Sketching Phase Spectra Using Group Delay and Magnitude Spectra Informations
If the magnitude spectrum is symmetric

$$M(\omega)=M(-\omega)\tag{1}$$

(as I assume), then your system is real-valued. The phase response of a real-valued system is asymmetric:

$$\phi(\omega)=-\phi(-\omega)\quad(\mod 2\pi)\tag{2}$$

This means that there can be two cases:


The phase goes through zero at $\omega=0$, i.e. the phase is given by $\phi(\omega)=-c\cdot\omega$, where $c$ is the constant group delay.
The phase is $\pm \pi$ at $\omega=0$, which means $\phi(\omega)=-c\cdot\omega\pm\pi$.
The phase jumps at $\omega=0$. This is only possible if the magnitude has a zero at $\omega=0$, i.e. $M(0)=0$. The phase jumps by $\pi$, which is simply a sign change of the (bipolar) amplitude function. In this case the phase is given by $$\phi(\omega)=\begin{cases}-\pi/2-c\cdot\omega,&amp;\quad\omega&gt;0\\\pi/2-c\cdot\omega,&amp;\quad\omega&lt;0\end{cases}$$