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

<p><strong>Anomalies</strong></p> <p>Solutions obtained with the python package:&nbsp;<a href="http://doi.org/10.5281/zenodo.5526558">anomalies</a>&nbsp; based on&nbsp; the method to find anomaly free solutions of the standard model extended with an Abelian Dark Symmetry with <em>N</em>&nbsp;right-handed singlet chiral fields described in&nbsp;<a href="https://arxiv.org/abs/1905.13729">arXiv:1905.13729</a>&nbsp;[PRL]:</p> <p><strong>Data scheme</strong></p> <ul> <li>&#39;l&#39;: integer lists &rarr; input&nbsp;to obtain the &#39;solution&#39;&nbsp; by using the&nbsp;<a href="http://doi.org/10.5281/zenodo.5526558">anomalies</a>&nbsp;package</li> <li>&#39;k&#39;:&nbsp;integer lists &rarr; input&nbsp;to obtain the &#39;solution&#39;&nbsp; by using hte&nbsp;&nbsp;<a href="http://doi.org/10.5281/zenodo.5526558">anomalies</a>&nbsp;package</li> <li>&#39;solution&#39;: list &rarr; of integers, <span class="math-tex">\(\large z_i\)</span>_&nbsp;which satisfy&nbsp;<span class="math-tex">\(\large\displaystyle{ \sum_{i=1}^N z_i=0}\)</span> and&nbsp; <span class="math-tex">\(\large\displaystyle{ \sum_{i=1}^N z_i^3=0}\)</span>&nbsp; .</li> <li>&#39;n&#39;: integer &rarr; number of integers in &#39;solution&#39;, <em>N</em>.</li> </ul> <pre>&nbsp; <strong>USAGE</strong></pre> <pre><code class="language-python">#Example of JSON file usage in Python with pandas (see also json module) &gt;&gt;&gt; import pandas as pd &gt;&gt;&gt; df=pd.read_json('solutions.json.gz') &gt;&gt;&gt; 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</code></pre> <p><strong>Data:</strong><br> 2 296 615&nbsp;&nbsp;solutions with&nbsp; &nbsp;<span class="math-tex">\(\large 5\le N\le 12\)</span>&nbsp;integers until `|32|`&nbsp;&nbsp;&nbsp;[JSON]</p>