & 0 & 0 & 0 & 1.0 & 1.0\\0 & 0 & 1.0 & 0 & 0 & 0\\0 & 0 & 0 & 1.0 & 0 & 0\\1.0 & 1.0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1.0\\0 & 0 & 1.0 & 0 & 0 & 0\\0 & 1.0 & 0 & 0 & 0 & 0\\1.0 & 0 & 0 & 1.0 & 1.0 & 0\end{matrix}\right]$

```python
sy.Matrix(meas)
```

$\displaystyle \left[\begin{matrix}1.0\\0.033497365197376\\0.095096727401987\\0.0198542809707603\\0.851551626429877\\0.0250314454391084\\0.095096727401987\\0.563785904394953\\0.316085922763952\end{matrix}\right]$

We can solve this matrix inversion multiple ways. First, we can use the np.linalg.lstsq routine, which is most useful for fully constrained systems. Alternatively, we can run a Gauss-Jordan elimination algorithm; this is useful for underconstrained systems, as it can help us determine which individual isotopologues are unsolved for, and which are well constrained.

```python
sol = np.linalg.lstsq(comp, meas, rcond = -1)
sol[0]
```

    array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
           0.02503145])

```python
AugMatrix = np.column_stack((comp, meas))
solve = ss.GJElim(AugMatrix, augMatrix = True)
sy.Matrix(solve[0])
```

$\displaystyle \left[\begin{matrix}1.0 & 0 & 0 & 0 & 0 & 0 & 0.287765722034924\\0 & 1.0 & 0 & 0 & 0 & 0 & 0.563785904394953\\0 & 0 & 1.0 & 0 & 0 & 0 & 0.095096727401987\\0 & 0 & 0 & 1.0 & 0 & 0 & 0.0198542809707603\\0 & 0 & 0 & 0 & 1.0 & 0 & 0.00846591975826753\\0 & 0 & 0 & 0 & 0 & 1.0 & 0.0250314454391084\\0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 3.46944695195361 \cdot 10^{-17}\\0 & 0 & 0 & 0 & 0 & 0 & 1.2490009027033 \cdot 10^{-16}\end{matrix}\right]$

This entire process is performed by the M1MonteCarlo function, which perturbs U Values, standard, and sample, then solves the system, for N steps. The options GJ and debugMatrix can both be set to True in order to see output from every step of the GJ Solution, which may help advanced users troubleshoot. They should look at the code to see exactly what this function is outputting in that case.

```python
M1Results = ss.M1MonteCarlo(processStandard, processSample, OCorrection, isotopologuesDict,
                            fragmentationDictionary,
                            N = 100, GJ = False, debugMatrix = False,
                            perturbTheoryOAmt = 0)
```

    100%|███████████████████████████████████████████████████████████████████████████████| 100/100 [00:00<00:00, 346.95it/s]

```python
M1Results
```

    {'GJ': [],
     'NUMPY': [array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145]),
      array([0.28776572, 0.5637859 , 0.09509673, 0.01985428, 0.00846592,
             0.02503145])],
     'Extra Info': {'Perturbed Samples': [],
      'O Correct': [],
      'StoreExpFactors': []}}

Next, we need to process these results and make sense of them. The key mathematical step here is going from M+N relative abundance space (where our solution is now) into U Value space, making use of the U^M+N variable. We encourage the user to review the relevant parts of the theory paper here. We will perform all of these steps for each solution to the Monte Carlo process; as an example, we take one solution and demonstrate the process.

We first take all the isotopologues that were introduced and assign their percent abundances from the solution.

```python
out = isotopologuesDict['M1'][['Number','Stochastic','Composition','Stochastic U','Precise Identity']].copy()
out[MNKey + ' M+N Relative Abundance'] = M1Results['NUMPY'][0]
out
```

      Number
      Stochastic
      Composition
      Stochastic U
      Precise Identity
      M1 M+N Relative Abundance

      00100000000000
      1
      0.01045
      13C
      0.0109
      13C Ccarboxyl
      0.287766

      01000000000000
      2
      0.020899
      13C
      0.0218
      13C Calphabeta
      0.563786

      00000100000000
      1
      0.003524
      15N
      0.003676
      15N Namine
      0.095097

      00001000000000
      2
      0.000728
      17O
      0.00076
      17O Ocarboxyl
      0.019854

      00000000000001
      2
      0.000299
      D
      0.000312
      D Hlost
      0.008466

      00000000000100
      6
      0.000896
      D
      0.000935
      D Hretained
      0.025031

Then, we calculate the U^M+1 value. The process for this is elaborated in the M+N theory paper; briefly, we take the observed U Value for some isotope of interest and divide by the sum of the percent abundances of all isotopologues with that isotopic composition. For example, we would take the 13C U value and divide by the M1 M+N Relative Abundance of 13C Ccarboxyl + 13C Calphabeta.

We may do this for multiple substitutions; the ones we will do it for are determined by the UMNSub parameter, a list of U Values to use. If we calculate it multiple ways, we take the average and use this as our U^M+1.

```python
#Perturb U Values
UPerturb = ss.PerturbUValue(UValuesSmp)

#Calculate UM1
UM1 = ss.calcUMN(MNKey, out, UPerturb, UMNSub = ['13C'])
out['UM1'] = UM1
out['Calc U Values'] = out[MNKey + ' M+N Relative Abundance'] * out['UM1']
out
```

      Number
      Stochastic
      Composition
      Stochastic U
      Precise Identity
      M1 M+N Relative Abundance
      UM1
      Calc U Values

      00100000000000
      1
      0.01045
      13C
      0.0109
      13C Ccarboxyl
      0.287766
      0.038269
      0.011012

      01000000000000
      2
      0.020899
      13C
      0.0218
      13C Calphabeta
      0.563786
      0.038269
      0.021575

      00000100000000
      1
      0.003524
      15N
      0.003676
      15N Namine
      0.095097
      0.038269
      0.003639

      00001000000000
      2
      0.000728
      17O
      0.00076
      17O Ocarboxyl
      0.019854
      0.038269
      0.000760

      00000000000001
      2
      0.000299
      D
      0.000312
      D Hlost
      0.008466
      0.038269
      0.000324

      00000000000100
      6
      0.000896
      D
      0.000935
      D Hretained
      0.025031
      0.038269
      0.000958

We can compute delta values directly using the Isotopologues dataframe. But it would be convenient to calculate them for our initial input dataframe, which lists the sites in a different order. So we next process this information to follow the same order as our input dataframe. Then we normalize fo the number of atoms, and compute both the absolute delta in VPDB etc. space and the relative sample standard delta. The "absolute delta" will generally be incorrect unless we have perfect knowledge of the standard; the relative delta will generally be accurate.

Keep in mind that relative deltas are not directly additive--if the sample is -40, and the standard is -30, the relative delta will not be precisely -10!

```python
#This section reassigns the solutions of the isotopologues dataframe to the right order for the
#site-specific dataframe
M1 = [0] * len(out.index)
UM1 = [0] * len(out.index)
U = [0] * len(out.index)
for i, v in out.iterrows():
    identity = v['Precise Identity'].split(' ')[1]
    index = list(df.index).index(identity)

    M1[index] = v[MNKey + ' M+N Relative Abundance']
    UM1[index] = v['UM1']
    U[index] = v['Calc U Values']

#calculate relevant information
normM1 = U / df['Number']
#This gives deltas in absolute reference frame
smpDeltasAbs = [op.ratioToDelta(x,y) for x, y in zip(df['IDS'], normM1)]

appxStd = df['deltas']

#This gives deltas relative to standard
relSmpStdDeltas = [op.compareRelDelta(atomID, delta1, delta2) for atomID, delta1, delta2 in zip(df['IDS'], appxStd, smpDeltasAbs)]

relSmpStdDeltas
```

    [-10.309278350514983,
     10.309278350514983,
     -4.440892098500626e-12,
     -9.999999999998789,
     24.999999999990585,
     39.99999999998649]

As before, we define a single function that takes care of all of this, repeating the process for the N results from the Monte Carlo model.

```python
processedResults = ss.processM1MCResults(M1Results, UValuesSmp, isotopologuesDict, df,
                                         UMNSub = ['13C'])
```

    100%|███████████████████████████████████████████████████████████████████████████████| 100/100 [00:00<00:00, 470.57it/s]

```python
processedResults
```

    {'PDB etc. Deltas': [[-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671],
      [-39.99999999999948,
       -20.000000000000682,
       -4.551914400963142e-12,
       -9.999999999998677,
       24.999999999990365,
       39.99999999998671]],
     'Relative Deltas': [[-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649],
      [-10.309278350514983,
       10.309278350514983,
       -4.440892098500626e-12,
       -9.999999999998789,
       24.999999999990585,
       39.99999999998649]],
     'M1 M+N Relative Abundance': [[0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468],
      [0.5637859043949535,
       0.2877657220349238,
       0.019854280970760228,
       0.0950967274019872,
       0.025031445439108225,
       0.008465919758267468]],
     'UM1': [[0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976],
      [0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976,
       0.038268824799999976]],
     'Calc U Values': [[0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959],
      [0.02157542400000001,
       0.011012455999999992,
       0.0007597999999999966,
       0.003639240000000005,
       0.0009579239999999911,
       0.0003239807999999959]]}

Finally, we update the original dataframe with these answers, calculating means and errors (standard deviations) for each value.

```python
ss.updateSiteSpecificDfM1MC(processedResults, df)
```

      IDS
      Number
      deltas
      full_01
      44_01
      PDB etc. Deltas
      PDB etc. Deltas Error
      Relative Deltas
      Relative Deltas Error
      M1 M+N Relative Abundance
      M1 M+N Relative Abundance Error
      UM1
      UM1 Error
      Calc U Values
      Calc U Values Error

      Calphabeta
      C
      2
      -30
      1
      1
      -4.000000e+01
      4.263256e-14
      -1.030928e+01
      1.065814e-14
      0.563786
      7.771561e-16
      0.038269
      6.245005e-17
      0.021575
      5.898060e-17

      Ccarboxyl
      C
      1
      -30
      1
      x
      -2.000000e+01
      0.000000e+00
      1.030928e+01
      1.065814e-14
      0.287766
      2.775558e-16
      0.038269
      6.245005e-17
      0.011012
      1.040834e-17

      Ocarboxyl
      O
      2
      0
      1
      x
      -4.551914e-12
      0.000000e+00
      -4.440892e-12
      0.000000e+00
      0.019854
      2.081668e-17
      0.038269
      6.245005e-17
      0.000760
      1.084202e-19

      Namine
      N
      1
      0
      1
      1
      -1.000000e+01
      1.776357e-14
      -1.000000e+01
      1.598721e-14
      0.095097
      1.249001e-16
      0.038269
      6.245005e-17
      0.003639
      2.602085e-18

      Hretained
      H
      6
      0
      1
      1
      2.500000e+01
      3.907985e-14
      2.500000e+01
      7.105427e-15
      0.025031
      1.387779e-17
      0.038269
      6.245005e-17
      0.000958
      1.626303e-18

      Hlost
      H
      2
      0
      1
      x
      4.000000e+01
      7.105427e-14
      4.000000e+01
      4.263256e-14
      0.008466
      1.734723e-17
      0.038269
      6.245005e-17
      0.000324
      3.252607e-19