How to clean the indexes, and ideally not create an additional array
Here is a review of the solution.

^ is xor in Python. It is not for computation of exponentials.

When running code outside a method / class, it is a good practice to put the code inside a main guard. See here for more explanation.
 if __name__ == &quot;__main__&quot;:
    ...

When you are providing quick answers on a forum, the guard might not always be necessary. However, if you are writing reusable code for yourself, it is better to adopt the practice.

By convention, _ is used to represent a don't-care variable, which won't be used after its value is assigned, e.g. v = [[] for _ in range(4)]. It is undesirable to refer to it in an expression like answer[_].

The output is a pure text file. It is unnecessary to open it in binary mode (b). The original question does not suggest an append mode (a) either.

The q-1 index would no longer work if q is changed to a different group of values. Therefore, it is better to use enumerate in this case:
for i, q in enumerate(RANGE_Q):
   ...
   export[i, 0] = q
   ...

A better approach is to use zip:
for q, output_row in zip(RANGE_Q, output_arr):
    ...
    output_row[0] = q
    ...


The assignments to the output numpy array can be improved, as shown in my solution below.


Here is my solution.
import numpy as np

if __name__ == &quot;__main__&quot;:
    # Define constants
    RANGE_Q = range(1, 11)               # Range of q values
    POLY_DEG = 4                         # Degree of polynomial
    OUTPUT_PATH = &quot;/tmp/latest_foo.csv&quot;  # Output csv path

    # Compute roots
    roots_arr = np.array([np.roots([1, 3*q*q, 4*q, np.sqrt(q), q]) for q in RANGE_Q])
    
    # Construct output array and assign values
    output_arr = np.empty(shape=(len(RANGE_Q), POLY_DEG * 2 + 1))
    output_arr[:, 0] = RANGE_Q
    output_arr[:, 1::2] = roots_arr.real
    output_arr[:, 2::2] = roots_arr.imag

    # Save results to output file
    np.savetxt(OUTPUT_PATH, output_arr, fmt=&quot;%.4g&quot;, delimiter=',')