Hyperfine_Structure_Rotation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "af763860-93eb-4bbb-954c-aba78052e8b6",
   "metadata": {},
   "source": [
    "# Hyperfine Rotation Calculation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bf12d31-1bfe-4b8b-afe5-3974fcba116a",
   "metadata": {},
   "source": [
    "## The etoa matrix coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "015568ea-a25c-4103-be31-cbe42eb0385b",
   "metadata": {},
   "source": [
    "I've already derived this, but done fairly little to test it or implement it I think."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "27a2636f-f972-45bd-843b-4a41c9cf18b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sympy.physics.wigner import wigner_9j\n",
    "from sympy.physics.quantum.cg import CG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e9ff7bfe-1dee-4540-aeed-b2167138d1a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import MoleculeCalculation as mol"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcf494e3-25aa-49c8-8ed5-f326e3e5329b",
   "metadata": {},
   "source": [
    "For fine structure rotation we had\n",
    "$$\n",
    "\\langle j \\Omega j_a j_b | L \\Lambda L_a L_b; S \\Sigma S_a S_b \\rangle = \\sqrt{\\breve{S}\\breve{j_a}\\breve{j_b}\\breve{L}} C^{j\\Omega}_{LS\\Lambda\\Sigma} \\begin{Bmatrix}\n",
    "L_a & S_a & j_a\\\\\n",
    "L_b & S_b & j_b\\\\\n",
    "L & S & j\n",
    "\\end{Bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78980332-dbff-4fa5-a601-a0e2fc48c8fd",
   "metadata": {},
   "source": [
    "With hyperfine, we have:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b1f9536-fadc-4007-840e-f6efd77417c6",
   "metadata": {},
   "source": [
    "$$\n",
    "\\langle j \\Omega j_a j_b | L \\Lambda L_a L_b; S \\Sigma S_a S_b \\rangle = \\sqrt{\\breve{S}\\breve{j_a}\\breve{j_b}\\breve{L}} C^{j\\Omega}_{LS\\Lambda\\Sigma} \\begin{Bmatrix}\n",
    "L_a & S_a & j_a\\\\\n",
    "L_b & S_b & j_b\\\\\n",
    "L & S & j\n",
    "\\end{Bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27ea8e29-1735-4fd1-824e-f3ea62397cc0",
   "metadata": {},
   "source": [
    "$$\n",
    "\\langle f \\phi f_a f_b |L_a \\Lambda_a L_b \\Lambda_b S \\Sigma I \\iota\\rangle = \\sum_{L, j, j_a j_b} \n",
    "\\bigg(\n",
    "C^{L\\Lambda}_{l_a \\Lambda_a, l_b \\Lambda_b} \n",
    "C_{L\\Lambda S\\Sigma}^{j\\Omega} \n",
    "C_{j\\Omega I \\iota}^{f \\phi}\n",
    "\\bigg)\n",
    "\\sqrt{\\breve{j}_a\\breve{j}_b\\breve{f}_a\\breve{f}_b\n",
    "\\breve{L}\\breve{S}\\breve{J}\\breve{I}}\n",
    "\\begin{Bmatrix}\n",
    "l_a & s_a & j_a\\\\\n",
    "l_b & s_b & j_b\\\\\n",
    "L & S & j\n",
    "\\end{Bmatrix}\n",
    "\\begin{Bmatrix}\n",
    "j_a & i_a & f_a\\\\\n",
    "j_b & i_b & f_b\\\\\n",
    "j & I & f\n",
    "\\end{Bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f089c135-94fa-409f-8d70-f68b2cd63427",
   "metadata": {},
   "source": [
    "So I can test my coefficient function by summing over all of the lhs states:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5dda5fa2-24c4-4dd7-bc72-72b0f77f4350",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display, Latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3affa90-64b6-4ee2-b596-4f7c2301ea9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import Miscellaneous as misc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41fef50f-9ef4-470e-8cd9-83c794554acc",
   "metadata": {},
   "source": [
    "So I'm having trouble with the coefficient $\\langle 4,4,2,2|0,1,1,3,3\\rangle$ which my algorithm is claiming is the unphysical value -1.15. Clearly wrong, it's magnitude is larger than 1. So I'm going to manually decompose it to see what the true value should be and hopefully figure out the root of the problem. The strategy will be to convert both sides to $|l \\lambda s \\sigma i \\iota\\rangle_{a,b}$ states."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71a7818a-f2b8-4d74-90c5-4b4dfd9d9b10",
   "metadata": {},
   "source": [
    "This coefficient is of the form $\\langle f \\phi f_a f_b| l_a \\lambda_a l_b \\lambda_b S \\Sigma I \\iota\\rangle$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c830a218-76f8-4da5-992c-9a38a42c4224",
   "metadata": {},
   "source": [
    "So first I will decompose it to $\\langle f_a \\phi_a f_b \\phi_b|l \\lambda s \\sigma i \\iota\\rangle_{a,b}$. Thankfully the first step here is trivial for the chosen state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9de9d59-0ceb-46ce-89d2-34793c12a8cb",
   "metadata": {},
   "source": [
    "$\\langle 4,4,2,2|0,1,1,3,3\\rangle=\\langle 2,2| \\langle 2,2| \n",
    "|0,0,\\frac{1}{2},\\frac{1}{2},\\frac{3}{2},\\frac{3}{2}\\rangle|1,0,\\frac{1}{2},\\frac{1}{2},\\frac{3}{2},\\frac{3}{2}\\rangle$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7868c19-5152-458a-90f5-e3fc324838c3",
   "metadata": {},
   "source": [
    "Then I do the standard decomposition $\\langle f_a \\phi_a|\\rightarrow\\langle j_a,\\omega_a,i_a,\\iota_a|$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "319f914e-fa6b-4dab-b6ab-25da8429701d",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bigg(\\big\\langle\\frac{1}{2}\\frac{1}{2} \\frac{3}{2} \\frac{3}{2} \\big|\\bigg)\n",
    "\\bigg(C_{\\frac{3}{2}\\frac{3}{2}\\frac{ 3}{2 }\\frac{1}{2}}^{2,2} \\langle \\frac{3}{2} \\frac{3}{2} \\frac{3}{2} \\frac{1}{2}|\n",
    "+C_{\\frac{3}{2}\\frac{1}{2}\\frac{ 3}{2 }\\frac{3}{2}}^{2,2}\\langle\\frac{3}{2} \\frac{1}{2} \\frac{3}{2}\\frac{3}{2} |\\bigg)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b5d65c55-5cb9-43a8-a454-efe4faa2f57a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CG(3/2,3/2,3/2,1/2,2,2).doit()**2+CG(3/2,1/2,3/2,3/2,2,2).doit()**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73fbd17c-0028-4d4f-b7c3-faa174ef4b93",
   "metadata": {},
   "source": [
    "And finally taking $\\langle j_a \\omega_a i_a \\iota_a|\\rightarrow \\langle l_a \\lambda_a s_a \\sigma_a i_a \\iota_a|$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c75b3953-3266-4bba-a268-ff6dc4c7ce36",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bigg(\\big\\langle 00;\\frac{1}{2}\\frac{1}{2};\\frac{3}{2} \\frac{3}{2} \\big|\\bigg)\n",
    "\\bigg(C_{\\frac{3}{2}\\frac{3}{2}\\frac{3}{2}\\frac{1}{2}}^{2,2} \\langle 11;\\frac{1}{2}\\frac{1}{2};\\frac{3}{2} \\frac{1}{2}|\n",
    "+C_{\\frac{3}{2}\\frac{1}{2}\\frac{ 3}{2 }\\frac{3}{2}}^{2,2}\n",
    "(|\\rangle+|\\rangle)\\bigg)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8b8ebf4-2514-4c86-af71-a640ce494b48",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bigg(\\big\\langle 00;\\frac{1}{2}\\frac{1}{2};\\frac{3}{2} \\frac{3}{2} \\big|\\bigg)\n",
    "\\bigg(C_{\\frac{3}{2}\\frac{3}{2}\\frac{3}{2}\\frac{1}{2}}^{2,2} \\langle 11;\\frac{1}{2}\\frac{1}{2};\\frac{3}{2} \\frac{1}{2}|\n",
    "+C_{\\frac{3}{2}\\frac{1}{2}\\frac{ 3}{2 }\\frac{3}{2}}^{2,2}\n",
    "(C_{11\\frac{1}{2},-\\frac{1}{2}}^{\\frac{3}{2}\\frac{1}{2}}\n",
    "\\langle1,1;\\frac{1}{2},-\\frac{1}{2};\\frac{3}{2}\\frac{3}{2}|\n",
    "+C_{10\\frac{1}{2}\\frac{1}{2}}^{\\frac{3}{2}\\frac{1}{2}}\n",
    "\\langle1,0;\\frac{1}{2},\\frac{1}{2};\\frac{3}{2}\\frac{3}{2}|)\\bigg)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4bf3579b-030f-4271-926d-4cc8fd755b24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.0$"
      ],
      "text/plain": [
       "1.00000000000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CG(1,1,1/2,-1/2,3/2,1/2).doit()**2+CG(1,0,1/2,1/2,3/2,1/2).doit()**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87a7f7e5-8b3f-4d9e-9e2b-45840359ae24",
   "metadata": {},
   "source": [
    "And so the result is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21d7eb73-910d-4b0f-8b09-2ca3d1704a38",
   "metadata": {},
   "source": [
    "$$\n",
    "\\big\\langle 00;\\frac{1}{2}\\frac{1}{2};\\frac{3}{2} \\frac{3}{2} \\big|\\\\\n",
    "\\bigg(C_{\\frac{3}{2}\\frac{3}{2}\\frac{3}{2}\\frac{1}{2}}^{2,2} \\langle 11;\\frac{1}{2}\\frac{1}{2};\\frac{3}{2} \\frac{1}{2}|\n",
    "+C_{\\frac{3}{2}\\frac{1}{2}\\frac{ 3}{2 }\\frac{3}{2}}^{2,2}\n",
    "(C_{11\\frac{1}{2},-\\frac{1}{2}}^{\\frac{3}{2}\\frac{1}{2}}\n",
    "\\langle1,1;\\frac{1}{2},-\\frac{1}{2};\\frac{3}{2}\\frac{3}{2}|\n",
    "+C_{10\\frac{1}{2}\\frac{1}{2}}^{\\frac{3}{2}\\frac{1}{2}}\n",
    "\\langle1,0;\\frac{1}{2},\\frac{1}{2};\\frac{3}{2}\\frac{3}{2}|)\\bigg)\n",
    "|0,0,\\frac{1}{2},\\frac{1}{2},\\frac{3}{2},\\frac{3}{2}\\rangle|1,0,\\frac{1}{2},\\frac{1}{2},\\frac{3}{2},\\frac{3}{2}\\rangle\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdcc9885-52e5-47d0-8194-041b2116eaa0",
   "metadata": {},
   "source": [
    "can quickly eliminate the unexcited atom:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cc69813-0517-479b-9fcc-80ef0e0ceefe",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bigg(C_{\\frac{3}{2}\\frac{3}{2}\\frac{3}{2}\\frac{1}{2}}^{2,2} \\langle 11;\\frac{1}{2}\\frac{1}{2};\\frac{3}{2} \\frac{1}{2}|\n",
    "+C_{\\frac{3}{2}\\frac{1}{2}\\frac{ 3}{2 }\\frac{3}{2}}^{2,2}\n",
    "(C_{11\\frac{1}{2},-\\frac{1}{2}}^{\\frac{3}{2}\\frac{1}{2}}\n",
    "\\langle1,1;\\frac{1}{2},-\\frac{1}{2};\\frac{3}{2}\\frac{3}{2}|\n",
    "+C_{10\\frac{1}{2}\\frac{1}{2}}^{\\frac{3}{2}\\frac{1}{2}}\n",
    "\\langle1,0;\\frac{1}{2},\\frac{1}{2};\\frac{3}{2}\\frac{3}{2}|)\\bigg)\n",
    "|1,0,\\frac{1}{2},\\frac{1}{2},\\frac{3}{2},\\frac{3}{2}\\rangle\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3605146e-1487-47a5-8b19-accdd6ae2e6f",
   "metadata": {},
   "source": [
    "so the result is just one of these pairs:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f336307-5e86-497a-ab57-53ea0f6f5467",
   "metadata": {},
   "source": [
    "$$\n",
    "C_{\\frac{3}{2}\\frac{1}{2}\\frac{ 3}{2 }\\frac{3}{2}}^{2,2}C_{10\\frac{1}{2}\\frac{1}{2}}^{\\frac{3}{2}\\frac{1}{2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f0611323-2d05-4429-a816-125c0e42bb6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5773502691896257"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(CG(3/2,1/2,3/2,3/2,2,2).doit()*CG(1,0,1/2,1/2,3/2,1/2).doit())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17804aa7-35b0-48bc-ad10-66d25b9cfeff",
   "metadata": {},
   "source": [
    "Okay. now I know what the answer should be, but why is my algorithm not giving me this lol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "526b527f-efba-4bc9-9555-09fbf2917afb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def subcoef_HFS_2(f_a, f_b, f_, phi_, j_a, j_b,\n",
    "                S_,Sigma_,\n",
    "                I_,iota_,\n",
    "                Lambda_,\n",
    "                Omega_,\n",
    "                checks=False,\n",
    "                verbose=False):\n",
    "    def br(x):\n",
    "        return 2*x+1\n",
    "    val = 0\n",
    "    L_=1\n",
    "    l_a=0\n",
    "    l_b=1    \n",
    "    lambda_a=0\n",
    "    lambda_b=Lambda_\n",
    "    s_a=s_b=1/2\n",
    "    i_a = i_b = 3/2\n",
    "    if checks:\n",
    "        if phi_ != iota_+Omega_:\n",
    "            raise ValueError('Bad phi,iota,omega:',phi_,iota_,Omega_)\n",
    "        if Omega_ != Sigma_+Lambda_:\n",
    "            raise ValueError('Bad Omega,Sigma,Lambda:',Omega_,Sigma_,Lambda_)\n",
    "        if I_ not in np.arange(abs(i_a-i_b), i_a+i_b+1,1):\n",
    "            raise ValueError('Bad values: I,i_a,i_b='+str(I_)+','+str(i_a)+','+str(i_b))\n",
    "        if f_ not in np.arange(abs(f_a-f_b), f_a+f_b+1,1):\n",
    "            raise ValueError('Bad values: f,f_a,f_b='+str(f_)+','+str(f_a)+','+str(f_b))\n",
    "        if abs(Sigma_)>S_:\n",
    "            raise ValueError('Bad values: S,Sigma='+str(S_)+','+str(Sigma_))\n",
    "        #assert(abs(Lambda_)<=L_)\n",
    "    for j_ in np.arange( abs(j_a-j_b), j_a+j_b+1, 1):\n",
    "        c2 = float(CG(1,Lambda_,S_,Sigma_,j_,Omega_).doit())\n",
    "        c3 = float(CG(I_,iota_,j_,Omega_,f_,phi_).doit())\n",
    "        coefs = c2*c3\n",
    "        rec1 = recoupling(j_,j_a,j_b,L_,S_,l_a,s_a,l_b,s_b)\n",
    "        rec2 = recoupling(f_,f_a,f_b,j_,I_,j_a,i_a,j_b,i_b)\n",
    "        term = coefs * rec1*rec2\n",
    "        if verbose:\n",
    "            print(term)\n",
    "        val += term\n",
    "    return val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "e1632221-0f51-49be-a0ab-ddfa044a8b44",
   "metadata": {},
   "outputs": [],
   "source": [
    "def recoupling(j,j_12,j_34,j_13,j_24,j_1,j_2,j_3,j_4):\n",
    "    # caluculates <j,m_j,j_12,j_34|j,m_j,j_13,j_24>.\n",
    "    def br(x):\n",
    "        return 2*x+1\n",
    "    brs = np.sqrt(br(j_12)*br(j_34)*br(j_13)*br(j_24))\n",
    "    wigTerm = float(wigner_9j_with_table(j_1,j_2,j_12,j_3,j_4,j_34,j_13,j_24,j))\n",
    "    return brs*wigTerm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "id": "de508bd8-6735-49f3-bd9d-e55fd86aee74",
   "metadata": {},
   "outputs": [],
   "source": [
    "def subcoef_HFS_3(f_a, f_b, f_, phi_, j_a, j_b,\n",
    "                S_,Sigma_,\n",
    "                I_,iota_,\n",
    "                Lambda_,\n",
    "                Omega_,\n",
    "                checks=False,\n",
    "                verbose=False):\n",
    "    # with table acceleration for both cg and wigner 9j calculations, and using \"recoupling\" function to organize parts of calc.\n",
    "    def br(x):\n",
    "        return 2*x+1\n",
    "    val = 0\n",
    "    L_=1\n",
    "    l_a=0\n",
    "    l_b=1    \n",
    "    lambda_a=0\n",
    "    lambda_b=Lambda_\n",
    "    s_a=s_b=1/2\n",
    "    i_a = i_b = 3/2\n",
    "    for j_ in np.arange( abs(j_a-j_b), j_a+j_b+1, 1):\n",
    "        c2 = CG_with_table(1,Lambda_,S_,Sigma_,j_,Omega_)\n",
    "        c3 = CG_with_table(I_,iota_,j_,Omega_,f_,phi_)\n",
    "        coefs = c2*c3\n",
    "        rec1 = recoupling(j_,j_a,j_b,L_,S_,l_a,s_a,l_b,s_b)\n",
    "        rec2 = recoupling(f_,f_a,f_b,j_,I_,j_a,i_a,j_b,i_b)\n",
    "        term = coefs * rec1*rec2\n",
    "        if verbose:\n",
    "            print(term)\n",
    "        val += term\n",
    "    return val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "id": "fedac077-c40c-42a8-ade1-c5dd04dfb785",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "63.2 µs ± 6.44 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "val = subcoef_HFS_3( f_a,f_b,f_,phi,j_a, j_b,\n",
    "                     S_, Sigma, I_, iota, Lambda, Omega,\n",
    "                     False, False )"
   ]
  },
  {
   "attachments": {
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     "image/png": 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    }
   },
   "cell_type": "markdown",
   "id": "1ed98e7e-3d1f-4449-bd38-c80fc36da98a",
   "metadata": {},
   "source": [
    "![image.png](attachment:297a938c-f1fd-4c1b-84a5-f8b617a3b932.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d976914-2272-4478-972f-770de0f5cab1",
   "metadata": {},
   "source": [
    "### testing subcoef"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "id": "ee51c12e-3c7b-4c36-b758-51bb4d7f8ba0",
   "metadata": {},
   "outputs": [],
   "source": [
    "wigner_9j_table = {}\n",
    "def wigner_9j_with_table(j1,j2,j3,j4,j5,j6,j7,j8,j9):\n",
    "    # the sympy calculation is slow, so I implemented this little table lookup function which is ~100X faster.\n",
    "    # it just saves the results and preferentially retrieves them from this dictionary rather than recalculate them.\n",
    "    vals = [j1,j2,j3,j4,j5,j6,j7,j8,j9]\n",
    "    indexStr = ''.join([str(x)+','for x in vals])\n",
    "    if indexStr not in wigner_9j_table:\n",
    "        wigner_9j_table[indexStr] = float(wigner_9j(*vals))\n",
    "    return wigner_9j_table[indexStr]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "id": "21de4529-d28b-4f60-905a-2d055a007402",
   "metadata": {},
   "outputs": [],
   "source": [
    "CG_table = {}\n",
    "def CG_with_table(j1, mj1, j2, mj2, j3, mj3):\n",
    "    vals = [j1, mj1, j2, mj2, j3, mj3]\n",
    "    indexStr = ''.join([str(x)+','for x in vals])\n",
    "    if indexStr not in CG_table:\n",
    "        CG_table[indexStr] = float(CG(*vals).doit())\n",
    "    return CG_table[indexStr]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b2110b-8392-41cf-aec3-70af2caaf4c6",
   "metadata": {},
   "source": [
    "### testing etoa matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "1e376cb2-a905-4e1c-8450-c847225a0dda",
   "metadata": {},
   "outputs": [],
   "source": [
    "def createCaseE_BasisHfs(F_rel,verbose=False):\n",
    "    # for j and ell, J goes from J=j-ell or zero to J=j+ell\n",
    "    # given J and j, ell goes from ell=J+j to ell = J-j\n",
    "    # cases in this case_E do not have a good total angular momentum J=ell+j. For example, |j_a j_b j ell > = |1/2 1/2 1 1> couples to states\n",
    "    # of J = 2 (ell = J-1) and J = 0 (ell = j+1) to help read the table in the potassium paper. however, the way I am working with this I am segmenting my states by \n",
    "    # the case A basis which does have good J, so I only want the states that will couple to my case A basis.\n",
    "    caseE_BasisRef = []\n",
    "    j_a = 1/2\n",
    "    i_a = i_b = 3/2\n",
    "    for totalParity in [\"+\",\"-\"]:\n",
    "        for f_a in np.arange(abs(i_a - j_a), i_a + j_a+1,1):\n",
    "            for j_b in [1/2,3/2]:\n",
    "                for f_a in np.arange(abs(i_b - j_b), i_b + j_b+1,1):\n",
    "                    for f in np.arange(abs(f_a-f_b),f_a+f_b+1,1, dtype=float):\n",
    "                        for ell in np.arange(F_rel-f,F_rel+f+1,1, dtype=float):\n",
    "                            state = mol.multiplyableDict({\"f\": f, \n",
    "                                                          \"f_a\":f_a, 'j_a':j_a,'i_a':i_a,\n",
    "                                                          \"f_b\":f_b, 'j_b':j_b,'i_b':i_b,\n",
    "                                                          \"ell\":ell, \"totalParity\":totalParity})\n",
    "                            if state not in caseE_BasisRef:\n",
    "                                caseE_BasisRef.append(state)\n",
    "    return caseE_BasisRef"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "id": "f003c851-7975-47b0-aef5-d468017a90aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_EtoA_Matrix_Hfs(caseA_Basis, caseE_Basis, verbose=False):\n",
    "    res = np.zeros((len(caseA_Basis), len(caseE_Basis)))\n",
    "    count=0\n",
    "    for extraQN in [-1]:\n",
    "        for aind, stateA in enumerate(caseA_Basis):\n",
    "            misc.loopProgress(count, len(caseA_Basis)*len(caseE_Basis))\n",
    "            for eind, stateE in enumerate(caseE_Basis):\n",
    "                if not checkValid(stateA, stateE):\n",
    "                    continue\n",
    "                res[aind, eind] = coef_hfs(stateA, stateE, stateA['F'])\n",
    "                print(stateA, stateE, res[aind, eind])\n",
    "                count += 1\n",
    "        print('')\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "id": "7777244b-4378-4c5a-bd47-d960185f9a5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calcCoef(stateA,stateE, pv, verbose=False):\n",
    "    stateSignedSigma = stateA['|Omega|']-stateA['|Lambda|']\n",
    "    return coef_fs( stateE['ja'], stateE['jb'], stateE['j'], stateE['ell'], stateA[\"L\"], stateA[\"S\"], \n",
    "                    1/2, 1/2, stateA[\"|Lambda|\"], stateSignedSigma, stateA[\"|Omega|\"], pv, stateA[\"J\"],\n",
    "                    verbose=verbose )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "id": "889c9575-7f68-4651-ab4b-44489d6da068",
   "metadata": {},
   "outputs": [],
   "source": [
    "def checkValid(stateA, stateE):\n",
    "    f_a = stateE['f_a']\n",
    "    f_b = stateE['f_a']\n",
    "    f_ = stateE['f']\n",
    "    j_a = stateE['j_a']\n",
    "    j_b = stateE['j_b']\n",
    "    S_ = stateA['S']\n",
    "    phi_ = stateA['phi']\n",
    "    I_ = stateA['i']\n",
    "    iota_ = stateA['|iota|']\n",
    "    Lambda_ = stateA['|Lambda|']\n",
    "    Omega_ = phi_-iota_\n",
    "    Sigma_ = Omega_-Lambda_\n",
    "    ell = stateE['ell']\n",
    "    l_a = 0\n",
    "    l_b = 1\n",
    "    L_ = 1\n",
    "    p=0\n",
    "    if ell < 0:\n",
    "        return False\n",
    "    if phi_ != iota_+Omega_:\n",
    "        #raise ValueError('Bad phi,iota,omega:',phi_,iota_,Omega_)\n",
    "        return False\n",
    "    if Omega_ != Sigma_+Lambda_:\n",
    "        #raise ValueError('Bad Omega,Sigma,Lambda:',Omega_,Sigma_,Lambda_)\n",
    "        return False\n",
    "    if I_ not in np.arange(abs(i_a-i_b), i_a+i_b+1,1):\n",
    "        #raise ValueError('Bad values: I,i_a,i_b='+str(I_)+','+str(i_a)+','+str(i_b))\n",
    "        return False\n",
    "    if f_ not in np.arange(abs(f_a-f_b), f_a+f_b+1,1):\n",
    "        return False\n",
    "        #raise ValueError('Bad values: f,f_a,f_b='+str(f_)+','+str(f_a)+','+str(f_b))\n",
    "    if abs(Sigma_)>S_:\n",
    "        #raise ValueError('Bad values: S,Sigma='+str(S_)+','+str(Sigma_))\n",
    "        return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "id": "58ffc7e2-e8d0-4f10-8ba5-e731faf826f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def coef_hfs(stateA, stateE, F_):\n",
    "    f_a = stateE['f_a']\n",
    "    f_b = stateE['f_a']\n",
    "    f_ = stateE['f']\n",
    "    j_a = stateE['j_a']\n",
    "    j_b = stateE['j_b']\n",
    "    S_ = stateA['S']\n",
    "    phi_ = stateA['phi']\n",
    "    I_ = stateA['i']\n",
    "    iota_ = stateA['|iota|']\n",
    "    Lambda_ = stateA['|Lambda|']\n",
    "    Omega_ = phi_-iota_\n",
    "    Sigma_ = Omega_-Lambda_\n",
    "    ell = stateE['ell']\n",
    "    l_a = 0\n",
    "    l_b = 1\n",
    "    L_ = 1\n",
    "    p=0\n",
    "\n",
    "    phase = (-1)**(ell-phi-F_)\n",
    "    tDelta = 1 if Lambda==0 and Sigma==0 and iota==0 else 0\n",
    "    frac = (1+(-1)**(l_b+ell+p)*(1-tDelta))/np.sqrt(2-tDelta)\n",
    "    cgCoef = CG_with_table(f_,-phi,F_,phi,ell,0)\n",
    "    subC = subcoef_HFS_3( f_a,f_b,f_,phi,j_a,j_b,S_,Sigma_,I_,iota_,Lambda_,Omega_ )\n",
    "    return phase*frac*cgCoef*subC"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "475abfbe-5226-4de6-b09b-644f7e62ced8",
   "metadata": {},
   "source": [
    "Should be 4 bases relevant for hfs rotation of the two different parities I think."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da4ed25b-a83a-4474-a36f-15a44eb28b34",
   "metadata": {},
   "source": [
    "Testing single unsymmetrized symmetrized state decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "id": "3b22e677-3031-4a89-9c7d-3acd42314505",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total: 0.9999999999999992\n"
     ]
    }
   ],
   "source": [
    "S_, Sigma = 1,1\n",
    "i_a = i_b = 3/2\n",
    "I_, iota = 3,1\n",
    "Lambda = -1\n",
    "Omega=Sigma+Lambda\n",
    "phi=Omega+iota\n",
    "sumv=0\n",
    "ket = ','.join([str(v_) for v_ in [Lambda,S_,Sigma,I_,iota]])+r'\\rangle$'\n",
    "\n",
    "j_a = 1/2\n",
    "for f_a in np.arange(abs(i_a - j_a), i_a + j_a+1,1):\n",
    "    for j_b in [1/2,3/2]:\n",
    "        for f_b in np.arange(abs(i_a-j_b),i_a+j_b+1,1):\n",
    "            for f_ in np.arange(abs(f_a-f_b),f_a+f_b+1,1):\n",
    "                if abs(phi) > f_:\n",
    "                    continue\n",
    "                if f_ > S_+1+I_:\n",
    "                    continue\n",
    "                if f_ < min([abs(I_-(S_+1)),abs(S_-(I_+1))]):\n",
    "                    continue\n",
    "                val = subcoef_HFS_3( f_a,f_b,f_,phi,j_a, j_b,\n",
    "                                     S_, Sigma, I_, iota, Lambda, Omega,\n",
    "                                     False, False )\n",
    "                sumv += val**2\n",
    "                #display(Latex(r'$\\langle'+','.join([str(v_) for v_ in [f_,phi,f_a,f_b]])+'|'+ket+'->'+misc.round_sig_str(val**2)))\n",
    "print('Total:',sumv)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c494a8b-acd7-42b2-b388-578feb109a9d",
   "metadata": {},
   "source": [
    "### testing single sym state decomp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "id": "1607c8b6-5571-4881-8e01-085d6de1e6de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'f': 2.0,\n",
       " 'f_a': 1.0,\n",
       " 'j_a': 0.5,\n",
       " 'i_a': 1.5,\n",
       " 'f_b': 3.0,\n",
       " 'j_b': 0.5,\n",
       " 'i_b': 1.5,\n",
       " 'ell': -2.0,\n",
       " 'totalParity': '+'}"
      ]
     },
     "execution_count": 279,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "caseE_basis[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "id": "8da714d7-1859-43ba-8d06-90c6a9f42f49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'L': 1,\n",
       " '|Lambda|': 1,\n",
       " 'sigma': 'g',\n",
       " 'S': 1,\n",
       " '|Sigma|': 1,\n",
       " 'i': 0.0,\n",
       " '|iota|': 0.0,\n",
       " 'i1': 1.5,\n",
       " 'i2': 1.5,\n",
       " '|Omega|': 0,\n",
       " 'phi': 0.0,\n",
       " 'sigma_vxz': -1,\n",
       " 'sigma_v2xz': -1.0,\n",
       " 'F': 0}"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "caseA_basis[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "id": "24b60f59-e741-492b-8bb7-b4d06ea64838",
   "metadata": {},
   "outputs": [],
   "source": [
    "Fv=0\n",
    "caseE_basis = createCaseE_BasisHfs(Fv)\n",
    "caseA_basis = mol.createCaseABasis_Sym([1], [0,1], [3/2], sigmavals=['g', 'u'],Fv=Fv)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c36e210-36b7-4cac-9acb-003d5afc9400",
   "metadata": {},
   "source": [
    "#### testing matrix generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "id": "b6d0bda2-23ea-4128-9c32-f3b70216c593",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 A dict_keys(['-e', '+e']) 194\n",
      "0 E dict_keys(['+e', '-e']) 84\n",
      "0 A dict_keys(['-e', '+e']) 190\n",
      "0 E dict_keys(['+e', '-e']) 84\n"
     ]
    }
   ],
   "source": [
    "fvals=range(0,1)\n",
    "#jvals = [3,10,100,1000]\n",
    "superdata = {}\n",
    "for totalParity in ['+','-']:\n",
    "    for fValNum, Fv in enumerate(fvals):\n",
    "        #caseAMostlySymHfs = mol.createCaseABasis_Sym([1],[0,1], [3/2], sigmavals=['g', 'u'], Fv=Fv)\n",
    "        caseE_basis = createCaseE_BasisHfs(Fv)\n",
    "        parity = ('e' if ((-1)**Fv)==1 else 'f')\n",
    "        rotSymBase_E = {}\n",
    "        for state in caseE_basis:\n",
    "            if (-1)**state['ell'] != -1:\n",
    "                continue\n",
    "            #print(state['totalParity'],'!')\n",
    "            label = state['totalParity'] + ('e' if ((-1)**(Fv))==1 else 'f')\n",
    "            if label[-1] != parity:\n",
    "                continue\n",
    "            if label not in rotSymBase_E:\n",
    "                rotSymBase_E[label] = []\n",
    "            if state not in rotSymBase_E[label]:\n",
    "                rotSymBase_E[label].append(state)\n",
    "        caseA_basis = mol.createCaseABasis_Sym([1], [0,1], [3/2], sigmavals=['g', 'u'],Fv=Fv)\n",
    "        rotSymBase_A = {}\n",
    "        for state in caseA_basis:\n",
    "            parity_ = '-' if state['sigma_v2xz'] == -1 else '+'\n",
    "            label = parity_ + ('e' if ((-1)**(state['F']))==1 else 'f')\n",
    "            if label[-1] != parity:\n",
    "                continue\n",
    "            if label not in rotSymBase_A:\n",
    "                rotSymBase_A[label] = []\n",
    "            if state not in rotSymBase_A[label]:\n",
    "                rotSymBase_A[label].append(state)\n",
    "            #rotSymBase_A[label].append(state)\n",
    "        #label = sigmaParity+parity\n",
    "        # this is the symmetry which will be analyzed in this round\n",
    "        label = totalParity+parity\n",
    "        #print(totalParity)\n",
    "        print(Fv,'A',rotSymBase_A.keys(),len(rotSymBase_A[label]))\n",
    "        print(Fv,'E',rotSymBase_E.keys(),len(rotSymBase_E[label]))\n",
    "        #etoa = create_EtoA_Matrix_Hfs(rotSymBase_A[label], rotSymBase_E[label], verbose=False).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "id": "90520dba-28cb-4c95-b412-30f2846b3c43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(etoa.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "id": "f9d6ebf6-c58e-4145-ac92-5f984e2c1b12",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 0.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 1.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 0.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 1.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 0.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 1.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
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      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 1.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': -2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
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      "{'L': 1, '|Lambda|': 0, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 0, 'phi': 2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
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      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
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      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
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      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
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      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'g', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 4.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 1.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -3.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 0, '|Sigma|': 0, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 0.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 1.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -3.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 1.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -4.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': -2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 0.0, 'sigma_vxz': -1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 0, 'i': 3.0, '|iota|': 3.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 1, 'phi': 2.0, 'sigma_vxz': -1, 'sigma_v2xz': -1.0, 'F': 0}\n",
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      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': -4.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': -2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': 0.0, 'sigma_vxz': 1, 'sigma_v2xz': -1, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 1.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': 2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': 1.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 2.0, '|iota|': 1.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': 3.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 0.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': 2.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n",
      "{'L': 1, '|Lambda|': 1, 'sigma': 'u', 'S': 1, '|Sigma|': 1, 'i': 3.0, '|iota|': 2.0, 'i1': 1.5, 'i2': 1.5, '|Omega|': 2, 'phi': 4.0, 'sigma_vxz': 1, 'sigma_v2xz': -1.0, 'F': 0}\n"
     ]
    }
   ],
   "source": [
    "for x in rotSymBase_A[label]:\n",
    "    print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "f5048db9-9bd5-41cc-9443-cb60fa2790d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'L': 1,\n",
       " '|Lambda|': 1,\n",
       " 'sigma': 'g',\n",
       " 'S': 1,\n",
       " '|Sigma|': 1,\n",
       " 'i': 0.0,\n",
       " '|iota|': 0.0,\n",
       " 'i1': 1.5,\n",
       " 'i2': 1.5,\n",
       " '|Omega|': 0,\n",
       " 'phi': 0.0,\n",
       " 'sigma_vxz': -1,\n",
       " 'sigma_v2xz': -1.0,\n",
       " 'F': 0}"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rotSymBase_A['-e'][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "851c77f0-3704-48ec-a181-6918d4623000",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe29a77d-c127-4319-9219-c43bcb11bdaa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "94f7de27-1c63-498e-a602-974ea0506e08",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a2fdc4f-902d-4204-bd45-b45f3cf8aab2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28e15725-8889-42a1-b6ac-50f7b0290c4f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2044da5-9770-47d2-9dc1-e816d1f134a9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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