Что делает данная програмима 
from itertools import product


# Класс для представления элементов конечного поля
class FieldElement:
    def __init__(self, coeffs, modulus, irreducible_poly):
        self.modulus = modulus
        self.irreducible_poly = [c % modulus for c in irreducible_poly]
        self.coeffs = [c % modulus for c in coeffs]
        self.reduce()

    def reduce(self):
        # Приводим полином по модулю неприводимого полинома
        while len(self.coeffs) >= len(self.irreducible_poly):
            lead_coeff = self.coeffs[-1]
            if lead_coeff == 0:
                self.coeffs.pop()
                continue
            deg_diff = len(self.coeffs) - len(self.irreducible_poly)
            # Вычитаем (ведущий коэффициент * x^{deg_diff} * неприводимый полином)
            for i in range(len(self.irreducible_poly)):
                idx = i + deg_diff
                self.coeffs[idx] -= lead_coeff * self.irreducible_poly[i]
                self.coeffs[idx] %= self.modulus
            # Удаляем последний коэффициент (должен быть нулем)
            self.coeffs.pop()
        # Убираем ведущие нули
        while len(self.coeffs) > 1 and self.coeffs[-1] == 0:
            self.coeffs.pop()
        if not self.coeffs:
            self.coeffs = [0]

    def __add__(self, other):
        max_len = max(len(self.coeffs), len(other.coeffs))
        result_coeffs = [0] * max_len
        for i in range(max_len):
            a = self.coeffs[i] if i < len(self.coeffs) else 0
            b = other.coeffs[i] if i < len(other.coeffs) else 0
            result_coeffs[i] = (a + b) % self.modulus
        return FieldElement(result_coeffs, self.modulus, self.irreducible_poly)

    def __sub__(self, other):
        max_len = max(len(self.coeffs), len(other.coeffs))
        result_coeffs = [0] * max_len
        for i in range(max_len):
            a = self.coeffs[i] if i < len(self.coeffs) else 0
            b = other.coeffs[i] if i < len(other.coeffs) else 0
            result_coeffs[i] = (a - b) % self.modulus
        return FieldElement(result_coeffs, self.modulus, self.irreducible_poly)

    def __mul__(self, other):
        result_coeffs = [0] * (len(self.coeffs) + len(other.coeffs) - 1)
        for i in range(len(self.coeffs)):
            for j in range(len(other.coeffs)):
                idx = i + j
                result_coeffs[idx] += self.coeffs[i] * other.coeffs[j]
                result_coeffs[idx] %= self.modulus
        return FieldElement(result_coeffs, self.modulus, self.irreducible_poly)

    def __pow__(self, exponent):
        result = FieldElement([1], self.modulus, self.irreducible_poly)
        base = FieldElement(self.coeffs[:], self.modulus, self.irreducible_poly)
        exp = exponent
        while exp > 0:
            if exp % 2 == 1:
                result = result * base
            base = base * base
            exp //= 2
        return result

    def __eq__(self, other):
        # Убираем ведущие нули для сравнения
        self_coeffs = self.coeffs[:]
        other_coeffs = other.coeffs[:]
        while len(self_coeffs) > 1 and self_coeffs[-1] == 0:
            self_coeffs.pop()
        while len(other_coeffs) > 1 and other_coeffs[-1] == 0:
            other_coeffs.pop()
        return self_coeffs == other_coeffs

    def __repr__(self):
        return f"FieldElement({self.coeffs})"


def find_roots_of_unity(modulus, irreducible_poly, k):
    degree = len(irreducible_poly) - 1
    # Генерируем все ненулевые элементы поля
    field_elements = []
    for coeffs in product(range(modulus), repeat=degree):
        if all(c == 0 for c in coeffs):
            continue  # Пропускаем нулевой элемент
        element = FieldElement(list(coeffs), modulus, irreducible_poly)
        field_elements.append(element)
    roots = []
    one = FieldElement([1], modulus, irreducible_poly)
    for element in field_elements:
        power = element ** k
        if power == one:
            roots.append(element)
    return roots


def main():
    modulus_input = input("Введите модуль p (простое число): ")
    modulus = int(modulus_input)
    irreducible_poly_input = input(
        "Введите коэффициенты неприводимого полинома f(x), начиная с коэффициента при старшей степени, через пробел: ")
    irreducible_poly_coeffs = list(map(int, irreducible_poly_input.strip().split()))
    irreducible_poly_coeffs = [c % modulus for c in irreducible_poly_coeffs]
    irreducible_poly_coeffs = irreducible_poly_coeffs[::-1]  # Разворачиваем список для внутреннего представления
    k_input = input("Введите степень корня из единицы k (натуральное число): ")
    k = int(k_input)

    roots = find_roots_of_unity(modulus, irreducible_poly_coeffs, k)
    print(f"Корни из 1 степени {k} в конечном поле:")
    if not roots:
        print("Нет корней данной степени в этом поле.")
    else:
        for root in roots:
            print(root)


if __name__ == "__main__":
    main()