Set of N integers between -30 and 30 with sum and cubic sum up to zero for 4<N<13

Anomalies

Solutions obtained with the python package: anomalies  based on  the method to find anomaly free solutions of the standard model extended with an Abelian Dark Symmetry with N right-handed singlet chiral fields described in arXiv:1905.13729 [PRL]:

Data scheme

• 'l': integer lists → input to obtain the 'solution'  by using the anomalies package
• 'k': integer lists → input to obtain the 'solution'  by using hte  anomalies package
• 'solution': list → of integers, \(\large z_i\) which satisfy \(\large\displaystyle{ \sum_{i=1}^N z_i=0}\) and  \(\large\displaystyle{ \sum_{i=1}^N z_i^3=0}\)  .
• 'n': integer → number of integers in 'solution', N.

 
USAGE

#Example of JSON file usage in Python with pandas (see also json module)
>>> import pandas as pd
>>> df=pd.read_json('solutions.json')
>>> df[:2]
          l        k            solution  gcd  n
0    [1, 2]  [0, -3]   [1, 5, -7, -8, 9]    1  5
1  [-2, -1]  [0, -1]  [2, 4, -7, -9, 10]    1  5

Data:
390074 solutions with   \(\large 5\le N\le 12\) integers until `|32|`   [JSON]