diff --git a/examples/pace/multi-elem/coupling_coefficients.yace b/examples/pace/multi-elem/coupling_coefficients.yace
new file mode 100644
index 0000000000..2953222216
--- /dev/null
+++ b/examples/pace/multi-elem/coupling_coefficients.yace
@@ -0,0 +1,294 @@
+elements: [H, N, O] 
+E0: [0.000000, 0.000000, 0.000000] 
+deltaSplineBins: 0.001000 
+embeddings:
+  0: {ndensity: 1, FS_parameters: [1.0, 1.0], npoti: FinnisSinclair, rho_core_cutoff: 100000, drho_core_cutoff: 250}
+  1: {ndensity: 1, FS_parameters: [1.0, 1.0], npoti: FinnisSinclair, rho_core_cutoff: 100000, drho_core_cutoff: 250}
+  2: {ndensity: 1, FS_parameters: [1.0, 1.0], npoti: FinnisSinclair, rho_core_cutoff: 100000, drho_core_cutoff: 250}
+bonds:
+  [0, 0]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.0, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [0, 1]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.5, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [0, 2]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.7, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [1, 0]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.5, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [1, 1]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 4.4, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [1, 2]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.7, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [2, 0]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.7, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [2, 1]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.7, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+  [2, 2]: {nradmax: 2, lmax: 2, nradbasemax: 2, radbasename: ChebExpCos, radparameters: [3.3], radcoefficients: [[[1, 0], [1, 0], [1, 0]], [[0, 1], [0, 1], [0, 1]]], prehc: 0, lambdahc: 3.3, rcut: 5.5, dcut: 0.01, rcut_in: 0.1, dcut_in: 0.01, inner_cutoff_type: distance}
+functions:
+  0:
+    - {mu0: 0, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [0], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 0, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [0], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 0, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [1], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 0, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [1], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 0, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [2], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 0, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [2], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 0, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 0, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 1, 2], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
+    - {mu0: 0, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 2, 2], ns: [1, 1, 1], ls: [2, 1, 1], ms_combs: [-2, 1, 1, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 2, -1, -1], ctildes: [0.25819888974716115, -0.18257418583505536, -0.18257418583505536, 0.10540925533894599, 0.21081851067789198, 0.10540925533894599, -0.18257418583505536, -0.18257418583505536, 0.25819888974716115]}
+    - {mu0: 0, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 2], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
+    - {mu0: 0, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
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+    - {mu0: 0, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 0], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 0, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [2, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+  1:
+    - {mu0: 1, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [1], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 1, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [1], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 1, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [2], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 1, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [2], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 1, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [0], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 1, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [0], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
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+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
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+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 1, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
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+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 1, 2], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 1, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 0, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 2, 2], ns: [1, 1, 1], ls: [2, 1, 1], ms_combs: [-2, 1, 1, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 2, -1, -1], ctildes: [0.25819888974716115, -0.18257418583505536, -0.18257418583505536, 0.10540925533894599, 0.21081851067789198, 0.10540925533894599, -0.18257418583505536, -0.18257418583505536, 0.25819888974716115]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 1], ns: [1, 1, 1], ls: [2, 1, 1], ms_combs: [-2, 1, 1, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 2, -1, -1], ctildes: [0.25819888974716115, -0.18257418583505536, -0.18257418583505536, 0.10540925533894599, 0.21081851067789198, 0.10540925533894599, -0.18257418583505536, -0.18257418583505536, 0.25819888974716115]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 0, 0], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 2], ns: [1, 1, 1], ls: [2, 1, 1], ms_combs: [-2, 1, 1, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 2, -1, -1], ctildes: [0.25819888974716115, -0.18257418583505536, -0.18257418583505536, 0.10540925533894599, 0.21081851067789198, 0.10540925533894599, -0.18257418583505536, -0.18257418583505536, 0.25819888974716115]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 1], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [1, 2, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 2, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 2], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 0, 1], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 2, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [2, 2, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 2, 2], ns: [1, 1, 1], ls: [2, 1, 1], ms_combs: [-2, 1, 1, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 2, -1, -1], ctildes: [0.25819888974716115, -0.18257418583505536, -0.18257418583505536, 0.10540925533894599, 0.21081851067789198, 0.10540925533894599, -0.18257418583505536, -0.18257418583505536, 0.25819888974716115]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 0, 2], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 2, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [2, 2, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 1, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 1, 1], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 0], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 1, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [2, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+  2:
+    - {mu0: 2, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [0], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 2, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [1], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 2, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [0], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 2, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [1], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 2, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [2], ns: [1], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 2, rank: 1, ndensity: 1, num_ms_combs: 1, mus: [2], ns: [2], ls: [0], ms_combs: [0], ctildes: [1.0]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 1], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [2, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 1], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 0], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 1], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [0, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [1, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [1, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 1], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [2, 2], ns: [2, 2], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 0], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [1, 1], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [1, 2], ns: [2, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 3, mus: [1, 2], ns: [2, 1], ls: [1, 1], ms_combs: [-1, 1, 0, 0, 1, -1], ctildes: [0.5773502691896257, -0.5773502691896257, 0.5773502691896257]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [0, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 2, ndensity: 1, num_ms_combs: 5, mus: [2, 2], ns: [1, 2], ls: [2, 2], ms_combs: [-2, 2, -1, 1, 0, 0, 1, -1, 2, -2], ctildes: [0.4472135954999579, -0.4472135954999579, 0.447213595499958, -0.4472135954999579, 0.4472135954999579]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [1, 2, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 2, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 0, 0], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
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+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
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+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 1], ns: [1, 1, 1], ls: [2, 1, 1], ms_combs: [-2, 1, 1, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 2, -1, -1], ctildes: [0.25819888974716115, -0.18257418583505536, -0.18257418583505536, 0.10540925533894599, 0.21081851067789198, 0.10540925533894599, -0.18257418583505536, -0.18257418583505536, 0.25819888974716115]}
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+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 0, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 0, 1], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
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+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [2, 2, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 1, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [2, 2, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 2], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [0, 1, 1], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 1, 2], ns: [1, 1, 1], ls: [1, 2, 1], ms_combs: [-1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -2, 1, 1, -1, 0, 1, 0, -1], ctildes: [0.10540925533894599, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.21081851067789198, -0.18257418583505536, 0.25819888974716115, -0.18257418583505536, 0.10540925533894599]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 1, 1], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 2, 2], ns: [1, 1, 1], ls: [2, 1, 1], ms_combs: [-2, 1, 1, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 2, -1, -1], ctildes: [0.25819888974716115, -0.18257418583505536, -0.18257418583505536, 0.10540925533894599, 0.21081851067789198, 0.10540925533894599, -0.18257418583505536, -0.18257418583505536, 0.25819888974716115]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 9, mus: [1, 2, 2], ns: [1, 1, 1], ls: [1, 1, 2], ms_combs: [-1, -1, 2, -1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, 0, -1, 1, 1, -2], ctildes: [0.19999999999999998, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.16329931618554522, -0.1414213562373095, 0.08164965809277261, -0.1414213562373095, 0.19999999999999998]}
+    - {mu0: 2, rank: 3, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1], ns: [1, 1, 1], ls: [2, 2, 2], ms_combs: [-2, 0, 2, -2, 1, 1, -2, 2, 0, -1, -1, 2, -1, 0, 1, -1, 1, 0, -1, 2, -1, 0, -2, 2, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 2, -2, 1, -2, 1, 1, -1, 0, 1, 0, -1, 1, 1, -2, 2, -2, 0, 2, -1, -1, 2, 0, -2], ctildes: [0.10690449676496976, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, 0.05345224838248488, -0.10690449676496976, 0.05345224838248488, 0.10690449676496976, -0.1309307341415954, 0.05345224838248488, 0.05345224838248488, -0.1309307341415954, 0.10690449676496976, -0.1309307341415954, 0.10690449676496976]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 0], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 0, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 0, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 1, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [0, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1, 1], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 1, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 1, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [1, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
+    - {mu0: 2, rank: 4, ndensity: 1, num_ms_combs: 19, mus: [2, 2, 2, 2], ns: [1, 1, 1, 1], ls: [1, 1, 1, 1], ms_combs: [-1, -1, 1, 1, -1, 0, 0, 1, -1, 0, 1, 0, -1, 1, -1, 1, -1, 1, 0, 0, -1, 1, 1, -1, 0, -1, 0, 1, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 0, 0, 1, -1, 1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 1, -1, -1], ctildes: [0.0, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, -0.3333333333333333, 0.3333333333333333, -0.3333333333333333, 0.0, 0.0, 0.3333333333333333, -0.3333333333333333, 0.3333333333333333, 0.0, 0.0, 0.0]}
diff --git a/examples/pace/multi-elem/latte_cell_0.data b/examples/pace/multi-elem/latte_cell_0.data
new file mode 100644
index 0000000000..b18ec13a4d
--- /dev/null
+++ b/examples/pace/multi-elem/latte_cell_0.data
@@ -0,0 +1,172 @@
+latte_cell_0.data (written by ASE) 
+
+161 	 atoms 
+3  atom types
+0.0                      12  xlo xhi
+0.0                      12  ylo yhi
+0.0                      12  zlo zhi
+
+
+Atoms 
+
+     1   3      1.2688096799999999      2.0079938400000001      2.7446829899999998
+     2   1      1.5343068200000001      2.0638766500000001      3.7105626900000002
+     3   1      1.7848279600000001      2.6755003400000001      2.2268847200000002
+     4   1              1.56251195      1.1089126899999999      2.3978115199999999
+     5   1             11.61728216              5.71881094      2.4732045999999999
+     6   2      6.5501865600000002      4.7439566800000001      3.6526025500000001
+     7   1      6.4564895299999998      4.1571673000000002      2.6975267999999999
+     8   2               2.0835561              1.59406078      8.5498047600000007
+     9   1      1.1041162499999999      1.4971771599999999      8.1507879200000009
+    10   1              2.60115534      2.2945960400000001              7.95374187
+    11   1      1.9817723300000001      2.0194066400000001      9.5128239400000005
+    12   1     0.99333338000000004      3.6983907299999998      8.1903947899999991
+    13   3      4.9484070999999998      5.3645501400000004              9.16152503
+    14   1      9.0716170599999995      9.3748453999999999      4.2276462400000003
+    15   2     0.30864418999999998      7.7136657499999997      2.9274995599999998
+    16   1              0.47661671              10.1807211              3.71160091
+    17   1              1.07465334      7.8226921999999997      3.5771466900000002
+    18   1     0.38402249999999999      8.3770493300000002      2.1748437100000002
+    19   1      11.435413410000001      7.7903735999999997      3.4040245499999999
+    20   3      6.1570384599999999             10.25988474              3.50899568
+    21   1      5.5932224399999999      9.5632944700000007      3.1446559000000001
+    22   2      1.7785569000000001      7.6312579300000003      9.1488452299999992
+    23   1      2.5594048599999999              6.96832838      9.3069700199999996
+    24   1              2.12441551      8.4547986999999996      8.6428622900000001
+    25   1              1.04552782      7.1697722800000001      8.5894244999999998
+    26   1     0.34824445999999998             10.17844028      9.1629463799999993
+    27   3      5.9638830399999998      10.723709400000001      9.4568803900000002
+    28   1      6.5890835699999997      10.926486110000001      8.7981925800000003
+    29   2      7.1065890400000002              1.83029753      3.3452543600000002
+    30   1      6.9229304999999997      1.8465022099999999      4.3089037100000001
+    31   1      8.0780433600000006      1.9303052199999999      3.2089521400000001
+    32   1      5.6795373600000003      10.471831630000001      4.3244390499999996
+    33   1              6.82999417     0.95850113000000003      2.9815288199999999
+    34   2      11.383805349999999      4.6301225199999996      2.5393688399999998
+    35   1     0.37927047000000003      4.1943216300000001              2.59073807
+    36   3      5.2376410099999999              1.91523463      9.7240636400000007
+    37   1      4.7887202499999999      2.7036936499999999      9.5698142300000004
+    38   1      9.8129906699999996      9.2075140700000002              4.08265499
+    39   1      4.7980879500000002      1.1403494700000001      9.6739962800000008
+    40   1      5.4455845600000004      2.0102099999999998      10.620773509999999
+    41   3     0.90954338999999995      4.6240093199999999      8.3108110600000007
+    42   1      11.909735319999999      4.7483814000000004      8.2500624600000005
+    43   2      7.3223424499999998               7.5866457      3.0245226500000002
+    44   1      7.4470362200000002      8.3169646700000008      3.7148003300000001
+    45   1      6.9073805300000002               7.9385021      2.1723768699999999
+    46   1      5.5542868500000004      5.1176065800000003      3.7655251999999999
+    47   1      6.8124309500000004      6.7778811599999997      3.3973232499999999
+    48   2     0.29575823000000001             11.04303794      3.1016142499999999
+    49   1     0.86490721999999998             11.83879228      3.6389974500000002
+    50   3              6.85201686      8.0846369300000003      8.8762878799999996
+    51   1      7.3351430100000004      7.4263498700000001      9.3821674799999997
+    52   1      6.7919613300000004      7.7595477199999996      7.9716174799999999
+    53   1      3.8990487699999998      6.4283490399999996      8.8832409600000002
+    54   1              5.95997296      9.9329723199999993      9.4746654699999997
+    55   3      11.403658979999999      10.371960359999999      9.2766092199999992
+    56   1      10.983666360000001      9.5157199800000001      9.1478757300000009
+    57   3      1.5223279700000001      5.3327331100000004     0.57537605999999997
+    58   1      2.3815113999999999      5.7251991200000001     0.77945295999999997
+    59   1     0.92079957000000001      6.0931282299999996     0.62203253000000003
+    60   3             11.23490924      2.9153355200000002      6.7585064099999999
+    61   1      10.792340190000001      2.9755225099999998      5.9000018399999998
+    62   1      10.751242059999999      2.1896156000000002      7.1807401500000001
+    63   3             11.39027944      7.3462855600000001      6.7258299499999996
+    64   1             10.92025679              6.69831954      7.2776696599999999
+    65   1             11.12238028      7.0632020999999998      5.8394107799999997
+    66   3      8.4684319499999994             10.71736286             10.60018556
+    67   1      8.5672201599999998      11.420466080000001             11.25794033
+    68   1      9.0803109800000001             10.04804949              10.9406517
+    69   3      6.5851757299999996      9.9940623399999993      6.5574614899999997
+    70   1      7.0276325799999997             10.76096604      6.1723333699999996
+    71   1      5.7419327400000002      10.384583920000001      6.8228822999999998
+    72   3      1.7600546399999999              1.01771919      5.4926787700000004
+    73   1      1.9704209100000001              1.01748419      6.4429703700000003
+    74   1              1.42973007              0.11076352      5.3470644900000002
+    75   1              2.61130613      9.7034123700000006      10.450306830000001
+    76   3              3.05086908             10.48131334      10.085189310000001
+    77   1      3.0032693199999998             10.93357295      9.3652121000000008
+    78   3      6.4631532199999997      8.7652058299999993      11.967847969999999
+    79   1      6.4506808400000004      9.6596595300000008      11.588956019999999
+    80   1      5.6611629700000003      8.3535737700000006      11.638443329999999
+    81   3      1.1745999300000001      5.2420690800000003      5.1001449699999997
+    82   1              1.31932881      5.5236392399999996      6.0128966300000002
+    83   1     0.58053834999999998      4.4898134599999997      5.2325565000000003
+    84   3      6.7275549699999999     0.78840874999999999      7.3817280900000002
+    85   1      6.3887965600000003              1.54670982      6.8634520400000003
+    86   1      7.6791783999999996     0.94039024000000004      7.2649461000000004
+    87   3      8.5476657199999995   0.0064750299999999997      5.0450514100000001
+    88   1      8.8736290899999997             11.10484108      4.8601807900000003
+    89   1      8.0477597599999999     0.20198361000000001      4.2357399400000002
+    90   3      1.2895030000000001      8.4280097900000008             11.82038504
+    91   1      1.4766666399999999      8.1087866399999999             10.87290333
+    92   1              2.10220669      8.1947620200000006              0.29510553
+    93   3      9.6797907599999995      6.4207335499999996      4.3469150599999997
+    94   1      8.9271530099999996              6.72940235      3.7974122399999999
+    95   1             10.20024126      5.9167739199999998              3.66976111
+    96   3              3.57411616      6.7041021699999996      3.8825478499999999
+    97   1      2.8894899500000002      6.1560529800000001      4.2980848099999998
+    98   1      4.3613707699999997      6.4304732400000004      4.3804965400000002
+    99   3               4.7506556      11.441853350000001              1.12537088
+   100   1      4.0861192800000001      10.748523670000001      1.1923347099999999
+   101   1      5.5035301600000004      10.965688249999999     0.73651277000000004
+   102   3      9.5254526399999992      4.8994443900000002      8.3732284099999994
+   103   1      8.7885959800000002      4.3508043900000004      8.6632831400000008
+   104   1      9.6149067499999994      4.6084911499999999      7.4540068699999997
+   105   3      4.1970746700000001              1.34592128              3.67401439
+   106   1      4.9437011999999996     0.74406280999999996                3.514068
+   107   1      4.1905534900000001      1.7730376000000001      2.7963049400000002
+   108   3              1.88232618             11.95451227     0.60024434000000004
+   109   1      2.0464587299999999             11.02454723              0.38329541
+   110   1      1.1518493700000001     0.17494340999999999             11.99928285
+   111   3      3.7593842199999998             11.01685511      6.4562050800000002
+   112   1      3.2125414299999999              10.4553747      5.8894917099999997
+   113   1      3.4166026899999999      10.821557670000001      7.3296563900000002
+   114   3      9.7039841399999993              3.95001545      11.894743249999999
+   115   1      10.461666060000001      3.9163117999999999      11.285435229999999
+   116   1             10.09834695      4.4026997400000001     0.68193007999999999
+   117   3      8.5639596400000002      3.5169507499999999      5.6224104199999996
+   118   1      8.3966650299999994      2.6262214699999999      5.2638164300000003
+   119   1      7.9695371399999999      4.0825059799999996      5.0049407400000003
+   120   3      9.6736245000000007     0.48030482000000002      7.9257577799999996
+   121   1      9.6131980400000003      11.883419180000001      7.1680923999999999
+   122   1      9.9784050299999993             11.90238635              8.63894187
+   123   3      3.9424153099999999      6.9650296699999998             11.60258943
+   124   1      4.2767152700000004      6.8460048999999996      10.670225220000001
+   125   1      4.6570638500000001      6.5129461500000003    0.091159879999999999
+   126   3      3.0570173199999999      9.6631958499999993      3.6611250599999998
+   127   1      2.5400490100000002      9.5743355000000001      2.8444047600000002
+   128   1      2.9314874400000002      8.7809807200000005      4.0425234200000002
+   129   3      7.4549612700000001      5.8430850799999998      11.011384720000001
+   130   1      8.1675884100000005      5.4639182799999997             10.47644287
+   131   1      6.7135573700000002      5.8393818399999997      10.361099749999999
+   132   3      9.8029139300000008      7.9578901699999998             10.21404942
+   133   1             10.38910242      8.3400641400000008             10.87949429
+   134   1      9.0637612000000001      7.6392374099999998      10.756928869999999
+   135   3      4.4963435599999997      4.1067935799999997             11.73387805
+   136   1      4.5473727899999998      4.9577970899999997             11.19223377
+   137   1      5.3588818399999996      4.1756111699999998     0.20355936999999999
+   138   3      9.5923448100000002      7.3418014600000001              1.34856172
+   139   1      8.8715593300000002      7.4776837199999999              2.05040471
+   140   1      9.0443221699999992      7.2732200799999998              0.54011714
+   141   3      7.0350963100000001              3.22348773               0.7070824
+   142   1      7.1784470499999999      4.1340314300000003      1.0184109699999999
+   143   1      7.7787854400000001      2.7888888399999998              1.15838887
+   144   3      9.2124107800000008     0.48085899999999998              1.21751966
+   145   1      9.6620436499999993      11.657271079999999              1.45318397
+   146   1      9.9404883900000005              1.11619136              1.18684594
+   147   3              1.19704207      9.5859959200000002      6.6190888899999996
+   148   1              0.25606413      9.6737366500000004      6.8319340899999998
+   149   1      1.2690051899999999      8.6249354900000004      6.5480112500000001
+   150   3     0.78256133999999999      2.6040609300000002      11.453408359999999
+   151   1              0.61502181      3.5607405999999999             11.40300991
+   152   1              1.55655312      2.5457368800000002      10.866733030000001
+   153   3      5.8627936099999998      7.1217054800000001              5.89173203
+   154   1      6.3432410700000004      7.9400136699999999      6.0855840299999997
+   155   1      5.5077296699999998      6.8468306800000001      6.7436875799999996
+   156   3      10.887828150000001      9.9637482500000001     0.51092815999999996
+   157   1             11.78841776      10.322043069999999     0.44704989000000001
+   158   1             11.02688182      9.2051906700000004      1.0976661299999999
+   159   3              3.93073389      4.1645674499999998      5.7137877000000001
+   160   1      4.6884062999999996      3.5788913299999998      5.5644605800000004
+   161   1      4.2956948500000003      4.7644888099999996      6.3801669700000003
diff --git a/examples/pace/multi-elem/latte_cell_0.xyz b/examples/pace/multi-elem/latte_cell_0.xyz
new file mode 100644
index 0000000000..afe0a27f35
--- /dev/null
+++ b/examples/pace/multi-elem/latte_cell_0.xyz
@@ -0,0 +1,163 @@
+161
+Lattice="12.0 0.0 0.0 0.0 12.0 0.0 0.0 0.0 12.0" Properties=species:S:1:pos:R:3 pbc="T T T"
+O        1.26880968       2.00799384       2.74468299
+H        1.53430682       2.06387665       3.71056269
+H        1.78482796       2.67550034       2.22688472
+H        1.56251195       1.10891269       2.39781152
+H       11.61728216       5.71881094       2.47320460
+N        6.55018656       4.74395668       3.65260255
+H        6.45648953       4.15716730       2.69752680
+N        2.08355610       1.59406078       8.54980476
+H        1.10411625       1.49717716       8.15078792
+H        2.60115534       2.29459604       7.95374187
+H        1.98177233       2.01940664       9.51282394
+H        0.99333338       3.69839073       8.19039479
+O        4.94840710       5.36455014       9.16152503
+H        9.07161706       9.37484540       4.22764624
+N        0.30864419       7.71366575       2.92749956
+H        0.47661671      10.18072110       3.71160091
+H        1.07465334       7.82269220       3.57714669
+H        0.38402250       8.37704933       2.17484371
+H       11.43541341       7.79037360       3.40402455
+O        6.15703846      10.25988474       3.50899568
+H        5.59322244       9.56329447       3.14465590
+N        1.77855690       7.63125793       9.14884523
+H        2.55940486       6.96832838       9.30697002
+H        2.12441551       8.45479870       8.64286229
+H        1.04552782       7.16977228       8.58942450
+H        0.34824446      10.17844028       9.16294638
+O        5.96388304      10.72370940       9.45688039
+H        6.58908357      10.92648611       8.79819258
+N        7.10658904       1.83029753       3.34525436
+H        6.92293050       1.84650221       4.30890371
+H        8.07804336       1.93030522       3.20895214
+H        5.67953736      10.47183163       4.32443905
+H        6.82999417       0.95850113       2.98152882
+N       11.38380535       4.63012252       2.53936884
+H        0.37927047       4.19432163       2.59073807
+O        5.23764101       1.91523463       9.72406364
+H        4.78872025       2.70369365       9.56981423
+H        9.81299067       9.20751407       4.08265499
+H        4.79808795       1.14034947       9.67399628
+H        5.44558456       2.01021000      10.62077351
+O        0.90954339       4.62400932       8.31081106
+H       11.90973532       4.74838140       8.25006246
+N        7.32234245       7.58664570       3.02452265
+H        7.44703622       8.31696467       3.71480033
+H        6.90738053       7.93850210       2.17237687
+H        5.55428685       5.11760658       3.76552520
+H        6.81243095       6.77788116       3.39732325
+N        0.29575823      11.04303794       3.10161425
+H        0.86490722      11.83879228       3.63899745
+O        6.85201686       8.08463693       8.87628788
+H        7.33514301       7.42634987       9.38216748
+H        6.79196133       7.75954772       7.97161748
+H        3.89904877       6.42834904       8.88324096
+H        5.95997296       9.93297232       9.47466547
+O       11.40365898      10.37196036       9.27660922
+H       10.98366636       9.51571998       9.14787573
+O        1.52232797       5.33273311       0.57537606
+H        2.38151140       5.72519912       0.77945296
+H        0.92079957       6.09312823       0.62203253
+O       11.23490924       2.91533552       6.75850641
+H       10.79234019       2.97552251       5.90000184
+H       10.75124206       2.18961560       7.18074015
+O       11.39027944       7.34628556       6.72582995
+H       10.92025679       6.69831954       7.27766966
+H       11.12238028       7.06320210       5.83941078
+O        8.46843195      10.71736286      10.60018556
+H        8.56722016      11.42046608      11.25794033
+H        9.08031098      10.04804949      10.94065170
+O        6.58517573       9.99406234       6.55746149
+H        7.02763258      10.76096604       6.17233337
+H        5.74193274      10.38458392       6.82288230
+O        1.76005464       1.01771919       5.49267877
+H        1.97042091       1.01748419       6.44297037
+H        1.42973007       0.11076352       5.34706449
+H        2.61130613       9.70341237      10.45030683
+O        3.05086908      10.48131334      10.08518931
+H        3.00326932      10.93357295       9.36521210
+O        6.46315322       8.76520583      11.96784797
+H        6.45068084       9.65965953      11.58895602
+H        5.66116297       8.35357377      11.63844333
+O        1.17459993       5.24206908       5.10014497
+H        1.31932881       5.52363924       6.01289663
+H        0.58053835       4.48981346       5.23255650
+O        6.72755497       0.78840875       7.38172809
+H        6.38879656       1.54670982       6.86345204
+H        7.67917840       0.94039024       7.26494610
+O        8.54766572       0.00647503       5.04505141
+H        8.87362909      11.10484108       4.86018079
+H        8.04775976       0.20198361       4.23573994
+O        1.28950300       8.42800979      11.82038504
+H        1.47666664       8.10878664      10.87290333
+H        2.10220669       8.19476202       0.29510553
+O        9.67979076       6.42073355       4.34691506
+H        8.92715301       6.72940235       3.79741224
+H       10.20024126       5.91677392       3.66976111
+O        3.57411616       6.70410217       3.88254785
+H        2.88948995       6.15605298       4.29808481
+H        4.36137077       6.43047324       4.38049654
+O        4.75065560      11.44185335       1.12537088
+H        4.08611928      10.74852367       1.19233471
+H        5.50353016      10.96568825       0.73651277
+O        9.52545264       4.89944439       8.37322841
+H        8.78859598       4.35080439       8.66328314
+H        9.61490675       4.60849115       7.45400687
+O        4.19707467       1.34592128       3.67401439
+H        4.94370120       0.74406281       3.51406800
+H        4.19055349       1.77303760       2.79630494
+O        1.88232618      11.95451227       0.60024434
+H        2.04645873      11.02454723       0.38329541
+H        1.15184937       0.17494341      11.99928285
+O        3.75938422      11.01685511       6.45620508
+H        3.21254143      10.45537470       5.88949171
+H        3.41660269      10.82155767       7.32965639
+O        9.70398414       3.95001545      11.89474325
+H       10.46166606       3.91631180      11.28543523
+H       10.09834695       4.40269974       0.68193008
+O        8.56395964       3.51695075       5.62241042
+H        8.39666503       2.62622147       5.26381643
+H        7.96953714       4.08250598       5.00494074
+O        9.67362450       0.48030482       7.92575778
+H        9.61319804      11.88341918       7.16809240
+H        9.97840503      11.90238635       8.63894187
+O        3.94241531       6.96502967      11.60258943
+H        4.27671527       6.84600490      10.67022522
+H        4.65706385       6.51294615       0.09115988
+O        3.05701732       9.66319585       3.66112506
+H        2.54004901       9.57433550       2.84440476
+H        2.93148744       8.78098072       4.04252342
+O        7.45496127       5.84308508      11.01138472
+H        8.16758841       5.46391828      10.47644287
+H        6.71355737       5.83938184      10.36109975
+O        9.80291393       7.95789017      10.21404942
+H       10.38910242       8.34006414      10.87949429
+H        9.06376120       7.63923741      10.75692887
+O        4.49634356       4.10679358      11.73387805
+H        4.54737279       4.95779709      11.19223377
+H        5.35888184       4.17561117       0.20355937
+O        9.59234481       7.34180146       1.34856172
+H        8.87155933       7.47768372       2.05040471
+H        9.04432217       7.27322008       0.54011714
+O        7.03509631       3.22348773       0.70708240
+H        7.17844705       4.13403143       1.01841097
+H        7.77878544       2.78888884       1.15838887
+O        9.21241078       0.48085900       1.21751966
+H        9.66204365      11.65727108       1.45318397
+H        9.94048839       1.11619136       1.18684594
+O        1.19704207       9.58599592       6.61908889
+H        0.25606413       9.67373665       6.83193409
+H        1.26900519       8.62493549       6.54801125
+O        0.78256134       2.60406093      11.45340836
+H        0.61502181       3.56074060      11.40300991
+H        1.55655312       2.54573688      10.86673303
+O        5.86279361       7.12170548       5.89173203
+H        6.34324107       7.94001367       6.08558403
+H        5.50772967       6.84683068       6.74368758
+O       10.88782815       9.96374825       0.51092816
+H       11.78841776      10.32204307       0.44704989
+H       11.02688182       9.20519067       1.09766613
+O        3.93073389       4.16456745       5.71378770
+H        4.68840630       3.57889133       5.56446058
+H        4.29569485       4.76448881       6.38016697
diff --git a/examples/pace/multi-elem/latte_cell_0_chi_i.npy b/examples/pace/multi-elem/latte_cell_0_chi_i.npy
new file mode 100644
index 0000000000..27f0878145
Binary files /dev/null and b/examples/pace/multi-elem/latte_cell_0_chi_i.npy differ
diff --git a/examples/pace/multi-elem/loop.sh b/examples/pace/multi-elem/loop.sh
new file mode 100755
index 0000000000..cd9f6da895
--- /dev/null
+++ b/examples/pace/multi-elem/loop.sh
@@ -0,0 +1,7 @@
+for (( ; ; ))
+do 
+    python test_en.py
+    if [[ $? -eq 139 ]]; then 
+        break 
+    fi
+done
diff --git a/examples/pace/multi-elem/test_en.py b/examples/pace/multi-elem/test_en.py
new file mode 100644
index 0000000000..b9dc064189
--- /dev/null
+++ b/examples/pace/multi-elem/test_en.py
@@ -0,0 +1,84 @@
+from __future__ import print_function
+import sys, os
+import ctypes
+import numpy as np
+from ase.io import read,write
+from lammps import lammps, LMP_TYPE_ARRAY, LMP_STYLE_GLOBAL
+
+# get MPI settings from LAMMPS
+def run_struct(f):
+    file_prefix = f.split('.')[0]
+    atoms = read(f)
+    lmp = lammps()
+
+    me = lmp.extract_setting("world_rank")
+    nprocs = lmp.extract_setting("world_size")
+
+    write('%s.data' % file_prefix,atoms,format='lammps-data')
+
+    cmds = ["-screen", "none", "-log", "none"]
+    lmp = lammps(cmdargs = cmds)
+
+    def run_lammps(dgradflag):
+
+        # simulation settings
+        fname = file_prefix
+        lmp.command("clear")
+        lmp.command("info all out log")
+        lmp.command('units  metal')
+        lmp.command('atom_style  atomic')
+        lmp.command("boundary    p p p")
+        lmp.command("atom_modify    map hash")
+        lmp.command('neighbor  2.3 bin')
+        # boundary
+        lmp.command('boundary  p p p')
+        # read atoms
+        lmp.command('read_data  %s.data' % fname )
+        lmp.command('mass  1 1.00')
+        lmp.command('mass  2 14.00')
+        lmp.command('mass  3 15.999')
+
+        # potential settings
+
+        lmp.command(f"pair_style     zero 5.7")
+        lmp.command(f"pair_coeff     * *")
+
+
+        if dgradflag:
+            lmp.command(f"compute     pace all pace coupling_coefficients.yace 1 1")
+        else:
+            lmp.command(f"compute     pace all pace coupling_coefficients.yace 1 0 ")
+
+        # run
+
+        lmp.command(f"thermo         100")
+        lmp.command(f"run {nsteps}")
+
+    # declare simulation/structure variables
+
+    nsteps = 0
+    ntypes = 3
+
+    # declare compute pace variables
+
+
+    bikflag = 1
+
+    # NUMBER of descriptors
+    nd = 91
+
+    dgradflag = 0
+    run_lammps(dgradflag)
+
+    lmp_pace = lmp.numpy.extract_compute("pace", LMP_STYLE_GLOBAL, LMP_TYPE_ARRAY)
+    print ('global shape',np.shape(lmp_pace))
+    np.save('%s_chi_i.npy' % file_prefix,lmp_pace)
+    lmp.close()
+    del lmp
+    return None
+
+
+import glob
+for f in sorted(glob.glob('*.xyz')):
+    print ('running %s' % f)
+    run_struct(f)