This example uses the function qn_eigenvalues() to compute the eigenvalues and for the spin-weighted quasinormal mode specified by and , and for a range of values of the dimensionless angular momentum parameter, . To invoke the program, type:
eigenvaluesfor the desired (integer) values of , , and . Make sure that and (the eigenvalues for negative values of can be inferred from the symmetries discussed in subsection ). The output of the program is five columns of data: the first column is the value of running from just greater than to just less than (or between and if ), the second and third columns are the real and imaginary parts of the eigenfrequency , and the fourth and fifth columns are the real and imaginary parts of the angular separation eigenvalue . For the values of , the eigenvalues correspond to the mode with azimuthal index so that the real part of the eigenfrequency is positive. A plot of the eigenfrequency output of the program eigenvalues for several runs with is shown in figure . The blue curves in figure can be compared to figure 5 of reference  keeping in mind the conversion factors between Leaver's convention (which is also used in ) and the convention used here (see subsection ).