diff --git a/.translate/state/eig_circulant.md.yml b/.translate/state/eig_circulant.md.yml
index bfabd85..57a13ec 100644
--- a/.translate/state/eig_circulant.md.yml
+++ b/.translate/state/eig_circulant.md.yml
@@ -1,6 +1,6 @@
-source-sha: 6a512f1f2079665601fd77fad821c19a8c75b292
-synced-at: "2026-07-18"
+source-sha: 113d0e29192fc36877f1ab3f3596e2ae1db00b07
+synced-at: "2026-07-31"
 model: claude-sonnet-5
-mode: RESYNC
+mode: UPDATE
 section-count: 6
-tool-version: 0.17.0
+tool-version: 0.24.0
diff --git a/lectures/eig_circulant.md b/lectures/eig_circulant.md
index 7417194..96773c8 100644
--- a/lectures/eig_circulant.md
+++ b/lectures/eig_circulant.md
@@ -383,7 +383,8 @@ $$
 我们用 $N=8$ 的情况来说明这一点。
 
 ```{code-cell} ipython3
-c = np.random.random(8)
+rng = np.random.default_rng()
+c = rng.random(8)
 ```
 
 ```{code-cell} ipython3