Quantum Ising/Heisenberg model, states representation

I am working with a Hamiltonian which looks like this (Heisenberg model)
$$ hat{H} = -frac{1}{2}sum_{j=1}^N left(
J_xsigma_j^xsigma_{j+1}^x
+J_ysigma_j^ysigma_{j+1}^y
+J_zsigma_j^zsigma_{j+1}^z + hsigma_j^z
right). $$

I have made a program which computes this Hamiltonian using Pauli matrices (spin 1/2). My working space is then the tensor product ($N$ times) of $mathbb{C}^2$. I know that the canonical base of my space can be expressed as a tensor product of base vectors of $mathbb{C}^2$, for example: $(1,0,0,0) = (1,0)otimes (1,0)$

This works fine when I am working with only $J_z$ not null (classical Ising model) because all the eigenstates can be expressed this way (all eigenstates are vectors of the canonical base). When I work with, for example, only $J_x$ not null (quantum Ising) I get eigenstates which are a bit more messy, for example $(0,1/sqrt{2},-1/sqrt{2},0)$.

This eigenstate can be expressed as a linear combination of canonical base vectors and those as a tensor product of the spin 1/2 Z base.

My problem is that I seek a "visual representation" of all states (or eigenspaces), I believe that any two level system can be represented in polar coordinates in $mathbb{R}^3$ (Bloch sphere) but I fail at doing so, how should I proceed? Let’s say I wanted to represent the state I used as a example before, which is non-degenerate, in a visual way, that is, in polar coordinates (it corresponds to the case of two 1/2 spins, so two points in polar coordinates would be required).