diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
index 2bc6c92b0..faa24a525 100644
Binary files a/.doctrees/environment.pickle and b/.doctrees/environment.pickle differ
diff --git a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
index a07cb5a86..d9b71648a 100644
--- a/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
+++ b/.doctrees/nbsphinx/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
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@@ -62,10 +62,10 @@
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@@ -92,10 +92,10 @@
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diff --git a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
index 9cf01df99..36165c39c 100644
--- a/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
+++ b/.doctrees/nbsphinx/tutorials/02-orbital-rotation.ipynb
@@ -43,10 +43,10 @@
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@@ -111,10 +111,10 @@
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@@ -160,10 +160,10 @@
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@@ -203,10 +203,10 @@
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diff --git a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
index ba3ac7a4c..1e8d6c050 100644
--- a/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
+++ b/.doctrees/nbsphinx/tutorials/03-double-factorized.ipynb
@@ -43,10 +43,10 @@
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@@ -93,10 +93,10 @@
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@@ -227,10 +227,10 @@
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@@ -285,10 +285,10 @@
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@@ -325,10 +325,10 @@
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@@ -367,10 +367,10 @@
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@@ -409,10 +409,10 @@
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@@ -450,10 +450,10 @@
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@@ -493,10 +493,10 @@
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@@ -535,10 +535,10 @@
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    "outputs": [
diff --git a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
index 5865bb50a..1aafe1e78 100644
--- a/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
+++ b/.doctrees/nbsphinx/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
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-     "shell.execute_reply": "2023-09-23T03:40:38.541461Z"
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@@ -80,10 +80,10 @@
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@@ -145,10 +145,10 @@
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@@ -222,10 +222,10 @@
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+     "shell.execute_reply": "2023-09-23T14:19:24.117738Z"
     }
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    "outputs": [
diff --git a/tutorials/01-introduction.ipynb b/tutorials/01-introduction.ipynb
index a07cb5a86..d9b71648a 100644
--- a/tutorials/01-introduction.ipynb
+++ b/tutorials/01-introduction.ipynb
@@ -16,10 +16,10 @@
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-     "shell.execute_reply": "2023-09-23T03:40:32.454859Z"
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    "outputs": [],
@@ -62,10 +62,10 @@
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@@ -92,10 +92,10 @@
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+     "shell.execute_reply": "2023-09-23T14:19:15.856011Z"
     }
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    "outputs": [],
diff --git a/tutorials/02-orbital-rotation.ipynb b/tutorials/02-orbital-rotation.ipynb
index 9cf01df99..36165c39c 100644
--- a/tutorials/02-orbital-rotation.ipynb
+++ b/tutorials/02-orbital-rotation.ipynb
@@ -43,10 +43,10 @@
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     }
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    "outputs": [],
@@ -111,10 +111,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:34.255707Z",
-     "iopub.status.busy": "2023-09-23T03:40:34.254663Z",
-     "iopub.status.idle": "2023-09-23T03:40:34.279561Z",
-     "shell.execute_reply": "2023-09-23T03:40:34.279092Z"
+     "iopub.execute_input": "2023-09-23T14:19:18.074867Z",
+     "iopub.status.busy": "2023-09-23T14:19:18.074510Z",
+     "iopub.status.idle": "2023-09-23T14:19:18.105795Z",
+     "shell.execute_reply": "2023-09-23T14:19:18.105084Z"
     }
    },
    "outputs": [],
@@ -160,10 +160,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:34.283279Z",
-     "iopub.status.busy": "2023-09-23T03:40:34.282361Z",
-     "iopub.status.idle": "2023-09-23T03:40:34.293531Z",
-     "shell.execute_reply": "2023-09-23T03:40:34.293052Z"
+     "iopub.execute_input": "2023-09-23T14:19:18.109590Z",
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+     "iopub.status.idle": "2023-09-23T14:19:18.127280Z",
+     "shell.execute_reply": "2023-09-23T14:19:18.126664Z"
     }
    },
    "outputs": [],
@@ -203,10 +203,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:34.297567Z",
-     "iopub.status.busy": "2023-09-23T03:40:34.296204Z",
-     "iopub.status.idle": "2023-09-23T03:40:34.302034Z",
-     "shell.execute_reply": "2023-09-23T03:40:34.301583Z"
+     "iopub.execute_input": "2023-09-23T14:19:18.130663Z",
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+     "iopub.status.idle": "2023-09-23T14:19:18.137873Z",
+     "shell.execute_reply": "2023-09-23T14:19:18.137285Z"
     }
    },
    "outputs": [],
diff --git a/tutorials/03-double-factorized.ipynb b/tutorials/03-double-factorized.ipynb
index ba3ac7a4c..1e8d6c050 100644
--- a/tutorials/03-double-factorized.ipynb
+++ b/tutorials/03-double-factorized.ipynb
@@ -43,10 +43,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:35.801422Z",
-     "iopub.status.busy": "2023-09-23T03:40:35.801200Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.187059Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.186502Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.222559Z",
+     "iopub.status.busy": "2023-09-23T14:19:20.222152Z",
+     "iopub.status.idle": "2023-09-23T14:19:20.707430Z",
+     "shell.execute_reply": "2023-09-23T14:19:20.706781Z"
     }
    },
    "outputs": [
@@ -93,10 +93,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.202566Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.202045Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.208058Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.207586Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.721056Z",
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+     "shell.execute_reply": "2023-09-23T14:19:20.726907Z"
     }
    },
    "outputs": [
@@ -227,10 +227,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.210551Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.210068Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.215213Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.214131Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.730659Z",
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+     "shell.execute_reply": "2023-09-23T14:19:20.734870Z"
     }
    },
    "outputs": [],
@@ -285,10 +285,10 @@
    "execution_count": 4,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.217674Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.217198Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.221241Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.220475Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.738617Z",
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+     "shell.execute_reply": "2023-09-23T14:19:20.741892Z"
     }
    },
    "outputs": [],
@@ -325,10 +325,10 @@
    "execution_count": 5,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.223653Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.223167Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.227636Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.227181Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.745491Z",
+     "iopub.status.busy": "2023-09-23T14:19:20.745129Z",
+     "iopub.status.idle": "2023-09-23T14:19:20.750307Z",
+     "shell.execute_reply": "2023-09-23T14:19:20.749773Z"
     }
    },
    "outputs": [
@@ -367,10 +367,10 @@
    "execution_count": 6,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.230481Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.229594Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.240146Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.239627Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.753199Z",
+     "iopub.status.busy": "2023-09-23T14:19:20.752843Z",
+     "iopub.status.idle": "2023-09-23T14:19:20.764779Z",
+     "shell.execute_reply": "2023-09-23T14:19:20.764123Z"
     }
    },
    "outputs": [
@@ -409,10 +409,10 @@
    "execution_count": 7,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.242402Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.242221Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.250226Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.249700Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.768400Z",
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+     "iopub.status.idle": "2023-09-23T14:19:20.780529Z",
+     "shell.execute_reply": "2023-09-23T14:19:20.779548Z"
     }
    },
    "outputs": [
@@ -450,10 +450,10 @@
    "execution_count": 8,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.252771Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.252416Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.285787Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.285278Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.783605Z",
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+     "iopub.status.idle": "2023-09-23T14:19:20.827930Z",
+     "shell.execute_reply": "2023-09-23T14:19:20.827323Z"
     }
    },
    "outputs": [
@@ -493,10 +493,10 @@
    "execution_count": 9,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:36.288175Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.287813Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.309288Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.308860Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.831137Z",
+     "iopub.status.busy": "2023-09-23T14:19:20.830546Z",
+     "iopub.status.idle": "2023-09-23T14:19:20.864312Z",
+     "shell.execute_reply": "2023-09-23T14:19:20.863730Z"
     }
    },
    "outputs": [
@@ -535,10 +535,10 @@
    "execution_count": 10,
    "metadata": {
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-     "iopub.execute_input": "2023-09-23T03:40:36.311609Z",
-     "iopub.status.busy": "2023-09-23T03:40:36.311239Z",
-     "iopub.status.idle": "2023-09-23T03:40:36.321239Z",
-     "shell.execute_reply": "2023-09-23T03:40:36.320806Z"
+     "iopub.execute_input": "2023-09-23T14:19:20.867250Z",
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+     "iopub.status.idle": "2023-09-23T14:19:20.890251Z",
+     "shell.execute_reply": "2023-09-23T14:19:20.889544Z"
     }
    },
    "outputs": [
diff --git a/tutorials/04-lucj.ipynb b/tutorials/04-lucj.ipynb
index 5865bb50a..1aafe1e78 100644
--- a/tutorials/04-lucj.ipynb
+++ b/tutorials/04-lucj.ipynb
@@ -14,10 +14,10 @@
    "execution_count": 1,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:38.174793Z",
-     "iopub.status.busy": "2023-09-23T03:40:38.174303Z",
-     "iopub.status.idle": "2023-09-23T03:40:38.541970Z",
-     "shell.execute_reply": "2023-09-23T03:40:38.541461Z"
+     "iopub.execute_input": "2023-09-23T14:19:23.121672Z",
+     "iopub.status.busy": "2023-09-23T14:19:23.121416Z",
+     "iopub.status.idle": "2023-09-23T14:19:23.576270Z",
+     "shell.execute_reply": "2023-09-23T14:19:23.575644Z"
     }
    },
    "outputs": [
@@ -80,10 +80,10 @@
    "execution_count": 2,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:38.544915Z",
-     "iopub.status.busy": "2023-09-23T03:40:38.544459Z",
-     "iopub.status.idle": "2023-09-23T03:40:38.640518Z",
-     "shell.execute_reply": "2023-09-23T03:40:38.640023Z"
+     "iopub.execute_input": "2023-09-23T14:19:23.580090Z",
+     "iopub.status.busy": "2023-09-23T14:19:23.579739Z",
+     "iopub.status.idle": "2023-09-23T14:19:23.709859Z",
+     "shell.execute_reply": "2023-09-23T14:19:23.709254Z"
     }
    },
    "outputs": [
@@ -145,10 +145,10 @@
    "execution_count": 3,
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2023-09-23T03:40:38.644392Z",
-     "iopub.status.busy": "2023-09-23T03:40:38.643438Z",
-     "iopub.status.idle": "2023-09-23T03:40:38.769874Z",
-     "shell.execute_reply": "2023-09-23T03:40:38.769372Z"
+     "iopub.execute_input": "2023-09-23T14:19:23.714435Z",
+     "iopub.status.busy": "2023-09-23T14:19:23.713156Z",
+     "iopub.status.idle": "2023-09-23T14:19:23.893762Z",
+     "shell.execute_reply": "2023-09-23T14:19:23.893058Z"
     }
    },
    "outputs": [
@@ -222,10 +222,10 @@
    "execution_count": 4,
    "metadata": {
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-     "iopub.execute_input": "2023-09-23T03:40:38.773775Z",
-     "iopub.status.busy": "2023-09-23T03:40:38.772826Z",
-     "iopub.status.idle": "2023-09-23T03:40:38.919685Z",
-     "shell.execute_reply": "2023-09-23T03:40:38.919182Z"
+     "iopub.execute_input": "2023-09-23T14:19:23.897410Z",
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+     "iopub.status.idle": "2023-09-23T14:19:24.118397Z",
+     "shell.execute_reply": "2023-09-23T14:19:24.117738Z"
     }
    },
    "outputs": [