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+++ b/Boson_sampling_TO_DO.ipynb
@@ -0,0 +1,48904 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "1c11286e",
+ "metadata": {},
+ "source": [
+ "# Quandela Training Seminar - Programming with Perceval"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "dad5a69d",
+ "metadata": {},
+ "source": [
+ "### Boson sampling"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "89e1f822",
+ "metadata": {},
+ "source": [
+ "Sampling is the problem of selecting data from a large set, usually to find a smaller set of data that is representative of the entire set. Naturally, as problem sizes grow, these types of problems become intractable for classical computers. This means that even if we are able to find a solution to our problem, the time it takes us to do so will be too long, deeming the solution no longer useful to us.\n",
+ "\n",
+ "In Perceval, we use photons as our bosons (indistinguishable subatomic particles with an integer spin) to perform the task of boson sampling. Boson sampling is a quantum sampling problem, drawing from a big probability distribution of output states of a system. As our knowledge of the quantum world grows and quantum hardware becomes better, we hope to offer solutions to problems previously thought intractable."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d38c01f3",
+ "metadata": {},
+ "source": [
+ "We are interested to simulate a boson sample with 14 photons and 60 modes, order of size comparable to what was done in Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a $10^{14}$-Dimensional Hilbert Space [1]."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "dede995f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from collections import Counter\n",
+ "import gzip\n",
+ "import pickle\n",
+ "import time\n",
+ "import random\n",
+ "import perceval as pcvl\n",
+ "from perceval.algorithm import Sampler"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "84be34da",
+ "metadata": {},
+ "source": [
+ "#### Boson sampling with a perfect source"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7ea02d3b",
+ "metadata": {},
+ "source": [
+ "Let's define all the required values below."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "ea14f365",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 14 #number of photons at the input\n",
+ "m = 60 #number of modes\n",
+ "N = 5000000 #number of samplings we want in the end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "75e1ee98",
+ "metadata": {},
+ "source": [
+ "Now we can generate a Haar random unitary with Perceval."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "21e960f7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Unitary_60 = pcvl.Matrix.random_unitary(m) #creates a random unitary of dimension 60"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7d6ca6fb",
+ "metadata": {},
+ "source": [
+ "To be able to decompose this unitary, first we have to choose a set of optical components we will use to do. The Mach-Zehnder interferometer (MZI) is a good choice as it is composed of only 2 beam splitters and 2 phase shifters and it is highly configurable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "19234775",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "Rx \n",
+ "Φ=φ_a \n",
+ "Rx \n",
+ "Φ=φ_b \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# TO DO: build your MZI - for this you will need a beam splitter, then a phase shifter on\n",
+ "# mode 0 and another beam splitter and then a phase shifter on mode 1\n",
+ "# HINT: Since we will be decomposing our unitary, don't give values to the parameters in the circuit.\n",
+ "# The beam splitters can remain in the default Rx gate convention and the phase shifters'\n",
+ "# parameters can be left undefined by using pcvl.Parameter(\"name_of_parameter\").\n",
+ "# Remember to name your two phi parameters differently!\n",
+ "pcvl.pdisplay(mzi) #display your MZI and check if it looks as described above"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "eb27d276",
+ "metadata": {},
+ "source": [
+ "No we can decompose the unitary into a set of MZIs using Reck's (traingular) scheme [2]. Naturally, since the matrix dimension is 60, this will be a huge circuit and may take some time to compile."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "bc9e5566",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "Φ=3.816136 \n",
+ "Φ=4.010218 \n",
+ "Φ=0.691042 \n",
+ "Φ=4.863586 \n",
+ "Φ=3.045536 \n",
+ "Φ=0.51946 \n",
+ "Φ=3.810742 \n",
+ "Φ=4.32163 \n",
+ "Φ=3.938265 \n",
+ "Φ=4.504834 \n",
+ "Φ=6.249366 \n",
+ "Φ=3.249696 \n",
+ "Φ=0.138522 \n",
+ "Φ=1.273747 \n",
+ "Φ=2.58034 \n",
+ "Φ=4.393693 \n",
+ "Φ=2.423585 \n",
+ "Φ=4.629328 \n",
+ "Φ=5.690853 \n",
+ "Φ=6.104519 \n",
+ "Φ=3.421678 \n",
+ "Φ=1.349138 \n",
+ "Φ=0.55333 \n",
+ "Φ=3.790889 \n",
+ "Φ=5.932651 \n",
+ "Φ=4.369467 \n",
+ "Φ=2.494834 \n",
+ "Φ=5.306912 \n",
+ "Φ=2.15989 \n",
+ "Φ=3.889154 \n",
+ "Φ=2.517412 \n",
+ "Φ=2.246299 \n",
+ "Φ=3.73517 \n",
+ "Φ=4.498719 \n",
+ "Φ=3.244504 \n",
+ "Φ=3.581996 \n",
+ "Φ=1.393125 \n",
+ "Φ=4.151796 \n",
+ "Φ=2.683883 \n",
+ "Φ=1.240942 \n",
+ "Φ=0.340174 \n",
+ "Φ=3.48663 \n",
+ "Φ=0.949722 \n",
+ "Φ=1.293172 \n",
+ "Φ=3.787945 \n",
+ "Φ=2.106081 \n",
+ "Φ=0.30652 \n",
+ "Φ=1.373746 \n",
+ "Φ=0.760249 \n",
+ "Φ=3.408446 \n",
+ "Φ=4.232327 \n",
+ "Φ=0.394715 \n",
+ "Φ=1.236003 \n",
+ "Φ=4.847875 \n",
+ "Φ=0.240215 \n",
+ "Φ=2.419465 \n",
+ "Φ=1.846335 \n",
+ "Φ=0.067265 \n",
+ "Φ=3.170262 \n",
+ "Φ=4.895206 \n",
+ "Rx \n",
+ "Φ=4.111167 \n",
+ "Rx \n",
+ "Φ=4.798768 \n",
+ "Rx \n",
+ "Φ=4.679726 \n",
+ "Rx \n",
+ "Φ=4.557504 \n",
+ "Rx \n",
+ "Φ=2.238335 \n",
+ "Rx \n",
+ "Φ=5.231757 \n",
+ "Rx \n",
+ "Φ=5.018765 \n",
+ "Rx \n",
+ "Φ=5.00668 \n",
+ "Rx \n",
+ "Φ=4.823779 \n",
+ "Rx \n",
+ "Φ=5.482968 \n",
+ "Rx \n",
+ "Φ=4.389771 \n",
+ "Rx \n",
+ "Φ=5.503168 \n",
+ "Rx \n",
+ "Φ=1.104411 \n",
+ "Rx \n",
+ "Φ=2.634775 \n",
+ "Rx \n",
+ "Φ=4.86731 \n",
+ "Rx \n",
+ "Φ=3.867882 \n",
+ "Rx \n",
+ "Φ=0.578086 \n",
+ "Rx \n",
+ "Φ=2.708509 \n",
+ "Rx \n",
+ "Φ=0.292954 \n",
+ "Rx \n",
+ "Φ=0.639817 \n",
+ "Rx \n",
+ "Φ=4.938755 \n",
+ "Rx \n",
+ "Φ=0.26351 \n",
+ "Rx \n",
+ "Φ=0.649944 \n",
+ "Rx \n",
+ "Φ=1.445288 \n",
+ "Rx \n",
+ "Φ=1.288006 \n",
+ "Rx \n",
+ "Φ=2.011957 \n",
+ "Rx \n",
+ "Φ=0.656606 \n",
+ "Rx \n",
+ "Φ=1.789616 \n",
+ "Rx \n",
+ "Φ=4.316199 \n",
+ "Rx \n",
+ "Φ=0.500276 \n",
+ "Rx \n",
+ "Φ=5.753627 \n",
+ "Rx \n",
+ "Φ=5.236824 \n",
+ "Rx \n",
+ "Φ=5.864152 \n",
+ "Rx \n",
+ "Φ=5.027697 \n",
+ "Rx \n",
+ "Φ=0.370843 \n",
+ "Rx \n",
+ "Φ=6.163542 \n",
+ "Rx \n",
+ "Φ=0.590149 \n",
+ "Rx \n",
+ "Φ=3.361783 \n",
+ "Rx \n",
+ "Φ=5.106832 \n",
+ "Rx \n",
+ "Φ=0.506531 \n",
+ "Rx \n",
+ "Φ=4.367286 \n",
+ "Rx \n",
+ "Φ=4.149371 \n",
+ "Rx \n",
+ "Φ=0.295156 \n",
+ "Rx \n",
+ "Φ=4.910675 \n",
+ "Rx \n",
+ "Φ=5.890782 \n",
+ "Rx \n",
+ "Φ=1.067684 \n",
+ "Rx \n",
+ "Φ=0.834866 \n",
+ "Rx \n",
+ "Φ=1.766803 \n",
+ "Rx \n",
+ "Φ=5.896167 \n",
+ "Rx \n",
+ "Φ=3.582371 \n",
+ "Rx \n",
+ "Φ=5.130454 \n",
+ "Rx \n",
+ "Φ=4.191583 \n",
+ "Rx \n",
+ "Φ=1.398723 \n",
+ "Rx \n",
+ "Φ=0.708826 \n",
+ "Rx \n",
+ "Φ=3.848973 \n",
+ "Rx \n",
+ "Φ=0.007539 \n",
+ "Rx \n",
+ "Φ=5.957073 \n",
+ "Rx \n",
+ "Φ=4.929918 \n",
+ "Rx \n",
+ "Φ=0.470306 \n",
+ "Rx \n",
+ "Φ=1.234868 \n",
+ "Rx \n",
+ "Φ=5.883131 \n",
+ "Rx \n",
+ "Φ=4.190691 \n",
+ "Rx \n",
+ "Φ=5.407502 \n",
+ "Rx \n",
+ "Φ=3.063063 \n",
+ "Rx \n",
+ "Φ=0.741908 \n",
+ "Rx \n",
+ "Φ=3.613984 \n",
+ "Rx \n",
+ "Φ=5.905017 \n",
+ "Rx \n",
+ "Φ=6.239608 \n",
+ "Rx \n",
+ "Φ=4.586435 \n",
+ "Rx \n",
+ "Φ=0.476804 \n",
+ "Rx \n",
+ "Φ=2.188401 \n",
+ "Rx \n",
+ "Φ=2.705943 \n",
+ "Rx \n",
+ "Φ=5.977386 \n",
+ "Rx \n",
+ "Φ=5.773445 \n",
+ "Rx \n",
+ "Φ=0.494187 \n",
+ "Rx \n",
+ "Φ=5.968146 \n",
+ "Rx \n",
+ "Φ=6.185182 \n",
+ "Rx \n",
+ "Φ=0.879328 \n",
+ "Rx \n",
+ "Φ=5.928112 \n",
+ "Rx \n",
+ "Φ=5.707495 \n",
+ "Rx \n",
+ "Φ=5.30698 \n",
+ "Rx \n",
+ "Φ=6.105315 \n",
+ "Rx \n",
+ "Φ=5.532099 \n",
+ "Rx \n",
+ "Φ=3.285435 \n",
+ "Rx \n",
+ "Φ=0.534954 \n",
+ "Rx \n",
+ "Φ=0.592085 \n",
+ "Rx \n",
+ "Φ=0.790503 \n",
+ "Rx \n",
+ "Φ=3.368243 \n",
+ "Rx \n",
+ "Φ=1.060728 \n",
+ "Rx \n",
+ "Φ=2.216159 \n",
+ "Rx \n",
+ "Φ=5.766026 \n",
+ "Rx \n",
+ "Φ=4.331543 \n",
+ "Rx \n",
+ "Φ=0.223964 \n",
+ "Rx \n",
+ "Φ=1.573842 \n",
+ "Rx \n",
+ "Φ=0.406852 \n",
+ "Rx \n",
+ "Φ=4.366317 \n",
+ "Rx \n",
+ "Φ=1.292481 \n",
+ "Rx \n",
+ "Φ=5.031463 \n",
+ "Rx \n",
+ "Φ=5.166416 \n",
+ "Rx \n",
+ "Φ=6.173081 \n",
+ "Rx \n",
+ "Φ=1.090456 \n",
+ "Rx \n",
+ "Φ=4.735713 \n",
+ "Rx \n",
+ "Φ=0.701705 \n",
+ "Rx \n",
+ "Φ=2.583912 \n",
+ "Rx \n",
+ "Φ=4.807318 \n",
+ "Rx \n",
+ "Φ=6.188227 \n",
+ "Rx \n",
+ "Φ=4.283213 \n",
+ "Rx \n",
+ "Φ=2.083521 \n",
+ "Rx \n",
+ "Φ=5.334074 \n",
+ "Rx \n",
+ "Φ=1.541775 \n",
+ "Rx \n",
+ "Φ=0.461365 \n",
+ "Rx \n",
+ "Φ=3.367578 \n",
+ "Rx \n",
+ "Φ=5.224168 \n",
+ "Rx \n",
+ "Φ=3.786129 \n",
+ "Rx \n",
+ "Φ=5.951465 \n",
+ "Rx \n",
+ "Φ=2.036483 \n",
+ "Rx \n",
+ "Φ=0.716593 \n",
+ "Rx \n",
+ "Φ=0.653814 \n",
+ "Rx \n",
+ "Φ=0.403793 \n",
+ "Rx \n",
+ "Φ=4.841495 \n",
+ "Rx \n",
+ "Φ=6.152504 \n",
+ "Rx \n",
+ "Φ=1.753119 \n",
+ "Rx \n",
+ "Φ=0.915715 \n",
+ "Rx \n",
+ "Φ=6.183754 \n",
+ "Rx \n",
+ "Φ=5.552007 \n",
+ "Rx \n",
+ "Φ=0.405352 \n",
+ "Rx \n",
+ "Φ=0.649651 \n",
+ "Rx \n",
+ "Φ=2.851103 \n",
+ "Rx \n",
+ "Φ=0.352729 \n",
+ "Rx \n",
+ "Φ=2.648613 \n",
+ "Rx \n",
+ "Φ=1.333794 \n",
+ "Rx \n",
+ "Φ=4.643844 \n",
+ "Rx \n",
+ "Φ=6.192925 \n",
+ "Rx \n",
+ "Φ=5.552185 \n",
+ "Rx \n",
+ "Φ=0.876964 \n",
+ "Rx \n",
+ "Φ=1.254354 \n",
+ "Rx \n",
+ "Φ=5.875212 \n",
+ "Rx \n",
+ "Φ=2.328009 \n",
+ "Rx \n",
+ "Φ=5.623293 \n",
+ "Rx \n",
+ "Φ=5.510579 \n",
+ "Rx \n",
+ "Φ=5.958951 \n",
+ "Rx \n",
+ "Φ=6.141232 \n",
+ "Rx \n",
+ "Φ=0.800049 \n",
+ "Rx \n",
+ "Φ=5.286289 \n",
+ "Rx \n",
+ "Φ=6.045347 \n",
+ "Rx \n",
+ "Φ=5.148291 \n",
+ "Rx \n",
+ "Φ=0.565298 \n",
+ "Rx \n",
+ "Φ=0.03593 \n",
+ "Rx \n",
+ "Φ=5.983408 \n",
+ "Rx \n",
+ "Φ=5.03917 \n",
+ "Rx \n",
+ "Φ=5.448441 \n",
+ "Rx \n",
+ "Φ=5.269003 \n",
+ "Rx \n",
+ "Φ=1.204242 \n",
+ "Rx \n",
+ "Φ=5.857423 \n",
+ "Rx \n",
+ "Φ=2.251163 \n",
+ "Rx \n",
+ "Φ=4.753022 \n",
+ "Rx \n",
+ "Φ=0.682843 \n",
+ "Rx \n",
+ "Φ=3.000533 \n",
+ "Rx \n",
+ "Φ=5.935015 \n",
+ "Rx \n",
+ "Φ=2.904912 \n",
+ "Rx \n",
+ "Φ=5.888742 \n",
+ "Rx \n",
+ "Φ=4.447837 \n",
+ "Rx \n",
+ "Φ=0.856083 \n",
+ "Rx \n",
+ "Φ=5.696131 \n",
+ "Rx \n",
+ "Φ=0.559776 \n",
+ "Rx \n",
+ "Φ=3.494746 \n",
+ "Rx \n",
+ "Φ=5.591853 \n",
+ "Rx \n",
+ "Φ=3.834896 \n",
+ "Rx \n",
+ "Φ=5.422421 \n",
+ "Rx \n",
+ "Φ=3.529429 \n",
+ "Rx \n",
+ "Φ=1.254754 \n",
+ "Rx \n",
+ "Φ=2.635342 \n",
+ "Rx \n",
+ "Φ=0.679982 \n",
+ "Rx \n",
+ "Φ=3.424967 \n",
+ "Rx \n",
+ "Φ=6.065396 \n",
+ "Rx \n",
+ "Φ=1.69365 \n",
+ "Rx \n",
+ "Φ=1.245323 \n",
+ "Rx \n",
+ "Φ=1.875654 \n",
+ "Rx \n",
+ "Φ=1.10281 \n",
+ "Rx \n",
+ "Φ=5.94631 \n",
+ "Rx \n",
+ "Φ=2.412097 \n",
+ "Rx \n",
+ "Φ=0.318832 \n",
+ "Rx \n",
+ "Φ=5.816157 \n",
+ "Rx \n",
+ "Φ=5.683556 \n",
+ "Rx \n",
+ "Φ=0.222807 \n",
+ "Rx \n",
+ "Φ=1.25624 \n",
+ "Rx \n",
+ "Φ=5.544027 \n",
+ "Rx \n",
+ "Φ=4.619689 \n",
+ "Rx \n",
+ "Φ=0.258315 \n",
+ "Rx \n",
+ "Φ=1.045031 \n",
+ "Rx \n",
+ "Φ=0.305626 \n",
+ "Rx \n",
+ "Φ=5.738826 \n",
+ "Rx \n",
+ "Φ=0.778546 \n",
+ "Rx \n",
+ "Φ=6.24891 \n",
+ "Rx \n",
+ "Φ=0.496022 \n",
+ "Rx \n",
+ "Φ=1.288108 \n",
+ "Rx \n",
+ "Φ=0.403505 \n",
+ "Rx \n",
+ "Φ=5.504552 \n",
+ "Rx \n",
+ "Φ=0.840011 \n",
+ "Rx \n",
+ "Φ=5.882125 \n",
+ "Rx \n",
+ "Φ=0.735589 \n",
+ "Rx \n",
+ "Φ=2.15312 \n",
+ "Rx \n",
+ "Φ=0.139734 \n",
+ "Rx \n",
+ "Φ=3.61675 \n",
+ "Rx \n",
+ "Φ=0.675296 \n",
+ "Rx \n",
+ "Φ=2.859581 \n",
+ "Rx \n",
+ "Φ=5.073108 \n",
+ "Rx \n",
+ "Φ=2.521006 \n",
+ "Rx \n",
+ "Φ=4.351672 \n",
+ "Rx \n",
+ "Φ=0.778585 \n",
+ "Rx \n",
+ "Φ=0.661831 \n",
+ "Rx \n",
+ "Φ=4.121133 \n",
+ "Rx \n",
+ "Φ=5.510561 \n",
+ "Rx \n",
+ "Φ=1.92584 \n",
+ "Rx \n",
+ "Φ=0.555191 \n",
+ "Rx \n",
+ "Φ=2.076437 \n",
+ "Rx \n",
+ "Φ=5.222039 \n",
+ "Rx \n",
+ "Φ=2.720047 \n",
+ "Rx \n",
+ "Φ=6.005232 \n",
+ "Rx \n",
+ "Φ=5.990629 \n",
+ "Rx \n",
+ "Φ=0.76667 \n",
+ "Rx \n",
+ "Φ=3.397702 \n",
+ "Rx \n",
+ "Φ=0.602444 \n",
+ "Rx \n",
+ "Φ=5.529282 \n",
+ "Rx \n",
+ "Φ=0.257937 \n",
+ "Rx \n",
+ "Φ=5.337912 \n",
+ "Rx \n",
+ "Φ=6.080914 \n",
+ "Rx \n",
+ "Φ=4.97531 \n",
+ "Rx \n",
+ "Φ=1.018485 \n",
+ "Rx \n",
+ "Φ=3.152843 \n",
+ "Rx \n",
+ "Φ=5.460362 \n",
+ "Rx \n",
+ "Φ=3.432201 \n",
+ "Rx \n",
+ "Φ=4.9188 \n",
+ "Rx \n",
+ "Φ=3.656346 \n",
+ "Rx \n",
+ "Φ=4.532256 \n",
+ "Rx \n",
+ "Φ=4.515144 \n",
+ "Rx \n",
+ "Φ=5.25766 \n",
+ "Rx \n",
+ "Φ=3.559666 \n",
+ "Rx \n",
+ "Φ=2.271279 \n",
+ "Rx \n",
+ "Φ=0.76858 \n",
+ "Rx \n",
+ "Φ=0.309922 \n",
+ "Rx \n",
+ "Φ=1.31112 \n",
+ "Rx \n",
+ "Φ=0.552972 \n",
+ "Rx \n",
+ "Φ=1.293348 \n",
+ "Rx \n",
+ "Φ=5.59553 \n",
+ "Rx \n",
+ "Φ=4.794579 \n",
+ "Rx \n",
+ "Φ=0.371401 \n",
+ "Rx \n",
+ "Φ=3.844747 \n",
+ "Rx \n",
+ "Φ=0.48024 \n",
+ "Rx \n",
+ "Φ=1.895073 \n",
+ "Rx \n",
+ "Φ=5.130186 \n",
+ "Rx \n",
+ "Φ=2.433952 \n",
+ "Rx \n",
+ "Φ=6.056596 \n",
+ "Rx \n",
+ "Φ=5.196549 \n",
+ "Rx \n",
+ "Φ=5.482927 \n",
+ "Rx \n",
+ "Φ=2.314022 \n",
+ "Rx \n",
+ "Φ=5.597915 \n",
+ "Rx \n",
+ "Φ=0.537686 \n",
+ "Rx \n",
+ "Φ=0.460969 \n",
+ "Rx \n",
+ "Φ=6.037437 \n",
+ "Rx \n",
+ "Φ=5.721382 \n",
+ "Rx \n",
+ "Φ=0.094011 \n",
+ "Rx \n",
+ "Φ=6.059151 \n",
+ "Rx \n",
+ "Φ=5.490896 \n",
+ "Rx \n",
+ "Φ=1.506382 \n",
+ "Rx \n",
+ "Φ=5.11387 \n",
+ "Rx \n",
+ "Φ=0.673847 \n",
+ "Rx \n",
+ "Φ=1.347644 \n",
+ "Rx \n",
+ "Φ=1.408244 \n",
+ "Rx \n",
+ "Φ=1.886661 \n",
+ "Rx \n",
+ "Φ=4.600362 \n",
+ "Rx \n",
+ "Φ=4.765711 \n",
+ "Rx \n",
+ "Φ=6.100399 \n",
+ "Rx \n",
+ "Φ=6.032626 \n",
+ "Rx \n",
+ "Φ=5.626348 \n",
+ "Rx \n",
+ "Φ=5.461269 \n",
+ "Rx \n",
+ "Φ=0.559568 \n",
+ "Rx \n",
+ "Φ=4.105584 \n",
+ "Rx \n",
+ "Φ=6.125924 \n",
+ "Rx \n",
+ "Φ=3.434089 \n",
+ "Rx \n",
+ "Φ=6.038115 \n",
+ "Rx \n",
+ "Φ=0.818199 \n",
+ "Rx \n",
+ "Φ=5.751651 \n",
+ "Rx \n",
+ "Φ=3.237513 \n",
+ "Rx \n",
+ "Φ=5.947411 \n",
+ "Rx \n",
+ "Φ=5.775262 \n",
+ "Rx \n",
+ "Φ=0.032946 \n",
+ "Rx \n",
+ "Φ=3.487864 \n",
+ "Rx \n",
+ "Φ=5.578233 \n",
+ "Rx \n",
+ "Φ=0.03494 \n",
+ "Rx \n",
+ "Φ=0.604967 \n",
+ "Rx \n",
+ "Φ=2.829807 \n",
+ "Rx \n",
+ "Φ=0.82484 \n",
+ "Rx \n",
+ "Φ=0.080448 \n",
+ "Rx \n",
+ "Φ=5.334842 \n",
+ "Rx \n",
+ "Φ=2.352312 \n",
+ "Rx \n",
+ "Φ=0.442029 \n",
+ "Rx \n",
+ "Φ=3.452828 \n",
+ "Rx \n",
+ "Φ=4.902159 \n",
+ "Rx \n",
+ "Φ=4.564227 \n",
+ "Rx \n",
+ "Φ=5.052621 \n",
+ "Rx \n",
+ "Φ=2.019212 \n",
+ "Rx \n",
+ "Φ=0.751452 \n",
+ "Rx \n",
+ "Φ=1.764954 \n",
+ "Rx \n",
+ "Φ=4.864384 \n",
+ "Rx \n",
+ "Φ=4.461536 \n",
+ "Rx \n",
+ "Φ=0.457642 \n",
+ "Rx \n",
+ "Φ=2.085509 \n",
+ "Rx \n",
+ "Φ=0.697387 \n",
+ "Rx \n",
+ "Φ=4.538641 \n",
+ "Rx \n",
+ "Φ=0.15097 \n",
+ "Rx \n",
+ "Φ=4.937475 \n",
+ "Rx \n",
+ "Φ=0.683027 \n",
+ "Rx \n",
+ "Φ=1.056382 \n",
+ "Rx \n",
+ "Φ=0.594254 \n",
+ "Rx \n",
+ "Φ=1.26071 \n",
+ "Rx \n",
+ "Φ=0.691985 \n",
+ "Rx \n",
+ "Φ=2.167483 \n",
+ "Rx \n",
+ "Φ=6.147681 \n",
+ "Rx \n",
+ "Φ=4.148376 \n",
+ "Rx \n",
+ "Φ=5.991078 \n",
+ "Rx \n",
+ "Φ=0.173982 \n",
+ "Rx \n",
+ "Φ=0.634188 \n",
+ "Rx \n",
+ "Φ=3.085025 \n",
+ "Rx \n",
+ "Φ=0.323437 \n",
+ "Rx \n",
+ "Φ=1.149445 \n",
+ "Rx \n",
+ "Φ=0.152023 \n",
+ "Rx \n",
+ "Φ=3.106661 \n",
+ "Rx \n",
+ "Φ=5.5909 \n",
+ "Rx \n",
+ "Φ=5.636135 \n",
+ "Rx \n",
+ "Φ=0.444195 \n",
+ "Rx \n",
+ "Φ=1.562035 \n",
+ "Rx \n",
+ "Φ=0.436904 \n",
+ "Rx \n",
+ "Φ=3.936772 \n",
+ "Rx \n",
+ "Φ=5.71758 \n",
+ "Rx \n",
+ "Φ=4.590366 \n",
+ "Rx \n",
+ "Φ=0.442376 \n",
+ "Rx \n",
+ "Φ=1.604465 \n",
+ "Rx \n",
+ "Φ=2.277571 \n",
+ "Rx \n",
+ "Φ=1.676089 \n",
+ "Rx \n",
+ "Φ=1.397397 \n",
+ "Rx \n",
+ "Φ=1.648678 \n",
+ "Rx \n",
+ "Φ=0.426358 \n",
+ "Rx \n",
+ "Φ=2.560536 \n",
+ "Rx \n",
+ "Φ=0.515554 \n",
+ "Rx \n",
+ "Φ=3.531953 \n",
+ "Rx \n",
+ "Φ=5.40073 \n",
+ "Rx \n",
+ "Φ=2.492931 \n",
+ "Rx \n",
+ "Φ=0.408546 \n",
+ "Rx \n",
+ "Φ=6.00019 \n",
+ "Rx \n",
+ "Φ=5.884334 \n",
+ "Rx \n",
+ "Φ=0.806948 \n",
+ "Rx \n",
+ "Φ=5.499504 \n",
+ "Rx \n",
+ "Φ=6.192439 \n",
+ "Rx \n",
+ "Φ=0.653464 \n",
+ "Rx \n",
+ "Φ=0.306885 \n",
+ "Rx \n",
+ "Φ=0.527804 \n",
+ "Rx \n",
+ "Φ=4.222791 \n",
+ "Rx \n",
+ "Φ=1.071051 \n",
+ "Rx \n",
+ "Φ=2.446701 \n",
+ "Rx \n",
+ "Φ=6.0465 \n",
+ "Rx \n",
+ "Φ=3.030736 \n",
+ "Rx \n",
+ "Φ=5.775913 \n",
+ "Rx \n",
+ "Φ=6.052705 \n",
+ "Rx \n",
+ "Φ=5.51065 \n",
+ "Rx \n",
+ "Φ=4.360849 \n",
+ "Rx \n",
+ "Φ=5.77816 \n",
+ "Rx \n",
+ "Φ=1.208785 \n",
+ "Rx \n",
+ "Φ=5.389978 \n",
+ "Rx \n",
+ "Φ=1.244357 \n",
+ "Rx \n",
+ "Φ=5.480961 \n",
+ "Rx \n",
+ "Φ=0.393527 \n",
+ "Rx \n",
+ "Φ=5.893412 \n",
+ "Rx \n",
+ "Φ=5.070905 \n",
+ "Rx \n",
+ "Φ=5.315692 \n",
+ "Rx \n",
+ "Φ=0.348756 \n",
+ "Rx \n",
+ "Φ=0.813499 \n",
+ "Rx \n",
+ "Φ=3.438958 \n",
+ "Rx \n",
+ "Φ=2.488806 \n",
+ "Rx \n",
+ "Φ=1.10161 \n",
+ "Rx \n",
+ "Φ=0.212947 \n",
+ "Rx \n",
+ "Φ=5.383655 \n",
+ "Rx \n",
+ "Φ=0.807251 \n",
+ "Rx \n",
+ "Φ=2.86702 \n",
+ "Rx \n",
+ "Φ=0.95765 \n",
+ "Rx \n",
+ "Φ=2.241206 \n",
+ "Rx \n",
+ "Φ=0.165837 \n",
+ "Rx \n",
+ "Φ=3.691645 \n",
+ "Rx \n",
+ "Φ=5.762626 \n",
+ "Rx \n",
+ "Φ=3.793299 \n",
+ "Rx \n",
+ "Φ=5.632533 \n",
+ "Rx \n",
+ "Φ=3.479519 \n",
+ "Rx \n",
+ "Φ=6.222873 \n",
+ "Rx \n",
+ "Φ=0.410909 \n",
+ "Rx \n",
+ "Φ=0.988811 \n",
+ "Rx \n",
+ "Φ=6.052097 \n",
+ "Rx \n",
+ "Φ=5.497817 \n",
+ "Rx \n",
+ "Φ=5.671982 \n",
+ "Rx \n",
+ "Φ=0.926386 \n",
+ "Rx \n",
+ "Φ=4.121945 \n",
+ "Rx \n",
+ "Φ=5.707714 \n",
+ "Rx \n",
+ "Φ=3.57431 \n",
+ "Rx \n",
+ "Φ=1.038994 \n",
+ "Rx \n",
+ "Φ=5.707628 \n",
+ "Rx \n",
+ "Φ=5.341893 \n",
+ "Rx \n",
+ "Φ=3.177383 \n",
+ "Rx \n",
+ "Φ=0.709591 \n",
+ "Rx \n",
+ "Φ=5.795729 \n",
+ "Rx \n",
+ "Φ=0.049651 \n",
+ "Rx \n",
+ "Φ=2.556792 \n",
+ "Rx \n",
+ "Φ=0.621709 \n",
+ "Rx \n",
+ "Φ=2.959595 \n",
+ "Rx \n",
+ "Φ=5.885783 \n",
+ "Rx \n",
+ "Φ=3.478934 \n",
+ "Rx \n",
+ "Φ=4.625776 \n",
+ "Rx \n",
+ "Φ=0.440591 \n",
+ "Rx \n",
+ "Φ=2.609147 \n",
+ "Rx \n",
+ "Φ=3.081812 \n",
+ "Rx \n",
+ "Φ=5.266368 \n",
+ "Rx \n",
+ "Φ=4.402574 \n",
+ "Rx \n",
+ "Φ=6.02446 \n",
+ "Rx \n",
+ "Φ=3.917143 \n",
+ "Rx \n",
+ "Φ=6.026132 \n",
+ "Rx \n",
+ "Φ=5.965583 \n",
+ "Rx \n",
+ "Φ=0.361244 \n",
+ "Rx \n",
+ "Φ=4.145178 \n",
+ "Rx \n",
+ "Φ=6.098362 \n",
+ "Rx \n",
+ "Φ=0.014796 \n",
+ "Rx \n",
+ "Φ=0.3997 \n",
+ "Rx \n",
+ "Φ=5.258728 \n",
+ "Rx \n",
+ "Φ=0.245968 \n",
+ "Rx \n",
+ "Φ=3.332304 \n",
+ "Rx \n",
+ "Φ=0.204017 \n",
+ "Rx \n",
+ "Φ=5.274594 \n",
+ "Rx \n",
+ "Φ=5.540388 \n",
+ "Rx \n",
+ "Φ=3.794239 \n",
+ "Rx \n",
+ "Φ=5.861092 \n",
+ "Rx \n",
+ "Φ=1.887455 \n",
+ "Rx \n",
+ "Φ=5.477751 \n",
+ "Rx \n",
+ "Φ=6.094766 \n",
+ "Rx \n",
+ "Φ=0.589588 \n",
+ "Rx \n",
+ "Φ=1.646275 \n",
+ "Rx \n",
+ "Φ=0.253535 \n",
+ "Rx \n",
+ "Φ=5.19575 \n",
+ "Rx \n",
+ "Φ=5.832339 \n",
+ "Rx \n",
+ "Φ=5.529996 \n",
+ "Rx \n",
+ "Φ=0.174249 \n",
+ "Rx \n",
+ "Φ=0.055412 \n",
+ "Rx \n",
+ "Φ=0.369165 \n",
+ "Rx \n",
+ "Φ=2.941869 \n",
+ "Rx \n",
+ "Φ=0.95613 \n",
+ "Rx \n",
+ "Φ=5.563012 \n",
+ "Rx \n",
+ "Φ=1.144801 \n",
+ "Rx \n",
+ "Φ=2.541998 \n",
+ "Rx \n",
+ "Φ=5.441632 \n",
+ "Rx \n",
+ "Φ=5.665062 \n",
+ "Rx \n",
+ "Φ=5.329839 \n",
+ "Rx \n",
+ "Φ=5.390441 \n",
+ "Rx \n",
+ "Φ=5.59517 \n",
+ "Rx \n",
+ "Φ=0.651666 \n",
+ "Rx \n",
+ "Φ=4.386967 \n",
+ "Rx \n",
+ "Φ=0.873506 \n",
+ "Rx \n",
+ "Φ=0.44286 \n",
+ "Rx \n",
+ "Φ=3.059708 \n",
+ "Rx \n",
+ "Φ=5.74655 \n",
+ "Rx \n",
+ "Φ=3.354411 \n",
+ "Rx \n",
+ "Φ=5.685407 \n",
+ "Rx \n",
+ "Φ=6.271435 \n",
+ "Rx \n",
+ "Φ=5.970342 \n",
+ "Rx \n",
+ "Φ=1.729997 \n",
+ "Rx \n",
+ "Φ=0.513922 \n",
+ "Rx \n",
+ "Φ=0.345606 \n",
+ "Rx \n",
+ "Φ=0.160364 \n",
+ "Rx \n",
+ "Φ=1.034036 \n",
+ "Rx \n",
+ "Φ=0.363697 \n",
+ "Rx \n",
+ "Φ=4.552649 \n",
+ "Rx \n",
+ "Φ=0.505565 \n",
+ "Rx \n",
+ "Φ=5.080065 \n",
+ "Rx \n",
+ "Φ=5.572168 \n",
+ "Rx \n",
+ "Φ=4.895953 \n",
+ "Rx \n",
+ "Φ=5.773544 \n",
+ "Rx \n",
+ "Φ=0.684394 \n",
+ "Rx \n",
+ "Φ=5.953957 \n",
+ "Rx \n",
+ "Φ=1.868683 \n",
+ "Rx \n",
+ "Φ=0.26808 \n",
+ "Rx \n",
+ "Φ=1.365323 \n",
+ "Rx \n",
+ "Φ=6.040389 \n",
+ "Rx \n",
+ "Φ=3.951247 \n",
+ "Rx \n",
+ "Φ=5.591268 \n",
+ "Rx \n",
+ "Φ=1.115203 \n",
+ "Rx \n",
+ "Φ=0.929745 \n",
+ "Rx \n",
+ "Φ=3.671094 \n",
+ "Rx \n",
+ "Φ=5.187432 \n",
+ "Rx \n",
+ "Φ=4.897287 \n",
+ "Rx \n",
+ "Φ=6.103978 \n",
+ "Rx \n",
+ "Φ=0.064582 \n",
+ "Rx \n",
+ "Φ=5.78929 \n",
+ "Rx \n",
+ "Φ=5.499949 \n",
+ "Rx \n",
+ "Φ=0.40333 \n",
+ "Rx \n",
+ "Φ=5.478814 \n",
+ "Rx \n",
+ "Φ=5.476877 \n",
+ "Rx \n",
+ "Φ=6.272425 \n",
+ "Rx \n",
+ "Φ=5.602262 \n",
+ "Rx \n",
+ "Φ=6.045495 \n",
+ "Rx \n",
+ "Φ=1.014917 \n",
+ "Rx \n",
+ "Φ=4.870618 \n",
+ "Rx \n",
+ "Φ=5.941364 \n",
+ "Rx \n",
+ "Φ=2.62115 \n",
+ "Rx \n",
+ "Φ=0.495693 \n",
+ "Rx \n",
+ "Φ=4.249803 \n",
+ "Rx \n",
+ "Φ=5.910705 \n",
+ "Rx \n",
+ "Φ=3.992782 \n",
+ "Rx \n",
+ "Φ=0.399467 \n",
+ "Rx \n",
+ "Φ=3.463013 \n",
+ "Rx \n",
+ "Φ=0.936905 \n",
+ "Rx \n",
+ "Φ=3.692586 \n",
+ "Rx \n",
+ "Φ=0.508965 \n",
+ "Rx \n",
+ "Φ=5.731854 \n",
+ "Rx \n",
+ "Φ=5.986298 \n",
+ "Rx \n",
+ "Φ=1.319504 \n",
+ "Rx \n",
+ "Φ=5.632258 \n",
+ "Rx \n",
+ "Φ=2.245879 \n",
+ "Rx \n",
+ "Φ=0.420665 \n",
+ "Rx \n",
+ "Φ=1.820597 \n",
+ "Rx \n",
+ "Φ=5.32624 \n",
+ "Rx \n",
+ "Φ=2.772043 \n",
+ "Rx \n",
+ "Φ=6.050412 \n",
+ "Rx \n",
+ "Φ=3.869199 \n",
+ "Rx \n",
+ "Φ=0.32471 \n",
+ "Rx \n",
+ "Φ=3.333698 \n",
+ "Rx \n",
+ "Φ=6.021444 \n",
+ "Rx \n",
+ "Φ=3.538862 \n",
+ "Rx \n",
+ "Φ=5.100892 \n",
+ "Rx \n",
+ "Φ=5.68698 \n",
+ "Rx \n",
+ "Φ=5.997609 \n",
+ "Rx \n",
+ "Φ=0.367749 \n",
+ "Rx \n",
+ "Φ=6.064768 \n",
+ "Rx \n",
+ "Φ=2.808211 \n",
+ "Rx \n",
+ "Φ=5.598608 \n",
+ "Rx \n",
+ "Φ=4.280651 \n",
+ "Rx \n",
+ "Φ=0.738796 \n",
+ "Rx \n",
+ "Φ=0.359443 \n",
+ "Rx \n",
+ "Φ=5.113844 \n",
+ "Rx \n",
+ "Φ=4.672468 \n",
+ "Rx \n",
+ "Φ=5.249619 \n",
+ "Rx \n",
+ "Φ=0.215846 \n",
+ "Rx \n",
+ "Φ=4.904875 \n",
+ "Rx \n",
+ "Φ=5.338997 \n",
+ "Rx \n",
+ "Φ=5.538879 \n",
+ "Rx \n",
+ "Φ=5.116698 \n",
+ "Rx \n",
+ "Φ=0.64096 \n",
+ "Rx \n",
+ "Φ=3.293761 \n",
+ "Rx \n",
+ "Φ=5.844496 \n",
+ "Rx \n",
+ "Φ=1.491882 \n",
+ "Rx \n",
+ "Φ=5.834535 \n",
+ "Rx \n",
+ "Φ=6.266952 \n",
+ "Rx \n",
+ "Φ=0.231428 \n",
+ "Rx \n",
+ "Φ=4.825308 \n",
+ "Rx \n",
+ "Φ=0.675455 \n",
+ "Rx \n",
+ "Φ=4.715618 \n",
+ "Rx \n",
+ "Φ=6.145477 \n",
+ "Rx \n",
+ "Φ=0.004037 \n",
+ "Rx \n",
+ "Φ=5.158862 \n",
+ "Rx \n",
+ "Φ=3.369199 \n",
+ "Rx \n",
+ "Φ=5.804774 \n",
+ "Rx \n",
+ "Φ=2.169729 \n",
+ "Rx \n",
+ "Φ=6.143086 \n",
+ "Rx \n",
+ "Φ=5.88023 \n",
+ "Rx \n",
+ "Φ=0.716596 \n",
+ "Rx \n",
+ "Φ=2.748763 \n",
+ "Rx \n",
+ "Φ=5.245144 \n",
+ "Rx \n",
+ "Φ=1.423123 \n",
+ "Rx \n",
+ "Φ=5.723868 \n",
+ "Rx \n",
+ "Φ=2.889604 \n",
+ "Rx \n",
+ "Φ=5.73382 \n",
+ "Rx \n",
+ "Φ=5.006678 \n",
+ "Rx \n",
+ "Φ=0.220705 \n",
+ "Rx \n",
+ "Φ=2.162038 \n",
+ "Rx \n",
+ "Φ=5.522914 \n",
+ "Rx \n",
+ "Φ=4.922113 \n",
+ "Rx \n",
+ "Φ=5.668667 \n",
+ "Rx \n",
+ "Φ=4.582551 \n",
+ "Rx \n",
+ "Φ=0.338757 \n",
+ "Rx \n",
+ "Φ=5.297967 \n",
+ "Rx \n",
+ "Φ=5.40702 \n",
+ "Rx \n",
+ "Φ=3.425866 \n",
+ "Rx \n",
+ "Φ=0.569833 \n",
+ "Rx \n",
+ "Φ=2.550067 \n",
+ "Rx \n",
+ "Φ=1.08323 \n",
+ "Rx \n",
+ "Φ=4.658903 \n",
+ "Rx \n",
+ "Φ=6.028077 \n",
+ "Rx \n",
+ "Φ=3.059846 \n",
+ "Rx \n",
+ "Φ=0.394903 \n",
+ "Rx \n",
+ "Φ=1.95923 \n",
+ "Rx \n",
+ "Φ=4.981399 \n",
+ "Rx \n",
+ "Φ=2.416769 \n",
+ "Rx \n",
+ "Φ=2.200501 \n",
+ "Rx \n",
+ "Φ=4.803453 \n",
+ "Rx \n",
+ "Φ=6.218475 \n",
+ "Rx \n",
+ "Φ=5.293279 \n",
+ "Rx \n",
+ "Φ=5.910487 \n",
+ "Rx \n",
+ "Φ=0.017424 \n",
+ "Rx \n",
+ "Φ=5.699953 \n",
+ "Rx \n",
+ "Φ=4.101439 \n",
+ "Rx \n",
+ "Φ=5.948572 \n",
+ "Rx \n",
+ "Φ=3.955862 \n",
+ "Rx \n",
+ "Φ=0.199616 \n",
+ "Rx \n",
+ "Φ=6.1524 \n",
+ "Rx \n",
+ "Φ=5.848672 \n",
+ "Rx \n",
+ "Φ=3.29141 \n",
+ "Rx \n",
+ "Φ=5.871175 \n",
+ "Rx \n",
+ "Φ=4.584176 \n",
+ "Rx \n",
+ "Φ=6.172786 \n",
+ "Rx \n",
+ "Φ=4.215571 \n",
+ "Rx \n",
+ "Φ=0.219702 \n",
+ "Rx \n",
+ "Φ=5.357694 \n",
+ "Rx \n",
+ "Φ=0.588621 \n",
+ "Rx \n",
+ "Φ=0.796209 \n",
+ "Rx \n",
+ "Φ=0.267153 \n",
+ "Rx \n",
+ "Φ=4.046767 \n",
+ "Rx \n",
+ "Φ=0.285468 \n",
+ "Rx \n",
+ "Φ=5.58557 \n",
+ "Rx \n",
+ "Φ=0.569798 \n",
+ "Rx \n",
+ "Φ=5.104734 \n",
+ "Rx \n",
+ "Φ=0.203044 \n",
+ "Rx \n",
+ "Φ=1.54279 \n",
+ "Rx \n",
+ "Φ=5.629851 \n",
+ "Rx \n",
+ "Φ=2.276301 \n",
+ "Rx \n",
+ "Φ=5.506982 \n",
+ "Rx \n",
+ "Φ=5.507067 \n",
+ "Rx \n",
+ "Φ=5.590512 \n",
+ "Rx \n",
+ "Φ=3.037182 \n",
+ "Rx \n",
+ "Φ=0.922182 \n",
+ "Rx \n",
+ "Φ=5.611233 \n",
+ "Rx \n",
+ "Φ=0.422143 \n",
+ "Rx \n",
+ "Φ=2.812007 \n",
+ "Rx \n",
+ "Φ=0.209277 \n",
+ "Rx \n",
+ "Φ=2.332124 \n",
+ "Rx \n",
+ "Φ=0.41518 \n",
+ "Rx \n",
+ "Φ=0.105469 \n",
+ "Rx \n",
+ "Φ=0.857114 \n",
+ "Rx \n",
+ "Φ=5.682467 \n",
+ "Rx \n",
+ "Φ=0.983445 \n",
+ "Rx \n",
+ "Φ=3.690203 \n",
+ "Rx \n",
+ "Φ=5.314439 \n",
+ "Rx \n",
+ "Φ=1.838969 \n",
+ "Rx \n",
+ "Φ=2.419455 \n",
+ "Rx \n",
+ "Φ=5.390959 \n",
+ "Rx \n",
+ "Φ=4.067388 \n",
+ "Rx \n",
+ "Φ=5.265258 \n",
+ "Rx \n",
+ "Φ=0.477379 \n",
+ "Rx \n",
+ "Φ=2.929825 \n",
+ "Rx \n",
+ "Φ=6.016577 \n",
+ "Rx \n",
+ "Φ=5.72474 \n",
+ "Rx \n",
+ "Φ=5.735746 \n",
+ "Rx \n",
+ "Φ=5.490343 \n",
+ "Rx \n",
+ "Φ=0.244737 \n",
+ "Rx \n",
+ "Φ=0.093864 \n",
+ "Rx \n",
+ "Φ=6.163369 \n",
+ "Rx \n",
+ "Φ=4.684547 \n",
+ "Rx \n",
+ "Φ=5.836186 \n",
+ "Rx \n",
+ "Φ=2.148812 \n",
+ "Rx \n",
+ "Φ=0.229644 \n",
+ "Rx \n",
+ "Φ=0.122718 \n",
+ "Rx \n",
+ "Φ=0.147226 \n",
+ "Rx \n",
+ "Φ=1.099638 \n",
+ "Rx \n",
+ "Φ=0.543051 \n",
+ "Rx \n",
+ "Φ=3.859599 \n",
+ "Rx \n",
+ "Φ=6.150594 \n",
+ "Rx \n",
+ "Φ=1.521992 \n",
+ "Rx \n",
+ "Φ=1.039816 \n",
+ "Rx \n",
+ "Φ=2.296459 \n",
+ "Rx \n",
+ "Φ=6.047517 \n",
+ "Rx \n",
+ "Φ=5.506269 \n",
+ "Rx \n",
+ "Φ=6.076713 \n",
+ "Rx \n",
+ "Φ=2.056638 \n",
+ "Rx \n",
+ "Φ=0.238015 \n",
+ "Rx \n",
+ "Φ=5.770754 \n",
+ "Rx \n",
+ "Φ=0.520825 \n",
+ "Rx \n",
+ "Φ=0.76241 \n",
+ "Rx \n",
+ "Φ=0.19925 \n",
+ "Rx \n",
+ "Φ=1.527306 \n",
+ "Rx \n",
+ "Φ=0.403382 \n",
+ "Rx \n",
+ "Φ=5.856351 \n",
+ "Rx \n",
+ "Φ=5.677914 \n",
+ "Rx \n",
+ "Φ=3.769758 \n",
+ "Rx \n",
+ "Φ=5.269437 \n",
+ "Rx \n",
+ "Φ=4.990839 \n",
+ "Rx \n",
+ "Φ=0.682524 \n",
+ "Rx \n",
+ "Φ=0.598236 \n",
+ "Rx \n",
+ "Φ=0.439628 \n",
+ "Rx \n",
+ "Φ=2.957199 \n",
+ "Rx \n",
+ "Φ=5.484201 \n",
+ "Rx \n",
+ "Φ=0.021418 \n",
+ "Rx \n",
+ "Φ=0.445561 \n",
+ "Rx \n",
+ "Φ=4.373176 \n",
+ "Rx \n",
+ "Φ=5.653504 \n",
+ "Rx \n",
+ "Φ=2.067441 \n",
+ "Rx \n",
+ "Φ=4.274569 \n",
+ "Rx \n",
+ "Φ=5.964213 \n",
+ "Rx \n",
+ "Φ=2.231541 \n",
+ "Rx \n",
+ "Φ=6.114936 \n",
+ "Rx \n",
+ "Φ=0.093337 \n",
+ "Rx \n",
+ "Φ=0.019955 \n",
+ "Rx \n",
+ "Φ=6.042181 \n",
+ "Rx \n",
+ "Φ=3.190376 \n",
+ "Rx \n",
+ "Φ=6.238858 \n",
+ "Rx \n",
+ "Φ=0.541327 \n",
+ "Rx \n",
+ "Φ=5.902791 \n",
+ "Rx \n",
+ "Φ=5.195998 \n",
+ "Rx \n",
+ "Φ=6.113575 \n",
+ "Rx \n",
+ "Φ=1.427451 \n",
+ "Rx \n",
+ "Φ=0.258085 \n",
+ "Rx \n",
+ "Φ=2.423441 \n",
+ "Rx \n",
+ "Φ=0.133222 \n",
+ "Rx \n",
+ "Φ=1.413268 \n",
+ "Rx \n",
+ "Φ=5.947855 \n",
+ "Rx \n",
+ "Φ=0.269122 \n",
+ "Rx \n",
+ "Φ=0.450593 \n",
+ "Rx \n",
+ "Φ=4.436088 \n",
+ "Rx \n",
+ "Φ=6.195168 \n",
+ "Rx \n",
+ "Φ=3.042674 \n",
+ "Rx \n",
+ "Φ=5.774974 \n",
+ "Rx \n",
+ "Φ=2.660357 \n",
+ "Rx \n",
+ "Φ=0.522278 \n",
+ "Rx \n",
+ "Φ=5.754474 \n",
+ "Rx \n",
+ "Φ=0.227203 \n",
+ "Rx \n",
+ "Φ=4.141827 \n",
+ "Rx \n",
+ "Φ=5.576982 \n",
+ "Rx \n",
+ "Φ=0.633933 \n",
+ "Rx \n",
+ "Φ=0.177753 \n",
+ "Rx \n",
+ "Φ=4.304442 \n",
+ "Rx \n",
+ "Φ=5.880523 \n",
+ "Rx \n",
+ "Φ=0.53588 \n",
+ "Rx \n",
+ "Φ=5.542716 \n",
+ "Rx \n",
+ "Φ=3.31531 \n",
+ "Rx \n",
+ "Φ=6.204582 \n",
+ "Rx \n",
+ "Φ=5.432882 \n",
+ "Rx \n",
+ "Φ=5.994762 \n",
+ "Rx \n",
+ "Φ=2.458468 \n",
+ "Rx \n",
+ "Φ=5.753867 \n",
+ "Rx \n",
+ "Φ=1.980775 \n",
+ "Rx \n",
+ "Φ=1.325169 \n",
+ "Rx \n",
+ "Φ=3.070916 \n",
+ "Rx \n",
+ "Φ=0.580697 \n",
+ "Rx \n",
+ "Φ=3.83876 \n",
+ "Rx \n",
+ "Φ=5.85581 \n",
+ "Rx \n",
+ "Φ=5.762809 \n",
+ "Rx \n",
+ "Φ=5.647271 \n",
+ "Rx \n",
+ "Φ=3.855965 \n",
+ "Rx \n",
+ "Φ=1.150993 \n",
+ "Rx \n",
+ "Φ=5.893975 \n",
+ "Rx \n",
+ "Φ=4.598866 \n",
+ "Rx \n",
+ "Φ=1.094243 \n",
+ "Rx \n",
+ "Φ=2.030832 \n",
+ "Rx \n",
+ "Φ=5.956455 \n",
+ "Rx \n",
+ "Φ=6.11105 \n",
+ "Rx \n",
+ "Φ=1.216368 \n",
+ "Rx \n",
+ "Φ=5.707755 \n",
+ "Rx \n",
+ "Φ=2.740713 \n",
+ "Rx \n",
+ "Φ=0.107237 \n",
+ "Rx \n",
+ "Φ=5.214346 \n",
+ "Rx \n",
+ "Φ=5.939324 \n",
+ "Rx \n",
+ "Φ=5.487156 \n",
+ "Rx \n",
+ "Φ=0.700745 \n",
+ "Rx \n",
+ "Φ=3.941168 \n",
+ "Rx \n",
+ "Φ=0.456103 \n",
+ "Rx \n",
+ "Φ=5.500603 \n",
+ "Rx \n",
+ "Φ=0.239863 \n",
+ "Rx \n",
+ "Φ=6.254082 \n",
+ "Rx \n",
+ "Φ=0.369538 \n",
+ "Rx \n",
+ "Φ=3.260581 \n",
+ "Rx \n",
+ "Φ=5.986911 \n",
+ "Rx \n",
+ "Φ=5.699078 \n",
+ "Rx \n",
+ "Φ=0.123895 \n",
+ "Rx \n",
+ "Φ=0.168214 \n",
+ "Rx \n",
+ "Φ=0.598502 \n",
+ "Rx \n",
+ "Φ=2.031381 \n",
+ "Rx \n",
+ "Φ=5.767624 \n",
+ "Rx \n",
+ "Φ=1.714811 \n",
+ "Rx \n",
+ "Φ=0.696723 \n",
+ "Rx \n",
+ "Φ=4.138627 \n",
+ "Rx \n",
+ "Φ=5.890336 \n",
+ "Rx \n",
+ "Φ=0.30598 \n",
+ "Rx \n",
+ "Φ=0.588127 \n",
+ "Rx \n",
+ "Φ=5.330174 \n",
+ "Rx \n",
+ "Φ=5.986883 \n",
+ "Rx \n",
+ "Φ=5.762938 \n",
+ "Rx \n",
+ "Φ=0.679186 \n",
+ "Rx \n",
+ "Φ=4.094739 \n",
+ "Rx \n",
+ "Φ=5.604207 \n",
+ "Rx \n",
+ "Φ=0.232575 \n",
+ "Rx \n",
+ "Φ=5.875659 \n",
+ "Rx \n",
+ "Φ=2.274241 \n",
+ "Rx \n",
+ "Φ=5.671712 \n",
+ "Rx \n",
+ "Φ=4.453421 \n",
+ "Rx \n",
+ "Φ=0.623544 \n",
+ "Rx \n",
+ "Φ=1.780345 \n",
+ "Rx \n",
+ "Φ=0.59897 \n",
+ "Rx \n",
+ "Φ=3.073695 \n",
+ "Rx \n",
+ "Φ=5.683233 \n",
+ "Rx \n",
+ "Φ=1.68671 \n",
+ "Rx \n",
+ "Φ=0.549226 \n",
+ "Rx \n",
+ "Φ=4.797519 \n",
+ "Rx \n",
+ "Φ=5.429404 \n",
+ "Rx \n",
+ "Φ=5.68189 \n",
+ "Rx \n",
+ "Φ=0.376 \n",
+ "Rx \n",
+ "Φ=2.925263 \n",
+ "Rx \n",
+ "Φ=1.769202 \n",
+ "Rx \n",
+ "Φ=3.1745 \n",
+ "Rx \n",
+ "Φ=1.679441 \n",
+ "Rx \n",
+ "Φ=4.887175 \n",
+ "Rx \n",
+ "Φ=0.052026 \n",
+ "Rx \n",
+ "Φ=1.514181 \n",
+ "Rx \n",
+ "Φ=6.228542 \n",
+ "Rx \n",
+ "Φ=1.478118 \n",
+ "Rx \n",
+ "Φ=0.472186 \n",
+ "Rx \n",
+ "Φ=2.922438 \n",
+ "Rx \n",
+ "Φ=5.992849 \n",
+ "Rx \n",
+ "Φ=2.85018 \n",
+ "Rx \n",
+ "Φ=0.30378 \n",
+ "Rx \n",
+ "Φ=4.017153 \n",
+ "Rx \n",
+ "Φ=6.083374 \n",
+ "Rx \n",
+ "Φ=5.454276 \n",
+ "Rx \n",
+ "Φ=5.961007 \n",
+ "Rx \n",
+ "Φ=5.482207 \n",
+ "Rx \n",
+ "Φ=6.012536 \n",
+ "Rx \n",
+ "Φ=6.199626 \n",
+ "Rx \n",
+ "Φ=6.243308 \n",
+ "Rx \n",
+ "Φ=5.611726 \n",
+ "Rx \n",
+ "Φ=5.961654 \n",
+ "Rx \n",
+ "Φ=2.806171 \n",
+ "Rx \n",
+ "Φ=0.480714 \n",
+ "Rx \n",
+ "Φ=0.523293 \n",
+ "Rx \n",
+ "Φ=0.759843 \n",
+ "Rx \n",
+ "Φ=0.916306 \n",
+ "Rx \n",
+ "Φ=5.886832 \n",
+ "Rx \n",
+ "Φ=4.351615 \n",
+ "Rx \n",
+ "Φ=0.433352 \n",
+ "Rx \n",
+ "Φ=5.957581 \n",
+ "Rx \n",
+ "Φ=0.295648 \n",
+ "Rx \n",
+ "Φ=3.981763 \n",
+ "Rx \n",
+ "Φ=5.380175 \n",
+ "Rx \n",
+ "Φ=6.032838 \n",
+ "Rx \n",
+ "Φ=5.572622 \n",
+ "Rx \n",
+ "Φ=3.151324 \n",
+ "Rx \n",
+ "Φ=6.061702 \n",
+ "Rx \n",
+ "Φ=5.257801 \n",
+ "Rx \n",
+ "Φ=6.075365 \n",
+ "Rx \n",
+ "Φ=3.256506 \n",
+ "Rx \n",
+ "Φ=0.089869 \n",
+ "Rx \n",
+ "Φ=3.066276 \n",
+ "Rx \n",
+ "Φ=5.972261 \n",
+ "Rx \n",
+ "Φ=3.367587 \n",
+ "Rx \n",
+ "Φ=1.020491 \n",
+ "Rx \n",
+ "Φ=2.72645 \n",
+ "Rx \n",
+ "Φ=0.759872 \n",
+ "Rx \n",
+ "Φ=4.715894 \n",
+ "Rx \n",
+ "Φ=5.291848 \n",
+ "Rx \n",
+ "Φ=4.900551 \n",
+ "Rx \n",
+ "Φ=5.709273 \n",
+ "Rx \n",
+ "Φ=4.776625 \n",
+ "Rx \n",
+ "Φ=1.455011 \n",
+ "Rx \n",
+ "Φ=3.94456 \n",
+ "Rx \n",
+ "Φ=5.446214 \n",
+ "Rx \n",
+ "Φ=4.517696 \n",
+ "Rx \n",
+ "Φ=5.628627 \n",
+ "Rx \n",
+ "Φ=2.040727 \n",
+ "Rx \n",
+ "Φ=4.030961 \n",
+ "Rx \n",
+ "Φ=3.656951 \n",
+ "Rx \n",
+ "Φ=6.234532 \n",
+ "Rx \n",
+ "Φ=2.442188 \n",
+ "Rx \n",
+ "Φ=5.616431 \n",
+ "Rx \n",
+ "Φ=4.244303 \n",
+ "Rx \n",
+ "Φ=0.072164 \n",
+ "Rx \n",
+ "Φ=2.224473 \n",
+ "Rx \n",
+ "Φ=5.663511 \n",
+ "Rx \n",
+ "Φ=2.157919 \n",
+ "Rx \n",
+ "Φ=0.354552 \n",
+ "Rx \n",
+ "Φ=5.131273 \n",
+ "Rx \n",
+ "Φ=5.913191 \n",
+ "Rx \n",
+ "Φ=4.58095 \n",
+ "Rx \n",
+ "Φ=0.089204 \n",
+ "Rx \n",
+ "Φ=5.804518 \n",
+ "Rx \n",
+ "Φ=0.34211 \n",
+ "Rx \n",
+ "Φ=5.761009 \n",
+ "Rx \n",
+ "Φ=0.175531 \n",
+ "Rx \n",
+ "Φ=1.051173 \n",
+ "Rx \n",
+ "Φ=5.527978 \n",
+ "Rx \n",
+ "Φ=1.370609 \n",
+ "Rx \n",
+ "Φ=0.367708 \n",
+ "Rx \n",
+ "Φ=1.649056 \n",
+ "Rx \n",
+ "Φ=6.171052 \n",
+ "Rx \n",
+ "Φ=0.02159 \n",
+ "Rx \n",
+ "Φ=5.891977 \n",
+ "Rx \n",
+ "Φ=0.126299 \n",
+ "Rx \n",
+ "Φ=0.141127 \n",
+ "Rx \n",
+ "Φ=0.58573 \n",
+ "Rx \n",
+ "Φ=0.259033 \n",
+ "Rx \n",
+ "Φ=0.376157 \n",
+ "Rx \n",
+ "Φ=0.829004 \n",
+ "Rx \n",
+ "Φ=4.780165 \n",
+ "Rx \n",
+ "Φ=0.444614 \n",
+ "Rx \n",
+ "Φ=4.162666 \n",
+ "Rx \n",
+ "Φ=0.319395 \n",
+ "Rx \n",
+ "Φ=4.466288 \n",
+ "Rx \n",
+ "Φ=5.547516 \n",
+ "Rx \n",
+ "Φ=1.235662 \n",
+ "Rx \n",
+ "Φ=0.292482 \n",
+ "Rx \n",
+ "Φ=1.20604 \n",
+ "Rx \n",
+ "Φ=0.248722 \n",
+ "Rx \n",
+ "Φ=5.796192 \n",
+ "Rx \n",
+ "Φ=0.270089 \n",
+ "Rx \n",
+ "Φ=5.554708 \n",
+ "Rx \n",
+ "Φ=0.953723 \n",
+ "Rx \n",
+ "Φ=1.405474 \n",
+ "Rx \n",
+ "Φ=0.868107 \n",
+ "Rx \n",
+ "Φ=2.588087 \n",
+ "Rx \n",
+ "Φ=1.143901 \n",
+ "Rx \n",
+ "Φ=0.91266 \n",
+ "Rx \n",
+ "Φ=0.642695 \n",
+ "Rx \n",
+ "Φ=2.921651 \n",
+ "Rx \n",
+ "Φ=0.529808 \n",
+ "Rx \n",
+ "Φ=2.473485 \n",
+ "Rx \n",
+ "Φ=0.505636 \n",
+ "Rx \n",
+ "Φ=5.757487 \n",
+ "Rx \n",
+ "Φ=1.974719 \n",
+ "Rx \n",
+ "Φ=0.972625 \n",
+ "Rx \n",
+ "Φ=4.833805 \n",
+ "Rx \n",
+ "Φ=0.247393 \n",
+ "Rx \n",
+ "Φ=5.78553 \n",
+ "Rx \n",
+ "Φ=0.346737 \n",
+ "Rx \n",
+ "Φ=0.512465 \n",
+ "Rx \n",
+ "Φ=4.994394 \n",
+ "Rx \n",
+ "Φ=5.637971 \n",
+ "Rx \n",
+ "Φ=3.284399 \n",
+ "Rx \n",
+ "Φ=5.751342 \n",
+ "Rx \n",
+ "Φ=4.939043 \n",
+ "Rx \n",
+ "Φ=6.142857 \n",
+ "Rx \n",
+ "Φ=1.851632 \n",
+ "Rx \n",
+ "Φ=0.661271 \n",
+ "Rx \n",
+ "Φ=3.410028 \n",
+ "Rx \n",
+ "Φ=6.138608 \n",
+ "Rx \n",
+ "Φ=4.878046 \n",
+ "Rx \n",
+ "Φ=5.642364 \n",
+ "Rx \n",
+ "Φ=3.221759 \n",
+ "Rx \n",
+ "Φ=5.988355 \n",
+ "Rx \n",
+ "Φ=3.363302 \n",
+ "Rx \n",
+ "Φ=0.256849 \n",
+ "Rx \n",
+ "Φ=0.877555 \n",
+ "Rx \n",
+ "Φ=0.151943 \n",
+ "Rx \n",
+ "Φ=5.359201 \n",
+ "Rx \n",
+ "Φ=0.126935 \n",
+ "Rx \n",
+ "Φ=2.312049 \n",
+ "Rx \n",
+ "Φ=6.051176 \n",
+ "Rx \n",
+ "Φ=4.151575 \n",
+ "Rx \n",
+ "Φ=0.53088 \n",
+ "Rx \n",
+ "Φ=1.879984 \n",
+ "Rx \n",
+ "Φ=0.463282 \n",
+ "Rx \n",
+ "Φ=0.330203 \n",
+ "Rx \n",
+ "Φ=6.134952 \n",
+ "Rx \n",
+ "Φ=5.460946 \n",
+ "Rx \n",
+ "Φ=0.242377 \n",
+ "Rx \n",
+ "Φ=2.215751 \n",
+ "Rx \n",
+ "Φ=5.923563 \n",
+ "Rx \n",
+ "Φ=2.452255 \n",
+ "Rx \n",
+ "Φ=0.796936 \n",
+ "Rx \n",
+ "Φ=2.229198 \n",
+ "Rx \n",
+ "Φ=0.496373 \n",
+ "Rx \n",
+ "Φ=0.274294 \n",
+ "Rx \n",
+ "Φ=0.378424 \n",
+ "Rx \n",
+ "Φ=0.118014 \n",
+ "Rx \n",
+ "Φ=0.474273 \n",
+ "Rx \n",
+ "Φ=2.042912 \n",
+ "Rx \n",
+ "Φ=5.704379 \n",
+ "Rx \n",
+ "Φ=2.15425 \n",
+ "Rx \n",
+ "Φ=0.645851 \n",
+ "Rx \n",
+ "Φ=0.789982 \n",
+ "Rx \n",
+ "Φ=6.142256 \n",
+ "Rx \n",
+ "Φ=5.262004 \n",
+ "Rx \n",
+ "Φ=5.496612 \n",
+ "Rx \n",
+ "Φ=5.371904 \n",
+ "Rx \n",
+ "Φ=5.274125 \n",
+ "Rx \n",
+ "Φ=0.809532 \n",
+ "Rx \n",
+ "Φ=4.867855 \n",
+ "Rx \n",
+ "Φ=6.233254 \n",
+ "Rx \n",
+ "Φ=4.478462 \n",
+ "Rx \n",
+ "Φ=3.212741 \n",
+ "Rx \n",
+ "Φ=1.834619 \n",
+ "Rx \n",
+ "Φ=4.474403 \n",
+ "Rx \n",
+ "Φ=4.29797 \n",
+ "Rx \n",
+ "Φ=4.968981 \n",
+ "Rx \n",
+ "Φ=5.698392 \n",
+ "Rx \n",
+ "Φ=2.711169 \n",
+ "Rx \n",
+ "Φ=6.096551 \n",
+ "Rx \n",
+ "Φ=4.422465 \n",
+ "Rx \n",
+ "Φ=6.208921 \n",
+ "Rx \n",
+ "Φ=1.437135 \n",
+ "Rx \n",
+ "Φ=6.020212 \n",
+ "Rx \n",
+ "Φ=6.199684 \n",
+ "Rx \n",
+ "Φ=0.290385 \n",
+ "Rx \n",
+ "Φ=0.683948 \n",
+ "Rx \n",
+ "Φ=0.514469 \n",
+ "Rx \n",
+ "Φ=4.501836 \n",
+ "Rx \n",
+ "Φ=0.685003 \n",
+ "Rx \n",
+ "Φ=5.659673 \n",
+ "Rx \n",
+ "Φ=5.739558 \n",
+ "Rx \n",
+ "Φ=3.821398 \n",
+ "Rx \n",
+ "Φ=0.309769 \n",
+ "Rx \n",
+ "Φ=2.094481 \n",
+ "Rx \n",
+ "Φ=0.374739 \n",
+ "Rx \n",
+ "Φ=0.646314 \n",
+ "Rx \n",
+ "Φ=5.620713 \n",
+ "Rx \n",
+ "Φ=2.246282 \n",
+ "Rx \n",
+ "Φ=0.236089 \n",
+ "Rx \n",
+ "Φ=3.754583 \n",
+ "Rx \n",
+ "Φ=0.550612 \n",
+ "Rx \n",
+ "Φ=0.399894 \n",
+ "Rx \n",
+ "Φ=0.411515 \n",
+ "Rx \n",
+ "Φ=3.821363 \n",
+ "Rx \n",
+ "Φ=0.160269 \n",
+ "Rx \n",
+ "Φ=2.216543 \n",
+ "Rx \n",
+ "Φ=0.84423 \n",
+ "Rx \n",
+ "Φ=4.490015 \n",
+ "Rx \n",
+ "Φ=0.588618 \n",
+ "Rx \n",
+ "Φ=2.883528 \n",
+ "Rx \n",
+ "Φ=5.769517 \n",
+ "Rx \n",
+ "Φ=3.19416 \n",
+ "Rx \n",
+ "Φ=0.776956 \n",
+ "Rx \n",
+ "Φ=1.635549 \n",
+ "Rx \n",
+ "Φ=0.696736 \n",
+ "Rx \n",
+ "Φ=1.331777 \n",
+ "Rx \n",
+ "Φ=5.756767 \n",
+ "Rx \n",
+ "Φ=0.571521 \n",
+ "Rx \n",
+ "Φ=0.734265 \n",
+ "Rx \n",
+ "Φ=3.247648 \n",
+ "Rx \n",
+ "Φ=0.442729 \n",
+ "Rx \n",
+ "Φ=0.881649 \n",
+ "Rx \n",
+ "Φ=0.449237 \n",
+ "Rx \n",
+ "Φ=5.895602 \n",
+ "Rx \n",
+ "Φ=5.865561 \n",
+ "Rx \n",
+ "Φ=3.882013 \n",
+ "Rx \n",
+ "Φ=4.7672 \n",
+ "Rx \n",
+ "Φ=0.01085 \n",
+ "Rx \n",
+ "Φ=1.538399 \n",
+ "Rx \n",
+ "Φ=0.153758 \n",
+ "Rx \n",
+ "Φ=5.151371 \n",
+ "Rx \n",
+ "Φ=5.180034 \n",
+ "Rx \n",
+ "Φ=1.196623 \n",
+ "Rx \n",
+ "Φ=3.642712 \n",
+ "Rx \n",
+ "Φ=4.345944 \n",
+ "Rx \n",
+ "Φ=2.22147 \n",
+ "Rx \n",
+ "Φ=1.576057 \n",
+ "Rx \n",
+ "Φ=5.802205 \n",
+ "Rx \n",
+ "Φ=0.737114 \n",
+ "Rx \n",
+ "Φ=3.053096 \n",
+ "Rx \n",
+ "Φ=0.418288 \n",
+ "Rx \n",
+ "Φ=6.159663 \n",
+ "Rx \n",
+ "Φ=0.234534 \n",
+ "Rx \n",
+ "Φ=5.415891 \n",
+ "Rx \n",
+ "Φ=5.781673 \n",
+ "Rx \n",
+ "Φ=4.917287 \n",
+ "Rx \n",
+ "Φ=6.113872 \n",
+ "Rx \n",
+ "Φ=3.75766 \n",
+ "Rx \n",
+ "Φ=5.905518 \n",
+ "Rx \n",
+ "Φ=0.199658 \n",
+ "Rx \n",
+ "Φ=0.287202 \n",
+ "Rx \n",
+ "Φ=3.656166 \n",
+ "Rx \n",
+ "Φ=5.952086 \n",
+ "Rx \n",
+ "Φ=0.777164 \n",
+ "Rx \n",
+ "Φ=0.106117 \n",
+ "Rx \n",
+ "Φ=3.989855 \n",
+ "Rx \n",
+ "Φ=0.192069 \n",
+ "Rx \n",
+ "Φ=5.172423 \n",
+ "Rx \n",
+ "Φ=0.658626 \n",
+ "Rx \n",
+ "Φ=0.607144 \n",
+ "Rx \n",
+ "Φ=5.824566 \n",
+ "Rx \n",
+ "Φ=4.594279 \n",
+ "Rx \n",
+ "Φ=0.322789 \n",
+ "Rx \n",
+ "Φ=5.92231 \n",
+ "Rx \n",
+ "Φ=6.081014 \n",
+ "Rx \n",
+ "Φ=4.774493 \n",
+ "Rx \n",
+ "Φ=5.701267 \n",
+ "Rx \n",
+ "Φ=0.969143 \n",
+ "Rx \n",
+ "Φ=5.90225 \n",
+ "Rx \n",
+ "Φ=1.669819 \n",
+ "Rx \n",
+ "Φ=0.615986 \n",
+ "Rx \n",
+ "Φ=3.068441 \n",
+ "Rx \n",
+ "Φ=0.124125 \n",
+ "Rx \n",
+ "Φ=3.874383 \n",
+ "Rx \n",
+ "Φ=0.597905 \n",
+ "Rx \n",
+ "Φ=2.035267 \n",
+ "Rx \n",
+ "Φ=5.532399 \n",
+ "Rx \n",
+ "Φ=4.804654 \n",
+ "Rx \n",
+ "Φ=5.734675 \n",
+ "Rx \n",
+ "Φ=2.515332 \n",
+ "Rx \n",
+ "Φ=0.209558 \n",
+ "Rx \n",
+ "Φ=0.377728 \n",
+ "Rx \n",
+ "Φ=5.873464 \n",
+ "Rx \n",
+ "Φ=2.236805 \n",
+ "Rx \n",
+ "Φ=0.603499 \n",
+ "Rx \n",
+ "Φ=3.985186 \n",
+ "Rx \n",
+ "Φ=5.424746 \n",
+ "Rx \n",
+ "Φ=5.527621 \n",
+ "Rx \n",
+ "Φ=0.768672 \n",
+ "Rx \n",
+ "Φ=3.409334 \n",
+ "Rx \n",
+ "Φ=0.45491 \n",
+ "Rx \n",
+ "Φ=4.582095 \n",
+ "Rx \n",
+ "Φ=0.648781 \n",
+ "Rx \n",
+ "Φ=1.955986 \n",
+ "Rx \n",
+ "Φ=5.870405 \n",
+ "Rx \n",
+ "Φ=1.97374 \n",
+ "Rx \n",
+ "Φ=5.055052 \n",
+ "Rx \n",
+ "Φ=5.092413 \n",
+ "Rx \n",
+ "Φ=0.430646 \n",
+ "Rx \n",
+ "Φ=0.962243 \n",
+ "Rx \n",
+ "Φ=5.744127 \n",
+ "Rx \n",
+ "Φ=1.282586 \n",
+ "Rx \n",
+ "Φ=5.36026 \n",
+ "Rx \n",
+ "Φ=5.930805 \n",
+ "Rx \n",
+ "Φ=2.637202 \n",
+ "Rx \n",
+ "Φ=4.649165 \n",
+ "Rx \n",
+ "Φ=0.512184 \n",
+ "Rx \n",
+ "Φ=2.843777 \n",
+ "Rx \n",
+ "Φ=0.702965 \n",
+ "Rx \n",
+ "Φ=0.673577 \n",
+ "Rx \n",
+ "Φ=6.185262 \n",
+ "Rx \n",
+ "Φ=5.015092 \n",
+ "Rx \n",
+ "Φ=0.533244 \n",
+ "Rx \n",
+ "Φ=2.31875 \n",
+ "Rx \n",
+ "Φ=6.02042 \n",
+ "Rx \n",
+ "Φ=2.001742 \n",
+ "Rx \n",
+ "Φ=6.00725 \n",
+ "Rx \n",
+ "Φ=4.650943 \n",
+ "Rx \n",
+ "Φ=0.440106 \n",
+ "Rx \n",
+ "Φ=2.238034 \n",
+ "Rx \n",
+ "Φ=5.964191 \n",
+ "Rx \n",
+ "Φ=4.52516 \n",
+ "Rx \n",
+ "Φ=0.226549 \n",
+ "Rx \n",
+ "Φ=3.217925 \n",
+ "Rx \n",
+ "Φ=5.97242 \n",
+ "Rx \n",
+ "Φ=0.9776 \n",
+ "Rx \n",
+ "Φ=6.037387 \n",
+ "Rx \n",
+ "Φ=2.909105 \n",
+ "Rx \n",
+ "Φ=5.986803 \n",
+ "Rx \n",
+ "Φ=2.770111 \n",
+ "Rx \n",
+ "Φ=0.51219 \n",
+ "Rx \n",
+ "Φ=4.642721 \n",
+ "Rx \n",
+ "Φ=0.62577 \n",
+ "Rx \n",
+ "Φ=3.775027 \n",
+ "Rx \n",
+ "Φ=5.72146 \n",
+ "Rx \n",
+ "Φ=0.041805 \n",
+ "Rx \n",
+ "Φ=5.983768 \n",
+ "Rx \n",
+ "Φ=5.270229 \n",
+ "Rx \n",
+ "Φ=5.821635 \n",
+ "Rx \n",
+ "Φ=4.288329 \n",
+ "Rx \n",
+ "Φ=0.049484 \n",
+ "Rx \n",
+ "Φ=5.14279 \n",
+ "Rx \n",
+ "Φ=6.016288 \n",
+ "Rx \n",
+ "Φ=2.461146 \n",
+ "Rx \n",
+ "Φ=0.282737 \n",
+ "Rx \n",
+ "Φ=2.710993 \n",
+ "Rx \n",
+ "Φ=0.408261 \n",
+ "Rx \n",
+ "Φ=5.209425 \n",
+ "Rx \n",
+ "Φ=0.181144 \n",
+ "Rx \n",
+ "Φ=4.748677 \n",
+ "Rx \n",
+ "Φ=0.042377 \n",
+ "Rx \n",
+ "Φ=5.393231 \n",
+ "Rx \n",
+ "Φ=6.020608 \n",
+ "Rx \n",
+ "Φ=4.512503 \n",
+ "Rx \n",
+ "Φ=6.070316 \n",
+ "Rx \n",
+ "Φ=4.057084 \n",
+ "Rx \n",
+ "Φ=6.126184 \n",
+ "Rx \n",
+ "Φ=5.84446 \n",
+ "Rx \n",
+ "Φ=0.693109 \n",
+ "Rx \n",
+ "Φ=1.407963 \n",
+ "Rx \n",
+ "Φ=0.134619 \n",
+ "Rx \n",
+ "Φ=0.36961 \n",
+ "Rx \n",
+ "Φ=0.704427 \n",
+ "Rx \n",
+ "Φ=2.635927 \n",
+ "Rx \n",
+ "Φ=0.736153 \n",
+ "Rx \n",
+ "Φ=2.535345 \n",
+ "Rx \n",
+ "Φ=1.216072 \n",
+ "Rx \n",
+ "Φ=1.715714 \n",
+ "Rx \n",
+ "Φ=5.19745 \n",
+ "Rx \n",
+ "Φ=4.748149 \n",
+ "Rx \n",
+ "Φ=1.68525 \n",
+ "Rx \n",
+ "Φ=2.389896 \n",
+ "Rx \n",
+ "Φ=0.514223 \n",
+ "Rx \n",
+ "Φ=1.849406 \n",
+ "Rx \n",
+ "Φ=5.582746 \n",
+ "Rx \n",
+ "Φ=1.020868 \n",
+ "Rx \n",
+ "Φ=0.211478 \n",
+ "Rx \n",
+ "Φ=2.050511 \n",
+ "Rx \n",
+ "Φ=5.734562 \n",
+ "Rx \n",
+ "Φ=1.389873 \n",
+ "Rx \n",
+ "Φ=6.037964 \n",
+ "Rx \n",
+ "Φ=0.915284 \n",
+ "Rx \n",
+ "Φ=0.437865 \n",
+ "Rx \n",
+ "Φ=3.864395 \n",
+ "Rx \n",
+ "Φ=6.097204 \n",
+ "Rx \n",
+ "Φ=6.140713 \n",
+ "Rx \n",
+ "Φ=0.169182 \n",
+ "Rx \n",
+ "Φ=2.210514 \n",
+ "Rx \n",
+ "Φ=6.221275 \n",
+ "Rx \n",
+ "Φ=3.957274 \n",
+ "Rx \n",
+ "Φ=0.192499 \n",
+ "Rx \n",
+ "Φ=0.051607 \n",
+ "Rx \n",
+ "Φ=0.483043 \n",
+ "Rx \n",
+ "Φ=4.342912 \n",
+ "Rx \n",
+ "Φ=0.190721 \n",
+ "Rx \n",
+ "Φ=3.175534 \n",
+ "Rx \n",
+ "Φ=0.609377 \n",
+ "Rx \n",
+ "Φ=3.790427 \n",
+ "Rx \n",
+ "Φ=6.074801 \n",
+ "Rx \n",
+ "Φ=1.646758 \n",
+ "Rx \n",
+ "Φ=0.109677 \n",
+ "Rx \n",
+ "Φ=5.377106 \n",
+ "Rx \n",
+ "Φ=0.509768 \n",
+ "Rx \n",
+ "Φ=5.187879 \n",
+ "Rx \n",
+ "Φ=5.955078 \n",
+ "Rx \n",
+ "Φ=1.279841 \n",
+ "Rx \n",
+ "Φ=6.013673 \n",
+ "Rx \n",
+ "Φ=5.079069 \n",
+ "Rx \n",
+ "Φ=0.541909 \n",
+ "Rx \n",
+ "Φ=6.192406 \n",
+ "Rx \n",
+ "Φ=0.407665 \n",
+ "Rx \n",
+ "Φ=4.04051 \n",
+ "Rx \n",
+ "Φ=5.828236 \n",
+ "Rx \n",
+ "Φ=1.633663 \n",
+ "Rx \n",
+ "Φ=6.179789 \n",
+ "Rx \n",
+ "Φ=6.029337 \n",
+ "Rx \n",
+ "Φ=5.707877 \n",
+ "Rx \n",
+ "Φ=4.85108 \n",
+ "Rx \n",
+ "Φ=0.633817 \n",
+ "Rx \n",
+ "Φ=2.25236 \n",
+ "Rx \n",
+ "Φ=0.234213 \n",
+ "Rx \n",
+ "Φ=4.853767 \n",
+ "Rx \n",
+ "Φ=0.620388 \n",
+ "Rx \n",
+ "Φ=2.751823 \n",
+ "Rx \n",
+ "Φ=5.279283 \n",
+ "Rx \n",
+ "Φ=1.991755 \n",
+ "Rx \n",
+ "Φ=0.795202 \n",
+ "Rx \n",
+ "Φ=3.611869 \n",
+ "Rx \n",
+ "Φ=5.810605 \n",
+ "Rx \n",
+ "Φ=0.664203 \n",
+ "Rx \n",
+ "Φ=5.766565 \n",
+ "Rx \n",
+ "Φ=2.214422 \n",
+ "Rx \n",
+ "Φ=5.705516 \n",
+ "Rx \n",
+ "Φ=2.125092 \n",
+ "Rx \n",
+ "Φ=5.439929 \n",
+ "Rx \n",
+ "Φ=4.463951 \n",
+ "Rx \n",
+ "Φ=0.078791 \n",
+ "Rx \n",
+ "Φ=6.106416 \n",
+ "Rx \n",
+ "Φ=1.3209 \n",
+ "Rx \n",
+ "Φ=0.634288 \n",
+ "Rx \n",
+ "Φ=4.462417 \n",
+ "Rx \n",
+ "Φ=1.94352 \n",
+ "Rx \n",
+ "Φ=5.548046 \n",
+ "Rx \n",
+ "Φ=1.172074 \n",
+ "Rx \n",
+ "Φ=5.87396 \n",
+ "Rx \n",
+ "Φ=1.381752 \n",
+ "Rx \n",
+ "Φ=0.336108 \n",
+ "Rx \n",
+ "Φ=5.214009 \n",
+ "Rx \n",
+ "Φ=5.492446 \n",
+ "Rx \n",
+ "Φ=3.309733 \n",
+ "Rx \n",
+ "Φ=5.890855 \n",
+ "Rx \n",
+ "Φ=4.248166 \n",
+ "Rx \n",
+ "Φ=0.149401 \n",
+ "Rx \n",
+ "Φ=3.950501 \n",
+ "Rx \n",
+ "Φ=0.26253 \n",
+ "Rx \n",
+ "Φ=0.747313 \n",
+ "Rx \n",
+ "Φ=5.661896 \n",
+ "Rx \n",
+ "Φ=0.339121 \n",
+ "Rx \n",
+ "Φ=0.215693 \n",
+ "Rx \n",
+ "Φ=0.13843 \n",
+ "Rx \n",
+ "Φ=6.162247 \n",
+ "Rx \n",
+ "Φ=0.694243 \n",
+ "Rx \n",
+ "Φ=6.108113 \n",
+ "Rx \n",
+ "Φ=0.705923 \n",
+ "Rx \n",
+ "Φ=0.093209 \n",
+ "Rx \n",
+ "Φ=4.36354 \n",
+ "Rx \n",
+ "Φ=5.8645 \n",
+ "Rx \n",
+ "Φ=3.87493 \n",
+ "Rx \n",
+ "Φ=0.446626 \n",
+ "Rx \n",
+ "Φ=1.090107 \n",
+ "Rx \n",
+ "Φ=0.304385 \n",
+ "Rx \n",
+ "Φ=4.571389 \n",
+ "Rx \n",
+ "Φ=6.029644 \n",
+ "Rx \n",
+ "Φ=0.671549 \n",
+ "Rx \n",
+ "Φ=5.936913 \n",
+ "Rx \n",
+ "Φ=2.954612 \n",
+ "Rx \n",
+ "Φ=5.535393 \n",
+ "Rx \n",
+ "Φ=1.513224 \n",
+ "Rx \n",
+ "Φ=6.129279 \n",
+ "Rx \n",
+ "Φ=1.843456 \n",
+ "Rx \n",
+ "Φ=0.513004 \n",
+ "Rx \n",
+ "Φ=1.368096 \n",
+ "Rx \n",
+ "Φ=0.27467 \n",
+ "Rx \n",
+ "Φ=1.062216 \n",
+ "Rx \n",
+ "Φ=0.339203 \n",
+ "Rx \n",
+ "Φ=2.894647 \n",
+ "Rx \n",
+ "Φ=0.527774 \n",
+ "Rx \n",
+ "Φ=4.973097 \n",
+ "Rx \n",
+ "Φ=0.329017 \n",
+ "Rx \n",
+ "Φ=1.479373 \n",
+ "Rx \n",
+ "Φ=0.840942 \n",
+ "Rx \n",
+ "Φ=0.131621 \n",
+ "Rx \n",
+ "Φ=0.479951 \n",
+ "Rx \n",
+ "Φ=1.04624 \n",
+ "Rx \n",
+ "Φ=5.963802 \n",
+ "Rx \n",
+ "Φ=4.341473 \n",
+ "Rx \n",
+ "Φ=0.121443 \n",
+ "Rx \n",
+ "Φ=0.610838 \n",
+ "Rx \n",
+ "Φ=1.174955 \n",
+ "Rx \n",
+ "Φ=3.833879 \n",
+ "Rx \n",
+ "Φ=5.752223 \n",
+ "Rx \n",
+ "Φ=3.872452 \n",
+ "Rx \n",
+ "Φ=0.619346 \n",
+ "Rx \n",
+ "Φ=2.289293 \n",
+ "Rx \n",
+ "Φ=5.905861 \n",
+ "Rx \n",
+ "Φ=5.496791 \n",
+ "Rx \n",
+ "Φ=0.93532 \n",
+ "Rx \n",
+ "Φ=2.272491 \n",
+ "Rx \n",
+ "Φ=5.587387 \n",
+ "Rx \n",
+ "Φ=2.706606 \n",
+ "Rx \n",
+ "Φ=1.787944 \n",
+ "Rx \n",
+ "Φ=2.547212 \n",
+ "Rx \n",
+ "Φ=4.685188 \n",
+ "Rx \n",
+ "Φ=2.155974 \n",
+ "Rx \n",
+ "Φ=5.85245 \n",
+ "Rx \n",
+ "Φ=0.778962 \n",
+ "Rx \n",
+ "Φ=5.708081 \n",
+ "Rx \n",
+ "Φ=2.884803 \n",
+ "Rx \n",
+ "Φ=6.000214 \n",
+ "Rx \n",
+ "Φ=0.098014 \n",
+ "Rx \n",
+ "Φ=0.287319 \n",
+ "Rx \n",
+ "Φ=5.162668 \n",
+ "Rx \n",
+ "Φ=0.121889 \n",
+ "Rx \n",
+ "Φ=1.06132 \n",
+ "Rx \n",
+ "Φ=0.140368 \n",
+ "Rx \n",
+ "Φ=4.603299 \n",
+ "Rx \n",
+ "Φ=0.243943 \n",
+ "Rx \n",
+ "Φ=5.616124 \n",
+ "Rx \n",
+ "Φ=6.143945 \n",
+ "Rx \n",
+ "Φ=1.144914 \n",
+ "Rx \n",
+ "Φ=0.247742 \n",
+ "Rx \n",
+ "Φ=5.044332 \n",
+ "Rx \n",
+ "Φ=5.933216 \n",
+ "Rx \n",
+ "Φ=4.11938 \n",
+ "Rx \n",
+ "Φ=0.480003 \n",
+ "Rx \n",
+ "Φ=1.883586 \n",
+ "Rx \n",
+ "Φ=0.371312 \n",
+ "Rx \n",
+ "Φ=5.11189 \n",
+ "Rx \n",
+ "Φ=5.94146 \n",
+ "Rx \n",
+ "Φ=5.968884 \n",
+ "Rx \n",
+ "Φ=0.681234 \n",
+ "Rx \n",
+ "Φ=0.929026 \n",
+ "Rx \n",
+ "Φ=5.834167 \n",
+ "Rx \n",
+ "Φ=6.155504 \n",
+ "Rx \n",
+ "Φ=5.882969 \n",
+ "Rx \n",
+ "Φ=1.754451 \n",
+ "Rx \n",
+ "Φ=0.482145 \n",
+ "Rx \n",
+ "Φ=0.433835 \n",
+ "Rx \n",
+ "Φ=0.188211 \n",
+ "Rx \n",
+ "Φ=1.926479 \n",
+ "Rx \n",
+ "Φ=0.150143 \n",
+ "Rx \n",
+ "Φ=3.666027 \n",
+ "Rx \n",
+ "Φ=5.846424 \n",
+ "Rx \n",
+ "Φ=4.894188 \n",
+ "Rx \n",
+ "Φ=5.990025 \n",
+ "Rx \n",
+ "Φ=3.054882 \n",
+ "Rx \n",
+ "Φ=0.162822 \n",
+ "Rx \n",
+ "Φ=1.322073 \n",
+ "Rx \n",
+ "Φ=5.763988 \n",
+ "Rx \n",
+ "Φ=1.858661 \n",
+ "Rx \n",
+ "Φ=5.678976 \n",
+ "Rx \n",
+ "Φ=4.820748 \n",
+ "Rx \n",
+ "Φ=5.672497 \n",
+ "Rx \n",
+ "Φ=2.795694 \n",
+ "Rx \n",
+ "Φ=0.480084 \n",
+ "Rx \n",
+ "Φ=6.174042 \n",
+ "Rx \n",
+ "Φ=0.378408 \n",
+ "Rx \n",
+ "Φ=2.042352 \n",
+ "Rx \n",
+ "Φ=6.178054 \n",
+ "Rx \n",
+ "Φ=1.064056 \n",
+ "Rx \n",
+ "Φ=6.071468 \n",
+ "Rx \n",
+ "Φ=5.017133 \n",
+ "Rx \n",
+ "Φ=5.782992 \n",
+ "Rx \n",
+ "Φ=2.77024 \n",
+ "Rx \n",
+ "Φ=0.383731 \n",
+ "Rx \n",
+ "Φ=4.827526 \n",
+ "Rx \n",
+ "Φ=5.503674 \n",
+ "Rx \n",
+ "Φ=3.06586 \n",
+ "Rx \n",
+ "Φ=0.545082 \n",
+ "Rx \n",
+ "Φ=1.514253 \n",
+ "Rx \n",
+ "Φ=0.257736 \n",
+ "Rx \n",
+ "Φ=2.384984 \n",
+ "Rx \n",
+ "Φ=5.912742 \n",
+ "Rx \n",
+ "Φ=3.099524 \n",
+ "Rx \n",
+ "Φ=5.952479 \n",
+ "Rx \n",
+ "Φ=4.247372 \n",
+ "Rx \n",
+ "Φ=0.66842 \n",
+ "Rx \n",
+ "Φ=3.811989 \n",
+ "Rx \n",
+ "Φ=2.023185 \n",
+ "Rx \n",
+ "Φ=5.97819 \n",
+ "Rx \n",
+ "Φ=6.116104 \n",
+ "Rx \n",
+ "Φ=1.626243 \n",
+ "Rx \n",
+ "Φ=0.427583 \n",
+ "Rx \n",
+ "Φ=3.592958 \n",
+ "Rx \n",
+ "Φ=0.532454 \n",
+ "Rx \n",
+ "Φ=1.164043 \n",
+ "Rx \n",
+ "Φ=0.391522 \n",
+ "Rx \n",
+ "Φ=4.747811 \n",
+ "Rx \n",
+ "Φ=0.183597 \n",
+ "Rx \n",
+ "Φ=3.8199 \n",
+ "Rx \n",
+ "Φ=0.235484 \n",
+ "Rx \n",
+ "Φ=3.68655 \n",
+ "Rx \n",
+ "Φ=6.141033 \n",
+ "Rx \n",
+ "Φ=1.97839 \n",
+ "Rx \n",
+ "Φ=6.187654 \n",
+ "Rx \n",
+ "Φ=3.238694 \n",
+ "Rx \n",
+ "Φ=5.985883 \n",
+ "Rx \n",
+ "Φ=3.045913 \n",
+ "Rx \n",
+ "Φ=0.429637 \n",
+ "Rx \n",
+ "Φ=2.580599 \n",
+ "Rx \n",
+ "Φ=6.147983 \n",
+ "Rx \n",
+ "Φ=6.215522 \n",
+ "Rx \n",
+ "Φ=0.451457 \n",
+ "Rx \n",
+ "Φ=0.256774 \n",
+ "Rx \n",
+ "Φ=0.449303 \n",
+ "Rx \n",
+ "Φ=3.386691 \n",
+ "Rx \n",
+ "Φ=5.897196 \n",
+ "Rx \n",
+ "Φ=5.50102 \n",
+ "Rx \n",
+ "Φ=0.179949 \n",
+ "Rx \n",
+ "Φ=2.51378 \n",
+ "Rx \n",
+ "Φ=0.274805 \n",
+ "Rx \n",
+ "Φ=4.798041 \n",
+ "Rx \n",
+ "Φ=5.8301 \n",
+ "Rx \n",
+ "Φ=2.391176 \n",
+ "Rx \n",
+ "Φ=0.664226 \n",
+ "Rx \n",
+ "Φ=4.111117 \n",
+ "Rx \n",
+ "Φ=0.682193 \n",
+ "Rx \n",
+ "Φ=5.67518 \n",
+ "Rx \n",
+ "Φ=6.1007 \n",
+ "Rx \n",
+ "Φ=5.546181 \n",
+ "Rx \n",
+ "Φ=5.573027 \n",
+ "Rx \n",
+ "Φ=3.661511 \n",
+ "Rx \n",
+ "Φ=5.735799 \n",
+ "Rx \n",
+ "Φ=2.352501 \n",
+ "Rx \n",
+ "Φ=5.771584 \n",
+ "Rx \n",
+ "Φ=3.355577 \n",
+ "Rx \n",
+ "Φ=5.648242 \n",
+ "Rx \n",
+ "Φ=0.918384 \n",
+ "Rx \n",
+ "Φ=5.506802 \n",
+ "Rx \n",
+ "Φ=1.408481 \n",
+ "Rx \n",
+ "Φ=5.722102 \n",
+ "Rx \n",
+ "Φ=1.810067 \n",
+ "Rx \n",
+ "Φ=5.714008 \n",
+ "Rx \n",
+ "Φ=2.974203 \n",
+ "Rx \n",
+ "Φ=0.619444 \n",
+ "Rx \n",
+ "Φ=3.506439 \n",
+ "Rx \n",
+ "Φ=5.223181 \n",
+ "Rx \n",
+ "Φ=4.503524 \n",
+ "Rx \n",
+ "Φ=0.650305 \n",
+ "Rx \n",
+ "Φ=2.109519 \n",
+ "Rx \n",
+ "Φ=0.34848 \n",
+ "Rx \n",
+ "Φ=5.102518 \n",
+ "Rx \n",
+ "Φ=1.162887 \n",
+ "Rx \n",
+ "Φ=1.247959 \n",
+ "Rx \n",
+ "Φ=0.228058 \n",
+ "Rx \n",
+ "Φ=2.038943 \n",
+ "Rx \n",
+ "Φ=0.562287 \n",
+ "Rx \n",
+ "Φ=2.785995 \n",
+ "Rx \n",
+ "Φ=5.593439 \n",
+ "Rx \n",
+ "Φ=1.745865 \n",
+ "Rx \n",
+ "Φ=5.33428 \n",
+ "Rx \n",
+ "Φ=0.774986 \n",
+ "Rx \n",
+ "Φ=0.442689 \n",
+ "Rx \n",
+ "Φ=1.274169 \n",
+ "Rx \n",
+ "Φ=1.022356 \n",
+ "Rx \n",
+ "Φ=4.138717 \n",
+ "Rx \n",
+ "Φ=0.218075 \n",
+ "Rx \n",
+ "Φ=2.106163 \n",
+ "Rx \n",
+ "Φ=0.201127 \n",
+ "Rx \n",
+ "Φ=3.56185 \n",
+ "Rx \n",
+ "Φ=0.192844 \n",
+ "Rx \n",
+ "Φ=1.292544 \n",
+ "Rx \n",
+ "Φ=0.303825 \n",
+ "Rx \n",
+ "Φ=4.453529 \n",
+ "Rx \n",
+ "Φ=0.209774 \n",
+ "Rx \n",
+ "Φ=1.023447 \n",
+ "Rx \n",
+ "Φ=0.125513 \n",
+ "Rx \n",
+ "Φ=4.701956 \n",
+ "Rx \n",
+ "Φ=5.843035 \n",
+ "Rx \n",
+ "Φ=2.132197 \n",
+ "Rx \n",
+ "Φ=5.699192 \n",
+ "Rx \n",
+ "Φ=1.76511 \n",
+ "Rx \n",
+ "Φ=6.093622 \n",
+ "Rx \n",
+ "Φ=5.164295 \n",
+ "Rx \n",
+ "Φ=0.52066 \n",
+ "Rx \n",
+ "Φ=3.739147 \n",
+ "Rx \n",
+ "Φ=0.305798 \n",
+ "Rx \n",
+ "Φ=3.025383 \n",
+ "Rx \n",
+ "Φ=0.286443 \n",
+ "Rx \n",
+ "Φ=3.112603 \n",
+ "Rx \n",
+ "Φ=0.363183 \n",
+ "Rx \n",
+ "Φ=5.492462 \n",
+ "Rx \n",
+ "Φ=0.221422 \n",
+ "Rx \n",
+ "Φ=0.309104 \n",
+ "Rx \n",
+ "Φ=6.068068 \n",
+ "Rx \n",
+ "Φ=3.054927 \n",
+ "Rx \n",
+ "Φ=5.819165 \n",
+ "Rx \n",
+ "Φ=5.531789 \n",
+ "Rx \n",
+ "Φ=5.96784 \n",
+ "Rx \n",
+ "Φ=0.504413 \n",
+ "Rx \n",
+ "Φ=0.654484 \n",
+ "Rx \n",
+ "Φ=5.128969 \n",
+ "Rx \n",
+ "Φ=0.169306 \n",
+ "Rx \n",
+ "Φ=5.11649 \n",
+ "Rx \n",
+ "Φ=5.85703 \n",
+ "Rx \n",
+ "Φ=1.728085 \n",
+ "Rx \n",
+ "Φ=0.291225 \n",
+ "Rx \n",
+ "Φ=3.346451 \n",
+ "Rx \n",
+ "Φ=0.107862 \n",
+ "Rx \n",
+ "Φ=0.667012 \n",
+ "Rx \n",
+ "Φ=0.297114 \n",
+ "Rx \n",
+ "Φ=5.268813 \n",
+ "Rx \n",
+ "Φ=5.752027 \n",
+ "Rx \n",
+ "Φ=4.236765 \n",
+ "Rx \n",
+ "Φ=5.768319 \n",
+ "Rx \n",
+ "Φ=4.465554 \n",
+ "Rx \n",
+ "Φ=0.508294 \n",
+ "Rx \n",
+ "Φ=5.274503 \n",
+ "Rx \n",
+ "Φ=0.218289 \n",
+ "Rx \n",
+ "Φ=2.277798 \n",
+ "Rx \n",
+ "Φ=5.436114 \n",
+ "Rx \n",
+ "Φ=2.484038 \n",
+ "Rx \n",
+ "Φ=0.762733 \n",
+ "Rx \n",
+ "Φ=4.294309 \n",
+ "Rx \n",
+ "Φ=5.909907 \n",
+ "Rx \n",
+ "Φ=3.754619 \n",
+ "Rx \n",
+ "Φ=5.470907 \n",
+ "Rx \n",
+ "Φ=3.292547 \n",
+ "Rx \n",
+ "Φ=5.825438 \n",
+ "Rx \n",
+ "Φ=5.312235 \n",
+ "Rx \n",
+ "Φ=5.49617 \n",
+ "Rx \n",
+ "Φ=5.926378 \n",
+ "Rx \n",
+ "Φ=5.391782 \n",
+ "Rx \n",
+ "Φ=5.589007 \n",
+ "Rx \n",
+ "Φ=5.902274 \n",
+ "Rx \n",
+ "Φ=2.009543 \n",
+ "Rx \n",
+ "Φ=4.873274 \n",
+ "Rx \n",
+ "Φ=0.035975 \n",
+ "Rx \n",
+ "Φ=0.300028 \n",
+ "Rx \n",
+ "Φ=2.393657 \n",
+ "Rx \n",
+ "Φ=5.514246 \n",
+ "Rx \n",
+ "Φ=5.655765 \n",
+ "Rx \n",
+ "Φ=4.952038 \n",
+ "Rx \n",
+ "Φ=6.241118 \n",
+ "Rx \n",
+ "Φ=6.086017 \n",
+ "Rx \n",
+ "Φ=1.986466 \n",
+ "Rx \n",
+ "Φ=6.134396 \n",
+ "Rx \n",
+ "Φ=4.935114 \n",
+ "Rx \n",
+ "Φ=6.058388 \n",
+ "Rx \n",
+ "Φ=1.026302 \n",
+ "Rx \n",
+ "Φ=5.971801 \n",
+ "Rx \n",
+ "Φ=3.771252 \n",
+ "Rx \n",
+ "Φ=0.181638 \n",
+ "Rx \n",
+ "Φ=4.807107 \n",
+ "Rx \n",
+ "Φ=5.947017 \n",
+ "Rx \n",
+ "Φ=5.726415 \n",
+ "Rx \n",
+ "Φ=5.487471 \n",
+ "Rx \n",
+ "Φ=0.118052 \n",
+ "Rx \n",
+ "Φ=6.189937 \n",
+ "Rx \n",
+ "Φ=6.015108 \n",
+ "Rx \n",
+ "Φ=6.177071 \n",
+ "Rx \n",
+ "Φ=0.15682 \n",
+ "Rx \n",
+ "Φ=0.349833 \n",
+ "Rx \n",
+ "Φ=6.172077 \n",
+ "Rx \n",
+ "Φ=6.02593 \n",
+ "Rx \n",
+ "Φ=4.625995 \n",
+ "Rx \n",
+ "Φ=5.845109 \n",
+ "Rx \n",
+ "Φ=0.374967 \n",
+ "Rx \n",
+ "Φ=0.184268 \n",
+ "Rx \n",
+ "Φ=1.289993 \n",
+ "Rx \n",
+ "Φ=6.149498 \n",
+ "Rx \n",
+ "Φ=0.007029 \n",
+ "Rx \n",
+ "Φ=0.543494 \n",
+ "Rx \n",
+ "Φ=1.202871 \n",
+ "Rx \n",
+ "Φ=0.212705 \n",
+ "Rx \n",
+ "Φ=4.387912 \n",
+ "Rx \n",
+ "Φ=5.958851 \n",
+ "Rx \n",
+ "Φ=2.60915 \n",
+ "Rx \n",
+ "Φ=0.664903 \n",
+ "Rx \n",
+ "Φ=4.306146 \n",
+ "Rx \n",
+ "Φ=0.38926 \n",
+ "Rx \n",
+ "Φ=3.113659 \n",
+ "Rx \n",
+ "Φ=0.644285 \n",
+ "Rx \n",
+ "Φ=5.034615 \n",
+ "Rx \n",
+ "Φ=0.324067 \n",
+ "Rx \n",
+ "Φ=2.842512 \n",
+ "Rx \n",
+ "Φ=0.270697 \n",
+ "Rx \n",
+ "Φ=2.426496 \n",
+ "Rx \n",
+ "Φ=5.937887 \n",
+ "Rx \n",
+ "Φ=3.263879 \n",
+ "Rx \n",
+ "Φ=6.105318 \n",
+ "Rx \n",
+ "Φ=1.791084 \n",
+ "Rx \n",
+ "Φ=5.902843 \n",
+ "Rx \n",
+ "Φ=1.50209 \n",
+ "Rx \n",
+ "Φ=0.109648 \n",
+ "Rx \n",
+ "Φ=3.226673 \n",
+ "Rx \n",
+ "Φ=0.276966 \n",
+ "Rx \n",
+ "Φ=3.07087 \n",
+ "Rx \n",
+ "Φ=0.209595 \n",
+ "Rx \n",
+ "Φ=1.555314 \n",
+ "Rx \n",
+ "Φ=0.451712 \n",
+ "Rx \n",
+ "Φ=2.222022 \n",
+ "Rx \n",
+ "Φ=1.286568 \n",
+ "Rx \n",
+ "Φ=3.706687 \n",
+ "Rx \n",
+ "Φ=5.21618 \n",
+ "Rx \n",
+ "Φ=1.859693 \n",
+ "Rx \n",
+ "Φ=0.574807 \n",
+ "Rx \n",
+ "Φ=5.218566 \n",
+ "Rx \n",
+ "Φ=5.346412 \n",
+ "Rx \n",
+ "Φ=5.483232 \n",
+ "Rx \n",
+ "Φ=0.574017 \n",
+ "Rx \n",
+ "Φ=1.378553 \n",
+ "Rx \n",
+ "Φ=0.578582 \n",
+ "Rx \n",
+ "Φ=4.332171 \n",
+ "Rx \n",
+ "Φ=0.879409 \n",
+ "Rx \n",
+ "Φ=2.993434 \n",
+ "Rx \n",
+ "Φ=5.556203 \n",
+ "Rx \n",
+ "Φ=0.523426 \n",
+ "Rx \n",
+ "Φ=4.891175 \n",
+ "Rx \n",
+ "Φ=1.902019 \n",
+ "Rx \n",
+ "Φ=2.204474 \n",
+ "Rx \n",
+ "Φ=3.825553 \n",
+ "Rx \n",
+ "Φ=0.870069 \n",
+ "Rx \n",
+ "Φ=4.474557 \n",
+ "Rx \n",
+ "Φ=0.194815 \n",
+ "Rx \n",
+ "Φ=0.670387 \n",
+ "Rx \n",
+ "Φ=0.107157 \n",
+ "Rx \n",
+ "Φ=3.331872 \n",
+ "Rx \n",
+ "Φ=0.206584 \n",
+ "Rx \n",
+ "Φ=1.314649 \n",
+ "Rx \n",
+ "Φ=6.007706 \n",
+ "Rx \n",
+ "Φ=4.612626 \n",
+ "Rx \n",
+ "Φ=0.575886 \n",
+ "Rx \n",
+ "Φ=1.005007 \n",
+ "Rx \n",
+ "Φ=5.645279 \n",
+ "Rx \n",
+ "Φ=0.951811 \n",
+ "Rx \n",
+ "Φ=5.662948 \n",
+ "Rx \n",
+ "Φ=1.696673 \n",
+ "Rx \n",
+ "Φ=5.949113 \n",
+ "Rx \n",
+ "Φ=0.39189 \n",
+ "Rx \n",
+ "Φ=0.097375 \n",
+ "Rx \n",
+ "Φ=2.281393 \n",
+ "Rx \n",
+ "Φ=5.972026 \n",
+ "Rx \n",
+ "Φ=0.857042 \n",
+ "Rx \n",
+ "Φ=5.839495 \n",
+ "Rx \n",
+ "Φ=4.966637 \n",
+ "Rx \n",
+ "Φ=0.388092 \n",
+ "Rx \n",
+ "Φ=0.068379 \n",
+ "Rx \n",
+ "Φ=0.135511 \n",
+ "Rx \n",
+ "Φ=5.867731 \n",
+ "Rx \n",
+ "Φ=0.487449 \n",
+ "Rx \n",
+ "Φ=2.924938 \n",
+ "Rx \n",
+ "Φ=0.178961 \n",
+ "Rx \n",
+ "Φ=2.986802 \n",
+ "Rx \n",
+ "Φ=0.523143 \n",
+ "Rx \n",
+ "Φ=1.842312 \n",
+ "Rx \n",
+ "Φ=0.203622 \n",
+ "Rx \n",
+ "Φ=3.928582 \n",
+ "Rx \n",
+ "Φ=0.555701 \n",
+ "Rx \n",
+ "Φ=4.771775 \n",
+ "Rx \n",
+ "Φ=6.144378 \n",
+ "Rx \n",
+ "Φ=0.18108 \n",
+ "Rx \n",
+ "Φ=0.706178 \n",
+ "Rx \n",
+ "Φ=3.839105 \n",
+ "Rx \n",
+ "Φ=6.147845 \n",
+ "Rx \n",
+ "Φ=2.89198 \n",
+ "Rx \n",
+ "Φ=0.742185 \n",
+ "Rx \n",
+ "Φ=4.587503 \n",
+ "Rx \n",
+ "Φ=5.991367 \n",
+ "Rx \n",
+ "Φ=1.469346 \n",
+ "Rx \n",
+ "Φ=5.831196 \n",
+ "Rx \n",
+ "Φ=0.704604 \n",
+ "Rx \n",
+ "Φ=0.324735 \n",
+ "Rx \n",
+ "Φ=5.018329 \n",
+ "Rx \n",
+ "Φ=0.11033 \n",
+ "Rx \n",
+ "Φ=5.816534 \n",
+ "Rx \n",
+ "Φ=0.428162 \n",
+ "Rx \n",
+ "Φ=6.076769 \n",
+ "Rx \n",
+ "Φ=5.654321 \n",
+ "Rx \n",
+ "Φ=5.001712 \n",
+ "Rx \n",
+ "Φ=0.877389 \n",
+ "Rx \n",
+ "Φ=0.512589 \n",
+ "Rx \n",
+ "Φ=0.224481 \n",
+ "Rx \n",
+ "Φ=1.236322 \n",
+ "Rx \n",
+ "Φ=5.78499 \n",
+ "Rx \n",
+ "Φ=1.704559 \n",
+ "Rx \n",
+ "Φ=0.594243 \n",
+ "Rx \n",
+ "Φ=4.112332 \n",
+ "Rx \n",
+ "Φ=0.616464 \n",
+ "Rx \n",
+ "Φ=5.169907 \n",
+ "Rx \n",
+ "Φ=5.385159 \n",
+ "Rx \n",
+ "Φ=5.434353 \n",
+ "Rx \n",
+ "Φ=4.929039 \n",
+ "Rx \n",
+ "Φ=3.923851 \n",
+ "Rx \n",
+ "Φ=0.681459 \n",
+ "Rx \n",
+ "Φ=1.232506 \n",
+ "Rx \n",
+ "Φ=0.691074 \n",
+ "Rx \n",
+ "Φ=0.714888 \n",
+ "Rx \n",
+ "Φ=4.936179 \n",
+ "Rx \n",
+ "Φ=1.249755 \n",
+ "Rx \n",
+ "Φ=5.296317 \n",
+ "Rx \n",
+ "Φ=0.095546 \n",
+ "Rx \n",
+ "Φ=4.590756 \n",
+ "Rx \n",
+ "Φ=2.13691 \n",
+ "Rx \n",
+ "Φ=5.519427 \n",
+ "Rx \n",
+ "Φ=3.500132 \n",
+ "Rx \n",
+ "Φ=5.866574 \n",
+ "Rx \n",
+ "Φ=6.230684 \n",
+ "Rx \n",
+ "Φ=0.291908 \n",
+ "Rx \n",
+ "Φ=3.150624 \n",
+ "Rx \n",
+ "Φ=0.196929 \n",
+ "Rx \n",
+ "Φ=3.897276 \n",
+ "Rx \n",
+ "Φ=5.951328 \n",
+ "Rx \n",
+ "Φ=2.401532 \n",
+ "Rx \n",
+ "Φ=6.112328 \n",
+ "Rx \n",
+ "Φ=1.359227 \n",
+ "Rx \n",
+ "Φ=0.19407 \n",
+ "Rx \n",
+ "Φ=5.856366 \n",
+ "Rx \n",
+ "Φ=5.911984 \n",
+ "Rx \n",
+ "Φ=3.140123 \n",
+ "Rx \n",
+ "Φ=5.863067 \n",
+ "Rx \n",
+ "Φ=1.57306 \n",
+ "Rx \n",
+ "Φ=5.711222 \n",
+ "Rx \n",
+ "Φ=5.245094 \n",
+ "Rx \n",
+ "Φ=0.22416 \n",
+ "Rx \n",
+ "Φ=2.623881 \n",
+ "Rx \n",
+ "Φ=0.235182 \n",
+ "Rx \n",
+ "Φ=0.823315 \n",
+ "Rx \n",
+ "Φ=6.053732 \n",
+ "Rx \n",
+ "Φ=1.590593 \n",
+ "Rx \n",
+ "Φ=5.956101 \n",
+ "Rx \n",
+ "Φ=4.824191 \n",
+ "Rx \n",
+ "Φ=5.994807 \n",
+ "Rx \n",
+ "Φ=5.413009 \n",
+ "Rx \n",
+ "Φ=5.989017 \n",
+ "Rx \n",
+ "Φ=0.294529 \n",
+ "Rx \n",
+ "Φ=0.283163 \n",
+ "Rx \n",
+ "Φ=3.60204 \n",
+ "Rx \n",
+ "Φ=6.09183 \n",
+ "Rx \n",
+ "Φ=3.654521 \n",
+ "Rx \n",
+ "Φ=0.448648 \n",
+ "Rx \n",
+ "Φ=4.062326 \n",
+ "Rx \n",
+ "Φ=0.3929 \n",
+ "Rx \n",
+ "Φ=1.632123 \n",
+ "Rx \n",
+ "Φ=0.400427 \n",
+ "Rx \n",
+ "Φ=5.654718 \n",
+ "Rx \n",
+ "Φ=5.937236 \n",
+ "Rx \n",
+ "Φ=4.240464 \n",
+ "Rx \n",
+ "Φ=0.36479 \n",
+ "Rx \n",
+ "Φ=3.318117 \n",
+ "Rx \n",
+ "Φ=6.000224 \n",
+ "Rx \n",
+ "Φ=4.550929 \n",
+ "Rx \n",
+ "Φ=0.436911 \n",
+ "Rx \n",
+ "Φ=0.979187 \n",
+ "Rx \n",
+ "Φ=0.113686 \n",
+ "Rx \n",
+ "Φ=2.362675 \n",
+ "Rx \n",
+ "Φ=5.850121 \n",
+ "Rx \n",
+ "Φ=4.666902 \n",
+ "Rx \n",
+ "Φ=5.99902 \n",
+ "Rx \n",
+ "Φ=4.484215 \n",
+ "Rx \n",
+ "Φ=1.087759 \n",
+ "Rx \n",
+ "Φ=6.206518 \n",
+ "Rx \n",
+ "Φ=0.251584 \n",
+ "Rx \n",
+ "Φ=3.652391 \n",
+ "Rx \n",
+ "Φ=6.252406 \n",
+ "Rx \n",
+ "Φ=2.738753 \n",
+ "Rx \n",
+ "Φ=5.96636 \n",
+ "Rx \n",
+ "Φ=4.305098 \n",
+ "Rx \n",
+ "Φ=4.883413 \n",
+ "Rx \n",
+ "Φ=4.605228 \n",
+ "Rx \n",
+ "Φ=0.752956 \n",
+ "Rx \n",
+ "Φ=6.117197 \n",
+ "Rx \n",
+ "Φ=0.52453 \n",
+ "Rx \n",
+ "Φ=4.32947 \n",
+ "Rx \n",
+ "Φ=5.589197 \n",
+ "Rx \n",
+ "Φ=6.122167 \n",
+ "Rx \n",
+ "Φ=5.946354 \n",
+ "Rx \n",
+ "Φ=1.257563 \n",
+ "Rx \n",
+ "Φ=5.789152 \n",
+ "Rx \n",
+ "Φ=2.168888 \n",
+ "Rx \n",
+ "Φ=0.859284 \n",
+ "Rx \n",
+ "Φ=1.515469 \n",
+ "Rx \n",
+ "Φ=5.870437 \n",
+ "Rx \n",
+ "Φ=2.64635 \n",
+ "Rx \n",
+ "Φ=0.787478 \n",
+ "Rx \n",
+ "Φ=1.022804 \n",
+ "Rx \n",
+ "Φ=5.639418 \n",
+ "Rx \n",
+ "Φ=0.221742 \n",
+ "Rx \n",
+ "Φ=3.764056 \n",
+ "Rx \n",
+ "Φ=2.54766 \n",
+ "Rx \n",
+ "Φ=6.166067 \n",
+ "Rx \n",
+ "Φ=1.76793 \n",
+ "Rx \n",
+ "Φ=5.508151 \n",
+ "Rx \n",
+ "Φ=4.380914 \n",
+ "Rx \n",
+ "Φ=5.979005 \n",
+ "Rx \n",
+ "Φ=1.469066 \n",
+ "Rx \n",
+ "Φ=6.073236 \n",
+ "Rx \n",
+ "Φ=0.585293 \n",
+ "Rx \n",
+ "Φ=6.089131 \n",
+ "Rx \n",
+ "Φ=4.452295 \n",
+ "Rx \n",
+ "Φ=0.217884 \n",
+ "Rx \n",
+ "Φ=1.524597 \n",
+ "Rx \n",
+ "Φ=5.994535 \n",
+ "Rx \n",
+ "Φ=0.772216 \n",
+ "Rx \n",
+ "Φ=0.519165 \n",
+ "Rx \n",
+ "Φ=4.97407 \n",
+ "Rx \n",
+ "Φ=0.220916 \n",
+ "Rx \n",
+ "Φ=0.290012 \n",
+ "Rx \n",
+ "Φ=5.744105 \n",
+ "Rx \n",
+ "Φ=1.703336 \n",
+ "Rx \n",
+ "Φ=0.346531 \n",
+ "Rx \n",
+ "Φ=2.066805 \n",
+ "Rx \n",
+ "Φ=5.867851 \n",
+ "Rx \n",
+ "Φ=6.029689 \n",
+ "Rx \n",
+ "Φ=5.977494 \n",
+ "Rx \n",
+ "Φ=0.013988 \n",
+ "Rx \n",
+ "Φ=6.073972 \n",
+ "Rx \n",
+ "Φ=1.983119 \n",
+ "Rx \n",
+ "Φ=0.54772 \n",
+ "Rx \n",
+ "Φ=4.454593 \n",
+ "Rx \n",
+ "Φ=0.35409 \n",
+ "Rx \n",
+ "Φ=5.879641 \n",
+ "Rx \n",
+ "Φ=6.006991 \n",
+ "Rx \n",
+ "Φ=5.307463 \n",
+ "Rx \n",
+ "Φ=5.848293 \n",
+ "Rx \n",
+ "Φ=0.4352 \n",
+ "Rx \n",
+ "Φ=5.894955 \n",
+ "Rx \n",
+ "Φ=4.709407 \n",
+ "Rx \n",
+ "Φ=5.91169 \n",
+ "Rx \n",
+ "Φ=3.310403 \n",
+ "Rx \n",
+ "Φ=0.196313 \n",
+ "Rx \n",
+ "Φ=4.357741 \n",
+ "Rx \n",
+ "Φ=0.525084 \n",
+ "Rx \n",
+ "Φ=3.153742 \n",
+ "Rx \n",
+ "Φ=0.211319 \n",
+ "Rx \n",
+ "Φ=2.621184 \n",
+ "Rx \n",
+ "Φ=0.194648 \n",
+ "Rx \n",
+ "Φ=4.027948 \n",
+ "Rx \n",
+ "Φ=0.640792 \n",
+ "Rx \n",
+ "Φ=2.940502 \n",
+ "Rx \n",
+ "Φ=0.475948 \n",
+ "Rx \n",
+ "Φ=4.481748 \n",
+ "Rx \n",
+ "Φ=0.645827 \n",
+ "Rx \n",
+ "Φ=4.710353 \n",
+ "Rx \n",
+ "Φ=5.77302 \n",
+ "Rx \n",
+ "Φ=4.014894 \n",
+ "Rx \n",
+ "Φ=0.372696 \n",
+ "Rx \n",
+ "Φ=0.295532 \n",
+ "Rx \n",
+ "Φ=5.951352 \n",
+ "Rx \n",
+ "Φ=3.726412 \n",
+ "Rx \n",
+ "Φ=0.557783 \n",
+ "Rx \n",
+ "Φ=3.070958 \n",
+ "Rx \n",
+ "Φ=5.839683 \n",
+ "Rx \n",
+ "Φ=2.913406 \n",
+ "Rx \n",
+ "Φ=0.08263 \n",
+ "Rx \n",
+ "Φ=5.914289 \n",
+ "Rx \n",
+ "Φ=5.585939 \n",
+ "Rx \n",
+ "Φ=0.512658 \n",
+ "Rx \n",
+ "Φ=1.021508 \n",
+ "Rx \n",
+ "Φ=0.892125 \n",
+ "Rx \n",
+ "Φ=5.702335 \n",
+ "Rx \n",
+ "Φ=0.080903 \n",
+ "Rx \n",
+ "Φ=0.233159 \n",
+ "Rx \n",
+ "Φ=1.924166 \n",
+ "Rx \n",
+ "Φ=0.902118 \n",
+ "Rx \n",
+ "Φ=1.574186 \n",
+ "Rx \n",
+ "Φ=5.846992 \n",
+ "Rx \n",
+ "Φ=1.475225 \n",
+ "Rx \n",
+ "Φ=1.325307 \n",
+ "Rx \n",
+ "Φ=1.033232 \n",
+ "Rx \n",
+ "Φ=4.983393 \n",
+ "Rx \n",
+ "Φ=4.527731 \n",
+ "Rx \n",
+ "Φ=1.176098 \n",
+ "Rx \n",
+ "Φ=6.042173 \n",
+ "Rx \n",
+ "Φ=4.969382 \n",
+ "Rx \n",
+ "Φ=2.157678 \n",
+ "Rx \n",
+ "Φ=6.100574 \n",
+ "Rx \n",
+ "Φ=4.21598 \n",
+ "Rx \n",
+ "Φ=0.16411 \n",
+ "Rx \n",
+ "Φ=2.541152 \n",
+ "Rx \n",
+ "Φ=5.996278 \n",
+ "Rx \n",
+ "Φ=1.088313 \n",
+ "Rx \n",
+ "Φ=6.101609 \n",
+ "Rx \n",
+ "Φ=5.663741 \n",
+ "Rx \n",
+ "Φ=0.201005 \n",
+ "Rx \n",
+ "Φ=2.915922 \n",
+ "Rx \n",
+ "Φ=0.105502 \n",
+ "Rx \n",
+ "Φ=3.403432 \n",
+ "Rx \n",
+ "Φ=5.929396 \n",
+ "Rx \n",
+ "Φ=4.460043 \n",
+ "Rx \n",
+ "Φ=0.502707 \n",
+ "Rx \n",
+ "Φ=5.286522 \n",
+ "Rx \n",
+ "Φ=0.250997 \n",
+ "Rx \n",
+ "Φ=2.318663 \n",
+ "Rx \n",
+ "Φ=0.249037 \n",
+ "Rx \n",
+ "Φ=5.485563 \n",
+ "Rx \n",
+ "Φ=0.321464 \n",
+ "Rx \n",
+ "Φ=5.411947 \n",
+ "Rx \n",
+ "Φ=0.318658 \n",
+ "Rx \n",
+ "Φ=4.668562 \n",
+ "Rx \n",
+ "Φ=0.248947 \n",
+ "Rx \n",
+ "Φ=4.088366 \n",
+ "Rx \n",
+ "Φ=0.548107 \n",
+ "Rx \n",
+ "Φ=4.816387 \n",
+ "Rx \n",
+ "Φ=5.967856 \n",
+ "Rx \n",
+ "Φ=0.509869 \n",
+ "Rx \n",
+ "Φ=5.975672 \n",
+ "Rx \n",
+ "Φ=4.361525 \n",
+ "Rx \n",
+ "Φ=6.031032 \n",
+ "Rx \n",
+ "Φ=4.450236 \n",
+ "Rx \n",
+ "Φ=0.653136 \n",
+ "Rx \n",
+ "Φ=5.907174 \n",
+ "Rx \n",
+ "Φ=6.195711 \n",
+ "Rx \n",
+ "Φ=3.081506 \n",
+ "Rx \n",
+ "Φ=0.385924 \n",
+ "Rx \n",
+ "Φ=4.594933 \n",
+ "Rx \n",
+ "Φ=0.342406 \n",
+ "Rx \n",
+ "Φ=3.969937 \n",
+ "Rx \n",
+ "Φ=5.959471 \n",
+ "Rx \n",
+ "Φ=4.976202 \n",
+ "Rx \n",
+ "Φ=0.440208 \n",
+ "Rx \n",
+ "Φ=3.563763 \n",
+ "Rx \n",
+ "Φ=6.16686 \n",
+ "Rx \n",
+ "Φ=2.841724 \n",
+ "Rx \n",
+ "Φ=5.989236 \n",
+ "Rx \n",
+ "Φ=0.232134 \n",
+ "Rx \n",
+ "Φ=0.466641 \n",
+ "Rx \n",
+ "Φ=2.907637 \n",
+ "Rx \n",
+ "Φ=0.598462 \n",
+ "Rx \n",
+ "Φ=4.965434 \n",
+ "Rx \n",
+ "Φ=0.619243 \n",
+ "Rx \n",
+ "Φ=1.687885 \n",
+ "Rx \n",
+ "Φ=0.482366 \n",
+ "Rx \n",
+ "Φ=3.384366 \n",
+ "Rx \n",
+ "Φ=0.512896 \n",
+ "Rx \n",
+ "Φ=2.584232 \n",
+ "Rx \n",
+ "Φ=5.830619 \n",
+ "Rx \n",
+ "Φ=3.365152 \n",
+ "Rx \n",
+ "Φ=5.757298 \n",
+ "Rx \n",
+ "Φ=3.749771 \n",
+ "Rx \n",
+ "Φ=5.584298 \n",
+ "Rx \n",
+ "Φ=3.615462 \n",
+ "Rx \n",
+ "Φ=5.688261 \n",
+ "Rx \n",
+ "Φ=4.968784 \n",
+ "Rx \n",
+ "Φ=6.177213 \n",
+ "Rx \n",
+ "Φ=1.754432 \n",
+ "Rx \n",
+ "Φ=5.820745 \n",
+ "Rx \n",
+ "Φ=3.695679 \n",
+ "Rx \n",
+ "Φ=0.553191 \n",
+ "Rx \n",
+ "Φ=2.485993 \n",
+ "Rx \n",
+ "Φ=0.151225 \n",
+ "Rx \n",
+ "Φ=0.150301 \n",
+ "Rx \n",
+ "Φ=0.377843 \n",
+ "Rx \n",
+ "Φ=0.963871 \n",
+ "Rx \n",
+ "Φ=0.846173 \n",
+ "Rx \n",
+ "Φ=0.684876 \n",
+ "Rx \n",
+ "Φ=5.837456 \n",
+ "Rx \n",
+ "Φ=5.702112 \n",
+ "Rx \n",
+ "Φ=0.542615 \n",
+ "Rx \n",
+ "Φ=5.899448 \n",
+ "Rx \n",
+ "Φ=5.388306 \n",
+ "Rx \n",
+ "Φ=3.891059 \n",
+ "Rx \n",
+ "Φ=1.354043 \n",
+ "Rx \n",
+ "Φ=5.933052 \n",
+ "Rx \n",
+ "Φ=0.086961 \n",
+ "Rx \n",
+ "Φ=6.15456 \n",
+ "Rx \n",
+ "Φ=0.287335 \n",
+ "Rx \n",
+ "Φ=2.632841 \n",
+ "Rx \n",
+ "Φ=0.248309 \n",
+ "Rx \n",
+ "Φ=3.037342 \n",
+ "Rx \n",
+ "Φ=6.20215 \n",
+ "Rx \n",
+ "Φ=3.258737 \n",
+ "Rx \n",
+ "Φ=6.225472 \n",
+ "Rx \n",
+ "Φ=1.857072 \n",
+ "Rx \n",
+ "Φ=0.327855 \n",
+ "Rx \n",
+ "Φ=4.619778 \n",
+ "Rx \n",
+ "Φ=0.483926 \n",
+ "Rx \n",
+ "Φ=6.028352 \n",
+ "Rx \n",
+ "Φ=0.303849 \n",
+ "Rx \n",
+ "Φ=6.021673 \n",
+ "Rx \n",
+ "Φ=6.111093 \n",
+ "Rx \n",
+ "Φ=3.375631 \n",
+ "Rx \n",
+ "Φ=6.150904 \n",
+ "Rx \n",
+ "Φ=2.392537 \n",
+ "Rx \n",
+ "Φ=5.981969 \n",
+ "Rx \n",
+ "Φ=1.215195 \n",
+ "Rx \n",
+ "Φ=0.427243 \n",
+ "Rx \n",
+ "Φ=5.909782 \n",
+ "Rx \n",
+ "Φ=0.306845 \n",
+ "Rx \n",
+ "Φ=3.220906 \n",
+ "Rx \n",
+ "Φ=5.690187 \n",
+ "Rx \n",
+ "Φ=0.989914 \n",
+ "Rx \n",
+ "Φ=0.558216 \n",
+ "Rx \n",
+ "Φ=4.766021 \n",
+ "Rx \n",
+ "Φ=5.897045 \n",
+ "Rx \n",
+ "Φ=3.920487 \n",
+ "Rx \n",
+ "Φ=0.224819 \n",
+ "Rx \n",
+ "Φ=1.033647 \n",
+ "Rx \n",
+ "Φ=5.821292 \n",
+ "Rx \n",
+ "Φ=5.220329 \n",
+ "Rx \n",
+ "Φ=5.726517 \n",
+ "Rx \n",
+ "Φ=3.34053 \n",
+ "Rx \n",
+ "Φ=0.009845 \n",
+ "Rx \n",
+ "Φ=5.51359 \n",
+ "Rx \n",
+ "Φ=0.268372 \n",
+ "Rx \n",
+ "Φ=3.845676 \n",
+ "Rx \n",
+ "Φ=0.139933 \n",
+ "Rx \n",
+ "Φ=1.266697 \n",
+ "Rx \n",
+ "Φ=6.152192 \n",
+ "Rx \n",
+ "Φ=0.436645 \n",
+ "Rx \n",
+ "Φ=0.470276 \n",
+ "Rx \n",
+ "Φ=0.81649 \n",
+ "Rx \n",
+ "Φ=0.808508 \n",
+ "Rx \n",
+ "Φ=5.62236 \n",
+ "Rx \n",
+ "Φ=1.118802 \n",
+ "Rx \n",
+ "Φ=3.632045 \n",
+ "Rx \n",
+ "Φ=6.120302 \n",
+ "Rx \n",
+ "Φ=2.741457 \n",
+ "Rx \n",
+ "Φ=5.946354 \n",
+ "Rx \n",
+ "Φ=5.827406 \n",
+ "Rx \n",
+ "Φ=5.75044 \n",
+ "Rx \n",
+ "Φ=0.215774 \n",
+ "Rx \n",
+ "Φ=5.526486 \n",
+ "Rx \n",
+ "Φ=5.824221 \n",
+ "Rx \n",
+ "Φ=0.242832 \n",
+ "Rx \n",
+ "Φ=0.571178 \n",
+ "Rx \n",
+ "Φ=0.544409 \n",
+ "Rx \n",
+ "Φ=1.683516 \n",
+ "Rx \n",
+ "Φ=5.49181 \n",
+ "Rx \n",
+ "Φ=5.205385 \n",
+ "Rx \n",
+ "Φ=0.87585 \n",
+ "Rx \n",
+ "Φ=3.693138 \n",
+ "Rx \n",
+ "Φ=0.314826 \n",
+ "Rx \n",
+ "Φ=5.339071 \n",
+ "Rx \n",
+ "Φ=0.772779 \n",
+ "Rx \n",
+ "Φ=3.970336 \n",
+ "Rx \n",
+ "Φ=5.699904 \n",
+ "Rx \n",
+ "Φ=2.062612 \n",
+ "Rx \n",
+ "Φ=0.313988 \n",
+ "Rx \n",
+ "Φ=1.355893 \n",
+ "Rx \n",
+ "Φ=0.060911 \n",
+ "Rx \n",
+ "Φ=4.166255 \n",
+ "Rx \n",
+ "Φ=5.931207 \n",
+ "Rx \n",
+ "Φ=1.947332 \n",
+ "Rx \n",
+ "Φ=0.114979 \n",
+ "Rx \n",
+ "Φ=1.035421 \n",
+ "Rx \n",
+ "Φ=1.46224 \n",
+ "Rx \n",
+ "Φ=1.339425 \n",
+ "Rx \n",
+ "Φ=4.943938 \n",
+ "Rx \n",
+ "Φ=3.823801 \n",
+ "Rx \n",
+ "Φ=1.391492 \n",
+ "Rx \n",
+ "Φ=2.81065 \n",
+ "Rx \n",
+ "Φ=4.702919 \n",
+ "Rx \n",
+ "Φ=6.130215 \n",
+ "Rx \n",
+ "Φ=0.245043 \n",
+ "Rx \n",
+ "Φ=4.954468 \n",
+ "Rx \n",
+ "Φ=5.991317 \n",
+ "Rx \n",
+ "Φ=0.160681 \n",
+ "Rx \n",
+ "Φ=0.467249 \n",
+ "Rx \n",
+ "Φ=0.597464 \n",
+ "Rx \n",
+ "Φ=0.21826 \n",
+ "Rx \n",
+ "Φ=5.478608 \n",
+ "Rx \n",
+ "Φ=0.235617 \n",
+ "Rx \n",
+ "Φ=0.519261 \n",
+ "Rx \n",
+ "Φ=6.155467 \n",
+ "Rx \n",
+ "Φ=2.189277 \n",
+ "Rx \n",
+ "Φ=5.688655 \n",
+ "Rx \n",
+ "Φ=3.87223 \n",
+ "Rx \n",
+ "Φ=0.300294 \n",
+ "Rx \n",
+ "Φ=4.336099 \n",
+ "Rx \n",
+ "Φ=5.519202 \n",
+ "Rx \n",
+ "Φ=2.357248 \n",
+ "Rx \n",
+ "Φ=0.420619 \n",
+ "Rx \n",
+ "Φ=4.243122 \n",
+ "Rx \n",
+ "Φ=6.035784 \n",
+ "Rx \n",
+ "Φ=2.069186 \n",
+ "Rx \n",
+ "Φ=6.031433 \n",
+ "Rx \n",
+ "Φ=3.481913 \n",
+ "Rx \n",
+ "Φ=0.106724 \n",
+ "Rx \n",
+ "Φ=5.4126 \n",
+ "Rx \n",
+ "Φ=6.179596 \n",
+ "Rx \n",
+ "Φ=2.245271 \n",
+ "Rx \n",
+ "Φ=0.119653 \n",
+ "Rx \n",
+ "Φ=5.410094 \n",
+ "Rx \n",
+ "Φ=0.364294 \n",
+ "Rx \n",
+ "Φ=2.32477 \n",
+ "Rx \n",
+ "Φ=0.115685 \n",
+ "Rx \n",
+ "Φ=5.820551 \n",
+ "Rx \n",
+ "Φ=0.658469 \n",
+ "Rx \n",
+ "Φ=5.061794 \n",
+ "Rx \n",
+ "Φ=0.146824 \n",
+ "Rx \n",
+ "Φ=1.157406 \n",
+ "Rx \n",
+ "Φ=6.028882 \n",
+ "Rx \n",
+ "Φ=6.088221 \n",
+ "Rx \n",
+ "Φ=0.2508 \n",
+ "Rx \n",
+ "Φ=1.507113 \n",
+ "Rx \n",
+ "Φ=5.873386 \n",
+ "Rx \n",
+ "Φ=0.545039 \n",
+ "Rx \n",
+ "Φ=0.204777 \n",
+ "Rx \n",
+ "Φ=1.550301 \n",
+ "Rx \n",
+ "Φ=0.492242 \n",
+ "Rx \n",
+ "Φ=3.208549 \n",
+ "Rx \n",
+ "Φ=0.337491 \n",
+ "Rx \n",
+ "Φ=3.999661 \n",
+ "Rx \n",
+ "Φ=6.059913 \n",
+ "Rx \n",
+ "Φ=1.27028 \n",
+ "Rx \n",
+ "Φ=0.285179 \n",
+ "Rx \n",
+ "Φ=6.090746 \n",
+ "Rx \n",
+ "Φ=5.859703 \n",
+ "Rx \n",
+ "Φ=0.131459 \n",
+ "Rx \n",
+ "Φ=0.258526 \n",
+ "Rx \n",
+ "Φ=0.70877 \n",
+ "Rx \n",
+ "Φ=6.19807 \n",
+ "Rx \n",
+ "Φ=3.408037 \n",
+ "Rx \n",
+ "Φ=0.732479 \n",
+ "Rx \n",
+ "Φ=0.761141 \n",
+ "Rx \n",
+ "Φ=0.712578 \n",
+ "Rx \n",
+ "Φ=4.74964 \n",
+ "Rx \n",
+ "Φ=0.615588 \n",
+ "Rx \n",
+ "Φ=1.301523 \n",
+ "Rx \n",
+ "Φ=0.606444 \n",
+ "Rx \n",
+ "Φ=4.946618 \n",
+ "Rx \n",
+ "Φ=5.760674 \n",
+ "Rx \n",
+ "Φ=6.101557 \n",
+ "Rx \n",
+ "Φ=5.589367 \n",
+ "Rx \n",
+ "Φ=4.40822 \n",
+ "Rx \n",
+ "Φ=0.73584 \n",
+ "Rx \n",
+ "Φ=4.587297 \n",
+ "Rx \n",
+ "Φ=5.491525 \n",
+ "Rx \n",
+ "Φ=3.509705 \n",
+ "Rx \n",
+ "Φ=1.18072 \n",
+ "Rx \n",
+ "Φ=4.701663 \n",
+ "Rx \n",
+ "Φ=5.650938 \n",
+ "Rx \n",
+ "Φ=3.622361 \n",
+ "Rx \n",
+ "Φ=4.877856 \n",
+ "Rx \n",
+ "Φ=3.947641 \n",
+ "Rx \n",
+ "Φ=0.694987 \n",
+ "Rx \n",
+ "Φ=2.191971 \n",
+ "Rx \n",
+ "Φ=1.107758 \n",
+ "Rx \n",
+ "Φ=2.035649 \n",
+ "Rx \n",
+ "Φ=0.126832 \n",
+ "Rx \n",
+ "Φ=0.521166 \n",
+ "Rx \n",
+ "Φ=5.047772 \n",
+ "Rx \n",
+ "Φ=4.720426 \n",
+ "Rx \n",
+ "Φ=5.493048 \n",
+ "Rx \n",
+ "Φ=3.582195 \n",
+ "Rx \n",
+ "Φ=0.162421 \n",
+ "Rx \n",
+ "Φ=1.003719 \n",
+ "Rx \n",
+ "Φ=6.065146 \n",
+ "Rx \n",
+ "Φ=0.837476 \n",
+ "Rx \n",
+ "Φ=0.218509 \n",
+ "Rx \n",
+ "Φ=6.173287 \n",
+ "Rx \n",
+ "Φ=5.836189 \n",
+ "Rx \n",
+ "Φ=4.332717 \n",
+ "Rx \n",
+ "Φ=6.053965 \n",
+ "Rx \n",
+ "Φ=4.517165 \n",
+ "Rx \n",
+ "Φ=0.132213 \n",
+ "Rx \n",
+ "Φ=1.621228 \n",
+ "Rx \n",
+ "Φ=0.458273 \n",
+ "Rx \n",
+ "Φ=0.311982 \n",
+ "Rx \n",
+ "Φ=0.085786 \n",
+ "Rx \n",
+ "Φ=4.554201 \n",
+ "Rx \n",
+ "Φ=6.094512 \n",
+ "Rx \n",
+ "Φ=6.201828 \n",
+ "Rx \n",
+ "Φ=6.014937 \n",
+ "Rx \n",
+ "Φ=2.06864 \n",
+ "Rx \n",
+ "Φ=5.933899 \n",
+ "Rx \n",
+ "Φ=1.862205 \n",
+ "Rx \n",
+ "Φ=0.138125 \n",
+ "Rx \n",
+ "Φ=4.153905 \n",
+ "Rx \n",
+ "Φ=5.869367 \n",
+ "Rx \n",
+ "Φ=5.101946 \n",
+ "Rx \n",
+ "Φ=0.304592 \n",
+ "Rx \n",
+ "Φ=1.314099 \n",
+ "Rx \n",
+ "Φ=6.012468 \n",
+ "Rx \n",
+ "Φ=2.254877 \n",
+ "Rx \n",
+ "Φ=0.231608 \n",
+ "Rx \n",
+ "Φ=1.626881 \n",
+ "Rx \n",
+ "Φ=0.627418 \n",
+ "Rx \n",
+ "Φ=1.274111 \n",
+ "Rx \n",
+ "Φ=5.825515 \n",
+ "Rx \n",
+ "Φ=2.400994 \n",
+ "Rx \n",
+ "Φ=0.430971 \n",
+ "Rx \n",
+ "Φ=3.342408 \n",
+ "Rx \n",
+ "Φ=5.713627 \n",
+ "Rx \n",
+ "Φ=1.813967 \n",
+ "Rx \n",
+ "Φ=5.994643 \n",
+ "Rx \n",
+ "Φ=5.890212 \n",
+ "Rx \n",
+ "Φ=0.326989 \n",
+ "Rx \n",
+ "Φ=0.481463 \n",
+ "Rx \n",
+ "Φ=5.57542 \n",
+ "Rx \n",
+ "Φ=2.617663 \n",
+ "Rx \n",
+ "Φ=5.880952 \n",
+ "Rx \n",
+ "Φ=5.815703 \n",
+ "Rx \n",
+ "Φ=5.891495 \n",
+ "Rx \n",
+ "Φ=5.631538 \n",
+ "Rx \n",
+ "Φ=6.270599 \n",
+ "Rx \n",
+ "Φ=1.827854 \n",
+ "Rx \n",
+ "Φ=0.366965 \n",
+ "Rx \n",
+ "Φ=5.569699 \n",
+ "Rx \n",
+ "Φ=0.130581 \n",
+ "Rx \n",
+ "Φ=3.546996 \n",
+ "Rx \n",
+ "Φ=0.31473 \n",
+ "Rx \n",
+ "Φ=2.297375 \n",
+ "Rx \n",
+ "Φ=0.339019 \n",
+ "Rx \n",
+ "Φ=3.604972 \n",
+ "Rx \n",
+ "Φ=6.030981 \n",
+ "Rx \n",
+ "Φ=5.778648 \n",
+ "Rx \n",
+ "Φ=6.008995 \n",
+ "Rx \n",
+ "Φ=2.16726 \n",
+ "Rx \n",
+ "Φ=6.16478 \n",
+ "Rx \n",
+ "Φ=3.956988 \n",
+ "Rx \n",
+ "Φ=0.268638 \n",
+ "Rx \n",
+ "Φ=0.665276 \n",
+ "Rx \n",
+ "Φ=0.669966 \n",
+ "Rx \n",
+ "Φ=4.192999 \n",
+ "Rx \n",
+ "Φ=5.74023 \n",
+ "Rx \n",
+ "Φ=5.454725 \n",
+ "Rx \n",
+ "Φ=5.729078 \n",
+ "Rx \n",
+ "Φ=5.799481 \n",
+ "Rx \n",
+ "Φ=5.531254 \n",
+ "Rx \n",
+ "Φ=4.632219 \n",
+ "Rx \n",
+ "Φ=0.541941 \n",
+ "Rx \n",
+ "Φ=5.070309 \n",
+ "Rx \n",
+ "Φ=5.877512 \n",
+ "Rx \n",
+ "Φ=6.1767 \n",
+ "Rx \n",
+ "Φ=0.817023 \n",
+ "Rx \n",
+ "Φ=3.753839 \n",
+ "Rx \n",
+ "Φ=0.490691 \n",
+ "Rx \n",
+ "Φ=5.951252 \n",
+ "Rx \n",
+ "Φ=0.961903 \n",
+ "Rx \n",
+ "Φ=4.512765 \n",
+ "Rx \n",
+ "Φ=5.855057 \n",
+ "Rx \n",
+ "Φ=0.11564 \n",
+ "Rx \n",
+ "Φ=0.613379 \n",
+ "Rx \n",
+ "Φ=0.013004 \n",
+ "Rx \n",
+ "Φ=1.105931 \n",
+ "Rx \n",
+ "Φ=0.626865 \n",
+ "Rx \n",
+ "Φ=4.436323 \n",
+ "Rx \n",
+ "Φ=3.234332 \n",
+ "Rx \n",
+ "Φ=0.295284 \n",
+ "Rx \n",
+ "Φ=4.386581 \n",
+ "Rx \n",
+ "Φ=0.079432 \n",
+ "Rx \n",
+ "Φ=3.531949 \n",
+ "Rx \n",
+ "Φ=0.108071 \n",
+ "Rx \n",
+ "Φ=2.714878 \n",
+ "Rx \n",
+ "Φ=6.183517 \n",
+ "Rx \n",
+ "Φ=2.665742 \n",
+ "Rx \n",
+ "Φ=0.298651 \n",
+ "Rx \n",
+ "Φ=2.474072 \n",
+ "Rx \n",
+ "Φ=6.036388 \n",
+ "Rx \n",
+ "Φ=1.577867 \n",
+ "Rx \n",
+ "Φ=0.157796 \n",
+ "Rx \n",
+ "Φ=0.150885 \n",
+ "Rx \n",
+ "Φ=0.196465 \n",
+ "Rx \n",
+ "Φ=3.253726 \n",
+ "Rx \n",
+ "Φ=6.048131 \n",
+ "Rx \n",
+ "Φ=4.088904 \n",
+ "Rx \n",
+ "Φ=0.290019 \n",
+ "Rx \n",
+ "Φ=2.350641 \n",
+ "Rx \n",
+ "Φ=5.964232 \n",
+ "Rx \n",
+ "Φ=0.664703 \n",
+ "Rx \n",
+ "Φ=5.742931 \n",
+ "Rx \n",
+ "Φ=2.293713 \n",
+ "Rx \n",
+ "Φ=5.888568 \n",
+ "Rx \n",
+ "Φ=3.071001 \n",
+ "Rx \n",
+ "Φ=5.9161 \n",
+ "Rx \n",
+ "Φ=4.283213 \n",
+ "Rx \n",
+ "Φ=0.512223 \n",
+ "Rx \n",
+ "Φ=3.490187 \n",
+ "Rx \n",
+ "Φ=5.795713 \n",
+ "Rx \n",
+ "Φ=0.929748 \n",
+ "Rx \n",
+ "Φ=0.256044 \n",
+ "Rx \n",
+ "Φ=5.641796 \n",
+ "Rx \n",
+ "Φ=0.660948 \n",
+ "Rx \n",
+ "Φ=2.448343 \n",
+ "Rx \n",
+ "Φ=0.441725 \n",
+ "Rx \n",
+ "Φ=3.733703 \n",
+ "Rx \n",
+ "Φ=0.04804 \n",
+ "Rx \n",
+ "Φ=4.107933 \n",
+ "Rx \n",
+ "Φ=6.161181 \n",
+ "Rx \n",
+ "Φ=6.215758 \n",
+ "Rx \n",
+ "Φ=0.681208 \n",
+ "Rx \n",
+ "Φ=1.676056 \n",
+ "Rx \n",
+ "Φ=6.113404 \n",
+ "Rx \n",
+ "Φ=2.837648 \n",
+ "Rx \n",
+ "Φ=0.282249 \n",
+ "Rx \n",
+ "Φ=0.251458 \n",
+ "Rx \n",
+ "Φ=0.448664 \n",
+ "Rx \n",
+ "Φ=1.01532 \n",
+ "Rx \n",
+ "Φ=0.313728 \n",
+ "Rx \n",
+ "Φ=3.081683 \n",
+ "Rx \n",
+ "Φ=0.576702 \n",
+ "Rx \n",
+ "Φ=2.176287 \n",
+ "Rx \n",
+ "Φ=5.660395 \n",
+ "Rx \n",
+ "Φ=2.069124 \n",
+ "Rx \n",
+ "Φ=0.275689 \n",
+ "Rx \n",
+ "Φ=0.777078 \n",
+ "Rx \n",
+ "Φ=5.866553 \n",
+ "Rx \n",
+ "Φ=1.103325 \n",
+ "Rx \n",
+ "Φ=0.359967 \n",
+ "Rx \n",
+ "Φ=3.725888 \n",
+ "Rx \n",
+ "Φ=5.91451 \n",
+ "Rx \n",
+ "Φ=5.145723 \n",
+ "Rx \n",
+ "Φ=6.119515 \n",
+ "Rx \n",
+ "Φ=0.782873 \n",
+ "Rx \n",
+ "Φ=6.036207 \n",
+ "Rx \n",
+ "Φ=0.51599 \n",
+ "Rx \n",
+ "Φ=0.216422 \n",
+ "Rx \n",
+ "Φ=4.33287 \n",
+ "Rx \n",
+ "Φ=0.416423 \n",
+ "Rx \n",
+ "Φ=2.981597 \n",
+ "Rx \n",
+ "Φ=5.224636 \n",
+ "Rx \n",
+ "Φ=2.290948 \n",
+ "Rx \n",
+ "Φ=5.818349 \n",
+ "Rx \n",
+ "Φ=0.248294 \n",
+ "Rx \n",
+ "Φ=5.68085 \n",
+ "Rx \n",
+ "Φ=4.256007 \n",
+ "Rx \n",
+ "Φ=5.383665 \n",
+ "Rx \n",
+ "Φ=0.00703 \n",
+ "Rx \n",
+ "Φ=6.138224 \n",
+ "Rx \n",
+ "Φ=2.133167 \n",
+ "Rx \n",
+ "Φ=1.631213 \n",
+ "Rx \n",
+ "Φ=1.942505 \n",
+ "Rx \n",
+ "Φ=0.519012 \n",
+ "Rx \n",
+ "Φ=4.873186 \n",
+ "Rx \n",
+ "Φ=0.153335 \n",
+ "Rx \n",
+ "Φ=5.334167 \n",
+ "Rx \n",
+ "Φ=5.837911 \n",
+ "Rx \n",
+ "Φ=5.658965 \n",
+ "Rx \n",
+ "Φ=1.160114 \n",
+ "Rx \n",
+ "Φ=2.936409 \n",
+ "Rx \n",
+ "Φ=2.203706 \n",
+ "Rx \n",
+ "Φ=4.737075 \n",
+ "Rx \n",
+ "Φ=1.307026 \n",
+ "Rx \n",
+ "Φ=0.653777 \n",
+ "Rx \n",
+ "Φ=6.058759 \n",
+ "Rx \n",
+ "Φ=5.062311 \n",
+ "Rx \n",
+ "Φ=0.355901 \n",
+ "Rx \n",
+ "Φ=3.401629 \n",
+ "Rx \n",
+ "Φ=6.251724 \n",
+ "Rx \n",
+ "Φ=2.74012 \n",
+ "Rx \n",
+ "Φ=0.292372 \n",
+ "Rx \n",
+ "Φ=1.535557 \n",
+ "Rx \n",
+ "Φ=0.262077 \n",
+ "Rx \n",
+ "Φ=4.578105 \n",
+ "Rx \n",
+ "Φ=6.178892 \n",
+ "Rx \n",
+ "Φ=1.730285 \n",
+ "Rx \n",
+ "Φ=5.721272 \n",
+ "Rx \n",
+ "Φ=5.009667 \n",
+ "Rx \n",
+ "Φ=0.357966 \n",
+ "Rx \n",
+ "Φ=4.807696 \n",
+ "Rx \n",
+ "Φ=0.190853 \n",
+ "Rx \n",
+ "Φ=1.184309 \n",
+ "Rx \n",
+ "Φ=6.010962 \n",
+ "Rx \n",
+ "Φ=2.44047 \n",
+ "Rx \n",
+ "Φ=0.260959 \n",
+ "Rx \n",
+ "Φ=6.10158 \n",
+ "Rx \n",
+ "Φ=5.866884 \n",
+ "Rx \n",
+ "Φ=5.975409 \n",
+ "Rx \n",
+ "Φ=0.146084 \n",
+ "Rx \n",
+ "Φ=1.698103 \n",
+ "Rx \n",
+ "Φ=0.241463 \n",
+ "Rx \n",
+ "Φ=5.535214 \n",
+ "Rx \n",
+ "Φ=5.951623 \n",
+ "Rx \n",
+ "Φ=2.195168 \n",
+ "Rx \n",
+ "Φ=5.821353 \n",
+ "Rx \n",
+ "Φ=6.188364 \n",
+ "Rx \n",
+ "Φ=0.460648 \n",
+ "Rx \n",
+ "Φ=2.571079 \n",
+ "Rx \n",
+ "Φ=0.246455 \n",
+ "Rx \n",
+ "Φ=2.562677 \n",
+ "Rx \n",
+ "Φ=0.194738 \n",
+ "Rx \n",
+ "Φ=1.162431 \n",
+ "Rx \n",
+ "Φ=5.886538 \n",
+ "Rx \n",
+ "Φ=2.281323 \n",
+ "Rx \n",
+ "Φ=0.537467 \n",
+ "Rx \n",
+ "Φ=0.060619 \n",
+ "Rx \n",
+ "Φ=6.062276 \n",
+ "Rx \n",
+ "Φ=0.519448 \n",
+ "Rx \n",
+ "Φ=0.25025 \n",
+ "Rx \n",
+ "Φ=6.040712 \n",
+ "Rx \n",
+ "Φ=5.312787 \n",
+ "Rx \n",
+ "Φ=4.472767 \n",
+ "Rx \n",
+ "Φ=0.44788 \n",
+ "Rx \n",
+ "Φ=0.463987 \n",
+ "Rx \n",
+ "Φ=5.556634 \n",
+ "Rx \n",
+ "Φ=3.636389 \n",
+ "Rx \n",
+ "Φ=0.18791 \n",
+ "Rx \n",
+ "Φ=5.361322 \n",
+ "Rx \n",
+ "Φ=5.955599 \n",
+ "Rx \n",
+ "Φ=4.178693 \n",
+ "Rx \n",
+ "Φ=6.184258 \n",
+ "Rx \n",
+ "Φ=4.19822 \n",
+ "Rx \n",
+ "Φ=5.912175 \n",
+ "Rx \n",
+ "Φ=3.331247 \n",
+ "Rx \n",
+ "Φ=5.73284 \n",
+ "Rx \n",
+ "Φ=5.750711 \n",
+ "Rx \n",
+ "Φ=5.434995 \n",
+ "Rx \n",
+ "Φ=1.720916 \n",
+ "Rx \n",
+ "Φ=5.91233 \n",
+ "Rx \n",
+ "Φ=3.813085 \n",
+ "Rx \n",
+ "Φ=0.565594 \n",
+ "Rx \n",
+ "Φ=0.947977 \n",
+ "Rx \n",
+ "Φ=1.016263 \n",
+ "Rx \n",
+ "Φ=2.117669 \n",
+ "Rx \n",
+ "Φ=6.009643 \n",
+ "Rx \n",
+ "Φ=5.382674 \n",
+ "Rx \n",
+ "Φ=5.617921 \n",
+ "Rx \n",
+ "Φ=3.755006 \n",
+ "Rx \n",
+ "Φ=0.381813 \n",
+ "Rx \n",
+ "Φ=5.062082 \n",
+ "Rx \n",
+ "Φ=0.66878 \n",
+ "Rx \n",
+ "Φ=3.469229 \n",
+ "Rx \n",
+ "Φ=0.694946 \n",
+ "Rx \n",
+ "Φ=1.962017 \n",
+ "Rx \n",
+ "Φ=0.160134 \n",
+ "Rx \n",
+ "Φ=5.852984 \n",
+ "Rx \n",
+ "Φ=0.404887 \n",
+ "Rx \n",
+ "Φ=0.494495 \n",
+ "Rx \n",
+ "Φ=0.414969 \n",
+ "Rx \n",
+ "Φ=6.064892 \n",
+ "Rx \n",
+ "Φ=0.874305 \n",
+ "Rx \n",
+ "Φ=2.785071 \n",
+ "Rx \n",
+ "Φ=1.207239 \n",
+ "Rx \n",
+ "Φ=6.237648 \n",
+ "Rx \n",
+ "Φ=0.774401 \n",
+ "Rx \n",
+ "Φ=2.0201 \n",
+ "Rx \n",
+ "Φ=0.550799 \n",
+ "Rx \n",
+ "Φ=6.127333 \n",
+ "Rx \n",
+ "Φ=0.666735 \n",
+ "Rx \n",
+ "Φ=2.327142 \n",
+ "Rx \n",
+ "Φ=4.464024 \n",
+ "Rx \n",
+ "Φ=3.719931 \n",
+ "Rx \n",
+ "Φ=0.265128 \n",
+ "Rx \n",
+ "Φ=0.652684 \n",
+ "Rx \n",
+ "Φ=0.189288 \n",
+ "Rx \n",
+ "Φ=2.113852 \n",
+ "Rx \n",
+ "Φ=0.221036 \n",
+ "Rx \n",
+ "Φ=5.366942 \n",
+ "Rx \n",
+ "Φ=0.329384 \n",
+ "Rx \n",
+ "Φ=4.726025 \n",
+ "Rx \n",
+ "Φ=5.990019 \n",
+ "Rx \n",
+ "Φ=3.024746 \n",
+ "Rx \n",
+ "Φ=6.054241 \n",
+ "Rx \n",
+ "Φ=4.195718 \n",
+ "Rx \n",
+ "Φ=0.350289 \n",
+ "Rx \n",
+ "Φ=3.463748 \n",
+ "Rx \n",
+ "Φ=0.692485 \n",
+ "Rx \n",
+ "Φ=3.805946 \n",
+ "Rx \n",
+ "Φ=0.146977 \n",
+ "Rx \n",
+ "Φ=4.187379 \n",
+ "Rx \n",
+ "Φ=6.067376 \n",
+ "Rx \n",
+ "Φ=4.535443 \n",
+ "Rx \n",
+ "Φ=0.262366 \n",
+ "Rx \n",
+ "Φ=3.055602 \n",
+ "Rx \n",
+ "Φ=5.999386 \n",
+ "Rx \n",
+ "Φ=2.325433 \n",
+ "Rx \n",
+ "Φ=0.211872 \n",
+ "Rx \n",
+ "Φ=2.68304 \n",
+ "Rx \n",
+ "Φ=0.435953 \n",
+ "Rx \n",
+ "Φ=3.111762 \n",
+ "Rx \n",
+ "Φ=6.062285 \n",
+ "Rx \n",
+ "Φ=4.895262 \n",
+ "Rx \n",
+ "Φ=6.037255 \n",
+ "Rx \n",
+ "Φ=4.019545 \n",
+ "Rx \n",
+ "Φ=0.2742 \n",
+ "Rx \n",
+ "Φ=1.596215 \n",
+ "Rx \n",
+ "Φ=0.302432 \n",
+ "Rx \n",
+ "Φ=2.746479 \n",
+ "Rx \n",
+ "Φ=0.429487 \n",
+ "Rx \n",
+ "Φ=1.548486 \n",
+ "Rx \n",
+ "Φ=6.054801 \n",
+ "Rx \n",
+ "Φ=1.780688 \n",
+ "Rx \n",
+ "Φ=0.458075 \n",
+ "Rx \n",
+ "Φ=0.911576 \n",
+ "Rx \n",
+ "Φ=0.362508 \n",
+ "Rx \n",
+ "Φ=4.852174 \n",
+ "Rx \n",
+ "Φ=0.547356 \n",
+ "Rx \n",
+ "Φ=1.762568 \n",
+ "Rx \n",
+ "Φ=6.192482 \n",
+ "Rx \n",
+ "Φ=4.592862 \n",
+ "Rx \n",
+ "Φ=0.27416 \n",
+ "Rx \n",
+ "Φ=4.107857 \n",
+ "Rx \n",
+ "Φ=5.989564 \n",
+ "Rx \n",
+ "Φ=0.679746 \n",
+ "Rx \n",
+ "Φ=0.37256 \n",
+ "Rx \n",
+ "Φ=2.562888 \n",
+ "Rx \n",
+ "Φ=6.024639 \n",
+ "Rx \n",
+ "Φ=4.59135 \n",
+ "Rx \n",
+ "Φ=5.773185 \n",
+ "Rx \n",
+ "Φ=3.339514 \n",
+ "Rx \n",
+ "Φ=6.183684 \n",
+ "Rx \n",
+ "Φ=3.225851 \n",
+ "Rx \n",
+ "Φ=5.494985 \n",
+ "Rx \n",
+ "Φ=5.777556 \n",
+ "Rx \n",
+ "Φ=0.713991 \n",
+ "Rx \n",
+ "Φ=4.080569 \n",
+ "Rx \n",
+ "Φ=5.980554 \n",
+ "Rx \n",
+ "Φ=2.391672 \n",
+ "Rx \n",
+ "Φ=6.156033 \n",
+ "Rx \n",
+ "Φ=4.552774 \n",
+ "Rx \n",
+ "Φ=0.214618 \n",
+ "Rx \n",
+ "Φ=5.046047 \n",
+ "Rx \n",
+ "Φ=0.446677 \n",
+ "Rx \n",
+ "Φ=2.710078 \n",
+ "Rx \n",
+ "Φ=5.823893 \n",
+ "Rx \n",
+ "Φ=2.474993 \n",
+ "Rx \n",
+ "Φ=5.987081 \n",
+ "Rx \n",
+ "Φ=1.709615 \n",
+ "Rx \n",
+ "Φ=5.828774 \n",
+ "Rx \n",
+ "Φ=3.001315 \n",
+ "Rx \n",
+ "Φ=5.513979 \n",
+ "Rx \n",
+ "Φ=2.793931 \n",
+ "Rx \n",
+ "Φ=5.138604 \n",
+ "Rx \n",
+ "Φ=3.574582 \n",
+ "Rx \n",
+ "Φ=0.421353 \n",
+ "Rx \n",
+ "Φ=2.252219 \n",
+ "Rx \n",
+ "Φ=5.423521 \n",
+ "Rx \n",
+ "Φ=4.044005 \n",
+ "Rx \n",
+ "Φ=6.080467 \n",
+ "Rx \n",
+ "Φ=3.847092 \n",
+ "Rx \n",
+ "Φ=5.517252 \n",
+ "Rx \n",
+ "Φ=1.457691 \n",
+ "Rx \n",
+ "Φ=5.574929 \n",
+ "Rx \n",
+ "Φ=2.85439 \n",
+ "Rx \n",
+ "Φ=4.961881 \n",
+ "Rx \n",
+ "Φ=1.646042 \n",
+ "Rx \n",
+ "Φ=0.703594 \n",
+ "Rx \n",
+ "Φ=4.39911 \n",
+ "Rx \n",
+ "Φ=4.809311 \n",
+ "Rx \n",
+ "Φ=0.970562 \n",
+ "Rx \n",
+ "Φ=4.049869 \n",
+ "Rx \n",
+ "Φ=1.752489 \n",
+ "Rx \n",
+ "Φ=0.127363 \n",
+ "Rx \n",
+ "Φ=4.222764 \n",
+ "Rx \n",
+ "Φ=0.27229 \n",
+ "Rx \n",
+ "Φ=0.063175 \n",
+ "Rx \n",
+ "Φ=6.214968 \n",
+ "Rx \n",
+ "Φ=4.771687 \n",
+ "Rx \n",
+ "Φ=5.960146 \n",
+ "Rx \n",
+ "Φ=1.701639 \n",
+ "Rx \n",
+ "Φ=6.077334 \n",
+ "Rx \n",
+ "Φ=2.105757 \n",
+ "Rx \n",
+ "Φ=5.862965 \n",
+ "Rx \n",
+ "Φ=4.201507 \n",
+ "Rx \n",
+ "Φ=6.064734 \n",
+ "Rx \n",
+ "Φ=4.657985 \n",
+ "Rx \n",
+ "Φ=0.31683 \n",
+ "Rx \n",
+ "Φ=1.00219 \n",
+ "Rx \n",
+ "Φ=5.957813 \n",
+ "Rx \n",
+ "Φ=0.129557 \n",
+ "Rx \n",
+ "Φ=5.921576 \n",
+ "Rx \n",
+ "Φ=4.769161 \n",
+ "Rx \n",
+ "Φ=6.141327 \n",
+ "Rx \n",
+ "Φ=1.731127 \n",
+ "Rx \n",
+ "Φ=0.326771 \n",
+ "Rx \n",
+ "Φ=5.078205 \n",
+ "Rx \n",
+ "Φ=5.692786 \n",
+ "Rx \n",
+ "Φ=2.124067 \n",
+ "Rx \n",
+ "Φ=5.737146 \n",
+ "Rx \n",
+ "Φ=6.204912 \n",
+ "Rx \n",
+ "Φ=6.123497 \n",
+ "Rx \n",
+ "Φ=4.113671 \n",
+ "Rx \n",
+ "Φ=0.225579 \n",
+ "Rx \n",
+ "Φ=3.858119 \n",
+ "Rx \n",
+ "Φ=0.291201 \n",
+ "Rx \n",
+ "Φ=5.528163 \n",
+ "Rx \n",
+ "Φ=0.543354 \n",
+ "Rx \n",
+ "Φ=2.734172 \n",
+ "Rx \n",
+ "Φ=5.921973 \n",
+ "Rx \n",
+ "Φ=5.566403 \n",
+ "Rx \n",
+ "Φ=0.28329 \n",
+ "Rx \n",
+ "Φ=2.29003 \n",
+ "Rx \n",
+ "Φ=6.124091 \n",
+ "Rx \n",
+ "Φ=4.006831 \n",
+ "Rx \n",
+ "Φ=6.077304 \n",
+ "Rx \n",
+ "Φ=4.394518 \n",
+ "Rx \n",
+ "Φ=0.236374 \n",
+ "Rx \n",
+ "Φ=4.657109 \n",
+ "Rx \n",
+ "Φ=6.208228 \n",
+ "Rx \n",
+ "Φ=1.662527 \n",
+ "Rx \n",
+ "Φ=5.588201 \n",
+ "Rx \n",
+ "Φ=3.920868 \n",
+ "Rx \n",
+ "Φ=0.165392 \n",
+ "Rx \n",
+ "Φ=4.071781 \n",
+ "Rx \n",
+ "Φ=0.39917 \n",
+ "Rx \n",
+ "Φ=1.183841 \n",
+ "Rx \n",
+ "Φ=5.978169 \n",
+ "Rx \n",
+ "Φ=4.280514 \n",
+ "Rx \n",
+ "Φ=5.697773 \n",
+ "Rx \n",
+ "Φ=0.840433 \n",
+ "Rx \n",
+ "Φ=0.279331 \n",
+ "Rx \n",
+ "Φ=3.700827 \n",
+ "Rx \n",
+ "Φ=5.973919 \n",
+ "Rx \n",
+ "Φ=4.428324 \n",
+ "Rx \n",
+ "Φ=5.973433 \n",
+ "Rx \n",
+ "Φ=5.77216 \n",
+ "Rx \n",
+ "Φ=5.982376 \n",
+ "Rx \n",
+ "Φ=1.072738 \n",
+ "Rx \n",
+ "Φ=5.825751 \n",
+ "Rx \n",
+ "Φ=2.079809 \n",
+ "Rx \n",
+ "Φ=0.456515 \n",
+ "Rx \n",
+ "Φ=5.656585 \n",
+ "Rx \n",
+ "Φ=0.459477 \n",
+ "Rx \n",
+ "Φ=4.883624 \n",
+ "Rx \n",
+ "Φ=0.44024 \n",
+ "Rx \n",
+ "Φ=4.198558 \n",
+ "Rx \n",
+ "Φ=0.420157 \n",
+ "Rx \n",
+ "Φ=1.155791 \n",
+ "Rx \n",
+ "Φ=0.519496 \n",
+ "Rx \n",
+ "Φ=1.635686 \n",
+ "Rx \n",
+ "Φ=0.469166 \n",
+ "Rx \n",
+ "Φ=5.494996 \n",
+ "Rx \n",
+ "Φ=0.380148 \n",
+ "Rx \n",
+ "Φ=3.677112 \n",
+ "Rx \n",
+ "Φ=0.229521 \n",
+ "Rx \n",
+ "Φ=0.206341 \n",
+ "Rx \n",
+ "Φ=5.628509 \n",
+ "Rx \n",
+ "Φ=2.87739 \n",
+ "Rx \n",
+ "Φ=5.909078 \n",
+ "Rx \n",
+ "Φ=4.922577 \n",
+ "Rx \n",
+ "Φ=0.666975 \n",
+ "Rx \n",
+ "Φ=3.871048 \n",
+ "Rx \n",
+ "Φ=1.101457 \n",
+ "Rx \n",
+ "Φ=5.358011 \n",
+ "Rx \n",
+ "Φ=5.406568 \n",
+ "Rx \n",
+ "Φ=0.905391 \n",
+ "Rx \n",
+ "Φ=4.891736 \n",
+ "Rx \n",
+ "Φ=3.998409 \n",
+ "Rx \n",
+ "Φ=1.153574 \n",
+ "Rx \n",
+ "Φ=5.095702 \n",
+ "Rx \n",
+ "Φ=0.761975 \n",
+ "Rx \n",
+ "Φ=4.219458 \n",
+ "Rx \n",
+ "Φ=4.583834 \n",
+ "Rx \n",
+ "Φ=1.990631 \n",
+ "Rx \n",
+ "Φ=0.25607 \n",
+ "Rx \n",
+ "Φ=2.818999 \n",
+ "Rx \n",
+ "Φ=6.159778 \n",
+ "Rx \n",
+ "Φ=4.546837 \n",
+ "Rx \n",
+ "Φ=0.226499 \n",
+ "Rx \n",
+ "Φ=4.645356 \n",
+ "Rx \n",
+ "Φ=6.083485 \n",
+ "Rx \n",
+ "Φ=1.789975 \n",
+ "Rx \n",
+ "Φ=0.338415 \n",
+ "Rx \n",
+ "Φ=3.742897 \n",
+ "Rx \n",
+ "Φ=6.03936 \n",
+ "Rx \n",
+ "Φ=0.107987 \n",
+ "Rx \n",
+ "Φ=0.162662 \n",
+ "Rx \n",
+ "Φ=1.416164 \n",
+ "Rx \n",
+ "Φ=6.014757 \n",
+ "Rx \n",
+ "Φ=1.880668 \n",
+ "Rx \n",
+ "Φ=6.064396 \n",
+ "Rx \n",
+ "Φ=5.421092 \n",
+ "Rx \n",
+ "Φ=6.201501 \n",
+ "Rx \n",
+ "Φ=1.618917 \n",
+ "Rx \n",
+ "Φ=0.338984 \n",
+ "Rx \n",
+ "Φ=0.792278 \n",
+ "Rx \n",
+ "Φ=0.354899 \n",
+ "Rx \n",
+ "Φ=3.800444 \n",
+ "Rx \n",
+ "Φ=0.185834 \n",
+ "Rx \n",
+ "Φ=2.957859 \n",
+ "Rx \n",
+ "Φ=0.612619 \n",
+ "Rx \n",
+ "Φ=4.947029 \n",
+ "Rx \n",
+ "Φ=0.119451 \n",
+ "Rx \n",
+ "Φ=0.050866 \n",
+ "Rx \n",
+ "Φ=6.070342 \n",
+ "Rx \n",
+ "Φ=5.281795 \n",
+ "Rx \n",
+ "Φ=6.230552 \n",
+ "Rx \n",
+ "Φ=3.12458 \n",
+ "Rx \n",
+ "Φ=6.065243 \n",
+ "Rx \n",
+ "Φ=1.436978 \n",
+ "Rx \n",
+ "Φ=0.221498 \n",
+ "Rx \n",
+ "Φ=1.211547 \n",
+ "Rx \n",
+ "Φ=0.304958 \n",
+ "Rx \n",
+ "Φ=0.323891 \n",
+ "Rx \n",
+ "Φ=6.049812 \n",
+ "Rx \n",
+ "Φ=1.580948 \n",
+ "Rx \n",
+ "Φ=5.918712 \n",
+ "Rx \n",
+ "Φ=0.623408 \n",
+ "Rx \n",
+ "Φ=5.874666 \n",
+ "Rx \n",
+ "Φ=1.700978 \n",
+ "Rx \n",
+ "Φ=6.162213 \n",
+ "Rx \n",
+ "Φ=1.840105 \n",
+ "Rx \n",
+ "Φ=0.651203 \n",
+ "Rx \n",
+ "Φ=3.161817 \n",
+ "Rx \n",
+ "Φ=0.229266 \n",
+ "Rx \n",
+ "Φ=2.454585 \n",
+ "Rx \n",
+ "Φ=0.114864 \n",
+ "Rx \n",
+ "Φ=2.610071 \n",
+ "Rx \n",
+ "Φ=5.896359 \n",
+ "Rx \n",
+ "Φ=2.03368 \n",
+ "Rx \n",
+ "Φ=0.313281 \n",
+ "Rx \n",
+ "Φ=3.329098 \n",
+ "Rx \n",
+ "Φ=6.003112 \n",
+ "Rx \n",
+ "Φ=3.589951 \n",
+ "Rx \n",
+ "Φ=0.053486 \n",
+ "Rx \n",
+ "Φ=1.406513 \n",
+ "Rx \n",
+ "Φ=0.195138 \n",
+ "Rx \n",
+ "Φ=0.499282 \n",
+ "Rx \n",
+ "Φ=0.199594 \n",
+ "Rx \n",
+ "Φ=6.013594 \n",
+ "Rx \n",
+ "Φ=6.197505 \n",
+ "Rx \n",
+ "Φ=5.178348 \n",
+ "Rx \n",
+ "Φ=0.829724 \n",
+ "Rx \n",
+ "Φ=1.940626 \n",
+ "Rx \n",
+ "Φ=5.555362 \n",
+ "Rx \n",
+ "Φ=5.529786 \n",
+ "Rx \n",
+ "Φ=5.90565 \n",
+ "Rx \n",
+ "Φ=2.906796 \n",
+ "Rx \n",
+ "Φ=0.349438 \n",
+ "Rx \n",
+ "Φ=4.172592 \n",
+ "Rx \n",
+ "Φ=0.789804 \n",
+ "Rx \n",
+ "Φ=3.555134 \n",
+ "Rx \n",
+ "Φ=5.397189 \n",
+ "Rx \n",
+ "Φ=1.326806 \n",
+ "Rx \n",
+ "Φ=4.975233 \n",
+ "Rx \n",
+ "Φ=2.462955 \n",
+ "Rx \n",
+ "Φ=1.054267 \n",
+ "Rx \n",
+ "Φ=4.10888 \n",
+ "Rx \n",
+ "Φ=5.926595 \n",
+ "Rx \n",
+ "Φ=4.157172 \n",
+ "Rx \n",
+ "Φ=0.511025 \n",
+ "Rx \n",
+ "Φ=0.375345 \n",
+ "Rx \n",
+ "Φ=5.62045 \n",
+ "Rx \n",
+ "Φ=5.349547 \n",
+ "Rx \n",
+ "Φ=5.585412 \n",
+ "Rx \n",
+ "Φ=2.554103 \n",
+ "Rx \n",
+ "Φ=0.834355 \n",
+ "Rx \n",
+ "Φ=4.037928 \n",
+ "Rx \n",
+ "Φ=5.607623 \n",
+ "Rx \n",
+ "Φ=0.222675 \n",
+ "Rx \n",
+ "Φ=0.363067 \n",
+ "Rx \n",
+ "Φ=1.821679 \n",
+ "Rx \n",
+ "Φ=5.50582 \n",
+ "Rx \n",
+ "Φ=2.398446 \n",
+ "Rx \n",
+ "Φ=0.766926 \n",
+ "Rx \n",
+ "Φ=4.265431 \n",
+ "Rx \n",
+ "Φ=4.912827 \n",
+ "Rx \n",
+ "Φ=5.107995 \n",
+ "Rx \n",
+ "Φ=6.037291 \n",
+ "Rx \n",
+ "Φ=5.501519 \n",
+ "Rx \n",
+ "Φ=5.807611 \n",
+ "Rx \n",
+ "Φ=2.469681 \n",
+ "Rx \n",
+ "Φ=5.987421 \n",
+ "Rx \n",
+ "Φ=2.78626 \n",
+ "Rx \n",
+ "Φ=6.079856 \n",
+ "Rx \n",
+ "Φ=1.981683 \n",
+ "Rx \n",
+ "Φ=5.774959 \n",
+ "Rx \n",
+ "Φ=4.873218 \n",
+ "Rx \n",
+ "Φ=0.417846 \n",
+ "Rx \n",
+ "Φ=3.198579 \n",
+ "Rx \n",
+ "Φ=5.897657 \n",
+ "Rx \n",
+ "Φ=1.643114 \n",
+ "Rx \n",
+ "Φ=6.12416 \n",
+ "Rx \n",
+ "Φ=3.080919 \n",
+ "Rx \n",
+ "Φ=6.202419 \n",
+ "Rx \n",
+ "Φ=5.342802 \n",
+ "Rx \n",
+ "Φ=0.184376 \n",
+ "Rx \n",
+ "Φ=5.092326 \n",
+ "Rx \n",
+ "Φ=0.479781 \n",
+ "Rx \n",
+ "Φ=5.517746 \n",
+ "Rx \n",
+ "Φ=0.217435 \n",
+ "Rx \n",
+ "Φ=0.665357 \n",
+ "Rx \n",
+ "Φ=0.244518 \n",
+ "Rx \n",
+ "Φ=2.021682 \n",
+ "Rx \n",
+ "Φ=6.136202 \n",
+ "Rx \n",
+ "Φ=3.599725 \n",
+ "Rx \n",
+ "Φ=0.51587 \n",
+ "Rx \n",
+ "Φ=3.841605 \n",
+ "Rx \n",
+ "Φ=5.812838 \n",
+ "Rx \n",
+ "Φ=4.664006 \n",
+ "Rx \n",
+ "Φ=0.427424 \n",
+ "Rx \n",
+ "Φ=2.780703 \n",
+ "Rx \n",
+ "Φ=5.657904 \n",
+ "Rx \n",
+ "Φ=3.900151 \n",
+ "Rx \n",
+ "Φ=5.91442 \n",
+ "Rx \n",
+ "Φ=5.572031 \n",
+ "Rx \n",
+ "Φ=0.641552 \n",
+ "Rx \n",
+ "Φ=0.086878 \n",
+ "Rx \n",
+ "Φ=0.258176 \n",
+ "Rx \n",
+ "Φ=6.26366 \n",
+ "Rx \n",
+ "Φ=0.324053 \n",
+ "Rx \n",
+ "Φ=4.562908 \n",
+ "Rx \n",
+ "Φ=6.029391 \n",
+ "Rx \n",
+ "Φ=6.079197 \n",
+ "Rx \n",
+ "Φ=0.360217 \n",
+ "Rx \n",
+ "Φ=0.52373 \n",
+ "Rx \n",
+ "Φ=0.313779 \n",
+ "Rx \n",
+ "Φ=0.525344 \n",
+ "Rx \n",
+ "Φ=5.998757 \n",
+ "Rx \n",
+ "Φ=4.076823 \n",
+ "Rx \n",
+ "Φ=6.065655 \n",
+ "Rx \n",
+ "Φ=4.433683 \n",
+ "Rx \n",
+ "Φ=5.981223 \n",
+ "Rx \n",
+ "Φ=1.095506 \n",
+ "Rx \n",
+ "Φ=6.045069 \n",
+ "Rx \n",
+ "Φ=2.697857 \n",
+ "Rx \n",
+ "Φ=5.651976 \n",
+ "Rx \n",
+ "Φ=0.29989 \n",
+ "Rx \n",
+ "Φ=5.649565 \n",
+ "Rx \n",
+ "Φ=3.669148 \n",
+ "Rx \n",
+ "Φ=6.046988 \n",
+ "Rx \n",
+ "Φ=4.189992 \n",
+ "Rx \n",
+ "Φ=5.68264 \n",
+ "Rx \n",
+ "Φ=6.220498 \n",
+ "Rx \n",
+ "Φ=0.221516 \n",
+ "Rx \n",
+ "Φ=1.132767 \n",
+ "Rx \n",
+ "Φ=0.317713 \n",
+ "Rx \n",
+ "Φ=6.23467 \n",
+ "Rx \n",
+ "Φ=0.37143 \n",
+ "Rx \n",
+ "Φ=0.33836 \n",
+ "Rx \n",
+ "Φ=0.070328 \n",
+ "Rx \n",
+ "Φ=4.289274 \n",
+ "Rx \n",
+ "Φ=5.705085 \n",
+ "Rx \n",
+ "Φ=4.478133 \n",
+ "Rx \n",
+ "Φ=0.619075 \n",
+ "Rx \n",
+ "Φ=0.417085 \n",
+ "Rx \n",
+ "Φ=5.451139 \n",
+ "Rx \n",
+ "Φ=1.790547 \n",
+ "Rx \n",
+ "Φ=0.48647 \n",
+ "Rx \n",
+ "Φ=5.843937 \n",
+ "Rx \n",
+ "Φ=0.405182 \n",
+ "Rx \n",
+ "Φ=0.156341 \n",
+ "Rx \n",
+ "Φ=5.497517 \n",
+ "Rx \n",
+ "Φ=3.022746 \n",
+ "Rx \n",
+ "Φ=5.505351 \n",
+ "Rx \n",
+ "Φ=3.104732 \n",
+ "Rx \n",
+ "Φ=6.109668 \n",
+ "Rx \n",
+ "Φ=2.495843 \n",
+ "Rx \n",
+ "Φ=5.614293 \n",
+ "Rx \n",
+ "Φ=1.207482 \n",
+ "Rx \n",
+ "Φ=5.332305 \n",
+ "Rx \n",
+ "Φ=0.530818 \n",
+ "Rx \n",
+ "Φ=5.782594 \n",
+ "Rx \n",
+ "Φ=1.52175 \n",
+ "Rx \n",
+ "Φ=5.540295 \n",
+ "Rx \n",
+ "Φ=3.925669 \n",
+ "Rx \n",
+ "Φ=5.991712 \n",
+ "Rx \n",
+ "Φ=1.788207 \n",
+ "Rx \n",
+ "Φ=5.498657 \n",
+ "Rx \n",
+ "Φ=0.584122 \n",
+ "Rx \n",
+ "Φ=1.214865 \n",
+ "Rx \n",
+ "Φ=2.212583 \n",
+ "Rx \n",
+ "Φ=4.943245 \n",
+ "Rx \n",
+ "Φ=3.35976 \n",
+ "Rx \n",
+ "Φ=6.104435 \n",
+ "Rx \n",
+ "Φ=3.458388 \n",
+ "Rx \n",
+ "Φ=6.001319 \n",
+ "Rx \n",
+ "Φ=3.999689 \n",
+ "Rx \n",
+ "Φ=0.58302 \n",
+ "Rx \n",
+ "Φ=1.485994 \n",
+ "Rx \n",
+ "Φ=5.967201 \n",
+ "Rx \n",
+ "Φ=5.920485 \n",
+ "Rx \n",
+ "Φ=0.389746 \n",
+ "Rx \n",
+ "Φ=4.680787 \n",
+ "Rx \n",
+ "Φ=0.053754 \n",
+ "Rx \n",
+ "Φ=3.103164 \n",
+ "Rx \n",
+ "Φ=6.096642 \n",
+ "Rx \n",
+ "Φ=1.716865 \n",
+ "Rx \n",
+ "Φ=0.160882 \n",
+ "Rx \n",
+ "Φ=2.140311 \n",
+ "Rx \n",
+ "Φ=6.125066 \n",
+ "Rx \n",
+ "Φ=5.738908 \n",
+ "Rx \n",
+ "Φ=6.079184 \n",
+ "Rx \n",
+ "Φ=1.781887 \n",
+ "Rx \n",
+ "Φ=0.211483 \n",
+ "Rx \n",
+ "Φ=4.816013 \n",
+ "Rx \n",
+ "Φ=0.175144 \n",
+ "Rx \n",
+ "Φ=1.865505 \n",
+ "Rx \n",
+ "Φ=5.781324 \n",
+ "Rx \n",
+ "Φ=2.657285 \n",
+ "Rx \n",
+ "Φ=0.115753 \n",
+ "Rx \n",
+ "Φ=1.029926 \n",
+ "Rx \n",
+ "Φ=0.195377 \n",
+ "Rx \n",
+ "Φ=6.194511 \n",
+ "Rx \n",
+ "Φ=5.856724 \n",
+ "Rx \n",
+ "Φ=6.058065 \n",
+ "Rx \n",
+ "Φ=6.093726 \n",
+ "Rx \n",
+ "Φ=0.109518 \n",
+ "Rx \n",
+ "Φ=0.306107 \n",
+ "Rx \n",
+ "Φ=1.852109 \n",
+ "Rx \n",
+ "Φ=0.312005 \n",
+ "Rx \n",
+ "Φ=2.11218 \n",
+ "Rx \n",
+ "Φ=6.243958 \n",
+ "Rx \n",
+ "Φ=0.103247 \n",
+ "Rx \n",
+ "Φ=0.298923 \n",
+ "Rx \n",
+ "Φ=0.346879 \n",
+ "Rx \n",
+ "Φ=6.119318 \n",
+ "Rx \n",
+ "Φ=2.58759 \n",
+ "Rx \n",
+ "Φ=6.079447 \n",
+ "Rx \n",
+ "Φ=0.725876 \n",
+ "Rx \n",
+ "Φ=0.378061 \n",
+ "Rx \n",
+ "Φ=4.422716 \n",
+ "Rx \n",
+ "Φ=6.039648 \n",
+ "Rx \n",
+ "Φ=1.268851 \n",
+ "Rx \n",
+ "Φ=0.390531 \n",
+ "Rx \n",
+ "Φ=0.126578 \n",
+ "Rx \n",
+ "Φ=0.246413 \n",
+ "Rx \n",
+ "Φ=3.402408 \n",
+ "Rx \n",
+ "Φ=5.826186 \n",
+ "Rx \n",
+ "Φ=4.233559 \n",
+ "Rx \n",
+ "Φ=6.051188 \n",
+ "Rx \n",
+ "Φ=0.79901 \n",
+ "Rx \n",
+ "Φ=5.776695 \n",
+ "Rx \n",
+ "Φ=4.974547 \n",
+ "Rx \n",
+ "Φ=5.895872 \n",
+ "Rx \n",
+ "Φ=3.418513 \n",
+ "Rx \n",
+ "Φ=5.734169 \n",
+ "Rx \n",
+ "Φ=3.609693 \n",
+ "Rx \n",
+ "Φ=5.952319 \n",
+ "Rx \n",
+ "Φ=6.143114 \n",
+ "Rx \n",
+ "Φ=0.201968 \n",
+ "Rx \n",
+ "Φ=5.889935 \n",
+ "Rx \n",
+ "Φ=5.740097 \n",
+ "Rx \n",
+ "Φ=2.527898 \n",
+ "Rx \n",
+ "Φ=0.367942 \n",
+ "Rx \n",
+ "Φ=3.220737 \n",
+ "Rx \n",
+ "Φ=5.510039 \n",
+ "Rx \n",
+ "Φ=2.457415 \n",
+ "Rx \n",
+ "Φ=0.365233 \n",
+ "Rx \n",
+ "Φ=1.85556 \n",
+ "Rx \n",
+ "Φ=0.048039 \n",
+ "Rx \n",
+ "Φ=4.766491 \n",
+ "Rx \n",
+ "Φ=6.083697 \n",
+ "Rx \n",
+ "Φ=3.502725 \n",
+ "Rx \n",
+ "Φ=5.818082 \n",
+ "Rx \n",
+ "Φ=1.045527 \n",
+ "Rx \n",
+ "Φ=0.229156 \n",
+ "Rx \n",
+ "Φ=3.842632 \n",
+ "Rx \n",
+ "Φ=6.264048 \n",
+ "Rx \n",
+ "Φ=2.871257 \n",
+ "Rx \n",
+ "Φ=1.01022 \n",
+ "Rx \n",
+ "Φ=3.458134 \n",
+ "Rx \n",
+ "Φ=0.911198 \n",
+ "Rx \n",
+ "Φ=1.366752 \n",
+ "Rx \n",
+ "Φ=0.424202 \n",
+ "Rx \n",
+ "Φ=5.229071 \n",
+ "Rx \n",
+ "Φ=5.865754 \n",
+ "Rx \n",
+ "Φ=1.05718 \n",
+ "Rx \n",
+ "Φ=5.766472 \n",
+ "Rx \n",
+ "Φ=5.956139 \n",
+ "Rx \n",
+ "Φ=5.148345 \n",
+ "Rx \n",
+ "Φ=3.360316 \n",
+ "Rx \n",
+ "Φ=5.497444 \n",
+ "Rx \n",
+ "Φ=2.301208 \n",
+ "Rx \n",
+ "Φ=0.686168 \n",
+ "Rx \n",
+ "Φ=0.992239 \n",
+ "Rx \n",
+ "Φ=5.204136 \n",
+ "Rx \n",
+ "Φ=3.756768 \n",
+ "Rx \n",
+ "Φ=5.477774 \n",
+ "Rx \n",
+ "Φ=1.3166 \n",
+ "Rx \n",
+ "Φ=4.862561 \n",
+ "Rx \n",
+ "Φ=0.788916 \n",
+ "Rx \n",
+ "Φ=6.069939 \n",
+ "Rx \n",
+ "Φ=1.026089 \n",
+ "Rx \n",
+ "Φ=6.193815 \n",
+ "Rx \n",
+ "Φ=3.011122 \n",
+ "Rx \n",
+ "Φ=6.114183 \n",
+ "Rx \n",
+ "Φ=4.348631 \n",
+ "Rx \n",
+ "Φ=0.177894 \n",
+ "Rx \n",
+ "Φ=4.211142 \n",
+ "Rx \n",
+ "Φ=0.173033 \n",
+ "Rx \n",
+ "Φ=1.205005 \n",
+ "Rx \n",
+ "Φ=5.991042 \n",
+ "Rx \n",
+ "Φ=5.584329 \n",
+ "Rx \n",
+ "Φ=0.072233 \n",
+ "Rx \n",
+ "Φ=5.464449 \n",
+ "Rx \n",
+ "Φ=6.027319 \n",
+ "Rx \n",
+ "Φ=3.454423 \n",
+ "Rx \n",
+ "Φ=0.267332 \n",
+ "Rx \n",
+ "Φ=4.027251 \n",
+ "Rx \n",
+ "Φ=0.530794 \n",
+ "Rx \n",
+ "Φ=4.032712 \n",
+ "Rx \n",
+ "Φ=5.842024 \n",
+ "Rx \n",
+ "Φ=1.959455 \n",
+ "Rx \n",
+ "Φ=5.870189 \n",
+ "Rx \n",
+ "Φ=1.918084 \n",
+ "Rx \n",
+ "Φ=0.355276 \n",
+ "Rx \n",
+ "Φ=5.648712 \n",
+ "Rx \n",
+ "Φ=5.950376 \n",
+ "Rx \n",
+ "Φ=5.696654 \n",
+ "Rx \n",
+ "Φ=5.585412 \n",
+ "Rx \n",
+ "Φ=1.120116 \n",
+ "Rx \n",
+ "Φ=0.461263 \n",
+ "Rx \n",
+ "Φ=0.963201 \n",
+ "Rx \n",
+ "Φ=6.113926 \n",
+ "Rx \n",
+ "Φ=0.405826 \n",
+ "Rx \n",
+ "Φ=5.871322 \n",
+ "Rx \n",
+ "Φ=1.32178 \n",
+ "Rx \n",
+ "Φ=6.011912 \n",
+ "Rx \n",
+ "Φ=5.990809 \n",
+ "Rx \n",
+ "Φ=5.570258 \n",
+ "Rx \n",
+ "Φ=3.702403 \n",
+ "Rx \n",
+ "Φ=6.239502 \n",
+ "Rx \n",
+ "Φ=1.369657 \n",
+ "Rx \n",
+ "Φ=0.214337 \n",
+ "Rx \n",
+ "Φ=5.438164 \n",
+ "Rx \n",
+ "Φ=0.44669 \n",
+ "Rx \n",
+ "Φ=1.118156 \n",
+ "Rx \n",
+ "Φ=0.625692 \n",
+ "Rx \n",
+ "Φ=5.240257 \n",
+ "Rx \n",
+ "Φ=6.106818 \n",
+ "Rx \n",
+ "Φ=1.066687 \n",
+ "Rx \n",
+ "Φ=0.456034 \n",
+ "Rx \n",
+ "Φ=2.676467 \n",
+ "Rx \n",
+ "Φ=5.966898 \n",
+ "Rx \n",
+ "Φ=3.619195 \n",
+ "Rx \n",
+ "Φ=6.155757 \n",
+ "Rx \n",
+ "Φ=1.812363 \n",
+ "Rx \n",
+ "Φ=6.126905 \n",
+ "Rx \n",
+ "Φ=0.276373 \n",
+ "Rx \n",
+ "Φ=6.054719 \n",
+ "Rx \n",
+ "Φ=2.815921 \n",
+ "Rx \n",
+ "Φ=6.138447 \n",
+ "Rx \n",
+ "Φ=1.996046 \n",
+ "Rx \n",
+ "Φ=0.446102 \n",
+ "Rx \n",
+ "Φ=1.144774 \n",
+ "Rx \n",
+ "Φ=6.178597 \n",
+ "Rx \n",
+ "Φ=1.401236 \n",
+ "Rx \n",
+ "Φ=5.854935 \n",
+ "Rx \n",
+ "Φ=1.722697 \n",
+ "Rx \n",
+ "Φ=6.20702 \n",
+ "Rx \n",
+ "Φ=3.183872 \n",
+ "Rx \n",
+ "Φ=0.672917 \n",
+ "Rx \n",
+ "Φ=4.230831 \n",
+ "Rx \n",
+ "Φ=0.293898 \n",
+ "Rx \n",
+ "Φ=4.913333 \n",
+ "Rx \n",
+ "Φ=6.032747 \n",
+ "Rx \n",
+ "Φ=4.945188 \n",
+ "Rx \n",
+ "Φ=6.152212 \n",
+ "Rx \n",
+ "Φ=5.333317 \n",
+ "Rx \n",
+ "Φ=0.434773 \n",
+ "Rx \n",
+ "Φ=0.602097 \n",
+ "Rx \n",
+ "Φ=6.092966 \n",
+ "Rx \n",
+ "Φ=0.935453 \n",
+ "Rx \n",
+ "Φ=5.913956 \n",
+ "Rx \n",
+ "Φ=2.758088 \n",
+ "Rx \n",
+ "Φ=6.232422 \n",
+ "Rx \n",
+ "Φ=3.56314 \n",
+ "Rx \n",
+ "Φ=6.078639 \n",
+ "Rx \n",
+ "Φ=3.199047 \n",
+ "Rx \n",
+ "Φ=5.869016 \n",
+ "Rx \n",
+ "Φ=2.866879 \n",
+ "Rx \n",
+ "Φ=0.341064 \n",
+ "Rx \n",
+ "Φ=1.812616 \n",
+ "Rx \n",
+ "Φ=0.469801 \n",
+ "Rx \n",
+ "Φ=1.859111 \n",
+ "Rx \n",
+ "Φ=6.160244 \n",
+ "Rx \n",
+ "Φ=6.027053 \n",
+ "Rx \n",
+ "Φ=5.185328 \n",
+ "Rx \n",
+ "Φ=4.276875 \n",
+ "Rx \n",
+ "Φ=0.672739 \n",
+ "Rx \n",
+ "Φ=6.242884 \n",
+ "Rx \n",
+ "Φ=5.826318 \n",
+ "Rx \n",
+ "Φ=1.277143 \n",
+ "Rx \n",
+ "Φ=5.085287 \n",
+ "Rx \n",
+ "Φ=5.952844 \n",
+ "Rx \n",
+ "Φ=1.334357 \n",
+ "Rx \n",
+ "Φ=3.807541 \n",
+ "Rx \n",
+ "Φ=5.099164 \n",
+ "Rx \n",
+ "Φ=4.708939 \n",
+ "Rx \n",
+ "Φ=3.618923 \n",
+ "Rx \n",
+ "Φ=5.343757 \n",
+ "Rx \n",
+ "Φ=6.03117 \n",
+ "Rx \n",
+ "Φ=0.663361 \n",
+ "Rx \n",
+ "Φ=0.256978 \n",
+ "Rx \n",
+ "Φ=5.501659 \n",
+ "Rx \n",
+ "Φ=5.822758 \n",
+ "Rx \n",
+ "Φ=5.024525 \n",
+ "Rx \n",
+ "Φ=6.035368 \n",
+ "Rx \n",
+ "Φ=1.690055 \n",
+ "Rx \n",
+ "Φ=6.053162 \n",
+ "Rx \n",
+ "Φ=1.472306 \n",
+ "Rx \n",
+ "Φ=6.000362 \n",
+ "Rx \n",
+ "Φ=2.512647 \n",
+ "Rx \n",
+ "Φ=6.114733 \n",
+ "Rx \n",
+ "Φ=1.188262 \n",
+ "Rx \n",
+ "Φ=6.10576 \n",
+ "Rx \n",
+ "Φ=4.462493 \n",
+ "Rx \n",
+ "Φ=6.194841 \n",
+ "Rx \n",
+ "Φ=0.112451 \n",
+ "Rx \n",
+ "Φ=0.393175 \n",
+ "Rx \n",
+ "Φ=3.19564 \n",
+ "Rx \n",
+ "Φ=0.077871 \n",
+ "Rx \n",
+ "Φ=5.701282 \n",
+ "Rx \n",
+ "Φ=6.128231 \n",
+ "Rx \n",
+ "Φ=5.959465 \n",
+ "Rx \n",
+ "Φ=6.192619 \n",
+ "Rx \n",
+ "Φ=1.347734 \n",
+ "Rx \n",
+ "Φ=0.565516 \n",
+ "Rx \n",
+ "Φ=0.234849 \n",
+ "Rx \n",
+ "Φ=0.128807 \n",
+ "Rx \n",
+ "Φ=5.027262 \n",
+ "Rx \n",
+ "Φ=0.450018 \n",
+ "Rx \n",
+ "Φ=0.170227 \n",
+ "Rx \n",
+ "Φ=6.079843 \n",
+ "Rx \n",
+ "Φ=1.461052 \n",
+ "Rx \n",
+ "Φ=6.212934 \n",
+ "Rx \n",
+ "Φ=4.922247 \n",
+ "Rx \n",
+ "Φ=6.002916 \n",
+ "Rx \n",
+ "Φ=1.921037 \n",
+ "Rx \n",
+ "Φ=0.125496 \n",
+ "Rx \n",
+ "Φ=5.286739 \n",
+ "Rx \n",
+ "Φ=0.112272 \n",
+ "Rx \n",
+ "Φ=1.991586 \n",
+ "Rx \n",
+ "Φ=5.781626 \n",
+ "Rx \n",
+ "Φ=2.67332 \n",
+ "Rx \n",
+ "Φ=6.063259 \n",
+ "Rx \n",
+ "Φ=0.989563 \n",
+ "Rx \n",
+ "Φ=5.705887 \n",
+ "Rx \n",
+ "Φ=3.341161 \n",
+ "Rx \n",
+ "Φ=0.417074 \n",
+ "Rx \n",
+ "Φ=1.907429 \n",
+ "Rx \n",
+ "Φ=0.613419 \n",
+ "Rx \n",
+ "Φ=1.254199 \n",
+ "Rx \n",
+ "Φ=0.162123 \n",
+ "Rx \n",
+ "Φ=6.168893 \n",
+ "Rx \n",
+ "Φ=6.136747 \n",
+ "Rx \n",
+ "Φ=1.68225 \n",
+ "Rx \n",
+ "Φ=5.87014 \n",
+ "Rx \n",
+ "Φ=4.1864 \n",
+ "Rx \n",
+ "Φ=5.968273 \n",
+ "Rx \n",
+ "Φ=3.820515 \n",
+ "Rx \n",
+ "Φ=6.01992 \n",
+ "Rx \n",
+ "Φ=4.566328 \n",
+ "Rx \n",
+ "Φ=5.490333 \n",
+ "Rx \n",
+ "Φ=2.750272 \n",
+ "Rx \n",
+ "Φ=5.825777 \n",
+ "Rx \n",
+ "Φ=1.9798 \n",
+ "Rx \n",
+ "Φ=0.299213 \n",
+ "Rx \n",
+ "Φ=4.169099 \n",
+ "Rx \n",
+ "Φ=5.914829 \n",
+ "Rx \n",
+ "Φ=1.566154 \n",
+ "Rx \n",
+ "Φ=0.091486 \n",
+ "Rx \n",
+ "Φ=0.248427 \n",
+ "Rx \n",
+ "Φ=6.029484 \n",
+ "Rx \n",
+ "Φ=4.129084 \n",
+ "Rx \n",
+ "Φ=6.210629 \n",
+ "Rx \n",
+ "Φ=6.180298 \n",
+ "Rx \n",
+ "Φ=5.597354 \n",
+ "Rx \n",
+ "Φ=5.852521 \n",
+ "Rx \n",
+ "Φ=0.07827 \n",
+ "Rx \n",
+ "Φ=5.109574 \n",
+ "Rx \n",
+ "Φ=0.247583 \n",
+ "Rx \n",
+ "Φ=1.254713 \n",
+ "Rx \n",
+ "Φ=0.249245 \n",
+ "Rx \n",
+ "Φ=1.765613 \n",
+ "Rx \n",
+ "Φ=0.83629 \n",
+ "Rx \n",
+ "Φ=4.134639 \n",
+ "Rx \n",
+ "Φ=5.526798 \n",
+ "Rx \n",
+ "Φ=3.109616 \n",
+ "Rx \n",
+ "Φ=5.563599 \n",
+ "Rx \n",
+ "Φ=3.365034 \n",
+ "Rx \n",
+ "Φ=0.890462 \n",
+ "Rx \n",
+ "Φ=1.594525 \n",
+ "Rx \n",
+ "Φ=0.994272 \n",
+ "Rx \n",
+ "Φ=4.927901 \n",
+ "Rx \n",
+ "Φ=0.703818 \n",
+ "Rx \n",
+ "Φ=3.555104 \n",
+ "Rx \n",
+ "Φ=0.221101 \n",
+ "Rx \n",
+ "Φ=0.175036 \n",
+ "Rx \n",
+ "Φ=5.890969 \n",
+ "Rx \n",
+ "Φ=0.255289 \n",
+ "Rx \n",
+ "Φ=5.258629 \n",
+ "Rx \n",
+ "Φ=4.794328 \n",
+ "Rx \n",
+ "Φ=1.091856 \n",
+ "Rx \n",
+ "Φ=3.657752 \n",
+ "Rx \n",
+ "Φ=0.966321 \n",
+ "Rx \n",
+ "Φ=3.078381 \n",
+ "Rx \n",
+ "Φ=5.401656 \n",
+ "Rx \n",
+ "Φ=1.130694 \n",
+ "Rx \n",
+ "Φ=1.296184 \n",
+ "Rx \n",
+ "Φ=2.765508 \n",
+ "Rx \n",
+ "Φ=4.391477 \n",
+ "Rx \n",
+ "Φ=3.5839 \n",
+ "Rx \n",
+ "Φ=5.821478 \n",
+ "Rx \n",
+ "Φ=2.952865 \n",
+ "Rx \n",
+ "Φ=0.487923 \n",
+ "Rx \n",
+ "Φ=3.471981 \n",
+ "Rx \n",
+ "Φ=6.008849 \n",
+ "Rx \n",
+ "Φ=5.543587 \n",
+ "Rx \n",
+ "Φ=5.912378 \n",
+ "Rx \n",
+ "Φ=4.717217 \n",
+ "Rx \n",
+ "Φ=5.954973 \n",
+ "Rx \n",
+ "Φ=6.048216 \n",
+ "Rx \n",
+ "Φ=0.377336 \n",
+ "Rx \n",
+ "Φ=3.172754 \n",
+ "Rx \n",
+ "Φ=6.130785 \n",
+ "Rx \n",
+ "Φ=5.897057 \n",
+ "Rx \n",
+ "Φ=5.750915 \n",
+ "Rx \n",
+ "Φ=3.128904 \n",
+ "Rx \n",
+ "Φ=6.165255 \n",
+ "Rx \n",
+ "Φ=4.930897 \n",
+ "Rx \n",
+ "Φ=0.062273 \n",
+ "Rx \n",
+ "Φ=5.242247 \n",
+ "Rx \n",
+ "Φ=5.871378 \n",
+ "Rx \n",
+ "Φ=1.324429 \n",
+ "Rx \n",
+ "Φ=6.081567 \n",
+ "Rx \n",
+ "Φ=0.909729 \n",
+ "Rx \n",
+ "Φ=5.916251 \n",
+ "Rx \n",
+ "Φ=3.480688 \n",
+ "Rx \n",
+ "Φ=6.154356 \n",
+ "Rx \n",
+ "Φ=3.799629 \n",
+ "Rx \n",
+ "Φ=0.450691 \n",
+ "Rx \n",
+ "Φ=5.106797 \n",
+ "Rx \n",
+ "Φ=0.321715 \n",
+ "Rx \n",
+ "Φ=0.452299 \n",
+ "Rx \n",
+ "Φ=0.185765 \n",
+ "Rx \n",
+ "Φ=4.161743 \n",
+ "Rx \n",
+ "Φ=0.335402 \n",
+ "Rx \n",
+ "Φ=5.993291 \n",
+ "Rx \n",
+ "Φ=0.192655 \n",
+ "Rx \n",
+ "Φ=3.009191 \n",
+ "Rx \n",
+ "Φ=0.208321 \n",
+ "Rx \n",
+ "Φ=3.3052 \n",
+ "Rx \n",
+ "Φ=0.166915 \n",
+ "Rx \n",
+ "Φ=6.070138 \n",
+ "Rx \n",
+ "Φ=0.437737 \n",
+ "Rx \n",
+ "Φ=1.63422 \n",
+ "Rx \n",
+ "Φ=0.429432 \n",
+ "Rx \n",
+ "Φ=1.775509 \n",
+ "Rx \n",
+ "Φ=0.24811 \n",
+ "Rx \n",
+ "Φ=0.295352 \n",
+ "Rx \n",
+ "Φ=0.213961 \n",
+ "Rx \n",
+ "Φ=0.501272 \n",
+ "Rx \n",
+ "Φ=5.986258 \n",
+ "Rx \n",
+ "Φ=1.321975 \n",
+ "Rx \n",
+ "Φ=5.99148 \n",
+ "Rx \n",
+ "Φ=0.182974 \n",
+ "Rx \n",
+ "Φ=0.098643 \n",
+ "Rx \n",
+ "Φ=5.286114 \n",
+ "Rx \n",
+ "Φ=0.502784 \n",
+ "Rx \n",
+ "Φ=5.820663 \n",
+ "Rx \n",
+ "Φ=0.612587 \n",
+ "Rx \n",
+ "Φ=0.006958 \n",
+ "Rx \n",
+ "Φ=6.062078 \n",
+ "Rx \n",
+ "Φ=2.920776 \n",
+ "Rx \n",
+ "Φ=5.781766 \n",
+ "Rx \n",
+ "Φ=2.287795 \n",
+ "Rx \n",
+ "Φ=5.903949 \n",
+ "Rx \n",
+ "Φ=4.880959 \n",
+ "Rx \n",
+ "Φ=5.888915 \n",
+ "Rx \n",
+ "Φ=1.652898 \n",
+ "Rx \n",
+ "Φ=0.235887 \n",
+ "Rx \n",
+ "Φ=5.251055 \n",
+ "Rx \n",
+ "Φ=6.058973 \n",
+ "Rx \n",
+ "Φ=1.342638 \n",
+ "Rx \n",
+ "Φ=0.306901 \n",
+ "Rx \n",
+ "Φ=3.328844 \n",
+ "Rx \n",
+ "Φ=0.445911 \n",
+ "Rx \n",
+ "Φ=5.874783 \n",
+ "Rx \n",
+ "Φ=6.095397 \n",
+ "Rx \n",
+ "Φ=3.90115 \n",
+ "Rx \n",
+ "Φ=0.64258 \n",
+ "Rx \n",
+ "Φ=0.561182 \n",
+ "Rx \n",
+ "Φ=0.335261 \n",
+ "Rx \n",
+ "Φ=4.537983 \n",
+ "Rx \n",
+ "Φ=0.49251 \n",
+ "Rx \n",
+ "Φ=0.753135 \n",
+ "Rx \n",
+ "Φ=5.672205 \n",
+ "Rx \n",
+ "Φ=4.746371 \n",
+ "Rx \n",
+ "Φ=5.77229 \n",
+ "Rx \n",
+ "Φ=3.547434 \n",
+ "Rx \n",
+ "Φ=0.834439 \n",
+ "Rx \n",
+ "Φ=3.128657 \n",
+ "Rx \n",
+ "Φ=0.310848 \n",
+ "Rx \n",
+ "Φ=5.628895 \n",
+ "Rx \n",
+ "Φ=6.10799 \n",
+ "Rx \n",
+ "Φ=3.764063 \n",
+ "Rx \n",
+ "Φ=0.55285 \n",
+ "Rx \n",
+ "Φ=5.153645 \n",
+ "Rx \n",
+ "Φ=0.346198 \n",
+ "Rx \n",
+ "Φ=3.223894 \n",
+ "Rx \n",
+ "Φ=0.569827 \n",
+ "Rx \n",
+ "Φ=3.319507 \n",
+ "Rx \n",
+ "Φ=0.989695 \n",
+ "Rx \n",
+ "Φ=6.256995 \n",
+ "Rx \n",
+ "Φ=0.362548 \n",
+ "Rx \n",
+ "Φ=4.089764 \n",
+ "Rx \n",
+ "Φ=0.983881 \n",
+ "Rx \n",
+ "Φ=5.07582 \n",
+ "Rx \n",
+ "Φ=0.228057 \n",
+ "Rx \n",
+ "Φ=2.628947 \n",
+ "Rx \n",
+ "Φ=4.601096 \n",
+ "Rx \n",
+ "Φ=1.348794 \n",
+ "Rx \n",
+ "Φ=5.936369 \n",
+ "Rx \n",
+ "Φ=1.656553 \n",
+ "Rx \n",
+ "Φ=3.702146 \n",
+ "Rx \n",
+ "Φ=2.915192 \n",
+ "Rx \n",
+ "Φ=6.146791 \n",
+ "Rx \n",
+ "Φ=5.368077 \n",
+ "Rx \n",
+ "Φ=0.093564 \n",
+ "Rx \n",
+ "Φ=0.141214 \n",
+ "Rx \n",
+ "Φ=0.211814 \n",
+ "Rx \n",
+ "Φ=2.730347 \n",
+ "Rx \n",
+ "Φ=0.361998 \n",
+ "Rx \n",
+ "Φ=0.282148 \n",
+ "Rx \n",
+ "Φ=0.227074 \n",
+ "Rx \n",
+ "Φ=3.338574 \n",
+ "Rx \n",
+ "Φ=0.243093 \n",
+ "Rx \n",
+ "Φ=5.987782 \n",
+ "Rx \n",
+ "Φ=6.058222 \n",
+ "Rx \n",
+ "Φ=6.085666 \n",
+ "Rx \n",
+ "Φ=0.152386 \n",
+ "Rx \n",
+ "Φ=4.283224 \n",
+ "Rx \n",
+ "Φ=0.167865 \n",
+ "Rx \n",
+ "Φ=1.515827 \n",
+ "Rx \n",
+ "Φ=0.231491 \n",
+ "Rx \n",
+ "Φ=1.096251 \n",
+ "Rx \n",
+ "Φ=0.500816 \n",
+ "Rx \n",
+ "Φ=0.761015 \n",
+ "Rx \n",
+ "Φ=5.872252 \n",
+ "Rx \n",
+ "Φ=0.094949 \n",
+ "Rx \n",
+ "Φ=5.911576 \n",
+ "Rx \n",
+ "Φ=4.105188 \n",
+ "Rx \n",
+ "Φ=0.386495 \n",
+ "Rx \n",
+ "Φ=4.462909 \n",
+ "Rx \n",
+ "Φ=0.082525 \n",
+ "Rx \n",
+ "Φ=0.568374 \n",
+ "Rx \n",
+ "Φ=5.751015 \n",
+ "Rx \n",
+ "Φ=0.698077 \n",
+ "Rx \n",
+ "Φ=0.652032 \n",
+ "Rx \n",
+ "Φ=0.491142 \n",
+ "Rx \n",
+ "Φ=0.289689 \n",
+ "Rx \n",
+ "Φ=0.924055 \n",
+ "Rx \n",
+ "Φ=5.881815 \n",
+ "Rx \n",
+ "Φ=5.346604 \n",
+ "Rx \n",
+ "Φ=5.964876 \n",
+ "Rx \n",
+ "Φ=2.586922 \n",
+ "Rx \n",
+ "Φ=5.860919 \n",
+ "Rx \n",
+ "Φ=1.222446 \n",
+ "Rx \n",
+ "Φ=0.179174 \n",
+ "Rx \n",
+ "Φ=4.558324 \n",
+ "Rx \n",
+ "Φ=6.119097 \n",
+ "Rx \n",
+ "Φ=3.932419 \n",
+ "Rx \n",
+ "Φ=0.255542 \n",
+ "Rx \n",
+ "Φ=0.662422 \n",
+ "Rx \n",
+ "Φ=5.881116 \n",
+ "Rx \n",
+ "Φ=2.588242 \n",
+ "Rx \n",
+ "Φ=5.910155 \n",
+ "Rx \n",
+ "Φ=4.676176 \n",
+ "Rx \n",
+ "Φ=5.889599 \n",
+ "Rx \n",
+ "Φ=3.350311 \n",
+ "Rx \n",
+ "Φ=0.213751 \n",
+ "Rx \n",
+ "Φ=5.211781 \n",
+ "Rx \n",
+ "Φ=0.185298 \n",
+ "Rx \n",
+ "Φ=4.459793 \n",
+ "Rx \n",
+ "Φ=0.203269 \n",
+ "Rx \n",
+ "Φ=3.533864 \n",
+ "Rx \n",
+ "Φ=5.837168 \n",
+ "Rx \n",
+ "Φ=0.952755 \n",
+ "Rx \n",
+ "Φ=5.704245 \n",
+ "Rx \n",
+ "Φ=1.951633 \n",
+ "Rx \n",
+ "Φ=0.148612 \n",
+ "Rx \n",
+ "Φ=2.626898 \n",
+ "Rx \n",
+ "Φ=5.824427 \n",
+ "Rx \n",
+ "Φ=5.269631 \n",
+ "Rx \n",
+ "Φ=5.771452 \n",
+ "Rx \n",
+ "Φ=0.887676 \n",
+ "Rx \n",
+ "Φ=0.295589 \n",
+ "Rx \n",
+ "Φ=1.368475 \n",
+ "Rx \n",
+ "Φ=0.759218 \n",
+ "Rx \n",
+ "Φ=0.86463 \n",
+ "Rx \n",
+ "Φ=5.910179 \n",
+ "Rx \n",
+ "Φ=2.67586 \n",
+ "Rx \n",
+ "Φ=6.071806 \n",
+ "Rx \n",
+ "Φ=3.939947 \n",
+ "Rx \n",
+ "Φ=5.512408 \n",
+ "Rx \n",
+ "Φ=3.108508 \n",
+ "Rx \n",
+ "Φ=0.666976 \n",
+ "Rx \n",
+ "Φ=4.360401 \n",
+ "Rx \n",
+ "Φ=0.347768 \n",
+ "Rx \n",
+ "Φ=3.37693 \n",
+ "Rx \n",
+ "Φ=0.312108 \n",
+ "Rx \n",
+ "Φ=5.196323 \n",
+ "Rx \n",
+ "Φ=5.797489 \n",
+ "Rx \n",
+ "Φ=2.645372 \n",
+ "Rx \n",
+ "Φ=0.627537 \n",
+ "Rx \n",
+ "Φ=1.120956 \n",
+ "Rx \n",
+ "Φ=0.130521 \n",
+ "Rx \n",
+ "Φ=0.164212 \n",
+ "Rx \n",
+ "Φ=0.593825 \n",
+ "Rx \n",
+ "Φ=0.768267 \n",
+ "Rx \n",
+ "Φ=5.587306 \n",
+ "Rx \n",
+ "Φ=0.121997 \n",
+ "Rx \n",
+ "Φ=0.782756 \n",
+ "Rx \n",
+ "Φ=2.841813 \n",
+ "Rx \n",
+ "Φ=5.752308 \n",
+ "Rx \n",
+ "Φ=2.407927 \n",
+ "Rx \n",
+ "Φ=6.090167 \n",
+ "Rx \n",
+ "Φ=2.833777 \n",
+ "Rx \n",
+ "Φ=0.36229 \n",
+ "Rx \n",
+ "Φ=4.882238 \n",
+ "Rx \n",
+ "Φ=5.664507 \n",
+ "Rx \n",
+ "Φ=3.956978 \n",
+ "Rx \n",
+ "Φ=1.062816 \n",
+ "Rx \n",
+ "Φ=0.330062 \n",
+ "Rx \n",
+ "Φ=5.289095 \n",
+ "Rx \n",
+ "Φ=1.013429 \n",
+ "Rx \n",
+ "Φ=6.180296 \n",
+ "Rx \n",
+ "Φ=0.65825 \n",
+ "Rx \n",
+ "Φ=1.873061 \n",
+ "Rx \n",
+ "Φ=6.127574 \n",
+ "Rx \n",
+ "Φ=3.409669 \n",
+ "Rx \n",
+ "Φ=4.207726 \n",
+ "Rx \n",
+ "Φ=0.039319 \n",
+ "Rx \n",
+ "Φ=2.361612 \n",
+ "Rx \n",
+ "Φ=6.119483 \n",
+ "Rx \n",
+ "Φ=1.944267 \n",
+ "Rx \n",
+ "Φ=5.929505 \n",
+ "Rx \n",
+ "Φ=4.927996 \n",
+ "Rx \n",
+ "Φ=0.265048 \n",
+ "Rx \n",
+ "Φ=3.960619 \n",
+ "Rx \n",
+ "Φ=0.231558 \n",
+ "Rx \n",
+ "Φ=4.756288 \n",
+ "Rx \n",
+ "Φ=5.964907 \n",
+ "Rx \n",
+ "Φ=2.755658 \n",
+ "Rx \n",
+ "Φ=0.048777 \n",
+ "Rx \n",
+ "Φ=0.594298 \n",
+ "Rx \n",
+ "Φ=6.210165 \n",
+ "Rx \n",
+ "Φ=6.102554 \n",
+ "Rx \n",
+ "Φ=0.050579 \n",
+ "Rx \n",
+ "Φ=1.168647 \n",
+ "Rx \n",
+ "Φ=0.072894 \n",
+ "Rx \n",
+ "Φ=3.197342 \n",
+ "Rx \n",
+ "Φ=0.202346 \n",
+ "Rx \n",
+ "Φ=1.465493 \n",
+ "Rx \n",
+ "Φ=0.248729 \n",
+ "Rx \n",
+ "Φ=0.610803 \n",
+ "Rx \n",
+ "Φ=5.878069 \n",
+ "Rx \n",
+ "Φ=4.355098 \n",
+ "Rx \n",
+ "Φ=0.389999 \n",
+ "Rx \n",
+ "Φ=1.87709 \n",
+ "Rx \n",
+ "Φ=0.407268 \n",
+ "Rx \n",
+ "Φ=3.62502 \n",
+ "Rx \n",
+ "Φ=5.940365 \n",
+ "Rx \n",
+ "Φ=1.042955 \n",
+ "Rx \n",
+ "Φ=5.807768 \n",
+ "Rx \n",
+ "Φ=6.068141 \n",
+ "Rx \n",
+ "Φ=6.054311 \n",
+ "Rx \n",
+ "Φ=3.344116 \n",
+ "Rx \n",
+ "Φ=0.199176 \n",
+ "Rx \n",
+ "Φ=2.105731 \n",
+ "Rx \n",
+ "Φ=6.103484 \n",
+ "Rx \n",
+ "Φ=2.251749 \n",
+ "Rx \n",
+ "Φ=0.381059 \n",
+ "Rx \n",
+ "Φ=4.906114 \n",
+ "Rx \n",
+ "Φ=0.272654 \n",
+ "Rx \n",
+ "Φ=0.022546 \n",
+ "Rx \n",
+ "Φ=0.215401 \n",
+ "Rx \n",
+ "Φ=0.622594 \n",
+ "Rx \n",
+ "Φ=0.324209 \n",
+ "Rx \n",
+ "Φ=3.795419 \n",
+ "Rx \n",
+ "Φ=0.556474 \n",
+ "Rx \n",
+ "Φ=3.104686 \n",
+ "Rx \n",
+ "Φ=0.085028 \n",
+ "Rx \n",
+ "Φ=5.094356 \n",
+ "Rx \n",
+ "Φ=0.185668 \n",
+ "Rx \n",
+ "Φ=2.84636 \n",
+ "Rx \n",
+ "Φ=5.721213 \n",
+ "Rx \n",
+ "Φ=0.044653 \n",
+ "Rx \n",
+ "Φ=5.875027 \n",
+ "Rx \n",
+ "Φ=4.102192 \n",
+ "Rx \n",
+ "Φ=6.035802 \n",
+ "Rx \n",
+ "Φ=0.609185 \n",
+ "Rx \n",
+ "Φ=0.203315 \n",
+ "Rx \n",
+ "Φ=5.517883 \n",
+ "Rx \n",
+ "Φ=5.845051 \n",
+ "Rx \n",
+ "Φ=2.676255 \n",
+ "Rx \n",
+ "Φ=0.4829 \n",
+ "Rx \n",
+ "Φ=5.464798 \n",
+ "Rx \n",
+ "Φ=0.407346 \n",
+ "Rx \n",
+ "Φ=1.77268 \n",
+ "Rx \n",
+ "Φ=0.069818 \n",
+ "Rx \n",
+ "Φ=0.142473 \n",
+ "Rx \n",
+ "Φ=0.603846 \n",
+ "Rx \n",
+ "Φ=4.581046 \n",
+ "Rx \n",
+ "Φ=0.5703 \n",
+ "Rx \n",
+ "Φ=5.177161 \n",
+ "Rx \n",
+ "Φ=0.375329 \n",
+ "Rx \n",
+ "Φ=5.604687 \n",
+ "Rx \n",
+ "Φ=5.895756 \n",
+ "Rx \n",
+ "Φ=3.636859 \n",
+ "Rx \n",
+ "Φ=5.918802 \n",
+ "Rx \n",
+ "Φ=2.939512 \n",
+ "Rx \n",
+ "Φ=6.038263 \n",
+ "Rx \n",
+ "Φ=0.158227 \n",
+ "Rx \n",
+ "Φ=0.516975 \n",
+ "Rx \n",
+ "Φ=1.219994 \n",
+ "Rx \n",
+ "Φ=0.084569 \n",
+ "Rx \n",
+ "Φ=1.662671 \n",
+ "Rx \n",
+ "Φ=5.949675 \n",
+ "Rx \n",
+ "Φ=1.601716 \n",
+ "Rx \n",
+ "Φ=0.507297 \n",
+ "Rx \n",
+ "Φ=5.560111 \n",
+ "Rx \n",
+ "Φ=0.46688 \n",
+ "Rx \n",
+ "Φ=1.045626 \n",
+ "Rx \n",
+ "Φ=6.06647 \n",
+ "Rx \n",
+ "Φ=2.635542 \n",
+ "Rx \n",
+ "Φ=5.552327 \n",
+ "Rx \n",
+ "Φ=0.080085 \n",
+ "Rx \n",
+ "Φ=0.368528 \n",
+ "Rx \n",
+ "Φ=4.986284 \n",
+ "Rx \n",
+ "Φ=0.675687 \n",
+ "Rx \n",
+ "Φ=0.34563 \n",
+ "Rx \n",
+ "Φ=5.774741 \n",
+ "Rx \n",
+ "Φ=5.246393 \n",
+ "Rx \n",
+ "Φ=0.7063 \n",
+ "Rx \n",
+ "Φ=1.151151 \n",
+ "Rx \n",
+ "Φ=0.351705 \n",
+ "Rx \n",
+ "Φ=0.410152 \n",
+ "Rx \n",
+ "Φ=5.800199 \n",
+ "Rx \n",
+ "Φ=4.482714 \n",
+ "Rx \n",
+ "Φ=0.676584 \n",
+ "Rx \n",
+ "Φ=1.023176 \n",
+ "Rx \n",
+ "Φ=5.36024 \n",
+ "Rx \n",
+ "Φ=2.637442 \n",
+ "Rx \n",
+ "Φ=2.024709 \n",
+ "Rx \n",
+ "Φ=5.455306 \n",
+ "Rx \n",
+ "Φ=0.531506 \n",
+ "Rx \n",
+ "Φ=3.115321 \n",
+ "Rx \n",
+ "Φ=1.283429 \n",
+ "Rx \n",
+ "Φ=5.281563 \n",
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+ "58 \n",
+ "59 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Linear_Circuit_60 = pcvl.Circuit.decomposition(Unitary_60, mzi, phase_shifter_fn=pcvl.PS, shape=\"triangle\")\n",
+ "pcvl.pdisplay(Linear_Circuit_60)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "41aed0bb",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# You can see the circuit is shaped like a triangle, this cuircuit composition is called the Reck scheme.\n",
+ "# TO DO: Test to see how the circuit composition looks like without the variable 'shape' defined.\n",
+ "# Do this with a smaller sized matrix to save time."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7d6ac933",
+ "metadata": {},
+ "source": [
+ "#### Running simulation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cd1e829a",
+ "metadata": {},
+ "source": [
+ "Now we can choose the way to perform the simulation of boson sampling with Perceval. The number of photons is within what we could simulate with the Naive backend, however the output space is far too big just to enumerate and store the states so we chose the CliffordClifford2017 backend instead. We encourage you to check out our multiple simulation backend options and their performance comparison on different types of problems available to view on the Perceval documentation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "a23c2a44",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "QPU = pcvl.Processor(\"CliffordClifford2017\", Linear_Circuit_60)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0e6a25f2",
+ "metadata": {},
+ "source": [
+ "Since this isn't a real problem and we are just trying to show the power of quantum computing when it comes to difficult problems to solve, such as boson sampling, we don't care what the input to our circuit is and can choose a random one."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "6ac056ec",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The input state: |0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0,0,0,1,0,1,0>\n"
+ ]
+ }
+ ],
+ "source": [
+ "def generate_input(n, m, modes = None):\n",
+ " \"This function randomly chooses an input with n photons in m modes.\"\n",
+ " if modes == None : #the function works with a given number of modes m, otherwise selecting them randomly\n",
+ " modes = sorted(random.sample(range(m),n))\n",
+ " state = \"|\"\n",
+ " for i in range(m):\n",
+ " state = state + \"0\"*(1 - (i in modes)) +\"1\"*(i in modes)+ \",\"*(i < m-1)\n",
+ " return pcvl.BasicState(state + \">\")\n",
+ "\n",
+ "input_state = generate_input(n, m)\n",
+ "print(\"The input state: \", input_state)\n",
+ "\n",
+ "# TO DO: Provide the processor with the input state defined above."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "faf263ef",
+ "metadata": {},
+ "source": [
+ "Using this input, our output states are states composed of n photons in m modes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "d6b24894",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The sampled outputs are:\n",
+ "|0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,0,2,0,0,0,0,0,0,0,1,2,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0>\n",
+ "|0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,2,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0>\n",
+ "|1,0,0,1,0,0,0,2,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0>\n",
+ "|0,0,0,1,0,0,0,3,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0>\n",
+ "|0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,2,1,0,0,0,0,0,0,0,0,0>\n",
+ "|1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1>\n",
+ "|1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,0,0,0,0,0,0,1,0,0,0>\n",
+ "|0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0>\n",
+ "|0,0,2,0,0,3,0,0,1,0,0,0,0,0,0,0,0,0,0,2,0,0,1,0,0,0,0,1,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0>\n",
+ "|0,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,2,0,1,0,0,1,0,0>\n"
+ ]
+ }
+ ],
+ "source": [
+ "QPU.min_detected_photons_filter(0) #we're telling the processor that we want to keep all outputs\n",
+ "# TO DO: What happens when you change the number you're filtering with? Can you filter by a number\n",
+ "# higher than the number of photons in the input state? Why?\n",
+ "\n",
+ "sampler = Sampler(QPU)\n",
+ "\n",
+ "print(\"The sampled outputs are:\")\n",
+ "for out_state in sampler.samples(10)[\"results\"]:\n",
+ " print(out_state)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "263d2ba0",
+ "metadata": {},
+ "source": [
+ "Now we can also perform boson sampling N times. This will take some time so let's save the results to a file."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "9cf2a385",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# if we want to launch parallel process\n",
+ "worker_id=1\n",
+ "\n",
+ "#store the input and the unitary\n",
+ "with open(\"%dphotons_%dmodes_%dsamples-worker%s-unitary.pkl\" %(n,m,N,worker_id), 'wb') as f:\n",
+ " pickle.dump(Unitary_60, f)\n",
+ "\n",
+ "with open(\"%dphotons_%dmodes_%dsamples-worker%s-inputstate.pkl\" %(n,m,N,worker_id), 'w') as f:\n",
+ " f.write(str(input_state)+\"\\n\")\n",
+ "\n",
+ "with gzip.open(\"%dphotons_%dmodes_%dsamples-worker%s-samples.txt.gz\" %(n,m,N,worker_id), 'wb') as f:\n",
+ " start = time.time()\n",
+ " for _ in range(N):\n",
+ " f.write((str(sampler.samples(1)[\"results\"][0])+\"\\n\").encode())\n",
+ " end = time.time()\n",
+ " f.write(str(\"==> %d\\n\" % (end-start)).encode())\n",
+ "f.close()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5d207441",
+ "metadata": {},
+ "source": [
+ "A little after (4 hours on a 3.1GHz Intel) - we do have 5M samples. We launched this on 32 threads for 2 days and collected 300 batches of 5M samples.\n",
+ "\n",
+ "Let us analyze the K-first mode bunching on these samples."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a1062d81",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "worker_id = 1\n",
+ "count = 0\n",
+ "bunching_distribution = Counter()\n",
+ "\n",
+ "with gzip.open(\"%dphotons_%dmodes_%dsamples-worker%s-samples.txt.gz\"%(n,m,N,worker_id), \"rt\") as f:\n",
+ " for l in f:\n",
+ " l = l.strip()\n",
+ " if l.startswith(\"|\") and l.endswith(\">\"):\n",
+ " try:\n",
+ " st = pcvl.BasicState(l)\n",
+ " count+=1\n",
+ " bunching_distribution[st.photon2mode(st.n-1)]+=1\n",
+ " except Exception:\n",
+ " pass\n",
+ "print(count, \"samples\")\n",
+ "print(\"Bunching Distribution:\", \"\\t\".join([str(bunching_distribution[k]) for k in range(m)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "576eb79b",
+ "metadata": {},
+ "source": [
+ "These numbers have been used on 300 samples for certification - see our article on Perceval for more details."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5a2ced3a",
+ "metadata": {},
+ "source": [
+ "#### Boson sampling with a non perfect source"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a95e1907",
+ "metadata": {},
+ "source": [
+ "Let's perform Boson sampling with a non perfect source. We declare a source with 90% brightness and purity. Here, we would reach the limits of the simulation if we use the same input as before, as for each photon at the entrance, we multiply by 3 the number of input states (0, 1 or 2 photons at the input), leading to $3^n$ states."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5c6bf7c1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "3 ** n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "fb96c9b6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "source = pcvl.Source(emission_probability=0.9, multiphoton_component=0.1)\n",
+ "QPU = pcvl.Processor(\"CliffordClifford2017\", Linear_Circuit_60, source)\n",
+ "QPU.with_input(pcvl.BasicState([0, 1, 1] + (m - 3) * [0])) #notice the change in input"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0216f7e4",
+ "metadata": {},
+ "source": [
+ "Computing the other way around, we can now check the source distribution of the processor to see how likely a state at the input of the linear circuit will be."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a8965f49",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pcvl.pdisplay(QPU.source_distribution, precision=1e-7, max_v=20)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "53795d58",
+ "metadata": {},
+ "source": [
+ "As expected, the most likely state to have been the input of the circuit was in fact the input we provided it with.\n",
+ "\n",
+ "Now we can launch the entire computation again starting from cell 8 to use this imperfect source QPU with the same nominal input, or from cell 7 for another random input."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "84b2a6a9",
+ "metadata": {},
+ "source": [
+ "### References"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "811e4838",
+ "metadata": {},
+ "source": [
+ "[1] Hui Wang, et al. Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a $10^{14}$-Dimensional Hilbert Space. Physical Review Letters, 123(25):250503, December 2019. Publisher: American Physical Society.\n",
+ "\n",
+ "[2] Michael Reck, Anton Zeilinger, Herbert J Bernstein, and Philip Bertani. Experimental realization of any discrete unitary operator. Physical review letters, 73(1):58, 1994."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/Boson_sampling_answers.ipynb b/Boson_sampling_answers.ipynb
new file mode 100644
index 0000000..189a010
--- /dev/null
+++ b/Boson_sampling_answers.ipynb
@@ -0,0 +1,48888 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "1c11286e",
+ "metadata": {},
+ "source": [
+ "# Quandela Training Seminar - Programming with Perceval"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "dad5a69d",
+ "metadata": {},
+ "source": [
+ "### Boson sampling"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "89e1f822",
+ "metadata": {},
+ "source": [
+ "Sampling is the problem of selecting data from a large set, usually to find a smaller set of data that is representative of the entire set. Naturally, as problem sizes grow, these types of problems become intractable for classical computers. This means that even if we are able to find a solution to our problem, the time it takes us to do so will be too long, deeming the solution no longer useful to us.\n",
+ "\n",
+ "In Perceval, we use photons as our bosons (indistinguishable subatomic particles with an integer spin) to perform the task of boson sampling. Boson sampling is a quantum sampling problem, drawing from a big probability distribution of output states of a system. As our knowledge of the quantum world grows and quantum hardware becomes better, we hope to offer solutions to problems previously thought intractable."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d38c01f3",
+ "metadata": {},
+ "source": [
+ "We are interested to simulate a boson sample with 14 photons and 60 modes, order of size comparable to what was done in Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a $10^{14}$-Dimensional Hilbert Space [1]."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "dede995f",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from collections import Counter\n",
+ "import gzip\n",
+ "import pickle\n",
+ "import time\n",
+ "import random\n",
+ "import perceval as pcvl\n",
+ "from perceval.algorithm import Sampler"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "84be34da",
+ "metadata": {},
+ "source": [
+ "#### Boson sampling with a perfect source"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7ea02d3b",
+ "metadata": {},
+ "source": [
+ "Let's define all the required values below."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "ea14f365",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 14 #number of photons at the input\n",
+ "m = 60 #number of modes\n",
+ "N = 5000000 #number of samplings we want in the end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "75e1ee98",
+ "metadata": {},
+ "source": [
+ "Now we can generate a Haar random unitary with Perceval."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "21e960f7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Unitary_60 = pcvl.Matrix.random_unitary(m) #creates a random unitary of dimension 60"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7d6ca6fb",
+ "metadata": {},
+ "source": [
+ "To be able to decompose this unitary, first we have to choose a set of optical components we will use to do. The Mach-Zehnder interferometer (MZI) is a good choice as it is composed of only 2 beam splitters and 2 phase shifters and it is highly configurable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "19234775",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "Rx \n",
+ "Φ=φ_a \n",
+ "Rx \n",
+ "Φ=φ_b \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "mzi = (pcvl.BS() // (0, pcvl.PS(phi=pcvl.Parameter(\"φ_a\")))\n",
+ " // pcvl.BS() // (1, pcvl.PS(phi=pcvl.Parameter(\"φ_b\"))))\n",
+ "pcvl.pdisplay(mzi)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "eb27d276",
+ "metadata": {},
+ "source": [
+ "No we can decompose the unitary into a set of MZIs using Reck's (traingular) scheme [2]. Naturally, since the matrix dimension is 60, this will be a huge circuit and may take some time to compile."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "bc9e5566",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "Φ=3.816136 \n",
+ "Φ=4.010218 \n",
+ "Φ=0.691042 \n",
+ "Φ=4.863586 \n",
+ "Φ=3.045536 \n",
+ "Φ=0.51946 \n",
+ "Φ=3.810742 \n",
+ "Φ=4.32163 \n",
+ "Φ=3.938265 \n",
+ "Φ=4.504834 \n",
+ "Φ=6.249366 \n",
+ "Φ=3.249696 \n",
+ "Φ=0.138522 \n",
+ "Φ=1.273747 \n",
+ "Φ=2.58034 \n",
+ "Φ=4.393693 \n",
+ "Φ=2.423585 \n",
+ "Φ=4.629328 \n",
+ "Φ=5.690853 \n",
+ "Φ=6.104519 \n",
+ "Φ=3.421678 \n",
+ "Φ=1.349138 \n",
+ "Φ=0.55333 \n",
+ "Φ=3.790889 \n",
+ "Φ=5.932651 \n",
+ "Φ=4.369467 \n",
+ "Φ=2.494834 \n",
+ "Φ=5.306912 \n",
+ "Φ=2.15989 \n",
+ "Φ=3.889154 \n",
+ "Φ=2.517412 \n",
+ "Φ=2.246299 \n",
+ "Φ=3.73517 \n",
+ "Φ=4.498719 \n",
+ "Φ=3.244504 \n",
+ "Φ=3.581996 \n",
+ "Φ=1.393125 \n",
+ "Φ=4.151796 \n",
+ "Φ=2.683883 \n",
+ "Φ=1.240942 \n",
+ "Φ=0.340174 \n",
+ "Φ=3.48663 \n",
+ "Φ=0.949722 \n",
+ "Φ=1.293172 \n",
+ "Φ=3.787945 \n",
+ "Φ=2.106081 \n",
+ "Φ=0.30652 \n",
+ "Φ=1.373746 \n",
+ "Φ=0.760249 \n",
+ "Φ=3.408446 \n",
+ "Φ=4.232327 \n",
+ "Φ=0.394715 \n",
+ "Φ=1.236003 \n",
+ "Φ=4.847875 \n",
+ "Φ=0.240215 \n",
+ "Φ=2.419465 \n",
+ "Φ=1.846335 \n",
+ "Φ=0.067265 \n",
+ "Φ=3.170262 \n",
+ "Φ=4.895206 \n",
+ "Rx \n",
+ "Φ=4.111167 \n",
+ "Rx \n",
+ "Φ=4.798768 \n",
+ "Rx \n",
+ "Φ=4.679726 \n",
+ "Rx \n",
+ "Φ=4.557504 \n",
+ "Rx \n",
+ "Φ=2.238335 \n",
+ "Rx \n",
+ "Φ=5.231757 \n",
+ "Rx \n",
+ "Φ=5.018765 \n",
+ "Rx \n",
+ "Φ=5.00668 \n",
+ "Rx \n",
+ "Φ=4.823779 \n",
+ "Rx \n",
+ "Φ=5.482968 \n",
+ "Rx \n",
+ "Φ=4.389771 \n",
+ "Rx \n",
+ "Φ=5.503168 \n",
+ "Rx \n",
+ "Φ=1.104411 \n",
+ "Rx \n",
+ "Φ=2.634775 \n",
+ "Rx \n",
+ "Φ=4.86731 \n",
+ "Rx \n",
+ "Φ=3.867882 \n",
+ "Rx \n",
+ "Φ=0.578086 \n",
+ "Rx \n",
+ "Φ=2.708509 \n",
+ "Rx \n",
+ "Φ=0.292954 \n",
+ "Rx \n",
+ "Φ=0.639817 \n",
+ "Rx \n",
+ "Φ=4.938755 \n",
+ "Rx \n",
+ "Φ=0.26351 \n",
+ "Rx \n",
+ "Φ=0.649944 \n",
+ "Rx \n",
+ "Φ=1.445288 \n",
+ "Rx \n",
+ "Φ=1.288006 \n",
+ "Rx \n",
+ "Φ=2.011957 \n",
+ "Rx \n",
+ "Φ=0.656606 \n",
+ "Rx \n",
+ "Φ=1.789616 \n",
+ "Rx \n",
+ "Φ=4.316199 \n",
+ "Rx \n",
+ "Φ=0.500276 \n",
+ "Rx \n",
+ "Φ=5.753627 \n",
+ "Rx \n",
+ "Φ=5.236824 \n",
+ "Rx \n",
+ "Φ=5.864152 \n",
+ "Rx \n",
+ "Φ=5.027697 \n",
+ "Rx \n",
+ "Φ=0.370843 \n",
+ "Rx \n",
+ "Φ=6.163542 \n",
+ "Rx \n",
+ "Φ=0.590149 \n",
+ "Rx \n",
+ "Φ=3.361783 \n",
+ "Rx \n",
+ "Φ=5.106832 \n",
+ "Rx \n",
+ "Φ=0.506531 \n",
+ "Rx \n",
+ "Φ=4.367286 \n",
+ "Rx \n",
+ "Φ=4.149371 \n",
+ "Rx \n",
+ "Φ=0.295156 \n",
+ "Rx \n",
+ "Φ=4.910675 \n",
+ "Rx \n",
+ "Φ=5.890782 \n",
+ "Rx \n",
+ "Φ=1.067684 \n",
+ "Rx \n",
+ "Φ=0.834866 \n",
+ "Rx \n",
+ "Φ=1.766803 \n",
+ "Rx \n",
+ "Φ=5.896167 \n",
+ "Rx \n",
+ "Φ=3.582371 \n",
+ "Rx \n",
+ "Φ=5.130454 \n",
+ "Rx \n",
+ "Φ=4.191583 \n",
+ "Rx \n",
+ "Φ=1.398723 \n",
+ "Rx \n",
+ "Φ=0.708826 \n",
+ "Rx \n",
+ "Φ=3.848973 \n",
+ "Rx \n",
+ "Φ=0.007539 \n",
+ "Rx \n",
+ "Φ=5.957073 \n",
+ "Rx \n",
+ "Φ=4.929918 \n",
+ "Rx \n",
+ "Φ=0.470306 \n",
+ "Rx \n",
+ "Φ=1.234868 \n",
+ "Rx \n",
+ "Φ=5.883131 \n",
+ "Rx \n",
+ "Φ=4.190691 \n",
+ "Rx \n",
+ "Φ=5.407502 \n",
+ "Rx \n",
+ "Φ=3.063063 \n",
+ "Rx \n",
+ "Φ=0.741908 \n",
+ "Rx \n",
+ "Φ=3.613984 \n",
+ "Rx \n",
+ "Φ=5.905017 \n",
+ "Rx \n",
+ "Φ=6.239608 \n",
+ "Rx \n",
+ "Φ=4.586435 \n",
+ "Rx \n",
+ "Φ=0.476804 \n",
+ "Rx \n",
+ "Φ=2.188401 \n",
+ "Rx \n",
+ "Φ=2.705943 \n",
+ "Rx \n",
+ "Φ=5.977386 \n",
+ "Rx \n",
+ "Φ=5.773445 \n",
+ "Rx \n",
+ "Φ=0.494187 \n",
+ "Rx \n",
+ "Φ=5.968146 \n",
+ "Rx \n",
+ "Φ=6.185182 \n",
+ "Rx \n",
+ "Φ=0.879328 \n",
+ "Rx \n",
+ "Φ=5.928112 \n",
+ "Rx \n",
+ "Φ=5.707495 \n",
+ "Rx \n",
+ "Φ=5.30698 \n",
+ "Rx \n",
+ "Φ=6.105315 \n",
+ "Rx \n",
+ "Φ=5.532099 \n",
+ "Rx \n",
+ "Φ=3.285435 \n",
+ "Rx \n",
+ "Φ=0.534954 \n",
+ "Rx \n",
+ "Φ=0.592085 \n",
+ "Rx \n",
+ "Φ=0.790503 \n",
+ "Rx \n",
+ "Φ=3.368243 \n",
+ "Rx \n",
+ "Φ=1.060728 \n",
+ "Rx \n",
+ "Φ=2.216159 \n",
+ "Rx \n",
+ "Φ=5.766026 \n",
+ "Rx \n",
+ "Φ=4.331543 \n",
+ "Rx \n",
+ "Φ=0.223964 \n",
+ "Rx \n",
+ "Φ=1.573842 \n",
+ "Rx \n",
+ "Φ=0.406852 \n",
+ "Rx \n",
+ "Φ=4.366317 \n",
+ "Rx \n",
+ "Φ=1.292481 \n",
+ "Rx \n",
+ "Φ=5.031463 \n",
+ "Rx \n",
+ "Φ=5.166416 \n",
+ "Rx \n",
+ "Φ=6.173081 \n",
+ "Rx \n",
+ "Φ=1.090456 \n",
+ "Rx \n",
+ "Φ=4.735713 \n",
+ "Rx \n",
+ "Φ=0.701705 \n",
+ "Rx \n",
+ "Φ=2.583912 \n",
+ "Rx \n",
+ "Φ=4.807318 \n",
+ "Rx \n",
+ "Φ=6.188227 \n",
+ "Rx \n",
+ "Φ=4.283213 \n",
+ "Rx \n",
+ "Φ=2.083521 \n",
+ "Rx \n",
+ "Φ=5.334074 \n",
+ "Rx \n",
+ "Φ=1.541775 \n",
+ "Rx \n",
+ "Φ=0.461365 \n",
+ "Rx \n",
+ "Φ=3.367578 \n",
+ "Rx \n",
+ "Φ=5.224168 \n",
+ "Rx \n",
+ "Φ=3.786129 \n",
+ "Rx \n",
+ "Φ=5.951465 \n",
+ "Rx \n",
+ "Φ=2.036483 \n",
+ "Rx \n",
+ "Φ=0.716593 \n",
+ "Rx \n",
+ "Φ=0.653814 \n",
+ "Rx \n",
+ "Φ=0.403793 \n",
+ "Rx \n",
+ "Φ=4.841495 \n",
+ "Rx \n",
+ "Φ=6.152504 \n",
+ "Rx \n",
+ "Φ=1.753119 \n",
+ "Rx \n",
+ "Φ=0.915715 \n",
+ "Rx \n",
+ "Φ=6.183754 \n",
+ "Rx \n",
+ "Φ=5.552007 \n",
+ "Rx \n",
+ "Φ=0.405352 \n",
+ "Rx \n",
+ "Φ=0.649651 \n",
+ "Rx \n",
+ "Φ=2.851103 \n",
+ "Rx \n",
+ "Φ=0.352729 \n",
+ "Rx \n",
+ "Φ=2.648613 \n",
+ "Rx \n",
+ "Φ=1.333794 \n",
+ "Rx \n",
+ "Φ=4.643844 \n",
+ "Rx \n",
+ "Φ=6.192925 \n",
+ "Rx \n",
+ "Φ=5.552185 \n",
+ "Rx \n",
+ "Φ=0.876964 \n",
+ "Rx \n",
+ "Φ=1.254354 \n",
+ "Rx \n",
+ "Φ=5.875212 \n",
+ "Rx \n",
+ "Φ=2.328009 \n",
+ "Rx \n",
+ "Φ=5.623293 \n",
+ "Rx \n",
+ "Φ=5.510579 \n",
+ "Rx \n",
+ "Φ=5.958951 \n",
+ "Rx \n",
+ "Φ=6.141232 \n",
+ "Rx \n",
+ "Φ=0.800049 \n",
+ "Rx \n",
+ "Φ=5.286289 \n",
+ "Rx \n",
+ "Φ=6.045347 \n",
+ "Rx \n",
+ "Φ=5.148291 \n",
+ "Rx \n",
+ "Φ=0.565298 \n",
+ "Rx \n",
+ "Φ=0.03593 \n",
+ "Rx \n",
+ "Φ=5.983408 \n",
+ "Rx \n",
+ "Φ=5.03917 \n",
+ "Rx \n",
+ "Φ=5.448441 \n",
+ "Rx \n",
+ "Φ=5.269003 \n",
+ "Rx \n",
+ "Φ=1.204242 \n",
+ "Rx \n",
+ "Φ=5.857423 \n",
+ "Rx \n",
+ "Φ=2.251163 \n",
+ "Rx \n",
+ "Φ=4.753022 \n",
+ "Rx \n",
+ "Φ=0.682843 \n",
+ "Rx \n",
+ "Φ=3.000533 \n",
+ "Rx \n",
+ "Φ=5.935015 \n",
+ "Rx \n",
+ "Φ=2.904912 \n",
+ "Rx \n",
+ "Φ=5.888742 \n",
+ "Rx \n",
+ "Φ=4.447837 \n",
+ "Rx \n",
+ "Φ=0.856083 \n",
+ "Rx \n",
+ "Φ=5.696131 \n",
+ "Rx \n",
+ "Φ=0.559776 \n",
+ "Rx \n",
+ "Φ=3.494746 \n",
+ "Rx \n",
+ "Φ=5.591853 \n",
+ "Rx \n",
+ "Φ=3.834896 \n",
+ "Rx \n",
+ "Φ=5.422421 \n",
+ "Rx \n",
+ "Φ=3.529429 \n",
+ "Rx \n",
+ "Φ=1.254754 \n",
+ "Rx \n",
+ "Φ=2.635342 \n",
+ "Rx \n",
+ "Φ=0.679982 \n",
+ "Rx \n",
+ "Φ=3.424967 \n",
+ "Rx \n",
+ "Φ=6.065396 \n",
+ "Rx \n",
+ "Φ=1.69365 \n",
+ "Rx \n",
+ "Φ=1.245323 \n",
+ "Rx \n",
+ "Φ=1.875654 \n",
+ "Rx \n",
+ "Φ=1.10281 \n",
+ "Rx \n",
+ "Φ=5.94631 \n",
+ "Rx \n",
+ "Φ=2.412097 \n",
+ "Rx \n",
+ "Φ=0.318832 \n",
+ "Rx \n",
+ "Φ=5.816157 \n",
+ "Rx \n",
+ "Φ=5.683556 \n",
+ "Rx \n",
+ "Φ=0.222807 \n",
+ "Rx \n",
+ "Φ=1.25624 \n",
+ "Rx \n",
+ "Φ=5.544027 \n",
+ "Rx \n",
+ "Φ=4.619689 \n",
+ "Rx \n",
+ "Φ=0.258315 \n",
+ "Rx \n",
+ "Φ=1.045031 \n",
+ "Rx \n",
+ "Φ=0.305626 \n",
+ "Rx \n",
+ "Φ=5.738826 \n",
+ "Rx \n",
+ "Φ=0.778546 \n",
+ "Rx \n",
+ "Φ=6.24891 \n",
+ "Rx \n",
+ "Φ=0.496022 \n",
+ "Rx \n",
+ "Φ=1.288108 \n",
+ "Rx \n",
+ "Φ=0.403505 \n",
+ "Rx \n",
+ "Φ=5.504552 \n",
+ "Rx \n",
+ "Φ=0.840011 \n",
+ "Rx \n",
+ "Φ=5.882125 \n",
+ "Rx \n",
+ "Φ=0.735589 \n",
+ "Rx \n",
+ "Φ=2.15312 \n",
+ "Rx \n",
+ "Φ=0.139734 \n",
+ "Rx \n",
+ "Φ=3.61675 \n",
+ "Rx \n",
+ "Φ=0.675296 \n",
+ "Rx \n",
+ "Φ=2.859581 \n",
+ "Rx \n",
+ "Φ=5.073108 \n",
+ "Rx \n",
+ "Φ=2.521006 \n",
+ "Rx \n",
+ "Φ=4.351672 \n",
+ "Rx \n",
+ "Φ=0.778585 \n",
+ "Rx \n",
+ "Φ=0.661831 \n",
+ "Rx \n",
+ "Φ=4.121133 \n",
+ "Rx \n",
+ "Φ=5.510561 \n",
+ "Rx \n",
+ "Φ=1.92584 \n",
+ "Rx \n",
+ "Φ=0.555191 \n",
+ "Rx \n",
+ "Φ=2.076437 \n",
+ "Rx \n",
+ "Φ=5.222039 \n",
+ "Rx \n",
+ "Φ=2.720047 \n",
+ "Rx \n",
+ "Φ=6.005232 \n",
+ "Rx \n",
+ "Φ=5.990629 \n",
+ "Rx \n",
+ "Φ=0.76667 \n",
+ "Rx \n",
+ "Φ=3.397702 \n",
+ "Rx \n",
+ "Φ=0.602444 \n",
+ "Rx \n",
+ "Φ=5.529282 \n",
+ "Rx \n",
+ "Φ=0.257937 \n",
+ "Rx \n",
+ "Φ=5.337912 \n",
+ "Rx \n",
+ "Φ=6.080914 \n",
+ "Rx \n",
+ "Φ=4.97531 \n",
+ "Rx \n",
+ "Φ=1.018485 \n",
+ "Rx \n",
+ "Φ=3.152843 \n",
+ "Rx \n",
+ "Φ=5.460362 \n",
+ "Rx \n",
+ "Φ=3.432201 \n",
+ "Rx \n",
+ "Φ=4.9188 \n",
+ "Rx \n",
+ "Φ=3.656346 \n",
+ "Rx \n",
+ "Φ=4.532256 \n",
+ "Rx \n",
+ "Φ=4.515144 \n",
+ "Rx \n",
+ "Φ=5.25766 \n",
+ "Rx \n",
+ "Φ=3.559666 \n",
+ "Rx \n",
+ "Φ=2.271279 \n",
+ "Rx \n",
+ "Φ=0.76858 \n",
+ "Rx \n",
+ "Φ=0.309922 \n",
+ "Rx \n",
+ "Φ=1.31112 \n",
+ "Rx \n",
+ "Φ=0.552972 \n",
+ "Rx \n",
+ "Φ=1.293348 \n",
+ "Rx \n",
+ "Φ=5.59553 \n",
+ "Rx \n",
+ "Φ=4.794579 \n",
+ "Rx \n",
+ "Φ=0.371401 \n",
+ "Rx \n",
+ "Φ=3.844747 \n",
+ "Rx \n",
+ "Φ=0.48024 \n",
+ "Rx \n",
+ "Φ=1.895073 \n",
+ "Rx \n",
+ "Φ=5.130186 \n",
+ "Rx \n",
+ "Φ=2.433952 \n",
+ "Rx \n",
+ "Φ=6.056596 \n",
+ "Rx \n",
+ "Φ=5.196549 \n",
+ "Rx \n",
+ "Φ=5.482927 \n",
+ "Rx \n",
+ "Φ=2.314022 \n",
+ "Rx \n",
+ "Φ=5.597915 \n",
+ "Rx \n",
+ "Φ=0.537686 \n",
+ "Rx \n",
+ "Φ=0.460969 \n",
+ "Rx \n",
+ "Φ=6.037437 \n",
+ "Rx \n",
+ "Φ=5.721382 \n",
+ "Rx \n",
+ "Φ=0.094011 \n",
+ "Rx \n",
+ "Φ=6.059151 \n",
+ "Rx \n",
+ "Φ=5.490896 \n",
+ "Rx \n",
+ "Φ=1.506382 \n",
+ "Rx \n",
+ "Φ=5.11387 \n",
+ "Rx \n",
+ "Φ=0.673847 \n",
+ "Rx \n",
+ "Φ=1.347644 \n",
+ "Rx \n",
+ "Φ=1.408244 \n",
+ "Rx \n",
+ "Φ=1.886661 \n",
+ "Rx \n",
+ "Φ=4.600362 \n",
+ "Rx \n",
+ "Φ=4.765711 \n",
+ "Rx \n",
+ "Φ=6.100399 \n",
+ "Rx \n",
+ "Φ=6.032626 \n",
+ "Rx \n",
+ "Φ=5.626348 \n",
+ "Rx \n",
+ "Φ=5.461269 \n",
+ "Rx \n",
+ "Φ=0.559568 \n",
+ "Rx \n",
+ "Φ=4.105584 \n",
+ "Rx \n",
+ "Φ=6.125924 \n",
+ "Rx \n",
+ "Φ=3.434089 \n",
+ "Rx \n",
+ "Φ=6.038115 \n",
+ "Rx \n",
+ "Φ=0.818199 \n",
+ "Rx \n",
+ "Φ=5.751651 \n",
+ "Rx \n",
+ "Φ=3.237513 \n",
+ "Rx \n",
+ "Φ=5.947411 \n",
+ "Rx \n",
+ "Φ=5.775262 \n",
+ "Rx \n",
+ "Φ=0.032946 \n",
+ "Rx \n",
+ "Φ=3.487864 \n",
+ "Rx \n",
+ "Φ=5.578233 \n",
+ "Rx \n",
+ "Φ=0.03494 \n",
+ "Rx \n",
+ "Φ=0.604967 \n",
+ "Rx \n",
+ "Φ=2.829807 \n",
+ "Rx \n",
+ "Φ=0.82484 \n",
+ "Rx \n",
+ "Φ=0.080448 \n",
+ "Rx \n",
+ "Φ=5.334842 \n",
+ "Rx \n",
+ "Φ=2.352312 \n",
+ "Rx \n",
+ "Φ=0.442029 \n",
+ "Rx \n",
+ "Φ=3.452828 \n",
+ "Rx \n",
+ "Φ=4.902159 \n",
+ "Rx \n",
+ "Φ=4.564227 \n",
+ "Rx \n",
+ "Φ=5.052621 \n",
+ "Rx \n",
+ "Φ=2.019212 \n",
+ "Rx \n",
+ "Φ=0.751452 \n",
+ "Rx \n",
+ "Φ=1.764954 \n",
+ "Rx \n",
+ "Φ=4.864384 \n",
+ "Rx \n",
+ "Φ=4.461536 \n",
+ "Rx \n",
+ "Φ=0.457642 \n",
+ "Rx \n",
+ "Φ=2.085509 \n",
+ "Rx \n",
+ "Φ=0.697387 \n",
+ "Rx \n",
+ "Φ=4.538641 \n",
+ "Rx \n",
+ "Φ=0.15097 \n",
+ "Rx \n",
+ "Φ=4.937475 \n",
+ "Rx \n",
+ "Φ=0.683027 \n",
+ "Rx \n",
+ "Φ=1.056382 \n",
+ "Rx \n",
+ "Φ=0.594254 \n",
+ "Rx \n",
+ "Φ=1.26071 \n",
+ "Rx \n",
+ "Φ=0.691985 \n",
+ "Rx \n",
+ "Φ=2.167483 \n",
+ "Rx \n",
+ "Φ=6.147681 \n",
+ "Rx \n",
+ "Φ=4.148376 \n",
+ "Rx \n",
+ "Φ=5.991078 \n",
+ "Rx \n",
+ "Φ=0.173982 \n",
+ "Rx \n",
+ "Φ=0.634188 \n",
+ "Rx \n",
+ "Φ=3.085025 \n",
+ "Rx \n",
+ "Φ=0.323437 \n",
+ "Rx \n",
+ "Φ=1.149445 \n",
+ "Rx \n",
+ "Φ=0.152023 \n",
+ "Rx \n",
+ "Φ=3.106661 \n",
+ "Rx \n",
+ "Φ=5.5909 \n",
+ "Rx \n",
+ "Φ=5.636135 \n",
+ "Rx \n",
+ "Φ=0.444195 \n",
+ "Rx \n",
+ "Φ=1.562035 \n",
+ "Rx \n",
+ "Φ=0.436904 \n",
+ "Rx \n",
+ "Φ=3.936772 \n",
+ "Rx \n",
+ "Φ=5.71758 \n",
+ "Rx \n",
+ "Φ=4.590366 \n",
+ "Rx \n",
+ "Φ=0.442376 \n",
+ "Rx \n",
+ "Φ=1.604465 \n",
+ "Rx \n",
+ "Φ=2.277571 \n",
+ "Rx \n",
+ "Φ=1.676089 \n",
+ "Rx \n",
+ "Φ=1.397397 \n",
+ "Rx \n",
+ "Φ=1.648678 \n",
+ "Rx \n",
+ "Φ=0.426358 \n",
+ "Rx \n",
+ "Φ=2.560536 \n",
+ "Rx \n",
+ "Φ=0.515554 \n",
+ "Rx \n",
+ "Φ=3.531953 \n",
+ "Rx \n",
+ "Φ=5.40073 \n",
+ "Rx \n",
+ "Φ=2.492931 \n",
+ "Rx \n",
+ "Φ=0.408546 \n",
+ "Rx \n",
+ "Φ=6.00019 \n",
+ "Rx \n",
+ "Φ=5.884334 \n",
+ "Rx \n",
+ "Φ=0.806948 \n",
+ "Rx \n",
+ "Φ=5.499504 \n",
+ "Rx \n",
+ "Φ=6.192439 \n",
+ "Rx \n",
+ "Φ=0.653464 \n",
+ "Rx \n",
+ "Φ=0.306885 \n",
+ "Rx \n",
+ "Φ=0.527804 \n",
+ "Rx \n",
+ "Φ=4.222791 \n",
+ "Rx \n",
+ "Φ=1.071051 \n",
+ "Rx \n",
+ "Φ=2.446701 \n",
+ "Rx \n",
+ "Φ=6.0465 \n",
+ "Rx \n",
+ "Φ=3.030736 \n",
+ "Rx \n",
+ "Φ=5.775913 \n",
+ "Rx \n",
+ "Φ=6.052705 \n",
+ "Rx \n",
+ "Φ=5.51065 \n",
+ "Rx \n",
+ "Φ=4.360849 \n",
+ "Rx \n",
+ "Φ=5.77816 \n",
+ "Rx \n",
+ "Φ=1.208785 \n",
+ "Rx \n",
+ "Φ=5.389978 \n",
+ "Rx \n",
+ "Φ=1.244357 \n",
+ "Rx \n",
+ "Φ=5.480961 \n",
+ "Rx \n",
+ "Φ=0.393527 \n",
+ "Rx \n",
+ "Φ=5.893412 \n",
+ "Rx \n",
+ "Φ=5.070905 \n",
+ "Rx \n",
+ "Φ=5.315692 \n",
+ "Rx \n",
+ "Φ=0.348756 \n",
+ "Rx \n",
+ "Φ=0.813499 \n",
+ "Rx \n",
+ "Φ=3.438958 \n",
+ "Rx \n",
+ "Φ=2.488806 \n",
+ "Rx \n",
+ "Φ=1.10161 \n",
+ "Rx \n",
+ "Φ=0.212947 \n",
+ "Rx \n",
+ "Φ=5.383655 \n",
+ "Rx \n",
+ "Φ=0.807251 \n",
+ "Rx \n",
+ "Φ=2.86702 \n",
+ "Rx \n",
+ "Φ=0.95765 \n",
+ "Rx \n",
+ "Φ=2.241206 \n",
+ "Rx \n",
+ "Φ=0.165837 \n",
+ "Rx \n",
+ "Φ=3.691645 \n",
+ "Rx \n",
+ "Φ=5.762626 \n",
+ "Rx \n",
+ "Φ=3.793299 \n",
+ "Rx \n",
+ "Φ=5.632533 \n",
+ "Rx \n",
+ "Φ=3.479519 \n",
+ "Rx \n",
+ "Φ=6.222873 \n",
+ "Rx \n",
+ "Φ=0.410909 \n",
+ "Rx \n",
+ "Φ=0.988811 \n",
+ "Rx \n",
+ "Φ=6.052097 \n",
+ "Rx \n",
+ "Φ=5.497817 \n",
+ "Rx \n",
+ "Φ=5.671982 \n",
+ "Rx \n",
+ "Φ=0.926386 \n",
+ "Rx \n",
+ "Φ=4.121945 \n",
+ "Rx \n",
+ "Φ=5.707714 \n",
+ "Rx \n",
+ "Φ=3.57431 \n",
+ "Rx \n",
+ "Φ=1.038994 \n",
+ "Rx \n",
+ "Φ=5.707628 \n",
+ "Rx \n",
+ "Φ=5.341893 \n",
+ "Rx \n",
+ "Φ=3.177383 \n",
+ "Rx \n",
+ "Φ=0.709591 \n",
+ "Rx \n",
+ "Φ=5.795729 \n",
+ "Rx \n",
+ "Φ=0.049651 \n",
+ "Rx \n",
+ "Φ=2.556792 \n",
+ "Rx \n",
+ "Φ=0.621709 \n",
+ "Rx \n",
+ "Φ=2.959595 \n",
+ "Rx \n",
+ "Φ=5.885783 \n",
+ "Rx \n",
+ "Φ=3.478934 \n",
+ "Rx \n",
+ "Φ=4.625776 \n",
+ "Rx \n",
+ "Φ=0.440591 \n",
+ "Rx \n",
+ "Φ=2.609147 \n",
+ "Rx \n",
+ "Φ=3.081812 \n",
+ "Rx \n",
+ "Φ=5.266368 \n",
+ "Rx \n",
+ "Φ=4.402574 \n",
+ "Rx \n",
+ "Φ=6.02446 \n",
+ "Rx \n",
+ "Φ=3.917143 \n",
+ "Rx \n",
+ "Φ=6.026132 \n",
+ "Rx \n",
+ "Φ=5.965583 \n",
+ "Rx \n",
+ "Φ=0.361244 \n",
+ "Rx \n",
+ "Φ=4.145178 \n",
+ "Rx \n",
+ "Φ=6.098362 \n",
+ "Rx \n",
+ "Φ=0.014796 \n",
+ "Rx \n",
+ "Φ=0.3997 \n",
+ "Rx \n",
+ "Φ=5.258728 \n",
+ "Rx \n",
+ "Φ=0.245968 \n",
+ "Rx \n",
+ "Φ=3.332304 \n",
+ "Rx \n",
+ "Φ=0.204017 \n",
+ "Rx \n",
+ "Φ=5.274594 \n",
+ "Rx \n",
+ "Φ=5.540388 \n",
+ "Rx \n",
+ "Φ=3.794239 \n",
+ "Rx \n",
+ "Φ=5.861092 \n",
+ "Rx \n",
+ "Φ=1.887455 \n",
+ "Rx \n",
+ "Φ=5.477751 \n",
+ "Rx \n",
+ "Φ=6.094766 \n",
+ "Rx \n",
+ "Φ=0.589588 \n",
+ "Rx \n",
+ "Φ=1.646275 \n",
+ "Rx \n",
+ "Φ=0.253535 \n",
+ "Rx \n",
+ "Φ=5.19575 \n",
+ "Rx \n",
+ "Φ=5.832339 \n",
+ "Rx \n",
+ "Φ=5.529996 \n",
+ "Rx \n",
+ "Φ=0.174249 \n",
+ "Rx \n",
+ "Φ=0.055412 \n",
+ "Rx \n",
+ "Φ=0.369165 \n",
+ "Rx \n",
+ "Φ=2.941869 \n",
+ "Rx \n",
+ "Φ=0.95613 \n",
+ "Rx \n",
+ "Φ=5.563012 \n",
+ "Rx \n",
+ "Φ=1.144801 \n",
+ "Rx \n",
+ "Φ=2.541998 \n",
+ "Rx \n",
+ "Φ=5.441632 \n",
+ "Rx \n",
+ "Φ=5.665062 \n",
+ "Rx \n",
+ "Φ=5.329839 \n",
+ "Rx \n",
+ "Φ=5.390441 \n",
+ "Rx \n",
+ "Φ=5.59517 \n",
+ "Rx \n",
+ "Φ=0.651666 \n",
+ "Rx \n",
+ "Φ=4.386967 \n",
+ "Rx \n",
+ "Φ=0.873506 \n",
+ "Rx \n",
+ "Φ=0.44286 \n",
+ "Rx \n",
+ "Φ=3.059708 \n",
+ "Rx \n",
+ "Φ=5.74655 \n",
+ "Rx \n",
+ "Φ=3.354411 \n",
+ "Rx \n",
+ "Φ=5.685407 \n",
+ "Rx \n",
+ "Φ=6.271435 \n",
+ "Rx \n",
+ "Φ=5.970342 \n",
+ "Rx \n",
+ "Φ=1.729997 \n",
+ "Rx \n",
+ "Φ=0.513922 \n",
+ "Rx \n",
+ "Φ=0.345606 \n",
+ "Rx \n",
+ "Φ=0.160364 \n",
+ "Rx \n",
+ "Φ=1.034036 \n",
+ "Rx \n",
+ "Φ=0.363697 \n",
+ "Rx \n",
+ "Φ=4.552649 \n",
+ "Rx \n",
+ "Φ=0.505565 \n",
+ "Rx \n",
+ "Φ=5.080065 \n",
+ "Rx \n",
+ "Φ=5.572168 \n",
+ "Rx \n",
+ "Φ=4.895953 \n",
+ "Rx \n",
+ "Φ=5.773544 \n",
+ "Rx \n",
+ "Φ=0.684394 \n",
+ "Rx \n",
+ "Φ=5.953957 \n",
+ "Rx \n",
+ "Φ=1.868683 \n",
+ "Rx \n",
+ "Φ=0.26808 \n",
+ "Rx \n",
+ "Φ=1.365323 \n",
+ "Rx \n",
+ "Φ=6.040389 \n",
+ "Rx \n",
+ "Φ=3.951247 \n",
+ "Rx \n",
+ "Φ=5.591268 \n",
+ "Rx \n",
+ "Φ=1.115203 \n",
+ "Rx \n",
+ "Φ=0.929745 \n",
+ "Rx \n",
+ "Φ=3.671094 \n",
+ "Rx \n",
+ "Φ=5.187432 \n",
+ "Rx \n",
+ "Φ=4.897287 \n",
+ "Rx \n",
+ "Φ=6.103978 \n",
+ "Rx \n",
+ "Φ=0.064582 \n",
+ "Rx \n",
+ "Φ=5.78929 \n",
+ "Rx \n",
+ "Φ=5.499949 \n",
+ "Rx \n",
+ "Φ=0.40333 \n",
+ "Rx \n",
+ "Φ=5.478814 \n",
+ "Rx \n",
+ "Φ=5.476877 \n",
+ "Rx \n",
+ "Φ=6.272425 \n",
+ "Rx \n",
+ "Φ=5.602262 \n",
+ "Rx \n",
+ "Φ=6.045495 \n",
+ "Rx \n",
+ "Φ=1.014917 \n",
+ "Rx \n",
+ "Φ=4.870618 \n",
+ "Rx \n",
+ "Φ=5.941364 \n",
+ "Rx \n",
+ "Φ=2.62115 \n",
+ "Rx \n",
+ "Φ=0.495693 \n",
+ "Rx \n",
+ "Φ=4.249803 \n",
+ "Rx \n",
+ "Φ=5.910705 \n",
+ "Rx \n",
+ "Φ=3.992782 \n",
+ "Rx \n",
+ "Φ=0.399467 \n",
+ "Rx \n",
+ "Φ=3.463013 \n",
+ "Rx \n",
+ "Φ=0.936905 \n",
+ "Rx \n",
+ "Φ=3.692586 \n",
+ "Rx \n",
+ "Φ=0.508965 \n",
+ "Rx \n",
+ "Φ=5.731854 \n",
+ "Rx \n",
+ "Φ=5.986298 \n",
+ "Rx \n",
+ "Φ=1.319504 \n",
+ "Rx \n",
+ "Φ=5.632258 \n",
+ "Rx \n",
+ "Φ=2.245879 \n",
+ "Rx \n",
+ "Φ=0.420665 \n",
+ "Rx \n",
+ "Φ=1.820597 \n",
+ "Rx \n",
+ "Φ=5.32624 \n",
+ "Rx \n",
+ "Φ=2.772043 \n",
+ "Rx \n",
+ "Φ=6.050412 \n",
+ "Rx \n",
+ "Φ=3.869199 \n",
+ "Rx \n",
+ "Φ=0.32471 \n",
+ "Rx \n",
+ "Φ=3.333698 \n",
+ "Rx \n",
+ "Φ=6.021444 \n",
+ "Rx \n",
+ "Φ=3.538862 \n",
+ "Rx \n",
+ "Φ=5.100892 \n",
+ "Rx \n",
+ "Φ=5.68698 \n",
+ "Rx \n",
+ "Φ=5.997609 \n",
+ "Rx \n",
+ "Φ=0.367749 \n",
+ "Rx \n",
+ "Φ=6.064768 \n",
+ "Rx \n",
+ "Φ=2.808211 \n",
+ "Rx \n",
+ "Φ=5.598608 \n",
+ "Rx \n",
+ "Φ=4.280651 \n",
+ "Rx \n",
+ "Φ=0.738796 \n",
+ "Rx \n",
+ "Φ=0.359443 \n",
+ "Rx \n",
+ "Φ=5.113844 \n",
+ "Rx \n",
+ "Φ=4.672468 \n",
+ "Rx \n",
+ "Φ=5.249619 \n",
+ "Rx \n",
+ "Φ=0.215846 \n",
+ "Rx \n",
+ "Φ=4.904875 \n",
+ "Rx \n",
+ "Φ=5.338997 \n",
+ "Rx \n",
+ "Φ=5.538879 \n",
+ "Rx \n",
+ "Φ=5.116698 \n",
+ "Rx \n",
+ "Φ=0.64096 \n",
+ "Rx \n",
+ "Φ=3.293761 \n",
+ "Rx \n",
+ "Φ=5.844496 \n",
+ "Rx \n",
+ "Φ=1.491882 \n",
+ "Rx \n",
+ "Φ=5.834535 \n",
+ "Rx \n",
+ "Φ=6.266952 \n",
+ "Rx \n",
+ "Φ=0.231428 \n",
+ "Rx \n",
+ "Φ=4.825308 \n",
+ "Rx \n",
+ "Φ=0.675455 \n",
+ "Rx \n",
+ "Φ=4.715618 \n",
+ "Rx \n",
+ "Φ=6.145477 \n",
+ "Rx \n",
+ "Φ=0.004037 \n",
+ "Rx \n",
+ "Φ=5.158862 \n",
+ "Rx \n",
+ "Φ=3.369199 \n",
+ "Rx \n",
+ "Φ=5.804774 \n",
+ "Rx \n",
+ "Φ=2.169729 \n",
+ "Rx \n",
+ "Φ=6.143086 \n",
+ "Rx \n",
+ "Φ=5.88023 \n",
+ "Rx \n",
+ "Φ=0.716596 \n",
+ "Rx \n",
+ "Φ=2.748763 \n",
+ "Rx \n",
+ "Φ=5.245144 \n",
+ "Rx \n",
+ "Φ=1.423123 \n",
+ "Rx \n",
+ "Φ=5.723868 \n",
+ "Rx \n",
+ "Φ=2.889604 \n",
+ "Rx \n",
+ "Φ=5.73382 \n",
+ "Rx \n",
+ "Φ=5.006678 \n",
+ "Rx \n",
+ "Φ=0.220705 \n",
+ "Rx \n",
+ "Φ=2.162038 \n",
+ "Rx \n",
+ "Φ=5.522914 \n",
+ "Rx \n",
+ "Φ=4.922113 \n",
+ "Rx \n",
+ "Φ=5.668667 \n",
+ "Rx \n",
+ "Φ=4.582551 \n",
+ "Rx \n",
+ "Φ=0.338757 \n",
+ "Rx \n",
+ "Φ=5.297967 \n",
+ "Rx \n",
+ "Φ=5.40702 \n",
+ "Rx \n",
+ "Φ=3.425866 \n",
+ "Rx \n",
+ "Φ=0.569833 \n",
+ "Rx \n",
+ "Φ=2.550067 \n",
+ "Rx \n",
+ "Φ=1.08323 \n",
+ "Rx \n",
+ "Φ=4.658903 \n",
+ "Rx \n",
+ "Φ=6.028077 \n",
+ "Rx \n",
+ "Φ=3.059846 \n",
+ "Rx \n",
+ "Φ=0.394903 \n",
+ "Rx \n",
+ "Φ=1.95923 \n",
+ "Rx \n",
+ "Φ=4.981399 \n",
+ "Rx \n",
+ "Φ=2.416769 \n",
+ "Rx \n",
+ "Φ=2.200501 \n",
+ "Rx \n",
+ "Φ=4.803453 \n",
+ "Rx \n",
+ "Φ=6.218475 \n",
+ "Rx \n",
+ "Φ=5.293279 \n",
+ "Rx \n",
+ "Φ=5.910487 \n",
+ "Rx \n",
+ "Φ=0.017424 \n",
+ "Rx \n",
+ "Φ=5.699953 \n",
+ "Rx \n",
+ "Φ=4.101439 \n",
+ "Rx \n",
+ "Φ=5.948572 \n",
+ "Rx \n",
+ "Φ=3.955862 \n",
+ "Rx \n",
+ "Φ=0.199616 \n",
+ "Rx \n",
+ "Φ=6.1524 \n",
+ "Rx \n",
+ "Φ=5.848672 \n",
+ "Rx \n",
+ "Φ=3.29141 \n",
+ "Rx \n",
+ "Φ=5.871175 \n",
+ "Rx \n",
+ "Φ=4.584176 \n",
+ "Rx \n",
+ "Φ=6.172786 \n",
+ "Rx \n",
+ "Φ=4.215571 \n",
+ "Rx \n",
+ "Φ=0.219702 \n",
+ "Rx \n",
+ "Φ=5.357694 \n",
+ "Rx \n",
+ "Φ=0.588621 \n",
+ "Rx \n",
+ "Φ=0.796209 \n",
+ "Rx \n",
+ "Φ=0.267153 \n",
+ "Rx \n",
+ "Φ=4.046767 \n",
+ "Rx \n",
+ "Φ=0.285468 \n",
+ "Rx \n",
+ "Φ=5.58557 \n",
+ "Rx \n",
+ "Φ=0.569798 \n",
+ "Rx \n",
+ "Φ=5.104734 \n",
+ "Rx \n",
+ "Φ=0.203044 \n",
+ "Rx \n",
+ "Φ=1.54279 \n",
+ "Rx \n",
+ "Φ=5.629851 \n",
+ "Rx \n",
+ "Φ=2.276301 \n",
+ "Rx \n",
+ "Φ=5.506982 \n",
+ "Rx \n",
+ "Φ=5.507067 \n",
+ "Rx \n",
+ "Φ=5.590512 \n",
+ "Rx \n",
+ "Φ=3.037182 \n",
+ "Rx \n",
+ "Φ=0.922182 \n",
+ "Rx \n",
+ "Φ=5.611233 \n",
+ "Rx \n",
+ "Φ=0.422143 \n",
+ "Rx \n",
+ "Φ=2.812007 \n",
+ "Rx \n",
+ "Φ=0.209277 \n",
+ "Rx \n",
+ "Φ=2.332124 \n",
+ "Rx \n",
+ "Φ=0.41518 \n",
+ "Rx \n",
+ "Φ=0.105469 \n",
+ "Rx \n",
+ "Φ=0.857114 \n",
+ "Rx \n",
+ "Φ=5.682467 \n",
+ "Rx \n",
+ "Φ=0.983445 \n",
+ "Rx \n",
+ "Φ=3.690203 \n",
+ "Rx \n",
+ "Φ=5.314439 \n",
+ "Rx \n",
+ "Φ=1.838969 \n",
+ "Rx \n",
+ "Φ=2.419455 \n",
+ "Rx \n",
+ "Φ=5.390959 \n",
+ "Rx \n",
+ "Φ=4.067388 \n",
+ "Rx \n",
+ "Φ=5.265258 \n",
+ "Rx \n",
+ "Φ=0.477379 \n",
+ "Rx \n",
+ "Φ=2.929825 \n",
+ "Rx \n",
+ "Φ=6.016577 \n",
+ "Rx \n",
+ "Φ=5.72474 \n",
+ "Rx \n",
+ "Φ=5.735746 \n",
+ "Rx \n",
+ "Φ=5.490343 \n",
+ "Rx \n",
+ "Φ=0.244737 \n",
+ "Rx \n",
+ "Φ=0.093864 \n",
+ "Rx \n",
+ "Φ=6.163369 \n",
+ "Rx \n",
+ "Φ=4.684547 \n",
+ "Rx \n",
+ "Φ=5.836186 \n",
+ "Rx \n",
+ "Φ=2.148812 \n",
+ "Rx \n",
+ "Φ=0.229644 \n",
+ "Rx \n",
+ "Φ=0.122718 \n",
+ "Rx \n",
+ "Φ=0.147226 \n",
+ "Rx \n",
+ "Φ=1.099638 \n",
+ "Rx \n",
+ "Φ=0.543051 \n",
+ "Rx \n",
+ "Φ=3.859599 \n",
+ "Rx \n",
+ "Φ=6.150594 \n",
+ "Rx \n",
+ "Φ=1.521992 \n",
+ "Rx \n",
+ "Φ=1.039816 \n",
+ "Rx \n",
+ "Φ=2.296459 \n",
+ "Rx \n",
+ "Φ=6.047517 \n",
+ "Rx \n",
+ "Φ=5.506269 \n",
+ "Rx \n",
+ "Φ=6.076713 \n",
+ "Rx \n",
+ "Φ=2.056638 \n",
+ "Rx \n",
+ "Φ=0.238015 \n",
+ "Rx \n",
+ "Φ=5.770754 \n",
+ "Rx \n",
+ "Φ=0.520825 \n",
+ "Rx \n",
+ "Φ=0.76241 \n",
+ "Rx \n",
+ "Φ=0.19925 \n",
+ "Rx \n",
+ "Φ=1.527306 \n",
+ "Rx \n",
+ "Φ=0.403382 \n",
+ "Rx \n",
+ "Φ=5.856351 \n",
+ "Rx \n",
+ "Φ=5.677914 \n",
+ "Rx \n",
+ "Φ=3.769758 \n",
+ "Rx \n",
+ "Φ=5.269437 \n",
+ "Rx \n",
+ "Φ=4.990839 \n",
+ "Rx \n",
+ "Φ=0.682524 \n",
+ "Rx \n",
+ "Φ=0.598236 \n",
+ "Rx \n",
+ "Φ=0.439628 \n",
+ "Rx \n",
+ "Φ=2.957199 \n",
+ "Rx \n",
+ "Φ=5.484201 \n",
+ "Rx \n",
+ "Φ=0.021418 \n",
+ "Rx \n",
+ "Φ=0.445561 \n",
+ "Rx \n",
+ "Φ=4.373176 \n",
+ "Rx \n",
+ "Φ=5.653504 \n",
+ "Rx \n",
+ "Φ=2.067441 \n",
+ "Rx \n",
+ "Φ=4.274569 \n",
+ "Rx \n",
+ "Φ=5.964213 \n",
+ "Rx \n",
+ "Φ=2.231541 \n",
+ "Rx \n",
+ "Φ=6.114936 \n",
+ "Rx \n",
+ "Φ=0.093337 \n",
+ "Rx \n",
+ "Φ=0.019955 \n",
+ "Rx \n",
+ "Φ=6.042181 \n",
+ "Rx \n",
+ "Φ=3.190376 \n",
+ "Rx \n",
+ "Φ=6.238858 \n",
+ "Rx \n",
+ "Φ=0.541327 \n",
+ "Rx \n",
+ "Φ=5.902791 \n",
+ "Rx \n",
+ "Φ=5.195998 \n",
+ "Rx \n",
+ "Φ=6.113575 \n",
+ "Rx \n",
+ "Φ=1.427451 \n",
+ "Rx \n",
+ "Φ=0.258085 \n",
+ "Rx \n",
+ "Φ=2.423441 \n",
+ "Rx \n",
+ "Φ=0.133222 \n",
+ "Rx \n",
+ "Φ=1.413268 \n",
+ "Rx \n",
+ "Φ=5.947855 \n",
+ "Rx \n",
+ "Φ=0.269122 \n",
+ "Rx \n",
+ "Φ=0.450593 \n",
+ "Rx \n",
+ "Φ=4.436088 \n",
+ "Rx \n",
+ "Φ=6.195168 \n",
+ "Rx \n",
+ "Φ=3.042674 \n",
+ "Rx \n",
+ "Φ=5.774974 \n",
+ "Rx \n",
+ "Φ=2.660357 \n",
+ "Rx \n",
+ "Φ=0.522278 \n",
+ "Rx \n",
+ "Φ=5.754474 \n",
+ "Rx \n",
+ "Φ=0.227203 \n",
+ "Rx \n",
+ "Φ=4.141827 \n",
+ "Rx \n",
+ "Φ=5.576982 \n",
+ "Rx \n",
+ "Φ=0.633933 \n",
+ "Rx \n",
+ "Φ=0.177753 \n",
+ "Rx \n",
+ "Φ=4.304442 \n",
+ "Rx \n",
+ "Φ=5.880523 \n",
+ "Rx \n",
+ "Φ=0.53588 \n",
+ "Rx \n",
+ "Φ=5.542716 \n",
+ "Rx \n",
+ "Φ=3.31531 \n",
+ "Rx \n",
+ "Φ=6.204582 \n",
+ "Rx \n",
+ "Φ=5.432882 \n",
+ "Rx \n",
+ "Φ=5.994762 \n",
+ "Rx \n",
+ "Φ=2.458468 \n",
+ "Rx \n",
+ "Φ=5.753867 \n",
+ "Rx \n",
+ "Φ=1.980775 \n",
+ "Rx \n",
+ "Φ=1.325169 \n",
+ "Rx \n",
+ "Φ=3.070916 \n",
+ "Rx \n",
+ "Φ=0.580697 \n",
+ "Rx \n",
+ "Φ=3.83876 \n",
+ "Rx \n",
+ "Φ=5.85581 \n",
+ "Rx \n",
+ "Φ=5.762809 \n",
+ "Rx \n",
+ "Φ=5.647271 \n",
+ "Rx \n",
+ "Φ=3.855965 \n",
+ "Rx \n",
+ "Φ=1.150993 \n",
+ "Rx \n",
+ "Φ=5.893975 \n",
+ "Rx \n",
+ "Φ=4.598866 \n",
+ "Rx \n",
+ "Φ=1.094243 \n",
+ "Rx \n",
+ "Φ=2.030832 \n",
+ "Rx \n",
+ "Φ=5.956455 \n",
+ "Rx \n",
+ "Φ=6.11105 \n",
+ "Rx \n",
+ "Φ=1.216368 \n",
+ "Rx \n",
+ "Φ=5.707755 \n",
+ "Rx \n",
+ "Φ=2.740713 \n",
+ "Rx \n",
+ "Φ=0.107237 \n",
+ "Rx \n",
+ "Φ=5.214346 \n",
+ "Rx \n",
+ "Φ=5.939324 \n",
+ "Rx \n",
+ "Φ=5.487156 \n",
+ "Rx \n",
+ "Φ=0.700745 \n",
+ "Rx \n",
+ "Φ=3.941168 \n",
+ "Rx \n",
+ "Φ=0.456103 \n",
+ "Rx \n",
+ "Φ=5.500603 \n",
+ "Rx \n",
+ "Φ=0.239863 \n",
+ "Rx \n",
+ "Φ=6.254082 \n",
+ "Rx \n",
+ "Φ=0.369538 \n",
+ "Rx \n",
+ "Φ=3.260581 \n",
+ "Rx \n",
+ "Φ=5.986911 \n",
+ "Rx \n",
+ "Φ=5.699078 \n",
+ "Rx \n",
+ "Φ=0.123895 \n",
+ "Rx \n",
+ "Φ=0.168214 \n",
+ "Rx \n",
+ "Φ=0.598502 \n",
+ "Rx \n",
+ "Φ=2.031381 \n",
+ "Rx \n",
+ "Φ=5.767624 \n",
+ "Rx \n",
+ "Φ=1.714811 \n",
+ "Rx \n",
+ "Φ=0.696723 \n",
+ "Rx \n",
+ "Φ=4.138627 \n",
+ "Rx \n",
+ "Φ=5.890336 \n",
+ "Rx \n",
+ "Φ=0.30598 \n",
+ "Rx \n",
+ "Φ=0.588127 \n",
+ "Rx \n",
+ "Φ=5.330174 \n",
+ "Rx \n",
+ "Φ=5.986883 \n",
+ "Rx \n",
+ "Φ=5.762938 \n",
+ "Rx \n",
+ "Φ=0.679186 \n",
+ "Rx \n",
+ "Φ=4.094739 \n",
+ "Rx \n",
+ "Φ=5.604207 \n",
+ "Rx \n",
+ "Φ=0.232575 \n",
+ "Rx \n",
+ "Φ=5.875659 \n",
+ "Rx \n",
+ "Φ=2.274241 \n",
+ "Rx \n",
+ "Φ=5.671712 \n",
+ "Rx \n",
+ "Φ=4.453421 \n",
+ "Rx \n",
+ "Φ=0.623544 \n",
+ "Rx \n",
+ "Φ=1.780345 \n",
+ "Rx \n",
+ "Φ=0.59897 \n",
+ "Rx \n",
+ "Φ=3.073695 \n",
+ "Rx \n",
+ "Φ=5.683233 \n",
+ "Rx \n",
+ "Φ=1.68671 \n",
+ "Rx \n",
+ "Φ=0.549226 \n",
+ "Rx \n",
+ "Φ=4.797519 \n",
+ "Rx \n",
+ "Φ=5.429404 \n",
+ "Rx \n",
+ "Φ=5.68189 \n",
+ "Rx \n",
+ "Φ=0.376 \n",
+ "Rx \n",
+ "Φ=2.925263 \n",
+ "Rx \n",
+ "Φ=1.769202 \n",
+ "Rx \n",
+ "Φ=3.1745 \n",
+ "Rx \n",
+ "Φ=1.679441 \n",
+ "Rx \n",
+ "Φ=4.887175 \n",
+ "Rx \n",
+ "Φ=0.052026 \n",
+ "Rx \n",
+ "Φ=1.514181 \n",
+ "Rx \n",
+ "Φ=6.228542 \n",
+ "Rx \n",
+ "Φ=1.478118 \n",
+ "Rx \n",
+ "Φ=0.472186 \n",
+ "Rx \n",
+ "Φ=2.922438 \n",
+ "Rx \n",
+ "Φ=5.992849 \n",
+ "Rx \n",
+ "Φ=2.85018 \n",
+ "Rx \n",
+ "Φ=0.30378 \n",
+ "Rx \n",
+ "Φ=4.017153 \n",
+ "Rx \n",
+ "Φ=6.083374 \n",
+ "Rx \n",
+ "Φ=5.454276 \n",
+ "Rx \n",
+ "Φ=5.961007 \n",
+ "Rx \n",
+ "Φ=5.482207 \n",
+ "Rx \n",
+ "Φ=6.012536 \n",
+ "Rx \n",
+ "Φ=6.199626 \n",
+ "Rx \n",
+ "Φ=6.243308 \n",
+ "Rx \n",
+ "Φ=5.611726 \n",
+ "Rx \n",
+ "Φ=5.961654 \n",
+ "Rx \n",
+ "Φ=2.806171 \n",
+ "Rx \n",
+ "Φ=0.480714 \n",
+ "Rx \n",
+ "Φ=0.523293 \n",
+ "Rx \n",
+ "Φ=0.759843 \n",
+ "Rx \n",
+ "Φ=0.916306 \n",
+ "Rx \n",
+ "Φ=5.886832 \n",
+ "Rx \n",
+ "Φ=4.351615 \n",
+ "Rx \n",
+ "Φ=0.433352 \n",
+ "Rx \n",
+ "Φ=5.957581 \n",
+ "Rx \n",
+ "Φ=0.295648 \n",
+ "Rx \n",
+ "Φ=3.981763 \n",
+ "Rx \n",
+ "Φ=5.380175 \n",
+ "Rx \n",
+ "Φ=6.032838 \n",
+ "Rx \n",
+ "Φ=5.572622 \n",
+ "Rx \n",
+ "Φ=3.151324 \n",
+ "Rx \n",
+ "Φ=6.061702 \n",
+ "Rx \n",
+ "Φ=5.257801 \n",
+ "Rx \n",
+ "Φ=6.075365 \n",
+ "Rx \n",
+ "Φ=3.256506 \n",
+ "Rx \n",
+ "Φ=0.089869 \n",
+ "Rx \n",
+ "Φ=3.066276 \n",
+ "Rx \n",
+ "Φ=5.972261 \n",
+ "Rx \n",
+ "Φ=3.367587 \n",
+ "Rx \n",
+ "Φ=1.020491 \n",
+ "Rx \n",
+ "Φ=2.72645 \n",
+ "Rx \n",
+ "Φ=0.759872 \n",
+ "Rx \n",
+ "Φ=4.715894 \n",
+ "Rx \n",
+ "Φ=5.291848 \n",
+ "Rx \n",
+ "Φ=4.900551 \n",
+ "Rx \n",
+ "Φ=5.709273 \n",
+ "Rx \n",
+ "Φ=4.776625 \n",
+ "Rx \n",
+ "Φ=1.455011 \n",
+ "Rx \n",
+ "Φ=3.94456 \n",
+ "Rx \n",
+ "Φ=5.446214 \n",
+ "Rx \n",
+ "Φ=4.517696 \n",
+ "Rx \n",
+ "Φ=5.628627 \n",
+ "Rx \n",
+ "Φ=2.040727 \n",
+ "Rx \n",
+ "Φ=4.030961 \n",
+ "Rx \n",
+ "Φ=3.656951 \n",
+ "Rx \n",
+ "Φ=6.234532 \n",
+ "Rx \n",
+ "Φ=2.442188 \n",
+ "Rx \n",
+ "Φ=5.616431 \n",
+ "Rx \n",
+ "Φ=4.244303 \n",
+ "Rx \n",
+ "Φ=0.072164 \n",
+ "Rx \n",
+ "Φ=2.224473 \n",
+ "Rx \n",
+ "Φ=5.663511 \n",
+ "Rx \n",
+ "Φ=2.157919 \n",
+ "Rx \n",
+ "Φ=0.354552 \n",
+ "Rx \n",
+ "Φ=5.131273 \n",
+ "Rx \n",
+ "Φ=5.913191 \n",
+ "Rx \n",
+ "Φ=4.58095 \n",
+ "Rx \n",
+ "Φ=0.089204 \n",
+ "Rx \n",
+ "Φ=5.804518 \n",
+ "Rx \n",
+ "Φ=0.34211 \n",
+ "Rx \n",
+ "Φ=5.761009 \n",
+ "Rx \n",
+ "Φ=0.175531 \n",
+ "Rx \n",
+ "Φ=1.051173 \n",
+ "Rx \n",
+ "Φ=5.527978 \n",
+ "Rx \n",
+ "Φ=1.370609 \n",
+ "Rx \n",
+ "Φ=0.367708 \n",
+ "Rx \n",
+ "Φ=1.649056 \n",
+ "Rx \n",
+ "Φ=6.171052 \n",
+ "Rx \n",
+ "Φ=0.02159 \n",
+ "Rx \n",
+ "Φ=5.891977 \n",
+ "Rx \n",
+ "Φ=0.126299 \n",
+ "Rx \n",
+ "Φ=0.141127 \n",
+ "Rx \n",
+ "Φ=0.58573 \n",
+ "Rx \n",
+ "Φ=0.259033 \n",
+ "Rx \n",
+ "Φ=0.376157 \n",
+ "Rx \n",
+ "Φ=0.829004 \n",
+ "Rx \n",
+ "Φ=4.780165 \n",
+ "Rx \n",
+ "Φ=0.444614 \n",
+ "Rx \n",
+ "Φ=4.162666 \n",
+ "Rx \n",
+ "Φ=0.319395 \n",
+ "Rx \n",
+ "Φ=4.466288 \n",
+ "Rx \n",
+ "Φ=5.547516 \n",
+ "Rx \n",
+ "Φ=1.235662 \n",
+ "Rx \n",
+ "Φ=0.292482 \n",
+ "Rx \n",
+ "Φ=1.20604 \n",
+ "Rx \n",
+ "Φ=0.248722 \n",
+ "Rx \n",
+ "Φ=5.796192 \n",
+ "Rx \n",
+ "Φ=0.270089 \n",
+ "Rx \n",
+ "Φ=5.554708 \n",
+ "Rx \n",
+ "Φ=0.953723 \n",
+ "Rx \n",
+ "Φ=1.405474 \n",
+ "Rx \n",
+ "Φ=0.868107 \n",
+ "Rx \n",
+ "Φ=2.588087 \n",
+ "Rx \n",
+ "Φ=1.143901 \n",
+ "Rx \n",
+ "Φ=0.91266 \n",
+ "Rx \n",
+ "Φ=0.642695 \n",
+ "Rx \n",
+ "Φ=2.921651 \n",
+ "Rx \n",
+ "Φ=0.529808 \n",
+ "Rx \n",
+ "Φ=2.473485 \n",
+ "Rx \n",
+ "Φ=0.505636 \n",
+ "Rx \n",
+ "Φ=5.757487 \n",
+ "Rx \n",
+ "Φ=1.974719 \n",
+ "Rx \n",
+ "Φ=0.972625 \n",
+ "Rx \n",
+ "Φ=4.833805 \n",
+ "Rx \n",
+ "Φ=0.247393 \n",
+ "Rx \n",
+ "Φ=5.78553 \n",
+ "Rx \n",
+ "Φ=0.346737 \n",
+ "Rx \n",
+ "Φ=0.512465 \n",
+ "Rx \n",
+ "Φ=4.994394 \n",
+ "Rx \n",
+ "Φ=5.637971 \n",
+ "Rx \n",
+ "Φ=3.284399 \n",
+ "Rx \n",
+ "Φ=5.751342 \n",
+ "Rx \n",
+ "Φ=4.939043 \n",
+ "Rx \n",
+ "Φ=6.142857 \n",
+ "Rx \n",
+ "Φ=1.851632 \n",
+ "Rx \n",
+ "Φ=0.661271 \n",
+ "Rx \n",
+ "Φ=3.410028 \n",
+ "Rx \n",
+ "Φ=6.138608 \n",
+ "Rx \n",
+ "Φ=4.878046 \n",
+ "Rx \n",
+ "Φ=5.642364 \n",
+ "Rx \n",
+ "Φ=3.221759 \n",
+ "Rx \n",
+ "Φ=5.988355 \n",
+ "Rx \n",
+ "Φ=3.363302 \n",
+ "Rx \n",
+ "Φ=0.256849 \n",
+ "Rx \n",
+ "Φ=0.877555 \n",
+ "Rx \n",
+ "Φ=0.151943 \n",
+ "Rx \n",
+ "Φ=5.359201 \n",
+ "Rx \n",
+ "Φ=0.126935 \n",
+ "Rx \n",
+ "Φ=2.312049 \n",
+ "Rx \n",
+ "Φ=6.051176 \n",
+ "Rx \n",
+ "Φ=4.151575 \n",
+ "Rx \n",
+ "Φ=0.53088 \n",
+ "Rx \n",
+ "Φ=1.879984 \n",
+ "Rx \n",
+ "Φ=0.463282 \n",
+ "Rx \n",
+ "Φ=0.330203 \n",
+ "Rx \n",
+ "Φ=6.134952 \n",
+ "Rx \n",
+ "Φ=5.460946 \n",
+ "Rx \n",
+ "Φ=0.242377 \n",
+ "Rx \n",
+ "Φ=2.215751 \n",
+ "Rx \n",
+ "Φ=5.923563 \n",
+ "Rx \n",
+ "Φ=2.452255 \n",
+ "Rx \n",
+ "Φ=0.796936 \n",
+ "Rx \n",
+ "Φ=2.229198 \n",
+ "Rx \n",
+ "Φ=0.496373 \n",
+ "Rx \n",
+ "Φ=0.274294 \n",
+ "Rx \n",
+ "Φ=0.378424 \n",
+ "Rx \n",
+ "Φ=0.118014 \n",
+ "Rx \n",
+ "Φ=0.474273 \n",
+ "Rx \n",
+ "Φ=2.042912 \n",
+ "Rx \n",
+ "Φ=5.704379 \n",
+ "Rx \n",
+ "Φ=2.15425 \n",
+ "Rx \n",
+ "Φ=0.645851 \n",
+ "Rx \n",
+ "Φ=0.789982 \n",
+ "Rx \n",
+ "Φ=6.142256 \n",
+ "Rx \n",
+ "Φ=5.262004 \n",
+ "Rx \n",
+ "Φ=5.496612 \n",
+ "Rx \n",
+ "Φ=5.371904 \n",
+ "Rx \n",
+ "Φ=5.274125 \n",
+ "Rx \n",
+ "Φ=0.809532 \n",
+ "Rx \n",
+ "Φ=4.867855 \n",
+ "Rx \n",
+ "Φ=6.233254 \n",
+ "Rx \n",
+ "Φ=4.478462 \n",
+ "Rx \n",
+ "Φ=3.212741 \n",
+ "Rx \n",
+ "Φ=1.834619 \n",
+ "Rx \n",
+ "Φ=4.474403 \n",
+ "Rx \n",
+ "Φ=4.29797 \n",
+ "Rx \n",
+ "Φ=4.968981 \n",
+ "Rx \n",
+ "Φ=5.698392 \n",
+ "Rx \n",
+ "Φ=2.711169 \n",
+ "Rx \n",
+ "Φ=6.096551 \n",
+ "Rx \n",
+ "Φ=4.422465 \n",
+ "Rx \n",
+ "Φ=6.208921 \n",
+ "Rx \n",
+ "Φ=1.437135 \n",
+ "Rx \n",
+ "Φ=6.020212 \n",
+ "Rx \n",
+ "Φ=6.199684 \n",
+ "Rx \n",
+ "Φ=0.290385 \n",
+ "Rx \n",
+ "Φ=0.683948 \n",
+ "Rx \n",
+ "Φ=0.514469 \n",
+ "Rx \n",
+ "Φ=4.501836 \n",
+ "Rx \n",
+ "Φ=0.685003 \n",
+ "Rx \n",
+ "Φ=5.659673 \n",
+ "Rx \n",
+ "Φ=5.739558 \n",
+ "Rx \n",
+ "Φ=3.821398 \n",
+ "Rx \n",
+ "Φ=0.309769 \n",
+ "Rx \n",
+ "Φ=2.094481 \n",
+ "Rx \n",
+ "Φ=0.374739 \n",
+ "Rx \n",
+ "Φ=0.646314 \n",
+ "Rx \n",
+ "Φ=5.620713 \n",
+ "Rx \n",
+ "Φ=2.246282 \n",
+ "Rx \n",
+ "Φ=0.236089 \n",
+ "Rx \n",
+ "Φ=3.754583 \n",
+ "Rx \n",
+ "Φ=0.550612 \n",
+ "Rx \n",
+ "Φ=0.399894 \n",
+ "Rx \n",
+ "Φ=0.411515 \n",
+ "Rx \n",
+ "Φ=3.821363 \n",
+ "Rx \n",
+ "Φ=0.160269 \n",
+ "Rx \n",
+ "Φ=2.216543 \n",
+ "Rx \n",
+ "Φ=0.84423 \n",
+ "Rx \n",
+ "Φ=4.490015 \n",
+ "Rx \n",
+ "Φ=0.588618 \n",
+ "Rx \n",
+ "Φ=2.883528 \n",
+ "Rx \n",
+ "Φ=5.769517 \n",
+ "Rx \n",
+ "Φ=3.19416 \n",
+ "Rx \n",
+ "Φ=0.776956 \n",
+ "Rx \n",
+ "Φ=1.635549 \n",
+ "Rx \n",
+ "Φ=0.696736 \n",
+ "Rx \n",
+ "Φ=1.331777 \n",
+ "Rx \n",
+ "Φ=5.756767 \n",
+ "Rx \n",
+ "Φ=0.571521 \n",
+ "Rx \n",
+ "Φ=0.734265 \n",
+ "Rx \n",
+ "Φ=3.247648 \n",
+ "Rx \n",
+ "Φ=0.442729 \n",
+ "Rx \n",
+ "Φ=0.881649 \n",
+ "Rx \n",
+ "Φ=0.449237 \n",
+ "Rx \n",
+ "Φ=5.895602 \n",
+ "Rx \n",
+ "Φ=5.865561 \n",
+ "Rx \n",
+ "Φ=3.882013 \n",
+ "Rx \n",
+ "Φ=4.7672 \n",
+ "Rx \n",
+ "Φ=0.01085 \n",
+ "Rx \n",
+ "Φ=1.538399 \n",
+ "Rx \n",
+ "Φ=0.153758 \n",
+ "Rx \n",
+ "Φ=5.151371 \n",
+ "Rx \n",
+ "Φ=5.180034 \n",
+ "Rx \n",
+ "Φ=1.196623 \n",
+ "Rx \n",
+ "Φ=3.642712 \n",
+ "Rx \n",
+ "Φ=4.345944 \n",
+ "Rx \n",
+ "Φ=2.22147 \n",
+ "Rx \n",
+ "Φ=1.576057 \n",
+ "Rx \n",
+ "Φ=5.802205 \n",
+ "Rx \n",
+ "Φ=0.737114 \n",
+ "Rx \n",
+ "Φ=3.053096 \n",
+ "Rx \n",
+ "Φ=0.418288 \n",
+ "Rx \n",
+ "Φ=6.159663 \n",
+ "Rx \n",
+ "Φ=0.234534 \n",
+ "Rx \n",
+ "Φ=5.415891 \n",
+ "Rx \n",
+ "Φ=5.781673 \n",
+ "Rx \n",
+ "Φ=4.917287 \n",
+ "Rx \n",
+ "Φ=6.113872 \n",
+ "Rx \n",
+ "Φ=3.75766 \n",
+ "Rx \n",
+ "Φ=5.905518 \n",
+ "Rx \n",
+ "Φ=0.199658 \n",
+ "Rx \n",
+ "Φ=0.287202 \n",
+ "Rx \n",
+ "Φ=3.656166 \n",
+ "Rx \n",
+ "Φ=5.952086 \n",
+ "Rx \n",
+ "Φ=0.777164 \n",
+ "Rx \n",
+ "Φ=0.106117 \n",
+ "Rx \n",
+ "Φ=3.989855 \n",
+ "Rx \n",
+ "Φ=0.192069 \n",
+ "Rx \n",
+ "Φ=5.172423 \n",
+ "Rx \n",
+ "Φ=0.658626 \n",
+ "Rx \n",
+ "Φ=0.607144 \n",
+ "Rx \n",
+ "Φ=5.824566 \n",
+ "Rx \n",
+ "Φ=4.594279 \n",
+ "Rx \n",
+ "Φ=0.322789 \n",
+ "Rx \n",
+ "Φ=5.92231 \n",
+ "Rx \n",
+ "Φ=6.081014 \n",
+ "Rx \n",
+ "Φ=4.774493 \n",
+ "Rx \n",
+ "Φ=5.701267 \n",
+ "Rx \n",
+ "Φ=0.969143 \n",
+ "Rx \n",
+ "Φ=5.90225 \n",
+ "Rx \n",
+ "Φ=1.669819 \n",
+ "Rx \n",
+ "Φ=0.615986 \n",
+ "Rx \n",
+ "Φ=3.068441 \n",
+ "Rx \n",
+ "Φ=0.124125 \n",
+ "Rx \n",
+ "Φ=3.874383 \n",
+ "Rx \n",
+ "Φ=0.597905 \n",
+ "Rx \n",
+ "Φ=2.035267 \n",
+ "Rx \n",
+ "Φ=5.532399 \n",
+ "Rx \n",
+ "Φ=4.804654 \n",
+ "Rx \n",
+ "Φ=5.734675 \n",
+ "Rx \n",
+ "Φ=2.515332 \n",
+ "Rx \n",
+ "Φ=0.209558 \n",
+ "Rx \n",
+ "Φ=0.377728 \n",
+ "Rx \n",
+ "Φ=5.873464 \n",
+ "Rx \n",
+ "Φ=2.236805 \n",
+ "Rx \n",
+ "Φ=0.603499 \n",
+ "Rx \n",
+ "Φ=3.985186 \n",
+ "Rx \n",
+ "Φ=5.424746 \n",
+ "Rx \n",
+ "Φ=5.527621 \n",
+ "Rx \n",
+ "Φ=0.768672 \n",
+ "Rx \n",
+ "Φ=3.409334 \n",
+ "Rx \n",
+ "Φ=0.45491 \n",
+ "Rx \n",
+ "Φ=4.582095 \n",
+ "Rx \n",
+ "Φ=0.648781 \n",
+ "Rx \n",
+ "Φ=1.955986 \n",
+ "Rx \n",
+ "Φ=5.870405 \n",
+ "Rx \n",
+ "Φ=1.97374 \n",
+ "Rx \n",
+ "Φ=5.055052 \n",
+ "Rx \n",
+ "Φ=5.092413 \n",
+ "Rx \n",
+ "Φ=0.430646 \n",
+ "Rx \n",
+ "Φ=0.962243 \n",
+ "Rx \n",
+ "Φ=5.744127 \n",
+ "Rx \n",
+ "Φ=1.282586 \n",
+ "Rx \n",
+ "Φ=5.36026 \n",
+ "Rx \n",
+ "Φ=5.930805 \n",
+ "Rx \n",
+ "Φ=2.637202 \n",
+ "Rx \n",
+ "Φ=4.649165 \n",
+ "Rx \n",
+ "Φ=0.512184 \n",
+ "Rx \n",
+ "Φ=2.843777 \n",
+ "Rx \n",
+ "Φ=0.702965 \n",
+ "Rx \n",
+ "Φ=0.673577 \n",
+ "Rx \n",
+ "Φ=6.185262 \n",
+ "Rx \n",
+ "Φ=5.015092 \n",
+ "Rx \n",
+ "Φ=0.533244 \n",
+ "Rx \n",
+ "Φ=2.31875 \n",
+ "Rx \n",
+ "Φ=6.02042 \n",
+ "Rx \n",
+ "Φ=2.001742 \n",
+ "Rx \n",
+ "Φ=6.00725 \n",
+ "Rx \n",
+ "Φ=4.650943 \n",
+ "Rx \n",
+ "Φ=0.440106 \n",
+ "Rx \n",
+ "Φ=2.238034 \n",
+ "Rx \n",
+ "Φ=5.964191 \n",
+ "Rx \n",
+ "Φ=4.52516 \n",
+ "Rx \n",
+ "Φ=0.226549 \n",
+ "Rx \n",
+ "Φ=3.217925 \n",
+ "Rx \n",
+ "Φ=5.97242 \n",
+ "Rx \n",
+ "Φ=0.9776 \n",
+ "Rx \n",
+ "Φ=6.037387 \n",
+ "Rx \n",
+ "Φ=2.909105 \n",
+ "Rx \n",
+ "Φ=5.986803 \n",
+ "Rx \n",
+ "Φ=2.770111 \n",
+ "Rx \n",
+ "Φ=0.51219 \n",
+ "Rx \n",
+ "Φ=4.642721 \n",
+ "Rx \n",
+ "Φ=0.62577 \n",
+ "Rx \n",
+ "Φ=3.775027 \n",
+ "Rx \n",
+ "Φ=5.72146 \n",
+ "Rx \n",
+ "Φ=0.041805 \n",
+ "Rx \n",
+ "Φ=5.983768 \n",
+ "Rx \n",
+ "Φ=5.270229 \n",
+ "Rx \n",
+ "Φ=5.821635 \n",
+ "Rx \n",
+ "Φ=4.288329 \n",
+ "Rx \n",
+ "Φ=0.049484 \n",
+ "Rx \n",
+ "Φ=5.14279 \n",
+ "Rx \n",
+ "Φ=6.016288 \n",
+ "Rx \n",
+ "Φ=2.461146 \n",
+ "Rx \n",
+ "Φ=0.282737 \n",
+ "Rx \n",
+ "Φ=2.710993 \n",
+ "Rx \n",
+ "Φ=0.408261 \n",
+ "Rx \n",
+ "Φ=5.209425 \n",
+ "Rx \n",
+ "Φ=0.181144 \n",
+ "Rx \n",
+ "Φ=4.748677 \n",
+ "Rx \n",
+ "Φ=0.042377 \n",
+ "Rx \n",
+ "Φ=5.393231 \n",
+ "Rx \n",
+ "Φ=6.020608 \n",
+ "Rx \n",
+ "Φ=4.512503 \n",
+ "Rx \n",
+ "Φ=6.070316 \n",
+ "Rx \n",
+ "Φ=4.057084 \n",
+ "Rx \n",
+ "Φ=6.126184 \n",
+ "Rx \n",
+ "Φ=5.84446 \n",
+ "Rx \n",
+ "Φ=0.693109 \n",
+ "Rx \n",
+ "Φ=1.407963 \n",
+ "Rx \n",
+ "Φ=0.134619 \n",
+ "Rx \n",
+ "Φ=0.36961 \n",
+ "Rx \n",
+ "Φ=0.704427 \n",
+ "Rx \n",
+ "Φ=2.635927 \n",
+ "Rx \n",
+ "Φ=0.736153 \n",
+ "Rx \n",
+ "Φ=2.535345 \n",
+ "Rx \n",
+ "Φ=1.216072 \n",
+ "Rx \n",
+ "Φ=1.715714 \n",
+ "Rx \n",
+ "Φ=5.19745 \n",
+ "Rx \n",
+ "Φ=4.748149 \n",
+ "Rx \n",
+ "Φ=1.68525 \n",
+ "Rx \n",
+ "Φ=2.389896 \n",
+ "Rx \n",
+ "Φ=0.514223 \n",
+ "Rx \n",
+ "Φ=1.849406 \n",
+ "Rx \n",
+ "Φ=5.582746 \n",
+ "Rx \n",
+ "Φ=1.020868 \n",
+ "Rx \n",
+ "Φ=0.211478 \n",
+ "Rx \n",
+ "Φ=2.050511 \n",
+ "Rx \n",
+ "Φ=5.734562 \n",
+ "Rx \n",
+ "Φ=1.389873 \n",
+ "Rx \n",
+ "Φ=6.037964 \n",
+ "Rx \n",
+ "Φ=0.915284 \n",
+ "Rx \n",
+ "Φ=0.437865 \n",
+ "Rx \n",
+ "Φ=3.864395 \n",
+ "Rx \n",
+ "Φ=6.097204 \n",
+ "Rx \n",
+ "Φ=6.140713 \n",
+ "Rx \n",
+ "Φ=0.169182 \n",
+ "Rx \n",
+ "Φ=2.210514 \n",
+ "Rx \n",
+ "Φ=6.221275 \n",
+ "Rx \n",
+ "Φ=3.957274 \n",
+ "Rx \n",
+ "Φ=0.192499 \n",
+ "Rx \n",
+ "Φ=0.051607 \n",
+ "Rx \n",
+ "Φ=0.483043 \n",
+ "Rx \n",
+ "Φ=4.342912 \n",
+ "Rx \n",
+ "Φ=0.190721 \n",
+ "Rx \n",
+ "Φ=3.175534 \n",
+ "Rx \n",
+ "Φ=0.609377 \n",
+ "Rx \n",
+ "Φ=3.790427 \n",
+ "Rx \n",
+ "Φ=6.074801 \n",
+ "Rx \n",
+ "Φ=1.646758 \n",
+ "Rx \n",
+ "Φ=0.109677 \n",
+ "Rx \n",
+ "Φ=5.377106 \n",
+ "Rx \n",
+ "Φ=0.509768 \n",
+ "Rx \n",
+ "Φ=5.187879 \n",
+ "Rx \n",
+ "Φ=5.955078 \n",
+ "Rx \n",
+ "Φ=1.279841 \n",
+ "Rx \n",
+ "Φ=6.013673 \n",
+ "Rx \n",
+ "Φ=5.079069 \n",
+ "Rx \n",
+ "Φ=0.541909 \n",
+ "Rx \n",
+ "Φ=6.192406 \n",
+ "Rx \n",
+ "Φ=0.407665 \n",
+ "Rx \n",
+ "Φ=4.04051 \n",
+ "Rx \n",
+ "Φ=5.828236 \n",
+ "Rx \n",
+ "Φ=1.633663 \n",
+ "Rx \n",
+ "Φ=6.179789 \n",
+ "Rx \n",
+ "Φ=6.029337 \n",
+ "Rx \n",
+ "Φ=5.707877 \n",
+ "Rx \n",
+ "Φ=4.85108 \n",
+ "Rx \n",
+ "Φ=0.633817 \n",
+ "Rx \n",
+ "Φ=2.25236 \n",
+ "Rx \n",
+ "Φ=0.234213 \n",
+ "Rx \n",
+ "Φ=4.853767 \n",
+ "Rx \n",
+ "Φ=0.620388 \n",
+ "Rx \n",
+ "Φ=2.751823 \n",
+ "Rx \n",
+ "Φ=5.279283 \n",
+ "Rx \n",
+ "Φ=1.991755 \n",
+ "Rx \n",
+ "Φ=0.795202 \n",
+ "Rx \n",
+ "Φ=3.611869 \n",
+ "Rx \n",
+ "Φ=5.810605 \n",
+ "Rx \n",
+ "Φ=0.664203 \n",
+ "Rx \n",
+ "Φ=5.766565 \n",
+ "Rx \n",
+ "Φ=2.214422 \n",
+ "Rx \n",
+ "Φ=5.705516 \n",
+ "Rx \n",
+ "Φ=2.125092 \n",
+ "Rx \n",
+ "Φ=5.439929 \n",
+ "Rx \n",
+ "Φ=4.463951 \n",
+ "Rx \n",
+ "Φ=0.078791 \n",
+ "Rx \n",
+ "Φ=6.106416 \n",
+ "Rx \n",
+ "Φ=1.3209 \n",
+ "Rx \n",
+ "Φ=0.634288 \n",
+ "Rx \n",
+ "Φ=4.462417 \n",
+ "Rx \n",
+ "Φ=1.94352 \n",
+ "Rx \n",
+ "Φ=5.548046 \n",
+ "Rx \n",
+ "Φ=1.172074 \n",
+ "Rx \n",
+ "Φ=5.87396 \n",
+ "Rx \n",
+ "Φ=1.381752 \n",
+ "Rx \n",
+ "Φ=0.336108 \n",
+ "Rx \n",
+ "Φ=5.214009 \n",
+ "Rx \n",
+ "Φ=5.492446 \n",
+ "Rx \n",
+ "Φ=3.309733 \n",
+ "Rx \n",
+ "Φ=5.890855 \n",
+ "Rx \n",
+ "Φ=4.248166 \n",
+ "Rx \n",
+ "Φ=0.149401 \n",
+ "Rx \n",
+ "Φ=3.950501 \n",
+ "Rx \n",
+ "Φ=0.26253 \n",
+ "Rx \n",
+ "Φ=0.747313 \n",
+ "Rx \n",
+ "Φ=5.661896 \n",
+ "Rx \n",
+ "Φ=0.339121 \n",
+ "Rx \n",
+ "Φ=0.215693 \n",
+ "Rx \n",
+ "Φ=0.13843 \n",
+ "Rx \n",
+ "Φ=6.162247 \n",
+ "Rx \n",
+ "Φ=0.694243 \n",
+ "Rx \n",
+ "Φ=6.108113 \n",
+ "Rx \n",
+ "Φ=0.705923 \n",
+ "Rx \n",
+ "Φ=0.093209 \n",
+ "Rx \n",
+ "Φ=4.36354 \n",
+ "Rx \n",
+ "Φ=5.8645 \n",
+ "Rx \n",
+ "Φ=3.87493 \n",
+ "Rx \n",
+ "Φ=0.446626 \n",
+ "Rx \n",
+ "Φ=1.090107 \n",
+ "Rx \n",
+ "Φ=0.304385 \n",
+ "Rx \n",
+ "Φ=4.571389 \n",
+ "Rx \n",
+ "Φ=6.029644 \n",
+ "Rx \n",
+ "Φ=0.671549 \n",
+ "Rx \n",
+ "Φ=5.936913 \n",
+ "Rx \n",
+ "Φ=2.954612 \n",
+ "Rx \n",
+ "Φ=5.535393 \n",
+ "Rx \n",
+ "Φ=1.513224 \n",
+ "Rx \n",
+ "Φ=6.129279 \n",
+ "Rx \n",
+ "Φ=1.843456 \n",
+ "Rx \n",
+ "Φ=0.513004 \n",
+ "Rx \n",
+ "Φ=1.368096 \n",
+ "Rx \n",
+ "Φ=0.27467 \n",
+ "Rx \n",
+ "Φ=1.062216 \n",
+ "Rx \n",
+ "Φ=0.339203 \n",
+ "Rx \n",
+ "Φ=2.894647 \n",
+ "Rx \n",
+ "Φ=0.527774 \n",
+ "Rx \n",
+ "Φ=4.973097 \n",
+ "Rx \n",
+ "Φ=0.329017 \n",
+ "Rx \n",
+ "Φ=1.479373 \n",
+ "Rx \n",
+ "Φ=0.840942 \n",
+ "Rx \n",
+ "Φ=0.131621 \n",
+ "Rx \n",
+ "Φ=0.479951 \n",
+ "Rx \n",
+ "Φ=1.04624 \n",
+ "Rx \n",
+ "Φ=5.963802 \n",
+ "Rx \n",
+ "Φ=4.341473 \n",
+ "Rx \n",
+ "Φ=0.121443 \n",
+ "Rx \n",
+ "Φ=0.610838 \n",
+ "Rx \n",
+ "Φ=1.174955 \n",
+ "Rx \n",
+ "Φ=3.833879 \n",
+ "Rx \n",
+ "Φ=5.752223 \n",
+ "Rx \n",
+ "Φ=3.872452 \n",
+ "Rx \n",
+ "Φ=0.619346 \n",
+ "Rx \n",
+ "Φ=2.289293 \n",
+ "Rx \n",
+ "Φ=5.905861 \n",
+ "Rx \n",
+ "Φ=5.496791 \n",
+ "Rx \n",
+ "Φ=0.93532 \n",
+ "Rx \n",
+ "Φ=2.272491 \n",
+ "Rx \n",
+ "Φ=5.587387 \n",
+ "Rx \n",
+ "Φ=2.706606 \n",
+ "Rx \n",
+ "Φ=1.787944 \n",
+ "Rx \n",
+ "Φ=2.547212 \n",
+ "Rx \n",
+ "Φ=4.685188 \n",
+ "Rx \n",
+ "Φ=2.155974 \n",
+ "Rx \n",
+ "Φ=5.85245 \n",
+ "Rx \n",
+ "Φ=0.778962 \n",
+ "Rx \n",
+ "Φ=5.708081 \n",
+ "Rx \n",
+ "Φ=2.884803 \n",
+ "Rx \n",
+ "Φ=6.000214 \n",
+ "Rx \n",
+ "Φ=0.098014 \n",
+ "Rx \n",
+ "Φ=0.287319 \n",
+ "Rx \n",
+ "Φ=5.162668 \n",
+ "Rx \n",
+ "Φ=0.121889 \n",
+ "Rx \n",
+ "Φ=1.06132 \n",
+ "Rx \n",
+ "Φ=0.140368 \n",
+ "Rx \n",
+ "Φ=4.603299 \n",
+ "Rx \n",
+ "Φ=0.243943 \n",
+ "Rx \n",
+ "Φ=5.616124 \n",
+ "Rx \n",
+ "Φ=6.143945 \n",
+ "Rx \n",
+ "Φ=1.144914 \n",
+ "Rx \n",
+ "Φ=0.247742 \n",
+ "Rx \n",
+ "Φ=5.044332 \n",
+ "Rx \n",
+ "Φ=5.933216 \n",
+ "Rx \n",
+ "Φ=4.11938 \n",
+ "Rx \n",
+ "Φ=0.480003 \n",
+ "Rx \n",
+ "Φ=1.883586 \n",
+ "Rx \n",
+ "Φ=0.371312 \n",
+ "Rx \n",
+ "Φ=5.11189 \n",
+ "Rx \n",
+ "Φ=5.94146 \n",
+ "Rx \n",
+ "Φ=5.968884 \n",
+ "Rx \n",
+ "Φ=0.681234 \n",
+ "Rx \n",
+ "Φ=0.929026 \n",
+ "Rx \n",
+ "Φ=5.834167 \n",
+ "Rx \n",
+ "Φ=6.155504 \n",
+ "Rx \n",
+ "Φ=5.882969 \n",
+ "Rx \n",
+ "Φ=1.754451 \n",
+ "Rx \n",
+ "Φ=0.482145 \n",
+ "Rx \n",
+ "Φ=0.433835 \n",
+ "Rx \n",
+ "Φ=0.188211 \n",
+ "Rx \n",
+ "Φ=1.926479 \n",
+ "Rx \n",
+ "Φ=0.150143 \n",
+ "Rx \n",
+ "Φ=3.666027 \n",
+ "Rx \n",
+ "Φ=5.846424 \n",
+ "Rx \n",
+ "Φ=4.894188 \n",
+ "Rx \n",
+ "Φ=5.990025 \n",
+ "Rx \n",
+ "Φ=3.054882 \n",
+ "Rx \n",
+ "Φ=0.162822 \n",
+ "Rx \n",
+ "Φ=1.322073 \n",
+ "Rx \n",
+ "Φ=5.763988 \n",
+ "Rx \n",
+ "Φ=1.858661 \n",
+ "Rx \n",
+ "Φ=5.678976 \n",
+ "Rx \n",
+ "Φ=4.820748 \n",
+ "Rx \n",
+ "Φ=5.672497 \n",
+ "Rx \n",
+ "Φ=2.795694 \n",
+ "Rx \n",
+ "Φ=0.480084 \n",
+ "Rx \n",
+ "Φ=6.174042 \n",
+ "Rx \n",
+ "Φ=0.378408 \n",
+ "Rx \n",
+ "Φ=2.042352 \n",
+ "Rx \n",
+ "Φ=6.178054 \n",
+ "Rx \n",
+ "Φ=1.064056 \n",
+ "Rx \n",
+ "Φ=6.071468 \n",
+ "Rx \n",
+ "Φ=5.017133 \n",
+ "Rx \n",
+ "Φ=5.782992 \n",
+ "Rx \n",
+ "Φ=2.77024 \n",
+ "Rx \n",
+ "Φ=0.383731 \n",
+ "Rx \n",
+ "Φ=4.827526 \n",
+ "Rx \n",
+ "Φ=5.503674 \n",
+ "Rx \n",
+ "Φ=3.06586 \n",
+ "Rx \n",
+ "Φ=0.545082 \n",
+ "Rx \n",
+ "Φ=1.514253 \n",
+ "Rx \n",
+ "Φ=0.257736 \n",
+ "Rx \n",
+ "Φ=2.384984 \n",
+ "Rx \n",
+ "Φ=5.912742 \n",
+ "Rx \n",
+ "Φ=3.099524 \n",
+ "Rx \n",
+ "Φ=5.952479 \n",
+ "Rx \n",
+ "Φ=4.247372 \n",
+ "Rx \n",
+ "Φ=0.66842 \n",
+ "Rx \n",
+ "Φ=3.811989 \n",
+ "Rx \n",
+ "Φ=2.023185 \n",
+ "Rx \n",
+ "Φ=5.97819 \n",
+ "Rx \n",
+ "Φ=6.116104 \n",
+ "Rx \n",
+ "Φ=1.626243 \n",
+ "Rx \n",
+ "Φ=0.427583 \n",
+ "Rx \n",
+ "Φ=3.592958 \n",
+ "Rx \n",
+ "Φ=0.532454 \n",
+ "Rx \n",
+ "Φ=1.164043 \n",
+ "Rx \n",
+ "Φ=0.391522 \n",
+ "Rx \n",
+ "Φ=4.747811 \n",
+ "Rx \n",
+ "Φ=0.183597 \n",
+ "Rx \n",
+ "Φ=3.8199 \n",
+ "Rx \n",
+ "Φ=0.235484 \n",
+ "Rx \n",
+ "Φ=3.68655 \n",
+ "Rx \n",
+ "Φ=6.141033 \n",
+ "Rx \n",
+ "Φ=1.97839 \n",
+ "Rx \n",
+ "Φ=6.187654 \n",
+ "Rx \n",
+ "Φ=3.238694 \n",
+ "Rx \n",
+ "Φ=5.985883 \n",
+ "Rx \n",
+ "Φ=3.045913 \n",
+ "Rx \n",
+ "Φ=0.429637 \n",
+ "Rx \n",
+ "Φ=2.580599 \n",
+ "Rx \n",
+ "Φ=6.147983 \n",
+ "Rx \n",
+ "Φ=6.215522 \n",
+ "Rx \n",
+ "Φ=0.451457 \n",
+ "Rx \n",
+ "Φ=0.256774 \n",
+ "Rx \n",
+ "Φ=0.449303 \n",
+ "Rx \n",
+ "Φ=3.386691 \n",
+ "Rx \n",
+ "Φ=5.897196 \n",
+ "Rx \n",
+ "Φ=5.50102 \n",
+ "Rx \n",
+ "Φ=0.179949 \n",
+ "Rx \n",
+ "Φ=2.51378 \n",
+ "Rx \n",
+ "Φ=0.274805 \n",
+ "Rx \n",
+ "Φ=4.798041 \n",
+ "Rx \n",
+ "Φ=5.8301 \n",
+ "Rx \n",
+ "Φ=2.391176 \n",
+ "Rx \n",
+ "Φ=0.664226 \n",
+ "Rx \n",
+ "Φ=4.111117 \n",
+ "Rx \n",
+ "Φ=0.682193 \n",
+ "Rx \n",
+ "Φ=5.67518 \n",
+ "Rx \n",
+ "Φ=6.1007 \n",
+ "Rx \n",
+ "Φ=5.546181 \n",
+ "Rx \n",
+ "Φ=5.573027 \n",
+ "Rx \n",
+ "Φ=3.661511 \n",
+ "Rx \n",
+ "Φ=5.735799 \n",
+ "Rx \n",
+ "Φ=2.352501 \n",
+ "Rx \n",
+ "Φ=5.771584 \n",
+ "Rx \n",
+ "Φ=3.355577 \n",
+ "Rx \n",
+ "Φ=5.648242 \n",
+ "Rx \n",
+ "Φ=0.918384 \n",
+ "Rx \n",
+ "Φ=5.506802 \n",
+ "Rx \n",
+ "Φ=1.408481 \n",
+ "Rx \n",
+ "Φ=5.722102 \n",
+ "Rx \n",
+ "Φ=1.810067 \n",
+ "Rx \n",
+ "Φ=5.714008 \n",
+ "Rx \n",
+ "Φ=2.974203 \n",
+ "Rx \n",
+ "Φ=0.619444 \n",
+ "Rx \n",
+ "Φ=3.506439 \n",
+ "Rx \n",
+ "Φ=5.223181 \n",
+ "Rx \n",
+ "Φ=4.503524 \n",
+ "Rx \n",
+ "Φ=0.650305 \n",
+ "Rx \n",
+ "Φ=2.109519 \n",
+ "Rx \n",
+ "Φ=0.34848 \n",
+ "Rx \n",
+ "Φ=5.102518 \n",
+ "Rx \n",
+ "Φ=1.162887 \n",
+ "Rx \n",
+ "Φ=1.247959 \n",
+ "Rx \n",
+ "Φ=0.228058 \n",
+ "Rx \n",
+ "Φ=2.038943 \n",
+ "Rx \n",
+ "Φ=0.562287 \n",
+ "Rx \n",
+ "Φ=2.785995 \n",
+ "Rx \n",
+ "Φ=5.593439 \n",
+ "Rx \n",
+ "Φ=1.745865 \n",
+ "Rx \n",
+ "Φ=5.33428 \n",
+ "Rx \n",
+ "Φ=0.774986 \n",
+ "Rx \n",
+ "Φ=0.442689 \n",
+ "Rx \n",
+ "Φ=1.274169 \n",
+ "Rx \n",
+ "Φ=1.022356 \n",
+ "Rx \n",
+ "Φ=4.138717 \n",
+ "Rx \n",
+ "Φ=0.218075 \n",
+ "Rx \n",
+ "Φ=2.106163 \n",
+ "Rx \n",
+ "Φ=0.201127 \n",
+ "Rx \n",
+ "Φ=3.56185 \n",
+ "Rx \n",
+ "Φ=0.192844 \n",
+ "Rx \n",
+ "Φ=1.292544 \n",
+ "Rx \n",
+ "Φ=0.303825 \n",
+ "Rx \n",
+ "Φ=4.453529 \n",
+ "Rx \n",
+ "Φ=0.209774 \n",
+ "Rx \n",
+ "Φ=1.023447 \n",
+ "Rx \n",
+ "Φ=0.125513 \n",
+ "Rx \n",
+ "Φ=4.701956 \n",
+ "Rx \n",
+ "Φ=5.843035 \n",
+ "Rx \n",
+ "Φ=2.132197 \n",
+ "Rx \n",
+ "Φ=5.699192 \n",
+ "Rx \n",
+ "Φ=1.76511 \n",
+ "Rx \n",
+ "Φ=6.093622 \n",
+ "Rx \n",
+ "Φ=5.164295 \n",
+ "Rx \n",
+ "Φ=0.52066 \n",
+ "Rx \n",
+ "Φ=3.739147 \n",
+ "Rx \n",
+ "Φ=0.305798 \n",
+ "Rx \n",
+ "Φ=3.025383 \n",
+ "Rx \n",
+ "Φ=0.286443 \n",
+ "Rx \n",
+ "Φ=3.112603 \n",
+ "Rx \n",
+ "Φ=0.363183 \n",
+ "Rx \n",
+ "Φ=5.492462 \n",
+ "Rx \n",
+ "Φ=0.221422 \n",
+ "Rx \n",
+ "Φ=0.309104 \n",
+ "Rx \n",
+ "Φ=6.068068 \n",
+ "Rx \n",
+ "Φ=3.054927 \n",
+ "Rx \n",
+ "Φ=5.819165 \n",
+ "Rx \n",
+ "Φ=5.531789 \n",
+ "Rx \n",
+ "Φ=5.96784 \n",
+ "Rx \n",
+ "Φ=0.504413 \n",
+ "Rx \n",
+ "Φ=0.654484 \n",
+ "Rx \n",
+ "Φ=5.128969 \n",
+ "Rx \n",
+ "Φ=0.169306 \n",
+ "Rx \n",
+ "Φ=5.11649 \n",
+ "Rx \n",
+ "Φ=5.85703 \n",
+ "Rx \n",
+ "Φ=1.728085 \n",
+ "Rx \n",
+ "Φ=0.291225 \n",
+ "Rx \n",
+ "Φ=3.346451 \n",
+ "Rx \n",
+ "Φ=0.107862 \n",
+ "Rx \n",
+ "Φ=0.667012 \n",
+ "Rx \n",
+ "Φ=0.297114 \n",
+ "Rx \n",
+ "Φ=5.268813 \n",
+ "Rx \n",
+ "Φ=5.752027 \n",
+ "Rx \n",
+ "Φ=4.236765 \n",
+ "Rx \n",
+ "Φ=5.768319 \n",
+ "Rx \n",
+ "Φ=4.465554 \n",
+ "Rx \n",
+ "Φ=0.508294 \n",
+ "Rx \n",
+ "Φ=5.274503 \n",
+ "Rx \n",
+ "Φ=0.218289 \n",
+ "Rx \n",
+ "Φ=2.277798 \n",
+ "Rx \n",
+ "Φ=5.436114 \n",
+ "Rx \n",
+ "Φ=2.484038 \n",
+ "Rx \n",
+ "Φ=0.762733 \n",
+ "Rx \n",
+ "Φ=4.294309 \n",
+ "Rx \n",
+ "Φ=5.909907 \n",
+ "Rx \n",
+ "Φ=3.754619 \n",
+ "Rx \n",
+ "Φ=5.470907 \n",
+ "Rx \n",
+ "Φ=3.292547 \n",
+ "Rx \n",
+ "Φ=5.825438 \n",
+ "Rx \n",
+ "Φ=5.312235 \n",
+ "Rx \n",
+ "Φ=5.49617 \n",
+ "Rx \n",
+ "Φ=5.926378 \n",
+ "Rx \n",
+ "Φ=5.391782 \n",
+ "Rx \n",
+ "Φ=5.589007 \n",
+ "Rx \n",
+ "Φ=5.902274 \n",
+ "Rx \n",
+ "Φ=2.009543 \n",
+ "Rx \n",
+ "Φ=4.873274 \n",
+ "Rx \n",
+ "Φ=0.035975 \n",
+ "Rx \n",
+ "Φ=0.300028 \n",
+ "Rx \n",
+ "Φ=2.393657 \n",
+ "Rx \n",
+ "Φ=5.514246 \n",
+ "Rx \n",
+ "Φ=5.655765 \n",
+ "Rx \n",
+ "Φ=4.952038 \n",
+ "Rx \n",
+ "Φ=6.241118 \n",
+ "Rx \n",
+ "Φ=6.086017 \n",
+ "Rx \n",
+ "Φ=1.986466 \n",
+ "Rx \n",
+ "Φ=6.134396 \n",
+ "Rx \n",
+ "Φ=4.935114 \n",
+ "Rx \n",
+ "Φ=6.058388 \n",
+ "Rx \n",
+ "Φ=1.026302 \n",
+ "Rx \n",
+ "Φ=5.971801 \n",
+ "Rx \n",
+ "Φ=3.771252 \n",
+ "Rx \n",
+ "Φ=0.181638 \n",
+ "Rx \n",
+ "Φ=4.807107 \n",
+ "Rx \n",
+ "Φ=5.947017 \n",
+ "Rx \n",
+ "Φ=5.726415 \n",
+ "Rx \n",
+ "Φ=5.487471 \n",
+ "Rx \n",
+ "Φ=0.118052 \n",
+ "Rx \n",
+ "Φ=6.189937 \n",
+ "Rx \n",
+ "Φ=6.015108 \n",
+ "Rx \n",
+ "Φ=6.177071 \n",
+ "Rx \n",
+ "Φ=0.15682 \n",
+ "Rx \n",
+ "Φ=0.349833 \n",
+ "Rx \n",
+ "Φ=6.172077 \n",
+ "Rx \n",
+ "Φ=6.02593 \n",
+ "Rx \n",
+ "Φ=4.625995 \n",
+ "Rx \n",
+ "Φ=5.845109 \n",
+ "Rx \n",
+ "Φ=0.374967 \n",
+ "Rx \n",
+ "Φ=0.184268 \n",
+ "Rx \n",
+ "Φ=1.289993 \n",
+ "Rx \n",
+ "Φ=6.149498 \n",
+ "Rx \n",
+ "Φ=0.007029 \n",
+ "Rx \n",
+ "Φ=0.543494 \n",
+ "Rx \n",
+ "Φ=1.202871 \n",
+ "Rx \n",
+ "Φ=0.212705 \n",
+ "Rx \n",
+ "Φ=4.387912 \n",
+ "Rx \n",
+ "Φ=5.958851 \n",
+ "Rx \n",
+ "Φ=2.60915 \n",
+ "Rx \n",
+ "Φ=0.664903 \n",
+ "Rx \n",
+ "Φ=4.306146 \n",
+ "Rx \n",
+ "Φ=0.38926 \n",
+ "Rx \n",
+ "Φ=3.113659 \n",
+ "Rx \n",
+ "Φ=0.644285 \n",
+ "Rx \n",
+ "Φ=5.034615 \n",
+ "Rx \n",
+ "Φ=0.324067 \n",
+ "Rx \n",
+ "Φ=2.842512 \n",
+ "Rx \n",
+ "Φ=0.270697 \n",
+ "Rx \n",
+ "Φ=2.426496 \n",
+ "Rx \n",
+ "Φ=5.937887 \n",
+ "Rx \n",
+ "Φ=3.263879 \n",
+ "Rx \n",
+ "Φ=6.105318 \n",
+ "Rx \n",
+ "Φ=1.791084 \n",
+ "Rx \n",
+ "Φ=5.902843 \n",
+ "Rx \n",
+ "Φ=1.50209 \n",
+ "Rx \n",
+ "Φ=0.109648 \n",
+ "Rx \n",
+ "Φ=3.226673 \n",
+ "Rx \n",
+ "Φ=0.276966 \n",
+ "Rx \n",
+ "Φ=3.07087 \n",
+ "Rx \n",
+ "Φ=0.209595 \n",
+ "Rx \n",
+ "Φ=1.555314 \n",
+ "Rx \n",
+ "Φ=0.451712 \n",
+ "Rx \n",
+ "Φ=2.222022 \n",
+ "Rx \n",
+ "Φ=1.286568 \n",
+ "Rx \n",
+ "Φ=3.706687 \n",
+ "Rx \n",
+ "Φ=5.21618 \n",
+ "Rx \n",
+ "Φ=1.859693 \n",
+ "Rx \n",
+ "Φ=0.574807 \n",
+ "Rx \n",
+ "Φ=5.218566 \n",
+ "Rx \n",
+ "Φ=5.346412 \n",
+ "Rx \n",
+ "Φ=5.483232 \n",
+ "Rx \n",
+ "Φ=0.574017 \n",
+ "Rx \n",
+ "Φ=1.378553 \n",
+ "Rx \n",
+ "Φ=0.578582 \n",
+ "Rx \n",
+ "Φ=4.332171 \n",
+ "Rx \n",
+ "Φ=0.879409 \n",
+ "Rx \n",
+ "Φ=2.993434 \n",
+ "Rx \n",
+ "Φ=5.556203 \n",
+ "Rx \n",
+ "Φ=0.523426 \n",
+ "Rx \n",
+ "Φ=4.891175 \n",
+ "Rx \n",
+ "Φ=1.902019 \n",
+ "Rx \n",
+ "Φ=2.204474 \n",
+ "Rx \n",
+ "Φ=3.825553 \n",
+ "Rx \n",
+ "Φ=0.870069 \n",
+ "Rx \n",
+ "Φ=4.474557 \n",
+ "Rx \n",
+ "Φ=0.194815 \n",
+ "Rx \n",
+ "Φ=0.670387 \n",
+ "Rx \n",
+ "Φ=0.107157 \n",
+ "Rx \n",
+ "Φ=3.331872 \n",
+ "Rx \n",
+ "Φ=0.206584 \n",
+ "Rx \n",
+ "Φ=1.314649 \n",
+ "Rx \n",
+ "Φ=6.007706 \n",
+ "Rx \n",
+ "Φ=4.612626 \n",
+ "Rx \n",
+ "Φ=0.575886 \n",
+ "Rx \n",
+ "Φ=1.005007 \n",
+ "Rx \n",
+ "Φ=5.645279 \n",
+ "Rx \n",
+ "Φ=0.951811 \n",
+ "Rx \n",
+ "Φ=5.662948 \n",
+ "Rx \n",
+ "Φ=1.696673 \n",
+ "Rx \n",
+ "Φ=5.949113 \n",
+ "Rx \n",
+ "Φ=0.39189 \n",
+ "Rx \n",
+ "Φ=0.097375 \n",
+ "Rx \n",
+ "Φ=2.281393 \n",
+ "Rx \n",
+ "Φ=5.972026 \n",
+ "Rx \n",
+ "Φ=0.857042 \n",
+ "Rx \n",
+ "Φ=5.839495 \n",
+ "Rx \n",
+ "Φ=4.966637 \n",
+ "Rx \n",
+ "Φ=0.388092 \n",
+ "Rx \n",
+ "Φ=0.068379 \n",
+ "Rx \n",
+ "Φ=0.135511 \n",
+ "Rx \n",
+ "Φ=5.867731 \n",
+ "Rx \n",
+ "Φ=0.487449 \n",
+ "Rx \n",
+ "Φ=2.924938 \n",
+ "Rx \n",
+ "Φ=0.178961 \n",
+ "Rx \n",
+ "Φ=2.986802 \n",
+ "Rx \n",
+ "Φ=0.523143 \n",
+ "Rx \n",
+ "Φ=1.842312 \n",
+ "Rx \n",
+ "Φ=0.203622 \n",
+ "Rx \n",
+ "Φ=3.928582 \n",
+ "Rx \n",
+ "Φ=0.555701 \n",
+ "Rx \n",
+ "Φ=4.771775 \n",
+ "Rx \n",
+ "Φ=6.144378 \n",
+ "Rx \n",
+ "Φ=0.18108 \n",
+ "Rx \n",
+ "Φ=0.706178 \n",
+ "Rx \n",
+ "Φ=3.839105 \n",
+ "Rx \n",
+ "Φ=6.147845 \n",
+ "Rx \n",
+ "Φ=2.89198 \n",
+ "Rx \n",
+ "Φ=0.742185 \n",
+ "Rx \n",
+ "Φ=4.587503 \n",
+ "Rx \n",
+ "Φ=5.991367 \n",
+ "Rx \n",
+ "Φ=1.469346 \n",
+ "Rx \n",
+ "Φ=5.831196 \n",
+ "Rx \n",
+ "Φ=0.704604 \n",
+ "Rx \n",
+ "Φ=0.324735 \n",
+ "Rx \n",
+ "Φ=5.018329 \n",
+ "Rx \n",
+ "Φ=0.11033 \n",
+ "Rx \n",
+ "Φ=5.816534 \n",
+ "Rx \n",
+ "Φ=0.428162 \n",
+ "Rx \n",
+ "Φ=6.076769 \n",
+ "Rx \n",
+ "Φ=5.654321 \n",
+ "Rx \n",
+ "Φ=5.001712 \n",
+ "Rx \n",
+ "Φ=0.877389 \n",
+ "Rx \n",
+ "Φ=0.512589 \n",
+ "Rx \n",
+ "Φ=0.224481 \n",
+ "Rx \n",
+ "Φ=1.236322 \n",
+ "Rx \n",
+ "Φ=5.78499 \n",
+ "Rx \n",
+ "Φ=1.704559 \n",
+ "Rx \n",
+ "Φ=0.594243 \n",
+ "Rx \n",
+ "Φ=4.112332 \n",
+ "Rx \n",
+ "Φ=0.616464 \n",
+ "Rx \n",
+ "Φ=5.169907 \n",
+ "Rx \n",
+ "Φ=5.385159 \n",
+ "Rx \n",
+ "Φ=5.434353 \n",
+ "Rx \n",
+ "Φ=4.929039 \n",
+ "Rx \n",
+ "Φ=3.923851 \n",
+ "Rx \n",
+ "Φ=0.681459 \n",
+ "Rx \n",
+ "Φ=1.232506 \n",
+ "Rx \n",
+ "Φ=0.691074 \n",
+ "Rx \n",
+ "Φ=0.714888 \n",
+ "Rx \n",
+ "Φ=4.936179 \n",
+ "Rx \n",
+ "Φ=1.249755 \n",
+ "Rx \n",
+ "Φ=5.296317 \n",
+ "Rx \n",
+ "Φ=0.095546 \n",
+ "Rx \n",
+ "Φ=4.590756 \n",
+ "Rx \n",
+ "Φ=2.13691 \n",
+ "Rx \n",
+ "Φ=5.519427 \n",
+ "Rx \n",
+ "Φ=3.500132 \n",
+ "Rx \n",
+ "Φ=5.866574 \n",
+ "Rx \n",
+ "Φ=6.230684 \n",
+ "Rx \n",
+ "Φ=0.291908 \n",
+ "Rx \n",
+ "Φ=3.150624 \n",
+ "Rx \n",
+ "Φ=0.196929 \n",
+ "Rx \n",
+ "Φ=3.897276 \n",
+ "Rx \n",
+ "Φ=5.951328 \n",
+ "Rx \n",
+ "Φ=2.401532 \n",
+ "Rx \n",
+ "Φ=6.112328 \n",
+ "Rx \n",
+ "Φ=1.359227 \n",
+ "Rx \n",
+ "Φ=0.19407 \n",
+ "Rx \n",
+ "Φ=5.856366 \n",
+ "Rx \n",
+ "Φ=5.911984 \n",
+ "Rx \n",
+ "Φ=3.140123 \n",
+ "Rx \n",
+ "Φ=5.863067 \n",
+ "Rx \n",
+ "Φ=1.57306 \n",
+ "Rx \n",
+ "Φ=5.711222 \n",
+ "Rx \n",
+ "Φ=5.245094 \n",
+ "Rx \n",
+ "Φ=0.22416 \n",
+ "Rx \n",
+ "Φ=2.623881 \n",
+ "Rx \n",
+ "Φ=0.235182 \n",
+ "Rx \n",
+ "Φ=0.823315 \n",
+ "Rx \n",
+ "Φ=6.053732 \n",
+ "Rx \n",
+ "Φ=1.590593 \n",
+ "Rx \n",
+ "Φ=5.956101 \n",
+ "Rx \n",
+ "Φ=4.824191 \n",
+ "Rx \n",
+ "Φ=5.994807 \n",
+ "Rx \n",
+ "Φ=5.413009 \n",
+ "Rx \n",
+ "Φ=5.989017 \n",
+ "Rx \n",
+ "Φ=0.294529 \n",
+ "Rx \n",
+ "Φ=0.283163 \n",
+ "Rx \n",
+ "Φ=3.60204 \n",
+ "Rx \n",
+ "Φ=6.09183 \n",
+ "Rx \n",
+ "Φ=3.654521 \n",
+ "Rx \n",
+ "Φ=0.448648 \n",
+ "Rx \n",
+ "Φ=4.062326 \n",
+ "Rx \n",
+ "Φ=0.3929 \n",
+ "Rx \n",
+ "Φ=1.632123 \n",
+ "Rx \n",
+ "Φ=0.400427 \n",
+ "Rx \n",
+ "Φ=5.654718 \n",
+ "Rx \n",
+ "Φ=5.937236 \n",
+ "Rx \n",
+ "Φ=4.240464 \n",
+ "Rx \n",
+ "Φ=0.36479 \n",
+ "Rx \n",
+ "Φ=3.318117 \n",
+ "Rx \n",
+ "Φ=6.000224 \n",
+ "Rx \n",
+ "Φ=4.550929 \n",
+ "Rx \n",
+ "Φ=0.436911 \n",
+ "Rx \n",
+ "Φ=0.979187 \n",
+ "Rx \n",
+ "Φ=0.113686 \n",
+ "Rx \n",
+ "Φ=2.362675 \n",
+ "Rx \n",
+ "Φ=5.850121 \n",
+ "Rx \n",
+ "Φ=4.666902 \n",
+ "Rx \n",
+ "Φ=5.99902 \n",
+ "Rx \n",
+ "Φ=4.484215 \n",
+ "Rx \n",
+ "Φ=1.087759 \n",
+ "Rx \n",
+ "Φ=6.206518 \n",
+ "Rx \n",
+ "Φ=0.251584 \n",
+ "Rx \n",
+ "Φ=3.652391 \n",
+ "Rx \n",
+ "Φ=6.252406 \n",
+ "Rx \n",
+ "Φ=2.738753 \n",
+ "Rx \n",
+ "Φ=5.96636 \n",
+ "Rx \n",
+ "Φ=4.305098 \n",
+ "Rx \n",
+ "Φ=4.883413 \n",
+ "Rx \n",
+ "Φ=4.605228 \n",
+ "Rx \n",
+ "Φ=0.752956 \n",
+ "Rx \n",
+ "Φ=6.117197 \n",
+ "Rx \n",
+ "Φ=0.52453 \n",
+ "Rx \n",
+ "Φ=4.32947 \n",
+ "Rx \n",
+ "Φ=5.589197 \n",
+ "Rx \n",
+ "Φ=6.122167 \n",
+ "Rx \n",
+ "Φ=5.946354 \n",
+ "Rx \n",
+ "Φ=1.257563 \n",
+ "Rx \n",
+ "Φ=5.789152 \n",
+ "Rx \n",
+ "Φ=2.168888 \n",
+ "Rx \n",
+ "Φ=0.859284 \n",
+ "Rx \n",
+ "Φ=1.515469 \n",
+ "Rx \n",
+ "Φ=5.870437 \n",
+ "Rx \n",
+ "Φ=2.64635 \n",
+ "Rx \n",
+ "Φ=0.787478 \n",
+ "Rx \n",
+ "Φ=1.022804 \n",
+ "Rx \n",
+ "Φ=5.639418 \n",
+ "Rx \n",
+ "Φ=0.221742 \n",
+ "Rx \n",
+ "Φ=3.764056 \n",
+ "Rx \n",
+ "Φ=2.54766 \n",
+ "Rx \n",
+ "Φ=6.166067 \n",
+ "Rx \n",
+ "Φ=1.76793 \n",
+ "Rx \n",
+ "Φ=5.508151 \n",
+ "Rx \n",
+ "Φ=4.380914 \n",
+ "Rx \n",
+ "Φ=5.979005 \n",
+ "Rx \n",
+ "Φ=1.469066 \n",
+ "Rx \n",
+ "Φ=6.073236 \n",
+ "Rx \n",
+ "Φ=0.585293 \n",
+ "Rx \n",
+ "Φ=6.089131 \n",
+ "Rx \n",
+ "Φ=4.452295 \n",
+ "Rx \n",
+ "Φ=0.217884 \n",
+ "Rx \n",
+ "Φ=1.524597 \n",
+ "Rx \n",
+ "Φ=5.994535 \n",
+ "Rx \n",
+ "Φ=0.772216 \n",
+ "Rx \n",
+ "Φ=0.519165 \n",
+ "Rx \n",
+ "Φ=4.97407 \n",
+ "Rx \n",
+ "Φ=0.220916 \n",
+ "Rx \n",
+ "Φ=0.290012 \n",
+ "Rx \n",
+ "Φ=5.744105 \n",
+ "Rx \n",
+ "Φ=1.703336 \n",
+ "Rx \n",
+ "Φ=0.346531 \n",
+ "Rx \n",
+ "Φ=2.066805 \n",
+ "Rx \n",
+ "Φ=5.867851 \n",
+ "Rx \n",
+ "Φ=6.029689 \n",
+ "Rx \n",
+ "Φ=5.977494 \n",
+ "Rx \n",
+ "Φ=0.013988 \n",
+ "Rx \n",
+ "Φ=6.073972 \n",
+ "Rx \n",
+ "Φ=1.983119 \n",
+ "Rx \n",
+ "Φ=0.54772 \n",
+ "Rx \n",
+ "Φ=4.454593 \n",
+ "Rx \n",
+ "Φ=0.35409 \n",
+ "Rx \n",
+ "Φ=5.879641 \n",
+ "Rx \n",
+ "Φ=6.006991 \n",
+ "Rx \n",
+ "Φ=5.307463 \n",
+ "Rx \n",
+ "Φ=5.848293 \n",
+ "Rx \n",
+ "Φ=0.4352 \n",
+ "Rx \n",
+ "Φ=5.894955 \n",
+ "Rx \n",
+ "Φ=4.709407 \n",
+ "Rx \n",
+ "Φ=5.91169 \n",
+ "Rx \n",
+ "Φ=3.310403 \n",
+ "Rx \n",
+ "Φ=0.196313 \n",
+ "Rx \n",
+ "Φ=4.357741 \n",
+ "Rx \n",
+ "Φ=0.525084 \n",
+ "Rx \n",
+ "Φ=3.153742 \n",
+ "Rx \n",
+ "Φ=0.211319 \n",
+ "Rx \n",
+ "Φ=2.621184 \n",
+ "Rx \n",
+ "Φ=0.194648 \n",
+ "Rx \n",
+ "Φ=4.027948 \n",
+ "Rx \n",
+ "Φ=0.640792 \n",
+ "Rx \n",
+ "Φ=2.940502 \n",
+ "Rx \n",
+ "Φ=0.475948 \n",
+ "Rx \n",
+ "Φ=4.481748 \n",
+ "Rx \n",
+ "Φ=0.645827 \n",
+ "Rx \n",
+ "Φ=4.710353 \n",
+ "Rx \n",
+ "Φ=5.77302 \n",
+ "Rx \n",
+ "Φ=4.014894 \n",
+ "Rx \n",
+ "Φ=0.372696 \n",
+ "Rx \n",
+ "Φ=0.295532 \n",
+ "Rx \n",
+ "Φ=5.951352 \n",
+ "Rx \n",
+ "Φ=3.726412 \n",
+ "Rx \n",
+ "Φ=0.557783 \n",
+ "Rx \n",
+ "Φ=3.070958 \n",
+ "Rx \n",
+ "Φ=5.839683 \n",
+ "Rx \n",
+ "Φ=2.913406 \n",
+ "Rx \n",
+ "Φ=0.08263 \n",
+ "Rx \n",
+ "Φ=5.914289 \n",
+ "Rx \n",
+ "Φ=5.585939 \n",
+ "Rx \n",
+ "Φ=0.512658 \n",
+ "Rx \n",
+ "Φ=1.021508 \n",
+ "Rx \n",
+ "Φ=0.892125 \n",
+ "Rx \n",
+ "Φ=5.702335 \n",
+ "Rx \n",
+ "Φ=0.080903 \n",
+ "Rx \n",
+ "Φ=0.233159 \n",
+ "Rx \n",
+ "Φ=1.924166 \n",
+ "Rx \n",
+ "Φ=0.902118 \n",
+ "Rx \n",
+ "Φ=1.574186 \n",
+ "Rx \n",
+ "Φ=5.846992 \n",
+ "Rx \n",
+ "Φ=1.475225 \n",
+ "Rx \n",
+ "Φ=1.325307 \n",
+ "Rx \n",
+ "Φ=1.033232 \n",
+ "Rx \n",
+ "Φ=4.983393 \n",
+ "Rx \n",
+ "Φ=4.527731 \n",
+ "Rx \n",
+ "Φ=1.176098 \n",
+ "Rx \n",
+ "Φ=6.042173 \n",
+ "Rx \n",
+ "Φ=4.969382 \n",
+ "Rx \n",
+ "Φ=2.157678 \n",
+ "Rx \n",
+ "Φ=6.100574 \n",
+ "Rx \n",
+ "Φ=4.21598 \n",
+ "Rx \n",
+ "Φ=0.16411 \n",
+ "Rx \n",
+ "Φ=2.541152 \n",
+ "Rx \n",
+ "Φ=5.996278 \n",
+ "Rx \n",
+ "Φ=1.088313 \n",
+ "Rx \n",
+ "Φ=6.101609 \n",
+ "Rx \n",
+ "Φ=5.663741 \n",
+ "Rx \n",
+ "Φ=0.201005 \n",
+ "Rx \n",
+ "Φ=2.915922 \n",
+ "Rx \n",
+ "Φ=0.105502 \n",
+ "Rx \n",
+ "Φ=3.403432 \n",
+ "Rx \n",
+ "Φ=5.929396 \n",
+ "Rx \n",
+ "Φ=4.460043 \n",
+ "Rx \n",
+ "Φ=0.502707 \n",
+ "Rx \n",
+ "Φ=5.286522 \n",
+ "Rx \n",
+ "Φ=0.250997 \n",
+ "Rx \n",
+ "Φ=2.318663 \n",
+ "Rx \n",
+ "Φ=0.249037 \n",
+ "Rx \n",
+ "Φ=5.485563 \n",
+ "Rx \n",
+ "Φ=0.321464 \n",
+ "Rx \n",
+ "Φ=5.411947 \n",
+ "Rx \n",
+ "Φ=0.318658 \n",
+ "Rx \n",
+ "Φ=4.668562 \n",
+ "Rx \n",
+ "Φ=0.248947 \n",
+ "Rx \n",
+ "Φ=4.088366 \n",
+ "Rx \n",
+ "Φ=0.548107 \n",
+ "Rx \n",
+ "Φ=4.816387 \n",
+ "Rx \n",
+ "Φ=5.967856 \n",
+ "Rx \n",
+ "Φ=0.509869 \n",
+ "Rx \n",
+ "Φ=5.975672 \n",
+ "Rx \n",
+ "Φ=4.361525 \n",
+ "Rx \n",
+ "Φ=6.031032 \n",
+ "Rx \n",
+ "Φ=4.450236 \n",
+ "Rx \n",
+ "Φ=0.653136 \n",
+ "Rx \n",
+ "Φ=5.907174 \n",
+ "Rx \n",
+ "Φ=6.195711 \n",
+ "Rx \n",
+ "Φ=3.081506 \n",
+ "Rx \n",
+ "Φ=0.385924 \n",
+ "Rx \n",
+ "Φ=4.594933 \n",
+ "Rx \n",
+ "Φ=0.342406 \n",
+ "Rx \n",
+ "Φ=3.969937 \n",
+ "Rx \n",
+ "Φ=5.959471 \n",
+ "Rx \n",
+ "Φ=4.976202 \n",
+ "Rx \n",
+ "Φ=0.440208 \n",
+ "Rx \n",
+ "Φ=3.563763 \n",
+ "Rx \n",
+ "Φ=6.16686 \n",
+ "Rx \n",
+ "Φ=2.841724 \n",
+ "Rx \n",
+ "Φ=5.989236 \n",
+ "Rx \n",
+ "Φ=0.232134 \n",
+ "Rx \n",
+ "Φ=0.466641 \n",
+ "Rx \n",
+ "Φ=2.907637 \n",
+ "Rx \n",
+ "Φ=0.598462 \n",
+ "Rx \n",
+ "Φ=4.965434 \n",
+ "Rx \n",
+ "Φ=0.619243 \n",
+ "Rx \n",
+ "Φ=1.687885 \n",
+ "Rx \n",
+ "Φ=0.482366 \n",
+ "Rx \n",
+ "Φ=3.384366 \n",
+ "Rx \n",
+ "Φ=0.512896 \n",
+ "Rx \n",
+ "Φ=2.584232 \n",
+ "Rx \n",
+ "Φ=5.830619 \n",
+ "Rx \n",
+ "Φ=3.365152 \n",
+ "Rx \n",
+ "Φ=5.757298 \n",
+ "Rx \n",
+ "Φ=3.749771 \n",
+ "Rx \n",
+ "Φ=5.584298 \n",
+ "Rx \n",
+ "Φ=3.615462 \n",
+ "Rx \n",
+ "Φ=5.688261 \n",
+ "Rx \n",
+ "Φ=4.968784 \n",
+ "Rx \n",
+ "Φ=6.177213 \n",
+ "Rx \n",
+ "Φ=1.754432 \n",
+ "Rx \n",
+ "Φ=5.820745 \n",
+ "Rx \n",
+ "Φ=3.695679 \n",
+ "Rx \n",
+ "Φ=0.553191 \n",
+ "Rx \n",
+ "Φ=2.485993 \n",
+ "Rx \n",
+ "Φ=0.151225 \n",
+ "Rx \n",
+ "Φ=0.150301 \n",
+ "Rx \n",
+ "Φ=0.377843 \n",
+ "Rx \n",
+ "Φ=0.963871 \n",
+ "Rx \n",
+ "Φ=0.846173 \n",
+ "Rx \n",
+ "Φ=0.684876 \n",
+ "Rx \n",
+ "Φ=5.837456 \n",
+ "Rx \n",
+ "Φ=5.702112 \n",
+ "Rx \n",
+ "Φ=0.542615 \n",
+ "Rx \n",
+ "Φ=5.899448 \n",
+ "Rx \n",
+ "Φ=5.388306 \n",
+ "Rx \n",
+ "Φ=3.891059 \n",
+ "Rx \n",
+ "Φ=1.354043 \n",
+ "Rx \n",
+ "Φ=5.933052 \n",
+ "Rx \n",
+ "Φ=0.086961 \n",
+ "Rx \n",
+ "Φ=6.15456 \n",
+ "Rx \n",
+ "Φ=0.287335 \n",
+ "Rx \n",
+ "Φ=2.632841 \n",
+ "Rx \n",
+ "Φ=0.248309 \n",
+ "Rx \n",
+ "Φ=3.037342 \n",
+ "Rx \n",
+ "Φ=6.20215 \n",
+ "Rx \n",
+ "Φ=3.258737 \n",
+ "Rx \n",
+ "Φ=6.225472 \n",
+ "Rx \n",
+ "Φ=1.857072 \n",
+ "Rx \n",
+ "Φ=0.327855 \n",
+ "Rx \n",
+ "Φ=4.619778 \n",
+ "Rx \n",
+ "Φ=0.483926 \n",
+ "Rx \n",
+ "Φ=6.028352 \n",
+ "Rx \n",
+ "Φ=0.303849 \n",
+ "Rx \n",
+ "Φ=6.021673 \n",
+ "Rx \n",
+ "Φ=6.111093 \n",
+ "Rx \n",
+ "Φ=3.375631 \n",
+ "Rx \n",
+ "Φ=6.150904 \n",
+ "Rx \n",
+ "Φ=2.392537 \n",
+ "Rx \n",
+ "Φ=5.981969 \n",
+ "Rx \n",
+ "Φ=1.215195 \n",
+ "Rx \n",
+ "Φ=0.427243 \n",
+ "Rx \n",
+ "Φ=5.909782 \n",
+ "Rx \n",
+ "Φ=0.306845 \n",
+ "Rx \n",
+ "Φ=3.220906 \n",
+ "Rx \n",
+ "Φ=5.690187 \n",
+ "Rx \n",
+ "Φ=0.989914 \n",
+ "Rx \n",
+ "Φ=0.558216 \n",
+ "Rx \n",
+ "Φ=4.766021 \n",
+ "Rx \n",
+ "Φ=5.897045 \n",
+ "Rx \n",
+ "Φ=3.920487 \n",
+ "Rx \n",
+ "Φ=0.224819 \n",
+ "Rx \n",
+ "Φ=1.033647 \n",
+ "Rx \n",
+ "Φ=5.821292 \n",
+ "Rx \n",
+ "Φ=5.220329 \n",
+ "Rx \n",
+ "Φ=5.726517 \n",
+ "Rx \n",
+ "Φ=3.34053 \n",
+ "Rx \n",
+ "Φ=0.009845 \n",
+ "Rx \n",
+ "Φ=5.51359 \n",
+ "Rx \n",
+ "Φ=0.268372 \n",
+ "Rx \n",
+ "Φ=3.845676 \n",
+ "Rx \n",
+ "Φ=0.139933 \n",
+ "Rx \n",
+ "Φ=1.266697 \n",
+ "Rx \n",
+ "Φ=6.152192 \n",
+ "Rx \n",
+ "Φ=0.436645 \n",
+ "Rx \n",
+ "Φ=0.470276 \n",
+ "Rx \n",
+ "Φ=0.81649 \n",
+ "Rx \n",
+ "Φ=0.808508 \n",
+ "Rx \n",
+ "Φ=5.62236 \n",
+ "Rx \n",
+ "Φ=1.118802 \n",
+ "Rx \n",
+ "Φ=3.632045 \n",
+ "Rx \n",
+ "Φ=6.120302 \n",
+ "Rx \n",
+ "Φ=2.741457 \n",
+ "Rx \n",
+ "Φ=5.946354 \n",
+ "Rx \n",
+ "Φ=5.827406 \n",
+ "Rx \n",
+ "Φ=5.75044 \n",
+ "Rx \n",
+ "Φ=0.215774 \n",
+ "Rx \n",
+ "Φ=5.526486 \n",
+ "Rx \n",
+ "Φ=5.824221 \n",
+ "Rx \n",
+ "Φ=0.242832 \n",
+ "Rx \n",
+ "Φ=0.571178 \n",
+ "Rx \n",
+ "Φ=0.544409 \n",
+ "Rx \n",
+ "Φ=1.683516 \n",
+ "Rx \n",
+ "Φ=5.49181 \n",
+ "Rx \n",
+ "Φ=5.205385 \n",
+ "Rx \n",
+ "Φ=0.87585 \n",
+ "Rx \n",
+ "Φ=3.693138 \n",
+ "Rx \n",
+ "Φ=0.314826 \n",
+ "Rx \n",
+ "Φ=5.339071 \n",
+ "Rx \n",
+ "Φ=0.772779 \n",
+ "Rx \n",
+ "Φ=3.970336 \n",
+ "Rx \n",
+ "Φ=5.699904 \n",
+ "Rx \n",
+ "Φ=2.062612 \n",
+ "Rx \n",
+ "Φ=0.313988 \n",
+ "Rx \n",
+ "Φ=1.355893 \n",
+ "Rx \n",
+ "Φ=0.060911 \n",
+ "Rx \n",
+ "Φ=4.166255 \n",
+ "Rx \n",
+ "Φ=5.931207 \n",
+ "Rx \n",
+ "Φ=1.947332 \n",
+ "Rx \n",
+ "Φ=0.114979 \n",
+ "Rx \n",
+ "Φ=1.035421 \n",
+ "Rx \n",
+ "Φ=1.46224 \n",
+ "Rx \n",
+ "Φ=1.339425 \n",
+ "Rx \n",
+ "Φ=4.943938 \n",
+ "Rx \n",
+ "Φ=3.823801 \n",
+ "Rx \n",
+ "Φ=1.391492 \n",
+ "Rx \n",
+ "Φ=2.81065 \n",
+ "Rx \n",
+ "Φ=4.702919 \n",
+ "Rx \n",
+ "Φ=6.130215 \n",
+ "Rx \n",
+ "Φ=0.245043 \n",
+ "Rx \n",
+ "Φ=4.954468 \n",
+ "Rx \n",
+ "Φ=5.991317 \n",
+ "Rx \n",
+ "Φ=0.160681 \n",
+ "Rx \n",
+ "Φ=0.467249 \n",
+ "Rx \n",
+ "Φ=0.597464 \n",
+ "Rx \n",
+ "Φ=0.21826 \n",
+ "Rx \n",
+ "Φ=5.478608 \n",
+ "Rx \n",
+ "Φ=0.235617 \n",
+ "Rx \n",
+ "Φ=0.519261 \n",
+ "Rx \n",
+ "Φ=6.155467 \n",
+ "Rx \n",
+ "Φ=2.189277 \n",
+ "Rx \n",
+ "Φ=5.688655 \n",
+ "Rx \n",
+ "Φ=3.87223 \n",
+ "Rx \n",
+ "Φ=0.300294 \n",
+ "Rx \n",
+ "Φ=4.336099 \n",
+ "Rx \n",
+ "Φ=5.519202 \n",
+ "Rx \n",
+ "Φ=2.357248 \n",
+ "Rx \n",
+ "Φ=0.420619 \n",
+ "Rx \n",
+ "Φ=4.243122 \n",
+ "Rx \n",
+ "Φ=6.035784 \n",
+ "Rx \n",
+ "Φ=2.069186 \n",
+ "Rx \n",
+ "Φ=6.031433 \n",
+ "Rx \n",
+ "Φ=3.481913 \n",
+ "Rx \n",
+ "Φ=0.106724 \n",
+ "Rx \n",
+ "Φ=5.4126 \n",
+ "Rx \n",
+ "Φ=6.179596 \n",
+ "Rx \n",
+ "Φ=2.245271 \n",
+ "Rx \n",
+ "Φ=0.119653 \n",
+ "Rx \n",
+ "Φ=5.410094 \n",
+ "Rx \n",
+ "Φ=0.364294 \n",
+ "Rx \n",
+ "Φ=2.32477 \n",
+ "Rx \n",
+ "Φ=0.115685 \n",
+ "Rx \n",
+ "Φ=5.820551 \n",
+ "Rx \n",
+ "Φ=0.658469 \n",
+ "Rx \n",
+ "Φ=5.061794 \n",
+ "Rx \n",
+ "Φ=0.146824 \n",
+ "Rx \n",
+ "Φ=1.157406 \n",
+ "Rx \n",
+ "Φ=6.028882 \n",
+ "Rx \n",
+ "Φ=6.088221 \n",
+ "Rx \n",
+ "Φ=0.2508 \n",
+ "Rx \n",
+ "Φ=1.507113 \n",
+ "Rx \n",
+ "Φ=5.873386 \n",
+ "Rx \n",
+ "Φ=0.545039 \n",
+ "Rx \n",
+ "Φ=0.204777 \n",
+ "Rx \n",
+ "Φ=1.550301 \n",
+ "Rx \n",
+ "Φ=0.492242 \n",
+ "Rx \n",
+ "Φ=3.208549 \n",
+ "Rx \n",
+ "Φ=0.337491 \n",
+ "Rx \n",
+ "Φ=3.999661 \n",
+ "Rx \n",
+ "Φ=6.059913 \n",
+ "Rx \n",
+ "Φ=1.27028 \n",
+ "Rx \n",
+ "Φ=0.285179 \n",
+ "Rx \n",
+ "Φ=6.090746 \n",
+ "Rx \n",
+ "Φ=5.859703 \n",
+ "Rx \n",
+ "Φ=0.131459 \n",
+ "Rx \n",
+ "Φ=0.258526 \n",
+ "Rx \n",
+ "Φ=0.70877 \n",
+ "Rx \n",
+ "Φ=6.19807 \n",
+ "Rx \n",
+ "Φ=3.408037 \n",
+ "Rx \n",
+ "Φ=0.732479 \n",
+ "Rx \n",
+ "Φ=0.761141 \n",
+ "Rx \n",
+ "Φ=0.712578 \n",
+ "Rx \n",
+ "Φ=4.74964 \n",
+ "Rx \n",
+ "Φ=0.615588 \n",
+ "Rx \n",
+ "Φ=1.301523 \n",
+ "Rx \n",
+ "Φ=0.606444 \n",
+ "Rx \n",
+ "Φ=4.946618 \n",
+ "Rx \n",
+ "Φ=5.760674 \n",
+ "Rx \n",
+ "Φ=6.101557 \n",
+ "Rx \n",
+ "Φ=5.589367 \n",
+ "Rx \n",
+ "Φ=4.40822 \n",
+ "Rx \n",
+ "Φ=0.73584 \n",
+ "Rx \n",
+ "Φ=4.587297 \n",
+ "Rx \n",
+ "Φ=5.491525 \n",
+ "Rx \n",
+ "Φ=3.509705 \n",
+ "Rx \n",
+ "Φ=1.18072 \n",
+ "Rx \n",
+ "Φ=4.701663 \n",
+ "Rx \n",
+ "Φ=5.650938 \n",
+ "Rx \n",
+ "Φ=3.622361 \n",
+ "Rx \n",
+ "Φ=4.877856 \n",
+ "Rx \n",
+ "Φ=3.947641 \n",
+ "Rx \n",
+ "Φ=0.694987 \n",
+ "Rx \n",
+ "Φ=2.191971 \n",
+ "Rx \n",
+ "Φ=1.107758 \n",
+ "Rx \n",
+ "Φ=2.035649 \n",
+ "Rx \n",
+ "Φ=0.126832 \n",
+ "Rx \n",
+ "Φ=0.521166 \n",
+ "Rx \n",
+ "Φ=5.047772 \n",
+ "Rx \n",
+ "Φ=4.720426 \n",
+ "Rx \n",
+ "Φ=5.493048 \n",
+ "Rx \n",
+ "Φ=3.582195 \n",
+ "Rx \n",
+ "Φ=0.162421 \n",
+ "Rx \n",
+ "Φ=1.003719 \n",
+ "Rx \n",
+ "Φ=6.065146 \n",
+ "Rx \n",
+ "Φ=0.837476 \n",
+ "Rx \n",
+ "Φ=0.218509 \n",
+ "Rx \n",
+ "Φ=6.173287 \n",
+ "Rx \n",
+ "Φ=5.836189 \n",
+ "Rx \n",
+ "Φ=4.332717 \n",
+ "Rx \n",
+ "Φ=6.053965 \n",
+ "Rx \n",
+ "Φ=4.517165 \n",
+ "Rx \n",
+ "Φ=0.132213 \n",
+ "Rx \n",
+ "Φ=1.621228 \n",
+ "Rx \n",
+ "Φ=0.458273 \n",
+ "Rx \n",
+ "Φ=0.311982 \n",
+ "Rx \n",
+ "Φ=0.085786 \n",
+ "Rx \n",
+ "Φ=4.554201 \n",
+ "Rx \n",
+ "Φ=6.094512 \n",
+ "Rx \n",
+ "Φ=6.201828 \n",
+ "Rx \n",
+ "Φ=6.014937 \n",
+ "Rx \n",
+ "Φ=2.06864 \n",
+ "Rx \n",
+ "Φ=5.933899 \n",
+ "Rx \n",
+ "Φ=1.862205 \n",
+ "Rx \n",
+ "Φ=0.138125 \n",
+ "Rx \n",
+ "Φ=4.153905 \n",
+ "Rx \n",
+ "Φ=5.869367 \n",
+ "Rx \n",
+ "Φ=5.101946 \n",
+ "Rx \n",
+ "Φ=0.304592 \n",
+ "Rx \n",
+ "Φ=1.314099 \n",
+ "Rx \n",
+ "Φ=6.012468 \n",
+ "Rx \n",
+ "Φ=2.254877 \n",
+ "Rx \n",
+ "Φ=0.231608 \n",
+ "Rx \n",
+ "Φ=1.626881 \n",
+ "Rx \n",
+ "Φ=0.627418 \n",
+ "Rx \n",
+ "Φ=1.274111 \n",
+ "Rx \n",
+ "Φ=5.825515 \n",
+ "Rx \n",
+ "Φ=2.400994 \n",
+ "Rx \n",
+ "Φ=0.430971 \n",
+ "Rx \n",
+ "Φ=3.342408 \n",
+ "Rx \n",
+ "Φ=5.713627 \n",
+ "Rx \n",
+ "Φ=1.813967 \n",
+ "Rx \n",
+ "Φ=5.994643 \n",
+ "Rx \n",
+ "Φ=5.890212 \n",
+ "Rx \n",
+ "Φ=0.326989 \n",
+ "Rx \n",
+ "Φ=0.481463 \n",
+ "Rx \n",
+ "Φ=5.57542 \n",
+ "Rx \n",
+ "Φ=2.617663 \n",
+ "Rx \n",
+ "Φ=5.880952 \n",
+ "Rx \n",
+ "Φ=5.815703 \n",
+ "Rx \n",
+ "Φ=5.891495 \n",
+ "Rx \n",
+ "Φ=5.631538 \n",
+ "Rx \n",
+ "Φ=6.270599 \n",
+ "Rx \n",
+ "Φ=1.827854 \n",
+ "Rx \n",
+ "Φ=0.366965 \n",
+ "Rx \n",
+ "Φ=5.569699 \n",
+ "Rx \n",
+ "Φ=0.130581 \n",
+ "Rx \n",
+ "Φ=3.546996 \n",
+ "Rx \n",
+ "Φ=0.31473 \n",
+ "Rx \n",
+ "Φ=2.297375 \n",
+ "Rx \n",
+ "Φ=0.339019 \n",
+ "Rx \n",
+ "Φ=3.604972 \n",
+ "Rx \n",
+ "Φ=6.030981 \n",
+ "Rx \n",
+ "Φ=5.778648 \n",
+ "Rx \n",
+ "Φ=6.008995 \n",
+ "Rx \n",
+ "Φ=2.16726 \n",
+ "Rx \n",
+ "Φ=6.16478 \n",
+ "Rx \n",
+ "Φ=3.956988 \n",
+ "Rx \n",
+ "Φ=0.268638 \n",
+ "Rx \n",
+ "Φ=0.665276 \n",
+ "Rx \n",
+ "Φ=0.669966 \n",
+ "Rx \n",
+ "Φ=4.192999 \n",
+ "Rx \n",
+ "Φ=5.74023 \n",
+ "Rx \n",
+ "Φ=5.454725 \n",
+ "Rx \n",
+ "Φ=5.729078 \n",
+ "Rx \n",
+ "Φ=5.799481 \n",
+ "Rx \n",
+ "Φ=5.531254 \n",
+ "Rx \n",
+ "Φ=4.632219 \n",
+ "Rx \n",
+ "Φ=0.541941 \n",
+ "Rx \n",
+ "Φ=5.070309 \n",
+ "Rx \n",
+ "Φ=5.877512 \n",
+ "Rx \n",
+ "Φ=6.1767 \n",
+ "Rx \n",
+ "Φ=0.817023 \n",
+ "Rx \n",
+ "Φ=3.753839 \n",
+ "Rx \n",
+ "Φ=0.490691 \n",
+ "Rx \n",
+ "Φ=5.951252 \n",
+ "Rx \n",
+ "Φ=0.961903 \n",
+ "Rx \n",
+ "Φ=4.512765 \n",
+ "Rx \n",
+ "Φ=5.855057 \n",
+ "Rx \n",
+ "Φ=0.11564 \n",
+ "Rx \n",
+ "Φ=0.613379 \n",
+ "Rx \n",
+ "Φ=0.013004 \n",
+ "Rx \n",
+ "Φ=1.105931 \n",
+ "Rx \n",
+ "Φ=0.626865 \n",
+ "Rx \n",
+ "Φ=4.436323 \n",
+ "Rx \n",
+ "Φ=3.234332 \n",
+ "Rx \n",
+ "Φ=0.295284 \n",
+ "Rx \n",
+ "Φ=4.386581 \n",
+ "Rx \n",
+ "Φ=0.079432 \n",
+ "Rx \n",
+ "Φ=3.531949 \n",
+ "Rx \n",
+ "Φ=0.108071 \n",
+ "Rx \n",
+ "Φ=2.714878 \n",
+ "Rx \n",
+ "Φ=6.183517 \n",
+ "Rx \n",
+ "Φ=2.665742 \n",
+ "Rx \n",
+ "Φ=0.298651 \n",
+ "Rx \n",
+ "Φ=2.474072 \n",
+ "Rx \n",
+ "Φ=6.036388 \n",
+ "Rx \n",
+ "Φ=1.577867 \n",
+ "Rx \n",
+ "Φ=0.157796 \n",
+ "Rx \n",
+ "Φ=0.150885 \n",
+ "Rx \n",
+ "Φ=0.196465 \n",
+ "Rx \n",
+ "Φ=3.253726 \n",
+ "Rx \n",
+ "Φ=6.048131 \n",
+ "Rx \n",
+ "Φ=4.088904 \n",
+ "Rx \n",
+ "Φ=0.290019 \n",
+ "Rx \n",
+ "Φ=2.350641 \n",
+ "Rx \n",
+ "Φ=5.964232 \n",
+ "Rx \n",
+ "Φ=0.664703 \n",
+ "Rx \n",
+ "Φ=5.742931 \n",
+ "Rx \n",
+ "Φ=2.293713 \n",
+ "Rx \n",
+ "Φ=5.888568 \n",
+ "Rx \n",
+ "Φ=3.071001 \n",
+ "Rx \n",
+ "Φ=5.9161 \n",
+ "Rx \n",
+ "Φ=4.283213 \n",
+ "Rx \n",
+ "Φ=0.512223 \n",
+ "Rx \n",
+ "Φ=3.490187 \n",
+ "Rx \n",
+ "Φ=5.795713 \n",
+ "Rx \n",
+ "Φ=0.929748 \n",
+ "Rx \n",
+ "Φ=0.256044 \n",
+ "Rx \n",
+ "Φ=5.641796 \n",
+ "Rx \n",
+ "Φ=0.660948 \n",
+ "Rx \n",
+ "Φ=2.448343 \n",
+ "Rx \n",
+ "Φ=0.441725 \n",
+ "Rx \n",
+ "Φ=3.733703 \n",
+ "Rx \n",
+ "Φ=0.04804 \n",
+ "Rx \n",
+ "Φ=4.107933 \n",
+ "Rx \n",
+ "Φ=6.161181 \n",
+ "Rx \n",
+ "Φ=6.215758 \n",
+ "Rx \n",
+ "Φ=0.681208 \n",
+ "Rx \n",
+ "Φ=1.676056 \n",
+ "Rx \n",
+ "Φ=6.113404 \n",
+ "Rx \n",
+ "Φ=2.837648 \n",
+ "Rx \n",
+ "Φ=0.282249 \n",
+ "Rx \n",
+ "Φ=0.251458 \n",
+ "Rx \n",
+ "Φ=0.448664 \n",
+ "Rx \n",
+ "Φ=1.01532 \n",
+ "Rx \n",
+ "Φ=0.313728 \n",
+ "Rx \n",
+ "Φ=3.081683 \n",
+ "Rx \n",
+ "Φ=0.576702 \n",
+ "Rx \n",
+ "Φ=2.176287 \n",
+ "Rx \n",
+ "Φ=5.660395 \n",
+ "Rx \n",
+ "Φ=2.069124 \n",
+ "Rx \n",
+ "Φ=0.275689 \n",
+ "Rx \n",
+ "Φ=0.777078 \n",
+ "Rx \n",
+ "Φ=5.866553 \n",
+ "Rx \n",
+ "Φ=1.103325 \n",
+ "Rx \n",
+ "Φ=0.359967 \n",
+ "Rx \n",
+ "Φ=3.725888 \n",
+ "Rx \n",
+ "Φ=5.91451 \n",
+ "Rx \n",
+ "Φ=5.145723 \n",
+ "Rx \n",
+ "Φ=6.119515 \n",
+ "Rx \n",
+ "Φ=0.782873 \n",
+ "Rx \n",
+ "Φ=6.036207 \n",
+ "Rx \n",
+ "Φ=0.51599 \n",
+ "Rx \n",
+ "Φ=0.216422 \n",
+ "Rx \n",
+ "Φ=4.33287 \n",
+ "Rx \n",
+ "Φ=0.416423 \n",
+ "Rx \n",
+ "Φ=2.981597 \n",
+ "Rx \n",
+ "Φ=5.224636 \n",
+ "Rx \n",
+ "Φ=2.290948 \n",
+ "Rx \n",
+ "Φ=5.818349 \n",
+ "Rx \n",
+ "Φ=0.248294 \n",
+ "Rx \n",
+ "Φ=5.68085 \n",
+ "Rx \n",
+ "Φ=4.256007 \n",
+ "Rx \n",
+ "Φ=5.383665 \n",
+ "Rx \n",
+ "Φ=0.00703 \n",
+ "Rx \n",
+ "Φ=6.138224 \n",
+ "Rx \n",
+ "Φ=2.133167 \n",
+ "Rx \n",
+ "Φ=1.631213 \n",
+ "Rx \n",
+ "Φ=1.942505 \n",
+ "Rx \n",
+ "Φ=0.519012 \n",
+ "Rx \n",
+ "Φ=4.873186 \n",
+ "Rx \n",
+ "Φ=0.153335 \n",
+ "Rx \n",
+ "Φ=5.334167 \n",
+ "Rx \n",
+ "Φ=5.837911 \n",
+ "Rx \n",
+ "Φ=5.658965 \n",
+ "Rx \n",
+ "Φ=1.160114 \n",
+ "Rx \n",
+ "Φ=2.936409 \n",
+ "Rx \n",
+ "Φ=2.203706 \n",
+ "Rx \n",
+ "Φ=4.737075 \n",
+ "Rx \n",
+ "Φ=1.307026 \n",
+ "Rx \n",
+ "Φ=0.653777 \n",
+ "Rx \n",
+ "Φ=6.058759 \n",
+ "Rx \n",
+ "Φ=5.062311 \n",
+ "Rx \n",
+ "Φ=0.355901 \n",
+ "Rx \n",
+ "Φ=3.401629 \n",
+ "Rx \n",
+ "Φ=6.251724 \n",
+ "Rx \n",
+ "Φ=2.74012 \n",
+ "Rx \n",
+ "Φ=0.292372 \n",
+ "Rx \n",
+ "Φ=1.535557 \n",
+ "Rx \n",
+ "Φ=0.262077 \n",
+ "Rx \n",
+ "Φ=4.578105 \n",
+ "Rx \n",
+ "Φ=6.178892 \n",
+ "Rx \n",
+ "Φ=1.730285 \n",
+ "Rx \n",
+ "Φ=5.721272 \n",
+ "Rx \n",
+ "Φ=5.009667 \n",
+ "Rx \n",
+ "Φ=0.357966 \n",
+ "Rx \n",
+ "Φ=4.807696 \n",
+ "Rx \n",
+ "Φ=0.190853 \n",
+ "Rx \n",
+ "Φ=1.184309 \n",
+ "Rx \n",
+ "Φ=6.010962 \n",
+ "Rx \n",
+ "Φ=2.44047 \n",
+ "Rx \n",
+ "Φ=0.260959 \n",
+ "Rx \n",
+ "Φ=6.10158 \n",
+ "Rx \n",
+ "Φ=5.866884 \n",
+ "Rx \n",
+ "Φ=5.975409 \n",
+ "Rx \n",
+ "Φ=0.146084 \n",
+ "Rx \n",
+ "Φ=1.698103 \n",
+ "Rx \n",
+ "Φ=0.241463 \n",
+ "Rx \n",
+ "Φ=5.535214 \n",
+ "Rx \n",
+ "Φ=5.951623 \n",
+ "Rx \n",
+ "Φ=2.195168 \n",
+ "Rx \n",
+ "Φ=5.821353 \n",
+ "Rx \n",
+ "Φ=6.188364 \n",
+ "Rx \n",
+ "Φ=0.460648 \n",
+ "Rx \n",
+ "Φ=2.571079 \n",
+ "Rx \n",
+ "Φ=0.246455 \n",
+ "Rx \n",
+ "Φ=2.562677 \n",
+ "Rx \n",
+ "Φ=0.194738 \n",
+ "Rx \n",
+ "Φ=1.162431 \n",
+ "Rx \n",
+ "Φ=5.886538 \n",
+ "Rx \n",
+ "Φ=2.281323 \n",
+ "Rx \n",
+ "Φ=0.537467 \n",
+ "Rx \n",
+ "Φ=0.060619 \n",
+ "Rx \n",
+ "Φ=6.062276 \n",
+ "Rx \n",
+ "Φ=0.519448 \n",
+ "Rx \n",
+ "Φ=0.25025 \n",
+ "Rx \n",
+ "Φ=6.040712 \n",
+ "Rx \n",
+ "Φ=5.312787 \n",
+ "Rx \n",
+ "Φ=4.472767 \n",
+ "Rx \n",
+ "Φ=0.44788 \n",
+ "Rx \n",
+ "Φ=0.463987 \n",
+ "Rx \n",
+ "Φ=5.556634 \n",
+ "Rx \n",
+ "Φ=3.636389 \n",
+ "Rx \n",
+ "Φ=0.18791 \n",
+ "Rx \n",
+ "Φ=5.361322 \n",
+ "Rx \n",
+ "Φ=5.955599 \n",
+ "Rx \n",
+ "Φ=4.178693 \n",
+ "Rx \n",
+ "Φ=6.184258 \n",
+ "Rx \n",
+ "Φ=4.19822 \n",
+ "Rx \n",
+ "Φ=5.912175 \n",
+ "Rx \n",
+ "Φ=3.331247 \n",
+ "Rx \n",
+ "Φ=5.73284 \n",
+ "Rx \n",
+ "Φ=5.750711 \n",
+ "Rx \n",
+ "Φ=5.434995 \n",
+ "Rx \n",
+ "Φ=1.720916 \n",
+ "Rx \n",
+ "Φ=5.91233 \n",
+ "Rx \n",
+ "Φ=3.813085 \n",
+ "Rx \n",
+ "Φ=0.565594 \n",
+ "Rx \n",
+ "Φ=0.947977 \n",
+ "Rx \n",
+ "Φ=1.016263 \n",
+ "Rx \n",
+ "Φ=2.117669 \n",
+ "Rx \n",
+ "Φ=6.009643 \n",
+ "Rx \n",
+ "Φ=5.382674 \n",
+ "Rx \n",
+ "Φ=5.617921 \n",
+ "Rx \n",
+ "Φ=3.755006 \n",
+ "Rx \n",
+ "Φ=0.381813 \n",
+ "Rx \n",
+ "Φ=5.062082 \n",
+ "Rx \n",
+ "Φ=0.66878 \n",
+ "Rx \n",
+ "Φ=3.469229 \n",
+ "Rx \n",
+ "Φ=0.694946 \n",
+ "Rx \n",
+ "Φ=1.962017 \n",
+ "Rx \n",
+ "Φ=0.160134 \n",
+ "Rx \n",
+ "Φ=5.852984 \n",
+ "Rx \n",
+ "Φ=0.404887 \n",
+ "Rx \n",
+ "Φ=0.494495 \n",
+ "Rx \n",
+ "Φ=0.414969 \n",
+ "Rx \n",
+ "Φ=6.064892 \n",
+ "Rx \n",
+ "Φ=0.874305 \n",
+ "Rx \n",
+ "Φ=2.785071 \n",
+ "Rx \n",
+ "Φ=1.207239 \n",
+ "Rx \n",
+ "Φ=6.237648 \n",
+ "Rx \n",
+ "Φ=0.774401 \n",
+ "Rx \n",
+ "Φ=2.0201 \n",
+ "Rx \n",
+ "Φ=0.550799 \n",
+ "Rx \n",
+ "Φ=6.127333 \n",
+ "Rx \n",
+ "Φ=0.666735 \n",
+ "Rx \n",
+ "Φ=2.327142 \n",
+ "Rx \n",
+ "Φ=4.464024 \n",
+ "Rx \n",
+ "Φ=3.719931 \n",
+ "Rx \n",
+ "Φ=0.265128 \n",
+ "Rx \n",
+ "Φ=0.652684 \n",
+ "Rx \n",
+ "Φ=0.189288 \n",
+ "Rx \n",
+ "Φ=2.113852 \n",
+ "Rx \n",
+ "Φ=0.221036 \n",
+ "Rx \n",
+ "Φ=5.366942 \n",
+ "Rx \n",
+ "Φ=0.329384 \n",
+ "Rx \n",
+ "Φ=4.726025 \n",
+ "Rx \n",
+ "Φ=5.990019 \n",
+ "Rx \n",
+ "Φ=3.024746 \n",
+ "Rx \n",
+ "Φ=6.054241 \n",
+ "Rx \n",
+ "Φ=4.195718 \n",
+ "Rx \n",
+ "Φ=0.350289 \n",
+ "Rx \n",
+ "Φ=3.463748 \n",
+ "Rx \n",
+ "Φ=0.692485 \n",
+ "Rx \n",
+ "Φ=3.805946 \n",
+ "Rx \n",
+ "Φ=0.146977 \n",
+ "Rx \n",
+ "Φ=4.187379 \n",
+ "Rx \n",
+ "Φ=6.067376 \n",
+ "Rx \n",
+ "Φ=4.535443 \n",
+ "Rx \n",
+ "Φ=0.262366 \n",
+ "Rx \n",
+ "Φ=3.055602 \n",
+ "Rx \n",
+ "Φ=5.999386 \n",
+ "Rx \n",
+ "Φ=2.325433 \n",
+ "Rx \n",
+ "Φ=0.211872 \n",
+ "Rx \n",
+ "Φ=2.68304 \n",
+ "Rx \n",
+ "Φ=0.435953 \n",
+ "Rx \n",
+ "Φ=3.111762 \n",
+ "Rx \n",
+ "Φ=6.062285 \n",
+ "Rx \n",
+ "Φ=4.895262 \n",
+ "Rx \n",
+ "Φ=6.037255 \n",
+ "Rx \n",
+ "Φ=4.019545 \n",
+ "Rx \n",
+ "Φ=0.2742 \n",
+ "Rx \n",
+ "Φ=1.596215 \n",
+ "Rx \n",
+ "Φ=0.302432 \n",
+ "Rx \n",
+ "Φ=2.746479 \n",
+ "Rx \n",
+ "Φ=0.429487 \n",
+ "Rx \n",
+ "Φ=1.548486 \n",
+ "Rx \n",
+ "Φ=6.054801 \n",
+ "Rx \n",
+ "Φ=1.780688 \n",
+ "Rx \n",
+ "Φ=0.458075 \n",
+ "Rx \n",
+ "Φ=0.911576 \n",
+ "Rx \n",
+ "Φ=0.362508 \n",
+ "Rx \n",
+ "Φ=4.852174 \n",
+ "Rx \n",
+ "Φ=0.547356 \n",
+ "Rx \n",
+ "Φ=1.762568 \n",
+ "Rx \n",
+ "Φ=6.192482 \n",
+ "Rx \n",
+ "Φ=4.592862 \n",
+ "Rx \n",
+ "Φ=0.27416 \n",
+ "Rx \n",
+ "Φ=4.107857 \n",
+ "Rx \n",
+ "Φ=5.989564 \n",
+ "Rx \n",
+ "Φ=0.679746 \n",
+ "Rx \n",
+ "Φ=0.37256 \n",
+ "Rx \n",
+ "Φ=2.562888 \n",
+ "Rx \n",
+ "Φ=6.024639 \n",
+ "Rx \n",
+ "Φ=4.59135 \n",
+ "Rx \n",
+ "Φ=5.773185 \n",
+ "Rx \n",
+ "Φ=3.339514 \n",
+ "Rx \n",
+ "Φ=6.183684 \n",
+ "Rx \n",
+ "Φ=3.225851 \n",
+ "Rx \n",
+ "Φ=5.494985 \n",
+ "Rx \n",
+ "Φ=5.777556 \n",
+ "Rx \n",
+ "Φ=0.713991 \n",
+ "Rx \n",
+ "Φ=4.080569 \n",
+ "Rx \n",
+ "Φ=5.980554 \n",
+ "Rx \n",
+ "Φ=2.391672 \n",
+ "Rx \n",
+ "Φ=6.156033 \n",
+ "Rx \n",
+ "Φ=4.552774 \n",
+ "Rx \n",
+ "Φ=0.214618 \n",
+ "Rx \n",
+ "Φ=5.046047 \n",
+ "Rx \n",
+ "Φ=0.446677 \n",
+ "Rx \n",
+ "Φ=2.710078 \n",
+ "Rx \n",
+ "Φ=5.823893 \n",
+ "Rx \n",
+ "Φ=2.474993 \n",
+ "Rx \n",
+ "Φ=5.987081 \n",
+ "Rx \n",
+ "Φ=1.709615 \n",
+ "Rx \n",
+ "Φ=5.828774 \n",
+ "Rx \n",
+ "Φ=3.001315 \n",
+ "Rx \n",
+ "Φ=5.513979 \n",
+ "Rx \n",
+ "Φ=2.793931 \n",
+ "Rx \n",
+ "Φ=5.138604 \n",
+ "Rx \n",
+ "Φ=3.574582 \n",
+ "Rx \n",
+ "Φ=0.421353 \n",
+ "Rx \n",
+ "Φ=2.252219 \n",
+ "Rx \n",
+ "Φ=5.423521 \n",
+ "Rx \n",
+ "Φ=4.044005 \n",
+ "Rx \n",
+ "Φ=6.080467 \n",
+ "Rx \n",
+ "Φ=3.847092 \n",
+ "Rx \n",
+ "Φ=5.517252 \n",
+ "Rx \n",
+ "Φ=1.457691 \n",
+ "Rx \n",
+ "Φ=5.574929 \n",
+ "Rx \n",
+ "Φ=2.85439 \n",
+ "Rx \n",
+ "Φ=4.961881 \n",
+ "Rx \n",
+ "Φ=1.646042 \n",
+ "Rx \n",
+ "Φ=0.703594 \n",
+ "Rx \n",
+ "Φ=4.39911 \n",
+ "Rx \n",
+ "Φ=4.809311 \n",
+ "Rx \n",
+ "Φ=0.970562 \n",
+ "Rx \n",
+ "Φ=4.049869 \n",
+ "Rx \n",
+ "Φ=1.752489 \n",
+ "Rx \n",
+ "Φ=0.127363 \n",
+ "Rx \n",
+ "Φ=4.222764 \n",
+ "Rx \n",
+ "Φ=0.27229 \n",
+ "Rx \n",
+ "Φ=0.063175 \n",
+ "Rx \n",
+ "Φ=6.214968 \n",
+ "Rx \n",
+ "Φ=4.771687 \n",
+ "Rx \n",
+ "Φ=5.960146 \n",
+ "Rx \n",
+ "Φ=1.701639 \n",
+ "Rx \n",
+ "Φ=6.077334 \n",
+ "Rx \n",
+ "Φ=2.105757 \n",
+ "Rx \n",
+ "Φ=5.862965 \n",
+ "Rx \n",
+ "Φ=4.201507 \n",
+ "Rx \n",
+ "Φ=6.064734 \n",
+ "Rx \n",
+ "Φ=4.657985 \n",
+ "Rx \n",
+ "Φ=0.31683 \n",
+ "Rx \n",
+ "Φ=1.00219 \n",
+ "Rx \n",
+ "Φ=5.957813 \n",
+ "Rx \n",
+ "Φ=0.129557 \n",
+ "Rx \n",
+ "Φ=5.921576 \n",
+ "Rx \n",
+ "Φ=4.769161 \n",
+ "Rx \n",
+ "Φ=6.141327 \n",
+ "Rx \n",
+ "Φ=1.731127 \n",
+ "Rx \n",
+ "Φ=0.326771 \n",
+ "Rx \n",
+ "Φ=5.078205 \n",
+ "Rx \n",
+ "Φ=5.692786 \n",
+ "Rx \n",
+ "Φ=2.124067 \n",
+ "Rx \n",
+ "Φ=5.737146 \n",
+ "Rx \n",
+ "Φ=6.204912 \n",
+ "Rx \n",
+ "Φ=6.123497 \n",
+ "Rx \n",
+ "Φ=4.113671 \n",
+ "Rx \n",
+ "Φ=0.225579 \n",
+ "Rx \n",
+ "Φ=3.858119 \n",
+ "Rx \n",
+ "Φ=0.291201 \n",
+ "Rx \n",
+ "Φ=5.528163 \n",
+ "Rx \n",
+ "Φ=0.543354 \n",
+ "Rx \n",
+ "Φ=2.734172 \n",
+ "Rx \n",
+ "Φ=5.921973 \n",
+ "Rx \n",
+ "Φ=5.566403 \n",
+ "Rx \n",
+ "Φ=0.28329 \n",
+ "Rx \n",
+ "Φ=2.29003 \n",
+ "Rx \n",
+ "Φ=6.124091 \n",
+ "Rx \n",
+ "Φ=4.006831 \n",
+ "Rx \n",
+ "Φ=6.077304 \n",
+ "Rx \n",
+ "Φ=4.394518 \n",
+ "Rx \n",
+ "Φ=0.236374 \n",
+ "Rx \n",
+ "Φ=4.657109 \n",
+ "Rx \n",
+ "Φ=6.208228 \n",
+ "Rx \n",
+ "Φ=1.662527 \n",
+ "Rx \n",
+ "Φ=5.588201 \n",
+ "Rx \n",
+ "Φ=3.920868 \n",
+ "Rx \n",
+ "Φ=0.165392 \n",
+ "Rx \n",
+ "Φ=4.071781 \n",
+ "Rx \n",
+ "Φ=0.39917 \n",
+ "Rx \n",
+ "Φ=1.183841 \n",
+ "Rx \n",
+ "Φ=5.978169 \n",
+ "Rx \n",
+ "Φ=4.280514 \n",
+ "Rx \n",
+ "Φ=5.697773 \n",
+ "Rx \n",
+ "Φ=0.840433 \n",
+ "Rx \n",
+ "Φ=0.279331 \n",
+ "Rx \n",
+ "Φ=3.700827 \n",
+ "Rx \n",
+ "Φ=5.973919 \n",
+ "Rx \n",
+ "Φ=4.428324 \n",
+ "Rx \n",
+ "Φ=5.973433 \n",
+ "Rx \n",
+ "Φ=5.77216 \n",
+ "Rx \n",
+ "Φ=5.982376 \n",
+ "Rx \n",
+ "Φ=1.072738 \n",
+ "Rx \n",
+ "Φ=5.825751 \n",
+ "Rx \n",
+ "Φ=2.079809 \n",
+ "Rx \n",
+ "Φ=0.456515 \n",
+ "Rx \n",
+ "Φ=5.656585 \n",
+ "Rx \n",
+ "Φ=0.459477 \n",
+ "Rx \n",
+ "Φ=4.883624 \n",
+ "Rx \n",
+ "Φ=0.44024 \n",
+ "Rx \n",
+ "Φ=4.198558 \n",
+ "Rx \n",
+ "Φ=0.420157 \n",
+ "Rx \n",
+ "Φ=1.155791 \n",
+ "Rx \n",
+ "Φ=0.519496 \n",
+ "Rx \n",
+ "Φ=1.635686 \n",
+ "Rx \n",
+ "Φ=0.469166 \n",
+ "Rx \n",
+ "Φ=5.494996 \n",
+ "Rx \n",
+ "Φ=0.380148 \n",
+ "Rx \n",
+ "Φ=3.677112 \n",
+ "Rx \n",
+ "Φ=0.229521 \n",
+ "Rx \n",
+ "Φ=0.206341 \n",
+ "Rx \n",
+ "Φ=5.628509 \n",
+ "Rx \n",
+ "Φ=2.87739 \n",
+ "Rx \n",
+ "Φ=5.909078 \n",
+ "Rx \n",
+ "Φ=4.922577 \n",
+ "Rx \n",
+ "Φ=0.666975 \n",
+ "Rx \n",
+ "Φ=3.871048 \n",
+ "Rx \n",
+ "Φ=1.101457 \n",
+ "Rx \n",
+ "Φ=5.358011 \n",
+ "Rx \n",
+ "Φ=5.406568 \n",
+ "Rx \n",
+ "Φ=0.905391 \n",
+ "Rx \n",
+ "Φ=4.891736 \n",
+ "Rx \n",
+ "Φ=3.998409 \n",
+ "Rx \n",
+ "Φ=1.153574 \n",
+ "Rx \n",
+ "Φ=5.095702 \n",
+ "Rx \n",
+ "Φ=0.761975 \n",
+ "Rx \n",
+ "Φ=4.219458 \n",
+ "Rx \n",
+ "Φ=4.583834 \n",
+ "Rx \n",
+ "Φ=1.990631 \n",
+ "Rx \n",
+ "Φ=0.25607 \n",
+ "Rx \n",
+ "Φ=2.818999 \n",
+ "Rx \n",
+ "Φ=6.159778 \n",
+ "Rx \n",
+ "Φ=4.546837 \n",
+ "Rx \n",
+ "Φ=0.226499 \n",
+ "Rx \n",
+ "Φ=4.645356 \n",
+ "Rx \n",
+ "Φ=6.083485 \n",
+ "Rx \n",
+ "Φ=1.789975 \n",
+ "Rx \n",
+ "Φ=0.338415 \n",
+ "Rx \n",
+ "Φ=3.742897 \n",
+ "Rx \n",
+ "Φ=6.03936 \n",
+ "Rx \n",
+ "Φ=0.107987 \n",
+ "Rx \n",
+ "Φ=0.162662 \n",
+ "Rx \n",
+ "Φ=1.416164 \n",
+ "Rx \n",
+ "Φ=6.014757 \n",
+ "Rx \n",
+ "Φ=1.880668 \n",
+ "Rx \n",
+ "Φ=6.064396 \n",
+ "Rx \n",
+ "Φ=5.421092 \n",
+ "Rx \n",
+ "Φ=6.201501 \n",
+ "Rx \n",
+ "Φ=1.618917 \n",
+ "Rx \n",
+ "Φ=0.338984 \n",
+ "Rx \n",
+ "Φ=0.792278 \n",
+ "Rx \n",
+ "Φ=0.354899 \n",
+ "Rx \n",
+ "Φ=3.800444 \n",
+ "Rx \n",
+ "Φ=0.185834 \n",
+ "Rx \n",
+ "Φ=2.957859 \n",
+ "Rx \n",
+ "Φ=0.612619 \n",
+ "Rx \n",
+ "Φ=4.947029 \n",
+ "Rx \n",
+ "Φ=0.119451 \n",
+ "Rx \n",
+ "Φ=0.050866 \n",
+ "Rx \n",
+ "Φ=6.070342 \n",
+ "Rx \n",
+ "Φ=5.281795 \n",
+ "Rx \n",
+ "Φ=6.230552 \n",
+ "Rx \n",
+ "Φ=3.12458 \n",
+ "Rx \n",
+ "Φ=6.065243 \n",
+ "Rx \n",
+ "Φ=1.436978 \n",
+ "Rx \n",
+ "Φ=0.221498 \n",
+ "Rx \n",
+ "Φ=1.211547 \n",
+ "Rx \n",
+ "Φ=0.304958 \n",
+ "Rx \n",
+ "Φ=0.323891 \n",
+ "Rx \n",
+ "Φ=6.049812 \n",
+ "Rx \n",
+ "Φ=1.580948 \n",
+ "Rx \n",
+ "Φ=5.918712 \n",
+ "Rx \n",
+ "Φ=0.623408 \n",
+ "Rx \n",
+ "Φ=5.874666 \n",
+ "Rx \n",
+ "Φ=1.700978 \n",
+ "Rx \n",
+ "Φ=6.162213 \n",
+ "Rx \n",
+ "Φ=1.840105 \n",
+ "Rx \n",
+ "Φ=0.651203 \n",
+ "Rx \n",
+ "Φ=3.161817 \n",
+ "Rx \n",
+ "Φ=0.229266 \n",
+ "Rx \n",
+ "Φ=2.454585 \n",
+ "Rx \n",
+ "Φ=0.114864 \n",
+ "Rx \n",
+ "Φ=2.610071 \n",
+ "Rx \n",
+ "Φ=5.896359 \n",
+ "Rx \n",
+ "Φ=2.03368 \n",
+ "Rx \n",
+ "Φ=0.313281 \n",
+ "Rx \n",
+ "Φ=3.329098 \n",
+ "Rx \n",
+ "Φ=6.003112 \n",
+ "Rx \n",
+ "Φ=3.589951 \n",
+ "Rx \n",
+ "Φ=0.053486 \n",
+ "Rx \n",
+ "Φ=1.406513 \n",
+ "Rx \n",
+ "Φ=0.195138 \n",
+ "Rx \n",
+ "Φ=0.499282 \n",
+ "Rx \n",
+ "Φ=0.199594 \n",
+ "Rx \n",
+ "Φ=6.013594 \n",
+ "Rx \n",
+ "Φ=6.197505 \n",
+ "Rx \n",
+ "Φ=5.178348 \n",
+ "Rx \n",
+ "Φ=0.829724 \n",
+ "Rx \n",
+ "Φ=1.940626 \n",
+ "Rx \n",
+ "Φ=5.555362 \n",
+ "Rx \n",
+ "Φ=5.529786 \n",
+ "Rx \n",
+ "Φ=5.90565 \n",
+ "Rx \n",
+ "Φ=2.906796 \n",
+ "Rx \n",
+ "Φ=0.349438 \n",
+ "Rx \n",
+ "Φ=4.172592 \n",
+ "Rx \n",
+ "Φ=0.789804 \n",
+ "Rx \n",
+ "Φ=3.555134 \n",
+ "Rx \n",
+ "Φ=5.397189 \n",
+ "Rx \n",
+ "Φ=1.326806 \n",
+ "Rx \n",
+ "Φ=4.975233 \n",
+ "Rx \n",
+ "Φ=2.462955 \n",
+ "Rx \n",
+ "Φ=1.054267 \n",
+ "Rx \n",
+ "Φ=4.10888 \n",
+ "Rx \n",
+ "Φ=5.926595 \n",
+ "Rx \n",
+ "Φ=4.157172 \n",
+ "Rx \n",
+ "Φ=0.511025 \n",
+ "Rx \n",
+ "Φ=0.375345 \n",
+ "Rx \n",
+ "Φ=5.62045 \n",
+ "Rx \n",
+ "Φ=5.349547 \n",
+ "Rx \n",
+ "Φ=5.585412 \n",
+ "Rx \n",
+ "Φ=2.554103 \n",
+ "Rx \n",
+ "Φ=0.834355 \n",
+ "Rx \n",
+ "Φ=4.037928 \n",
+ "Rx \n",
+ "Φ=5.607623 \n",
+ "Rx \n",
+ "Φ=0.222675 \n",
+ "Rx \n",
+ "Φ=0.363067 \n",
+ "Rx \n",
+ "Φ=1.821679 \n",
+ "Rx \n",
+ "Φ=5.50582 \n",
+ "Rx \n",
+ "Φ=2.398446 \n",
+ "Rx \n",
+ "Φ=0.766926 \n",
+ "Rx \n",
+ "Φ=4.265431 \n",
+ "Rx \n",
+ "Φ=4.912827 \n",
+ "Rx \n",
+ "Φ=5.107995 \n",
+ "Rx \n",
+ "Φ=6.037291 \n",
+ "Rx \n",
+ "Φ=5.501519 \n",
+ "Rx \n",
+ "Φ=5.807611 \n",
+ "Rx \n",
+ "Φ=2.469681 \n",
+ "Rx \n",
+ "Φ=5.987421 \n",
+ "Rx \n",
+ "Φ=2.78626 \n",
+ "Rx \n",
+ "Φ=6.079856 \n",
+ "Rx \n",
+ "Φ=1.981683 \n",
+ "Rx \n",
+ "Φ=5.774959 \n",
+ "Rx \n",
+ "Φ=4.873218 \n",
+ "Rx \n",
+ "Φ=0.417846 \n",
+ "Rx \n",
+ "Φ=3.198579 \n",
+ "Rx \n",
+ "Φ=5.897657 \n",
+ "Rx \n",
+ "Φ=1.643114 \n",
+ "Rx \n",
+ "Φ=6.12416 \n",
+ "Rx \n",
+ "Φ=3.080919 \n",
+ "Rx \n",
+ "Φ=6.202419 \n",
+ "Rx \n",
+ "Φ=5.342802 \n",
+ "Rx \n",
+ "Φ=0.184376 \n",
+ "Rx \n",
+ "Φ=5.092326 \n",
+ "Rx \n",
+ "Φ=0.479781 \n",
+ "Rx \n",
+ "Φ=5.517746 \n",
+ "Rx \n",
+ "Φ=0.217435 \n",
+ "Rx \n",
+ "Φ=0.665357 \n",
+ "Rx \n",
+ "Φ=0.244518 \n",
+ "Rx \n",
+ "Φ=2.021682 \n",
+ "Rx \n",
+ "Φ=6.136202 \n",
+ "Rx \n",
+ "Φ=3.599725 \n",
+ "Rx \n",
+ "Φ=0.51587 \n",
+ "Rx \n",
+ "Φ=3.841605 \n",
+ "Rx \n",
+ "Φ=5.812838 \n",
+ "Rx \n",
+ "Φ=4.664006 \n",
+ "Rx \n",
+ "Φ=0.427424 \n",
+ "Rx \n",
+ "Φ=2.780703 \n",
+ "Rx \n",
+ "Φ=5.657904 \n",
+ "Rx \n",
+ "Φ=3.900151 \n",
+ "Rx \n",
+ "Φ=5.91442 \n",
+ "Rx \n",
+ "Φ=5.572031 \n",
+ "Rx \n",
+ "Φ=0.641552 \n",
+ "Rx \n",
+ "Φ=0.086878 \n",
+ "Rx \n",
+ "Φ=0.258176 \n",
+ "Rx \n",
+ "Φ=6.26366 \n",
+ "Rx \n",
+ "Φ=0.324053 \n",
+ "Rx \n",
+ "Φ=4.562908 \n",
+ "Rx \n",
+ "Φ=6.029391 \n",
+ "Rx \n",
+ "Φ=6.079197 \n",
+ "Rx \n",
+ "Φ=0.360217 \n",
+ "Rx \n",
+ "Φ=0.52373 \n",
+ "Rx \n",
+ "Φ=0.313779 \n",
+ "Rx \n",
+ "Φ=0.525344 \n",
+ "Rx \n",
+ "Φ=5.998757 \n",
+ "Rx \n",
+ "Φ=4.076823 \n",
+ "Rx \n",
+ "Φ=6.065655 \n",
+ "Rx \n",
+ "Φ=4.433683 \n",
+ "Rx \n",
+ "Φ=5.981223 \n",
+ "Rx \n",
+ "Φ=1.095506 \n",
+ "Rx \n",
+ "Φ=6.045069 \n",
+ "Rx \n",
+ "Φ=2.697857 \n",
+ "Rx \n",
+ "Φ=5.651976 \n",
+ "Rx \n",
+ "Φ=0.29989 \n",
+ "Rx \n",
+ "Φ=5.649565 \n",
+ "Rx \n",
+ "Φ=3.669148 \n",
+ "Rx \n",
+ "Φ=6.046988 \n",
+ "Rx \n",
+ "Φ=4.189992 \n",
+ "Rx \n",
+ "Φ=5.68264 \n",
+ "Rx \n",
+ "Φ=6.220498 \n",
+ "Rx \n",
+ "Φ=0.221516 \n",
+ "Rx \n",
+ "Φ=1.132767 \n",
+ "Rx \n",
+ "Φ=0.317713 \n",
+ "Rx \n",
+ "Φ=6.23467 \n",
+ "Rx \n",
+ "Φ=0.37143 \n",
+ "Rx \n",
+ "Φ=0.33836 \n",
+ "Rx \n",
+ "Φ=0.070328 \n",
+ "Rx \n",
+ "Φ=4.289274 \n",
+ "Rx \n",
+ "Φ=5.705085 \n",
+ "Rx \n",
+ "Φ=4.478133 \n",
+ "Rx \n",
+ "Φ=0.619075 \n",
+ "Rx \n",
+ "Φ=0.417085 \n",
+ "Rx \n",
+ "Φ=5.451139 \n",
+ "Rx \n",
+ "Φ=1.790547 \n",
+ "Rx \n",
+ "Φ=0.48647 \n",
+ "Rx \n",
+ "Φ=5.843937 \n",
+ "Rx \n",
+ "Φ=0.405182 \n",
+ "Rx \n",
+ "Φ=0.156341 \n",
+ "Rx \n",
+ "Φ=5.497517 \n",
+ "Rx \n",
+ "Φ=3.022746 \n",
+ "Rx \n",
+ "Φ=5.505351 \n",
+ "Rx \n",
+ "Φ=3.104732 \n",
+ "Rx \n",
+ "Φ=6.109668 \n",
+ "Rx \n",
+ "Φ=2.495843 \n",
+ "Rx \n",
+ "Φ=5.614293 \n",
+ "Rx \n",
+ "Φ=1.207482 \n",
+ "Rx \n",
+ "Φ=5.332305 \n",
+ "Rx \n",
+ "Φ=0.530818 \n",
+ "Rx \n",
+ "Φ=5.782594 \n",
+ "Rx \n",
+ "Φ=1.52175 \n",
+ "Rx \n",
+ "Φ=5.540295 \n",
+ "Rx \n",
+ "Φ=3.925669 \n",
+ "Rx \n",
+ "Φ=5.991712 \n",
+ "Rx \n",
+ "Φ=1.788207 \n",
+ "Rx \n",
+ "Φ=5.498657 \n",
+ "Rx \n",
+ "Φ=0.584122 \n",
+ "Rx \n",
+ "Φ=1.214865 \n",
+ "Rx \n",
+ "Φ=2.212583 \n",
+ "Rx \n",
+ "Φ=4.943245 \n",
+ "Rx \n",
+ "Φ=3.35976 \n",
+ "Rx \n",
+ "Φ=6.104435 \n",
+ "Rx \n",
+ "Φ=3.458388 \n",
+ "Rx \n",
+ "Φ=6.001319 \n",
+ "Rx \n",
+ "Φ=3.999689 \n",
+ "Rx \n",
+ "Φ=0.58302 \n",
+ "Rx \n",
+ "Φ=1.485994 \n",
+ "Rx \n",
+ "Φ=5.967201 \n",
+ "Rx \n",
+ "Φ=5.920485 \n",
+ "Rx \n",
+ "Φ=0.389746 \n",
+ "Rx \n",
+ "Φ=4.680787 \n",
+ "Rx \n",
+ "Φ=0.053754 \n",
+ "Rx \n",
+ "Φ=3.103164 \n",
+ "Rx \n",
+ "Φ=6.096642 \n",
+ "Rx \n",
+ "Φ=1.716865 \n",
+ "Rx \n",
+ "Φ=0.160882 \n",
+ "Rx \n",
+ "Φ=2.140311 \n",
+ "Rx \n",
+ "Φ=6.125066 \n",
+ "Rx \n",
+ "Φ=5.738908 \n",
+ "Rx \n",
+ "Φ=6.079184 \n",
+ "Rx \n",
+ "Φ=1.781887 \n",
+ "Rx \n",
+ "Φ=0.211483 \n",
+ "Rx \n",
+ "Φ=4.816013 \n",
+ "Rx \n",
+ "Φ=0.175144 \n",
+ "Rx \n",
+ "Φ=1.865505 \n",
+ "Rx \n",
+ "Φ=5.781324 \n",
+ "Rx \n",
+ "Φ=2.657285 \n",
+ "Rx \n",
+ "Φ=0.115753 \n",
+ "Rx \n",
+ "Φ=1.029926 \n",
+ "Rx \n",
+ "Φ=0.195377 \n",
+ "Rx \n",
+ "Φ=6.194511 \n",
+ "Rx \n",
+ "Φ=5.856724 \n",
+ "Rx \n",
+ "Φ=6.058065 \n",
+ "Rx \n",
+ "Φ=6.093726 \n",
+ "Rx \n",
+ "Φ=0.109518 \n",
+ "Rx \n",
+ "Φ=0.306107 \n",
+ "Rx \n",
+ "Φ=1.852109 \n",
+ "Rx \n",
+ "Φ=0.312005 \n",
+ "Rx \n",
+ "Φ=2.11218 \n",
+ "Rx \n",
+ "Φ=6.243958 \n",
+ "Rx \n",
+ "Φ=0.103247 \n",
+ "Rx \n",
+ "Φ=0.298923 \n",
+ "Rx \n",
+ "Φ=0.346879 \n",
+ "Rx \n",
+ "Φ=6.119318 \n",
+ "Rx \n",
+ "Φ=2.58759 \n",
+ "Rx \n",
+ "Φ=6.079447 \n",
+ "Rx \n",
+ "Φ=0.725876 \n",
+ "Rx \n",
+ "Φ=0.378061 \n",
+ "Rx \n",
+ "Φ=4.422716 \n",
+ "Rx \n",
+ "Φ=6.039648 \n",
+ "Rx \n",
+ "Φ=1.268851 \n",
+ "Rx \n",
+ "Φ=0.390531 \n",
+ "Rx \n",
+ "Φ=0.126578 \n",
+ "Rx \n",
+ "Φ=0.246413 \n",
+ "Rx \n",
+ "Φ=3.402408 \n",
+ "Rx \n",
+ "Φ=5.826186 \n",
+ "Rx \n",
+ "Φ=4.233559 \n",
+ "Rx \n",
+ "Φ=6.051188 \n",
+ "Rx \n",
+ "Φ=0.79901 \n",
+ "Rx \n",
+ "Φ=5.776695 \n",
+ "Rx \n",
+ "Φ=4.974547 \n",
+ "Rx \n",
+ "Φ=5.895872 \n",
+ "Rx \n",
+ "Φ=3.418513 \n",
+ "Rx \n",
+ "Φ=5.734169 \n",
+ "Rx \n",
+ "Φ=3.609693 \n",
+ "Rx \n",
+ "Φ=5.952319 \n",
+ "Rx \n",
+ "Φ=6.143114 \n",
+ "Rx \n",
+ "Φ=0.201968 \n",
+ "Rx \n",
+ "Φ=5.889935 \n",
+ "Rx \n",
+ "Φ=5.740097 \n",
+ "Rx \n",
+ "Φ=2.527898 \n",
+ "Rx \n",
+ "Φ=0.367942 \n",
+ "Rx \n",
+ "Φ=3.220737 \n",
+ "Rx \n",
+ "Φ=5.510039 \n",
+ "Rx \n",
+ "Φ=2.457415 \n",
+ "Rx \n",
+ "Φ=0.365233 \n",
+ "Rx \n",
+ "Φ=1.85556 \n",
+ "Rx \n",
+ "Φ=0.048039 \n",
+ "Rx \n",
+ "Φ=4.766491 \n",
+ "Rx \n",
+ "Φ=6.083697 \n",
+ "Rx \n",
+ "Φ=3.502725 \n",
+ "Rx \n",
+ "Φ=5.818082 \n",
+ "Rx \n",
+ "Φ=1.045527 \n",
+ "Rx \n",
+ "Φ=0.229156 \n",
+ "Rx \n",
+ "Φ=3.842632 \n",
+ "Rx \n",
+ "Φ=6.264048 \n",
+ "Rx \n",
+ "Φ=2.871257 \n",
+ "Rx \n",
+ "Φ=1.01022 \n",
+ "Rx \n",
+ "Φ=3.458134 \n",
+ "Rx \n",
+ "Φ=0.911198 \n",
+ "Rx \n",
+ "Φ=1.366752 \n",
+ "Rx \n",
+ "Φ=0.424202 \n",
+ "Rx \n",
+ "Φ=5.229071 \n",
+ "Rx \n",
+ "Φ=5.865754 \n",
+ "Rx \n",
+ "Φ=1.05718 \n",
+ "Rx \n",
+ "Φ=5.766472 \n",
+ "Rx \n",
+ "Φ=5.956139 \n",
+ "Rx \n",
+ "Φ=5.148345 \n",
+ "Rx \n",
+ "Φ=3.360316 \n",
+ "Rx \n",
+ "Φ=5.497444 \n",
+ "Rx \n",
+ "Φ=2.301208 \n",
+ "Rx \n",
+ "Φ=0.686168 \n",
+ "Rx \n",
+ "Φ=0.992239 \n",
+ "Rx \n",
+ "Φ=5.204136 \n",
+ "Rx \n",
+ "Φ=3.756768 \n",
+ "Rx \n",
+ "Φ=5.477774 \n",
+ "Rx \n",
+ "Φ=1.3166 \n",
+ "Rx \n",
+ "Φ=4.862561 \n",
+ "Rx \n",
+ "Φ=0.788916 \n",
+ "Rx \n",
+ "Φ=6.069939 \n",
+ "Rx \n",
+ "Φ=1.026089 \n",
+ "Rx \n",
+ "Φ=6.193815 \n",
+ "Rx \n",
+ "Φ=3.011122 \n",
+ "Rx \n",
+ "Φ=6.114183 \n",
+ "Rx \n",
+ "Φ=4.348631 \n",
+ "Rx \n",
+ "Φ=0.177894 \n",
+ "Rx \n",
+ "Φ=4.211142 \n",
+ "Rx \n",
+ "Φ=0.173033 \n",
+ "Rx \n",
+ "Φ=1.205005 \n",
+ "Rx \n",
+ "Φ=5.991042 \n",
+ "Rx \n",
+ "Φ=5.584329 \n",
+ "Rx \n",
+ "Φ=0.072233 \n",
+ "Rx \n",
+ "Φ=5.464449 \n",
+ "Rx \n",
+ "Φ=6.027319 \n",
+ "Rx \n",
+ "Φ=3.454423 \n",
+ "Rx \n",
+ "Φ=0.267332 \n",
+ "Rx \n",
+ "Φ=4.027251 \n",
+ "Rx \n",
+ "Φ=0.530794 \n",
+ "Rx \n",
+ "Φ=4.032712 \n",
+ "Rx \n",
+ "Φ=5.842024 \n",
+ "Rx \n",
+ "Φ=1.959455 \n",
+ "Rx \n",
+ "Φ=5.870189 \n",
+ "Rx \n",
+ "Φ=1.918084 \n",
+ "Rx \n",
+ "Φ=0.355276 \n",
+ "Rx \n",
+ "Φ=5.648712 \n",
+ "Rx \n",
+ "Φ=5.950376 \n",
+ "Rx \n",
+ "Φ=5.696654 \n",
+ "Rx \n",
+ "Φ=5.585412 \n",
+ "Rx \n",
+ "Φ=1.120116 \n",
+ "Rx \n",
+ "Φ=0.461263 \n",
+ "Rx \n",
+ "Φ=0.963201 \n",
+ "Rx \n",
+ "Φ=6.113926 \n",
+ "Rx \n",
+ "Φ=0.405826 \n",
+ "Rx \n",
+ "Φ=5.871322 \n",
+ "Rx \n",
+ "Φ=1.32178 \n",
+ "Rx \n",
+ "Φ=6.011912 \n",
+ "Rx \n",
+ "Φ=5.990809 \n",
+ "Rx \n",
+ "Φ=5.570258 \n",
+ "Rx \n",
+ "Φ=3.702403 \n",
+ "Rx \n",
+ "Φ=6.239502 \n",
+ "Rx \n",
+ "Φ=1.369657 \n",
+ "Rx \n",
+ "Φ=0.214337 \n",
+ "Rx \n",
+ "Φ=5.438164 \n",
+ "Rx \n",
+ "Φ=0.44669 \n",
+ "Rx \n",
+ "Φ=1.118156 \n",
+ "Rx \n",
+ "Φ=0.625692 \n",
+ "Rx \n",
+ "Φ=5.240257 \n",
+ "Rx \n",
+ "Φ=6.106818 \n",
+ "Rx \n",
+ "Φ=1.066687 \n",
+ "Rx \n",
+ "Φ=0.456034 \n",
+ "Rx \n",
+ "Φ=2.676467 \n",
+ "Rx \n",
+ "Φ=5.966898 \n",
+ "Rx \n",
+ "Φ=3.619195 \n",
+ "Rx \n",
+ "Φ=6.155757 \n",
+ "Rx \n",
+ "Φ=1.812363 \n",
+ "Rx \n",
+ "Φ=6.126905 \n",
+ "Rx \n",
+ "Φ=0.276373 \n",
+ "Rx \n",
+ "Φ=6.054719 \n",
+ "Rx \n",
+ "Φ=2.815921 \n",
+ "Rx \n",
+ "Φ=6.138447 \n",
+ "Rx \n",
+ "Φ=1.996046 \n",
+ "Rx \n",
+ "Φ=0.446102 \n",
+ "Rx \n",
+ "Φ=1.144774 \n",
+ "Rx \n",
+ "Φ=6.178597 \n",
+ "Rx \n",
+ "Φ=1.401236 \n",
+ "Rx \n",
+ "Φ=5.854935 \n",
+ "Rx \n",
+ "Φ=1.722697 \n",
+ "Rx \n",
+ "Φ=6.20702 \n",
+ "Rx \n",
+ "Φ=3.183872 \n",
+ "Rx \n",
+ "Φ=0.672917 \n",
+ "Rx \n",
+ "Φ=4.230831 \n",
+ "Rx \n",
+ "Φ=0.293898 \n",
+ "Rx \n",
+ "Φ=4.913333 \n",
+ "Rx \n",
+ "Φ=6.032747 \n",
+ "Rx \n",
+ "Φ=4.945188 \n",
+ "Rx \n",
+ "Φ=6.152212 \n",
+ "Rx \n",
+ "Φ=5.333317 \n",
+ "Rx \n",
+ "Φ=0.434773 \n",
+ "Rx \n",
+ "Φ=0.602097 \n",
+ "Rx \n",
+ "Φ=6.092966 \n",
+ "Rx \n",
+ "Φ=0.935453 \n",
+ "Rx \n",
+ "Φ=5.913956 \n",
+ "Rx \n",
+ "Φ=2.758088 \n",
+ "Rx \n",
+ "Φ=6.232422 \n",
+ "Rx \n",
+ "Φ=3.56314 \n",
+ "Rx \n",
+ "Φ=6.078639 \n",
+ "Rx \n",
+ "Φ=3.199047 \n",
+ "Rx \n",
+ "Φ=5.869016 \n",
+ "Rx \n",
+ "Φ=2.866879 \n",
+ "Rx \n",
+ "Φ=0.341064 \n",
+ "Rx \n",
+ "Φ=1.812616 \n",
+ "Rx \n",
+ "Φ=0.469801 \n",
+ "Rx \n",
+ "Φ=1.859111 \n",
+ "Rx \n",
+ "Φ=6.160244 \n",
+ "Rx \n",
+ "Φ=6.027053 \n",
+ "Rx \n",
+ "Φ=5.185328 \n",
+ "Rx \n",
+ "Φ=4.276875 \n",
+ "Rx \n",
+ "Φ=0.672739 \n",
+ "Rx \n",
+ "Φ=6.242884 \n",
+ "Rx \n",
+ "Φ=5.826318 \n",
+ "Rx \n",
+ "Φ=1.277143 \n",
+ "Rx \n",
+ "Φ=5.085287 \n",
+ "Rx \n",
+ "Φ=5.952844 \n",
+ "Rx \n",
+ "Φ=1.334357 \n",
+ "Rx \n",
+ "Φ=3.807541 \n",
+ "Rx \n",
+ "Φ=5.099164 \n",
+ "Rx \n",
+ "Φ=4.708939 \n",
+ "Rx \n",
+ "Φ=3.618923 \n",
+ "Rx \n",
+ "Φ=5.343757 \n",
+ "Rx \n",
+ "Φ=6.03117 \n",
+ "Rx \n",
+ "Φ=0.663361 \n",
+ "Rx \n",
+ "Φ=0.256978 \n",
+ "Rx \n",
+ "Φ=5.501659 \n",
+ "Rx \n",
+ "Φ=5.822758 \n",
+ "Rx \n",
+ "Φ=5.024525 \n",
+ "Rx \n",
+ "Φ=6.035368 \n",
+ "Rx \n",
+ "Φ=1.690055 \n",
+ "Rx \n",
+ "Φ=6.053162 \n",
+ "Rx \n",
+ "Φ=1.472306 \n",
+ "Rx \n",
+ "Φ=6.000362 \n",
+ "Rx \n",
+ "Φ=2.512647 \n",
+ "Rx \n",
+ "Φ=6.114733 \n",
+ "Rx \n",
+ "Φ=1.188262 \n",
+ "Rx \n",
+ "Φ=6.10576 \n",
+ "Rx \n",
+ "Φ=4.462493 \n",
+ "Rx \n",
+ "Φ=6.194841 \n",
+ "Rx \n",
+ "Φ=0.112451 \n",
+ "Rx \n",
+ "Φ=0.393175 \n",
+ "Rx \n",
+ "Φ=3.19564 \n",
+ "Rx \n",
+ "Φ=0.077871 \n",
+ "Rx \n",
+ "Φ=5.701282 \n",
+ "Rx \n",
+ "Φ=6.128231 \n",
+ "Rx \n",
+ "Φ=5.959465 \n",
+ "Rx \n",
+ "Φ=6.192619 \n",
+ "Rx \n",
+ "Φ=1.347734 \n",
+ "Rx \n",
+ "Φ=0.565516 \n",
+ "Rx \n",
+ "Φ=0.234849 \n",
+ "Rx \n",
+ "Φ=0.128807 \n",
+ "Rx \n",
+ "Φ=5.027262 \n",
+ "Rx \n",
+ "Φ=0.450018 \n",
+ "Rx \n",
+ "Φ=0.170227 \n",
+ "Rx \n",
+ "Φ=6.079843 \n",
+ "Rx \n",
+ "Φ=1.461052 \n",
+ "Rx \n",
+ "Φ=6.212934 \n",
+ "Rx \n",
+ "Φ=4.922247 \n",
+ "Rx \n",
+ "Φ=6.002916 \n",
+ "Rx \n",
+ "Φ=1.921037 \n",
+ "Rx \n",
+ "Φ=0.125496 \n",
+ "Rx \n",
+ "Φ=5.286739 \n",
+ "Rx \n",
+ "Φ=0.112272 \n",
+ "Rx \n",
+ "Φ=1.991586 \n",
+ "Rx \n",
+ "Φ=5.781626 \n",
+ "Rx \n",
+ "Φ=2.67332 \n",
+ "Rx \n",
+ "Φ=6.063259 \n",
+ "Rx \n",
+ "Φ=0.989563 \n",
+ "Rx \n",
+ "Φ=5.705887 \n",
+ "Rx \n",
+ "Φ=3.341161 \n",
+ "Rx \n",
+ "Φ=0.417074 \n",
+ "Rx \n",
+ "Φ=1.907429 \n",
+ "Rx \n",
+ "Φ=0.613419 \n",
+ "Rx \n",
+ "Φ=1.254199 \n",
+ "Rx \n",
+ "Φ=0.162123 \n",
+ "Rx \n",
+ "Φ=6.168893 \n",
+ "Rx \n",
+ "Φ=6.136747 \n",
+ "Rx \n",
+ "Φ=1.68225 \n",
+ "Rx \n",
+ "Φ=5.87014 \n",
+ "Rx \n",
+ "Φ=4.1864 \n",
+ "Rx \n",
+ "Φ=5.968273 \n",
+ "Rx \n",
+ "Φ=3.820515 \n",
+ "Rx \n",
+ "Φ=6.01992 \n",
+ "Rx \n",
+ "Φ=4.566328 \n",
+ "Rx \n",
+ "Φ=5.490333 \n",
+ "Rx \n",
+ "Φ=2.750272 \n",
+ "Rx \n",
+ "Φ=5.825777 \n",
+ "Rx \n",
+ "Φ=1.9798 \n",
+ "Rx \n",
+ "Φ=0.299213 \n",
+ "Rx \n",
+ "Φ=4.169099 \n",
+ "Rx \n",
+ "Φ=5.914829 \n",
+ "Rx \n",
+ "Φ=1.566154 \n",
+ "Rx \n",
+ "Φ=0.091486 \n",
+ "Rx \n",
+ "Φ=0.248427 \n",
+ "Rx \n",
+ "Φ=6.029484 \n",
+ "Rx \n",
+ "Φ=4.129084 \n",
+ "Rx \n",
+ "Φ=6.210629 \n",
+ "Rx \n",
+ "Φ=6.180298 \n",
+ "Rx \n",
+ "Φ=5.597354 \n",
+ "Rx \n",
+ "Φ=5.852521 \n",
+ "Rx \n",
+ "Φ=0.07827 \n",
+ "Rx \n",
+ "Φ=5.109574 \n",
+ "Rx \n",
+ "Φ=0.247583 \n",
+ "Rx \n",
+ "Φ=1.254713 \n",
+ "Rx \n",
+ "Φ=0.249245 \n",
+ "Rx \n",
+ "Φ=1.765613 \n",
+ "Rx \n",
+ "Φ=0.83629 \n",
+ "Rx \n",
+ "Φ=4.134639 \n",
+ "Rx \n",
+ "Φ=5.526798 \n",
+ "Rx \n",
+ "Φ=3.109616 \n",
+ "Rx \n",
+ "Φ=5.563599 \n",
+ "Rx \n",
+ "Φ=3.365034 \n",
+ "Rx \n",
+ "Φ=0.890462 \n",
+ "Rx \n",
+ "Φ=1.594525 \n",
+ "Rx \n",
+ "Φ=0.994272 \n",
+ "Rx \n",
+ "Φ=4.927901 \n",
+ "Rx \n",
+ "Φ=0.703818 \n",
+ "Rx \n",
+ "Φ=3.555104 \n",
+ "Rx \n",
+ "Φ=0.221101 \n",
+ "Rx \n",
+ "Φ=0.175036 \n",
+ "Rx \n",
+ "Φ=5.890969 \n",
+ "Rx \n",
+ "Φ=0.255289 \n",
+ "Rx \n",
+ "Φ=5.258629 \n",
+ "Rx \n",
+ "Φ=4.794328 \n",
+ "Rx \n",
+ "Φ=1.091856 \n",
+ "Rx \n",
+ "Φ=3.657752 \n",
+ "Rx \n",
+ "Φ=0.966321 \n",
+ "Rx \n",
+ "Φ=3.078381 \n",
+ "Rx \n",
+ "Φ=5.401656 \n",
+ "Rx \n",
+ "Φ=1.130694 \n",
+ "Rx \n",
+ "Φ=1.296184 \n",
+ "Rx \n",
+ "Φ=2.765508 \n",
+ "Rx \n",
+ "Φ=4.391477 \n",
+ "Rx \n",
+ "Φ=3.5839 \n",
+ "Rx \n",
+ "Φ=5.821478 \n",
+ "Rx \n",
+ "Φ=2.952865 \n",
+ "Rx \n",
+ "Φ=0.487923 \n",
+ "Rx \n",
+ "Φ=3.471981 \n",
+ "Rx \n",
+ "Φ=6.008849 \n",
+ "Rx \n",
+ "Φ=5.543587 \n",
+ "Rx \n",
+ "Φ=5.912378 \n",
+ "Rx \n",
+ "Φ=4.717217 \n",
+ "Rx \n",
+ "Φ=5.954973 \n",
+ "Rx \n",
+ "Φ=6.048216 \n",
+ "Rx \n",
+ "Φ=0.377336 \n",
+ "Rx \n",
+ "Φ=3.172754 \n",
+ "Rx \n",
+ "Φ=6.130785 \n",
+ "Rx \n",
+ "Φ=5.897057 \n",
+ "Rx \n",
+ "Φ=5.750915 \n",
+ "Rx \n",
+ "Φ=3.128904 \n",
+ "Rx \n",
+ "Φ=6.165255 \n",
+ "Rx \n",
+ "Φ=4.930897 \n",
+ "Rx \n",
+ "Φ=0.062273 \n",
+ "Rx \n",
+ "Φ=5.242247 \n",
+ "Rx \n",
+ "Φ=5.871378 \n",
+ "Rx \n",
+ "Φ=1.324429 \n",
+ "Rx \n",
+ "Φ=6.081567 \n",
+ "Rx \n",
+ "Φ=0.909729 \n",
+ "Rx \n",
+ "Φ=5.916251 \n",
+ "Rx \n",
+ "Φ=3.480688 \n",
+ "Rx \n",
+ "Φ=6.154356 \n",
+ "Rx \n",
+ "Φ=3.799629 \n",
+ "Rx \n",
+ "Φ=0.450691 \n",
+ "Rx \n",
+ "Φ=5.106797 \n",
+ "Rx \n",
+ "Φ=0.321715 \n",
+ "Rx \n",
+ "Φ=0.452299 \n",
+ "Rx \n",
+ "Φ=0.185765 \n",
+ "Rx \n",
+ "Φ=4.161743 \n",
+ "Rx \n",
+ "Φ=0.335402 \n",
+ "Rx \n",
+ "Φ=5.993291 \n",
+ "Rx \n",
+ "Φ=0.192655 \n",
+ "Rx \n",
+ "Φ=3.009191 \n",
+ "Rx \n",
+ "Φ=0.208321 \n",
+ "Rx \n",
+ "Φ=3.3052 \n",
+ "Rx \n",
+ "Φ=0.166915 \n",
+ "Rx \n",
+ "Φ=6.070138 \n",
+ "Rx \n",
+ "Φ=0.437737 \n",
+ "Rx \n",
+ "Φ=1.63422 \n",
+ "Rx \n",
+ "Φ=0.429432 \n",
+ "Rx \n",
+ "Φ=1.775509 \n",
+ "Rx \n",
+ "Φ=0.24811 \n",
+ "Rx \n",
+ "Φ=0.295352 \n",
+ "Rx \n",
+ "Φ=0.213961 \n",
+ "Rx \n",
+ "Φ=0.501272 \n",
+ "Rx \n",
+ "Φ=5.986258 \n",
+ "Rx \n",
+ "Φ=1.321975 \n",
+ "Rx \n",
+ "Φ=5.99148 \n",
+ "Rx \n",
+ "Φ=0.182974 \n",
+ "Rx \n",
+ "Φ=0.098643 \n",
+ "Rx \n",
+ "Φ=5.286114 \n",
+ "Rx \n",
+ "Φ=0.502784 \n",
+ "Rx \n",
+ "Φ=5.820663 \n",
+ "Rx \n",
+ "Φ=0.612587 \n",
+ "Rx \n",
+ "Φ=0.006958 \n",
+ "Rx \n",
+ "Φ=6.062078 \n",
+ "Rx \n",
+ "Φ=2.920776 \n",
+ "Rx \n",
+ "Φ=5.781766 \n",
+ "Rx \n",
+ "Φ=2.287795 \n",
+ "Rx \n",
+ "Φ=5.903949 \n",
+ "Rx \n",
+ "Φ=4.880959 \n",
+ "Rx \n",
+ "Φ=5.888915 \n",
+ "Rx \n",
+ "Φ=1.652898 \n",
+ "Rx \n",
+ "Φ=0.235887 \n",
+ "Rx \n",
+ "Φ=5.251055 \n",
+ "Rx \n",
+ "Φ=6.058973 \n",
+ "Rx \n",
+ "Φ=1.342638 \n",
+ "Rx \n",
+ "Φ=0.306901 \n",
+ "Rx \n",
+ "Φ=3.328844 \n",
+ "Rx \n",
+ "Φ=0.445911 \n",
+ "Rx \n",
+ "Φ=5.874783 \n",
+ "Rx \n",
+ "Φ=6.095397 \n",
+ "Rx \n",
+ "Φ=3.90115 \n",
+ "Rx \n",
+ "Φ=0.64258 \n",
+ "Rx \n",
+ "Φ=0.561182 \n",
+ "Rx \n",
+ "Φ=0.335261 \n",
+ "Rx \n",
+ "Φ=4.537983 \n",
+ "Rx \n",
+ "Φ=0.49251 \n",
+ "Rx \n",
+ "Φ=0.753135 \n",
+ "Rx \n",
+ "Φ=5.672205 \n",
+ "Rx \n",
+ "Φ=4.746371 \n",
+ "Rx \n",
+ "Φ=5.77229 \n",
+ "Rx \n",
+ "Φ=3.547434 \n",
+ "Rx \n",
+ "Φ=0.834439 \n",
+ "Rx \n",
+ "Φ=3.128657 \n",
+ "Rx \n",
+ "Φ=0.310848 \n",
+ "Rx \n",
+ "Φ=5.628895 \n",
+ "Rx \n",
+ "Φ=6.10799 \n",
+ "Rx \n",
+ "Φ=3.764063 \n",
+ "Rx \n",
+ "Φ=0.55285 \n",
+ "Rx \n",
+ "Φ=5.153645 \n",
+ "Rx \n",
+ "Φ=0.346198 \n",
+ "Rx \n",
+ "Φ=3.223894 \n",
+ "Rx \n",
+ "Φ=0.569827 \n",
+ "Rx \n",
+ "Φ=3.319507 \n",
+ "Rx \n",
+ "Φ=0.989695 \n",
+ "Rx \n",
+ "Φ=6.256995 \n",
+ "Rx \n",
+ "Φ=0.362548 \n",
+ "Rx \n",
+ "Φ=4.089764 \n",
+ "Rx \n",
+ "Φ=0.983881 \n",
+ "Rx \n",
+ "Φ=5.07582 \n",
+ "Rx \n",
+ "Φ=0.228057 \n",
+ "Rx \n",
+ "Φ=2.628947 \n",
+ "Rx \n",
+ "Φ=4.601096 \n",
+ "Rx \n",
+ "Φ=1.348794 \n",
+ "Rx \n",
+ "Φ=5.936369 \n",
+ "Rx \n",
+ "Φ=1.656553 \n",
+ "Rx \n",
+ "Φ=3.702146 \n",
+ "Rx \n",
+ "Φ=2.915192 \n",
+ "Rx \n",
+ "Φ=6.146791 \n",
+ "Rx \n",
+ "Φ=5.368077 \n",
+ "Rx \n",
+ "Φ=0.093564 \n",
+ "Rx \n",
+ "Φ=0.141214 \n",
+ "Rx \n",
+ "Φ=0.211814 \n",
+ "Rx \n",
+ "Φ=2.730347 \n",
+ "Rx \n",
+ "Φ=0.361998 \n",
+ "Rx \n",
+ "Φ=0.282148 \n",
+ "Rx \n",
+ "Φ=0.227074 \n",
+ "Rx \n",
+ "Φ=3.338574 \n",
+ "Rx \n",
+ "Φ=0.243093 \n",
+ "Rx \n",
+ "Φ=5.987782 \n",
+ "Rx \n",
+ "Φ=6.058222 \n",
+ "Rx \n",
+ "Φ=6.085666 \n",
+ "Rx \n",
+ "Φ=0.152386 \n",
+ "Rx \n",
+ "Φ=4.283224 \n",
+ "Rx \n",
+ "Φ=0.167865 \n",
+ "Rx \n",
+ "Φ=1.515827 \n",
+ "Rx \n",
+ "Φ=0.231491 \n",
+ "Rx \n",
+ "Φ=1.096251 \n",
+ "Rx \n",
+ "Φ=0.500816 \n",
+ "Rx \n",
+ "Φ=0.761015 \n",
+ "Rx \n",
+ "Φ=5.872252 \n",
+ "Rx \n",
+ "Φ=0.094949 \n",
+ "Rx \n",
+ "Φ=5.911576 \n",
+ "Rx \n",
+ "Φ=4.105188 \n",
+ "Rx \n",
+ "Φ=0.386495 \n",
+ "Rx \n",
+ "Φ=4.462909 \n",
+ "Rx \n",
+ "Φ=0.082525 \n",
+ "Rx \n",
+ "Φ=0.568374 \n",
+ "Rx \n",
+ "Φ=5.751015 \n",
+ "Rx \n",
+ "Φ=0.698077 \n",
+ "Rx \n",
+ "Φ=0.652032 \n",
+ "Rx \n",
+ "Φ=0.491142 \n",
+ "Rx \n",
+ "Φ=0.289689 \n",
+ "Rx \n",
+ "Φ=0.924055 \n",
+ "Rx \n",
+ "Φ=5.881815 \n",
+ "Rx \n",
+ "Φ=5.346604 \n",
+ "Rx \n",
+ "Φ=5.964876 \n",
+ "Rx \n",
+ "Φ=2.586922 \n",
+ "Rx \n",
+ "Φ=5.860919 \n",
+ "Rx \n",
+ "Φ=1.222446 \n",
+ "Rx \n",
+ "Φ=0.179174 \n",
+ "Rx \n",
+ "Φ=4.558324 \n",
+ "Rx \n",
+ "Φ=6.119097 \n",
+ "Rx \n",
+ "Φ=3.932419 \n",
+ "Rx \n",
+ "Φ=0.255542 \n",
+ "Rx \n",
+ "Φ=0.662422 \n",
+ "Rx \n",
+ "Φ=5.881116 \n",
+ "Rx \n",
+ "Φ=2.588242 \n",
+ "Rx \n",
+ "Φ=5.910155 \n",
+ "Rx \n",
+ "Φ=4.676176 \n",
+ "Rx \n",
+ "Φ=5.889599 \n",
+ "Rx \n",
+ "Φ=3.350311 \n",
+ "Rx \n",
+ "Φ=0.213751 \n",
+ "Rx \n",
+ "Φ=5.211781 \n",
+ "Rx \n",
+ "Φ=0.185298 \n",
+ "Rx \n",
+ "Φ=4.459793 \n",
+ "Rx \n",
+ "Φ=0.203269 \n",
+ "Rx \n",
+ "Φ=3.533864 \n",
+ "Rx \n",
+ "Φ=5.837168 \n",
+ "Rx \n",
+ "Φ=0.952755 \n",
+ "Rx \n",
+ "Φ=5.704245 \n",
+ "Rx \n",
+ "Φ=1.951633 \n",
+ "Rx \n",
+ "Φ=0.148612 \n",
+ "Rx \n",
+ "Φ=2.626898 \n",
+ "Rx \n",
+ "Φ=5.824427 \n",
+ "Rx \n",
+ "Φ=5.269631 \n",
+ "Rx \n",
+ "Φ=5.771452 \n",
+ "Rx \n",
+ "Φ=0.887676 \n",
+ "Rx \n",
+ "Φ=0.295589 \n",
+ "Rx \n",
+ "Φ=1.368475 \n",
+ "Rx \n",
+ "Φ=0.759218 \n",
+ "Rx \n",
+ "Φ=0.86463 \n",
+ "Rx \n",
+ "Φ=5.910179 \n",
+ "Rx \n",
+ "Φ=2.67586 \n",
+ "Rx \n",
+ "Φ=6.071806 \n",
+ "Rx \n",
+ "Φ=3.939947 \n",
+ "Rx \n",
+ "Φ=5.512408 \n",
+ "Rx \n",
+ "Φ=3.108508 \n",
+ "Rx \n",
+ "Φ=0.666976 \n",
+ "Rx \n",
+ "Φ=4.360401 \n",
+ "Rx \n",
+ "Φ=0.347768 \n",
+ "Rx \n",
+ "Φ=3.37693 \n",
+ "Rx \n",
+ "Φ=0.312108 \n",
+ "Rx \n",
+ "Φ=5.196323 \n",
+ "Rx \n",
+ "Φ=5.797489 \n",
+ "Rx \n",
+ "Φ=2.645372 \n",
+ "Rx \n",
+ "Φ=0.627537 \n",
+ "Rx \n",
+ "Φ=1.120956 \n",
+ "Rx \n",
+ "Φ=0.130521 \n",
+ "Rx \n",
+ "Φ=0.164212 \n",
+ "Rx \n",
+ "Φ=0.593825 \n",
+ "Rx \n",
+ "Φ=0.768267 \n",
+ "Rx \n",
+ "Φ=5.587306 \n",
+ "Rx \n",
+ "Φ=0.121997 \n",
+ "Rx \n",
+ "Φ=0.782756 \n",
+ "Rx \n",
+ "Φ=2.841813 \n",
+ "Rx \n",
+ "Φ=5.752308 \n",
+ "Rx \n",
+ "Φ=2.407927 \n",
+ "Rx \n",
+ "Φ=6.090167 \n",
+ "Rx \n",
+ "Φ=2.833777 \n",
+ "Rx \n",
+ "Φ=0.36229 \n",
+ "Rx \n",
+ "Φ=4.882238 \n",
+ "Rx \n",
+ "Φ=5.664507 \n",
+ "Rx \n",
+ "Φ=3.956978 \n",
+ "Rx \n",
+ "Φ=1.062816 \n",
+ "Rx \n",
+ "Φ=0.330062 \n",
+ "Rx \n",
+ "Φ=5.289095 \n",
+ "Rx \n",
+ "Φ=1.013429 \n",
+ "Rx \n",
+ "Φ=6.180296 \n",
+ "Rx \n",
+ "Φ=0.65825 \n",
+ "Rx \n",
+ "Φ=1.873061 \n",
+ "Rx \n",
+ "Φ=6.127574 \n",
+ "Rx \n",
+ "Φ=3.409669 \n",
+ "Rx \n",
+ "Φ=4.207726 \n",
+ "Rx \n",
+ "Φ=0.039319 \n",
+ "Rx \n",
+ "Φ=2.361612 \n",
+ "Rx \n",
+ "Φ=6.119483 \n",
+ "Rx \n",
+ "Φ=1.944267 \n",
+ "Rx \n",
+ "Φ=5.929505 \n",
+ "Rx \n",
+ "Φ=4.927996 \n",
+ "Rx \n",
+ "Φ=0.265048 \n",
+ "Rx \n",
+ "Φ=3.960619 \n",
+ "Rx \n",
+ "Φ=0.231558 \n",
+ "Rx \n",
+ "Φ=4.756288 \n",
+ "Rx \n",
+ "Φ=5.964907 \n",
+ "Rx \n",
+ "Φ=2.755658 \n",
+ "Rx \n",
+ "Φ=0.048777 \n",
+ "Rx \n",
+ "Φ=0.594298 \n",
+ "Rx \n",
+ "Φ=6.210165 \n",
+ "Rx \n",
+ "Φ=6.102554 \n",
+ "Rx \n",
+ "Φ=0.050579 \n",
+ "Rx \n",
+ "Φ=1.168647 \n",
+ "Rx \n",
+ "Φ=0.072894 \n",
+ "Rx \n",
+ "Φ=3.197342 \n",
+ "Rx \n",
+ "Φ=0.202346 \n",
+ "Rx \n",
+ "Φ=1.465493 \n",
+ "Rx \n",
+ "Φ=0.248729 \n",
+ "Rx \n",
+ "Φ=0.610803 \n",
+ "Rx \n",
+ "Φ=5.878069 \n",
+ "Rx \n",
+ "Φ=4.355098 \n",
+ "Rx \n",
+ "Φ=0.389999 \n",
+ "Rx \n",
+ "Φ=1.87709 \n",
+ "Rx \n",
+ "Φ=0.407268 \n",
+ "Rx \n",
+ "Φ=3.62502 \n",
+ "Rx \n",
+ "Φ=5.940365 \n",
+ "Rx \n",
+ "Φ=1.042955 \n",
+ "Rx \n",
+ "Φ=5.807768 \n",
+ "Rx \n",
+ "Φ=6.068141 \n",
+ "Rx \n",
+ "Φ=6.054311 \n",
+ "Rx \n",
+ "Φ=3.344116 \n",
+ "Rx \n",
+ "Φ=0.199176 \n",
+ "Rx \n",
+ "Φ=2.105731 \n",
+ "Rx \n",
+ "Φ=6.103484 \n",
+ "Rx \n",
+ "Φ=2.251749 \n",
+ "Rx \n",
+ "Φ=0.381059 \n",
+ "Rx \n",
+ "Φ=4.906114 \n",
+ "Rx \n",
+ "Φ=0.272654 \n",
+ "Rx \n",
+ "Φ=0.022546 \n",
+ "Rx \n",
+ "Φ=0.215401 \n",
+ "Rx \n",
+ "Φ=0.622594 \n",
+ "Rx \n",
+ "Φ=0.324209 \n",
+ "Rx \n",
+ "Φ=3.795419 \n",
+ "Rx \n",
+ "Φ=0.556474 \n",
+ "Rx \n",
+ "Φ=3.104686 \n",
+ "Rx \n",
+ "Φ=0.085028 \n",
+ "Rx \n",
+ "Φ=5.094356 \n",
+ "Rx \n",
+ "Φ=0.185668 \n",
+ "Rx \n",
+ "Φ=2.84636 \n",
+ "Rx \n",
+ "Φ=5.721213 \n",
+ "Rx \n",
+ "Φ=0.044653 \n",
+ "Rx \n",
+ "Φ=5.875027 \n",
+ "Rx \n",
+ "Φ=4.102192 \n",
+ "Rx \n",
+ "Φ=6.035802 \n",
+ "Rx \n",
+ "Φ=0.609185 \n",
+ "Rx \n",
+ "Φ=0.203315 \n",
+ "Rx \n",
+ "Φ=5.517883 \n",
+ "Rx \n",
+ "Φ=5.845051 \n",
+ "Rx \n",
+ "Φ=2.676255 \n",
+ "Rx \n",
+ "Φ=0.4829 \n",
+ "Rx \n",
+ "Φ=5.464798 \n",
+ "Rx \n",
+ "Φ=0.407346 \n",
+ "Rx \n",
+ "Φ=1.77268 \n",
+ "Rx \n",
+ "Φ=0.069818 \n",
+ "Rx \n",
+ "Φ=0.142473 \n",
+ "Rx \n",
+ "Φ=0.603846 \n",
+ "Rx \n",
+ "Φ=4.581046 \n",
+ "Rx \n",
+ "Φ=0.5703 \n",
+ "Rx \n",
+ "Φ=5.177161 \n",
+ "Rx \n",
+ "Φ=0.375329 \n",
+ "Rx \n",
+ "Φ=5.604687 \n",
+ "Rx \n",
+ "Φ=5.895756 \n",
+ "Rx \n",
+ "Φ=3.636859 \n",
+ "Rx \n",
+ "Φ=5.918802 \n",
+ "Rx \n",
+ "Φ=2.939512 \n",
+ "Rx \n",
+ "Φ=6.038263 \n",
+ "Rx \n",
+ "Φ=0.158227 \n",
+ "Rx \n",
+ "Φ=0.516975 \n",
+ "Rx \n",
+ "Φ=1.219994 \n",
+ "Rx \n",
+ "Φ=0.084569 \n",
+ "Rx \n",
+ "Φ=1.662671 \n",
+ "Rx \n",
+ "Φ=5.949675 \n",
+ "Rx \n",
+ "Φ=1.601716 \n",
+ "Rx \n",
+ "Φ=0.507297 \n",
+ "Rx \n",
+ "Φ=5.560111 \n",
+ "Rx \n",
+ "Φ=0.46688 \n",
+ "Rx \n",
+ "Φ=1.045626 \n",
+ "Rx \n",
+ "Φ=6.06647 \n",
+ "Rx \n",
+ "Φ=2.635542 \n",
+ "Rx \n",
+ "Φ=5.552327 \n",
+ "Rx \n",
+ "Φ=0.080085 \n",
+ "Rx \n",
+ "Φ=0.368528 \n",
+ "Rx \n",
+ "Φ=4.986284 \n",
+ "Rx \n",
+ "Φ=0.675687 \n",
+ "Rx \n",
+ "Φ=0.34563 \n",
+ "Rx \n",
+ "Φ=5.774741 \n",
+ "Rx \n",
+ "Φ=5.246393 \n",
+ "Rx \n",
+ "Φ=0.7063 \n",
+ "Rx \n",
+ "Φ=1.151151 \n",
+ "Rx \n",
+ "Φ=0.351705 \n",
+ "Rx \n",
+ "Φ=0.410152 \n",
+ "Rx \n",
+ "Φ=5.800199 \n",
+ "Rx \n",
+ "Φ=4.482714 \n",
+ "Rx \n",
+ "Φ=0.676584 \n",
+ "Rx \n",
+ "Φ=1.023176 \n",
+ "Rx \n",
+ "Φ=5.36024 \n",
+ "Rx \n",
+ "Φ=2.637442 \n",
+ "Rx \n",
+ "Φ=2.024709 \n",
+ "Rx \n",
+ "Φ=5.455306 \n",
+ "Rx \n",
+ "Φ=0.531506 \n",
+ "Rx \n",
+ "Φ=3.115321 \n",
+ "Rx \n",
+ "Φ=1.283429 \n",
+ "Rx \n",
+ "Φ=5.281563 \n",
+ "0 \n",
+ "1 \n",
+ "2 \n",
+ "3 \n",
+ "4 \n",
+ "5 \n",
+ "6 \n",
+ "7 \n",
+ "8 \n",
+ "9 \n",
+ "10 \n",
+ "11 \n",
+ "12 \n",
+ "13 \n",
+ "14 \n",
+ "15 \n",
+ "16 \n",
+ "17 \n",
+ "18 \n",
+ "19 \n",
+ "20 \n",
+ "21 \n",
+ "22 \n",
+ "23 \n",
+ "24 \n",
+ "25 \n",
+ "26 \n",
+ "27 \n",
+ "28 \n",
+ "29 \n",
+ "30 \n",
+ "31 \n",
+ "32 \n",
+ "33 \n",
+ "34 \n",
+ "35 \n",
+ "36 \n",
+ "37 \n",
+ "38 \n",
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+ "58 \n",
+ "59 \n",
+ "0 \n",
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+ "5 \n",
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+ "15 \n",
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+ "18 \n",
+ "19 \n",
+ "20 \n",
+ "21 \n",
+ "22 \n",
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+ "27 \n",
+ "28 \n",
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+ "30 \n",
+ "31 \n",
+ "32 \n",
+ "33 \n",
+ "34 \n",
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+ "37 \n",
+ "38 \n",
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+ "41 \n",
+ "42 \n",
+ "43 \n",
+ "44 \n",
+ "45 \n",
+ "46 \n",
+ "47 \n",
+ "48 \n",
+ "49 \n",
+ "50 \n",
+ "51 \n",
+ "52 \n",
+ "53 \n",
+ "54 \n",
+ "55 \n",
+ "56 \n",
+ "57 \n",
+ "58 \n",
+ "59 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Linear_Circuit_60 = pcvl.Circuit.decomposition(Unitary_60, mzi, phase_shifter_fn=pcvl.PS, shape=\"triangle\")\n",
+ "pcvl.pdisplay(Linear_Circuit_60)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7d6ac933",
+ "metadata": {},
+ "source": [
+ "#### Running simulation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "cd1e829a",
+ "metadata": {},
+ "source": [
+ "Now we can choose the way to perform the simulation of boson sampling with Perceval. The number of photons is within what we could simulate with the Naive backend, however the output space is far too big just to enumerate and store the states so we chose the CliffordClifford2017 backend instead. We encourage you to check out our multiple simulation backend options and their performance comparison on different types of problems available to view on the Perceval documentation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "a23c2a44",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "QPU = pcvl.Processor(\"CliffordClifford2017\", Linear_Circuit_60)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0e6a25f2",
+ "metadata": {},
+ "source": [
+ "Since this isn't a real problem and we are just trying to show the power of quantum computing when it comes to difficult problems to solve, such as boson sampling, we don't care what the input to our circuit is and can choose a random one."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "6ac056ec",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The input state: |0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0,0,0,1,0,1,0>\n"
+ ]
+ }
+ ],
+ "source": [
+ "def generate_input(n, m, modes = None):\n",
+ " \"This function randomly chooses an input with n photons in m modes.\"\n",
+ " if modes == None : #the function works with a given number of modes m, otherwise selecting them randomly\n",
+ " modes = sorted(random.sample(range(m),n))\n",
+ " state = \"|\"\n",
+ " for i in range(m):\n",
+ " state = state + \"0\"*(1 - (i in modes)) +\"1\"*(i in modes)+ \",\"*(i < m-1)\n",
+ " return pcvl.BasicState(state + \">\")\n",
+ "\n",
+ "input_state = generate_input(n, m)\n",
+ "print(\"The input state: \", input_state)\n",
+ "QPU.with_input(input_state) #giving the processor the input state"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "faf263ef",
+ "metadata": {},
+ "source": [
+ "Using this input, our output states are states composed of n photons in m modes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "d6b24894",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The sampled outputs are:\n",
+ "|0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,0,2,0,0,0,0,0,0,0,1,2,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0>\n",
+ "|0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,2,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0>\n",
+ "|1,0,0,1,0,0,0,2,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,2,0,0>\n",
+ "|0,0,0,1,0,0,0,3,0,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0>\n",
+ "|0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,2,1,0,0,0,0,0,0,0,0,0>\n",
+ "|1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1>\n",
+ "|1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,0,0,0,0,0,0,1,0,0,0>\n",
+ "|0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0>\n",
+ "|0,0,2,0,0,3,0,0,1,0,0,0,0,0,0,0,0,0,0,2,0,0,1,0,0,0,0,1,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0>\n",
+ "|0,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,2,0,1,0,0,1,0,0>\n"
+ ]
+ }
+ ],
+ "source": [
+ "QPU.min_detected_photons_filter(0) #we're telling the processor that we want to keep all outputs\n",
+ "# We're telling Perceval that we need *at least* 0 photons in our output, thus we will keep all\n",
+ "# possible outputs. Naturally, we cannot observe more photons in the output than there were in the\n",
+ "# input so we'll never be able to filter by a number higher than the number of photons in the input.\n",
+ "\n",
+ "sampler = Sampler(QPU)\n",
+ "\n",
+ "print(\"The sampled outputs are:\")\n",
+ "for out_state in sampler.samples(10)[\"results\"]:\n",
+ " print(out_state)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "263d2ba0",
+ "metadata": {},
+ "source": [
+ "Now we can also perform boson sampling N times. This will take some time so let's save the results to a file."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "9cf2a385",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# if we want to launch parallel process\n",
+ "worker_id=1\n",
+ "\n",
+ "#store the input and the unitary\n",
+ "with open(\"%dphotons_%dmodes_%dsamples-worker%s-unitary.pkl\" %(n,m,N,worker_id), 'wb') as f:\n",
+ " pickle.dump(Unitary_60, f)\n",
+ "\n",
+ "with open(\"%dphotons_%dmodes_%dsamples-worker%s-inputstate.pkl\" %(n,m,N,worker_id), 'w') as f:\n",
+ " f.write(str(input_state)+\"\\n\")\n",
+ "\n",
+ "with gzip.open(\"%dphotons_%dmodes_%dsamples-worker%s-samples.txt.gz\" %(n,m,N,worker_id), 'wb') as f:\n",
+ " start = time.time()\n",
+ " for _ in range(N):\n",
+ " f.write((str(sampler.samples(1)[\"results\"][0])+\"\\n\").encode())\n",
+ " end = time.time()\n",
+ " f.write(str(\"==> %d\\n\" % (end-start)).encode())\n",
+ "f.close()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5d207441",
+ "metadata": {},
+ "source": [
+ "A little after (4 hours on a 3.1GHz Intel) - we do have 5M samples. We launched this on 32 threads for 2 days and collected 300 batches of 5M samples.\n",
+ "\n",
+ "Let us analyze the K-first mode bunching on these samples."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a1062d81",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "worker_id = 1\n",
+ "count = 0\n",
+ "bunching_distribution = Counter()\n",
+ "\n",
+ "with gzip.open(\"%dphotons_%dmodes_%dsamples-worker%s-samples.txt.gz\"%(n,m,N,worker_id), \"rt\") as f:\n",
+ " for l in f:\n",
+ " l = l.strip()\n",
+ " if l.startswith(\"|\") and l.endswith(\">\"):\n",
+ " try:\n",
+ " st = pcvl.BasicState(l)\n",
+ " count+=1\n",
+ " bunching_distribution[st.photon2mode(st.n-1)]+=1\n",
+ " except Exception:\n",
+ " pass\n",
+ "print(count, \"samples\")\n",
+ "print(\"Bunching Distribution:\", \"\\t\".join([str(bunching_distribution[k]) for k in range(m)]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "576eb79b",
+ "metadata": {},
+ "source": [
+ "These numbers have been used on 300 samples for certification - see our article on Perceval for more details."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5a2ced3a",
+ "metadata": {},
+ "source": [
+ "#### Boson sampling with a non perfect source"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a95e1907",
+ "metadata": {},
+ "source": [
+ "Let's perform Boson sampling with a non perfect source. We declare a source with 90% brightness and purity. Here, we would reach the limits of the simulation if we use the same input as before, as for each photon at the entrance, we multiply by 3 the number of input states (0, 1 or 2 photons at the input), leading to $3^n$ states."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5c6bf7c1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "3 ** n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "fb96c9b6",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "source = pcvl.Source(emission_probability=0.9, multiphoton_component=0.1)\n",
+ "QPU = pcvl.Processor(\"CliffordClifford2017\", Linear_Circuit_60, source)\n",
+ "QPU.with_input(pcvl.BasicState([0, 1, 1] + (m - 3) * [0])) #notice the change in input"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0216f7e4",
+ "metadata": {},
+ "source": [
+ "Computing the other way around, we can now check the source distribution of the processor to see how likely a state at the input of the linear circuit will be."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a8965f49",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pcvl.pdisplay(QPU.source_distribution, precision=1e-7, max_v=20)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "53795d58",
+ "metadata": {},
+ "source": [
+ "As expected, the most likely state to have been the input of the circuit was in fact the input we provided it with.\n",
+ "\n",
+ "Now we can launch the entire computation again starting from cell 8 to use this imperfect source QPU with the same nominal input, or from cell 7 for another random input."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "84b2a6a9",
+ "metadata": {},
+ "source": [
+ "### References"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "811e4838",
+ "metadata": {},
+ "source": [
+ "[1] Hui Wang, et al. Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a $10^{14}$-Dimensional Hilbert Space. Physical Review Letters, 123(25):250503, December 2019. Publisher: American Physical Society.\n",
+ "\n",
+ "[2] Michael Reck, Anton Zeilinger, Herbert J Bernstein, and Philip Bertani. Experimental realization of any discrete unitary operator. Physical review letters, 73(1):58, 1994."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/Differential_equation_resolution_TO_DO.ipynb b/Differential_equation_resolution_TO_DO.ipynb
new file mode 100644
index 0000000..12ec964
--- /dev/null
+++ b/Differential_equation_resolution_TO_DO.ipynb
@@ -0,0 +1,651 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "1c11286e",
+ "metadata": {},
+ "source": [
+ "# Quandela Training Seminar - Programming with Perceval"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7b0c92f7",
+ "metadata": {},
+ "source": [
+ "### Differential equation resolution"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a74dd31d",
+ "metadata": {},
+ "source": [
+ "Differential equations are used to describe variables that continuously vary with respect to a change in other variables. These equations can be used to model the behaviours of complex systems. A simple example of this can be found in economics, where we wish to study the relationships between some variables and predict their future behaviours."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5726700a",
+ "metadata": {},
+ "source": [
+ "#### Introduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e67d9ab4",
+ "metadata": {},
+ "source": [
+ "We present here a Perceval implementation of a Quantum Machine Learning algorithm for solving differential equations. Its aim is to approximate the solution to the differential equation considered in [1]:\n",
+ "\n",
+ "$$\\frac{df}{dx}+\\lambda f(x)(\\kappa+tan(\\lambda x))=0$$\n",
+ "\n",
+ "with boundary condition $f(0)=f_0$. The analytical solution is $f(x)=f_0\\;exp(-\\kappa \\lambda x) cos(\\lambda x)$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f5b00399",
+ "metadata": {},
+ "source": [
+ "#### QML loss function definition"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c47833b5",
+ "metadata": {},
+ "source": [
+ "In order to use QML to solve this differential equation, we first need to derive a loss function from it whose minimum is associated to the differential equation's analytical solution.\n",
+ "\n",
+ "Let $F[\\{d^mf/dx^m\\}_m,f,x]=0$ be a general differential equation verified by $f(x)$, where $F[.]$ is an operator acting on $f(x)$, its derivatives and $x$. For the solving of a differential equation, the loss function described in [1] consists of two terms $$\\mathcal{L}_{\\theta}[\\{d^mg/dx^m\\}_m,g,x]=\\mathcal{L}_{\\theta}^{(diff)}[\\{d^mg/dx^m\\}_m,g,x]+\\mathcal{L}_{\\theta}^{(boundary)}[g,x].$$\n",
+ "\n",
+ "The first term $\\mathcal{L}_{\\theta}^{(diff)}$ corresponds to the differential equation which has been discretised over a fixed regular grid of M points noted $x_i$: $$\\mathcal{L}_{\\theta}^{(diff)}[\\{d^mg/dx^m\\}_m,g,x]=\\frac{1}{M}\\sum_{i=1}^{M}L(F[d_x^mg(x_i),g(x_i),x_i],0),$$\n",
+ "\n",
+ "where $L(a,b)=(a-b)^2$ is the squared distance between two arguments. The second term $\\mathcal{L}_{\\theta}^{(boundary)}$ is associated with the initial conditions of our desired solution. It is defined as: $$\\mathcal{L}_{\\theta}^{(boundary)}[g,x]=\\eta L(g(x_0),f_0),$$\n",
+ "\n",
+ "where $\\eta$ is the weight granted to the boundary condition and $f_0$ is given by $f(x_0)=f_0$.\n",
+ "\n",
+ "Given a function approximator $f^{(n)}(x,\\pmb{\\theta},\\pmb{\\lambda})$, the loss function above will be minimised using a classical algorithm, updating the parameters $\\pmb{\\theta}$ based on samples obtained using a quantum device."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3f075260",
+ "metadata": {},
+ "source": [
+ "#### Quantum circuit architecture"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "52b0ae69",
+ "metadata": {},
+ "source": [
+ "The feature map used is presented in [2,3,4]. The quantum circuit architecture from [4] is expressed as $\\mathcal{U}(x,\\pmb{\\theta})=\\mathcal{W}^{(2)}(\\pmb{\\theta}_2)\\mathcal{S}(x)\\mathcal{W}^{(1)}(\\pmb{\\theta}_1)$. The phase-shift operator $\\mathcal{S}(x)$ incorporates the $x$ dependency of the function we wish to approximate. It is sandwiched between two universal interferometers $\\mathcal{W}^{(1)}(\\pmb{\\theta}_1)$ and $\\mathcal{W}^{(2)}(\\pmb{\\theta}_2)$, where the beam splitter parameters $\\pmb{\\theta}_1$ and $\\pmb{\\theta}_2$ of this mesh architecture are tunable to enable training of the circuit. The output measurement operator, noted $\\mathcal{M}(\\pmb{\\lambda})$ is the projection on the Fock states obtained using photon-number resolving detectors, multiplied by some coefficients $\\pmb{\\lambda}$ which can also be tunable. Formally, we have:\n",
+ "\n",
+ "$$ \\mathcal{M}(\\boldsymbol{\\lambda}) = \\sum_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\lambda_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\mathbf{\\left | n^{(f)}\\right \\rangle}\\mathbf{\\left \\langle n^{(f)}\\right |},\n",
+ "$$\n",
+ "\n",
+ "where the sum is taken over all $\\binom{n+m-1}{n}$ possible Fock states considering $n$ photons in $m$ modes. Let $\\mathbf{\\left | n^{(i)}\\right \\rangle} = \\left |n^{(i)}_1,n^{(i)}_2,\\dots,n^{(i)}_m\\right \\rangle$ be the input state consisting of $n$ photons where $n^{(i)}_j$ is the number of photons in input mode $j$. Given these elements, the circuit's output $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ is given by the following expectation value:\n",
+ "\n",
+ "$$\n",
+ "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\left\\langle\\mathbf{n}^{(i)}\\left|\\mathcal{U}^{\\dagger}(x, \\boldsymbol{\\theta}) \\mathcal{M}(\\boldsymbol{\\lambda}) \\mathcal{U}(x, \\boldsymbol{\\theta})\\right| \\mathbf{n}^{(i)}\\right\\rangle.\n",
+ "$$\n",
+ "\n",
+ "This expression can be rewritten as the following Fourier series \\[4\\]\n",
+ "\n",
+ "$$\n",
+ "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\sum_{\\omega \\in \\Omega_{n}} c_{\\omega}(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda}) e^{i \\omega x},\n",
+ "$$\n",
+ "\n",
+ "where $\\Omega_n = \\{-n, -n+1, \\dots, n-1, n \\}$ is the frequency spectrum one can reach with $n$ incoming photons and $\\{c_\\omega(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda})\\}$ are the Fourier coefficients. The $\\boldsymbol{\\lambda}$ parameters are sampled randomly in the interval $[-a;a]$, with $a$ a randomly chosen integer. $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ will serve as a function approximator for this chosen differential equation. Differentiation in the loss function is discretised as $\\frac{df}{dx} \\simeq \\frac{f(x+\\Delta x) - f(x-\\Delta x)}{2\\Delta x}$.\n",
+ "\n",
+ "$n, m,$ and $\\boldsymbol{\\lambda}$ are variable parameters defined below. $\\Delta x$ is the mesh size."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "664403cb",
+ "metadata": {},
+ "source": [
+ "## Perceval Simulation\n",
+ "\n",
+ "### Initialisation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "cb1aca2a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import perceval as pcvl\n",
+ "import numpy as np\n",
+ "from math import comb\n",
+ "from scipy.optimize import minimize\n",
+ "import time\n",
+ "import matplotlib.pyplot as plt\n",
+ "import matplotlib as mpl\n",
+ "import tqdm as tqdm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7b966a90",
+ "metadata": {},
+ "source": [
+ "We will run this notebook with 4 photons. We could use more photons, but the result with 4 photons is already satisfying."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "83c1de63",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "nphotons = 4"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "77763a57",
+ "metadata": {},
+ "source": [
+ "### Differential equation parameters\n",
+ "\n",
+ "We define here the value of the differential equation parameters and boundary condition $\\lambda, \\kappa, f_0$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "266fa65b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Differential equation parameters\n",
+ "lambd = 8\n",
+ "kappa = 0.1\n",
+ "\n",
+ "def F(u_prime, u, x): # DE, works with numpy arrays\n",
+ " return u_prime + lambd * u * (kappa + np.tan(lambd * x))\n",
+ "\n",
+ "# Boundary condition (f(x_0)=f_0)\n",
+ "x_0 = 0\n",
+ "f_0 = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "057a3ae0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Modeling parameters\n",
+ "n_grid = 50 # number of grid points of the discretized differential equation\n",
+ "range_min = 0 # minimum of the interval on which we wish to approximate our function\n",
+ "range_max = 1 # maximum of the interval on which we wish to approximate our function\n",
+ "X = np.linspace(range_min, range_max-range_min, n_grid) # Optimisation grid"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6bc40cc9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: write the differential equation's analytical solution (given above) in the form of a Python function\n",
+ "# that takes the variable x as input - we'll use this later to compare with our result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "6a4c54ba",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Parameters of the quantum machine learning procedure\n",
+ "N = nphotons # Number of photons\n",
+ "m = nphotons # Number of modes\n",
+ "eta = 5 # weight granted to the initial condition\n",
+ "a = 200 # Approximate boundaries of the interval that the image of the trial function can cover\n",
+ "fock_dim = comb(N + m - 1, N)\n",
+ "# lambda coefficients for all the possible outputs\n",
+ "lambda_random = 2 * a * np.random.rand(fock_dim) - a\n",
+ "# dx serves for the numerical differentiation of f\n",
+ "dx = (range_max-range_min) / (n_grid - 1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "662ad59e",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "|1,1,1,1>\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Input state with N photons and m modes\n",
+ "input_state = pcvl.BasicState([1]*N+[0]*(m-N))\n",
+ "print(input_state)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8b94a785",
+ "metadata": {},
+ "source": [
+ "## Definition of the circuit\n",
+ "\n",
+ "We will generate a Haar-random initial unitary using QR decomposition built in Perceval `Matrix.random_unitary`, the circuit is defined by the combination of 3 sub-circuits - the intermediate phase is a parameter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "b90ce704",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "W1 \n",
+ "Φ=px \n",
+ "W2 \n",
+ "0 \n",
+ "1 \n",
+ "2 \n",
+ "3 \n",
+ "0 \n",
+ "1 \n",
+ "2 \n",
+ "3 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "\"Haar unitary parameters\"\n",
+ "# number of parameters used for the two universal interferometers (2*m**2 per interferometer)\n",
+ "parameters = np.random.normal(size=4*m**2)\n",
+ "\n",
+ "px = pcvl.P(\"px\")\n",
+ "\n",
+ "#TO DO: build the circuit we'll use - remember the order of computation - mathematically\n",
+ "# we write W2SW1 but physically we perform W1SW2\n",
+ "# HINT 1: remember that S is just a phase shift, you can give it the angle controlled by\n",
+ "# parameter px and apply it on mode 0\n",
+ "# HINT 2: use pcvl.Unitary(pcvl.Matrix.random_unitary()) to create W1 and W2\n",
+ "# the first varible inside the function will be the size of the matrix - think about\n",
+ "# what defines its size!\n",
+ "# the second variable are the parameters - you can choose them from the previously\n",
+ "# defined 'parameters' variable but be careful not to use the same parameters for both W1 and W2!\n",
+ "# add all the parts of the circuit in correct order of computation in variable 'c'\n",
+ "\n",
+ "backend = pcvl.BackendFactory().get_backend(\"SLOS\")\n",
+ "backend.set_circuit(pcvl.Unitary(pcvl.Matrix.random_unitary(m)))\n",
+ "backend.preprocess([input_state])\n",
+ "\n",
+ "pcvl.pdisplay(c)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "79b7fef9",
+ "metadata": {},
+ "source": [
+ "### Expectation value and loss function computation\n",
+ "\n",
+ "The expectation value of the measurement operator $\\mathcal{M}(\\boldsymbol{\\lambda})$ is obtained directly from Fock state probabilities computed by Perceval. Given this expectation value, the code snippet below computes the loss function defined in the Introduction.\n",
+ "\n",
+ "Note the use of the `all_prob` simulator method giving directly access to the probabilities of all possible output states, including null probabilities (probabilities of observing the state with m modes and 0 photons as all photons were lost). This calculation is optimized in the SLOS backend."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "27aa9449",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def computation(params):\n",
+ " global current_loss\n",
+ " global computation_count\n",
+ " \"compute the loss function of a given differential equation in order for it to be optimized\"\n",
+ " computation_count += 1\n",
+ " f_theta_0 = 0 # boundary condition\n",
+ " coefs = lambda_random # coefficients of the M observable\n",
+ " # initial condition with the two universal interferometers and the phase shift in the middle\n",
+ " U_1 = pcvl.Matrix.random_unitary(m, params[:2 * m ** 2])\n",
+ " U_2 = pcvl.Matrix.random_unitary(m, params[2 * m ** 2:])\n",
+ "\n",
+ " px = pcvl.P(\"x\")\n",
+ " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n",
+ "\n",
+ " px.set_value(np.pi * x_0)\n",
+ " backend.set_circuit(c)\n",
+ " f_theta_0 = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ " # boundary condition given a weight eta\n",
+ " loss = eta * (f_theta_0 - f_0) ** 2 * len(X)\n",
+ "\n",
+ " # Y[0] is before the domain we are interested in (used for differentiation), x_0 is at Y[1]\n",
+ " Y = np.zeros(n_grid + 2)\n",
+ "\n",
+ " # x_0 is at the beginning of the domain, already calculated\n",
+ " Y[1] = f_theta_0\n",
+ "\n",
+ " px.set_value(np.pi * (range_min - dx))\n",
+ " backend.set_circuit(c)\n",
+ " Y[0] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ "\n",
+ " for i in range(1, n_grid):\n",
+ " x = X[i]\n",
+ " px.set_value(np.pi * x)\n",
+ " backend.set_circuit(c)\n",
+ " Y[i + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ " px.set_value(np.pi * (range_max + dx))\n",
+ " backend.set_circuit(c)\n",
+ " Y[n_grid + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ " # Differentiation\n",
+ " Y_prime = (Y[2:] - Y[:-2])/(2*dx)\n",
+ "\n",
+ " loss += np.sum((F(Y_prime, Y[1:-1], X))**2)\n",
+ "\n",
+ " current_loss = loss / len(X)\n",
+ " return current_loss"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ff86ccf8",
+ "metadata": {},
+ "source": [
+ "### Classical optimisation\n",
+ "\n",
+ "Finally the code below performs the optimisation procedure using the loss function defined in the previous section. To this end, we use a Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimiser \\[5\\] from the SciPy library. Since we're performing the optimization classically, this is considered a hybrid quantum-classical algorithm."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "51ca61eb",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def callbackF(parameters):\n",
+ " \"\"\"callback function called by scipy.optimize.minimize allowing to monitor progress\"\"\"\n",
+ " global current_loss\n",
+ " global computation_count\n",
+ " global loss_evolution\n",
+ " global start_time\n",
+ " now = time.time()\n",
+ " pbar.set_description(\"M= %d Loss: %0.5f #computations: %d elapsed: %0.5f\" % \n",
+ " (m, current_loss, computation_count, now-start_time))\n",
+ " pbar.update(1)\n",
+ " loss_evolution.append((current_loss, now-start_time))\n",
+ " computation_count = 0\n",
+ " start_time = now"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "a8dd63fd",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "M= 4 Loss: 0.02469 #computations: 325 elapsed: 4.56400: : 85it [01:47, 2.53s/it] "
+ ]
+ }
+ ],
+ "source": [
+ "computation_count = 0\n",
+ "current_loss = 0\n",
+ "start_time = time.time()\n",
+ "loss_evolution = []\n",
+ "\n",
+ "pbar = tqdm.tqdm()\n",
+ "res = minimize(computation, parameters, callback=callbackF, method='BFGS', options={'gtol': 1E-2})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "57d69698",
+ "metadata": {},
+ "source": [
+ "After the optimisation procedure, the optimal unitary parameters (in `res.x`) can be used to determine the quantum circuit parameters (beam-splitter reflectivity and phase-shifter angles) for an experimental realisation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "12b6343c",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Unitary parameters [ 1.33891468 0.18671167 0.23294109 0.66027105 -0.90538747 -0.16478482\n",
+ " -1.79778695 0.27640065 -0.42235108 -0.42638238 -0.55720517 -0.50342402\n",
+ " 2.98759829 0.58048485 -0.05092819 1.36887037 0.76989739 -0.45710592\n",
+ " 0.60972939 -1.30593682 0.31607202 0.80690103 -0.07061116 1.74802391\n",
+ " -0.33214799 -0.10327618 -0.09204192 0.08248837 0.44292407 1.5847011\n",
+ " -0.15747674 0.20716982 -0.39656236 -2.52802577 -0.13810356 1.15592549\n",
+ " -0.41093697 1.05903189 1.11363313 0.92263739 -0.85430684 0.86256034\n",
+ " 1.14379369 0.29563571 0.94241894 -1.00363776 -0.4509711 -1.69484381\n",
+ " -0.90294638 0.76882232 0.54888516 -1.35142993 -0.25475156 -0.6617475\n",
+ " -0.62901547 -0.35290343 -0.48896483 -1.07626614 -0.93944671 -0.10220152\n",
+ " -0.51258919 0.07453675 -0.15409034 0.22112889]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Unitary parameters\", res.x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b5fc2804",
+ "metadata": {},
+ "source": [
+ "### Plotting the approximation\n",
+ "\n",
+ "We can now plot the result of our optimisation in order to compare the QML algorithm's output and the analytical solution of the differential equation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "1e37ce40",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def plot_solution(m, N, X, optim_params, lambda_random):\n",
+ " Y = []\n",
+ " U_1 = pcvl.Matrix.random_unitary(m, optim_params[:2 * m ** 2])\n",
+ " U_2 = pcvl.Matrix.random_unitary(m, optim_params[2 * m ** 2:])\n",
+ " px = pcvl.P(\"x\")\n",
+ " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n",
+ "\n",
+ " for x in X:\n",
+ " px.set_value(np.pi * x)\n",
+ " backend.set_circuit(c)\n",
+ " f_theta = np.sum(np.multiply(backend.all_prob(input_state), lambda_random))\n",
+ " Y.append(f_theta)\n",
+ " exact = u(X)\n",
+ " plt.plot(X, Y, label=\"Approximation with {} photons\".format(N))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "28a1d993",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "X = np.linspace(range_min, range_max, 200)\n",
+ "\n",
+ "# Change the plot size\n",
+ "default_figsize = mpl.rcParamsDefault['figure.figsize']\n",
+ "mpl.rcParams['figure.figsize'] = [1 * value for value in default_figsize]\n",
+ "\n",
+ "plot_solution(m, N, X, res.x, lambda_random)\n",
+ "\n",
+ "plt.plot(X, u(X), 'r', label='Analytical solution')\n",
+ "plt.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "82740227",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'Loss function value')"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot([v[0] for v in loss_evolution])\n",
+ "plt.yscale(\"log\")\n",
+ "plt.xlabel(\"Number of epochs\")\n",
+ "plt.ylabel(\"Loss function value\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "6fdb8bee",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: repeat the computation with 5 photons and 3 photons. Can you notice the change in graphs?\n",
+ "# Why does the accuracy of our solution depend on the amount of photons we use?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3541e471",
+ "metadata": {},
+ "source": [
+ "## References\n",
+ "\n",
+ "> [1] O. Kyriienko, A. E. Paine, and V. E. Elfving, “Solving nonlinear differential equations with differentiable quantum circuits”, [Physical Review A](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.052416) **103**, 052416 (2021).\n",
+ "\n",
+ "> [2] A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, “Data re-uploading for a universal quantum classifier”, [Quantum](https://quantum-journal.org/papers/q-2020-02-06-226/) **4**, 226 (2020).\n",
+ "\n",
+ "> [3] M. Schuld, R. Sweke, and J. J. Meyer, “Effect of data encoding on the expressive power of variational quantum-machine-learning models”, [Physical Review A]( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.032430) **103**, 032430 (2021).\n",
+ "\n",
+ "> [4] B. Y. Gan, D. Leykam, D. G. Angelakis, and D. G. Angelakis, “Fock State-enhanced Expressivity of Quantum Machine Learning Models”, in [Conference on Lasers andElectro-Optics](https://opg.optica.org/abstract.cfm?uri=CLEO_AT-2021-JW1A.73) (2021), paper JW1A.73. Optica Publishing Group, (2021).\n",
+ "\n",
+ "> [5] R. Fletcher, Practical methods of optimization. [John Wiley & Sons](https://onlinelibrary.wiley.com/doi/book/10.1002/9781118723203). (2013)."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/Differential_equation_resolution_answers.ipynb b/Differential_equation_resolution_answers.ipynb
new file mode 100644
index 0000000..08f4b9d
--- /dev/null
+++ b/Differential_equation_resolution_answers.ipynb
@@ -0,0 +1,643 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "1c11286e",
+ "metadata": {},
+ "source": [
+ "# Quandela Training Seminar - Programming with Perceval"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7b0c92f7",
+ "metadata": {},
+ "source": [
+ "### Differential equation resolution"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a74dd31d",
+ "metadata": {},
+ "source": [
+ "Differential equations are used to describe variables that continuously vary with respect to a change in other variables. These equations can be used to model the behaviours of complex systems. A simple example of this can be found in economics, where we wish to study the relationships between some variables and predict their future behaviours."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5726700a",
+ "metadata": {},
+ "source": [
+ "#### Introduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e67d9ab4",
+ "metadata": {},
+ "source": [
+ "We present here a Perceval implementation of a Quantum Machine Learning algorithm for solving differential equations. Its aim is to approximate the solution to the differential equation considered in [1]:\n",
+ "\n",
+ "$$\\frac{df}{dx}+\\lambda f(x)(\\kappa+tan(\\lambda x))=0$$\n",
+ "\n",
+ "with boundary condition $f(0)=f_0$. The analytical solution is $f(x)=f_0\\;exp(-\\kappa \\lambda x) cos(\\lambda x)$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f5b00399",
+ "metadata": {},
+ "source": [
+ "#### QML loss function definition"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c47833b5",
+ "metadata": {},
+ "source": [
+ "In order to use QML to solve this differential equation, we first need to derive a loss function from it whose minimum is associated to the differential equation's analytical solution.\n",
+ "\n",
+ "Let $F[\\{d^mf/dx^m\\}_m,f,x]=0$ be a general differential equation verified by $f(x)$, where $F[.]$ is an operator acting on $f(x)$, its derivatives and $x$. For the solving of a differential equation, the loss function described in [1] consists of two terms $$\\mathcal{L}_{\\theta}[\\{d^mg/dx^m\\}_m,g,x]=\\mathcal{L}_{\\theta}^{(diff)}[\\{d^mg/dx^m\\}_m,g,x]+\\mathcal{L}_{\\theta}^{(boundary)}[g,x].$$\n",
+ "\n",
+ "The first term $\\mathcal{L}_{\\theta}^{(diff)}$ corresponds to the differential equation which has been discretised over a fixed regular grid of M points noted $x_i$: $$\\mathcal{L}_{\\theta}^{(diff)}[\\{d^mg/dx^m\\}_m,g,x]=\\frac{1}{M}\\sum_{i=1}^{M}L(F[d_x^mg(x_i),g(x_i),x_i],0),$$\n",
+ "\n",
+ "where $L(a,b)=(a-b)^2$ is the squared distance between two arguments. The second term $\\mathcal{L}_{\\theta}^{(boundary)}$ is associated with the initial conditions of our desired solution. It is defined as: $$\\mathcal{L}_{\\theta}^{(boundary)}[g,x]=\\eta L(g(x_0),f_0),$$\n",
+ "\n",
+ "where $\\eta$ is the weight granted to the boundary condition and $f_0$ is given by $f(x_0)=f_0$.\n",
+ "\n",
+ "Given a function approximator $f^{(n)}(x,\\pmb{\\theta},\\pmb{\\lambda})$, the loss function above will be minimised using a classical algorithm, updating the parameters $\\pmb{\\theta}$ based on samples obtained using a quantum device."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3f075260",
+ "metadata": {},
+ "source": [
+ "#### Quantum circuit architecture"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "52b0ae69",
+ "metadata": {},
+ "source": [
+ "The feature map used is presented in [2,3,4]. The quantum circuit architecture from [4] is expressed as $\\mathcal{U}(x,\\pmb{\\theta})=\\mathcal{W}^{(2)}(\\pmb{\\theta}_2)\\mathcal{S}(x)\\mathcal{W}^{(1)}(\\pmb{\\theta}_1)$. The phase-shift operator $\\mathcal{S}(x)$ incorporates the $x$ dependency of the function we wish to approximate. It is sandwiched between two universal interferometers $\\mathcal{W}^{(1)}(\\pmb{\\theta}_1)$ and $\\mathcal{W}^{(2)}(\\pmb{\\theta}_2)$, where the beam splitter parameters $\\pmb{\\theta}_1$ and $\\pmb{\\theta}_2$ of this mesh architecture are tunable to enable training of the circuit. The output measurement operator, noted $\\mathcal{M}(\\pmb{\\lambda})$ is the projection on the Fock states obtained using photon-number resolving detectors, multiplied by some coefficients $\\pmb{\\lambda}$ which can also be tunable. Formally, we have:\n",
+ "\n",
+ "$$ \\mathcal{M}(\\boldsymbol{\\lambda}) = \\sum_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\lambda_{\\mathbf{\\left | n^{(f)}\\right \\rangle}}\\mathbf{\\left | n^{(f)}\\right \\rangle}\\mathbf{\\left \\langle n^{(f)}\\right |},\n",
+ "$$\n",
+ "\n",
+ "where the sum is taken over all $\\binom{n+m-1}{n}$ possible Fock states considering $n$ photons in $m$ modes. Let $\\mathbf{\\left | n^{(i)}\\right \\rangle} = \\left |n^{(i)}_1,n^{(i)}_2,\\dots,n^{(i)}_m\\right \\rangle$ be the input state consisting of $n$ photons where $n^{(i)}_j$ is the number of photons in input mode $j$. Given these elements, the circuit's output $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ is given by the following expectation value:\n",
+ "\n",
+ "$$\n",
+ "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\left\\langle\\mathbf{n}^{(i)}\\left|\\mathcal{U}^{\\dagger}(x, \\boldsymbol{\\theta}) \\mathcal{M}(\\boldsymbol{\\lambda}) \\mathcal{U}(x, \\boldsymbol{\\theta})\\right| \\mathbf{n}^{(i)}\\right\\rangle.\n",
+ "$$\n",
+ "\n",
+ "This expression can be rewritten as the following Fourier series \\[4\\]\n",
+ "\n",
+ "$$\n",
+ "f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})=\\sum_{\\omega \\in \\Omega_{n}} c_{\\omega}(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda}) e^{i \\omega x},\n",
+ "$$\n",
+ "\n",
+ "where $\\Omega_n = \\{-n, -n+1, \\dots, n-1, n \\}$ is the frequency spectrum one can reach with $n$ incoming photons and $\\{c_\\omega(\\boldsymbol{\\theta}, \\boldsymbol{\\lambda})\\}$ are the Fourier coefficients. The $\\boldsymbol{\\lambda}$ parameters are sampled randomly in the interval $[-a;a]$, with $a$ a randomly chosen integer. $f^{(n)}(x, \\boldsymbol{\\theta}, \\boldsymbol{\\lambda})$ will serve as a function approximator for this chosen differential equation. Differentiation in the loss function is discretised as $\\frac{df}{dx} \\simeq \\frac{f(x+\\Delta x) - f(x-\\Delta x)}{2\\Delta x}$.\n",
+ "\n",
+ "$n, m,$ and $\\boldsymbol{\\lambda}$ are variable parameters defined below. $\\Delta x$ is the mesh size."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "664403cb",
+ "metadata": {},
+ "source": [
+ "## Perceval Simulation\n",
+ "\n",
+ "### Initialisation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "cb1aca2a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import perceval as pcvl\n",
+ "import numpy as np\n",
+ "from math import comb\n",
+ "from scipy.optimize import minimize\n",
+ "import time\n",
+ "import matplotlib.pyplot as plt\n",
+ "import matplotlib as mpl\n",
+ "import tqdm as tqdm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7b966a90",
+ "metadata": {},
+ "source": [
+ "We will run this notebook with 4 photons. We could use more photons, but the result with 4 photons is already satisfying."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "83c1de63",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "nphotons = 4"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "77763a57",
+ "metadata": {},
+ "source": [
+ "### Differential equation parameters\n",
+ "\n",
+ "We define here the value of the differential equation parameters and boundary condition $\\lambda, \\kappa, f_0$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "266fa65b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Differential equation parameters\n",
+ "lambd = 8\n",
+ "kappa = 0.1\n",
+ "\n",
+ "def F(u_prime, u, x): # DE, works with numpy arrays\n",
+ " return u_prime + lambd * u * (kappa + np.tan(lambd * x))\n",
+ "\n",
+ "# Boundary condition (f(x_0)=f_0)\n",
+ "x_0 = 0\n",
+ "f_0 = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "057a3ae0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Modeling parameters\n",
+ "n_grid = 50 # number of grid points of the discretized differential equation\n",
+ "range_min = 0 # minimum of the interval on which we wish to approximate our function\n",
+ "range_max = 1 # maximum of the interval on which we wish to approximate our function\n",
+ "X = np.linspace(range_min, range_max-range_min, n_grid) # Optimisation grid"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "d6aaeb2b",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Differential equation's exact solution - for comparison\n",
+ "def u(x):\n",
+ " return np.exp(- kappa*lambd*x)*np.cos(lambd*x)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "6a4c54ba",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Parameters of the quantum machine learning procedure\n",
+ "N = nphotons # Number of photons\n",
+ "m = nphotons # Number of modes\n",
+ "eta = 5 # weight granted to the initial condition\n",
+ "a = 200 # Approximate boundaries of the interval that the image of the trial function can cover\n",
+ "fock_dim = comb(N + m - 1, N)\n",
+ "# lambda coefficients for all the possible outputs\n",
+ "lambda_random = 2 * a * np.random.rand(fock_dim) - a\n",
+ "# dx serves for the numerical differentiation of f\n",
+ "dx = (range_max-range_min) / (n_grid - 1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "662ad59e",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "|1,1,1,1>\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Input state with N photons and m modes\n",
+ "input_state = pcvl.BasicState([1]*N+[0]*(m-N))\n",
+ "print(input_state)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8b94a785",
+ "metadata": {},
+ "source": [
+ "## Definition of the circuit\n",
+ "\n",
+ "We will generate a Haar-random initial unitary using QR decomposition built in Perceval `Matrix.random_unitary`, the circuit is defined by the combination of 3 sub-circuits - the intermediate phase is a parameter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "b90ce704",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "W1 \n",
+ "Φ=px \n",
+ "W2 \n",
+ "0 \n",
+ "1 \n",
+ "2 \n",
+ "3 \n",
+ "0 \n",
+ "1 \n",
+ "2 \n",
+ "3 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "\"Haar unitary parameters\"\n",
+ "# number of parameters used for the two universal interferometers (2*m**2 per interferometer)\n",
+ "parameters = np.random.normal(size=4*m**2)\n",
+ "\n",
+ "px = pcvl.P(\"px\")\n",
+ "c = pcvl.Unitary(pcvl.Matrix.random_unitary(m, parameters[:2 * m ** 2]), name=\"W1\")\\\n",
+ " // (0, pcvl.PS(px))\\\n",
+ " // pcvl.Unitary(pcvl.Matrix.random_unitary(m, parameters[2 * m ** 2:]), name=\"W2\")\n",
+ "\n",
+ "backend = pcvl.BackendFactory().get_backend(\"SLOS\")\n",
+ "backend.set_circuit(pcvl.Unitary(pcvl.Matrix.random_unitary(m)))\n",
+ "backend.preprocess([input_state])\n",
+ "\n",
+ "pcvl.pdisplay(c)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "79b7fef9",
+ "metadata": {},
+ "source": [
+ "### Expectation value and loss function computation\n",
+ "\n",
+ "The expectation value of the measurement operator $\\mathcal{M}(\\boldsymbol{\\lambda})$ is obtained directly from Fock state probabilities computed by Perceval. Given this expectation value, the code snippet below computes the loss function defined in the Introduction.\n",
+ "\n",
+ "Note the use of the `all_prob` simulator method giving directly access to the probabilities of all possible output states, including null probabilities (probabilities of observing the state with m modes and 0 photons as all photons were lost). This calculation is optimized in the SLOS backend."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "27aa9449",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def computation(params):\n",
+ " global current_loss\n",
+ " global computation_count\n",
+ " \"compute the loss function of a given differential equation in order for it to be optimized\"\n",
+ " computation_count += 1\n",
+ " f_theta_0 = 0 # boundary condition\n",
+ " coefs = lambda_random # coefficients of the M observable\n",
+ " # initial condition with the two universal interferometers and the phase shift in the middle\n",
+ " U_1 = pcvl.Matrix.random_unitary(m, params[:2 * m ** 2])\n",
+ " U_2 = pcvl.Matrix.random_unitary(m, params[2 * m ** 2:])\n",
+ "\n",
+ " px = pcvl.P(\"x\")\n",
+ " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n",
+ "\n",
+ " px.set_value(np.pi * x_0)\n",
+ " backend.set_circuit(c)\n",
+ " f_theta_0 = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ " # boundary condition given a weight eta\n",
+ " loss = eta * (f_theta_0 - f_0) ** 2 * len(X)\n",
+ "\n",
+ " # Y[0] is before the domain we are interested in (used for differentiation), x_0 is at Y[1]\n",
+ " Y = np.zeros(n_grid + 2)\n",
+ "\n",
+ " # x_0 is at the beginning of the domain, already calculated\n",
+ " Y[1] = f_theta_0\n",
+ "\n",
+ " px.set_value(np.pi * (range_min - dx))\n",
+ " backend.set_circuit(c)\n",
+ " Y[0] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ "\n",
+ " for i in range(1, n_grid):\n",
+ " x = X[i]\n",
+ " px.set_value(np.pi * x)\n",
+ " backend.set_circuit(c)\n",
+ " Y[i + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ " px.set_value(np.pi * (range_max + dx))\n",
+ " backend.set_circuit(c)\n",
+ " Y[n_grid + 1] = np.sum(np.multiply(backend.all_prob(input_state), coefs))\n",
+ "\n",
+ " # Differentiation\n",
+ " Y_prime = (Y[2:] - Y[:-2])/(2*dx)\n",
+ "\n",
+ " loss += np.sum((F(Y_prime, Y[1:-1], X))**2)\n",
+ "\n",
+ " current_loss = loss / len(X)\n",
+ " return current_loss"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ff86ccf8",
+ "metadata": {},
+ "source": [
+ "### Classical optimisation\n",
+ "\n",
+ "Finally the code below performs the optimisation procedure using the loss function defined in the previous section. To this end, we use a Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimiser \\[5\\] from the SciPy library. Since we're performing the optimization classically, this is considered a hybrid quantum-classical algorithm."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "51ca61eb",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def callbackF(parameters):\n",
+ " \"\"\"callback function called by scipy.optimize.minimize allowing to monitor progress\"\"\"\n",
+ " global current_loss\n",
+ " global computation_count\n",
+ " global loss_evolution\n",
+ " global start_time\n",
+ " now = time.time()\n",
+ " pbar.set_description(\"M= %d Loss: %0.5f #computations: %d elapsed: %0.5f\" % \n",
+ " (m, current_loss, computation_count, now-start_time))\n",
+ " pbar.update(1)\n",
+ " loss_evolution.append((current_loss, now-start_time))\n",
+ " computation_count = 0\n",
+ " start_time = now"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "a8dd63fd",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "M= 4 Loss: 0.02469 #computations: 325 elapsed: 4.56400: : 85it [01:47, 2.53s/it] "
+ ]
+ }
+ ],
+ "source": [
+ "computation_count = 0\n",
+ "current_loss = 0\n",
+ "start_time = time.time()\n",
+ "loss_evolution = []\n",
+ "\n",
+ "pbar = tqdm.tqdm()\n",
+ "res = minimize(computation, parameters, callback=callbackF, method='BFGS', options={'gtol': 1E-2})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "57d69698",
+ "metadata": {},
+ "source": [
+ "After the optimisation procedure, the optimal unitary parameters (in `res.x`) can be used to determine the quantum circuit parameters (beam-splitter reflectivity and phase-shifter angles) for an experimental realisation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "12b6343c",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Unitary parameters [ 1.33891468 0.18671167 0.23294109 0.66027105 -0.90538747 -0.16478482\n",
+ " -1.79778695 0.27640065 -0.42235108 -0.42638238 -0.55720517 -0.50342402\n",
+ " 2.98759829 0.58048485 -0.05092819 1.36887037 0.76989739 -0.45710592\n",
+ " 0.60972939 -1.30593682 0.31607202 0.80690103 -0.07061116 1.74802391\n",
+ " -0.33214799 -0.10327618 -0.09204192 0.08248837 0.44292407 1.5847011\n",
+ " -0.15747674 0.20716982 -0.39656236 -2.52802577 -0.13810356 1.15592549\n",
+ " -0.41093697 1.05903189 1.11363313 0.92263739 -0.85430684 0.86256034\n",
+ " 1.14379369 0.29563571 0.94241894 -1.00363776 -0.4509711 -1.69484381\n",
+ " -0.90294638 0.76882232 0.54888516 -1.35142993 -0.25475156 -0.6617475\n",
+ " -0.62901547 -0.35290343 -0.48896483 -1.07626614 -0.93944671 -0.10220152\n",
+ " -0.51258919 0.07453675 -0.15409034 0.22112889]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"Unitary parameters\", res.x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b5fc2804",
+ "metadata": {},
+ "source": [
+ "### Plotting the approximation\n",
+ "\n",
+ "We can now plot the result of our optimisation in order to compare the QML algorithm's output and the analytical solution of the differential equation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "1e37ce40",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def plot_solution(m, N, X, optim_params, lambda_random):\n",
+ " Y = []\n",
+ " U_1 = pcvl.Matrix.random_unitary(m, optim_params[:2 * m ** 2])\n",
+ " U_2 = pcvl.Matrix.random_unitary(m, optim_params[2 * m ** 2:])\n",
+ " px = pcvl.P(\"x\")\n",
+ " c = pcvl.Unitary(U_2) // (0, pcvl.PS(px)) // pcvl.Unitary(U_1)\n",
+ "\n",
+ " for x in X:\n",
+ " px.set_value(np.pi * x)\n",
+ " backend.set_circuit(c)\n",
+ " f_theta = np.sum(np.multiply(backend.all_prob(input_state), lambda_random))\n",
+ " Y.append(f_theta)\n",
+ " exact = u(X)\n",
+ " plt.plot(X, Y, label=\"Approximation with {} photons\".format(N))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "28a1d993",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "X = np.linspace(range_min, range_max, 200)\n",
+ "\n",
+ "# Change the plot size\n",
+ "default_figsize = mpl.rcParamsDefault['figure.figsize']\n",
+ "mpl.rcParams['figure.figsize'] = [1 * value for value in default_figsize]\n",
+ "\n",
+ "plot_solution(m, N, X, res.x, lambda_random)\n",
+ "\n",
+ "plt.plot(X, u(X), 'r', label='Analytical solution')\n",
+ "plt.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "82740227",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'Loss function value')"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.plot([v[0] for v in loss_evolution])\n",
+ "plt.yscale(\"log\")\n",
+ "plt.xlabel(\"Number of epochs\")\n",
+ "plt.ylabel(\"Loss function value\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "35848cc4",
+ "metadata": {},
+ "source": [
+ "Repeating the entire computation with 3 photons would damage the accuracy of our solution but with 5 photons the accuracy would improve (the first graph above would have the two lines closer to one another). We used 4 photons as the solution is already satisfying.\n",
+ "\n",
+ "Why is the accuracy lower with 3 photons? Lowering the amount of photons lowers the expressibility of our circuit, deeming our ability to find a good solution to the differential equation lower."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3541e471",
+ "metadata": {},
+ "source": [
+ "## References\n",
+ "\n",
+ "> [1] O. Kyriienko, A. E. Paine, and V. E. Elfving, “Solving nonlinear differential equations with differentiable quantum circuits”, [Physical Review A](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.052416) **103**, 052416 (2021).\n",
+ "\n",
+ "> [2] A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, “Data re-uploading for a universal quantum classifier”, [Quantum](https://quantum-journal.org/papers/q-2020-02-06-226/) **4**, 226 (2020).\n",
+ "\n",
+ "> [3] M. Schuld, R. Sweke, and J. J. Meyer, “Effect of data encoding on the expressive power of variational quantum-machine-learning models”, [Physical Review A]( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.032430) **103**, 032430 (2021).\n",
+ "\n",
+ "> [4] B. Y. Gan, D. Leykam, D. G. Angelakis, and D. G. Angelakis, “Fock State-enhanced Expressivity of Quantum Machine Learning Models”, in [Conference on Lasers andElectro-Optics](https://opg.optica.org/abstract.cfm?uri=CLEO_AT-2021-JW1A.73) (2021), paper JW1A.73. Optica Publishing Group, (2021).\n",
+ "\n",
+ "> [5] R. Fletcher, Practical methods of optimization. [John Wiley & Sons](https://onlinelibrary.wiley.com/doi/book/10.1002/9781118723203). (2013)."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/One-qubit_and_two-qubit_gates_TO_DO.ipynb b/One-qubit_and_two-qubit_gates_TO_DO.ipynb
new file mode 100644
index 0000000..385fd2f
--- /dev/null
+++ b/One-qubit_and_two-qubit_gates_TO_DO.ipynb
@@ -0,0 +1,831 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "a682dc1b",
+ "metadata": {},
+ "source": [
+ "# Quandela Training Seminar - Programming with Perceval"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "2d8e0129",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import perceval as pcvl\n",
+ "from perceval.components.unitary_components import PERM,PS,BS\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4abe4fee",
+ "metadata": {},
+ "source": [
+ "### One and two-qubit gates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "854d6776",
+ "metadata": {},
+ "source": [
+ "Below is a list of commonly used quantum gates that can easily be applied to optical quantum computing in Perceval. The list is split into two, for one-qubit and two-qubit gates.\n",
+ "\n",
+ "Before we start, a quick reminder that we use a dual-rail encoding. This means that we encode one physical qubit using 2 modes, where a photon found in one or the other mode represent the qubit's excited or ground state."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2e2158fb",
+ "metadata": {},
+ "source": [
+ "#### One-qubit gates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "29a27b3e",
+ "metadata": {},
+ "source": [
+ "One-qubit gates can be applied to quantum optical systems in Perceval in the form of beam splitters with different reflectivity angles, applied to 2 input modes, phase shifters or simple permutations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "237a0279",
+ "metadata": {},
+ "source": [
+ "##### Pauli-X gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0ce83f80",
+ "metadata": {},
+ "source": [
+ "A Pauli-X gate or the NOT gate can be built by applying a permutation that swaps the two input modes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "ab1b39ac",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: design the Pauli-X gate in Perceval and display it"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b9fdeb79",
+ "metadata": {},
+ "source": [
+ "To check this is correct, you can print the unitary matrix that drives the action of this beam splitter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "a6031764",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "$\\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pcvl.pdisplay(Pauli_X.compute_unitary())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d2f3d761",
+ "metadata": {},
+ "source": [
+ "##### Pauli-Y gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c8ae306e",
+ "metadata": {},
+ "source": [
+ "Similarly, for the Pauli-Y gate we can first apply the Pauli-X gate and then add phase shifters with phases $-\\frac{\\pi}{2}$ and $\\frac{\\pi}{2}$ on modes 0 and 1 respectively."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "f62be79b",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "Φ=3*pi/2 \n",
+ "Φ=pi/2 \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Pauli_Y = PERM([1,0]) // (0,PS(-np.pi/2)) // (1,PS(np.pi/2))\n",
+ "pcvl.pdisplay(Pauli_Y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "baeced45",
+ "metadata": {},
+ "source": [
+ "We can again check the matrix of this unitary transformation to convince ourselves it works correctly."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "54210de0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: check the unitary"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fa0f830d",
+ "metadata": {},
+ "source": [
+ "##### Pauli-Z gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "44400661",
+ "metadata": {},
+ "source": [
+ "To apply a Pauli-Z gate, we can note that it is a rotation on the Z axis with an angle of $\\pi$. We can build this gate in Perceval by applying a phase shifter with phase $\\pi$ on the second of the two modes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "8338b147",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: design the Pauli-Z gate in Perceval and display it"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e4840d31",
+ "metadata": {},
+ "source": [
+ "And once again we can verify the action of this circuit by checking its unitary."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "d66cb5fe",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: check the unitary"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ec2bb996",
+ "metadata": {},
+ "source": [
+ "##### Hadamard gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3cedd273",
+ "metadata": {},
+ "source": [
+ "Finally, we apply a Hadamard gate by using a beam splitter with a predefined reflectivity angle that ensures the action of a Hadamard gate."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "63692ec7",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "H \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Hadamard = BS.H()\n",
+ "pcvl.pdisplay(Hadamard)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ea170bfe",
+ "metadata": {},
+ "source": [
+ "And we can print its unitary to check its action as well."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "e3b24ab3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: check the unitary"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9188c1d4",
+ "metadata": {},
+ "source": [
+ "#### Two-qubit gates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8c44eeb1",
+ "metadata": {},
+ "source": [
+ "##### CZ-gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "14888fa0",
+ "metadata": {},
+ "source": [
+ "The CZ-gate is a two-qubit controlled-Z gate, meaning that the action of the Pauli-Z gate is performed on the target qubit if the control logical qubit is $|1\\rangle$.\n",
+ "\n",
+ "The controlled-Z gate and its full circuit decomposition can be found in the Perceval catalog. This circuit also requires the use of ancillas and heralded gates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "eb65193d",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "HERALDED CZ DOCUMENTATION\n",
+ "--------------------------\n",
+ "\n",
+ "CZ gate with 2 heralded modes\n",
+ "\n",
+ "Scientific article reference: https://arxiv.org/abs/quant-ph/0110144\n",
+ "\n",
+ "Schema:\n",
+ " ╭─────╮\n",
+ "ctrl (dual rail) ─────┤ ├───── ctrl (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " │ │\n",
+ "data (dual rail) ─────┤ ├───── data (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " ╰─────╯\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "HERALDED CZ \n",
+ "Φ=pi \n",
+ "Φ=pi \n",
+ "Θ=1.910786 \n",
+ "H \n",
+ "Θ=1.910786 \n",
+ "H \n",
+ "Θ=10.655584 \n",
+ "H \n",
+ "Θ=0.615403 \n",
+ "H \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "1 \n",
+ "[herald1] \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "1 \n",
+ "[herald1] \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from perceval.components import catalog\n",
+ "print(catalog['heralded cz'].doc)\n",
+ "heralded_cz = catalog['heralded cz'].as_processor().build()\n",
+ "\n",
+ "pcvl.pdisplay(heralded_cz, recursive=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ef6bc00f",
+ "metadata": {},
+ "source": [
+ "Note that there's another way that we can build the CZ-gate. You may have seen before that the following holds: $Z=HXH$. It can similarly be shown that one can build a CZ-gate by applying a CNOT-gate sandwiched between two Hadamard gates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9c2f97a7",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: Use the previously defined Pauli-Z, Pauli-X and Hadamard gates to prove the claim that a Pauli-X gate sandwiched between two Hadamard gates\n",
+ "# has the same action as a Pauli-Z gate. Display their unitaries and convince yourself that this is true."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3edb4686",
+ "metadata": {},
+ "source": [
+ "##### CNOT-gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8eb49074",
+ "metadata": {},
+ "source": [
+ "A CNOT-gate (controlled-NOT gate) is a two-qubit gate where one qubit acts as a control and the other as a target. If the control logical qubit is $|1\\rangle$, the target qubit is flipped (the Pauli-X or NOT-gate is applied), otherwise no action is taken."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3bae9549",
+ "metadata": {},
+ "source": [
+ "Knill, Laflamme and Milburn famously showed that a CNOT circuit can be built in a photonic quantum setting simply by using ancillas (additional photons) in an optical circuit with linear optical components and measurement. This is an important result and can be used for generation of entanglement.\n",
+ "\n",
+ "You can find the full circuit decomposition in the Perceval catalog.\n",
+ "\n",
+ "Note that this circuit requires the use of heralded gates and ancillas. The ancillas are measured separately from the other photons in the circuit and their measurement is used to check whether a gate performed its action well. This gate is then referred to as a heralded gate. Its action needs to be checked because two-qubit gates in dual-rail encoding are probabilistic, and therefore have a probability to fail."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "cad8bbd1",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "HERALDED CNOT DOCUMENTATION\n",
+ "----------------------------\n",
+ "\n",
+ "CNOT gate with 4 heralded modes\n",
+ "\n",
+ "Scientific article reference: https://doi.org/10.1073/pnas.1018839108\n",
+ "\n",
+ "Schema:\n",
+ " ╭─────╮\n",
+ "ctrl (dual rail) ─────┤ ├───── ctrl (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " │ │\n",
+ "data (dual rail) ─────┤ ├───── data (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " ╰─────╯\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "HERALDED CNOT \n",
+ "H \n",
+ "H \n",
+ "Θ=2.145993 \n",
+ "H \n",
+ "Θ=2.145993 \n",
+ "H \n",
+ "H \n",
+ "Θ=1.028622 \n",
+ "H \n",
+ "Θ=1.028622 \n",
+ "H \n",
+ "H \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "0 \n",
+ "[herald1] \n",
+ "1 \n",
+ "[herald2] \n",
+ "0 \n",
+ "[herald3] \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "0 \n",
+ "[herald1] \n",
+ "1 \n",
+ "[herald2] \n",
+ "0 \n",
+ "[herald3] \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print(catalog['heralded cnot'].doc)\n",
+ "heralded_cnot = catalog['heralded cnot'].as_processor().build()\n",
+ "\n",
+ "pcvl.pdisplay(heralded_cnot, recursive=True) # we set recursive=True to show the full set of linear optical components used to build this circuit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f8a05954",
+ "metadata": {},
+ "source": [
+ "##### SWAP gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "444762bd",
+ "metadata": {},
+ "source": [
+ "A two-qubit SWAP gate swaps the two qubit wires qubits travel through. For example the state $|1,0\\rangle$ becomes $|0,1\\rangle$ after passing through a SWAP gate."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "772f9af0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#TO DO: create and display a two-qubit SWAP gate, keeping in mind the dual-rail encoding"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/One-qubit_and_two-qubit_gates_answers.ipynb b/One-qubit_and_two-qubit_gates_answers.ipynb
new file mode 100644
index 0000000..4792fed
--- /dev/null
+++ b/One-qubit_and_two-qubit_gates_answers.ipynb
@@ -0,0 +1,1023 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "a682dc1b",
+ "metadata": {},
+ "source": [
+ "# Quandela Training Seminar - Programming with Perceval"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "7917bf96",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import perceval as pcvl\n",
+ "from perceval.components.unitary_components import PERM,PS,BS\n",
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4abe4fee",
+ "metadata": {},
+ "source": [
+ "### One and two-qubit gates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "854d6776",
+ "metadata": {},
+ "source": [
+ "Below is a list of commonly used quantum gates that can easily be applied to optical quantum computing in Perceval. The list is split into two, for one-qubit and two-qubit gates.\n",
+ "\n",
+ "Before we start, a quick reminder that we use a dual-rail encoding. This means that we encode one physical qubit using 2 modes, where a photon found in one or the other mode represent the qubit's excited or ground state."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2e2158fb",
+ "metadata": {},
+ "source": [
+ "#### One-qubit gates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "29a27b3e",
+ "metadata": {},
+ "source": [
+ "One-qubit gates can be applied to quantum optical systems in Perceval in the form of beam splitters with different reflectivity angles, applied to 2 input modes, phase shifters or simple permutations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "237a0279",
+ "metadata": {},
+ "source": [
+ "##### Pauli-X gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0ce83f80",
+ "metadata": {},
+ "source": [
+ "A Pauli-X gate or the NOT gate can be built by applying a permutation that swaps the two input modes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "ab1b39ac",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Pauli_X = PERM([1,0])\n",
+ "pcvl.pdisplay(Pauli_X)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b9fdeb79",
+ "metadata": {},
+ "source": [
+ "To check this is correct, you can print the unitary matrix that drives the action of this beam splitter."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "a6031764",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "$\\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pcvl.pdisplay(Pauli_X.compute_unitary())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d2f3d761",
+ "metadata": {},
+ "source": [
+ "##### Pauli-Y gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c8ae306e",
+ "metadata": {},
+ "source": [
+ "Similarly, for the Pauli-Y gate we can first apply the Pauli-X gate and then add phase shifters with phases $-\\frac{\\pi}{2}$ and $\\frac{\\pi}{2}$ on modes 0 and 1 respectively."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "f62be79b",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "Φ=3*pi/2 \n",
+ "Φ=pi/2 \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Pauli_Y = PERM([1,0]) // (0,PS(-np.pi/2)) // (1,PS(np.pi/2))\n",
+ "pcvl.pdisplay(Pauli_Y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "baeced45",
+ "metadata": {},
+ "source": [
+ "We can again check the matrix of this unitary transformation to convince ourselves it works correctly."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "54210de0",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "$\\left[\\begin{matrix}0 & - i\\\\i & 0\\end{matrix}\\right]$"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pcvl.pdisplay(Pauli_Y.compute_unitary())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fa0f830d",
+ "metadata": {},
+ "source": [
+ "##### Pauli-Z gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "44400661",
+ "metadata": {},
+ "source": [
+ "To apply a Pauli-Z gate, we can note that it is a rotation on the Z axis with an angle of $\\pi$. We can build this gate in Perceval by applying a phase shifter with phase $\\pi$ on the second of the two modes."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "8338b147",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "Φ=pi \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Pauli_Z=pcvl.Circuit(2) // (1,PS(phi=np.pi))\n",
+ "pcvl.pdisplay(Pauli_Z)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e4840d31",
+ "metadata": {},
+ "source": [
+ "And once again we can verify the action of this circuit by checking its unitary."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "d66cb5fe",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "$\\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pcvl.pdisplay(Pauli_Z.compute_unitary())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ec2bb996",
+ "metadata": {},
+ "source": [
+ "##### Hadamard gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3cedd273",
+ "metadata": {},
+ "source": [
+ "Finally, we apply a Hadamard gate by using a beam splitter with a predefined reflectivity angle that ensures the action of a Hadamard gate."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "63692ec7",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "H \n",
+ "0 \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Hadamard = BS.H()\n",
+ "pcvl.pdisplay(Hadamard)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ea170bfe",
+ "metadata": {},
+ "source": [
+ "And we can print its unitary to check its action as well."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "e3b24ab3",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "$\\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pcvl.pdisplay(Hadamard.compute_unitary())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9188c1d4",
+ "metadata": {},
+ "source": [
+ "#### Two-qubit gates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8c44eeb1",
+ "metadata": {},
+ "source": [
+ "##### CZ-gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "14888fa0",
+ "metadata": {},
+ "source": [
+ "The CZ-gate is a two-qubit controlled-Z gate, meaning that the action of the Pauli-Z gate is performed on the target qubit if the control logical qubit is $|1\\rangle$.\n",
+ "\n",
+ "The controlled-Z gate and its full circuit decomposition can be found in the Perceval catalog. This circuit also requires the use of ancillas and heralded gates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "5be59512",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "HERALDED CZ DOCUMENTATION\n",
+ "--------------------------\n",
+ "\n",
+ "CZ gate with 2 heralded modes\n",
+ "\n",
+ "Scientific article reference: https://arxiv.org/abs/quant-ph/0110144\n",
+ "\n",
+ "Schema:\n",
+ " ╭─────╮\n",
+ "ctrl (dual rail) ─────┤ ├───── ctrl (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " │ │\n",
+ "data (dual rail) ─────┤ ├───── data (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " ╰─────╯\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "HERALDED CZ \n",
+ "Φ=pi \n",
+ "Φ=pi \n",
+ "Θ=1.910786 \n",
+ "H \n",
+ "Θ=1.910786 \n",
+ "H \n",
+ "Θ=10.655584 \n",
+ "H \n",
+ "Θ=0.615403 \n",
+ "H \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "1 \n",
+ "[herald1] \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "1 \n",
+ "[herald1] \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from perceval.components import catalog\n",
+ "print(catalog['heralded cz'].doc)\n",
+ "heralded_cz = catalog['heralded cz'].as_processor().build()\n",
+ "\n",
+ "pcvl.pdisplay(heralded_cz, recursive=True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8141ad80",
+ "metadata": {},
+ "source": [
+ "Notice the 2 ancillary heralded modes, each of which has an input photon. These are used in the outer beam splitters (left top and bottom) that balance detection probability, while the inner (top right beam splitter) creates interference between the two qubits encoded in dual-rail encoding."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ef6bc00f",
+ "metadata": {},
+ "source": [
+ "Note that there's another way that we can build the CZ-gate. You may have seen before that the following holds: $Z=HXH$. It can similarly be shown that one can build a CZ-gate by applying a CNOT-gate sandwiched between two Hadamard gates."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "id": "bb384b95",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "$\\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "$\\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# proving that Z=HXH holds, using the previously defined gates\n",
+ "HXH = Hadamard // Pauli_X // Hadamard\n",
+ "pcvl.pdisplay(HXH.compute_unitary())\n",
+ "pcvl.pdisplay(Pauli_Z.compute_unitary())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3edb4686",
+ "metadata": {},
+ "source": [
+ "##### CNOT-gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8eb49074",
+ "metadata": {},
+ "source": [
+ "A CNOT-gate (controlled-NOT gate) is a two-qubit gate where one qubit acts as a control and the other as a target. If the control logical qubit is $|1\\rangle$, the target qubit is flipped (the Pauli-X or NOT-gate is applied), otherwise no action is taken."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3bae9549",
+ "metadata": {},
+ "source": [
+ "Knill, Laflamme and Milburn famously showed that a CNOT circuit can be built in a photonic quantum setting simply by using ancillas (additional photons) in an optical circuit with linear optical components and measurement. This is an important result and can be used for generation of entanglement.\n",
+ "\n",
+ "You can find the full circuit decomposition in the Perceval catalog.\n",
+ "\n",
+ "Note that this circuit requires the use of heralded gates and ancillas. The ancillas are measured separately from the other photons in the circuit and their measurement is used to check whether a gate performed its action well. This gate is then referred to as a heralded gate. Its action needs to be checked because two-qubit gates in dual-rail encoding are probabilistic, and therefore have a probability to fail."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "cad8bbd1",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "HERALDED CNOT DOCUMENTATION\n",
+ "----------------------------\n",
+ "\n",
+ "CNOT gate with 4 heralded modes\n",
+ "\n",
+ "Scientific article reference: https://doi.org/10.1073/pnas.1018839108\n",
+ "\n",
+ "Schema:\n",
+ " ╭─────╮\n",
+ "ctrl (dual rail) ─────┤ ├───── ctrl (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " │ │\n",
+ "data (dual rail) ─────┤ ├───── data (dual rail)\n",
+ " ─────┤ ├─────\n",
+ " ╰─────╯\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "HERALDED CNOT \n",
+ "H \n",
+ "H \n",
+ "Θ=2.145993 \n",
+ "H \n",
+ "Θ=2.145993 \n",
+ "H \n",
+ "H \n",
+ "Θ=1.028622 \n",
+ "H \n",
+ "Θ=1.028622 \n",
+ "H \n",
+ "H \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "0 \n",
+ "[herald1] \n",
+ "1 \n",
+ "[herald2] \n",
+ "0 \n",
+ "[herald3] \n",
+ "1 \n",
+ "0 \n",
+ "1 \n",
+ "[ctrl] \n",
+ "2 \n",
+ "3 \n",
+ "[data] \n",
+ "[herald0] \n",
+ "0 \n",
+ "[herald1] \n",
+ "1 \n",
+ "[herald2] \n",
+ "0 \n",
+ "[herald3] \n",
+ "1 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print(catalog['heralded cnot'].doc)\n",
+ "heralded_cnot = catalog['heralded cnot'].as_processor().build()\n",
+ "\n",
+ "pcvl.pdisplay(heralded_cnot, recursive=True) # we set recursive=True to show the full set of linear optical components used to build this circuit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a8d2497f",
+ "metadata": {},
+ "source": [
+ "Note that there's another way that we can build the CNOT-gate. You may have seen before that the following holds: $X=HZH$. It can similarly be shown that one can build a CNOT-gate by applying a CZ-gate sandwiched between two Hadamard gates. Since the CZ-gate requires only 2 ancillary modes, here the CNOT gate would also require only 2."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f8a05954",
+ "metadata": {},
+ "source": [
+ "##### SWAP gate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "444762bd",
+ "metadata": {},
+ "source": [
+ "A two-qubit SWAP gate swaps the two quantum wires qubits travel through. For example the state $|1,0\\rangle$ becomes $|0,1\\rangle$ after passing through a SWAP gate.\n",
+ "\n",
+ "In optical quantum computing, the SWAP gate can easily be applied by swapping modes, not forgetting that in our case a quantum wire is represented by two modes as we use dual-rail encoding."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "772f9af0",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n",
+ " \n",
+ "0 \n",
+ "1 \n",
+ "2 \n",
+ "3 \n",
+ "0 \n",
+ "1 \n",
+ "2 \n",
+ "3 \n",
+ " "
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "SWAP = PERM([2,3,0,1])\n",
+ "pcvl.pdisplay(SWAP)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.10.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}