VerticaPy
Python API for Vertica Data Science at Scale
Best Practices¶
As with all software, VerticaPy has a performance cost. To get the best performance, we need to understand the architectures of Vertica and VerticaPy. In this lesson, we'll go through some optimization steps.
1. Optimize your architecture at the database-level¶
At the end of the day, VerticaPy is an abstraction of SQL, so any database-level optimizations you make carry over to VerticaPy.
Optimizing Vertica mostly comes down to optimizing projections. Think in advance about your data architecture before creating a vDataFrame so we only select the essential columns.
In the following example, we use the 'usecols' parameter of the vDataFrame to select the most essential columns in our dataset.
In [13]:
import verticapy as vp
from verticapy.datasets import load_titanic
load_titanic() # loading the dataset in Vertica in case we do not have it
vdf = vp.vDataFrame("public.titanic",
usecols = ["survived", "pclass", "age"])
display(vdf)
 | 123 pclassInt | 123 survivedInt | 123 ageNumeric(6,3) |
| 1 | 1 | 0 | 2.0 |
| 2 | 1 | 0 | 30.0 |
| 3 | 1 | 0 | 25.0 |
| 4 | 1 | 0 | 39.0 |
| 5 | 1 | 0 | 71.0 |
| 6 | 1 | 0 | 47.0 |
| 7 | 1 | 0 | [null] |
| 8 | 1 | 0 | 24.0 |
| 9 | 1 | 0 | 36.0 |
| 10 | 1 | 0 | 25.0 |
| 11 | 1 | 0 | 45.0 |
| 12 | 1 | 0 | 42.0 |
| 13 | 1 | 0 | 41.0 |
| 14 | 1 | 0 | 48.0 |
| 15 | 1 | 0 | [null] |
| 16 | 1 | 0 | 45.0 |
| 17 | 1 | 0 | [null] |
| 18 | 1 | 0 | 33.0 |
| 19 | 1 | 0 | 28.0 |
| 20 | 1 | 0 | 17.0 |
| 21 | 1 | 0 | 49.0 |
| 22 | 1 | 0 | 36.0 |
| 23 | 1 | 0 | 46.0 |
| 24 | 1 | 0 | [null] |
| 25 | 1 | 0 | 27.0 |
| 26 | 1 | 0 | [null] |
| 27 | 1 | 0 | 47.0 |
| 28 | 1 | 0 | 37.0 |
| 29 | 1 | 0 | [null] |
| 30 | 1 | 0 | 70.0 |
| 31 | 1 | 0 | 39.0 |
| 32 | 1 | 0 | 31.0 |
| 33 | 1 | 0 | 50.0 |
| 34 | 1 | 0 | 39.0 |
| 35 | 1 | 0 | 36.0 |
| 36 | 1 | 0 | [null] |
| 37 | 1 | 0 | 30.0 |
| 38 | 1 | 0 | 19.0 |
| 39 | 1 | 0 | 64.0 |
| 40 | 1 | 0 | [null] |
| 41 | 1 | 0 | [null] |
| 42 | 1 | 0 | 37.0 |
| 43 | 1 | 0 | 47.0 |
| 44 | 1 | 0 | 24.0 |
| 45 | 1 | 0 | 71.0 |
| 46 | 1 | 0 | 38.0 |
| 47 | 1 | 0 | 46.0 |
| 48 | 1 | 0 | [null] |
| 49 | 1 | 0 | 45.0 |
| 50 | 1 | 0 | 40.0 |
| 51 | 1 | 0 | 55.0 |
| 52 | 1 | 0 | 42.0 |
| 53 | 1 | 0 | [null] |
| 54 | 1 | 0 | 55.0 |
| 55 | 1 | 0 | 42.0 |
| 56 | 1 | 0 | [null] |
| 57 | 1 | 0 | 50.0 |
| 58 | 1 | 0 | 46.0 |
| 59 | 1 | 0 | 50.0 |
| 60 | 1 | 0 | 32.5 |
| 61 | 1 | 0 | 58.0 |
| 62 | 1 | 0 | 41.0 |
| 63 | 1 | 0 | [null] |
| 64 | 1 | 0 | [null] |
| 65 | 1 | 0 | 29.0 |
| 66 | 1 | 0 | 30.0 |
| 67 | 1 | 0 | 30.0 |
| 68 | 1 | 0 | 19.0 |
| 69 | 1 | 0 | 46.0 |
| 70 | 1 | 0 | 54.0 |
| 71 | 1 | 0 | 28.0 |
| 72 | 1 | 0 | 65.0 |
| 73 | 1 | 0 | 44.0 |
| 74 | 1 | 0 | 55.0 |
| 75 | 1 | 0 | 47.0 |
| 76 | 1 | 0 | 37.0 |
| 77 | 1 | 0 | 58.0 |
| 78 | 1 | 0 | 64.0 |
| 79 | 1 | 0 | 65.0 |
| 80 | 1 | 0 | 28.5 |
| 81 | 1 | 0 | [null] |
| 82 | 1 | 0 | 45.5 |
| 83 | 1 | 0 | 23.0 |
| 84 | 1 | 0 | 29.0 |
| 85 | 1 | 0 | 18.0 |
| 86 | 1 | 0 | 47.0 |
| 87 | 1 | 0 | 38.0 |
| 88 | 1 | 0 | 22.0 |
| 89 | 1 | 0 | [null] |
| 90 | 1 | 0 | 31.0 |
| 91 | 1 | 0 | [null] |
| 92 | 1 | 0 | 36.0 |
| 93 | 1 | 0 | 55.0 |
| 94 | 1 | 0 | 33.0 |
| 95 | 1 | 0 | 61.0 |
| 96 | 1 | 0 | 50.0 |
| 97 | 1 | 0 | 56.0 |
| 98 | 1 | 0 | 56.0 |
| 99 | 1 | 0 | 24.0 |
| 100 | 1 | 0 | [null] |
Rows: 1-100 | Columns: 3
2. Save the current relation when you can¶
The vDataFrame works just like a view. If the final generated relation uses a lot of different functions, it will drastically increase the computation time for each method call.
Smaller transformations won't slow down the process much, but heavier transformations (multiple joins, heavy use of advanced analytical funcions, moving windows, etc.) can cause noticeable slowdown. If you make these kinds of changes, you should save the vDataFrame structure. Let's look at an example.
In [14]:
# Doing multiple operation
vdf = vp.vDataFrame("public.titanic")
vdf["sex"].label_encode()["boat"].fillna(method = "0ifnull")["name"].str_extract(
' ([A-Za-z]+)\.').eval("family_size", expr = "parch + sibsp + 1").drop(
columns = ["cabin", "body", "ticket", "home.dest"])["fare"].fill_outliers().fillna()
print(vdf.current_relation())
We can look at the query plan of the new relation. This will help us understand how Vertica will execute the different aggregations.
In [15]:
print(vdf.explain())
We did plenty of operations and we must keep in mind that each method call will use this relation for its computations. We can save the result as a table in the Vertica database and use the parameter 'inplace' to change the current relation of the vDataFrame by the new one.
In [17]:
vp.drop("public.titanic_clean", method = "table")
vdf.to_db("public.titanic_clean",
relation_type = "table",
inplace = True)
print(vdf.current_relation())
When we're dealing with very large datasets, we have to think a bit before saving some transformations. Ideally, you'll want to do a proper data exploration first and then perform the heavier transformations only when they're really neeed.
3. Stick to essential columns¶
Columnar databases perform faster queries when there are fewer columns. Since Vertica is a columnar MPP database, so it's important to understand that most of the optimizations are made in projections. VerticaPy doesn't manage this part, so it's important that the data you're working with is well-organized, particularly for larger volumes of data.
Most vDataFrame methods will automatically pick up all numerical columns - even if doing so has a significant performance impact - so it's important to be a little picky and only select the essential columns for any given use case. Let's look at an example.
In [23]:
vdf = vp.vDataFrame("public.titanic")
vp.set_option("sql_on", True)
vdf.avg()
Out[23]:
| avg |
| "pclass" | 2.28444084278768 |
| "survived" | 0.364667747163695 |
| "age" | 30.1524573721163 |
| "sibsp" | 0.504051863857374 |
| "parch" | 0.378444084278768 |
| "fare" | 33.9637936739659 |
| "body" | 164.14406779661 |
Rows: 1-7 | Columns: 2
Here, we didn't use the 'columns' parameter to pick on any specific columns, so we ended up computing the average of all the numerical columns of the vDataFrame. This isn't a big deal when we're dealing with smaller volumes of data (less than a TB), but with larger volumes of data, we have to be more careful with which columns we use.
In [24]:
vdf.avg(columns = ["age", "survived"])
Out[24]:
| avg |
| "age" | 30.1524573721163 |
| "survived" | 0.364667747163695 |
Rows: 1-2 | Columns: 2
If you just want to exclude a few columns, you can simply get a list of all the columns and specify the unwanted columns with the 'get_columns' method.
In [25]:
vdf.get_columns()
Out[25]:
In [26]:
vdf.get_columns(exclude_columns = ["boat", "embarked"])
Out[26]:
If you only want numerical columns, you can use the 'numcol'. This works the same way as 'get_columns', so you can also exclude columns in the same way.
In [27]:
vdf.numcol()
Out[27]:
In [28]:
vdf.numcol(exclude_columns = ["body", "sibsp"])
Out[28]:
Let's compute a correlation matrix of our numerical columns excluding 'body' and 'sibsp'.
In [29]:
vdf.corr(columns = vdf.numcol(exclude_columns = ["parch", "sibsp"]))
Out[29]:
| "pclass" | "survived" | "age" | "fare" | "body" |
| "pclass" | 1.0 | -0.335856950271864 | -0.400828642351015 | -0.561687581153705 | -0.0472355333131433 |
| "survived" | -0.335856950271864 | 1.0 | -0.0422446185581737 | 0.264150360783869 | [null] |
| "age" | -0.400828642351015 | -0.0422446185581737 | 1.0 | 0.178575164117464 | 0.0581765649177871 |
| "fare" | -0.561687581153705 | 0.264150360783869 | 0.178575164117464 | 1.0 | -0.0372842548942878 |
| "body" | -0.0472355333131433 | [null] | 0.0581765649177871 | -0.0372842548942878 | 1.0 |
Rows: 1-5 | Columns: 6
Let's turn off the SQL code generation.
In [30]:
vp.set_option("sql_on", False)
4. Use the help function¶
The 'help' function is very useful for quickly viewing parameters.
In [31]:
help(vdf.agg)
5. Close your connections¶
More connections to the database will increase the concurrency on the system, so try to close all of your connections after using them. VerticaPy simplifies the connection process by allowing the user to create an auto-connection, but it will not close it until you use the 'close_connection' function.
To demonstrate, let's create a database connection. Once we're done, we'll close it.
In [32]:
import verticapy as vp
vp.connect("VerticaDSN")
We can use it to create a vDataFrame perform some operations on the data.
In [34]:
vdf = vp.vDataFrame("public.titanic")
vdf["sex"].label_encode()["boat"].fillna(method = "0ifnull")["name"].str_extract(
' ([A-Za-z]+)\.').eval("family_size", expr = "parch + sibsp + 1").drop(
columns = ["cabin", "body", "ticket", "home.dest"])["fare"].fill_outliers().fillna()
Out[34]:
| 123 pclassInt | 123 survivedInt | Abc nameVarchar(164) | 123 sexInt | 123 ageFloat | 123 sibspInt | 123 parchInt | 123 fareFloat | Abc embarkedVarchar(20) | 123 boatBool | 123 family_sizeInteger |
| 1 | 1 | 0 | Miss. | 0 | 2.0 | 1 | 2 | 151.55 | S | 0 | 4 |
| 2 | 1 | 0 | Mr. | 1 | 30.0 | 1 | 2 | 151.55 | S | 0 | 4 |
| 3 | 1 | 0 | Mrs. | 0 | 25.0 | 1 | 2 | 151.55 | S | 0 | 4 |
| 4 | 1 | 0 | Mr. | 1 | 39.0 | 0 | 0 | 0.0 | S | 0 | 1 |
| 5 | 1 | 0 | Mr. | 1 | 71.0 | 0 | 0 | 49.5042 | C | 0 | 1 |
| 6 | 1 | 0 | Col. | 1 | 47.0 | 1 | 0 | 227.525 | C | 0 | 2 |
| 7 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 25.925 | S | 0 | 1 |
| 8 | 1 | 0 | Mr. | 1 | 24.0 | 0 | 1 | 244.5480856064831 | C | 0 | 2 |
| 9 | 1 | 0 | Mr. | 1 | 36.0 | 0 | 0 | 75.2417 | C | 1 | 1 |
| 10 | 1 | 0 | Mr. | 1 | 25.0 | 0 | 0 | 26.0 | C | 0 | 1 |
| 11 | 1 | 0 | Mr. | 1 | 45.0 | 0 | 0 | 35.5 | S | 0 | 1 |
| 12 | 1 | 0 | Mr. | 1 | 42.0 | 0 | 0 | 26.55 | S | 0 | 1 |
| 13 | 1 | 0 | Mr. | 1 | 41.0 | 0 | 0 | 30.5 | S | 0 | 1 |
| 14 | 1 | 0 | Mr. | 1 | 48.0 | 0 | 0 | 50.4958 | C | 0 | 1 |
| 15 | 1 | 0 | Dr. | 1 | 30.1524573721163 | 0 | 0 | 39.6 | C | 0 | 1 |
| 16 | 1 | 0 | Major. | 1 | 45.0 | 0 | 0 | 26.55 | S | 0 | 1 |
| 17 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 31.0 | S | 0 | 1 |
| 18 | 1 | 0 | Mr. | 1 | 33.0 | 0 | 0 | 5.0 | S | 0 | 1 |
| 19 | 1 | 0 | Mr. | 1 | 28.0 | 0 | 0 | 47.1 | S | 0 | 1 |
| 20 | 1 | 0 | Mr. | 1 | 17.0 | 0 | 0 | 47.1 | S | 0 | 1 |
| 21 | 1 | 0 | Mr. | 1 | 49.0 | 0 | 0 | 26.0 | S | 0 | 1 |
| 22 | 1 | 0 | Mr. | 1 | 36.0 | 1 | 0 | 78.85 | S | 0 | 2 |
| 23 | 1 | 0 | Mr. | 1 | 46.0 | 1 | 0 | 61.175 | S | 0 | 2 |
| 24 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 0.0 | S | 0 | 1 |
| 25 | 1 | 0 | Mr. | 1 | 27.0 | 1 | 0 | 136.7792 | C | 0 | 2 |
| 26 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 52.0 | S | 0 | 1 |
| 27 | 1 | 0 | Mr. | 1 | 47.0 | 0 | 0 | 25.5875 | S | 0 | 1 |
| 28 | 1 | 0 | Mr. | 1 | 37.0 | 1 | 1 | 83.1583 | C | 0 | 3 |
| 29 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 26.55 | S | 0 | 1 |
| 30 | 1 | 0 | Capt. | 1 | 70.0 | 1 | 1 | 71.0 | S | 0 | 3 |
| 31 | 1 | 0 | Mr. | 1 | 39.0 | 1 | 0 | 71.2833 | C | 0 | 2 |
| 32 | 1 | 0 | Mr. | 1 | 31.0 | 1 | 0 | 52.0 | S | 0 | 2 |
| 33 | 1 | 0 | Mr. | 1 | 50.0 | 1 | 0 | 106.425 | C | 0 | 2 |
| 34 | 1 | 0 | Mr. | 1 | 39.0 | 0 | 0 | 29.7 | C | 0 | 1 |
| 35 | 1 | 0 | Miss. | 0 | 36.0 | 0 | 0 | 31.6792 | C | 0 | 1 |
| 36 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 221.7792 | S | 0 | 1 |
| 37 | 1 | 0 | Mr. | 1 | 30.0 | 0 | 0 | 27.75 | C | 0 | 1 |
| 38 | 1 | 0 | Mr. | 1 | 19.0 | 3 | 2 | 244.5480856064831 | S | 0 | 6 |
| 39 | 1 | 0 | Mr. | 1 | 64.0 | 1 | 4 | 244.5480856064831 | S | 0 | 6 |
| 40 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 26.55 | S | 0 | 1 |
| 41 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 0.0 | S | 0 | 1 |
| 42 | 1 | 0 | Mr. | 1 | 37.0 | 1 | 0 | 53.1 | S | 0 | 2 |
| 43 | 1 | 0 | Mr. | 1 | 47.0 | 0 | 0 | 38.5 | S | 0 | 1 |
| 44 | 1 | 0 | Mr. | 1 | 24.0 | 0 | 0 | 79.2 | C | 0 | 1 |
| 45 | 1 | 0 | Mr. | 1 | 71.0 | 0 | 0 | 34.6542 | C | 0 | 1 |
| 46 | 1 | 0 | Mr. | 1 | 38.0 | 0 | 1 | 153.4625 | S | 0 | 2 |
| 47 | 1 | 0 | Mr. | 1 | 46.0 | 0 | 0 | 79.2 | C | 0 | 1 |
| 48 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 42.4 | S | 0 | 1 |
| 49 | 1 | 0 | Mr. | 1 | 45.0 | 1 | 0 | 83.475 | S | 0 | 2 |
| 50 | 1 | 0 | Mr. | 1 | 40.0 | 0 | 0 | 0.0 | S | 0 | 1 |
| 51 | 1 | 0 | Mr. | 1 | 55.0 | 1 | 1 | 93.5 | S | 0 | 3 |
| 52 | 1 | 0 | Mr. | 1 | 42.0 | 0 | 0 | 42.5 | S | 0 | 1 |
| 53 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 51.8625 | S | 0 | 1 |
| 54 | 1 | 0 | Mr. | 1 | 55.0 | 0 | 0 | 50.0 | S | 0 | 1 |
| 55 | 1 | 0 | Mr. | 1 | 42.0 | 1 | 0 | 52.0 | S | 0 | 2 |
| 56 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 30.6958 | C | 1 | 1 |
| 57 | 1 | 0 | Miss. | 0 | 50.0 | 0 | 0 | 28.7125 | C | 0 | 1 |
| 58 | 1 | 0 | Mr. | 1 | 46.0 | 0 | 0 | 26.0 | S | 0 | 1 |
| 59 | 1 | 0 | Mr. | 1 | 50.0 | 0 | 0 | 26.0 | S | 0 | 1 |
| 60 | 1 | 0 | Mr. | 1 | 32.5 | 0 | 0 | 211.5 | C | 0 | 1 |
| 61 | 1 | 0 | Mr. | 1 | 58.0 | 0 | 0 | 29.7 | C | 0 | 1 |
| 62 | 1 | 0 | Mr. | 1 | 41.0 | 1 | 0 | 51.8625 | S | 0 | 2 |
| 63 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 26.55 | S | 0 | 1 |
| 64 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 27.7208 | C | 0 | 1 |
| 65 | 1 | 0 | Mr. | 1 | 29.0 | 0 | 0 | 30.0 | S | 0 | 1 |
| 66 | 1 | 0 | Mr. | 1 | 30.0 | 0 | 0 | 45.5 | S | 0 | 1 |
| 67 | 1 | 0 | Mr. | 1 | 30.0 | 0 | 0 | 26.0 | S | 0 | 1 |
| 68 | 1 | 0 | Mr. | 1 | 19.0 | 1 | 0 | 53.1 | S | 0 | 2 |
| 69 | 1 | 0 | Mr. | 1 | 46.0 | 0 | 0 | 75.2417 | C | 0 | 1 |
| 70 | 1 | 0 | Mr. | 1 | 54.0 | 0 | 0 | 51.8625 | S | 0 | 1 |
| 71 | 1 | 0 | Mr. | 1 | 28.0 | 1 | 0 | 82.1708 | C | 0 | 2 |
| 72 | 1 | 0 | Mr. | 1 | 65.0 | 0 | 0 | 26.55 | S | 0 | 1 |
| 73 | 1 | 0 | Dr. | 1 | 44.0 | 2 | 0 | 90.0 | Q | 0 | 3 |
| 74 | 1 | 0 | Mr. | 1 | 55.0 | 0 | 0 | 30.5 | S | 0 | 1 |
| 75 | 1 | 0 | Mr. | 1 | 47.0 | 0 | 0 | 42.4 | S | 0 | 1 |
| 76 | 1 | 0 | Mr. | 1 | 37.0 | 0 | 1 | 29.7 | C | 0 | 2 |
| 77 | 1 | 0 | Mr. | 1 | 58.0 | 0 | 2 | 113.275 | C | 0 | 3 |
| 78 | 1 | 0 | Mr. | 1 | 64.0 | 0 | 0 | 26.0 | S | 0 | 1 |
| 79 | 1 | 0 | Mr. | 1 | 65.0 | 0 | 1 | 61.9792 | C | 0 | 2 |
| 80 | 1 | 0 | Mr. | 1 | 28.5 | 0 | 0 | 27.7208 | C | 0 | 1 |
| 81 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 0.0 | S | 0 | 1 |
| 82 | 1 | 0 | Mr. | 1 | 45.5 | 0 | 0 | 28.5 | S | 0 | 1 |
| 83 | 1 | 0 | Mr. | 1 | 23.0 | 0 | 0 | 93.5 | S | 0 | 1 |
| 84 | 1 | 0 | Mr. | 1 | 29.0 | 1 | 0 | 66.6 | S | 0 | 2 |
| 85 | 1 | 0 | Mr. | 1 | 18.0 | 1 | 0 | 108.9 | C | 0 | 2 |
| 86 | 1 | 0 | Mr. | 1 | 47.0 | 0 | 0 | 52.0 | S | 0 | 1 |
| 87 | 1 | 0 | Jonkheer. | 1 | 38.0 | 0 | 0 | 0.0 | S | 0 | 1 |
| 88 | 1 | 0 | Mr. | 1 | 22.0 | 0 | 0 | 135.6333 | C | 0 | 1 |
| 89 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 227.525 | C | 0 | 1 |
| 90 | 1 | 0 | Mr. | 1 | 31.0 | 0 | 0 | 50.4958 | S | 0 | 1 |
| 91 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 50.0 | S | 0 | 1 |
| 92 | 1 | 0 | Mr. | 1 | 36.0 | 0 | 0 | 40.125 | C | 0 | 1 |
| 93 | 1 | 0 | Mr. | 1 | 55.0 | 1 | 0 | 59.4 | C | 0 | 2 |
| 94 | 1 | 0 | Mr. | 1 | 33.0 | 0 | 0 | 26.55 | S | 0 | 1 |
| 95 | 1 | 0 | Mr. | 1 | 61.0 | 1 | 3 | 244.5480856064831 | C | 0 | 5 |
| 96 | 1 | 0 | Mr. | 1 | 50.0 | 1 | 0 | 55.9 | S | 0 | 2 |
| 97 | 1 | 0 | Mr. | 1 | 56.0 | 0 | 0 | 26.55 | S | 0 | 1 |
| 98 | 1 | 0 | Mr. | 1 | 56.0 | 0 | 0 | 30.6958 | C | 0 | 1 |
| 99 | 1 | 0 | Mr. | 1 | 24.0 | 1 | 0 | 60.0 | S | 0 | 2 |
| 100 | 1 | 0 | Mr. | 1 | 30.1524573721163 | 0 | 0 | 26.0 | S | 0 | 1 |
Rows: 1-100 | Columns: 11
We can then close the connection when we are done.
In [35]:
vp.close_connection()
It is very important to follow the previous process when you are working in an environment with multiple users.
6. Understand the time complexity of methods¶
Some techniques are more computationally expensive than others. For example, a 'kendall' correlation is very expensive compared to a 'pearson' correlation. This is because a 'kendall' correlation uses a cross join, giving it a time complexity of O(n*n) (where 'n' is the number of rows). We'll demonstrate this with the 'titanic' dataset.
In [41]:
import time
vdf = vp.vDataFrame("public.titanic")
start_time = time.time()
x = vdf.corr(method = "pearson", show = False)
print("Pearson, time: {0}".format(time.time() - start_time))
start_time = time.time()
x = vdf.corr(method = "kendall", show = False)
print("Kendall, time: {0}".format(time.time() - start_time))
As you can see, a Kendall Correlation Matrix is noticeably slower (around 100 times more than Pearson) because of its time complexity. Keep this in mind when using methods on larger datasets.
7. Limit the number of elements in a plot¶
Graphics are a powerful way to understand data, but graphs can be difficult to parse if it has too many elements. Let's draw a multi-histogram where one column is categorical with thousands of categories.
In [42]:
vdf.hist(["name", "survived"])
Out[42]:
VerticaPy will try to draw it, but it could take time with a large dataset. Worse, it might be completely incomprehensible. Instead, we should try to create graphics with as few categories as possible.
In [43]:
vdf.hist(["pclass", "survived"])
Out[43]:
Try to always check the cardinality of your variables before creating graphics.
In [44]:
vdf.nunique()
Out[44]:
| approx_unique |
| "pclass" | 3.0 |
| "survived" | 2.0 |
| "name" | 1233.0 |
| "sex" | 2.0 |
| "age" | 96.0 |
| "sibsp" | 7.0 |
| "parch" | 8.0 |
| "ticket" | 888.0 |
| "fare" | 275.0 |
| "cabin" | 181.0 |
| "embarked" | 3.0 |
| "boat" | 26.0 |
| "body" | 118.0 |
| "home.dest" | 355.0 |
Rows: 1-14 | Columns: 2
8. Filter unneeded data¶
Filtering should be the first action you perform when you prepare your data. Proper filtering will help you avoid unnecessary computation and therefore drastically improve the performance of every method you call. While the performance impact isn't as important for small datasets, when working with large ones, you'll always want to filter your data in some way.
In the following example, our goal is to analyze the passengers on the Titanic that didn't have a lifeboat. Since we aren't concerned at all with passengers with a lifeboat, we can simply filter them out of the dataset and move on from there.
In [45]:
vdf.filter("boat IS NOT NULL")
Out[45]:
| 123 pclassInt | 123 survivedInt | Abc Varchar(164) | Abc sexVarchar(20) | 123 ageNumeric(6,3) | 123 sibspInt | 123 parchInt | Abc ticketVarchar(36) | 123 fareNumeric(10,5) | Abc cabinVarchar(30) | Abc embarkedVarchar(20) | Abc boatVarchar(100) | 123 bodyInt | Abc Varchar(100) |
| 1 | 1 | 0 | male | 36.0 | 0 | 0 | 13050 | 75.2417 | C6 | C | A | [null] | ||
| 2 | 1 | 0 | male | [null] | 0 | 0 | PC 17600 | 30.6958 | [null] | C | 14 | [null] | ||
| 3 | 1 | 1 | female | 29.0 | 0 | 0 | 24160 | 211.3375 | B5 | S | 2 | [null] | ||
| 4 | 1 | 1 | male | 0.92 | 1 | 2 | 113781 | 151.55 | C22 C26 | S | 11 | [null] | ||
| 5 | 1 | 1 | male | 48.0 | 0 | 0 | 19952 | 26.55 | E12 | S | 3 | [null] | ||
| 6 | 1 | 1 | female | 63.0 | 1 | 0 | 13502 | 77.9583 | D7 | S | 10 | [null] | ||
| 7 | 1 | 1 | female | 53.0 | 2 | 0 | 11769 | 51.4792 | C101 | S | D | [null] | ||
| 8 | 1 | 1 | female | 18.0 | 1 | 0 | PC 17757 | 227.525 | C62 C64 | C | 4 | [null] | ||
| 9 | 1 | 1 | female | 24.0 | 0 | 0 | PC 17477 | 69.3 | B35 | C | 9 | [null] | ||
| 10 | 1 | 1 | male | 80.0 | 0 | 0 | 27042 | 30.0 | A23 | S | B | [null] | ||
| 11 | 1 | 1 | female | 50.0 | 0 | 1 | PC 17558 | 247.5208 | B58 B60 | C | 6 | [null] | ||
| 12 | 1 | 1 | female | 32.0 | 0 | 0 | 11813 | 76.2917 | D15 | C | 8 | [null] | ||
| 13 | 1 | 1 | male | 37.0 | 1 | 1 | 11751 | 52.5542 | D35 | S | 5 | [null] | ||
| 14 | 1 | 1 | female | 47.0 | 1 | 1 | 11751 | 52.5542 | D35 | S | 5 | [null] | ||
| 15 | 1 | 1 | male | 26.0 | 0 | 0 | 111369 | 30.0 | C148 | C | 5 | [null] | ||
| 16 | 1 | 1 | female | 42.0 | 0 | 0 | PC 17757 | 227.525 | [null] | C | 4 | [null] | ||
| 17 | 1 | 1 | female | 29.0 | 0 | 0 | PC 17483 | 221.7792 | C97 | S | 8 | [null] | ||
| 18 | 1 | 1 | male | 25.0 | 1 | 0 | 11967 | 91.0792 | B49 | C | 7 | [null] | ||
| 19 | 1 | 1 | female | 19.0 | 1 | 0 | 11967 | 91.0792 | B49 | C | 7 | [null] | ||
| 20 | 1 | 1 | female | 35.0 | 0 | 0 | PC 17760 | 135.6333 | C99 | S | 8 | [null] | ||
| 21 | 1 | 1 | male | 28.0 | 0 | 0 | 110564 | 26.55 | C52 | S | D | [null] | ||
| 22 | 1 | 1 | male | 40.0 | 0 | 0 | 112277 | 31.0 | A31 | C | 7 | [null] | ||
| 23 | 1 | 1 | female | 30.0 | 0 | 0 | 36928 | 164.8667 | C7 | S | 8 | [null] | ||
| 24 | 1 | 1 | female | 58.0 | 0 | 0 | 113783 | 26.55 | C103 | S | 8 | [null] | ||
| 25 | 1 | 1 | female | 45.0 | 0 | 0 | PC 17608 | 262.375 | [null] | C | 4 | [null] | ||
| 26 | 1 | 1 | female | 22.0 | 0 | 1 | 113505 | 55.0 | E33 | S | 6 | [null] | ||
| 27 | 1 | 1 | female | 44.0 | 0 | 0 | PC 17610 | 27.7208 | B4 | C | 6 | [null] | ||
| 28 | 1 | 1 | female | 59.0 | 2 | 0 | 11769 | 51.4792 | C101 | S | D | [null] | ||
| 29 | 1 | 1 | female | 60.0 | 0 | 0 | 11813 | 76.2917 | D15 | C | 8 | [null] | ||
| 30 | 1 | 1 | female | 41.0 | 0 | 0 | 16966 | 134.5 | E40 | C | 3 | [null] | ||
| 31 | 1 | 1 | male | 42.0 | 0 | 0 | PC 17476 | 26.2875 | E24 | S | 5 | [null] | ||
| 32 | 1 | 1 | female | 53.0 | 0 | 0 | PC 17606 | 27.4458 | [null] | C | 6 | [null] | ||
| 33 | 1 | 1 | male | 36.0 | 0 | 1 | PC 17755 | 512.3292 | B51 B53 B55 | C | 3 | [null] | ||
| 34 | 1 | 1 | female | 58.0 | 0 | 1 | PC 17755 | 512.3292 | B51 B53 B55 | C | 3 | [null] | ||
| 35 | 1 | 1 | male | 11.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | 4 | [null] | ||
| 36 | 1 | 1 | female | 14.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | 4 | [null] | ||
| 37 | 1 | 1 | male | 36.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | C | [null] | ||
| 38 | 1 | 1 | female | 36.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | 4 | [null] | ||
| 39 | 1 | 1 | female | [null] | 0 | 0 | 17770 | 27.7208 | [null] | C | 5 | [null] | ||
| 40 | 1 | 1 | female | 76.0 | 1 | 0 | 19877 | 78.85 | C46 | S | 6 | [null] | ||
| 41 | 1 | 1 | female | 47.0 | 1 | 0 | W.E.P. 5734 | 61.175 | E31 | S | 4 | [null] | ||
| 42 | 1 | 1 | male | 27.0 | 1 | 0 | 113806 | 53.1 | E8 | S | 5 | [null] | ||
| 43 | 1 | 1 | female | 33.0 | 1 | 0 | 113806 | 53.1 | E8 | S | 5 | [null] | ||
| 44 | 1 | 1 | female | 36.0 | 0 | 0 | PC 17608 | 262.375 | B61 | C | 4 | [null] | ||
| 45 | 1 | 1 | female | 30.0 | 0 | 0 | 110152 | 86.5 | B77 | S | 8 | [null] | ||
| 46 | 1 | 1 | male | 45.0 | 0 | 0 | PC 17594 | 29.7 | A9 | C | 7 | [null] | ||
| 47 | 1 | 1 | female | [null] | 0 | 1 | 113505 | 55.0 | E33 | S | 6 | [null] | ||
| 48 | 1 | 1 | female | 26.0 | 1 | 0 | 13508 | 136.7792 | C89 | C | 4 | [null] | ||
| 49 | 1 | 1 | female | 22.0 | 0 | 0 | 113781 | 151.55 | [null] | S | 11 | [null] | ||
| 50 | 1 | 1 | female | 39.0 | 1 | 1 | PC 17756 | 83.1583 | E49 | C | 14 | [null] | ||
| 51 | 1 | 1 | female | 64.0 | 0 | 2 | PC 17756 | 83.1583 | E45 | C | 14 | [null] | ||
| 52 | 1 | 1 | female | 55.0 | 2 | 0 | 11770 | 25.7 | C101 | S | 2 | [null] | ||
| 53 | 1 | 1 | female | 36.0 | 0 | 2 | WE/P 5735 | 71.0 | B22 | S | 7 | [null] | ||
| 54 | 1 | 1 | female | 64.0 | 1 | 1 | 112901 | 26.55 | B26 | S | 7 | [null] | ||
| 55 | 1 | 1 | female | 38.0 | 1 | 0 | PC 17599 | 71.2833 | C85 | C | 4 | [null] | ||
| 56 | 1 | 1 | male | 51.0 | 0 | 0 | 113055 | 26.55 | E17 | S | 5 9 | [null] | ||
| 57 | 1 | 1 | male | 27.0 | 0 | 0 | 113804 | 30.5 | [null] | S | 3 | [null] | ||
| 58 | 1 | 1 | female | 33.0 | 0 | 0 | 113781 | 151.55 | [null] | S | 8 | [null] | ||
| 59 | 1 | 1 | female | 27.0 | 1 | 2 | F.C. 12750 | 52.0 | B71 | S | 3 | [null] | ||
| 60 | 1 | 1 | male | 31.0 | 1 | 0 | 17474 | 57.0 | B20 | S | 3 | [null] | ||
| 61 | 1 | 1 | female | 17.0 | 1 | 0 | 17474 | 57.0 | B20 | S | 3 | [null] | ||
| 62 | 1 | 1 | male | 53.0 | 1 | 1 | 33638 | 81.8583 | A34 | S | 13 | [null] | ||
| 63 | 1 | 1 | male | 4.0 | 0 | 2 | 33638 | 81.8583 | A34 | S | 5 | [null] | ||
| 64 | 1 | 1 | female | 54.0 | 1 | 1 | 33638 | 81.8583 | A34 | S | 5 | [null] | ||
| 65 | 1 | 1 | female | 27.0 | 1 | 1 | PC 17558 | 247.5208 | B58 B60 | C | 6 | [null] | ||
| 66 | 1 | 1 | female | 48.0 | 1 | 0 | PC 17761 | 106.425 | C86 | C | 2 | [null] | ||
| 67 | 1 | 1 | female | 23.0 | 0 | 1 | 11767 | 83.1583 | C54 | C | 7 | [null] | ||
| 68 | 1 | 1 | female | 38.0 | 0 | 0 | PC 17757 | 227.525 | C45 | C | 4 | [null] | ||
| 69 | 1 | 1 | female | 54.0 | 1 | 0 | 36947 | 78.2667 | D20 | C | 4 | [null] | ||
| 70 | 1 | 1 | female | [null] | 0 | 0 | PC 17598 | 31.6833 | [null] | S | 7 | [null] | ||
| 71 | 1 | 1 | female | [null] | 0 | 0 | 17421 | 110.8833 | [null] | C | 4 | [null] | ||
| 72 | 1 | 1 | female | 24.0 | 3 | 2 | 19950 | 263.0 | C23 C25 C27 | S | 10 | [null] | ||
| 73 | 1 | 1 | female | 28.0 | 3 | 2 | 19950 | 263.0 | C23 C25 C27 | S | 10 | [null] | ||
| 74 | 1 | 1 | female | 23.0 | 3 | 2 | 19950 | 263.0 | C23 C25 C27 | S | 10 | [null] | ||
| 75 | 1 | 1 | female | 60.0 | 1 | 4 | 19950 | 263.0 | C23 C25 C27 | S | 10 | [null] | ||
| 76 | 1 | 1 | female | 30.0 | 0 | 0 | PC 17485 | 56.9292 | E36 | C | 1 | [null] | ||
| 77 | 1 | 1 | male | 50.0 | 2 | 0 | PC 17611 | 133.65 | [null] | S | 5 | [null] | ||
| 78 | 1 | 1 | male | 43.0 | 1 | 0 | 17765 | 27.7208 | D40 | C | 5 | [null] | ||
| 79 | 1 | 1 | female | [null] | 1 | 0 | PC 17611 | 133.65 | [null] | S | 5 | [null] | ||
| 80 | 1 | 1 | female | 22.0 | 0 | 2 | 13568 | 49.5 | B39 | C | 5 | [null] | ||
| 81 | 1 | 1 | male | 60.0 | 1 | 1 | 13567 | 79.2 | B41 | C | 5 | [null] | ||
| 82 | 1 | 1 | female | 48.0 | 1 | 1 | 13567 | 79.2 | B41 | C | 5 | [null] | ||
| 83 | 1 | 1 | female | 35.0 | 1 | 0 | 113803 | 53.1 | C123 | S | D | [null] | ||
| 84 | 1 | 1 | female | 35.0 | 0 | 0 | 113503 | 211.5 | C130 | C | 4 | [null] | ||
| 85 | 1 | 1 | female | 22.0 | 0 | 1 | 112378 | 59.4 | [null] | C | 7 | [null] | ||
| 86 | 1 | 1 | female | 45.0 | 0 | 1 | 112378 | 59.4 | [null] | C | 7 | [null] | ||
| 87 | 1 | 1 | male | 49.0 | 1 | 0 | 17453 | 89.1042 | C92 | C | 5 | [null] | ||
| 88 | 1 | 1 | female | [null] | 1 | 0 | 17453 | 89.1042 | C92 | C | 5 | [null] | ||
| 89 | 1 | 1 | male | 53.0 | 0 | 0 | 113780 | 28.5 | C51 | C | B | [null] | ||
| 90 | 1 | 1 | female | 19.0 | 0 | 0 | 112053 | 30.0 | B42 | S | 3 | [null] | ||
| 91 | 1 | 1 | female | 58.0 | 0 | 1 | PC 17582 | 153.4625 | C125 | S | 3 | [null] | ||
| 92 | 1 | 1 | male | 23.0 | 0 | 1 | PC 17759 | 63.3583 | D10 D12 | C | 7 | [null] | ||
| 93 | 1 | 1 | female | 45.0 | 0 | 1 | PC 17759 | 63.3583 | D10 D12 | C | 7 | [null] | ||
| 94 | 1 | 1 | male | 25.0 | 1 | 0 | 11765 | 55.4417 | E50 | C | 5 | [null] | ||
| 95 | 1 | 1 | female | 25.0 | 1 | 0 | 11765 | 55.4417 | E50 | C | 5 | [null] | ||
| 96 | 1 | 1 | male | 48.0 | 1 | 0 | PC 17572 | 76.7292 | D33 | C | 3 | [null] | ||
| 97 | 1 | 1 | female | 49.0 | 1 | 0 | PC 17572 | 76.7292 | D33 | C | 3 | [null] | ||
| 98 | 1 | 1 | female | 35.0 | 1 | 0 | 36973 | 83.475 | C83 | S | D | [null] | ||
| 99 | 1 | 1 | male | 27.0 | 0 | 0 | PC 17572 | 76.7292 | D49 | C | 3 | [null] | ||
| 100 | 1 | 1 | male | [null] | 0 | 0 | 16988 | 30.0 | D45 | S | 3 | [null] |
Rows: 1-100 of 439 | Columns: 14
9. Filter unneeded columns¶
Again, you should always try to cut down your dataset to the essential columns, but writing an explicit command to exclude columns can be cumbersome. Another way to do this is by simply dropping the columns with the 'drop' method.
In [46]:
vdf.drop(["name", "body"])
Out[46]:
| 123 pclassInt | 123 survivedInt | Abc sexVarchar(20) | 123 ageNumeric(6,3) | 123 sibspInt | 123 parchInt | Abc ticketVarchar(36) | 123 fareNumeric(10,5) | Abc cabinVarchar(30) | Abc embarkedVarchar(20) | Abc boatVarchar(100) | Abc Varchar(100) |
| 1 | 1 | 0 | male | 36.0 | 0 | 0 | 13050 | 75.2417 | C6 | C | A | |
| 2 | 1 | 0 | male | [null] | 0 | 0 | PC 17600 | 30.6958 | [null] | C | 14 | |
| 3 | 1 | 1 | female | 29.0 | 0 | 0 | 24160 | 211.3375 | B5 | S | 2 | |
| 4 | 1 | 1 | male | 0.92 | 1 | 2 | 113781 | 151.55 | C22 C26 | S | 11 | |
| 5 | 1 | 1 | male | 48.0 | 0 | 0 | 19952 | 26.55 | E12 | S | 3 | |
| 6 | 1 | 1 | female | 63.0 | 1 | 0 | 13502 | 77.9583 | D7 | S | 10 | |
| 7 | 1 | 1 | female | 53.0 | 2 | 0 | 11769 | 51.4792 | C101 | S | D | |
| 8 | 1 | 1 | female | 18.0 | 1 | 0 | PC 17757 | 227.525 | C62 C64 | C | 4 | |
| 9 | 1 | 1 | female | 24.0 | 0 | 0 | PC 17477 | 69.3 | B35 | C | 9 | |
| 10 | 1 | 1 | male | 80.0 | 0 | 0 | 27042 | 30.0 | A23 | S | B | |
| 11 | 1 | 1 | female | 50.0 | 0 | 1 | PC 17558 | 247.5208 | B58 B60 | C | 6 | |
| 12 | 1 | 1 | female | 32.0 | 0 | 0 | 11813 | 76.2917 | D15 | C | 8 | |
| 13 | 1 | 1 | male | 37.0 | 1 | 1 | 11751 | 52.5542 | D35 | S | 5 | |
| 14 | 1 | 1 | female | 47.0 | 1 | 1 | 11751 | 52.5542 | D35 | S | 5 | |
| 15 | 1 | 1 | male | 26.0 | 0 | 0 | 111369 | 30.0 | C148 | C | 5 | |
| 16 | 1 | 1 | female | 42.0 | 0 | 0 | PC 17757 | 227.525 | [null] | C | 4 | |
| 17 | 1 | 1 | female | 29.0 | 0 | 0 | PC 17483 | 221.7792 | C97 | S | 8 | |
| 18 | 1 | 1 | male | 25.0 | 1 | 0 | 11967 | 91.0792 | B49 | C | 7 | |
| 19 | 1 | 1 | female | 19.0 | 1 | 0 | 11967 | 91.0792 | B49 | C | 7 | |
| 20 | 1 | 1 | female | 35.0 | 0 | 0 | PC 17760 | 135.6333 | C99 | S | 8 | |
| 21 | 1 | 1 | male | 28.0 | 0 | 0 | 110564 | 26.55 | C52 | S | D | |
| 22 | 1 | 1 | male | 40.0 | 0 | 0 | 112277 | 31.0 | A31 | C | 7 | |
| 23 | 1 | 1 | female | 30.0 | 0 | 0 | 36928 | 164.8667 | C7 | S | 8 | |
| 24 | 1 | 1 | female | 58.0 | 0 | 0 | 113783 | 26.55 | C103 | S | 8 | |
| 25 | 1 | 1 | female | 45.0 | 0 | 0 | PC 17608 | 262.375 | [null] | C | 4 | |
| 26 | 1 | 1 | female | 22.0 | 0 | 1 | 113505 | 55.0 | E33 | S | 6 | |
| 27 | 1 | 1 | female | 44.0 | 0 | 0 | PC 17610 | 27.7208 | B4 | C | 6 | |
| 28 | 1 | 1 | female | 59.0 | 2 | 0 | 11769 | 51.4792 | C101 | S | D | |
| 29 | 1 | 1 | female | 60.0 | 0 | 0 | 11813 | 76.2917 | D15 | C | 8 | |
| 30 | 1 | 1 | female | 41.0 | 0 | 0 | 16966 | 134.5 | E40 | C | 3 | |
| 31 | 1 | 1 | male | 42.0 | 0 | 0 | PC 17476 | 26.2875 | E24 | S | 5 | |
| 32 | 1 | 1 | female | 53.0 | 0 | 0 | PC 17606 | 27.4458 | [null] | C | 6 | |
| 33 | 1 | 1 | male | 36.0 | 0 | 1 | PC 17755 | 512.3292 | B51 B53 B55 | C | 3 | |
| 34 | 1 | 1 | female | 58.0 | 0 | 1 | PC 17755 | 512.3292 | B51 B53 B55 | C | 3 | |
| 35 | 1 | 1 | male | 11.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | 4 | |
| 36 | 1 | 1 | female | 14.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | 4 | |
| 37 | 1 | 1 | male | 36.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | C | |
| 38 | 1 | 1 | female | 36.0 | 1 | 2 | 113760 | 120.0 | B96 B98 | S | 4 | |
| 39 | 1 | 1 | female | [null] | 0 | 0 | 17770 | 27.7208 | [null] | C | 5 | |
| 40 | 1 | 1 | female | 76.0 | 1 | 0 | 19877 | 78.85 | C46 | S | 6 | |
| 41 | 1 | 1 | female | 47.0 | 1 | 0 | W.E.P. 5734 | 61.175 | E31 | S | 4 | |
| 42 | 1 | 1 | male | 27.0 | 1 | 0 | 113806 | 53.1 | E8 | S | 5 | |
| 43 | 1 | 1 | female | 33.0 | 1 | 0 | 113806 | 53.1 | E8 | S | 5 | |
| 44 | 1 | 1 | female | 36.0 | 0 | 0 | PC 17608 | 262.375 | B61 | C | 4 | |
| 45 | 1 | 1 | female | 30.0 | 0 | 0 | 110152 | 86.5 | B77 | S | 8 | |
| 46 | 1 | 1 | male | 45.0 | 0 | 0 | PC 17594 | 29.7 | A9 | C | 7 | |
| 47 | 1 | 1 | female | [null] | 0 | 1 | 113505 | 55.0 | E33 | S | 6 | |
| 48 | 1 | 1 | female | 26.0 | 1 | 0 | 13508 | 136.7792 | C89 | C | 4 | |
| 49 | 1 | 1 | female | 22.0 | 0 | 0 | 113781 | 151.55 | [null] | S | 11 | |
| 50 | 1 | 1 | female | 39.0 | 1 | 1 | PC 17756 | 83.1583 | E49 | C | 14 | |
| 51 | 1 | 1 | female | 64.0 | 0 | 2 | PC 17756 | 83.1583 | E45 | C | 14 | |
| 52 | 1 | 1 | female | 55.0 | 2 | 0 | 11770 | 25.7 | C101 | S | 2 | |
| 53 | 1 | 1 | female | 36.0 | 0 | 2 | WE/P 5735 | 71.0 | B22 | S | 7 | |
| 54 | 1 | 1 | female | 64.0 | 1 | 1 | 112901 | 26.55 | B26 | S | 7 | |
| 55 | 1 | 1 | female | 38.0 | 1 | 0 | PC 17599 | 71.2833 | C85 | C | 4 | |
| 56 | 1 | 1 | male | 51.0 | 0 | 0 | 113055 | 26.55 | E17 | S | 5 9 | |
| 57 | 1 | 1 | male | 27.0 | 0 | 0 | 113804 | 30.5 | [null] | S | 3 | |
| 58 | 1 | 1 | female | 33.0 | 0 | 0 | 113781 | 151.55 | [null] | S | 8 | |
| 59 | 1 | 1 | female | 27.0 | 1 | 2 | F.C. 12750 | 52.0 | B71 | S | 3 | |
| 60 | 1 | 1 | male | 31.0 | 1 | 0 | 17474 | 57.0 | B20 | S | 3 | |
| 61 | 1 | 1 | female | 17.0 | 1 | 0 | 17474 | 57.0 | B20 | S | 3 | |
| 62 | 1 | 1 | male | 53.0 | 1 | 1 | 33638 | 81.8583 | A34 | S | 13 | |
| 63 | 1 | 1 | male | 4.0 | 0 | 2 | 33638 | 81.8583 | A34 | S | 5 | |
| 64 | 1 | 1 | female | 54.0 | 1 | 1 | 33638 | 81.8583 | A34 | S | 5 | |
| 65 | 1 | 1 | female | 27.0 | 1 | 1 | PC 17558 | 247.5208 | B58 B60 | C | 6 | |
| 66 | 1 | 1 | female | 48.0 | 1 | 0 | PC 17761 | 106.425 | C86 | C | 2 | |
| 67 | 1 | 1 | female | 23.0 | 0 | 1 | 11767 | 83.1583 | C54 | C | 7 | |
| 68 | 1 | 1 | female | 38.0 | 0 | 0 | PC 17757 | 227.525 | C45 | C | 4 | |
| 69 | 1 | 1 | female | 54.0 | 1 | 0 | 36947 | 78.2667 | D20 | C | 4 | |
| 70 | 1 | 1 | female | [null] | 0 | 0 | PC 17598 | 31.6833 | [null] | S | 7 | |
| 71 | 1 | 1 | female | [null] | 0 | 0 | 17421 | 110.8833 | [null] | C | 4 | |
| 72 | 1 | 1 | female | 24.0 | 3 | 2 | 19950 | 263.0 | C23 C25 C27 | S | 10 | |
| 73 | 1 | 1 | female | 28.0 | 3 | 2 | 19950 | 263.0 | C23 C25 C27 | S | 10 | |
| 74 | 1 | 1 | female | 23.0 | 3 | 2 | 19950 | 263.0 | C23 C25 C27 | S | 10 | |
| 75 | 1 | 1 | female | 60.0 | 1 | 4 | 19950 | 263.0 | C23 C25 C27 | S | 10 | |
| 76 | 1 | 1 | female | 30.0 | 0 | 0 | PC 17485 | 56.9292 | E36 | C | 1 | |
| 77 | 1 | 1 | male | 50.0 | 2 | 0 | PC 17611 | 133.65 | [null] | S | 5 | |
| 78 | 1 | 1 | male | 43.0 | 1 | 0 | 17765 | 27.7208 | D40 | C | 5 | |
| 79 | 1 | 1 | female | [null] | 1 | 0 | PC 17611 | 133.65 | [null] | S | 5 | |
| 80 | 1 | 1 | female | 22.0 | 0 | 2 | 13568 | 49.5 | B39 | C | 5 | |
| 81 | 1 | 1 | male | 60.0 | 1 | 1 | 13567 | 79.2 | B41 | C | 5 | |
| 82 | 1 | 1 | female | 48.0 | 1 | 1 | 13567 | 79.2 | B41 | C | 5 | |
| 83 | 1 | 1 | female | 35.0 | 1 | 0 | 113803 | 53.1 | C123 | S | D | |
| 84 | 1 | 1 | female | 35.0 | 0 | 0 | 113503 | 211.5 | C130 | C | 4 | |
| 85 | 1 | 1 | female | 22.0 | 0 | 1 | 112378 | 59.4 | [null] | C | 7 | |
| 86 | 1 | 1 | female | 45.0 | 0 | 1 | 112378 | 59.4 | [null] | C | 7 | |
| 87 | 1 | 1 | male | 49.0 | 1 | 0 | 17453 | 89.1042 | C92 | C | 5 | |
| 88 | 1 | 1 | female | [null] | 1 | 0 | 17453 | 89.1042 | C92 | C | 5 | |
| 89 | 1 | 1 | male | 53.0 | 0 | 0 | 113780 | 28.5 | C51 | C | B | |
| 90 | 1 | 1 | female | 19.0 | 0 | 0 | 112053 | 30.0 | B42 | S | 3 | |
| 91 | 1 | 1 | female | 58.0 | 0 | 1 | PC 17582 | 153.4625 | C125 | S | 3 | |
| 92 | 1 | 1 | male | 23.0 | 0 | 1 | PC 17759 | 63.3583 | D10 D12 | C | 7 | |
| 93 | 1 | 1 | female | 45.0 | 0 | 1 | PC 17759 | 63.3583 | D10 D12 | C | 7 | |
| 94 | 1 | 1 | male | 25.0 | 1 | 0 | 11765 | 55.4417 | E50 | C | 5 | |
| 95 | 1 | 1 | female | 25.0 | 1 | 0 | 11765 | 55.4417 | E50 | C | 5 | |
| 96 | 1 | 1 | male | 48.0 | 1 | 0 | PC 17572 | 76.7292 | D33 | C | 3 | |
| 97 | 1 | 1 | female | 49.0 | 1 | 0 | PC 17572 | 76.7292 | D33 | C | 3 | |
| 98 | 1 | 1 | female | 35.0 | 1 | 0 | 36973 | 83.475 | C83 | S | D | |
| 99 | 1 | 1 | male | 27.0 | 0 | 0 | PC 17572 | 76.7292 | D49 | C | 3 | |
| 100 | 1 | 1 | male | [null] | 0 | 0 | 16988 | 30.0 | D45 | S | 3 |
Rows: 1-100 of 439 | Columns: 12
By using the 'drop' method, VerticaPy will simply exclude the specified columns from the SELECT query during SQL code generation.
In [47]:
print(vdf.current_relation())
10. Maximize your ressources¶
You might encounter datasets with hundreds of columns. These datasets can be resource intensive because you have to compute many aggregations at the same time. VerticaPy allows you to control the number of queries you'll send to the system, allowing for some useful optimizations.
Let's generate a large dataset and see what we can do to handle it.
In [52]:
from verticapy.datasets import gen_dataset
features_ranges = {}
for i in range(600):
features_ranges[f"x{i}"] = {"type": float, "range": [0, 1]}
vp.drop("test_dataset", method = "table")
vdf = gen_dataset(features_ranges, nrows = 10000).to_db("test_dataset",
relation_type = "table",
inplace = True)
vdf
Out[52]:
| 123 x0Float | 123 x1Float | 123 x2Float | 123 x3Float | 123 x4Float | 123 x5Float | 123 x6Float | 123 x7Float | 123 x8Float | 123 x9Float | 123 x10Float | 123 x11Float | 123 x12Float | 123 x13Float | 123 x14Float | 123 x15Float | 123 x16Float | 123 x17Float | 123 x18Float | 123 x19Float | 123 x20Float | 123 x21Float | 123 x22Float | 123 x23Float | 123 x24Float | ... | 123 x575Float | 123 x576Float | 123 x577Float | 123 x578Float | 123 x579Float | 123 x580Float | 123 x581Float | 123 x582Float | 123 x583Float | 123 x584Float | 123 x585Float | 123 x586Float | 123 x587Float | 123 x588Float | 123 x589Float | 123 x590Float | 123 x591Float | 123 x592Float | 123 x593Float | 123 x594Float | 123 x595Float | 123 x596Float | 123 x597Float | 123 x598Float | 123 x599Float |
| 1 | 5.20595349371433e-05 | 0.485537143424153 | 0.310573806287721 | 0.17678599152714 | 0.878996989224106 | 0.672955710673705 | 0.427016830304638 | 0.973969946848229 | 0.0463997314218432 | 0.815124413464218 | 0.391868985490873 | 0.881440195720643 | 0.927366451360285 | 0.972796163288876 | 0.438081233995035 | 0.899093058193102 | 0.270564198726788 | 0.828351575415581 | 0.670606910251081 | 0.00691566616296768 | 0.244990032864735 | 0.237273046979681 | 0.593805334996432 | 0.418030732544139 | 0.754198654321954 | ... | 0.167198063107207 | 0.66410061926581 | 0.591387247433886 | 0.801861852407455 | 0.160147324670106 | 0.394959231372923 | 0.574036001926288 | 0.367323393234983 | 0.12169961235486 | 0.319393459474668 | 0.644115259405226 | 0.404665975831449 | 0.228299217764288 | 0.893671463243663 | 0.653764561284333 | 0.0432208550628275 | 0.867323723621666 | 0.161540731554851 | 0.501341378316283 | 0.934534269152209 | 0.546305241528898 | 0.360079299192876 | 0.205802466021851 | 0.738606488797814 | 0.974907765863463 |
| 2 | 9.12342220544815e-05 | 0.590735004516318 | 0.882021387806162 | 0.807899940526113 | 0.711216947296634 | 0.188597822096199 | 0.0914702252484858 | 0.0544094850774854 | 0.145819653989747 | 0.491020490648225 | 0.564146702410653 | 0.479361131088808 | 0.0683218501508236 | 0.170866159722209 | 0.998306306544691 | 0.353908515535295 | 0.657991246320307 | 0.950230355840176 | 0.597807428101078 | 0.955734903225675 | 0.8572982782498 | 0.35656450339593 | 0.792389542330056 | 0.778561599552631 | 0.957219142001122 | ... | 0.517275118036196 | 0.78418490383774 | 0.464827378746122 | 0.225700930459425 | 0.979388368315995 | 0.519117088522762 | 0.250407279236242 | 0.102565104607493 | 0.229686575941741 | 0.114929591305554 | 0.426856120815501 | 0.501485610380769 | 0.556145877111703 | 0.334615163039416 | 0.623225529445335 | 0.270954991923645 | 0.145561676472425 | 0.531705247005448 | 0.303247437812388 | 0.885837420355529 | 0.167087592883036 | 0.242697077337652 | 0.599079611944035 | 0.747869855258614 | 0.142291998490691 |
| 3 | 0.000313950935378671 | 0.971825310494751 | 0.25097096292302 | 0.184859347296879 | 0.390021583763883 | 0.848451353842393 | 0.717313979519531 | 0.218293828656897 | 0.919568052748218 | 0.0344389842357486 | 0.428135209018365 | 0.876995357684791 | 0.27770495088771 | 0.168209461728111 | 0.873780781868845 | 0.567112604621798 | 0.976665391819552 | 0.673653927864507 | 0.205331231001765 | 0.585696727968752 | 0.0154113282915205 | 0.353451657108963 | 0.467424136819318 | 0.846257669152692 | 0.817340336041525 | ... | 0.67054178006947 | 0.540544708259404 | 0.917200654977933 | 0.728609589394182 | 0.597091436386108 | 0.197245578747243 | 0.107135031139478 | 0.0679437993094325 | 0.789403797360137 | 0.777199340285733 | 0.767102502984926 | 0.410148833645508 | 0.699540945002809 | 0.965898974332958 | 0.161106799496338 | 0.976732995826751 | 0.995254686335102 | 0.61504055862315 | 0.0883637766819447 | 0.586336502805352 | 0.913205028045923 | 0.00139876455068588 | 0.582190479850397 | 0.121553729521111 | 0.834747690008953 |
| 4 | 0.000348165864124894 | 0.514557993272319 | 0.11887997132726 | 0.295070218853652 | 0.665599208325148 | 0.298725477885455 | 0.68120707408525 | 0.800706213572994 | 0.263220171676949 | 0.354912436101586 | 0.114155641989782 | 0.37006649048999 | 0.808830021880567 | 0.53140323003754 | 0.94215980428271 | 0.911958450218663 | 0.298196947900578 | 0.347267954843119 | 0.812091138912365 | 0.23330820677802 | 0.934122515143827 | 0.924393917899579 | 0.480800931807607 | 0.0956339514814317 | 0.156290424754843 | ... | 0.768978404812515 | 0.956076709553599 | 0.0353506035171449 | 0.482680244836956 | 0.720112280687317 | 0.40887110074982 | 0.119812757940963 | 0.571051431354135 | 0.596502817468718 | 0.247205943567678 | 0.984226516680792 | 0.0681454793084413 | 0.920964878750965 | 0.108473145635799 | 0.956578589975834 | 0.0854171137325466 | 0.985457987058908 | 0.707029990386218 | 0.709613722283393 | 0.771255206782371 | 0.72974056028761 | 0.932461752556264 | 0.315052018268034 | 0.723329573636875 | 0.242409084457904 |
| 5 | 0.000543929636478424 | 0.430594844510779 | 0.45327917044051 | 0.361475860700011 | 0.947569382376969 | 0.318890801863745 | 0.324479850940406 | 0.85119098960422 | 0.442027089186013 | 0.419261903269216 | 0.0473281478043646 | 0.680384134873748 | 0.260326553368941 | 0.395267856074497 | 0.375534699298441 | 0.456479738699272 | 0.687495809979737 | 0.172390855615959 | 0.896469952305779 | 0.110564883798361 | 0.157864786684513 | 0.907979461597279 | 0.482405613409355 | 0.621053696144372 | 0.0376831751782447 | ... | 0.568237458355725 | 0.139524054713547 | 0.20069858757779 | 0.0393721011932939 | 0.704097861424088 | 0.886494970181957 | 0.407103452598676 | 0.604970705928281 | 0.454309214837849 | 0.854147390928119 | 0.446033544372767 | 0.280742262955755 | 0.774687433615327 | 0.464250945486128 | 0.121843478642404 | 0.00450773374177516 | 0.250076497904956 | 0.677564952522516 | 0.345467021688819 | 0.961186888394877 | 0.0738108425866812 | 0.656103662680835 | 0.723669653059915 | 0.717909814557061 | 0.663673594594002 |
| 6 | 0.00065303361043334 | 0.704251058632508 | 0.467781809857115 | 0.264956458704546 | 0.395995118888095 | 0.497432985110208 | 0.201243643881753 | 0.642188858240843 | 0.0634401268325746 | 0.0744246849790215 | 0.445458367699757 | 0.314175287261605 | 0.703889897326007 | 0.322278953623027 | 0.893158378778026 | 0.360803448362276 | 0.094298658426851 | 0.308781487168744 | 0.530132415471599 | 0.792136463336647 | 0.364130642730743 | 0.0571534272748977 | 0.773166512837633 | 0.997822631383315 | 0.648393482901156 | ... | 0.0140404445119202 | 0.742923176847398 | 0.258339375257492 | 0.552029890706763 | 0.683688709046692 | 0.95612878468819 | 0.349498979514465 | 0.0754324006848037 | 0.311314723221585 | 0.436544922180474 | 0.141199418576434 | 0.402274329215288 | 0.544963134918362 | 0.487752554705366 | 0.460722686257213 | 0.868628986412659 | 0.081838998477906 | 0.853526944061741 | 0.41887966892682 | 0.240077747963369 | 0.618126435671002 | 0.170666457619518 | 0.207266625482589 | 0.447347375331447 | 0.745776536874473 |
| 7 | 0.000682923709973693 | 0.644610994961113 | 0.616245283046737 | 0.123426298610866 | 0.443946395535022 | 0.643657223321497 | 0.441787774208933 | 0.150944351218641 | 0.559415593510494 | 0.605078289285302 | 0.315637140069157 | 0.154103143606335 | 0.134863581275567 | 0.848456078441814 | 0.453098441939801 | 0.838772770715877 | 0.872466262429953 | 0.227294779382646 | 0.727198318811134 | 0.975423069670796 | 0.937626459402964 | 0.496109237428755 | 0.269249163800851 | 0.0692040659487247 | 0.379938506986946 | ... | 0.037696061655879 | 0.775120094651356 | 0.636968676932156 | 0.86673281993717 | 0.808848927961662 | 0.332977320067585 | 0.085852179909125 | 0.37671291991137 | 0.896897500148043 | 0.995074050500989 | 0.88267021602951 | 0.801379155600443 | 0.64041000767611 | 0.255462269065902 | 0.301744208205491 | 0.243042844347656 | 0.261499479878694 | 0.171056173043326 | 0.360516448505223 | 0.708982574520633 | 0.421358312247321 | 0.214519023662433 | 0.444327210076153 | 0.437608614098281 | 0.838648703182116 |
| 8 | 0.000793067505583167 | 0.253356415778399 | 0.415544093353674 | 0.7858901550062 | 0.518841414479539 | 0.58124653249979 | 0.838872970547527 | 0.253339023096487 | 0.537777259014547 | 0.511636992683634 | 0.876401922665536 | 0.330910145072266 | 0.837250211276114 | 0.891292826039717 | 0.0300761514808983 | 0.492607116000727 | 0.677193257724866 | 0.932157736970112 | 0.135663843713701 | 0.0830265819095075 | 0.538005317561328 | 0.943019419442862 | 0.0444187875837088 | 0.731323141837493 | 0.396121923113242 | ... | 0.873294182820246 | 0.955755655420944 | 0.0719545548781753 | 0.231276272563264 | 0.522659169510007 | 0.603492273483425 | 0.505635055946186 | 0.503558372845873 | 0.668043007608503 | 0.93298056605272 | 0.569968913914636 | 0.178924583597109 | 0.906137820100412 | 0.683470293879509 | 0.937676642322913 | 0.155517283128574 | 0.561612573219463 | 0.939914074027911 | 0.979315676027909 | 0.770145743153989 | 0.991599828703329 | 0.574154407950118 | 0.987718650372699 | 0.860681550344452 | 0.111758790444583 |
| 9 | 0.000808189157396555 | 0.617995445150882 | 0.696658476255834 | 0.911908351117745 | 0.0746490750461817 | 0.0270547145046294 | 0.778803712688386 | 0.830991541268304 | 0.522100063739344 | 0.621482615824789 | 0.369138852693141 | 0.104004176333547 | 0.229563752422109 | 0.14387673069723 | 0.080871112877503 | 0.733459386974573 | 0.613935362081975 | 0.601380746113136 | 0.84580114739947 | 0.575360710499808 | 0.999191816197708 | 0.881340791704133 | 0.0409915717318654 | 0.602274929638952 | 0.533451740629971 | ... | 0.504118523327634 | 0.892249741125852 | 0.465759584447369 | 0.100535372737795 | 0.305523607414216 | 0.898552039405331 | 0.0169904972426593 | 0.233689826447517 | 0.62591705750674 | 0.607556416653097 | 0.187945291632786 | 0.52122471225448 | 0.838821975514293 | 0.904034097446129 | 0.523557051550597 | 0.73128763679415 | 0.403599898330867 | 0.00886141718365252 | 0.378119049360976 | 0.880755959777161 | 0.755399168236181 | 0.957178877666593 | 0.474744056118652 | 0.380020038690418 | 0.911325834225863 |
| 10 | 0.000822716159746051 | 0.303757929708809 | 0.674965204903856 | 0.985240588197485 | 0.448494721669704 | 0.285802850499749 | 0.162648947909474 | 0.700317578390241 | 0.335482957074419 | 0.806018033064902 | 0.0216339391190559 | 0.0320320068858564 | 0.485301839886233 | 0.0921966573223472 | 0.368745758431032 | 0.396297462750226 | 0.696527161635458 | 0.130280503071845 | 0.570096999173984 | 0.78883409849368 | 0.908887054305524 | 0.297445093281567 | 0.255620962474495 | 0.991246218094602 | 0.430116546107456 | ... | 0.827182898530737 | 0.60562601312995 | 0.829281496116892 | 0.0895934132859111 | 0.0667535986285657 | 0.800689417868853 | 0.964669033652171 | 0.271402568323538 | 0.171136529650539 | 0.360468459781259 | 0.947657118318602 | 0.875000069616362 | 0.647767289076 | 0.818007030757144 | 0.159016718389466 | 0.00837163557298481 | 0.471277346136048 | 0.89308297378011 | 0.187736437655985 | 0.340545450104401 | 0.876182594336569 | 0.743140260688961 | 0.837466723285615 | 0.0150935670826584 | 0.494878334226087 |
| 11 | 0.000979060772806406 | 0.439807241782546 | 0.626514463685453 | 0.0704199536703527 | 0.313154702074826 | 0.350070314481854 | 0.404403449269012 | 0.308721815003082 | 0.576431647641584 | 0.069539297837764 | 0.581332214409485 | 0.835125667275861 | 0.444976998027414 | 0.728649721946567 | 0.550182907609269 | 0.0309040464926511 | 0.077445977833122 | 0.336784617509693 | 0.491119947517291 | 0.627216346329078 | 0.615304162492976 | 0.590732817072421 | 0.617980676004663 | 0.661433363566175 | 0.592870745575055 | ... | 0.989247507182881 | 0.606482609407976 | 0.451556464657187 | 0.915223909541965 | 0.344954282743856 | 0.338236053241417 | 0.277097255922854 | 0.0497198225930333 | 0.376942702569067 | 0.595391295151785 | 0.390230144606903 | 0.746718790847808 | 0.757885016966611 | 0.573431629687548 | 0.305864129215479 | 0.825817208969966 | 0.252157980576158 | 0.574568703304976 | 0.121699206763878 | 0.257007281994447 | 0.412975249113515 | 0.0925130390096456 | 0.77945464826189 | 0.564663758967072 | 0.506397417979315 |
| 12 | 0.0012155210133642 | 0.883985784370452 | 0.352868965826929 | 0.797740332083777 | 0.263176858890802 | 0.110168233979493 | 0.335146982455626 | 0.291956132277846 | 0.812865078914911 | 0.553404935868457 | 0.570459637558088 | 0.979303489904851 | 0.456594166345894 | 0.302682279143482 | 0.0374956335872412 | 0.518069498473778 | 0.560094220098108 | 0.917768871644512 | 0.145746572874486 | 0.375868327915668 | 0.12068030401133 | 0.621982222190127 | 0.760595121188089 | 0.363929099170491 | 0.565927936695516 | ... | 0.844578788382933 | 0.778860011370853 | 0.397549991961569 | 0.0570717882364988 | 0.587523450143635 | 0.518542894395068 | 0.897789266193286 | 0.387835014611483 | 0.121033942559734 | 0.0230447070207447 | 0.413844920927659 | 0.0581372829619795 | 0.164068690501153 | 0.407412171596661 | 0.0962606160901487 | 0.27744196751155 | 0.210342114092782 | 0.712765108095482 | 0.0527696670033038 | 0.684582213871181 | 0.572715175803751 | 0.148106813430786 | 0.835204422939569 | 0.394506021868438 | 0.931154929101467 |
| 13 | 0.00122272502630949 | 0.477404269156978 | 0.19990209909156 | 0.759050338063389 | 0.0388436249922961 | 0.407309964764863 | 0.591277974657714 | 0.47440811409615 | 0.131456343922764 | 0.474242814118043 | 0.867372315376997 | 0.992270730668679 | 0.621839912375435 | 0.187569168861955 | 0.527094645658508 | 0.341643687104806 | 0.00877402303740382 | 0.395672247977927 | 0.193200543988496 | 0.326539155561477 | 0.00400001229718328 | 0.431387247052044 | 0.473783513298258 | 0.2622687718831 | 0.969983835238963 | ... | 0.926902265986428 | 0.590721808839589 | 0.659011690411717 | 0.850724686868489 | 0.0285641741938889 | 0.032567011192441 | 0.0273406757041812 | 0.168776686303318 | 0.761819479987025 | 0.825367737794295 | 0.821021991083398 | 0.302254410926253 | 0.1713817124255 | 0.26707330532372 | 0.192642115987837 | 0.927367725642398 | 0.211459572426975 | 0.0366603487636894 | 0.587632954353467 | 0.434821502305567 | 0.402778218965977 | 0.685957787092775 | 0.3709532963112 | 0.112047117669135 | 0.449244070798159 |
| 14 | 0.00124088628217578 | 0.123232251266018 | 0.0491360132582486 | 0.7285117036663 | 0.724426823202521 | 0.483166047371924 | 0.71372785163112 | 0.54733308381401 | 0.767123328289017 | 0.918681692797691 | 0.464807256590575 | 0.74905575090088 | 0.583089330466464 | 0.969299776479602 | 0.240440557245165 | 0.747496804455295 | 0.867428982164711 | 0.50176784559153 | 0.302795181516558 | 0.0780076670926064 | 0.908116687554866 | 0.566949767060578 | 0.510913741309196 | 0.557512517087162 | 0.190470670117065 | ... | 0.376021456671879 | 0.8046071047429 | 0.984454573132098 | 0.932276993058622 | 0.250375719740987 | 0.157552828779444 | 0.585303905420005 | 0.697764873271808 | 0.492770636687055 | 0.0583197835367173 | 0.202639327617362 | 0.497301240451634 | 0.214147181017324 | 0.366506737656891 | 0.286924257175997 | 0.739711924921721 | 0.387391082942486 | 0.987649523187429 | 0.313321807421744 | 0.398228157078847 | 0.844916604226455 | 0.76379580446519 | 0.0663863702211529 | 0.0659465317148715 | 0.597346164518967 |
| 15 | 0.00128592201508582 | 0.185471499571577 | 0.891624335898086 | 0.322646433487535 | 0.775136170210317 | 0.134920759592205 | 0.339664105093107 | 0.0538386884145439 | 0.985101283527911 | 0.389699057210237 | 0.628861238947138 | 0.492273819167167 | 0.859987538540736 | 0.738167456351221 | 0.747640180634335 | 0.0241205340716988 | 0.412530588917434 | 0.403384874807671 | 0.406851162435487 | 0.102106692967936 | 0.71690228767693 | 0.91077243280597 | 0.505991469137371 | 0.786306343972683 | 0.91901424783282 | ... | 0.599143637809902 | 0.00419124215841293 | 0.0847040708176792 | 0.560537424869835 | 0.297780649736524 | 0.049675605725497 | 0.556981625035405 | 0.28523177606985 | 0.888519194209948 | 0.708997382549569 | 0.33950416999869 | 0.623499667737633 | 0.644333380507305 | 0.347213328350335 | 0.985950018977746 | 0.840902822557837 | 0.448860564734787 | 0.98492409195751 | 0.788467522943392 | 0.734548958949745 | 0.596327672945336 | 0.219835221301764 | 0.948731280630454 | 0.834234661189839 | 0.0788629774469882 |
| 16 | 0.00154074560850859 | 0.280672378372401 | 0.882977313594893 | 0.491562168812379 | 0.800795097602531 | 0.175362455425784 | 0.311117413453758 | 0.403004108928144 | 0.177599671529606 | 0.669150166912004 | 0.379910706775263 | 0.831938385730609 | 0.0761382468044758 | 0.0467099014203995 | 0.0730760756414384 | 0.512423468055204 | 0.234202104387805 | 0.883032552199438 | 0.534998510964215 | 0.824408713728189 | 0.40216643223539 | 0.609903406584635 | 0.726666519651189 | 0.208236549980938 | 0.73925386602059 | ... | 0.175668640527874 | 0.214630600530654 | 0.345384965185076 | 0.958297756500542 | 0.621003513224423 | 0.708888341905549 | 0.432672992814332 | 0.914457609178498 | 0.607247246662155 | 0.0557838331442326 | 0.727823192952201 | 0.427479673177004 | 0.123860427876934 | 0.877718182047829 | 0.0109882694669068 | 0.604168449295685 | 0.118925310671329 | 0.0356483845971525 | 0.0649548007640988 | 0.670976559165865 | 0.774983137845993 | 0.64326729089953 | 0.587219550041482 | 0.888819209299982 | 0.79414251097478 |
| 17 | 0.0016654257196933 | 0.778196984203532 | 0.659533353755251 | 0.246978946495801 | 0.0224184808321297 | 0.701998605160043 | 0.582918283063918 | 0.640966822160408 | 0.290585124399513 | 0.119497678009793 | 0.999480966478586 | 0.716302403016016 | 0.0784759121015668 | 0.864410747075453 | 0.776035652030259 | 0.748223545495421 | 0.173026808304712 | 0.44580436241813 | 0.421882817754522 | 0.0635467148385942 | 0.128841838333756 | 0.528268333291635 | 0.410372210433707 | 0.420093975495547 | 0.16772858472541 | ... | 0.934764522826299 | 0.985120735364035 | 0.766936106141657 | 0.335562450345606 | 0.446464815875515 | 0.0111520690843463 | 0.0203325457405299 | 0.515958416508511 | 0.0674429947976023 | 0.389096916653216 | 0.614479128969833 | 0.935233022086322 | 0.639485286781564 | 0.048544357996434 | 0.995590083301067 | 0.541006152518094 | 0.848364024655893 | 0.864834308391437 | 0.705561394570395 | 0.93699673213996 | 0.277231702581048 | 0.78810752206482 | 0.502315928693861 | 0.845786549150944 | 0.617131968261674 |
| 18 | 0.00175128947012126 | 0.259256069082767 | 0.113250391790643 | 0.870733674382791 | 0.675403461791575 | 0.0601712241768837 | 0.0634823106229305 | 0.157455421518534 | 0.176179820438847 | 0.964077307377011 | 0.0342567923944443 | 0.343149433843791 | 0.68204446346499 | 0.380135304061696 | 0.631588784046471 | 0.396081093465909 | 0.408708244096488 | 0.00102172931656241 | 0.244162667542696 | 0.509765082038939 | 0.0496358049567789 | 0.0533007276244462 | 0.399678663583472 | 0.0932091611903161 | 0.940141053404659 | ... | 0.479975715279579 | 0.323709133546799 | 0.670055463677272 | 0.815319207496941 | 0.930998708121479 | 0.434917772887275 | 0.281861413037404 | 0.372292265063152 | 0.380077326437458 | 0.607661009533331 | 0.558372992556542 | 0.887468344997615 | 0.322468775091693 | 0.500013162614778 | 0.60718729486689 | 0.0749267647042871 | 0.287192546529695 | 0.571574591565877 | 0.317876994609833 | 0.918881508754566 | 0.429699965752661 | 0.941587090259418 | 0.668535564327613 | 0.624940167879686 | 0.292631980031729 |
| 19 | 0.00181635073386133 | 0.242102888878435 | 0.00021177064627409 | 0.90293863392435 | 0.87546885968186 | 0.551202750299126 | 0.0469476615544409 | 0.21516750450246 | 0.763185414019972 | 0.626650914549828 | 0.107004105113447 | 0.999311251798645 | 0.869598855730146 | 0.983423954807222 | 0.984280199743807 | 0.552646518684924 | 0.443487047916278 | 0.698614867171273 | 0.843118510441855 | 0.920109957223758 | 0.218127122381702 | 0.132170933764428 | 0.60343127255328 | 0.236888254759833 | 0.377079385099933 | ... | 0.108614815399051 | 0.576327720656991 | 0.588918798137456 | 0.422253480646759 | 0.758955131983384 | 0.92791401501745 | 0.191754296887666 | 0.331489301286638 | 0.699054997414351 | 0.848761372035369 | 0.126403575763106 | 0.809720243094489 | 0.877048951108009 | 0.0617622924037278 | 0.400628424249589 | 0.837284710025415 | 0.512817999348044 | 0.782036032294855 | 0.370354010490701 | 0.625848481897265 | 0.163105859421194 | 0.707284276839346 | 0.357400600798428 | 0.280699106166139 | 0.726346959127113 |
| 20 | 0.0018408028408885 | 0.227226342307404 | 0.468834885861725 | 0.0139007919933647 | 0.0404569543898106 | 0.432291188975796 | 0.613395373336971 | 0.0145679463166744 | 0.157078780466691 | 0.788319696672261 | 0.0138724420685321 | 0.496700122021139 | 0.302493382012472 | 0.787486731773242 | 0.13831971748732 | 0.330691324314103 | 0.719035096932203 | 0.108658116776496 | 0.914797928184271 | 0.812537739053369 | 0.336076081497595 | 0.680065952707082 | 0.498570543713868 | 0.628384815528989 | 0.885234787361696 | ... | 0.229260152671486 | 0.664317598100752 | 0.520595400128514 | 0.804775080876425 | 0.724761490477249 | 0.0535247467923909 | 0.372372682206333 | 0.575766700319946 | 0.84159395028837 | 0.533071851823479 | 0.172009165398777 | 0.196993597317487 | 0.956938977120444 | 0.428973820991814 | 0.810806995723397 | 0.42091130441986 | 0.707973761251196 | 0.303927457425743 | 0.193020030390471 | 0.278255666606128 | 0.602426636964083 | 0.539657266810536 | 0.926985857775435 | 0.7284386951942 | 0.777186896419153 |
| 21 | 0.00185824302025139 | 0.338837305782363 | 0.670170639641583 | 0.244203261099756 | 0.153362667188048 | 0.541855717310682 | 0.230501741636544 | 0.763440659502521 | 0.751571699045599 | 0.111677905311808 | 0.873304505134001 | 0.993746685329825 | 0.239230471430346 | 0.298558803042397 | 0.0107789118774235 | 0.067267655627802 | 0.959416897967458 | 0.831225040834397 | 0.824842949630693 | 0.916154369944707 | 0.674379291711375 | 0.115535460878164 | 0.598540955223143 | 0.70435454742983 | 0.0289285178296268 | ... | 0.853493904462084 | 0.771468677325174 | 0.807504807598889 | 0.323207265464589 | 0.459966313093901 | 0.993318783352152 | 0.394627513596788 | 0.629148403648287 | 0.764780845027417 | 0.530294203665107 | 0.860919277416542 | 0.827346798731014 | 0.22794887656346 | 0.875086251180619 | 0.177336633205414 | 0.0115733172278851 | 0.249137481907383 | 0.525983948027715 | 0.0788937355391681 | 0.882358906557783 | 0.489859696244821 | 0.490411963546649 | 0.918894510483369 | 0.597481280332431 | 0.562899688724428 |
| 22 | 0.00192855484783649 | 0.816469486337155 | 0.575522120110691 | 0.932992073008791 | 0.407928848173469 | 0.0109509692993015 | 0.212679030606523 | 0.156490429770201 | 0.812899318756536 | 0.959593267645687 | 0.224073556950316 | 0.130848328582942 | 0.566319170407951 | 0.0231973228510469 | 0.65333611308597 | 0.415811566868797 | 0.680884641595185 | 0.00852023065090179 | 0.182956015691161 | 0.259651773609221 | 0.360814395127818 | 0.539801678853109 | 0.562829199479893 | 0.307394834933802 | 0.543532406911254 | ... | 0.782709994120523 | 0.896962755825371 | 0.472562312148511 | 0.146009382791817 | 0.0536086133215576 | 0.758615199010819 | 0.369422902585939 | 0.709227430168539 | 0.847090091789141 | 0.396638606674969 | 0.337419296847656 | 0.759972046129405 | 0.183744407491758 | 0.197077492251992 | 0.0569350928999484 | 0.494416482048109 | 0.773257306078449 | 0.118675285950303 | 0.0416563060134649 | 0.5386572254356 | 0.926416327944025 | 0.295365379657596 | 0.0392289648298174 | 0.929422247922048 | 0.199250851292163 |
| 23 | 0.00199801963753998 | 0.00688267382793128 | 0.508428258821368 | 0.621033438015729 | 0.911280547035858 | 0.514414832694456 | 0.277881667949259 | 0.195791038451716 | 0.38580413791351 | 0.433834604686126 | 0.987401814665645 | 0.412022516829893 | 0.187727359123528 | 0.503223000094295 | 0.762268049642444 | 0.408281420823187 | 0.0457012359984219 | 0.979375208960846 | 0.200488107977435 | 0.556764390319586 | 0.740395630244166 | 0.801069190260023 | 0.830809336621314 | 0.739727368811145 | 0.183104071998969 | ... | 0.761424590600654 | 0.304378101835027 | 0.535638845991343 | 0.182664848631248 | 0.381600006483495 | 0.689274847507477 | 0.773183154175058 | 0.606363612925634 | 0.0561812440864742 | 0.873904557432979 | 0.42879754723981 | 0.896460646064952 | 0.293605883372948 | 0.892334886360914 | 0.789473324315622 | 0.750905855325982 | 0.29129442339763 | 0.817534980364144 | 0.238359867129475 | 0.832047089934349 | 0.951067251618952 | 0.28014234919101 | 0.863640069495887 | 0.888815487967804 | 0.901973480125889 |
| 24 | 0.0021014092490077 | 0.600262133637443 | 0.55819131527096 | 0.689667031634599 | 0.365543809486553 | 0.0308162609580904 | 0.835542572895065 | 0.43014994636178 | 0.756613352103159 | 0.242749175056815 | 0.751121151261032 | 0.169945689849555 | 0.972938545513898 | 0.636660831747577 | 0.675466644577682 | 0.513627538923174 | 0.535949922399595 | 0.590873416280374 | 0.479178189998493 | 0.510455195093527 | 0.582929033320397 | 0.35101545159705 | 0.927863268414512 | 0.610111832385883 | 0.621727875899523 | ... | 0.786631781840697 | 0.45221703662537 | 0.0247342598158866 | 0.504603497684002 | 0.7817629838828 | 0.0852067202795297 | 0.736560858553275 | 0.661940552061424 | 0.275093703530729 | 0.872653346741572 | 0.584675083635375 | 0.549375568516552 | 0.0668016709387302 | 0.221170792123303 | 0.594928338192403 | 0.279037617379799 | 0.938731277594343 | 0.6798471652437 | 0.142878976650536 | 0.91899765143171 | 0.391283277887851 | 0.823296562302858 | 0.676810617325827 | 0.580565449316055 | 0.387454377254471 |
| 25 | 0.00212023174390197 | 0.333340668817982 | 0.253254133276641 | 0.797214773017913 | 0.702215720433742 | 0.781050799647346 | 0.446938759181648 | 0.111412237863988 | 0.341665116371587 | 0.681202507810667 | 0.9257473340258 | 0.299111519474536 | 0.340889874147251 | 0.257330172229558 | 0.734987122938037 | 0.823258630232885 | 0.188953697914258 | 0.850203767651692 | 0.565788706298918 | 0.251629044301808 | 0.707615840481594 | 0.650274767773226 | 0.723261547507718 | 0.00934986211359501 | 0.0553575977683067 | ... | 0.809485564706847 | 0.248955243965611 | 0.19732007291168 | 0.361539772478864 | 0.0601984630338848 | 0.414072412531823 | 0.25092742824927 | 0.815381627297029 | 0.0521525081712753 | 0.406116212485358 | 0.0511640638578683 | 0.161374435061589 | 0.214974366361275 | 0.813511271728203 | 0.328055417630821 | 0.821085318224505 | 0.156881765462458 | 0.229560988023877 | 0.0574342471081764 | 0.234826399479061 | 0.740954866632819 | 0.320053423987702 | 0.634846408618614 | 0.944572363514453 | 0.922276116674766 |
| 26 | 0.00229606800712645 | 0.894937090808526 | 0.0648511976469308 | 0.148057063110173 | 0.512402550084516 | 0.829288055421785 | 0.922408348647878 | 0.682506443932652 | 0.996557072037831 | 0.292202893411741 | 0.793867905857041 | 0.368900209898129 | 0.211583824362606 | 0.735909970477223 | 0.705801137257367 | 0.524681633803993 | 0.290918205864727 | 0.368123656604439 | 0.605680143926293 | 0.634261987404898 | 0.735784065444022 | 0.839369429275393 | 0.792373429751024 | 0.332430504262447 | 0.697182196425274 | ... | 0.883641992229968 | 0.418139985064045 | 0.850059950724244 | 0.416652688058093 | 0.319001046707854 | 0.331953756278381 | 0.935391739942133 | 0.405601422768086 | 0.509008913766593 | 0.242766731884331 | 0.682179525494576 | 0.346943971235305 | 0.198916143504903 | 0.735445962520316 | 0.655461816349998 | 0.436180625110865 | 0.561643845168874 | 0.0679253120906651 | 0.0453141557518393 | 0.80834530107677 | 0.318166084587574 | 0.569211430847645 | 0.533066477859393 | 0.40408538444899 | 0.877461397321895 |
| 27 | 0.00231995363719761 | 0.574499198701233 | 0.479497223393992 | 0.269348715664819 | 0.583839793456718 | 0.610583076952025 | 0.9918818899896 | 0.723537885118276 | 0.29284657118842 | 0.939218657324091 | 0.361175301251933 | 0.389325539581478 | 0.21966540091671 | 0.954651636769995 | 0.0062391865067184 | 0.615794162498787 | 0.494698899798095 | 0.953266580821946 | 0.33217579848133 | 0.364622656488791 | 0.816049644025043 | 0.85624152328819 | 0.420965426135808 | 0.670364147983491 | 0.299294254044071 | ... | 0.743701202562079 | 0.0893695279955864 | 0.934393740724772 | 0.75909957382828 | 0.383331809658557 | 0.0662043082993478 | 0.414367269491777 | 0.120048105483875 | 0.55271059833467 | 0.425887944642454 | 0.148628477705643 | 0.099306063959375 | 0.60765039618127 | 0.16826595668681 | 0.776394628454 | 0.635458091506734 | 0.622557790251449 | 0.654026739997789 | 0.214921149658039 | 0.656950485659763 | 0.450434996280819 | 0.347716996679083 | 0.579979803180322 | 0.72959623625502 | 0.315415993565693 |
| 28 | 0.00237814616411924 | 0.328291387762874 | 0.421741724014282 | 0.562241226434708 | 0.518273789435625 | 0.64277029922232 | 0.0803035423159599 | 0.613901773933321 | 0.700658264802769 | 0.348946628859267 | 0.378437761915848 | 0.96102084312588 | 0.575939162634313 | 0.758291290374473 | 0.916874386835843 | 0.193646249361336 | 0.510012024780735 | 0.784793227678165 | 0.672208037227392 | 0.0741871329955757 | 0.324070474365726 | 0.985830797115341 | 0.294081768253818 | 0.420305538922548 | 0.663534839404747 | ... | 0.068865031702444 | 0.154663608176634 | 0.624199086334556 | 0.820680560078472 | 0.611905822763219 | 0.618837132817134 | 0.460138885071501 | 0.206646002596244 | 0.268642919836566 | 0.487919009290636 | 0.54632123070769 | 0.0481793119106442 | 0.623233071528375 | 0.266513609094545 | 0.00588682689704001 | 0.845463220495731 | 0.579313507536426 | 0.136679907795042 | 0.561424757353961 | 0.0458304670173675 | 0.794112343108281 | 0.894011942669749 | 0.705282331677154 | 0.610441399272531 | 0.159171662060544 |
| 29 | 0.00245688739232719 | 0.888363576726988 | 0.317529069958255 | 0.260590631281957 | 0.72574328049086 | 0.502948276698589 | 0.337283283239231 | 0.180198902264237 | 0.470010871766135 | 0.490925875026733 | 0.318050340050831 | 0.693566280417144 | 0.96426822245121 | 0.482484764652327 | 0.961613294668496 | 0.400739456526935 | 0.0123781755100936 | 0.212384321261197 | 0.614503851393238 | 0.667901515960693 | 0.510301039088517 | 0.636024930747226 | 0.351982586551458 | 0.473447813652456 | 0.710800992557779 | ... | 0.564755058614537 | 0.912978576961905 | 0.752664663596079 | 0.213276635389775 | 0.565893113147467 | 0.539459512801841 | 0.620103787165135 | 0.721809772076085 | 0.550579498521984 | 0.782020379323512 | 0.247514217160642 | 0.14196842443198 | 0.315855283755809 | 0.401565317995846 | 0.457198316929862 | 0.613735509105027 | 0.637034167069942 | 0.528673027874902 | 0.396274161990732 | 0.899473952595145 | 0.327078405302018 | 0.642983475001529 | 0.751434952719137 | 0.938661250984296 | 0.649262356571853 |
| 30 | 0.00262342393398285 | 0.435443616006523 | 0.00575482891872525 | 0.35038059996441 | 0.226600979221985 | 0.432043447159231 | 0.219179271487519 | 0.142263480927795 | 0.528332787333056 | 0.166417756350711 | 0.404738083016127 | 0.0919169234111905 | 0.709988206857815 | 0.221811372321099 | 0.268875791225582 | 0.83326313807629 | 0.586084255715832 | 0.607523065293208 | 0.524825238622725 | 0.162145837210119 | 0.45316101051867 | 0.56183876725845 | 0.915365730645135 | 0.337649665307254 | 0.897212808253244 | ... | 0.272942123468965 | 0.113366536097601 | 0.612857539905235 | 0.939239308238029 | 0.612927117617801 | 0.439482862595469 | 0.324528135824949 | 0.619077258976176 | 0.751834698487073 | 0.790630005765706 | 0.170190277742222 | 0.31867199903354 | 0.290349806658924 | 0.505875493166968 | 0.80645440868102 | 0.385964334476739 | 0.331886192085221 | 0.277922910172492 | 0.0989581865724176 | 0.618394369492307 | 0.614364792359993 | 0.337085843319073 | 0.0555405907798558 | 0.568272173870355 | 0.417519848095253 |
| 31 | 0.00265661929734051 | 0.233604044420645 | 0.154674642952159 | 0.20734699559398 | 0.129894758341834 | 0.308994544204324 | 0.153213268378749 | 0.703051693271846 | 0.544093576958403 | 0.301436702953652 | 0.559439905220643 | 0.297492073383182 | 0.814981606788933 | 0.601676020305604 | 0.177293838001788 | 0.294233977328986 | 0.868303266121075 | 0.544370670104399 | 0.208468266995624 | 0.689001269405708 | 0.00629413803108037 | 0.0514409933239222 | 0.543670303188264 | 0.723811825271696 | 0.914192294236273 | ... | 0.170503036584705 | 0.529984891181812 | 0.748115975642577 | 0.438477165065706 | 0.0105155971832573 | 0.874313783366233 | 0.0581022226251662 | 0.524641685420647 | 0.0597456027753651 | 0.451322933658957 | 0.287416146835312 | 0.000749221304431558 | 0.0616424982436001 | 0.85344085493125 | 0.521899901563302 | 0.336585639743134 | 0.603681788546965 | 0.43775239540264 | 0.201148092513904 | 0.117573149269447 | 0.77823152509518 | 0.228107163449749 | 0.105071109952405 | 0.915290450677276 | 0.898755661677569 |
| 32 | 0.00280914781615138 | 0.671240695519373 | 0.130032918183133 | 0.857616907916963 | 0.616999097866938 | 0.211817761650309 | 0.412596693495288 | 0.544890288263559 | 0.378286787541583 | 0.658102142857388 | 0.485088926274329 | 0.343446394428611 | 0.0950792075600475 | 0.654239452211186 | 0.379127501277253 | 0.20900071435608 | 0.190490665379912 | 0.840795011492446 | 0.403923029545695 | 0.149794495664537 | 0.859441242413595 | 0.254619705025107 | 0.253213867079467 | 0.833299791673198 | 0.132330614374951 | ... | 0.294122199993581 | 0.584084391593933 | 0.890566063579172 | 0.361675830557942 | 0.137697903206572 | 0.501630789833143 | 0.511742963688448 | 0.798591198632494 | 0.0760694285854697 | 0.0450899847783148 | 0.614368106005713 | 0.369974457658827 | 0.967022526310757 | 0.971603771904483 | 0.993630901211873 | 0.100453261984512 | 0.0201376907061785 | 0.380880827549845 | 0.5589455133304 | 0.975890525616705 | 0.285631553037092 | 0.624506171559915 | 0.393633222207427 | 0.809272889280692 | 0.388840372441337 |
| 33 | 0.00291598867624998 | 0.469349483260885 | 0.40488360193558 | 0.976271624676883 | 0.81754529918544 | 0.717530540656298 | 0.176391615765169 | 0.322254589293152 | 0.275100007886067 | 0.123195387655869 | 0.854215772822499 | 0.152976710582152 | 0.168612874578685 | 0.932161060394719 | 0.258664250606671 | 0.368882106151432 | 0.642827446805313 | 0.596267045475543 | 0.78629544028081 | 0.857970173237845 | 0.074953933712095 | 0.460302785271779 | 0.175863744691014 | 0.0781305325217545 | 0.362727939384058 | ... | 0.438740658573806 | 0.0650218348018825 | 0.483201798982918 | 0.0906684075016528 | 0.75584897515364 | 0.734921594848856 | 0.0520704155787826 | 0.678939774399623 | 0.485095809912309 | 0.910375472158194 | 0.0278428050223738 | 0.673360026907176 | 0.196820240234956 | 0.909403823316097 | 0.96757023781538 | 0.249046185519546 | 0.747162183746696 | 0.889505429659039 | 0.232712908647954 | 0.0687923936638981 | 0.749856255715713 | 0.553692282410339 | 0.485509524587542 | 0.570043925428763 | 0.123877165373415 |
| 34 | 0.00295075424946845 | 0.752080471953377 | 0.927080085501075 | 0.676588472211733 | 0.145305966958404 | 0.990650948137045 | 0.486672486877069 | 0.899637139635161 | 0.11753646354191 | 0.410862946882844 | 0.890014256816357 | 0.465360411442816 | 0.867269611451775 | 0.142796025844291 | 0.0382851022295654 | 0.900031937519088 | 0.541122051887214 | 0.273285012692213 | 0.978699575411156 | 0.193189743673429 | 0.746548868017271 | 0.746743169147521 | 0.384537698933855 | 0.18610900035128 | 0.419202369172126 | ... | 0.916567996377125 | 0.355271090054885 | 0.0449989710468799 | 0.196870251558721 | 0.437671930296347 | 0.383191644446924 | 0.233108018990606 | 0.0491329140495509 | 0.98706271359697 | 0.220664479071274 | 0.125456861918792 | 0.693342390703037 | 0.41156729310751 | 0.656783124431968 | 0.132763837231323 | 0.294767085229978 | 0.174554331228137 | 0.472542515955865 | 0.176419395720586 | 0.0810340188909322 | 0.0243790224194527 | 0.447855221573263 | 0.0155898209195584 | 0.595561402849853 | 0.508690778166056 |
| 35 | 0.00298465066589415 | 0.00471880054101348 | 0.423242166871205 | 0.448847176972777 | 0.482658875640482 | 0.490059984382242 | 0.276396255008876 | 0.79678833228536 | 0.749730166047812 | 0.728841377189383 | 0.434022579807788 | 0.750054371776059 | 0.698614856693894 | 0.644883789122105 | 0.851070581469685 | 0.948046802310273 | 0.355669980170205 | 0.132497925776988 | 0.126497498713434 | 0.495950541691855 | 0.970650220056996 | 0.747004285221919 | 0.741926323855296 | 0.434224577154964 | 0.0233239543158561 | ... | 0.453180570621043 | 0.691821031738073 | 0.15551860560663 | 0.334431348601356 | 0.356739384122193 | 0.408895551459864 | 0.474668124224991 | 0.646951925009489 | 0.792683714767918 | 0.0944881637115031 | 0.133352915989235 | 0.790962738683447 | 0.990898564225063 | 0.763694444205612 | 0.81355939945206 | 0.373281859792769 | 0.419338103849441 | 0.232999444240704 | 0.133902364177629 | 0.159517250023782 | 0.374121132306755 | 0.23352990206331 | 0.845121007179841 | 0.616322759073228 | 0.967735582729802 |
| 36 | 0.00321246823295951 | 0.255996472202241 | 0.167158168042079 | 0.63697260664776 | 0.494525003712624 | 0.39834220870398 | 0.769820443820208 | 0.661194241140038 | 0.606449404498562 | 0.802332860184833 | 0.333509913645685 | 0.120107821654528 | 0.511995058739558 | 0.0184341568965465 | 0.75331404292956 | 0.183275694493204 | 0.76121402811259 | 0.0981954836752266 | 0.154177918098867 | 0.774685870856047 | 0.273392584174871 | 0.878519853344187 | 0.072082482278347 | 0.812517619226128 | 0.966873846016824 | ... | 0.157514396589249 | 0.545718298759311 | 0.585524810943753 | 0.808543046237901 | 0.427939169574529 | 0.659729087958112 | 0.653476937208325 | 0.825968105345964 | 0.150807911762968 | 0.0363802220672369 | 0.511285114800557 | 0.104466018732637 | 0.933146112831309 | 0.490836617536843 | 0.235146143706515 | 0.0661466105375439 | 0.424147698562592 | 0.452357989503071 | 0.868621371453628 | 0.194498109864071 | 0.375028274254873 | 0.0472560892812908 | 0.666779254097492 | 0.608251665718853 | 0.83725716220215 |
| 37 | 0.00326714431867003 | 0.0174660191405565 | 0.767397797899321 | 0.486941671697423 | 0.179142937762663 | 0.0388191926758736 | 0.058632698841393 | 0.93272793921642 | 0.00518345576710999 | 0.745745988097042 | 0.0636269624810666 | 0.142167937941849 | 0.123958287294954 | 0.561215912690386 | 0.0583879987243563 | 0.214020606363192 | 0.855987261980772 | 0.34434140753001 | 0.856188560836017 | 0.190549340331927 | 0.643895004643127 | 0.354317616438493 | 0.0906851778272539 | 0.0877404543571174 | 0.149301011580974 | ... | 0.215895066503435 | 0.159743331838399 | 0.209419013001025 | 0.44718486815691 | 0.698766723508015 | 0.387042219517753 | 0.986150799319148 | 0.970136865507811 | 0.172170792706311 | 0.397120789624751 | 0.782227281248197 | 0.125850205076858 | 0.431781690567732 | 0.105974669102579 | 0.7010509732645 | 0.754344484535977 | 0.630134075880051 | 0.460583282401785 | 0.565713193733245 | 0.869257467100397 | 0.526022603968158 | 0.576158982003108 | 0.791660006856546 | 0.570430608466268 | 0.296845989534631 |
| 38 | 0.00343606760725379 | 0.872089479351416 | 0.427031415747479 | 0.783827807987109 | 0.468945624772459 | 0.885118836304173 | 0.577483307104558 | 0.316306815715507 | 0.643368247663602 | 0.797441647620872 | 0.571363317081705 | 0.939394322456792 | 0.834206420462579 | 0.427698265295476 | 0.108525566989556 | 0.318552517332137 | 0.728174756048247 | 0.295206972630695 | 0.378771479008719 | 0.0272987494245172 | 0.476261809933931 | 0.798434495925903 | 0.848329036030918 | 0.390233047772199 | 0.615119263064116 | ... | 0.282748674973845 | 0.931264373008162 | 0.836066073039547 | 0.569496796932071 | 0.879836764652282 | 0.175700651248917 | 0.58625450800173 | 0.515442076139152 | 0.483866753522307 | 0.152078261366114 | 0.927417221479118 | 0.88806808530353 | 0.788923309184611 | 0.190547303529456 | 0.665914306649938 | 0.227963931392878 | 0.341033497592434 | 0.721618991112337 | 0.389198728837073 | 0.152012875769287 | 0.742140771588311 | 0.351852362742648 | 0.451655799988657 | 0.272458662977442 | 0.275019130902365 |
| 39 | 0.00352300843223929 | 0.915988270426169 | 0.756346836686134 | 0.748829989228398 | 0.339556987863034 | 0.809970701113343 | 0.415563558228314 | 0.313897841842845 | 0.689000322716311 | 0.618055416736752 | 0.630551312118769 | 0.781374559737742 | 0.570669265696779 | 0.839040300110355 | 0.0957652218639851 | 0.969012186396867 | 0.378043979406357 | 0.436420301208273 | 0.688114636344835 | 0.269603253342211 | 0.738249947316945 | 0.394821299705654 | 0.313961697742343 | 0.929383381735533 | 0.743298690998927 | ... | 0.520362263079733 | 0.796207675943151 | 0.760845784563571 | 0.471272265305743 | 0.0758121402468532 | 0.893820916535333 | 0.182337804697454 | 0.483851918252185 | 0.668182422406971 | 0.541739117354155 | 0.172647176543251 | 0.451564599294215 | 0.917229424929246 | 0.262078544590622 | 0.981973067624494 | 0.825070995138958 | 0.265207782620564 | 0.257506407564506 | 0.467070138314739 | 0.254689825931564 | 0.217051470885053 | 0.43015126674436 | 0.353581800591201 | 0.17922296654433 | 0.904685341520235 |
| 40 | 0.0036735434550792 | 0.696800325298682 | 0.707175667630509 | 0.115501058520749 | 0.195810850709677 | 0.425887756049633 | 0.755632003303617 | 0.864974323427305 | 0.15028068702668 | 0.569188983878121 | 0.739296954590827 | 0.213339786510915 | 0.0509087680839002 | 0.764093637466431 | 0.677369228331372 | 0.39398123556748 | 0.583633958827704 | 0.0600933700334281 | 0.715155296958983 | 0.346099941059947 | 0.882725200150162 | 0.511865077773109 | 0.960763346171007 | 0.347176643321291 | 0.355430125957355 | ... | 0.773049798328429 | 0.763940198579803 | 0.320950758177787 | 0.205818864051253 | 0.958738413639367 | 0.110330988187343 | 0.876869629602879 | 0.143649420700967 | 0.41688177222386 | 0.829592682421207 | 0.738943091826513 | 0.304125551600009 | 0.331985725322738 | 0.840897630900145 | 0.709520239382982 | 0.947338208323345 | 0.0130847429390997 | 0.131683319108561 | 0.167587323114276 | 0.0146973512601107 | 0.361174535937607 | 0.552811660571024 | 0.583490462973714 | 0.253317506751046 | 0.751678226049989 |
| 41 | 0.00368419336155057 | 0.180366545915604 | 0.801115330075845 | 0.0280407930258662 | 0.4069808521308 | 0.740113783394918 | 0.903245680965483 | 0.238793359370902 | 0.739117383956909 | 0.655939477030188 | 0.843325359281152 | 0.92596345464699 | 0.292597211431712 | 0.788282975787297 | 0.312822371022776 | 0.806999240303412 | 0.175411092350259 | 0.27281416207552 | 0.158725636545569 | 0.657643004087731 | 0.436349863186479 | 0.791702603921294 | 0.119963391451165 | 0.475137493340299 | 0.265262400032952 | ... | 0.257866690866649 | 0.239980244543403 | 0.643581798067316 | 0.109940534457564 | 0.892730526858941 | 0.210337310098112 | 0.160712252836674 | 0.850766386603937 | 0.246179474284872 | 0.924878936493769 | 0.991947884205729 | 0.77385615115054 | 0.848044507903978 | 0.327669225167483 | 0.30477303173393 | 0.626208555651829 | 0.0585553732234985 | 0.293514188844711 | 0.417798350797966 | 0.985895997146145 | 0.715284518199041 | 0.385656688129529 | 0.841511073289439 | 0.126855174778029 | 0.854628147790208 |
| 42 | 0.0036886075977236 | 0.705337426858023 | 0.783166819950566 | 0.976659056963399 | 0.477033994859084 | 0.363209182629362 | 0.912831365363672 | 0.0958778401836753 | 0.940856399945915 | 0.149647668236867 | 0.153804332017899 | 0.658942473586649 | 0.388763905502856 | 0.640996936941519 | 0.399806711357087 | 0.252021841472015 | 0.863459216430783 | 0.339574544457719 | 0.913095327559859 | 0.417228745296597 | 0.325512520037591 | 0.228801223216578 | 0.719302760669962 | 0.199060673359782 | 0.973977883579209 | ... | 0.264396278886124 | 0.35553465038538 | 0.0389254230540246 | 0.920941951684654 | 0.271604564972222 | 0.787591272732243 | 0.761817314429209 | 0.377568684518337 | 0.357816752744839 | 0.361824744381011 | 0.984705524286255 | 0.333815657068044 | 0.00810636044479907 | 0.280569039518014 | 0.741570368874818 | 0.0328889398369938 | 0.745346313342452 | 0.368773948866874 | 0.82162807113491 | 0.515859337989241 | 0.633900862187147 | 0.485551285324618 | 0.947682336671278 | 0.597785558085889 | 0.823801580118015 |
| 43 | 0.00402670679613948 | 0.509442075854167 | 0.0928169921971858 | 0.793479028856382 | 0.0682689452078193 | 0.579685264965519 | 0.871931936359033 | 0.492362440330908 | 0.566057496704161 | 0.384659636765718 | 0.279908248921856 | 0.436410341178998 | 0.925620130030438 | 0.173231835011393 | 0.970664369408041 | 0.647773654200137 | 0.620112270815298 | 0.655411206418648 | 0.163464660523459 | 0.00388226332142949 | 0.463833277113736 | 0.0476436156313866 | 0.328799114795402 | 0.228894370608032 | 0.521346292458475 | ... | 0.367164153140038 | 0.303013495868072 | 0.529742926824838 | 0.300348907709122 | 0.261524944799021 | 0.33526824391447 | 0.589596569538116 | 0.291044994955882 | 0.4669262196403 | 0.995389070129022 | 0.7263829393778 | 0.0439706249162555 | 0.315604906296358 | 0.971861486323178 | 0.717963960953057 | 0.141105521703139 | 0.977323145139962 | 0.748933990485966 | 0.720704961102456 | 0.480863932752982 | 0.288139648735523 | 0.742276803124696 | 0.150112389586866 | 0.0473991595208645 | 0.00763164437375963 |
| 44 | 0.00423010461963713 | 0.30574262351729 | 0.992454842431471 | 0.804230775684118 | 0.530852598836645 | 0.632649562787265 | 0.269270051969215 | 0.886003164341673 | 0.0897746784612536 | 0.203865877585486 | 0.877019582083449 | 0.157536962069571 | 0.481505720177665 | 0.124504279810935 | 0.807116419542581 | 0.00651024817489088 | 0.0880216248333454 | 0.717539999168366 | 0.137658807681873 | 0.0527230892330408 | 0.620065597817302 | 0.879375886404887 | 0.344474737765267 | 0.505645018769428 | 0.844413203885779 | ... | 0.690914444159716 | 0.417095759883523 | 0.325701702386141 | 0.829242274863645 | 0.0937670639250427 | 0.344381019705907 | 0.310739417560399 | 0.0600167280063033 | 0.503772325348109 | 0.127327775582671 | 0.492342396173626 | 0.487777962116525 | 0.78721454879269 | 0.251459035091102 | 0.44183359364979 | 0.800137482816353 | 0.234936214750633 | 0.577205004636198 | 0.648418336641043 | 0.796812066342682 | 0.283818808849901 | 0.00862591830082238 | 0.355931947007775 | 0.714035667246208 | 0.45701154624112 |
| 45 | 0.00452669081278145 | 0.750805834773928 | 0.574280372122303 | 0.928068094188347 | 0.570725104305893 | 0.0604273655917495 | 0.739134729607031 | 0.977790241595358 | 0.423410237766802 | 0.582917384337634 | 0.29918238078244 | 0.542088611982763 | 0.927717842161655 | 0.354259949177504 | 0.435206018155441 | 0.847207005135715 | 0.747068133903667 | 0.910992112243548 | 0.879880684660748 | 0.727371386718005 | 0.813802567077801 | 0.337375801522285 | 0.553341380320489 | 0.792219292139634 | 0.300718312384561 | ... | 0.494887131964788 | 0.0925602910574526 | 0.473483083071187 | 0.989679614780471 | 0.912478304933757 | 0.944417269667611 | 0.854643840808421 | 0.144622368272394 | 0.129672765498981 | 0.691316657001153 | 0.177754152566195 | 0.356099260505289 | 0.582053420832381 | 0.667543210787699 | 0.498253778554499 | 0.887969996314496 | 0.114291863748804 | 0.212831700453535 | 0.58528151572682 | 0.302424246910959 | 0.158549334621057 | 0.111122798640281 | 0.901147782802582 | 0.782189185963944 | 0.462889114394784 |
| 46 | 0.00473698182031512 | 0.214349813759327 | 0.224341207649559 | 0.84179819887504 | 0.702824129955843 | 0.980134609388188 | 0.143901354866102 | 0.328493831446394 | 0.960100287571549 | 0.727654415881261 | 0.495418918086216 | 0.77272543264553 | 0.166930574458092 | 0.90797113487497 | 0.608581138541922 | 0.630864892620593 | 0.667927198577672 | 0.073452808894217 | 0.203242799732834 | 0.283800048520789 | 0.548403061460704 | 0.959561683936045 | 0.452687822515145 | 0.737832180224359 | 0.421178415883332 | ... | 0.224699669284746 | 0.201944555621594 | 0.667440991615877 | 0.0232000811956823 | 0.389207436237484 | 0.187629098305479 | 0.654893848812208 | 0.748101821169257 | 0.160462932661176 | 0.0411589818540961 | 0.380874985130504 | 0.388922778889537 | 0.378196926089004 | 0.558801003964618 | 0.933735421393067 | 0.89017803571187 | 0.553879963699728 | 0.0916542580816895 | 0.354400751646608 | 0.684661499923095 | 0.292309124721214 | 0.871065630810335 | 0.625566760078073 | 0.288621737854555 | 0.939042134210467 |
| 47 | 0.00476286024786532 | 0.836114055244252 | 0.837525868555531 | 0.965482759289443 | 0.0160295655950904 | 0.658297091722488 | 0.505912245251238 | 0.549740843242034 | 0.149947789264843 | 0.255757369101048 | 0.357184710912406 | 0.807608532719314 | 0.791414334438741 | 0.639044532319531 | 0.6140786788892 | 0.934156289789826 | 0.400101950624958 | 0.564593808259815 | 0.23266275273636 | 0.886818083701655 | 0.889073841273785 | 0.110653733834624 | 0.712232932914048 | 0.056368266697973 | 0.24745393707417 | ... | 0.925618458772078 | 0.143784253625199 | 0.856142996577546 | 0.842799369012937 | 0.493987491354346 | 0.750533042941242 | 0.308190849842504 | 0.325865569524467 | 0.901600686134771 | 0.631627542199567 | 0.750640895450488 | 0.763290709583089 | 0.194563149474561 | 0.976976301521063 | 0.961578693473712 | 0.882049453211948 | 0.822609586408362 | 0.877968843327835 | 0.645151824923232 | 0.0207159765996039 | 0.713466387009248 | 0.153326391940936 | 0.709627649979666 | 0.370645152404904 | 0.908937876112759 |
| 48 | 0.00479959626682103 | 0.983347967965528 | 0.199761302908882 | 0.885531137464568 | 0.378334950190037 | 0.974497438408434 | 0.931729815434664 | 0.209295121254399 | 0.66887050238438 | 0.35045656026341 | 0.880845135077834 | 0.783079408574849 | 0.62961516273208 | 0.936688259476796 | 0.96360481553711 | 0.206115780165419 | 0.991191446315497 | 0.455237242626026 | 0.954850438283756 | 0.818361527984962 | 0.647938291309401 | 0.0315653989091516 | 0.747258190065622 | 0.954540964914486 | 0.581155929481611 | ... | 0.0787219605408609 | 0.828237555222586 | 0.887137093581259 | 0.801653066650033 | 0.993105851812288 | 0.146623109234497 | 0.130853310925886 | 0.166279268916696 | 0.102255538105965 | 0.84395745024085 | 0.0209886108059436 | 0.84993973467499 | 0.520146890776232 | 0.414994343882427 | 0.481278932653368 | 0.216828421456739 | 0.970814424566925 | 0.698048872174695 | 0.405724448384717 | 0.704912021989003 | 0.952228411566466 | 0.952961194794625 | 0.373041369719431 | 0.921536028617993 | 0.0878170446958393 |
| 49 | 0.00488140480592847 | 0.524222281295806 | 0.499292870750651 | 0.708093800814822 | 0.517133219633251 | 0.189567418769002 | 0.707515886519104 | 0.706973049091175 | 0.817357455845922 | 0.412872039014474 | 0.603129540802911 | 0.990753757767379 | 0.344340038020164 | 0.045671301195398 | 0.0835681911557913 | 0.883559462847188 | 0.395059061003849 | 0.651755982544273 | 0.378139660693705 | 0.853526815772057 | 0.155795847764239 | 0.0349411065690219 | 0.52974665700458 | 0.52593653020449 | 0.15980627737008 | ... | 0.482276149094105 | 0.44123838446103 | 0.225013507995754 | 0.381806456949562 | 0.71720629837364 | 0.440248777391389 | 0.22712494712323 | 0.559043838642538 | 0.654458036646247 | 0.51047696149908 | 0.476318512111902 | 0.0310608786530793 | 0.937506078742445 | 0.176274497061968 | 0.75912709813565 | 0.214081209385768 | 0.278777916682884 | 0.480185191147029 | 0.761540069943294 | 0.95697542023845 | 0.000637263525277376 | 0.699494462925941 | 0.716110824607313 | 0.617361793294549 | 0.137643382884562 |
| 50 | 0.00505432579666376 | 0.690568790538236 | 0.0169835956767201 | 0.211873911553994 | 0.547386519145221 | 0.0584771861322224 | 0.931694719009101 | 0.697539074812084 | 0.610914738615975 | 0.249827107414603 | 0.0872564092278481 | 0.855939489323646 | 0.00873246463015676 | 0.649173375451937 | 0.234148127725348 | 0.28349857032299 | 0.455814302433282 | 0.257493371842429 | 0.416839299490675 | 0.000120812561362982 | 0.0229729732964188 | 0.462184741161764 | 0.0450461807195097 | 0.0888513568788767 | 0.689823579974473 | ... | 0.941694996319711 | 0.763309699716046 | 0.523958109086379 | 0.895590773550794 | 0.764240783872083 | 0.227259850827977 | 0.121178415603936 | 0.424205884570256 | 0.0549439680762589 | 0.941350265406072 | 0.426042396808043 | 0.600360754877329 | 0.0858097053132951 | 0.955021466361359 | 0.459916316671297 | 0.423167607048526 | 0.198052329709753 | 0.37333817104809 | 0.803478067042306 | 0.384270762093365 | 0.107271750457585 | 0.0957185525912791 | 0.235862274188548 | 0.754920317325741 | 0.706385037861764 |
| 51 | 0.00512500805780292 | 0.827614021953195 | 0.703118539648131 | 0.576497901463881 | 0.671205264050514 | 0.661198281683028 | 0.388944616541266 | 0.179182987427339 | 0.546743328217417 | 0.781425960361958 | 0.088243555277586 | 0.661002407083288 | 0.526145328767598 | 0.417304700938985 | 0.093505181837827 | 0.289715328486636 | 0.618347828974947 | 0.46070433780551 | 0.0590937456581742 | 0.281086340546608 | 0.760990387992933 | 0.71445231558755 | 0.0154505309183151 | 0.0634302312973887 | 0.206493706442416 | ... | 0.968307285103947 | 0.566233396297321 | 0.513326822081581 | 0.783582857111469 | 0.663560000946745 | 0.411058322526515 | 0.0880736727267504 | 0.132443085778505 | 0.680312181124464 | 0.383419493446127 | 0.757161130663007 | 0.680475580738857 | 0.117753422819078 | 0.157238294836134 | 0.330677137011662 | 0.569066962692887 | 0.111120779300109 | 0.493091724347323 | 0.735164624638855 | 0.204683241900057 | 0.668521163752303 | 0.214693202404305 | 0.699373301584274 | 0.495767338899896 | 0.261702405754477 |
| 52 | 0.00520264054648578 | 0.37451825896278 | 0.590862171025947 | 0.426462145755067 | 0.745872053783387 | 0.239919811952859 | 0.157852987758815 | 0.191093631088734 | 0.701260586967692 | 0.0760978597681969 | 0.336872569750994 | 0.740855416515842 | 0.697961072670296 | 0.458756172563881 | 0.269183449679986 | 0.420093926833943 | 0.333815529709682 | 0.395095819374546 | 0.524135649204254 | 0.859959032852203 | 0.10505484114401 | 0.58579178689979 | 0.963171456940472 | 0.364666988607496 | 0.567441117716953 | ... | 0.115891814930364 | 0.121773079270497 | 0.98600075324066 | 0.58562890207395 | 0.193033816292882 | 0.659056507749483 | 0.900533061707392 | 0.0826640217565 | 0.437835696619004 | 0.405601023463532 | 0.377416545990855 | 0.189662701683119 | 0.868696409743279 | 0.254848034121096 | 0.0259360033087432 | 0.0398855174425989 | 0.469520740909502 | 0.0533843659795821 | 0.468733243411407 | 0.148431882029399 | 0.631232254207134 | 0.172822681022808 | 0.824347700690851 | 0.93830328527838 | 0.103494475828484 |
| 53 | 0.00521824508905411 | 0.0714192937593907 | 0.159337566467002 | 0.581812658114359 | 0.82346655940637 | 0.777217993047088 | 0.569754800293595 | 0.423051534919068 | 0.536448602098972 | 0.0228377971798182 | 0.0102931384462863 | 0.456319727003574 | 0.641540755983442 | 0.974343610228971 | 0.777845579199493 | 0.434660000260919 | 0.863987089367583 | 0.242845957400277 | 0.504589875461534 | 0.105210327776149 | 0.187730490695685 | 0.628220844781026 | 0.791648703161627 | 0.107384183909744 | 0.922496233135462 | ... | 0.199464450590312 | 0.923920396016911 | 0.386428144061938 | 0.752949501620606 | 0.903868575114757 | 0.385481948265806 | 0.49189395015128 | 0.635764608858153 | 0.921837404835969 | 0.417788412421942 | 0.240100019611418 | 0.120114990742877 | 0.295489036943763 | 0.964884912129492 | 0.40690956544131 | 0.281516160350293 | 0.246586277615279 | 0.204052596120164 | 0.275398768950254 | 0.543992935679853 | 0.484465285902843 | 0.201371617615223 | 0.64131143828854 | 0.0651052410248667 | 0.556392027297989 |
| 54 | 0.00527134723961353 | 0.553741885116324 | 0.622059793677181 | 0.411058360245079 | 0.594796582357958 | 0.998178163776174 | 0.0673196299467236 | 0.691934961592779 | 0.229514035629109 | 0.0650876190047711 | 0.26779804751277 | 0.665094716241583 | 0.954613594571128 | 0.252820969093591 | 0.121582161169499 | 0.91386285959743 | 0.785386012634262 | 0.274311537388712 | 0.286236028885469 | 0.333381644217297 | 0.495322435861453 | 0.905963342171162 | 0.18889824883081 | 0.897838899632916 | 0.233361870516092 | ... | 0.398123752558604 | 0.53675076039508 | 0.532170563237742 | 0.577048750594258 | 0.446032384643331 | 0.210522084264085 | 0.3500934203621 | 0.0171492609661072 | 0.407096095150337 | 0.271899845218286 | 0.507563258055598 | 0.350707409903407 | 0.917466146638617 | 0.694407988106832 | 0.876535395625979 | 0.653655853820965 | 0.512658874969929 | 0.00273235235363245 | 0.648519926238805 | 0.667786063393578 | 0.79034771816805 | 0.739739292766899 | 0.670149973826483 | 0.638394994661212 | 0.576765945414081 |
| 55 | 0.00542729999870062 | 0.0985194828826934 | 0.0728782333899289 | 0.446197254350409 | 0.0383569365367293 | 0.950907492777333 | 0.726860936963931 | 0.881905190879479 | 0.800478731980547 | 0.992161565693095 | 0.689319999422878 | 0.294599803863093 | 0.979263986693695 | 0.856468619545922 | 0.816245506284758 | 0.467275898903608 | 0.251817981945351 | 0.325231060385704 | 0.511251300107688 | 0.11912576132454 | 0.108868513721973 | 0.508450768189505 | 0.240525492932647 | 0.112725934013724 | 0.0696287837345153 | ... | 0.207609720993787 | 0.642661877442151 | 0.480729275383055 | 0.00706184399314225 | 0.993240012554452 | 0.727059090044349 | 0.25663784192875 | 0.0154145730193704 | 0.316912158159539 | 0.873230698751286 | 0.564369517378509 | 0.999410609016195 | 0.362703620223328 | 0.8900362981949 | 0.882028897060081 | 0.148179254261777 | 0.658518724376336 | 0.965112134814262 | 0.224565503187478 | 0.365837063873187 | 0.669350707903504 | 0.627502098213881 | 0.565758740063757 | 0.335802071960643 | 0.774254606105387 |
| 56 | 0.00544631341472268 | 0.735852956306189 | 0.487795706605539 | 0.0355693679302931 | 0.394807943608612 | 0.305062146158889 | 0.0942887940909714 | 0.99047701433301 | 0.566958552459255 | 0.525522305397317 | 0.0737494355998933 | 0.887795954477042 | 0.286399983102456 | 0.378877202514559 | 0.361680257832631 | 0.801333107519895 | 0.658419626764953 | 0.173034155275673 | 0.0831867689266801 | 0.163236397318542 | 0.0987118708435446 | 0.430613863049075 | 0.453095584874973 | 0.628351008752361 | 0.948123715817928 | ... | 0.00651476811617613 | 0.872416977304965 | 0.36028571985662 | 0.123713189503178 | 0.211845577228814 | 0.853335168445483 | 0.383790580555797 | 0.122639119857922 | 0.57526146271266 | 0.158461109967902 | 0.766276198672131 | 0.669847244629636 | 0.519548968877643 | 0.218205115525052 | 0.157665038947016 | 0.349522384582087 | 0.809814345091581 | 0.386572048999369 | 0.337738613830879 | 0.416080208029598 | 0.63756100856699 | 0.270918486174196 | 0.891746119130403 | 0.247705178102478 | 0.484020983567461 |
| 57 | 0.00545631721615791 | 0.305394103052095 | 0.29820118076168 | 0.00925620901398361 | 0.343991097062826 | 0.971826896304265 | 0.859859268181026 | 0.497204449726269 | 0.181239414960146 | 0.663282196270302 | 0.406200075987726 | 0.599387107416987 | 0.825712693622336 | 0.676284324377775 | 0.0393648790195584 | 0.886655397713184 | 0.24561089114286 | 0.464101059362292 | 0.579860230209306 | 0.472144911298528 | 0.815574490698054 | 0.979079034877941 | 0.389423839049414 | 0.474789742846042 | 0.417906230548397 | ... | 0.892327177338302 | 0.588445978937671 | 0.608459653798491 | 0.939743687398732 | 0.307338567217812 | 0.0837919416371733 | 0.560717491200194 | 0.139057053253055 | 0.227872353279963 | 0.904547612182796 | 0.900656980928034 | 0.696299152681604 | 0.919404983054847 | 0.509884606348351 | 0.844755557132885 | 0.77221998362802 | 0.062881066929549 | 0.402440675534308 | 0.826083685038611 | 0.704642984550446 | 0.802286474267021 | 0.575704629998654 | 0.303442992502823 | 0.00908147776499391 | 0.690210870932788 |
| 58 | 0.00557069736532867 | 0.169041889719665 | 0.0845173369161785 | 0.321709681302309 | 0.95312004070729 | 0.0795205279719085 | 0.707029960583895 | 0.742534856544808 | 0.196845590835437 | 0.958732389612123 | 0.0731615456752479 | 0.83250481961295 | 0.399593784939498 | 0.559280209476128 | 0.95247405115515 | 0.222460243850946 | 0.0176083645783365 | 0.247554098255932 | 0.24964742641896 | 0.771993004018441 | 0.709956546779722 | 0.537342629395425 | 0.907542179338634 | 0.648541401373222 | 0.191595482407138 | ... | 0.591596155427396 | 0.23478740779683 | 0.560605133417994 | 0.86390245007351 | 0.0304068378172815 | 0.916414356324822 | 0.149083462078124 | 0.0499617294408381 | 0.3127451390028 | 0.721559287514538 | 0.378752666525543 | 0.957897295011207 | 0.906150951748714 | 0.943777846172452 | 0.0179806191008538 | 0.988482322311029 | 0.996675929054618 | 0.939084586687386 | 0.855752362404019 | 0.569500973448157 | 0.217251345748082 | 0.272108389995992 | 0.81089296285063 | 0.0480965082533658 | 0.255817198893055 |
| 59 | 0.00564605835825205 | 0.544793791603297 | 0.990786865586415 | 0.651332662673667 | 0.584917139494792 | 0.117638921132311 | 0.748902311082929 | 0.00785179901868105 | 0.0115098177921027 | 0.587179303634912 | 0.447049296228215 | 0.958314894000068 | 0.963415954727679 | 0.493093417258933 | 0.609253925969824 | 0.851687761023641 | 0.301526920637116 | 0.738525769906119 | 0.434798765229061 | 0.736535971751437 | 0.106563571142033 | 0.427481764229015 | 0.159937845310196 | 0.225487580057234 | 0.198753843549639 | ... | 0.69197680009529 | 0.451267498545349 | 0.188985091401264 | 0.0100830351002514 | 0.712163930060342 | 0.602918043732643 | 0.79509056545794 | 0.353838163428009 | 0.111203168518841 | 0.164469091454521 | 0.0130493813194335 | 0.510315428487957 | 0.680935632903129 | 0.419645985821262 | 0.760716098826379 | 0.475737958913669 | 0.0283176575321704 | 0.675537645816803 | 0.384217160521075 | 0.344267901265994 | 0.416631872300059 | 0.12836930830963 | 0.941057031275705 | 0.921958645107225 | 0.868505738908425 |
| 60 | 0.00570800062268972 | 0.198968801880255 | 0.896845533046871 | 0.665047334739938 | 0.394065778004006 | 0.739075126824901 | 0.552949122153223 | 0.272848259657621 | 0.313062062487006 | 0.100554176839069 | 0.101312134182081 | 0.462837106082588 | 0.0926090141292661 | 0.995647232513875 | 0.885885623749346 | 0.331631659762934 | 0.485577845247462 | 0.515355945797637 | 0.411299631698057 | 0.650160254212096 | 0.794810887193307 | 0.335056693991646 | 0.679949279874563 | 0.430276995524764 | 0.624311592895538 | ... | 0.392839779146016 | 0.561602892586961 | 0.689319182420149 | 0.335443465970457 | 0.826380433049053 | 0.786911040311679 | 0.844813093077391 | 0.915422697318718 | 0.781959864776582 | 0.164912825450301 | 0.798505070386454 | 0.261323653394356 | 0.32370206923224 | 0.100966332480311 | 0.971965884556994 | 0.685685842297971 | 0.59806994930841 | 0.540637192549184 | 0.0651711048558354 | 0.119002857711166 | 0.794661332853138 | 0.6804163698107 | 0.880039382493123 | 0.236424328526482 | 0.637372372439131 |
| 61 | 0.0058420873247087 | 0.487439940217882 | 0.0693616156931967 | 0.89277281309478 | 0.0551342705730349 | 0.0147391075734049 | 0.52953960117884 | 0.658191449940205 | 0.955283769639209 | 0.00758825987577438 | 0.475520375417545 | 0.663741127355024 | 0.430226403987035 | 0.437200151849538 | 0.484099780907854 | 0.67703814455308 | 0.212137770373374 | 0.706954997032881 | 0.0879658933263272 | 0.67021671985276 | 0.820963212987408 | 0.389813278801739 | 0.315542730735615 | 0.421470998320729 | 0.136344005586579 | ... | 0.835738538997248 | 0.246223162161186 | 0.739300994668156 | 0.314018340082839 | 0.232958232518286 | 0.536079223966226 | 0.112768521066755 | 0.929051347775385 | 0.208263790467754 | 0.0137410047464073 | 0.294796554138884 | 0.565313895465806 | 0.219081635121256 | 0.0439939878415316 | 0.0948074669577181 | 0.580463244579732 | 0.458400409901515 | 0.827435329323635 | 0.529704233398661 | 0.723242719192058 | 0.0687298693228513 | 0.764891817234457 | 0.298130952520296 | 0.396604548441246 | 0.0769238772336394 |
| 62 | 0.00590499979443848 | 0.391575067071244 | 0.898628495633602 | 0.136368808569387 | 0.220068388851359 | 0.26619123108685 | 0.665186803555116 | 0.542669781250879 | 0.776496385922655 | 0.430105364648625 | 0.99472586507909 | 0.275531146442518 | 0.349392972420901 | 0.154154501855373 | 0.319782954407856 | 0.278363812016323 | 0.0158668914809823 | 0.696407308103517 | 0.373180317692459 | 0.222168841399252 | 0.202204985776916 | 0.861552017740905 | 0.407200349727646 | 0.730437344638631 | 0.966627455316484 | ... | 0.671018757857382 | 0.900934290606529 | 0.56561130983755 | 0.851075064390898 | 0.20046322606504 | 0.500900564249605 | 0.987607581308112 | 0.974705578293651 | 0.176390126347542 | 0.0207057495135814 | 0.844529106747359 | 0.030980511335656 | 0.716507225995883 | 0.957390898372978 | 0.585414851782843 | 0.600086432415992 | 0.0944792036898434 | 0.751511522335932 | 0.777004393516108 | 0.445599037921056 | 0.212778838351369 | 0.514373308513314 | 0.38302701106295 | 0.964558941544965 | 0.718018828425556 |
| 63 | 0.00594114954583347 | 0.484230004949495 | 0.630423789843917 | 0.720760194351897 | 0.422395578352734 | 0.826316798338667 | 0.600536709651351 | 0.369269155664369 | 0.679336395580322 | 0.280543027678505 | 0.931420272914693 | 0.448502925690264 | 0.713021065341309 | 0.227055686758831 | 0.2243634222541 | 0.793138012290001 | 0.663551743375137 | 0.926951827248558 | 0.989303613780066 | 0.425094344653189 | 0.527628286508843 | 0.218839923851192 | 0.240632872795686 | 0.583602123195305 | 0.513336884789169 | ... | 0.683383374009281 | 0.746661324286833 | 0.451061997329816 | 0.476843532640487 | 0.277614664053544 | 0.550605454016477 | 0.415795621694997 | 0.832812234759331 | 0.261570092523471 | 0.0566035029478371 | 0.498389723245054 | 0.380211926298216 | 0.801916132913902 | 0.152119207195938 | 0.728500999743119 | 0.959260194795206 | 0.54931360646151 | 0.778833430726081 | 0.626358143752441 | 0.838291369611397 | 0.513856633100659 | 0.215462549356744 | 0.0295965452678502 | 0.298683980945498 | 0.377853292971849 |
| 64 | 0.00615661987103522 | 0.447072439594194 | 0.221893213689327 | 0.815467176958919 | 0.596651979722083 | 0.427047847304493 | 0.184567391406745 | 0.0379652315750718 | 0.444271012675017 | 0.197746000485495 | 0.783588877879083 | 0.513650454813614 | 0.155840025749058 | 0.668285081861541 | 0.610434213886037 | 0.469725417671725 | 0.731709834188223 | 0.66630583582446 | 0.558878999901935 | 0.587267091264948 | 0.611247513210401 | 0.614875691244379 | 0.560765519971028 | 0.636904052924365 | 0.589660397497937 | ... | 0.346603437326849 | 0.516251941444352 | 0.218349524075165 | 0.834674652433023 | 0.149607346160337 | 0.93225156608969 | 0.995467644184828 | 0.304275540402159 | 0.297435573767871 | 0.318236448336393 | 0.925672550918534 | 0.280976849608123 | 0.456860654987395 | 0.705273384228349 | 0.578284494346008 | 0.751134120160714 | 0.653562900843099 | 0.447299349820241 | 0.221959253773093 | 0.0823768530972302 | 0.737201862968504 | 0.425570802064613 | 0.469516803976148 | 0.664528833935037 | 0.90504606324248 |
| 65 | 0.00628059101291001 | 0.549754005391151 | 0.0045338049530983 | 0.0241978417616338 | 0.471716393018141 | 0.0648758469615132 | 0.0303512501996011 | 0.472237220499665 | 0.748754013096914 | 0.698003396624699 | 0.498764364048839 | 0.162996264174581 | 0.0990795297548175 | 0.398633745498955 | 0.0060644734185189 | 0.568024926120415 | 0.756457894807681 | 0.661690522450954 | 0.433324183803052 | 0.362961675273255 | 0.616922209272161 | 0.0594514997210354 | 0.58208642131649 | 0.037406598450616 | 0.644680310739204 | ... | 0.937964684562758 | 0.35049789166078 | 0.978162533137947 | 0.0674188705161214 | 0.620797558454797 | 0.151775966165587 | 0.24486660794355 | 0.30133219435811 | 0.902768721804023 | 0.745845432160422 | 0.316673438530415 | 0.905689388513565 | 0.546344048110768 | 0.934831596445292 | 0.97572159813717 | 0.206695037893951 | 0.377468114253134 | 0.893174293218181 | 0.620981719344854 | 0.532660934375599 | 0.11658920487389 | 0.0646670996211469 | 0.506771944463253 | 0.703987681539729 | 0.543073687469587 |
| 66 | 0.00633476674556732 | 0.738304937724024 | 0.74841011594981 | 0.921433058800176 | 0.967548111220822 | 0.163020230596885 | 0.401544687338173 | 0.490575413219631 | 0.542124524479732 | 0.254861178109422 | 0.922306173713878 | 0.215199573431164 | 0.872025811811909 | 0.608058465644717 | 0.464131153421476 | 0.524804233340546 | 0.696040601003915 | 0.437937969807535 | 0.813645685091615 | 0.555530182085931 | 0.852384305791929 | 0.62653797166422 | 0.641515050083399 | 0.19779527746141 | 0.512076980667189 | ... | 0.730301426257938 | 0.131093593547121 | 0.448068164288998 | 0.635414177551866 | 0.00721331709064543 | 0.551071592373773 | 0.0251445933245122 | 0.776527154492214 | 0.985724705969915 | 0.262483998201787 | 0.660443781642243 | 0.846791256219149 | 0.35382856358774 | 0.0880519009660929 | 0.297485028160736 | 0.83629097067751 | 0.710215501487255 | 0.555339266080409 | 0.0954319047741592 | 0.370054064085707 | 0.0335839453618973 | 0.951411831425503 | 0.0160303281154484 | 0.679028244223446 | 0.998649308923632 |
| 67 | 0.00638544512912631 | 0.941511775599793 | 0.546686662361026 | 0.699786011362448 | 0.705667800270021 | 0.131462624063715 | 0.492481377441436 | 0.725087354425341 | 0.925374175887555 | 0.0744244263041764 | 0.925326310331002 | 0.778084733756259 | 0.205815176479518 | 0.168940907809883 | 0.0394548727199435 | 0.00899476744234562 | 0.472349484916776 | 0.370055108331144 | 0.643902158364654 | 0.563138714293018 | 0.668321651406586 | 0.175200837664306 | 0.481037037679926 | 0.601291084429249 | 0.0145862658973783 | ... | 0.683009847532958 | 0.818389215273783 | 0.302881058072671 | 0.930826785741374 | 0.766588233876973 | 0.148208820493892 | 0.644987488165498 | 0.181205921107903 | 0.291710464982316 | 0.991313207894564 | 0.701859974535182 | 0.247684045927599 | 0.371166828786954 | 0.402126244734973 | 0.122621424030513 | 0.0840797310229391 | 0.929270796012133 | 0.896337271900848 | 0.52519920701161 | 0.763792431214824 | 0.19958356115967 | 0.597418514778838 | 0.569526616018265 | 0.0012095954734832 | 0.206739773275331 |
| 68 | 0.00651065865531564 | 0.475664632627741 | 0.428303945111111 | 0.859996163286269 | 0.0321815363131464 | 0.818971471162513 | 0.127970324130729 | 0.921520633390173 | 0.088681862456724 | 0.331066616578028 | 0.0534393787384033 | 0.421275367960334 | 0.88759691407904 | 0.418694625375792 | 0.251191190909594 | 0.0309862776193768 | 0.0261411408428103 | 0.374657333130017 | 0.792295670835301 | 0.197602693689987 | 0.0768451585900038 | 0.478126965230331 | 0.290141612291336 | 0.992431435501203 | 0.682844300055876 | ... | 0.0210224143229425 | 0.749447588576004 | 0.345643219305202 | 0.0425607108045369 | 0.450924847507849 | 0.345898891566321 | 0.569545896258205 | 0.304115048376843 | 0.432041010120884 | 0.594655183842406 | 0.457033712649718 | 0.493312561651692 | 0.165640730177984 | 0.729507842101157 | 0.308968669269234 | 0.226114997174591 | 0.733951854286715 | 0.287185763241723 | 0.588735180674121 | 0.872738984180614 | 0.0295674267690629 | 0.0946803677361459 | 0.948019489413127 | 0.9235199179966 | 0.161282002460212 |
| 69 | 0.00656046136282384 | 0.797171119134873 | 0.288634080672637 | 0.494870118098333 | 0.813360549742356 | 0.436410437570885 | 0.842438233783469 | 0.58216352481395 | 0.917958627687767 | 0.44272288447246 | 0.0442893046420068 | 0.189115293789655 | 0.183122775983065 | 0.994660494849086 | 0.94699795008637 | 0.857225917978212 | 0.258060197811574 | 0.156136627774686 | 0.51731138327159 | 0.329815814038739 | 0.978100047446787 | 0.795227215625346 | 0.98312115506269 | 0.216169424122199 | 0.783465703483671 | ... | 0.329937838017941 | 0.884640621487051 | 0.16293820226565 | 0.449362881714478 | 0.0710684722289443 | 0.0364347212016582 | 0.49746175785549 | 0.768346241908148 | 0.694723262218758 | 0.826166328508407 | 0.611795277101919 | 0.235825744923204 | 0.37462752033025 | 0.143886419013143 | 0.757440359797329 | 0.244343176018447 | 0.707631783094257 | 0.126047337893397 | 0.108920849626884 | 0.156606360105798 | 0.704907646868378 | 0.0462954370304942 | 0.52998843928799 | 0.78701173979789 | 0.197143775643781 |
| 70 | 0.00657574785873294 | 0.352227679686621 | 0.492475457489491 | 0.310397456167266 | 0.432682123500854 | 0.699385559884831 | 0.67428210307844 | 0.0910754317883402 | 0.985856577055529 | 0.687817454803735 | 0.928337495308369 | 0.213592503452674 | 0.155283652478829 | 0.898122626822442 | 0.803376113530248 | 0.0665000416338444 | 0.460270224604756 | 0.537181950872764 | 0.317130245734006 | 0.679161380277947 | 0.459542093798518 | 0.781457018805668 | 0.814549545291811 | 0.334851087769493 | 0.29418298183009 | ... | 0.441248019458726 | 0.802127701928839 | 0.85187879553996 | 0.658467934001237 | 0.148695159470662 | 0.293667646823451 | 0.248471408616751 | 0.199193751672283 | 0.757652404950932 | 0.830052750883624 | 0.591490574646741 | 0.861025701276958 | 0.668310489272699 | 0.0824921233579516 | 0.211331780068576 | 0.262832366628572 | 0.884846568573266 | 0.38670669705607 | 0.549011681461707 | 0.0452686639036983 | 0.92093288176693 | 0.782242261106148 | 0.331069324864075 | 0.271381579805166 | 0.372715212870389 |
| 71 | 0.00682911975309253 | 0.868317244341597 | 0.549027282511815 | 0.77025717520155 | 0.191666702739894 | 0.808811294846237 | 0.926700678886846 | 0.0958568463101983 | 0.646217144560069 | 0.466239494504407 | 0.144059315090999 | 0.0928183938376606 | 0.866366318194196 | 0.538384463870898 | 0.748409320600331 | 0.125675105722621 | 0.736115707317367 | 0.310470917494968 | 0.333933878457174 | 0.557596778729931 | 0.121679296251386 | 0.644164627883583 | 0.104068741435185 | 0.771546210628003 | 0.794571666279808 | ... | 0.701536195585504 | 0.811793448869139 | 0.484984323382378 | 0.239383753621951 | 0.0218076333403587 | 0.881916151382029 | 0.848265812499449 | 0.039835493080318 | 0.13742034859024 | 0.660754258977249 | 0.0544981616549194 | 0.530355736380443 | 0.807092265458778 | 0.0766181137878448 | 0.166320539778098 | 0.0925438283011317 | 0.233007735339925 | 0.19564870884642 | 0.743887966498733 | 0.518424159381539 | 0.574929814087227 | 0.038033788325265 | 0.862003441900015 | 0.384783646790311 | 0.215177863603458 |
| 72 | 0.00698163546621799 | 0.728059047134593 | 0.68312806263566 | 0.164526244159788 | 0.86857085605152 | 0.752310901414603 | 0.975309886969626 | 0.846578204073012 | 0.0563092664815485 | 0.136846524197608 | 0.707643772941083 | 0.0835250450763851 | 0.62306144181639 | 0.857015942456201 | 0.59089875058271 | 0.0640106007922441 | 0.291410281322896 | 0.347186318365857 | 0.296509623527527 | 0.771266937255859 | 0.515718540176749 | 0.985502079827711 | 0.548783425008878 | 0.711964412825182 | 0.271678839810193 | ... | 0.440869985381141 | 0.497206464176998 | 0.757482857210562 | 0.0686040241271257 | 0.648093755356967 | 0.607987774768844 | 0.929217565106228 | 0.377513075247407 | 0.555798971792683 | 0.459594802930951 | 0.525122804567218 | 0.460054504685104 | 0.170211069751531 | 0.816819702275097 | 0.23021863005124 | 0.781994383316487 | 0.452477667247877 | 0.332613818347454 | 0.47990637156181 | 0.325769690331072 | 0.203475970542058 | 0.219561533769593 | 0.611538598779589 | 0.959557513007894 | 0.710627269698307 |
| 73 | 0.00718412874266505 | 0.677680395310745 | 0.901857769582421 | 0.385380365420133 | 0.0620515856426209 | 0.841634018346667 | 0.328076672740281 | 0.971451830584556 | 0.237240971066058 | 0.904532900312915 | 0.863475633086637 | 0.282673157285899 | 0.268474434502423 | 0.0841402150690556 | 0.33090363885276 | 0.811034300131723 | 0.607221523299813 | 0.0250429084990174 | 0.681572931818664 | 0.399765432113782 | 0.0969279925338924 | 0.265895780641586 | 0.766410032985732 | 0.642015063669533 | 0.988675465108827 | ... | 0.455664976034313 | 0.710396942449734 | 0.711332200793549 | 0.571864167228341 | 0.718981811311096 | 0.698714041151106 | 0.40675477986224 | 0.147630956955254 | 0.488514805678278 | 0.663752328138798 | 0.462097636424005 | 0.248474461492151 | 0.70487299375236 | 0.128251363057643 | 0.501165776513517 | 0.987679339479655 | 0.500115028116852 | 0.38312945025973 | 0.452078427188098 | 0.763456704327837 | 0.926631178474054 | 0.635719169862568 | 0.373527989955619 | 0.183575409697369 | 0.945515254279599 |
| 74 | 0.00720121734775603 | 0.707387377973646 | 0.98860705178231 | 0.639340686844662 | 0.610892586177215 | 0.797362731071189 | 0.578484339173883 | 0.668206557864323 | 0.443102199817076 | 0.653704979224131 | 0.761572478571907 | 0.46780481771566 | 0.237201286712661 | 0.0925363376736641 | 0.432081060949713 | 0.837176946923137 | 0.672002395614982 | 0.218305013841018 | 0.683667270932347 | 0.534095093142241 | 0.66444715927355 | 0.63436704617925 | 0.809637748636305 | 0.901468150317669 | 0.450080034555867 | ... | 0.631029587704688 | 0.627312702126801 | 0.74876123573631 | 0.813889425480738 | 0.20568797388114 | 0.581934130750597 | 0.144452826585621 | 0.816414088476449 | 0.0451749914791435 | 0.0998552038799971 | 0.502311483956873 | 0.754276427673176 | 0.56634085951373 | 0.791217556456104 | 0.27728162589483 | 0.931077834684402 | 0.121988345170394 | 0.553421165561303 | 0.0154673624783754 | 0.207687050569803 | 0.462445833021775 | 0.575175800826401 | 0.950012678746134 | 0.829519178718328 | 0.764692864613608 |
| 75 | 0.00725987157784402 | 0.842313644010574 | 0.313897647196427 | 0.066051215166226 | 0.381024438422173 | 0.963394361315295 | 0.091963168932125 | 0.807384464656934 | 0.631033020559698 | 0.446038549067453 | 0.468436724739149 | 0.996978126699105 | 0.702013148227707 | 0.281902451533824 | 0.23004759196192 | 0.964012711541727 | 0.425178336212412 | 0.66078269155696 | 0.569979896768928 | 0.341391057474539 | 0.76207425375469 | 0.0569733660668135 | 0.950227770023048 | 0.593796862754971 | 0.973077251110226 | ... | 0.561233582906425 | 0.591281367698684 | 0.766740415710956 | 0.458158097229898 | 0.803744134726003 | 0.945316541008651 | 0.0993914986029267 | 0.70188323315233 | 0.0510620535351336 | 0.829396773129702 | 0.241598475724459 | 0.634693173225969 | 0.497103233123198 | 0.041390607599169 | 0.143768025096506 | 0.862474144203588 | 0.940692620584741 | 0.359276844654232 | 0.445789540419355 | 0.683154890080914 | 0.466648225672543 | 0.733543248847127 | 0.125190794467926 | 0.726791135733947 | 0.967011082684621 |
| 76 | 0.00728158606216311 | 0.940816054586321 | 0.646537492983043 | 0.42660152236931 | 0.0817383960820735 | 0.45672770915553 | 0.506339125102386 | 0.493641458218917 | 0.847502418793738 | 0.980269070947543 | 0.230346301104873 | 0.910561337601393 | 0.57748263864778 | 0.551961095072329 | 0.287492562783882 | 0.00839215517044067 | 0.692887503886595 | 0.40620077913627 | 0.665181382093579 | 0.585072318324819 | 0.847657689359039 | 0.255783489439636 | 0.937995733926073 | 0.373016970232129 | 0.392282221466303 | ... | 0.942408423870802 | 0.585757347289473 | 0.246606351109222 | 0.791330257663503 | 0.0688130829948932 | 0.912553544389084 | 0.654293050523847 | 0.57167005026713 | 0.146462410222739 | 0.971753689460456 | 0.460492011159658 | 0.697808968136087 | 0.27038931986317 | 0.87086090631783 | 0.637818279443309 | 0.683485442539677 | 0.591055633733049 | 0.15233781398274 | 0.294953393051401 | 0.950384094147012 | 0.906562840333208 | 0.0185577422380447 | 0.66390008549206 | 0.558682711562142 | 0.431690049124882 |
| 77 | 0.00732194725424051 | 0.707103992346674 | 0.0061132435221225 | 0.695179809583351 | 0.398335141595453 | 0.0608573008794338 | 0.82301367027685 | 0.180415448732674 | 0.595447074389085 | 0.195492023136467 | 0.603927334304899 | 0.423503763973713 | 0.284650744171813 | 0.894684506347403 | 0.634346285602078 | 0.378240681486204 | 0.186581342481077 | 0.775384893408045 | 0.600175555096939 | 0.362711285240948 | 0.380434508435428 | 0.745089190779254 | 0.519666069652885 | 0.55595698277466 | 0.693609786219895 | ... | 0.977349830558524 | 0.78353309398517 | 0.775061671854928 | 0.213244894053787 | 0.51811342779547 | 0.969225008739159 | 0.352282004896551 | 0.878066633129492 | 0.296063489280641 | 0.709360636305064 | 0.415603258879855 | 0.179403548361734 | 0.823751583695412 | 0.97744945064187 | 0.78063845471479 | 0.027719427831471 | 0.89355136686936 | 0.794622207293287 | 0.0288766289595515 | 0.634151700185612 | 0.252941307611763 | 0.093156271846965 | 0.879052481846884 | 0.868689072085544 | 0.726065846392885 |
| 78 | 0.00752387614920735 | 0.156840761192143 | 0.424860244849697 | 0.519036102574319 | 0.509909392334521 | 0.418433520710096 | 0.425273899454623 | 0.654145006323233 | 0.117508988128975 | 0.170952392509207 | 0.0924288406968117 | 0.213562131626531 | 0.929053150583059 | 0.098350903717801 | 0.578957028687 | 0.746274020522833 | 0.827142435824499 | 0.49697329592891 | 0.222607275703922 | 0.810913977446035 | 0.649135254556313 | 0.964049411704764 | 0.884694288717583 | 0.346024075523019 | 0.325957860099152 | ... | 0.977310488233343 | 0.4237327685114 | 0.394783783005551 | 0.0591748564038426 | 0.637313363607973 | 0.99550954462029 | 0.0548290109727532 | 0.0546899486798793 | 0.572416414041072 | 0.415849097073078 | 0.532312872353941 | 0.999929730547592 | 0.447779558831826 | 0.0636921420227736 | 0.936094822827727 | 0.729822429595515 | 0.00459188572131097 | 0.515288845170289 | 0.721570347435772 | 0.278987759025767 | 0.489658471895382 | 0.180347237735987 | 0.548097838647664 | 0.301517448155209 | 0.269841637928039 |
| 79 | 0.00762112089432776 | 0.542065954068676 | 0.902843551710248 | 0.250275341328233 | 0.827013357309625 | 0.256030266871676 | 0.861521449871361 | 0.7572091948241 | 0.531383079010993 | 0.765265924390405 | 0.637120622210205 | 0.845045689726248 | 0.0613085990771651 | 0.124252619221807 | 0.856487578246742 | 0.15668640518561 | 0.991338263498619 | 0.458177980268374 | 0.109488517977297 | 0.371611663838848 | 0.212626181077212 | 0.528204880189151 | 0.720061585307121 | 0.370146951405331 | 0.974099460057914 | ... | 0.595534216379747 | 0.127570807468146 | 0.867574765812606 | 0.483153002336621 | 0.413393792463467 | 0.745257247705013 | 0.376062227413058 | 0.660460311919451 | 0.602246492169797 | 0.036833498859778 | 0.543292017886415 | 0.358778820373118 | 0.748138988856226 | 0.855232767993584 | 0.922239225590602 | 0.345518391113728 | 0.319740194827318 | 0.0387605037540197 | 0.405176592292264 | 0.105353318853304 | 0.264506435487419 | 0.292714140377939 | 0.341139578027651 | 0.41856228094548 | 0.865933437133208 |
| 80 | 0.00771480705589056 | 0.980334376916289 | 0.903367675142363 | 0.79636874073185 | 0.417939914623275 | 0.783775319112465 | 0.871277383295819 | 0.569282444659621 | 0.562941672978923 | 0.00527995591983199 | 0.0930614802055061 | 0.98293914552778 | 0.929179901257157 | 0.0389671209268272 | 0.634487443836406 | 0.3663773201406 | 0.742187170078978 | 0.129297606181353 | 0.457299483707175 | 0.234784751432016 | 0.687279452104121 | 0.544995278585702 | 0.449781134258956 | 0.133588414173573 | 0.680513290455565 | ... | 0.945276156533509 | 0.520313991932198 | 0.559680359438062 | 0.663886188762262 | 0.120652508689091 | 0.565715723671019 | 0.789741576649249 | 0.941839308245108 | 0.284751672996208 | 0.228937928099185 | 0.569738500053063 | 0.00643966626375914 | 0.451334442012012 | 0.274095777887851 | 0.542847673175856 | 0.889585854485631 | 0.684653083328158 | 0.309453279711306 | 0.874792905291542 | 0.00168142071925104 | 0.443135217064992 | 0.485857455525547 | 0.622362722177058 | 0.48247589240782 | 0.329070713138208 |
| 81 | 0.00779346819035709 | 0.223168045980856 | 0.742175885243341 | 0.317552546504885 | 0.198293497087434 | 0.74115232587792 | 0.822459247196093 | 0.853637885535136 | 0.380582608515397 | 0.731988111045212 | 0.342725861351937 | 0.138068814529106 | 0.833861187333241 | 0.765297099947929 | 0.951284000882879 | 0.78773146122694 | 0.631443910999224 | 0.962064067134634 | 0.669475900940597 | 0.802538022631779 | 0.974192890804261 | 0.598798935068771 | 0.421059768414125 | 0.250097605399787 | 0.786808451404795 | ... | 0.374597914284095 | 0.919180124998093 | 0.114861520938575 | 0.793429704150185 | 0.778294675052166 | 0.70930807874538 | 0.863591709639877 | 0.421748571330681 | 0.347288007615134 | 0.934128675609827 | 0.917313354788348 | 0.0727860184852034 | 0.336637143744156 | 0.260976730147377 | 0.208932279609144 | 0.23643753468059 | 0.5020088898018 | 0.733957422664389 | 0.136327358661219 | 0.795450125122443 | 0.396693319547921 | 0.312987976241857 | 0.87041130522266 | 0.835299459286034 | 0.122979815118015 |
| 82 | 0.00780424359254539 | 0.968357490375638 | 0.635946255875751 | 0.13696676469408 | 0.628371802857146 | 0.310079649789259 | 0.0519770262762904 | 0.510796279180795 | 0.371049638837576 | 0.00868491851724684 | 0.710981341777369 | 0.393583359662443 | 0.632969946134835 | 0.711548673920333 | 0.610078744823113 | 0.768936233595014 | 0.47095975629054 | 0.26475773495622 | 0.911403006641194 | 0.401140340138227 | 0.249423361383379 | 0.162512097042054 | 0.974585358519107 | 0.481346258195117 | 0.422414863249287 | ... | 0.63474842114374 | 0.485606302740052 | 0.54615698591806 | 0.637584548676386 | 0.901926809456199 | 0.1940332215745 | 0.87876290618442 | 0.56005020509474 | 0.259138135937974 | 0.754459945717826 | 0.842256424017251 | 0.724441095022485 | 0.973328242078424 | 0.69243303919211 | 0.359915914479643 | 0.233602562686428 | 0.573187325848266 | 0.382502714870498 | 0.0342947107274085 | 0.279322032118216 | 0.787587276194245 | 0.613153238082305 | 0.0304125340189785 | 0.242927330778912 | 0.934404178755358 |
| 83 | 0.00809661857783794 | 0.0369409332051873 | 0.0536470201332122 | 0.382373302476481 | 0.00529614952392876 | 0.585262270178646 | 0.910579259041697 | 0.476680542808026 | 0.332685433560982 | 0.718727569561452 | 0.888929296284914 | 0.646438805619255 | 0.933225862216204 | 0.803833205252886 | 0.806296348804608 | 0.311599633656442 | 0.484703203430399 | 0.751726769376546 | 0.711068680975586 | 0.167824439238757 | 0.82163227070123 | 0.599958144361153 | 0.207287652883679 | 0.609612182481214 | 0.0432701839599758 | ... | 0.71062865620479 | 0.199578552274033 | 0.320377057418227 | 0.138474680716172 | 0.580643323482946 | 0.782337641576305 | 0.653342346660793 | 0.74182208487764 | 0.895956537453458 | 0.450113014318049 | 0.749081689631566 | 0.432037452468649 | 0.948916658991948 | 0.730837019393221 | 0.742800795007497 | 0.99526504566893 | 0.489831771003082 | 0.274795898236334 | 0.706216650549322 | 0.412183904089034 | 0.521649173460901 | 0.286092692520469 | 0.610302924644202 | 0.604934175265953 | 0.344411331694573 |
| 84 | 0.00811288761906326 | 0.0159373194910586 | 0.412028322229162 | 0.308050378691405 | 0.791499812388793 | 0.375869796611369 | 0.927958965301514 | 0.107205977430567 | 0.0854067069012672 | 0.41549759497866 | 0.951565777882934 | 0.58354236674495 | 0.276748593430966 | 0.149854149902239 | 0.0807694518007338 | 0.616585955955088 | 0.990254365606233 | 0.135925389593467 | 0.174017656827345 | 0.394419782329351 | 0.0610502427443862 | 0.246863748878241 | 0.1866390760988 | 0.119562466396019 | 0.204099249560386 | ... | 0.271866985596716 | 0.0793808000162244 | 0.657269649906084 | 0.349631606368348 | 0.907046241918579 | 0.902267505647615 | 0.181135179009289 | 0.645079802023247 | 0.195805130526423 | 0.436799280112609 | 0.124091898323968 | 0.0761534601915628 | 0.138281237334013 | 0.361373919760808 | 0.813160588499159 | 0.796888197306544 | 0.345552418148145 | 0.429933369159698 | 0.917352278484032 | 0.853381048422307 | 0.74546004133299 | 0.822871149284765 | 0.732983190799132 | 0.555578442057595 | 0.54755100258626 |
| 85 | 0.00814585760235786 | 0.00413368199951947 | 0.731472193496302 | 0.640315623488277 | 0.303209384903312 | 0.763653335161507 | 0.360259722918272 | 0.478188654640689 | 0.876662259688601 | 0.801234483486041 | 0.744920742930844 | 0.103613714920357 | 0.00901968823745847 | 0.512746682390571 | 0.454988797893748 | 0.986107738222927 | 0.828254500404 | 0.880448216805235 | 0.417732247151434 | 0.833560945000499 | 0.273299460299313 | 0.272788619156927 | 0.199562469497323 | 0.623809821903706 | 0.753334004664794 | ... | 0.644644601503387 | 0.817317159613594 | 0.234825018094853 | 0.00271241716109216 | 0.463839984731749 | 0.302459234837443 | 0.216193082509562 | 0.593858885345981 | 0.0309136086143553 | 0.637637983076274 | 0.469095273409039 | 0.824292267905548 | 0.783540899632499 | 0.403209747979417 | 0.281883239746094 | 0.512243475066498 | 0.312500447500497 | 0.275327023817226 | 0.889187695458531 | 0.11286882031709 | 0.346073950175196 | 0.9593984936364 | 0.6118769061286 | 0.724676445126534 | 0.688248282531276 |
| 86 | 0.0082339181099087 | 0.439815185032785 | 0.554286793805659 | 0.43014442618005 | 0.954653581604362 | 0.166237527970225 | 0.611960029229522 | 0.551252590492368 | 0.726785575039685 | 0.390191324520856 | 0.326701766578481 | 0.994571433169767 | 0.785082671092823 | 0.752328243805096 | 0.331591414054856 | 0.247560543008149 | 0.934237871784717 | 0.482842283090577 | 0.68744211178273 | 0.0347144063562155 | 0.363268404267728 | 0.507811791263521 | 0.919127548579127 | 0.263085678219795 | 0.0753815695643425 | ... | 0.0296448357403278 | 0.718780467053875 | 0.594495103694499 | 0.109877361217514 | 0.521152646280825 | 0.732395916478708 | 0.722311813384295 | 0.588815452065319 | 0.758633071323857 | 0.11084463680163 | 0.63188322680071 | 0.924329469911754 | 0.912409216631204 | 0.823309609433636 | 0.998873119009659 | 0.886260823346674 | 0.88202647655271 | 0.651101163821295 | 0.61684012087062 | 0.890842443099245 | 0.273374434327707 | 0.455691984621808 | 0.632568347733468 | 0.155469369143248 | 0.817534783855081 |
| 87 | 0.00848092022351921 | 0.222356282873079 | 0.29351053875871 | 0.197558671468869 | 0.195558101404458 | 0.602790989680216 | 0.813749768771231 | 0.0774901276454329 | 0.781322402879596 | 0.279261991614476 | 0.869432922219858 | 0.73684075800702 | 0.374639065703377 | 0.972875922452658 | 0.882515258854255 | 0.81845522695221 | 0.406602134695277 | 0.44088463159278 | 0.162957599153742 | 0.6679845105391 | 0.846003010170534 | 0.611140089342371 | 0.988292069174349 | 0.493441754253581 | 0.0526971917133778 | ... | 0.718595174606889 | 0.53255936363712 | 0.753517876612023 | 0.421683304477483 | 0.635499072493985 | 0.0179416493047029 | 0.0656900003086776 | 0.333390511805192 | 0.292213526787236 | 0.927701366366819 | 0.981569889932871 | 0.747983646579087 | 0.989795314380899 | 0.650222146883607 | 0.508151067653671 | 0.0499754971824586 | 0.579670913983136 | 0.789158394094557 | 0.0798017394263297 | 0.0955222737975419 | 0.31137506198138 | 0.260038833832368 | 0.555723301367834 | 0.164155967300758 | 0.313900409033522 |
| 88 | 0.00851803249679506 | 0.529020482907072 | 0.69007230643183 | 0.454014534363523 | 0.219051675405353 | 0.151521884137765 | 0.853487001499161 | 0.639228207524866 | 0.457068851450458 | 0.521847967989743 | 0.126012114342302 | 0.00032291654497385 | 0.200706353643909 | 0.849997863406315 | 0.325347895501181 | 0.547759938752279 | 0.20888876891695 | 0.753733812365681 | 0.237308284500614 | 0.278668432263657 | 0.854778473963961 | 0.827688863035291 | 0.809503264958039 | 0.319368686992675 | 0.0587892103940248 | ... | 0.818787793861702 | 0.62223787419498 | 0.240042709279805 | 0.203716139541939 | 0.297722151502967 | 0.80036340537481 | 0.0113077347632498 | 0.743841422721744 | 0.373102647485211 | 0.694920117966831 | 0.0461184016894549 | 0.0825039790943265 | 0.594297927571461 | 0.439089559949934 | 0.676635204581544 | 0.811122391140088 | 0.808245287509635 | 0.344671705504879 | 0.202105782227591 | 0.277317958185449 | 0.235388107132167 | 0.310788674978539 | 0.488032161723822 | 0.925330803496763 | 0.613092022249475 |
| 89 | 0.00885382643900812 | 0.875200126087293 | 0.982419854030013 | 0.204924191115424 | 0.412543873535469 | 0.522105760406703 | 0.576879120664671 | 0.659603044623509 | 0.634677389403805 | 0.624296225141734 | 0.756125740706921 | 0.0454057171009481 | 0.447754234541208 | 0.376160613261163 | 0.790130971232429 | 0.322863636305556 | 0.686073221731931 | 0.896026724018157 | 0.908665336668491 | 0.536640047095716 | 0.270938848610967 | 0.464944191742688 | 0.95084630465135 | 0.86090446007438 | 0.488551297690719 | ... | 0.754612621618435 | 0.676015567500144 | 0.637408159906045 | 0.897257248405367 | 0.718231537146494 | 0.535554763395339 | 0.961939284112304 | 0.473900581942871 | 0.81944497092627 | 0.481163071934134 | 0.0627267865929753 | 0.267334070289508 | 0.941490361699834 | 0.366474045207724 | 0.287446354050189 | 0.698967295698822 | 0.629469709238037 | 0.616491289110854 | 0.992155366810039 | 0.342704983893782 | 0.627644948894158 | 0.679178569233045 | 0.681971471756697 | 0.486125104362145 | 0.789176452672109 |
| 90 | 0.00909327482804656 | 0.128973981831223 | 0.585047417320311 | 0.961765482323244 | 0.319019561400637 | 0.869328566361219 | 0.621508100070059 | 0.434283448616043 | 0.785585893085226 | 0.33180279051885 | 0.344007721869275 | 0.596239636885002 | 0.461911451537162 | 0.21808414789848 | 0.723105450393632 | 0.0964482720009983 | 0.0366877815686166 | 0.328646128065884 | 0.63519585528411 | 0.00530118169263005 | 0.624044875847176 | 0.90113859763369 | 0.880166816525161 | 0.594454572768882 | 0.570577051257715 | ... | 0.137337640160695 | 0.0659334463998675 | 0.352443094132468 | 0.0889705712907016 | 0.345827830955386 | 0.112868036841974 | 0.268827310297638 | 0.667821195907891 | 0.180004886118695 | 0.117464266950265 | 0.522005806211382 | 0.341894189361483 | 0.00285228621214628 | 0.84081483958289 | 0.565816243644804 | 0.611177121289074 | 0.277431181631982 | 0.901691494509578 | 0.782857570797205 | 0.184909287374467 | 0.505605682730675 | 0.624057317618281 | 0.420271919807419 | 0.231838702922687 | 0.267497834283859 |
| 91 | 0.00924704596400261 | 0.147553584072739 | 0.508063717279583 | 0.0280664165038615 | 0.889239056035876 | 0.319859089097008 | 0.501303313067183 | 0.0080767769832164 | 0.674704367760569 | 0.0536098938900977 | 0.588253404013813 | 0.600049520842731 | 0.159225630341098 | 0.688707916764542 | 0.0628255733754486 | 0.260248673148453 | 0.76441271812655 | 0.641464220127091 | 0.852677256334573 | 0.735715687973425 | 0.413087195949629 | 0.151502442779019 | 0.213725346140563 | 0.570855492958799 | 0.79311825032346 | ... | 0.172636086586863 | 0.813442215090618 | 0.148976140189916 | 0.923411395167932 | 0.975955854170024 | 0.64114390569739 | 0.146189942024648 | 0.191325946012512 | 0.847241767216474 | 0.478967381408438 | 0.7584393681027 | 0.722657972481102 | 0.597211310639977 | 0.230858143419027 | 0.490496747428551 | 0.0957626651506871 | 0.0134728618431836 | 0.815792707493529 | 0.428366154665127 | 0.693225861294195 | 0.122978422790766 | 0.157362345606089 | 0.733569935429841 | 0.768718275241554 | 0.226525850361213 |
| 92 | 0.00946435495279729 | 0.824762779287994 | 0.34288594732061 | 0.164894312852994 | 0.405423355987296 | 0.85442597954534 | 0.123315159929916 | 0.672841741004959 | 0.128158869920298 | 0.766058131819591 | 0.897360787261277 | 0.830298717366531 | 0.490808403119445 | 0.684051705058664 | 0.0883453129790723 | 0.157781578367576 | 0.470300262561068 | 0.0115521510597318 | 0.399971244856715 | 0.860135365277529 | 0.697626510169357 | 0.074061332270503 | 0.414312256034464 | 0.31688860594295 | 0.915141411591321 | ... | 0.556628802558407 | 0.53928406490013 | 0.822887854417786 | 0.708682701922953 | 0.808626908110455 | 0.460458771325648 | 0.427666814997792 | 0.542982555460185 | 0.522565717576072 | 0.444793164497241 | 0.636407538317144 | 0.241194425150752 | 0.239957341225818 | 0.103442708030343 | 0.990831021452323 | 0.928504563868046 | 0.370891367085278 | 0.689060932258144 | 0.0426494430284947 | 0.364038313506171 | 0.394912627991289 | 0.0560588038060814 | 0.233480089111254 | 0.106471472419798 | 0.0113272164016962 |
| 93 | 0.00946715474128723 | 0.975761613575742 | 0.230816222727299 | 0.61213770089671 | 0.46798948594369 | 0.232269518543035 | 0.118327436735854 | 0.562298651784658 | 0.593704466242343 | 0.728178257821128 | 0.131951568415388 | 0.365087065612897 | 0.715448807692155 | 0.73199857538566 | 0.463408313691616 | 0.816567642847076 | 0.126444064313546 | 0.148065130924806 | 0.44316343893297 | 0.0763151512946934 | 0.284235691884533 | 0.742862357292324 | 0.470074087148532 | 0.522779753897339 | 0.198329889215529 | ... | 0.0281978989951313 | 0.326949591748416 | 0.802360552828759 | 0.57794566755183 | 0.867350146872923 | 0.264165885047987 | 0.563569794176146 | 0.297489050077274 | 0.0122422354761511 | 0.953188708750531 | 0.951445504557341 | 0.316069049062207 | 0.357745043933392 | 0.396531745791435 | 0.979395239148289 | 0.835883058840409 | 0.110199433518574 | 0.42473488394171 | 0.185772756114602 | 0.856243706541136 | 0.916559862205759 | 0.390161706600338 | 0.0822050855495036 | 0.643564132740721 | 0.935100894887 |
| 94 | 0.00961066340096295 | 0.227654562797397 | 0.834150770911947 | 0.981298056896776 | 0.899406693177298 | 0.0208894666284323 | 0.751334445551038 | 0.880268483189866 | 0.545818760758266 | 0.0479917649645358 | 0.673765507293865 | 0.282674903282896 | 0.281462321989238 | 0.239131658570841 | 0.00358489039354026 | 0.336417121114209 | 0.0970285041257739 | 0.514011580962688 | 0.356756030814722 | 0.36862086574547 | 0.122383130481467 | 0.668651483487338 | 0.792449047323316 | 0.65835903887637 | 0.375716412439942 | ... | 0.89136874768883 | 0.318790392717347 | 0.354550857329741 | 0.748397490475327 | 0.369620862882584 | 0.302043829346076 | 0.298142929794267 | 0.331247650552541 | 0.897372888401151 | 0.626443963265046 | 0.508510891115293 | 0.552126254420727 | 0.368940379237756 | 0.68098700302653 | 0.988300702068955 | 0.56815616087988 | 0.896302396198735 | 0.877572525758296 | 0.00254485569894314 | 0.556959882844239 | 0.707723527448252 | 0.610067375004292 | 0.393116349820048 | 0.502664403291419 | 0.818634700961411 |
| 95 | 0.00962293264456093 | 0.0935416608117521 | 0.310996977146715 | 0.316919288598001 | 0.848661946831271 | 0.377989716129377 | 0.236697892425582 | 0.152540335198864 | 0.996203216724098 | 0.578429543878883 | 0.933971300721169 | 0.166959035443142 | 0.312051014043391 | 0.521615908714011 | 0.685657419729978 | 0.259214965160936 | 0.653513116994873 | 0.746125767473131 | 0.645119206281379 | 0.993007513927296 | 0.569327380042523 | 0.0146142092999071 | 0.179485923843458 | 0.717313044937328 | 0.362865807721391 | ... | 0.488936898065731 | 0.916940055321902 | 0.304699439555407 | 0.65645625651814 | 0.805591923883185 | 0.952860370045528 | 0.235715942457318 | 0.0355088151991367 | 0.125833974452689 | 0.637661880813539 | 0.870334678096697 | 0.862889683572575 | 0.102916307281703 | 0.513829084811732 | 0.140632378635928 | 0.49310958548449 | 0.331888370681554 | 0.0984242493286729 | 0.306810255628079 | 0.458505577407777 | 0.629166439175606 | 0.993265094934031 | 0.947291647549719 | 0.816449363017455 | 0.783945296891034 |
| 96 | 0.00965966377407312 | 0.857680878834799 | 0.618562259478495 | 0.635788084706292 | 0.635648869909346 | 0.911934737116098 | 0.31212760694325 | 0.241023585898802 | 0.150937253376469 | 0.0972512166481465 | 0.109026144258678 | 0.531022537266836 | 0.596848331158981 | 0.539019796298817 | 0.661908267764375 | 0.561519115930423 | 0.370649161282927 | 0.250235031126067 | 0.527783554280177 | 0.790883158100769 | 0.615695554530248 | 0.380817835684866 | 0.620204798644409 | 0.558063487056643 | 0.975162257906049 | ... | 0.583026437321678 | 0.533838965231553 | 0.506023583002388 | 0.596368263708428 | 0.507013481808826 | 0.656014763284475 | 0.0596953327767551 | 0.938907453790307 | 0.272512170020491 | 0.843718450749293 | 0.52405965141952 | 0.0485840237233788 | 0.586388068273664 | 0.114708211272955 | 0.633130878675729 | 0.0397592925000936 | 0.298787088133395 | 0.732442778302357 | 0.353591227671131 | 0.400159884477034 | 0.197048142086715 | 0.343612517695874 | 0.559787548612803 | 0.817266907310113 | 0.783271288964897 |
| 97 | 0.00972658186219633 | 0.692959072766826 | 0.0486342338845134 | 0.783238548086956 | 0.160770263755694 | 0.5298073918093 | 0.93237027246505 | 0.547930711181834 | 0.986777379410341 | 0.698071001563221 | 0.983585368841887 | 0.738127237418666 | 0.520279544172809 | 0.185567562934011 | 0.437042931094766 | 0.607841359684244 | 0.582788614556193 | 0.65520309843123 | 0.464414179790765 | 0.25547610828653 | 0.527615664992481 | 0.984283751808107 | 0.738952532177791 | 0.139970470918342 | 0.719137626932934 | ... | 0.760172463487834 | 0.555020049447194 | 0.204106678720564 | 0.322754994500428 | 0.310017777141184 | 0.785715121775866 | 0.269620047416538 | 0.663912531454116 | 0.853543356060982 | 0.66764345834963 | 0.801393907051533 | 0.631188481813297 | 0.67289001098834 | 0.914906073594466 | 0.457231434527785 | 0.346458432497457 | 0.397624600445852 | 0.631416477728635 | 0.827926503727213 | 0.968088918132707 | 0.511030979687348 | 0.577628522878513 | 0.19390199938789 | 0.255057224771008 | 0.899868222884834 |
| 98 | 0.00985606969334185 | 0.667693499941379 | 0.931646558223292 | 0.689672989305109 | 0.200394773622975 | 0.0672223132569343 | 0.0913151344284415 | 0.895141348708421 | 0.44139987975359 | 0.723404487362131 | 0.0973884623963386 | 0.148741463664919 | 0.447361073922366 | 0.896779636386782 | 0.003855150192976 | 0.756954731652513 | 0.714324184227735 | 0.989547198405489 | 0.13273108471185 | 0.657627671724185 | 0.316266902722418 | 0.653663638746366 | 0.49544447963126 | 0.190211180597544 | 0.520473257405683 | ... | 0.569248368730769 | 0.677836274728179 | 0.450819859048352 | 0.723862473387271 | 0.863013072870672 | 0.509118453366682 | 0.218852573307231 | 0.0714990610722452 | 0.0981308096088469 | 0.045087018981576 | 0.289558774093166 | 0.0309762973338366 | 0.118349929805845 | 0.220141991274431 | 0.955611336510628 | 0.939826196292415 | 0.115448526805267 | 0.951977925375104 | 0.854286523535848 | 0.097131050657481 | 0.749721223954111 | 0.950510227121413 | 0.569369619945064 | 0.397779510123655 | 0.0303781612310559 |
| 99 | 0.0101318615488708 | 0.662880232790485 | 0.122057115659118 | 0.740471428958699 | 0.935664381599054 | 0.679875571746379 | 0.338068253593519 | 0.686561811482534 | 0.469989400822669 | 0.179946760646999 | 0.633446159306914 | 0.579075969057158 | 0.173217358300462 | 0.860771061154082 | 0.00376510107889771 | 0.756900643231347 | 0.759280733531341 | 0.606717823306099 | 0.715507024899125 | 0.633010727819055 | 0.417071977863088 | 0.579058602685109 | 0.271589594660327 | 0.165139456978068 | 0.637616327730939 | ... | 0.219777278136462 | 0.975613878574222 | 0.000115433475002646 | 0.00662260083481669 | 0.361153847305104 | 0.179624821292236 | 0.242538495222107 | 0.540843163384125 | 0.976923468289897 | 0.980032498715445 | 0.316799078835174 | 0.169800930656493 | 0.286071908427402 | 0.0811776891350746 | 0.487389508867636 | 0.979992950335145 | 0.116272666025907 | 0.83669591974467 | 0.928404540289193 | 0.711673312820494 | 0.397445381619036 | 0.7378370387014 | 0.207517934497446 | 0.922513144090772 | 0.870160201331601 |
| 100 | 0.0103061466943473 | 0.110453602625057 | 0.552420568885282 | 0.672776134684682 | 0.18031755881384 | 0.053813717328012 | 0.710754769854248 | 0.579055867623538 | 0.691381671698764 | 0.727991050574929 | 0.553623089566827 | 0.0668222503736615 | 0.950091493781656 | 0.182638361817226 | 0.665211591869593 | 0.793377450900152 | 0.717621367191896 | 0.508317811880261 | 0.016812197631225 | 0.170683601871133 | 0.164249985478818 | 0.685464148642495 | 0.889310171129182 | 0.00224538566544652 | 0.157580882310867 | ... | 0.384168792981654 | 0.280128390528262 | 0.537432349519804 | 0.333254691911861 | 0.0851389255840331 | 0.645773645956069 | 0.0350734158419073 | 0.367705639451742 | 0.442660799715668 | 0.0404679160565138 | 0.483725734753534 | 0.549227622337639 | 0.31340526137501 | 0.477974840672687 | 0.135994026437402 | 0.0823690549004823 | 0.258681894512847 | 0.838722283951938 | 0.218102322425693 | 0.89637154713273 | 0.509305321378633 | 0.474014234496281 | 0.212072994327173 | 0.482526635052636 | 0.977601603372023 |
Rows: 1-100 | Columns: 600
To see what is happening when you compute aggregations, turn on the SQL code generation and turn off the cache.
In [58]:
vp.set_option("sql_on", True)
vp.set_option("cache", False)
When you compute aggregations, VerticaPy allows you to send multiple queries iteratively or at the same time. To see this in action, let's compute the average of each dataset column.
You can see that sending one big query is quite resource expensive:
In [55]:
display(vdf.avg(ncols_block = 600))
| avg |
| "x0" | 0.495328640506021 |
| "x1" | 0.498410496117291 |
| "x2" | 0.499796020665369 |
| "x3" | 0.500288217322272 |
| "x4" | 0.501549792736745 |
| "x5" | 0.502030357531738 |
| "x6" | 0.498203794788383 |
| "x7" | 0.499528634219361 |
| "x8" | 0.498655800491967 |
| "x9" | 0.501991024077614 |
| "x10" | 0.499470449560788 |
| "x11" | 0.503527408929076 |
| "x12" | 0.494434265249921 |
| "x13" | 0.500999432951491 |
| "x14" | 0.499102837571758 |
| "x15" | 0.499115148377954 |
| "x16" | 0.498147533271462 |
| "x17" | 0.503055292108236 |
| "x18" | 0.498873396961717 |
| "x19" | 0.500234201267036 |
| "x20" | 0.500846420762525 |
| "x21" | 0.497544945688546 |
| "x22" | 0.499816283349297 |
| "x23" | 0.49421561504358 |
| "x24" | 0.498501294320636 |
| "x25" | 0.49881612469398 |
| "x26" | 0.500256177358888 |
| "x27" | 0.497643181022117 |
| "x28" | 0.497196014247974 |
| "x29" | 0.496317569292686 |
| "x30" | 0.499120011079405 |
| "x31" | 0.504665919276001 |
| "x32" | 0.497500529544335 |
| "x33" | 0.501751783046429 |
| "x34" | 0.495941181869968 |
| "x35" | 0.493580291184946 |
| "x36" | 0.502128273874149 |
| "x37" | 0.500820784376212 |
| "x38" | 0.498700643126364 |
| "x39" | 0.504414001272083 |
| "x40" | 0.50297581018405 |
| "x41" | 0.498589111867477 |
| "x42" | 0.493329039907991 |
| "x43" | 0.495365951688774 |
| "x44" | 0.501398265630705 |
| "x45" | 0.497031733239675 |
| "x46" | 0.49858817340259 |
| "x47" | 0.499666033335752 |
| "x48" | 0.497840583433164 |
| "x49" | 0.497329473723052 |
| "x50" | 0.49669896126797 |
| "x51" | 0.496988497646665 |
| "x52" | 0.495283583330153 |
| "x53" | 0.503541071587382 |
| "x54" | 0.502496378843393 |
| "x55" | 0.506106085637049 |
| "x56" | 0.503235346138873 |
| "x57" | 0.502128457865585 |
| "x58" | 0.501718418996432 |
| "x59" | 0.501931357378722 |
| "x60" | 0.492535700597335 |
| "x61" | 0.496213648770773 |
| "x62" | 0.501711242381227 |
| "x63" | 0.49593384194742 |
| "x64" | 0.501410126678646 |
| "x65" | 0.496181363479933 |
| "x66" | 0.502847261195513 |
| "x67" | 0.499017013058043 |
| "x68" | 0.500901301923464 |
| "x69" | 0.502686372651509 |
| "x70" | 0.503725287213479 |
| "x71" | 0.49858107758367 |
| "x72" | 0.500332314733882 |
| "x73" | 0.503799533855729 |
| "x74" | 0.497731596026267 |
| "x75" | 0.500254210987454 |
| "x76" | 0.503705967230629 |
| "x77" | 0.497663569217268 |
| "x78" | 0.498292489934526 |
| "x79" | 0.504205192289595 |
| "x80" | 0.501272203026921 |
| "x81" | 0.498586322333827 |
| "x82" | 0.501165568577242 |
| "x83" | 0.507249641807377 |
| "x84" | 0.499038335806946 |
| "x85" | 0.500589053839631 |
| "x86" | 0.504052388792532 |
| "x87" | 0.497889207095001 |
| "x88" | 0.500446273626364 |
| "x89" | 0.499201328990585 |
| "x90" | 0.502505042524263 |
| "x91" | 0.498666686973721 |
| "x92" | 0.4980780772798 |
| "x93" | 0.498206184870098 |
| "x94" | 0.501078245462058 |
| "x95" | 0.502400306417863 |
| "x96" | 0.496301139098872 |
| "x97" | 0.499954794859467 |
| "x98" | 0.495530540163047 |
| "x99" | 0.499518119273777 |
| "x100" | 0.502472493177536 |
| "x101" | 0.504902573059266 |
| "x102" | 0.498767855446343 |
| "x103" | 0.498763861700776 |
| "x104" | 0.494740242705843 |
| "x105" | 0.50120537653435 |
| "x106" | 0.500558270047256 |
| "x107" | 0.501785635916004 |
| "x108" | 0.500023144892836 |
| "x109" | 0.500689867577143 |
| "x110" | 0.500623461510986 |
| "x111" | 0.502040224120254 |
| "x112" | 0.49922121064926 |
| "x113" | 0.499335735470266 |
| "x114" | 0.502046788542392 |
| "x115" | 0.498266887489939 |
| "x116" | 0.502299062704365 |
| "x117" | 0.499504777825647 |
| "x118" | 0.498147775378544 |
| "x119" | 0.500105008480838 |
| "x120" | 0.500926059096353 |
| "x121" | 0.498799051559274 |
| "x122" | 0.498231966562965 |
| "x123" | 0.502014504623017 |
| "x124" | 0.496966086774343 |
| "x125" | 0.497726782605075 |
| "x126" | 0.501800164589402 |
| "x127" | 0.504625166970142 |
| "x128" | 0.494857996223634 |
| "x129" | 0.504154442140413 |
| "x130" | 0.495419377293601 |
| "x131" | 0.495755362548213 |
| "x132" | 0.499762857829197 |
| "x133" | 0.498344265133003 |
| "x134" | 0.504667159711616 |
| "x135" | 0.500426490560034 |
| "x136" | 0.495148637985485 |
| "x137" | 0.499247576732608 |
| "x138" | 0.500246977145318 |
| "x139" | 0.498025120325852 |
| "x140" | 0.49665202575603 |
| "x141" | 0.50157614965036 |
| "x142" | 0.494219642718253 |
| "x143" | 0.501118474691175 |
| "x144" | 0.498214634110243 |
| "x145" | 0.497676468651718 |
| "x146" | 0.4999434025286 |
| "x147" | 0.50381975648317 |
| "x148" | 0.499791994529241 |
| "x149" | 0.501425083181378 |
| "x150" | 0.503124807463679 |
| "x151" | 0.503843662469694 |
| "x152" | 0.499438914951705 |
| "x153" | 0.499690357795637 |
| "x154" | 0.492923485315032 |
| "x155" | 0.498921156159765 |
| "x156" | 0.505832323109452 |
| "x157" | 0.50427568726968 |
| "x158" | 0.501047079447447 |
| "x159" | 0.501144096319587 |
| "x160" | 0.500279258508724 |
| "x161" | 0.501948064998072 |
| "x162" | 0.500822011614218 |
| "x163" | 0.497227232640726 |
| "x164" | 0.495996041991841 |
| "x165" | 0.501643313851114 |
| "x166" | 0.493981937356992 |
| "x167" | 0.501158596251789 |
| "x168" | 0.492721518449881 |
| "x169" | 0.502087166458927 |
| "x170" | 0.496132122005289 |
| "x171" | 0.50004740234639 |
| "x172" | 0.507995243759337 |
| "x173" | 0.495010604015226 |
| "x174" | 0.504332425329136 |
| "x175" | 0.500722138965363 |
| "x176" | 0.501477807205217 |
| "x177" | 0.503222832425241 |
| "x178" | 0.496611627437011 |
| "x179" | 0.501386782278749 |
| "x180" | 0.496568095402792 |
| "x181" | 0.49866127618046 |
| "x182" | 0.499939231952606 |
| "x183" | 0.49839989884852 |
| "x184" | 0.49844872907605 |
| "x185" | 0.499527396393754 |
| "x186" | 0.505675627022749 |
| "x187" | 0.502176277364884 |
| "x188" | 0.50282409973233 |
| "x189" | 0.501910180421011 |
| "x190" | 0.499091349298926 |
| "x191" | 0.503729833525093 |
| "x192" | 0.501052054715296 |
| "x193" | 0.497996389698493 |
| "x194" | 0.501086532175215 |
| "x195" | 0.497719087828533 |
| "x196" | 0.50029780225656 |
| "x197" | 0.497283518747846 |
| "x198" | 0.50029253732739 |
| "x199" | 0.503720246048248 |
| "x200" | 0.50173565008766 |
| "x201" | 0.505880159354582 |
| "x202" | 0.495958490648027 |
| "x203" | 0.501755221227929 |
| "x204" | 0.501195751817548 |
| "x205" | 0.502214450883982 |
| "x206" | 0.500531362394965 |
| "x207" | 0.50205923199188 |
| "x208" | 0.50295131285931 |
| "x209" | 0.502243809388275 |
| "x210" | 0.507529762405949 |
| "x211" | 0.504731268971018 |
| "x212" | 0.496389128514612 |
| "x213" | 0.501199241986056 |
| "x214" | 0.49963519236967 |
| "x215" | 0.503726938822726 |
| "x216" | 0.500616870596819 |
| "x217" | 0.499451167386491 |
| "x218" | 0.505073839902342 |
| "x219" | 0.495555917869695 |
| "x220" | 0.503535190937086 |
| "x221" | 0.500010514657409 |
| "x222" | 0.501485859632539 |
| "x223" | 0.501452482858882 |
| "x224" | 0.496859017808642 |
| "x225" | 0.499720605799975 |
| "x226" | 0.49902702385562 |
| "x227" | 0.493869393159961 |
| "x228" | 0.500975813526777 |
| "x229" | 0.503612502819882 |
| "x230" | 0.500296765768202 |
| "x231" | 0.501570096647646 |
| "x232" | 0.501653867180506 |
| "x233" | 0.495997469444037 |
| "x234" | 0.500007144648512 |
| "x235" | 0.501950742057967 |
| "x236" | 0.501136892649159 |
| "x237" | 0.497207203832921 |
| "x238" | 0.497366881357762 |
| "x239" | 0.503939381418563 |
| "x240" | 0.500307605826342 |
| "x241" | 0.500278400719655 |
| "x242" | 0.496130419079564 |
| "x243" | 0.498876399969449 |
| "x244" | 0.498236415238259 |
| "x245" | 0.505986941487947 |
| "x246" | 0.499224769213772 |
| "x247" | 0.501577037782432 |
| "x248" | 0.502718629168347 |
| "x249" | 0.497431639110297 |
| "x250" | 0.497242679194268 |
| "x251" | 0.500110229029763 |
| "x252" | 0.499876112394035 |
| "x253" | 0.500209626919613 |
| "x254" | 0.498006003626087 |
| "x255" | 0.501028609297518 |
| "x256" | 0.497476164073031 |
| "x257" | 0.49678638799903 |
| "x258" | 0.503028783134325 |
| "x259" | 0.500678621253278 |
| "x260" | 0.501899834921793 |
| "x261" | 0.49799142391663 |
| "x262" | 0.502971393630072 |
| "x263" | 0.503649817536864 |
| "x264" | 0.501297247359576 |
| "x265" | 0.498187974785664 |
| "x266" | 0.500154159696493 |
| "x267" | 0.498174033115013 |
| "x268" | 0.502259716476523 |
| "x269" | 0.500892450533505 |
| "x270" | 0.49974688360109 |
| "x271" | 0.503252161878953 |
| "x272" | 0.500539697517548 |
| "x273" | 0.504436443216214 |
| "x274" | 0.502837233404955 |
| "x275" | 0.500573441805621 |
| "x276" | 0.502325369855715 |
| "x277" | 0.502028237938345 |
| "x278" | 0.499332443716889 |
| "x279" | 0.502182460590545 |
| "x280" | 0.496923384860391 |
| "x281" | 0.502459710514196 |
| "x282" | 0.494431597842555 |
| "x283" | 0.498645268598385 |
| "x284" | 0.496526186001836 |
| "x285" | 0.500086312099337 |
| "x286" | 0.501093746714317 |
| "x287" | 0.499139699267014 |
| "x288" | 0.496876103397319 |
| "x289" | 0.501409091628436 |
| "x290" | 0.49791826228518 |
| "x291" | 0.498047744078701 |
| "x292" | 0.503011588848778 |
| "x293" | 0.494279091265984 |
| "x294" | 0.50145187503472 |
| "x295" | 0.500172946690372 |
| "x296" | 0.497979902947624 |
| "x297" | 0.492805902662501 |
| "x298" | 0.499126493594469 |
| "x299" | 0.498135944902035 |
| "x300" | 0.497372175921849 |
| "x301" | 0.499937077994528 |
| "x302" | 0.498308722825442 |
| "x303" | 0.49533371287086 |
| "x304" | 0.498127515137498 |
| "x305" | 0.498703532381309 |
| "x306" | 0.499237531865598 |
| "x307" | 0.497270844759117 |
| "x308" | 0.498935120696947 |
| "x309" | 0.505050902428967 |
| "x310" | 0.494586903066631 |
| "x311" | 0.501683675867925 |
| "x312" | 0.498886407341203 |
| "x313" | 0.502651175533538 |
| "x314" | 0.502610984513233 |
| "x315" | 0.499020783808059 |
| "x316" | 0.497362622722238 |
| "x317" | 0.497419736533822 |
| "x318" | 0.499328824524721 |
| "x319" | 0.499461412384966 |
| "x320" | 0.496635588650592 |
| "x321" | 0.50164939600958 |
| "x322" | 0.495475489443797 |
| "x323" | 0.504439370975946 |
| "x324" | 0.492955837118463 |
| "x325" | 0.50213546285443 |
| "x326" | 0.501837605465343 |
| "x327" | 0.505604026965867 |
| "x328" | 0.501586500711599 |
| "x329" | 0.495532248499035 |
| "x330" | 0.497800878073298 |
| "x331" | 0.499882971630897 |
| "x332" | 0.500076033881283 |
| "x333" | 0.495062761539174 |
| "x334" | 0.496449061025702 |
| "x335" | 0.504990343881771 |
| "x336" | 0.500045601881808 |
| "x337" | 0.501849232240906 |
| "x338" | 0.496911254709517 |
| "x339" | 0.504145932986075 |
| "x340" | 0.498204576935223 |
| "x341" | 0.499988833210897 |
| "x342" | 0.501985481519345 |
| "x343" | 0.501642016830575 |
| "x344" | 0.50208484286801 |
| "x345" | 0.501863940183376 |
| "x346" | 0.504740945380134 |
| "x347" | 0.494465954249515 |
| "x348" | 0.501264774960466 |
| "x349" | 0.503402628929587 |
| "x350" | 0.497616449450352 |
| "x351" | 0.498765651370934 |
| "x352" | 0.4989254358629 |
| "x353" | 0.50183583012505 |
| "x354" | 0.496825986894267 |
| "x355" | 0.498098364283633 |
| "x356" | 0.501767813966167 |
| "x357" | 0.498895416097227 |
| "x358" | 0.501967324887938 |
| "x359" | 0.502795286852052 |
| "x360" | 0.499872073752759 |
| "x361" | 0.498643346011383 |
| "x362" | 0.495098243173491 |
| "x363" | 0.498941021885141 |
| "x364" | 0.502219445838453 |
| "x365" | 0.502615964374412 |
| "x366" | 0.505264188127546 |
| "x367" | 0.500322223420395 |
| "x368" | 0.496345346435811 |
| "x369" | 0.504413213725598 |
| "x370" | 0.500707079809252 |
| "x371" | 0.497611740602506 |
| "x372" | 0.496615198885486 |
| "x373" | 0.500618592508254 |
| "x374" | 0.496569180697575 |
| "x375" | 0.504701023442182 |
| "x376" | 0.500255297750491 |
| "x377" | 0.498582437623548 |
| "x378" | 0.501286069167382 |
| "x379" | 0.503165722717438 |
| "x380" | 0.500378197866748 |
| "x381" | 0.503250720378035 |
| "x382" | 0.497218099547946 |
| "x383" | 0.501221833311347 |
| "x384" | 0.498849412409216 |
| "x385" | 0.501107512276433 |
| "x386" | 0.50047080468561 |
| "x387" | 0.498652378063696 |
| "x388" | 0.500216451354371 |
| "x389" | 0.504704176720278 |
| "x390" | 0.496354370877845 |
| "x391" | 0.503721972145187 |
| "x392" | 0.497143805629993 |
| "x393" | 0.50330190141215 |
| "x394" | 0.49937959353358 |
| "x395" | 0.498948919450445 |
| "x396" | 0.500168919996172 |
| "x397" | 0.502578267350467 |
| "x398" | 0.506101156181982 |
| "x399" | 0.503158229905623 |
| "x400" | 0.498680288048205 |
| "x401" | 0.501676260473486 |
| "x402" | 0.493510792666185 |
| "x403" | 0.499031297577242 |
| "x404" | 0.506920870206016 |
| "x405" | 0.502246720495657 |
| "x406" | 0.498294070439227 |
| "x407" | 0.501426641905122 |
| "x408" | 0.500076049703243 |
| "x409" | 0.498691384791536 |
| "x410" | 0.498929796277476 |
| "x411" | 0.501708653254574 |
| "x412" | 0.497889006545767 |
| "x413" | 0.504986315847584 |
| "x414" | 0.50249145781952 |
| "x415" | 0.498517542092968 |
| "x416" | 0.502209066824149 |
| "x417" | 0.50141426213542 |
| "x418" | 0.499224397290451 |
| "x419" | 0.502355230133631 |
| "x420" | 0.495981889346498 |
| "x421" | 0.498214948748122 |
| "x422" | 0.503087869197689 |
| "x423" | 0.503969026273629 |
| "x424" | 0.502452665825631 |
| "x425" | 0.497048816487961 |
| "x426" | 0.495624019407202 |
| "x427" | 0.499317652632738 |
| "x428" | 0.500914652247867 |
| "x429" | 0.499057770106616 |
| "x430" | 0.501268080979818 |
| "x431" | 0.498147857934493 |
| "x432" | 0.499914153201319 |
| "x433" | 0.495786726674158 |
| "x434" | 0.501682487738878 |
| "x435" | 0.496457202862645 |
| "x436" | 0.508543896326539 |
| "x437" | 0.501061310318136 |
| "x438" | 0.502894218938588 |
| "x439" | 0.502274609185918 |
| "x440" | 0.502498467199877 |
| "x441" | 0.501282249764865 |
| "x442" | 0.497290669186227 |
| "x443" | 0.501401792088733 |
| "x444" | 0.501240313977888 |
| "x445" | 0.497915219181264 |
| "x446" | 0.505064357985207 |
| "x447" | 0.502044832450291 |
| "x448" | 0.501214603475481 |
| "x449" | 0.500469672076427 |
| "x450" | 0.499569192343717 |
| "x451" | 0.504505589536461 |
| "x452" | 0.502298843947589 |
| "x453" | 0.497023923462909 |
| "x454" | 0.505475943069602 |
| "x455" | 0.495570238801069 |
| "x456" | 0.502516490759049 |
| "x457" | 0.50001143220698 |
| "x458" | 0.50056624143261 |
| "x459" | 0.500763978589862 |
| "x460" | 0.503351329483651 |
| "x461" | 0.495937412253953 |
| "x462" | 0.502993626758666 |
| "x463" | 0.50376565954613 |
| "x464" | 0.503578705062647 |
| "x465" | 0.499874845132907 |
| "x466" | 0.49710460913037 |
| "x467" | 0.500236035677022 |
| "x468" | 0.504071040146146 |
| "x469" | 0.502116545564379 |
| "x470" | 0.4970413170774 |
| "x471" | 0.497961502568331 |
| "x472" | 0.498185959877749 |
| "x473" | 0.500172177500324 |
| "x474" | 0.49990327054779 |
| "x475" | 0.505754457844445 |
| "x476" | 0.506156544381194 |
| "x477" | 0.502520981100039 |
| "x478" | 0.498271713060327 |
| "x479" | 0.499427241228428 |
| "x480" | 0.501416352765658 |
| "x481" | 0.497885700659943 |
| "x482" | 0.496553136685677 |
| "x483" | 0.499256669682357 |
| "x484" | 0.499976025144919 |
| "x485" | 0.502863525254768 |
| "x486" | 0.502828509843699 |
| "x487" | 0.497056779966387 |
| "x488" | 0.498057491645007 |
| "x489" | 0.499423123476515 |
| "x490" | 0.495550263123354 |
| "x491" | 0.496354107240075 |
| "x492" | 0.500804190374236 |
| "x493" | 0.502665761463973 |
| "x494" | 0.49879279964203 |
| "x495" | 0.50084074535016 |
| "x496" | 0.49858958128395 |
| "x497" | 0.498756470166892 |
| "x498" | 0.49870276355634 |
| "x499" | 0.49877461641808 |
| "x500" | 0.495528407560149 |
| "x501" | 0.499308988225553 |
| "x502" | 0.496989637391805 |
| "x503" | 0.497052493863879 |
| "x504" | 0.502207657987811 |
| "x505" | 0.497782883539819 |
| "x506" | 0.499157336530695 |
| "x507" | 0.499570190191874 |
| "x508" | 0.501303651056089 |
| "x509" | 0.501275910730497 |
| "x510" | 0.50475483049925 |
| "x511" | 0.49744029519686 |
| "x512" | 0.50021479274095 |
| "x513" | 0.502164487606823 |
| "x514" | 0.502737027523154 |
| "x515" | 0.505453019243362 |
| "x516" | 0.505072508157813 |
| "x517" | 0.497371969039645 |
| "x518" | 0.499832538922224 |
| "x519" | 0.500174262844981 |
| "x520" | 0.502035293567949 |
| "x521" | 0.49500378929202 |
| "x522" | 0.494185061220149 |
| "x523" | 0.497007539583836 |
| "x524" | 0.500462249073479 |
| "x525" | 0.501112031996949 |
| "x526" | 0.50448007855895 |
| "x527" | 0.500180586358835 |
| "x528" | 0.502937457214855 |
| "x529" | 0.495785512156505 |
| "x530" | 0.496734989838139 |
| "x531" | 0.49939898383636 |
| "x532" | 0.498502123921341 |
| "x533" | 0.504866269736877 |
| "x534" | 0.494965157273132 |
| "x535" | 0.495690308914194 |
| "x536" | 0.498892336926609 |
| "x537" | 0.501628264661017 |
| "x538" | 0.503607030711207 |
| "x539" | 0.498502264841949 |
| "x540" | 0.497903406035737 |
| "x541" | 0.49658684479869 |
| "x542" | 0.501395893062139 |
| "x543" | 0.499979672330362 |
| "x544" | 0.499520966207422 |
| "x545" | 0.496572526952415 |
| "x546" | 0.499305491672084 |
| "x547" | 0.49969866590458 |
| "x548" | 0.503476167464792 |
| "x549" | 0.495446928177774 |
| "x550" | 0.505830715886923 |
| "x551" | 0.495616547828494 |
| "x552" | 0.502230194019736 |
| "x553" | 0.503146120540239 |
| "x554" | 0.500894720273721 |
| "x555" | 0.500924644357059 |
| "x556" | 0.499140572330775 |
| "x557" | 0.500774686140707 |
| "x558" | 0.498897955308785 |
| "x559" | 0.50650362433407 |
| "x560" | 0.503777572448854 |
| "x561" | 0.4953408519377 |
| "x562" | 0.501732075663935 |
| "x563" | 0.501186506923474 |
| "x564" | 0.497129871141445 |
| "x565" | 0.506832370619941 |
| "x566" | 0.502918937394116 |
| "x567" | 0.497088979613851 |
| "x568" | 0.495986605457426 |
| "x569" | 0.502320092254644 |
| "x570" | 0.494138077245164 |
| "x571" | 0.497765557831619 |
| "x572" | 0.499874999663862 |
| "x573" | 0.497969851170666 |
| "x574" | 0.502105102461041 |
| "x575" | 0.498697688769549 |
| "x576" | 0.495100045574782 |
| "x577" | 0.502766133953678 |
| "x578" | 0.496227313589025 |
| "x579" | 0.49932494115436 |
| "x580" | 0.501537018946954 |
| "x581" | 0.495884116988792 |
| "x582" | 0.499084989017015 |
| "x583" | 0.494322689776961 |
| "x584" | 0.501757184752147 |
| "x585" | 0.504229674753267 |
| "x586" | 0.497673269462539 |
| "x587" | 0.503275601157756 |
| "x588" | 0.498003026509518 |
| "x589" | 0.497905468545761 |
| "x590" | 0.498104806767451 |
| "x591" | 0.497433767945156 |
| "x592" | 0.49946368073097 |
| "x593" | 0.502132979064411 |
| "x594" | 0.503633827587846 |
| "x595" | 0.497655095852725 |
| "x596" | 0.495839959227457 |
| "x597" | 0.502938682934688 |
| "x598" | 0.500326397570572 |
| "x599" | 0.501134085538425 |
Rows: 1-600 | Columns: 2
By using blocks of 100 columns, you reduce your impact on the system.
In [56]:
display(vdf.avg(ncols_block = 100))