diff --git a/bmad/modules/complex_taylor_mod.f90 b/bmad/modules/complex_taylor_mod.f90
index fa528154ac..82edcdb8a8 100644
--- a/bmad/modules/complex_taylor_mod.f90
+++ b/bmad/modules/complex_taylor_mod.f90
@@ -263,7 +263,8 @@ function complex_taylor_coef2 (complex_taylor, i1, i2, i3, &
 !   out_type       -- character(*), optional: Determins the string to be used for the output type column.
 !                       '' (default)  -> '1', '2', '3', etc.
 !                       'PHASE'       -> 'X', 'Px, 'Y', 'Py', 'Z', 'Pz'
-!                       'SPIN'        -> 'S1', 'Sx', 'Sy', 'Sz' (quaternion representation)
+!                       'SPIN'        -> 'S1', 'Sx', 'Sy', 'Sz'  ! If size = 4: quaternion representation
+!                       'SPIN'        -> 'Sx', 'Sy', 'Sz'  ! If size = 3: 
 !                       'NONE'        -> No out column
 !                       Anything else -> Use this for the output column.
 !   clean          -- logical, optional: If True then do not include terms whose coefficients
@@ -352,7 +353,11 @@ subroutine type_complex_taylors (complex_taylor, max_order, lines, n_lines, file
     case ('PHASE')
       if (i <=6) out_str = ' ' // phase_out(i) // ':'
     case ('SPIN')
-      if (i <=4) out_str = ' ' // spin_out(i) // ':'
+      if (nt == 4) then 
+        out_str = ' ' // spin_out(i) // ':'
+      elseif (nt == 3) then
+        out_str = ' ' // spin_out(i+1) // ':'
+      endif
     case default
       out_str = o_type // ':'
     end select
diff --git a/tao/code/tao_show_this.f90 b/tao/code/tao_show_this.f90
index 326943578d..9fbdbec538 100644
--- a/tao/code/tao_show_this.f90
+++ b/tao/code/tao_show_this.f90
@@ -4539,7 +4539,8 @@ subroutine tao_show_this (what, result_id, lines, nl)
     do i = 1, 3
       ctaylor(i) = ptc_nf%isf%x(i)
     enddo
-    call type_complex_taylors(ctaylor)
+
+    call type_complex_taylors(ctaylor, out_type = 'SPIN')
     return
   endif
 
diff --git a/tao/doc/command-list.tex b/tao/doc/command-list.tex
index 1d93508ee1..9e0e6cf661 100644
--- a/tao/doc/command-list.tex
+++ b/tao/doc/command-list.tex
@@ -3013,8 +3013,8 @@ \subsection{show spin}
 Syntax:
 \begin{example}
   show spin \{-element \{<ref_ele_name>\} <ele_name>\} \{-flip_n_axis\} \{-g_map\}
-                  \{-n_axis <nx>, <ny>, <nz>\} \{-l_axis <lx>, <ly>, <lz>\}
-                  \{-ignore_kinetic <ele_list>\}
+                  \{-ignore_kinetic <ele_list>\} \{-isf\}
+                  \{-l_axis <lx>, <ly>, <lz>\} \{-n_axis <nx>, <ny>, <nz>\} 
                   \{-x_zero <ele_list>\} \{-y_zero <ele_list>\} \{-z_zero <ele_list>\}
 \end{example}
 
@@ -3063,6 +3063,10 @@ \subsection{show spin}
 
 The \vn{-flip_n_axis} switch, if present, will flip the direction of the displayed $n$-axis. 
 
+The \vn{-isf} switch, if present, will print the invariant spin field which are three taylor series
+for the three components of the spin $(S_x, S_y, S_z)$. The independent variables are the six orbital
+phase space coordinates $(x, p_x, y, p_y, z, p_z)$.
+
 The \vn{-x_zero}, \vn{-y_zero}, and \vn{-z_zero} options are for testing if supressing certain terms
 in the linear part of the spin transport map for a set of elements selected by the user will
 significantly affect the polarization. This is discussed in the section ``\vn{Linear dn/dpz
diff --git a/tao/doc/cover-page.tex b/tao/doc/cover-page.tex
index bb1ed7c377..5ee535a859 100644
--- a/tao/doc/cover-page.tex
+++ b/tao/doc/cover-page.tex
@@ -2,7 +2,7 @@
 
 \begin{flushright}
 \large
-Revision: May 7, 2024 \\
+Revision: June 28, 2024 \\
 \end{flushright}
 
 \vfill