Recompose a table from an SQL with row and colum ID in Python

I'm reading from an SQLite table created by a program I have no control on.

The idea behind the layout of this SQL table eludes me, but that's the way it is.

This table looks like this in SQL:

What it really is, and what I'd like to get in python-pandas dataframe is this:

So far, this only way I can think of doing this is by getting a list of RowID, looping on them, and reconstructing the table.

But I'm wondering if there's an easier and faster way (database is huge), either when doing the SELECT statement or later on the pandas dataframe itself.

To load the data I'm using:

import pandas as pd
import sqlite3

con = sqlite3.connect(sql_path)
#Simplified here, to produce the Table I filter on a few things
df = pd.read_sql('SELECT * from Table',con=con, index_col='RowID')

I've desperately tried and failed to use a bunch of stuff including pd.pivot or pd.groupby but it might just be because I don't know how to use it properly.

Version:

Python: 2.7.8 | Pandas: 0.16.0 | sqlite3: 2.6.0