fig2main.csv contains the data in the main panels of Fig. 2. The first column is the linewidths of each mode in order. The second column is the excitation of each mode when the electric dipole mode is excited. The third column is the excitation when the magnetic dipole mode is excited. The electric dipole mode is number 4291 while the magnetic dipole mode is number 111.

fig2inset contains the polarization amplitude shown in the inset of Fig. 2. The first column is for the electric dipole excitation and the second is the magnetic dipole excitation. The components given are y1,...,y4,z1,...,z4 where the atoms are labelled as in Fig. S1. The x components are exactly zero. 

fig3a_s3.csv gives the data in Fig. 3(a) and Fig. S3. The first column is a list of detunings in units of \gamma. The second is the total transmitted complex electric field (for amplitude 1 input plane wave) and the third is the sccattered field. The amplitude and phase can be extracted from the complex field. 

fig3b.csv gives the data in Fig. 3(b). The first column is a list of detunings in units of \gamma. The second is the electric dipole component, the third the magnetic dipole component, and the fourth the quadrupole component.

fig4.csv gives the data in Fig. 4. It consists of a 251 x 251 grid of values of the total transmitted field, at a distance 5\lambda, from the lattice, where each pixel corresponds to a point from -50/(2*pi) to 50/(2*pi) in steps of 0.4/(2*pi) in the y and z direction.

figs1.csv contains the eigenvectors displayed in Fig. S1. each column is a separate eigenvector wiht each row giving the component in directions x1,...x4,y1,...y4,...z1,...z4, where labels 1 to 4 are illustrated in the figure. Eigenvectors are in the order a,b,...i given in the figure, while the last three columns give the orthogonal eigenvectors degenerate with (a), (f), and (i) respectively.

figs2.csv gives the data shown in Fig. S2. The first column gives the total atom number N. The second column gives the linewidth of the electric dipole mode, and the third column gives the linewidth of the magnetic dipole mode.

figs4.csv gives the data in Fig. S4. It consists of a 251 x 251 grid of values of the total transmitted field, at a distance 5\lambda, from the lattice, where each pixel corresponds to a point from -50/(2*pi) to 50/(2*pi) in steps of 0.4/(2*pi) in the y and z direction.