Reproducing murmuration plots in literature

• SageMath >= 10.6

The following python libraries have to be installed inside SageMath shell:

• numpy
• matplotlib
• tqdm

sage --sh
pip install numpy matplotlib tqdm
exit

• He-Lee-Oliver-Podznyakov, "Murmuration of Elliptic Curves", Experimental Mathematics 2024

  • Reproduce Figure 1

• Sutherland, "Letter to Rubinstein and Sarnak"

  • Reproduce figures in page 2 and 3

sage ellcurve.sage

The generated plots will be saved under the directory plots/ellcurve.

• Lee-Oliver-Podznyakov, "Murmuration of Dirichlet Characters", IMRN 2025

  • Reproduce Figure 1, 2, and 3.

sage dirichlet.sage

The generated plots will be saved under the directory plots/dirichlet.

• Zubrilina, "Murmuration", Inventiones 2025

  • Reproduce Figure 2, 3, and 4.

• Martin, "Distribution of local signs of modular forms and murmurations of Fourier coefficients"

  • Reproduce Figure 3 and 4

sage modform.sage

The generated plots will be saved under the directory plots/modform.