Programm doesnt use output operator

I'm currently working on a programm that should be a queue as a doubly linked list. The programm works, but my problem is that it doesn't use the output operator for 'Queue_element'. It just uses the standard output operator. How do i need to change my programm that it would use it?

Here is my code so far:

#include <iostream>

using namespace std;

template<typename T> class Queue;

template<typename T> class Queue_element {
private:
    T value;
    Queue_element<T>* next;
    Queue_element<T>* prev;

public:
    Queue_element() { value = 0; next = nullptr; prev = nullptr; }
    Queue_element(T n) { value = n; next = nullptr; prev = nullptr; }

    template<typename S> friend ostream& operator<<(ostream& os, const Queue_element<S>& queue_el);
    template<typename S> friend ostream& operator<<(ostream& os, const Queue<S>& queue);
    friend class Queue<T>;
};

template<typename T> class Queue {
private:
    Queue_element<T>* head;
    Queue_element<T>* tail;

public:
    Queue() { head = nullptr; tail = nullptr; }
    void push(T n);
    bool empty() const;

    template<typename S> friend ostream& operator<<(ostream& os, const Queue<S>& queue);
};

template<typename T> bool Queue<T>::empty() const
{
    if (this->head == nullptr && this->tail == nullptr) { return true; }
    else return false;
};

template<typename T> void Queue<T>::push(T n) {
    Queue_element<T>* q = new Queue_element<T>(n);
    if (this->empty()) { this->head = q; this->tail = q; }
    else { this->tail->next = q; q->prev = tail; this->tail = q; }
}

template<typename S>
ostream& operator<<(ostream& os, const Queue_element<S>& queue_el) {
    os << queue_el.value;
    return os;
}

template<typename S>
ostream& operator<<(ostream& os, const Queue<S>& queue){
    Queue_element<S>* q = queue.head;
    while(q != nullptr){
        os << q->value << " ";
        q = q->next;
    }
return os;
}

int main()
{
    Queue<string> q1;
    q1.push("test");
    cout << q1 << endl;
    return 0;
}

While this is the output operator i'm talking about:

template<typename S>
ostream& operator<<(ostream& os, const Queue_element<S>& queue_el) {
    os << queue_el.value;
    return os;
}

Would appreciate any help!