Work 1: Problem 3 matlab + report

Work 1/report/Work1_report.tex

@@ -76,7 +76,7 @@
 % Request a title page or header
 \InsertTitle
 
-\section{Εισαγωγή}
+\section*{Εισαγωγή}
 Η παρούσα εργασία έχει ως αντικείμενο τη μελέτη ενός απλοποιημένου δυναμικού συστήματος — συγκεκριμένα ενός γραμμικοποιημένου εκκρεμούς με ροπή εισόδου — με σκοπό την κατανόηση της συμπεριφοράς του και την εκτίμηση των φυσικών παραμέτρων του μέσω της μεθόδου των ελαχίστων τετραγώνων.
 Στο πρώτο μέρος της εργασίας εξετάζεται η δυναμική του συστήματος, η οποία περιγράφεται από μία διαφορική εξίσωση δευτέρας τάξης, και προσεγγίζεται τόσο θεωρητικά όσο και αριθμητικά μέσω προσομοίωσης στο περιβάλλον MATLAB.
 \par
@@ -84,7 +84,7 @@
 Στη συνέχεια, εφαρμόζεται ημιτονική διέγερση και εξετάζεται η απόκριση του συστήματος. Ιδιαίτερο ενδιαφέρον παρουσιάζει ο τρόπος με τον οποίο το σύστημα φτάνει στη μόνιμη περιοδική του συμπεριφορά, καθώς και ο ρυθμός με τον οποίο αποκλίνουν οι ταλαντώσεις από τη μεταβατική φάση.
 Η ανάλυση αυτή θέτει τη βάση για τα επόμενα μέρη της εργασίας, όπου επιχειρείται η εκτίμηση των παραμέτρων του μοντέλου με τη χρήση δεδομένων εξόδου του συστήματος.
 
-\subsection{Παραδοτέα}
+\subsection*{Παραδοτέα}
 Τα παραδοτέα της εργασίας αποτελούνται από:
 \begin{itemize}
     \item Την παρούσα αναφορά.
@@ -92,7 +92,7 @@
     \item Το \href{https://git.hoo2.net/hoo2/SystemModling}{σύνδεσμο} με το αποθετήριο που περιέχει όλο το project με τον κώδικα της MATLAB, της αναφοράς και τα παραδοτέα.
 \end{itemize}
 
-\section{Θέμα 1 – Μοντελοποίηση και Προσομοίωση Συστήματος Εκκρεμούς}
+\section*{Θέμα 1 – Μοντελοποίηση και Προσομοίωση Συστήματος Εκκρεμούς}
 
 Το σύστημα που μελετάται περιγράφεται από τη γραμμικοποιημένη διαφορική εξίσωση:
 \[
@@ -132,16 +132,14 @@
 Η προσομοίωση του Θέματος 1 χρησίμευσε όχι μόνο για την παρατήρηση της δυναμικής του συστήματος, αλλά και για την παραγωγή των δεδομένων που χρησιμοποιήθηκαν στο Θέμα 2 για την εκτίμηση των παραμέτρων. Η ακρίβεια των αποτελεσμάτων του Θέματος 2 επιβεβαιώνει τη σωστή ρύθμιση και υλοποίηση της προσομοίωσης.
 
 \subsection*{Παρατήρηση Συμπεριφοράς Συστήματος}
-
 Βλέπουμε ότι το σύστημα παρουσιάζει περιοδική απόκριση, η οποία όμως δεν σταθεροποιείται γρήγορα.
 Όπως φαίνεται στο Σχήμα~\ref{fig:20s}, το πλάτος των ταλαντώσεων συνεχίζει να μεταβάλλεται ακόμη και μετά από 20 δευτερόλεπτα, γεγονός που δείχνει ότι το σύστημα βρίσκεται ακόμη σε μεταβατική κατάσταση.
-
+\par
 Η καθυστερημένη σύγκλιση οφείλεται κυρίως:
 \begin{itemize}
     \item στην πολύ μικρή τιμή του συντελεστή απόσβεσης ($c = 0.15$), και
     \item στο γεγονός ότι η συχνότητα της εισόδου ($\omega = 2$ rad/s) είναι κοντά στη φυσική συχνότητα του εκκρεμούς ($\omega_n = \sqrt{g/L} \approx 2.8$ rad/s), προκαλώντας φαινόμενο ενίσχυσης (quasi-resonance).
 \end{itemize}
-
 Για τον λόγο αυτό, επεκτείναμε τη διάρκεια προσομοίωσης στα $90$ δευτερόλεπτα.
 Όπως φαίνεται στο Σχήμα~\ref{fig:90s}, το σύστημα σταθεροποιείται τελικά σε περιοδική μορφή περίπου μετά από $50$ δευτερόλεπτα.
 
@@ -152,7 +150,7 @@
     Απόκριση του συστήματος για $t \in [0, 90]$ sec. Το σύστημα σταθεροποιείται σε περιοδική συμπεριφορά μετά τα $50$ sec.
 }
 
-\section{Θέμα 2 – Εκτίμηση Παραμέτρων με τη Μέθοδο Ελαχίστων Τετραγώνων}
+\section*{Θέμα 2 – Εκτίμηση Παραμέτρων με τη Μέθοδο Ελαχίστων Τετραγώνων}
 
 Η εξίσωση που περιγράφει τη δυναμική του εκκρεμούς είναι της μορφής:
 \[
@@ -167,8 +165,7 @@
 
 Στόχος του παρόντος ερωτήματος είναι η εκτίμηση του διανύσματος $\theta$ με χρήση μετρήσεων από την έξοδο του συστήματος και της εισόδου $u(t)$, εφαρμόζοντας τη μέθοδο των ελαχίστων τετραγώνων.
 
-\subsection{Υποερώτημα (α)}
-
+\subsection*{Υποερώτημα 2α}
 Στο πρώτο υποερώτημα θεωρείται ότι είναι διαθέσιμες μετρήσεις όλων των μεταβλητών κατάστασης, δηλαδή $q(t)$, $\dot{q}(t)$ και $\ddot{q}(t)$, καθώς και της εισόδου $u(t)$.
 Δημιουργείται λοιπόν το πρόβλημα παλινδρόμησης:
 \[
@@ -180,7 +177,6 @@
 \[
     \hat{\theta} = (X^T X)^{-1} X^T u
 \]
-
 Αφού εκτιμηθούν οι παράμετροι, χρησιμοποιούνται για να υπολογιστεί η επιτάχυνση $\ddot{q}_{\text{est}}(t)$ και στη συνέχεια η ανακατασκευή της απόκρισης $q_{\text{est}}(t)$ με αριθμητική ολοκλήρωση.
 Η διαδικασία υλοποιείται με ένα απλό βρόχο επανάληψης (for loop), όπου για κάθε χρονικό βήμα $k$ υπολογίζονται διαδοχικά:
 \[
@@ -189,21 +185,16 @@
     \[
     q_{\text{est}}(k) = q_{\text{est}}(k-1) + T_s \cdot \dot{q}_{\text{est}}(k-1)
 \]
-
 Στο Σχήμα~\ref{fig:prob2a} παρουσιάζονται η πραγματική και η εκτιμώμενη γωνία, καθώς και το σφάλμα $e_q(t)$ μεταξύ τους.
 
 \InsertFigure{!ht}{1}{fig:prob2a}{../scripts/Prob2_20s_Ts0.1.png}{
     Αποτελέσματα εκτίμησης παραμέτρων με χρήση όλων των μεταβλητών κατάστασης.
 }
-
 \paragraph*{Συμπεράσματα:}
 Η εκτίμηση παρουσιάζει υψηλή ακρίβεια, με σχετικό σφάλμα μικρότερο του 6\% για όλες τις παραμέτρους.
 Ο αλγόριθμος κατάφερε να ανακατασκευάσει την απόκριση με μικρό σφάλμα, επιβεβαιώνοντας τη θεωρητική εγκυρότητα της μεθόδου.
 
-\vspace{1em}
-
-\subsection{Υποερώτημα (β)}
-
+\subsection*{Υποερώτημα 2β}
 Στη δεύτερη περίπτωση θεωρούμε ότι διαθέσιμες είναι μόνο οι μετρήσεις της γωνίας $q(t)$ και της εισόδου $u(t)$.
 Οι παράγωγοι $\dot{q}(t)$ και $\ddot{q}(t)$ υπολογίζονται αριθμητικά από το σήμα $q(t)$ με χρήση διαφορικών τελεστών 2ης τάξης ακρίβειας (κεντρικών διαφορών):
 \[
@@ -211,7 +202,6 @@
     \quad
     \ddot{q}(t_k) \approx \frac{q_{k+1} - 2q_k + q_{k-1}}{T_s^2}
 \]
-
 Ακολουθείται η ίδια διαδικασία παλινδρόμησης με την περίπτωση (α), όπως και η ανακατασκευή της απόκρισης. Το Σχήμα~\ref{fig:prob2b} δείχνει τα αντίστοιχα αποτελέσματα.
 
 \InsertFigure{!ht}{1}{fig:prob2b}{../scripts/Prob2b_20s_Ts0.1.png}{
@@ -221,10 +211,7 @@
 \paragraph*{Συμπεράσματα:}
 Παρά τον περιορισμό στη διαθέσιμη πληροφορία, η εκτίμηση παρέμεινε εξαιρετικά ακριβής, με μικρές αποκλίσεις από την πραγματική τιμή. Το γεγονός αυτό δείχνει την ισχυρή ταυτοποιησιμότητα του συστήματος και τη δυνατότητα εφαρμογής της μεθόδου ακόμη και με ελλιπή δεδομένα.
 
-\vspace{1em}
-
-\subsection{Σύγκριση των δύο περιπτώσεων}
-
+\subsection*{Σύγκριση των δύο περιπτώσεων}
 Ο παρακάτω πίνακας συγκρίνει τις πραγματικές και εκτιμώμενες τιμές για τα δύο υποερωτήματα:
 
 \begin{center}
@@ -239,6 +226,133 @@
 
 Παρατηρούμε ότι και στις δύο περιπτώσεις οι εκτιμήσεις είναι ακριβείς και σταθερές, με τις αποκλίσεις να κυμαίνονται σε χαμηλά επίπεδα. Μάλιστα, το γεγονός ότι τα σφάλματα είναι αντίστοιχα ακόμα και όταν χρησιμοποιείται λιγότερη πληροφορία (περίπτωση 2β), αποτελεί ένδειξη για τη σταθερότητα και αξιοπιστία της μεθόδου. Ταυτόχρονα, αναδεικνύει την ιδιαίτερη σημασία της επιλογής σήματος διέγερσης και της ποιότητας των δεδομένων.
 
+\section*{Θέμα 3 – Ανάλυση Ευαισθησίας της Εκτίμησης Παραμέτρων}
+
+\subsection*{Υποερώτημα 3α: Επίδραση Λευκού Θορύβου στις Μετρήσεις}
+Στο υποερώτημα αυτό προστέθηκε λευκός γκαουσιανός θόρυβος στα δεδομένα $q(t)$ και επαναλήφθηκε η διαδικασία εκτίμησης παραμέτρων από το Θέμα~2β.
+Χρησιμοποιήθηκαν δύο διαφορετικά επίπεδα θορύβου, με τυπική απόκλιση $\sigma = 0.001$ και $\sigma = 0.0025$, διατηρώντας σταθερή την είσοδο και την περίοδο δειγματοληψίας ($T_s = 0.1$ sec).
+Οι εκτιμήσεις συγκρίθηκαν με την αντίστοιχη χωρίς θόρυβο, τόσο ως προς το σφάλμα στις παραμέτρους όσο και στην ανακατασκευή της απόκρισης $q(t)$.
+
+\begin{figure}[H]
+%    \centering
+    \hspace{-2em}
+    \begin{minipage}{0.49\textwidth}
+        \centering
+        \includegraphics[width=1.15\linewidth]{../scripts/Prob3a_NoiseStd0.0010.png}
+        \caption{Εκτίμηση με $\sigma = 0.001$}
+    \end{minipage}
+    \hspace{0.5em}
+    \begin{minipage}{0.49\textwidth}
+        \centering
+        \includegraphics[width=1.15\linewidth]{../scripts/Prob3a_NoiseStd0.0025.png}
+        \caption{Εκτίμηση με $\sigma = 0.0025$}
+    \end{minipage}
+\end{figure}
+
+\paragraph*{Παρατηρήσεις:}
+Για μικρό θόρυβο ($\sigma = 0.001$) η ακρίβεια παραμένει υψηλή (σφάλμα περίπου $10\%$).
+Όταν ο θόρυβος αυξάνεται ($\sigma = 0.0025$), οι εκτιμήσεις επιδεινώνονται σημαντικά, κυρίως για το $mL^2$.
+Το γεγονός αυτό οφείλεται στην αριθμητική παραγώγιση, η οποία είναι ιδιαίτερα ευαίσθητη στον θόρυβο.
+
+\subsection*{Υποερώτημα 3β: Επίδραση της Περιόδου Δειγματοληψίας $T_s$}
+Στο υποερώτημα αυτό μελετάται η ακρίβεια των εκτιμήσεων σε συνάρτηση με την περίοδο δειγματοληψίας $T_s$.
+Η προσομοίωση έγινε για διάρκεια $T = 20$ sec, ενώ τα δεδομένα δειγματοληττήθηκαν ξανά για διαφορετικές τιμές:
+\[
+    T_s \in \{0.01, 0.05, 0.1, 0.2, 0.5\} \text{ sec}
+\]
+
+Η εκτίμηση έγινε με τον ίδιο τρόπο όπως στο Θέμα~2β.
+Παρακάτω παρουσιάζονται τα σφάλματα εκτίμησης για κάθε παράμετρο:
+\begin{table}[H]
+    \centering
+    \begin{tabular}{c|cc|cc|cc}
+        $T_s$ [sec]
+        & $mL^2$ & Σφάλμα (\%)
+        & $c$ & Σφάλμα (\%)
+        & $mgL$ & Σφάλμα (\%) \\
+        \hline
+        0.010 & 1.1708 & 0.09 & 0.1502 & 0.17 & 9.1928 & 0.04 \\
+        0.050 & 1.1737 & 0.16 & 0.1505 & 0.34 & 9.2009 & 0.04 \\
+        0.100 & 1.1826 & 0.92 & 0.1513 & 0.89 & 9.2249 & 0.31 \\
+        0.200 & 1.2188 & 4.00 & 0.1547 & 3.16 & 9.3210 & 1.35 \\
+        0.500 & 1.5186 & 29.59 & 0.1818 & 21.20 & 10.0959 & 9.78 \\
+    \end{tabular}
+    \caption{Εκτιμήσεις και ποσοστά σφάλματος παραμέτρων για διαφορετικές περιόδους $T_s$}
+\end{table}
+
+\InsertFigure{!ht}{1}{fig:3b}{../scripts/Prob3b_SamplingPeriodEffect.png}{
+    Σφάλμα εκτίμησης ως προς την περίοδο δειγματοληψίας $T_s$.
+}
+
+\paragraph*{Παρατηρήσεις:}
+Για $T_s \leq 0.1$ sec οι εκτιμήσεις είναι εξαιρετικά ακριβείς.
+Από το $T_s = 0.2$ sec παρατηρείται σταδιακή επιδείνωση, ενώ στο $T_s = 0.5$ sec οι αποκλίσεις είναι σημαντικές.
+Το φαινόμενο αυτό οφείλεται στην απώλεια πληροφορίας κατά τη δειγματοληψία, και υπογραμμίζει την ανάγκη για επιλογή κατάλληλης συχνότητας δειγματοληψίας ανάλογα με τη δυναμική του συστήματος.
+
+\subsection{Υποερώτημα 3γ: Επίδραση του Πλάτους Εισόδου $A_0$}
+
+Σε αυτό το υποερώτημα μελετάται η επίδραση του πλάτους της ημιτονικής εισόδου $A_0$ στην ακρίβεια της εκτίμησης παραμέτρων.
+Η διάρκεια προσομοίωσης διατηρήθηκε σταθερή στα $T = 20$ sec και η περίοδος δειγματοληψίας στα $T_s = 0.1$ sec.
+Το πλάτος $A_0$ έλαβε τις τιμές:
+\[
+    A_0 \in \{1, 2, 4, 6, 8, 16, 32\}
+\]
+
+Για κάθε τιμή, πραγματοποιήθηκε εκ νέου προσομοίωση, δειγματοληψία και εκτίμηση παραμέτρων με τη μέθοδο ελαχίστων τετραγώνων, όπως περιγράφεται στο Θέμα~2β.
+Παρακάτω παρουσιάζονται τα σφάλματα εκτίμησης για διαφορετικά πλάτη:
+\begin{table}[H]
+    \centering
+    \begin{tabular}{c|cc|cc|cc}
+        $A_0$
+        & $mL^2$ & Σφάλμα (\%)
+        & $c$ & Σφάλμα (\%)
+        & $mgL$ & Σφάλμα (\%) \\
+        \hline
+        1  & 1.1826 & 0.91 & 0.1514 & 0.90 & 9.2247 & 0.30 \\
+        2  & 1.1827 & 0.92 & 0.1513 & 0.90 & 9.2250 & 0.31 \\
+        4  & 1.1826 & 0.92 & 0.1513 & 0.89 & 9.2249 & 0.31 \\
+        6  & 1.1826 & 0.92 & 0.1513 & 0.90 & 9.2249 & 0.30 \\
+        8  & 1.1826 & 0.92 & 0.1513 & 0.90 & 9.2248 & 0.30 \\
+        16 & 1.1826 & 0.92 & 0.1513 & 0.90 & 9.2248 & 0.30 \\
+        32 & 1.1826 & 0.92 & 0.1513 & 0.89 & 9.2248 & 0.30 \\
+    \end{tabular}
+    \caption{Εκτιμήσεις και ποσοστά σφάλματος παραμέτρων για διαφορετικά πλάτη $A_0$}
+\end{table}
+
+\InsertFigure{!ht}{1}{fig:3c}{../scripts/Prob3c_AmplitudeEffect.png}{
+    Σφάλμα εκτίμησης παραμέτρων συναρτήσει του πλάτους εισόδου $A_0$.
+}
+
+\paragraph*{Παρατηρήσεις:}
+Τα αποτελέσματα δείχνουν ότι η ακρίβεια των εκτιμήσεων παραμένει σχεδόν σταθερή ανεξαρτήτως του πλάτους $A_0$.
+Το μέγιστο σχετικό σφάλμα κυμαίνεται εντός του $1\%$ για όλες τις παραμέτρους.
+Το εύρημα αυτό είναι αναμενόμενο, καθώς το υπό μελέτη σύστημα είναι γραμμικό ως προς τη ροπή εισόδου $u(t)$.
+Η εξίσωση:
+\[
+    mL^2 \ddot{q}(t) + c \dot{q}(t) + mgL q(t) = A_0 \sin(\omega t)
+\]
+δείχνει ότι το $A_0$ αποτελεί απλώς έναν γραμμικό πολλαπλασιαστικό συντελεστή της εισόδου, χωρίς να επηρεάζει τη δομή του συστήματος.
+
+Συνεπώς, οι πραγματικές παράμετροι του συστήματος δεν εξαρτώνται από το μέγεθος του $A_0$.
+Το μόνο που μπορεί να επηρεάζεται είναι η αριθμητική ακρίβεια των παραγώγων (και κατ’ επέκταση της εκτίμησης), μέσω του λόγου σήματος προς αριθμητικό σφάλμα κατά την παραγώγιση (numerical SNR).
+Ωστόσο, για τις τιμές $A_0$ που εξετάστηκαν, η ακρίβεια παρέμεινε υψηλή.
+
+\section*{Συμπεράσματα}
 
+Στην παρούσα εργασία μελετήθηκε η εκτίμηση παραμέτρων ενός γραμμικοποιημένου μοντέλου εκκρεμούς, με εφαρμογή της μεθόδου των ελαχίστων τετραγώνων (Least Squares).
+Αρχικά πραγματοποιήθηκε αριθμητική προσομοίωση του συστήματος, εξετάζοντας τη δυναμική του και τον ρυθμό σταθεροποίησης της απόκρισής του.
+\par
+Στη συνέχεια, χρησιμοποιήθηκαν τα δεδομένα της προσομοίωσης για την εκτίμηση των παραμέτρων $mL^2$, $c$ και $mgL$, με βάση μόνο τις μετρήσεις της γωνίας $q(t)$ και της εισόδου $u(t)$.
+Τα αποτελέσματα έδειξαν ότι, υπό ιδανικές συνθήκες, η μέθοδος οδηγεί σε πολύ ακριβείς εκτιμήσεις.
+\par
+Η ανάλυση των Υποερωτημάτων του Θέματος~3 ανέδειξε τη συμπεριφορά της μεθόδου σε ρεαλιστικότερα σενάρια.
+Διαπιστώθηκε ότι:
+\begin{itemize}
+    \item Η προσθήκη λευκού θορύβου στο $q(t)$ μειώνει σημαντικά την ακρίβεια, λόγω της ευαισθησίας της αριθμητικής παραγώγισης στον θόρυβο.
+    \item Η περίοδος δειγματοληψίας επηρεάζει έντονα την ποιότητα εκτίμησης: πολύ αραιή δειγματοληψία οδηγεί σε μεγάλη απώλεια πληροφορίας.
+    \item Το πλάτος της εισόδου $A_0$ δεν επηρεάζει ουσιαστικά την ακρίβεια, καθώς η δομή του συστήματος είναι γραμμική ως προς το $A_0$.
+\end{itemize}
+\par
+Συνολικά, η μελέτη ανέδειξε τις δυνατότητες αλλά και τους περιορισμούς της μεθόδου LS σε διακριτοχρονικές συνθήκες, παρέχοντας πολύτιμα συμπεράσματα για τη χρήση της σε εφαρμογές δυναμικής μοντελοποίησης.
 
 \end{document}

Work 1/scripts/Problem3a.m

@@ -0,0 +1,114 @@
+% === Problem 3a: Effect of Noise on Parameter Estimation ===
+
+clear; close all;
+
+% True system parameters
+m = 0.75;
+L = 1.25;
+c = 0.15;
+g = 9.81;
+
+mL2_true = m * L^2;
+mgL_true = m * g * L;
+theta_true = [mL2_true; c; mgL_true];
+
+% Load clean data
+data = readtable('problem1_data.csv');
+t = data.t;
+q_clean = data.q;
+u = data.u;
+Ts = t(2) - t(1);
+N = length(t);
+
+% Derivatives from clean q
+dq_clean = zeros(N,1);
+ddq_clean = zeros(N,1);
+for k = 2:N-1
+    dq_clean(k) = (q_clean(k+1) - q_clean(k-1)) / (2*Ts);
+    ddq_clean(k) = (q_clean(k+1) - 2*q_clean(k) + q_clean(k-1)) / Ts^2;
+end
+
+% LS estimation on clean data
+X_clean = [ddq_clean, dq_clean, q_clean];
+theta_hat_clean = (X_clean' * X_clean) \ (X_clean' * u);
+rel_error_clean = abs((theta_hat_clean - theta_true) ./ theta_true) * 100;
+
+% Reconstruct q̂_clean
+q_hat_clean = zeros(N, 1);
+dq_hat_clean = zeros(N, 1);
+q_hat_clean(1) = q_clean(1);
+dq_hat_clean(1) = dq_clean(1);
+for k = 2:N
+    ddq_hat_clean_k = (1/theta_hat_clean(1)) * ...
+        (u(k-1) - theta_hat_clean(2)*dq_clean(k-1) - theta_hat_clean(3)*q_clean(k-1));
+    dq_hat_clean(k) = dq_hat_clean(k-1) + Ts * ddq_hat_clean_k;
+    q_hat_clean(k) = q_hat_clean(k-1) + Ts * dq_hat_clean(k-1);
+end
+
+% === Loop over noise levels ===
+noise_levels = [0.001, 0.0025];
+
+for i = 1:length(noise_levels)
+    noise_std = noise_levels(i);
+    q_noisy = q_clean + noise_std * randn(size(q_clean));
+
+    % Derivatives from noisy q
+    dq_noisy = zeros(N,1);
+    ddq_noisy = zeros(N,1);
+    for k = 2:N-1
+        dq_noisy(k) = (q_noisy(k+1) - q_noisy(k-1)) / (2*Ts);
+        ddq_noisy(k) = (q_noisy(k+1) - 2*q_noisy(k) + q_noisy(k-1)) / Ts^2;
+    end
+
+    % LS estimation on noisy data
+    X_noisy = [ddq_noisy, dq_noisy, q_noisy];
+    theta_hat_noisy = (X_noisy' * X_noisy) \ (X_noisy' * u);
+    rel_error_noisy = abs((theta_hat_noisy - theta_true) ./ theta_true) * 100;
+
+    % Reconstruct q̂_noisy
+    q_hat_noisy = zeros(N,1);
+    dq_hat_noisy = zeros(N,1);
+    q_hat_noisy(1) = q_noisy(1);
+    dq_hat_noisy(1) = dq_noisy(1);
+    for k = 2:N
+        ddq_hat_noisy_k = (1/theta_hat_noisy(1)) * ...
+            (u(k-1) - theta_hat_noisy(2)*dq_noisy(k-1) - theta_hat_noisy(3)*q_noisy(k-1));
+        dq_hat_noisy(k) = dq_hat_noisy(k-1) + Ts * ddq_hat_noisy_k;
+        q_hat_noisy(k) = q_hat_noisy(k-1) + Ts * dq_hat_noisy(k-1);
+    end
+
+    % Print results
+    fprintf('\n--- Noise std = %.4f ---\n', noise_std);
+    fprintf('Clean:  mL2=%.4f (%.2f%%), c=%.4f (%.2f%%), mgL=%.4f (%.2f%%)\n', ...
+        theta_hat_clean(1), rel_error_clean(1), ...
+        theta_hat_clean(2), rel_error_clean(2), ...
+        theta_hat_clean(3), rel_error_clean(3));
+    fprintf('Noisy:  mL2=%.4f (%.2f%%), c=%.4f (%.2f%%), mgL=%.4f (%.2f%%)\n', ...
+        theta_hat_noisy(1), rel_error_noisy(1), ...
+        theta_hat_noisy(2), rel_error_noisy(2), ...
+        theta_hat_noisy(3), rel_error_noisy(3));
+
+    % === Combined plot ===
+    figure('Name', sprintf('Noise std = %.4f', noise_std), 'Position', [100, 100, 1000, 800]);
+
+    subplot(2,1,1);
+    plot(t, q_clean, 'b', ...
+         t, q_hat_clean, 'g--', ...
+         t, q_hat_noisy, 'r:');
+    legend('Actual q(t)', 'Estimated (clean)', 'Estimated (noisy)');
+    title(sprintf('Estimated Output (σ = %.4f)', noise_std));
+    ylabel('q(t) [rad]');
+    grid on;
+
+    subplot(2,1,2);
+    bar([rel_error_clean, rel_error_noisy]);
+    set(gca, 'XTickLabel', {'mL^2', 'c', 'mgL'});
+    legend({'No Noise', sprintf('With Noise (σ=%.4f)', noise_std)}, 'Location', 'northwest');
+    ylabel('Relative Error [%]');
+    title('Estimation Error');
+    grid on;
+
+    % Save figure
+    filename = sprintf('Prob3a_NoiseStd%.4f.png', noise_std);
+    saveas(gcf, filename);
+end

Work 1/scripts/Problem3b.m

@@ -0,0 +1,80 @@
+% === Problem 3b: Effect of Sampling Period Ts on Estimation Accuracy ===
+
+clear; close all;
+
+% True parameters
+m = 0.75;
+L = 1.25;
+c = 0.15;
+g = 9.81;
+
+mL2_true = m * L^2;
+mgL_true = m * g * L;
+theta_true = [mL2_true; c; mgL_true];
+
+% Parameters of input
+A0 = 4;
+omega = 2;
+
+% Time settings
+T_final = 20;
+dt = 1e-4;
+t_full = 0:dt:T_final;
+
+% Simulate system with very fine resolution
+odefun = @(t, x) [
+    x(2);
+    (1/(m*L^2)) * (A0*sin(omega*t) - c*x(2) - m*g*L*x(1))
+];
+x0 = [0; 0];
+[t_sim, x_sim] = ode45(odefun, t_full, x0);
+
+% Sampling periods to test
+Ts_list = [0.01, 0.05, 0.1, 0.2, 0.5];
+n_cases = length(Ts_list);
+rel_errors_all = zeros(3, n_cases);
+
+for i = 1:n_cases
+    Ts = Ts_list(i);
+
+    % Resample at this Ts
+    t_sampled = t_sim(1):Ts:t_sim(end);
+    q = interp1(t_sim, x_sim(:,1), t_sampled);
+    u = A0 * sin(omega * t_sampled);
+
+    N = length(t_sampled);
+
+    % Compute dq and ddq with central differences
+    dq = zeros(N,1);
+    ddq = zeros(N,1);
+    for k = 2:N-1
+        dq(k) = (q(k+1) - q(k-1)) / (2*Ts);
+        ddq(k) = (q(k+1) - 2*q(k) + q(k-1)) / Ts^2;
+    end
+
+    % LS Estimation
+    idx = 2:N-1;        % Truncate to valid range (2:N-1)
+    X = [ddq(idx), dq(idx), q(idx)'];
+    y = u(idx).';
+    theta_hat = (X' * X) \ (X' * y);
+
+    rel_error = abs((theta_hat - theta_true) ./ theta_true) * 100;
+    rel_errors_all(:, i) = rel_error;
+
+    % Print
+    fprintf('Ts = %.3f s → mL^2=%.4f (%.2f%%), c=%.4f (%.2f%%), mgL=%.4f (%.2f%%)\n', ...
+        Ts, theta_hat(1), rel_error(1), ...
+        theta_hat(2), rel_error(2), ...
+        theta_hat(3), rel_error(3));
+end
+
+% === Plot ===
+figure('Name', 'Problem 3b - Effect of Sampling Period', 'Position', [100, 100, 1000, 600]);
+plot(Ts_list, rel_errors_all', '-o', 'LineWidth', 2, 'MarkerSize', 4);
+legend({'mL^2', 'c', 'mgL'}, 'Location', 'northwest');
+xlabel('Sampling Period Ts [sec]');
+ylabel('Relative Error [%]');
+title('Effect of Ts on Parameter Estimation');
+grid on;
+
+saveas(gcf, 'Prob3b_SamplingPeriodEffect.png');

Work 1/scripts/Problem3c.m

@@ -0,0 +1,78 @@
+% === Problem 3c: Effect of Input Amplitude A0 on Estimation Accuracy ===
+
+clear; close all;
+
+% True system parameters
+m = 0.75;
+L = 1.25;
+c = 0.15;
+g = 9.81;
+
+mL2_true = m * L^2;
+mgL_true = m * g * L;
+theta_true = [mL2_true; c; mgL_true];
+
+% Simulation settings
+omega = 2;       % input frequency
+Ts = 0.1;        % sampling period
+dt = 1e-4;       % integration resolution
+T_final = 20;    % simulation time
+
+% Amplitudes to test
+A0_list = [1, 2, 4, 6, 8, 16, 32];
+n_cases = length(A0_list);
+rel_errors_all = zeros(3, n_cases);
+
+for i = 1:n_cases
+    A0 = A0_list(i);
+
+    % Simulate system
+    t_full = 0:dt:T_final;
+    odefun = @(t, x) [
+        x(2);
+        (1/(m*L^2)) * (A0*sin(omega*t) - c*x(2) - m*g*L*x(1))
+    ];
+    x0 = [0; 0];
+    [t_sim, x_sim] = ode45(odefun, t_full, x0);
+
+    % Resample at Ts
+    t_sampled = t_sim(1):Ts:t_sim(end);
+    q = interp1(t_sim, x_sim(:,1), t_sampled);
+    u = A0 * sin(omega * t_sampled);
+    N = length(t_sampled);
+
+    % Estimate derivatives
+    dq = zeros(N,1);
+    ddq = zeros(N,1);
+    for k = 2:N-1
+        dq(k) = (q(k+1) - q(k-1)) / (2*Ts);
+        ddq(k) = (q(k+1) - 2*q(k) + q(k-1)) / Ts^2;
+    end
+
+    % LS Estimation
+    idx = 2:N-1;
+    X = [ddq(idx), dq(idx), q(idx)'];
+    y = u(idx).';
+    theta_hat = (X' * X) \ (X' * y);
+
+    rel_error = abs((theta_hat - theta_true) ./ theta_true) * 100;
+    rel_errors_all(:, i) = rel_error;
+
+    % Print
+    fprintf('A0 = %d → mL^2=%.4f (%.2f%%), c=%.4f (%.2f%%), mgL=%.4f (%.2f%%)\n', ...
+        A0, theta_hat(1), rel_error(1), ...
+        theta_hat(2), rel_error(2), ...
+        theta_hat(3), rel_error(3));
+end
+
+% === Plot ===
+figure('Name', 'Problem 3c - Effect of A0', 'Position', [100, 100, 1000, 600]);
+plot(A0_list, rel_errors_all', '-o', 'LineWidth', 2, 'MarkerSize', 4);
+legend({'mL^2', 'c', 'mgL'}, 'Location', 'northeast');
+xlabel('Input Amplitude A_0');
+ylabel('Relative Error [%]');
+title('Effect of Input Amplitude on Parameter Estimation');
+grid on;
+ylim([0 1.1]);
+
+saveas(gcf, 'Prob3c_AmplitudeEffect.png');

Work 1/scripts/problem3_data_T10s.csv

@@ -0,0 +1,102 @@
+t,q,dq,ddq,u
+0,0,0,0,0
+0.1,0.00112730370377742,0.0336536743050961,0.657669343872878,0.794677323180245
+0.2,0.00883130084628362,0.130095105060834,1.23031152735571,1.5576733692346
+0.3,0.0288384132623469,0.277086967848714,1.6472957578342,2.25856989358014
+0.4,0.0653184832567522,0.456177260208145,1.85826392239339,2.86942436359809
+0.5,0.120381192475091,0.64441963262565,1.82183441394098,3.36588393923159
+0.6,0.19366224583284,0.816729955124557,1.5387129073771,3.72815634386891
+0.7,0.28233042826436,0.947731422726794,1.01198704123085,3.94179891995384
+0.8,0.381118481108189,1.01514724688817,0.281130829714293,3.99829441216602
+0.9,0.48271784224916,1.00127150126433,-0.606890939324855,3.89539052351278
+1,0.578248293996883,0.894322024572221,-1.54403616041735,3.63718970730273
+1.1,0.658338384140432,0.691502504394097,-2.46777849195839,3.23398561527836
+1.2,0.713750689364397,0.398398200996943,-3.35626893527373,2.7018527222046
+1.3,0.735600305235625,0.0284599263544737,-4.00825914367234,2.06200548728586
+1.4,0.71736732967013,-0.396782279453475,-4.38489881755735,1.33995260062362
+1.5,0.655285365929061,-0.849118356836855,-4.531083639236,0.564480032239469
+1.6,0.547892565795632,-1.29622623806606,-4.3244857319699,-0.23349657371032
+1.7,0.397254908342504,-1.70407791327366,-3.73168898607231,-1.02216440810733
+1.8,0.209300361028653,-2.04006080855522,-2.86613213766537,-1.77008177317941
+1.9,-0.00731550766185135,-2.27387198043844,-1.72922293231809,-2.44743156377088
+2,-0.241223605675537,-2.38106324008954,-0.381252753564326,-3.02720998123171
+2.1,-0.478944231224866,-2.34680237646659,1.08356113140267,-3.48630308965435
+2.2,-0.705829245460168,-2.16426570569947,2.58237734005865,-3.80640829555806
+2.3,-0.906890486294884,-1.83629821096442,3.93455844050654,-3.97476401453386
+2.4,-1.06860614272453,-1.37787653165824,5.11374520668299,-3.98465843534336
+2.5,-1.17918434708735,-0.81284329382283,6.09389607575295,-3.83569709865255
+2.6,-1.22882359069265,-0.17295878351365,6.62469772469187,-3.53381862288061
+2.7,-1.21221585705102,0.503754630673891,6.74037610639779,-3.09105795022395
+2.8,-1.12820436234541,1.17582411838087,6.533191358181,-2.52506655148928
+2.9,-0.978860954057995,1.79981035847128,5.85182622072886,-1.85840871765503
+3,-0.770999283563291,2.33562906493079,4.75245091059759,-1.1176619927957
+3.1,-0.515613103962611,2.74891875894459,3.39005668287868,-0.332357611269986
+3.2,-0.226326357533143,3.01046279160286,1.78219595985548,0.466196819401975
+3.3,0.0807823484948785,3.10169417161173,0.0444195098736388,1.24616545405351
+3.4,0.388335249621637,3.01614941528424,-1.75393602905129,1.97645340455444
+3.5,0.678348790457882,2.7560797824945,-3.43408611860293,2.62794639487516
+3.6,0.934021470108098,2.33567935225527,-4.86907935984763,3.17467145539661
+3.7,1.14100335615984,1.78100950577136,-6.08628991994047,3.59483238324651
+3.8,1.28712234301217,1.12495585256584,-6.94253943286844,3.87167868812595
+3.9,1.36381593553582,0.406902302885183,-7.28297214851448,3.99417338149842
+4,1.36767980657433,-0.330174021755641,-7.26531793532952,3.95743298649353
+4.1,1.29889049825954,-1.04224588166547,-6.8546938160307,3.76292222671909
+4.2,1.16155425178444,-1.68650054567169,-5.94967344220412,3.41839563235312
+4.3,0.964721270887307,-2.22697247599071,-4.74230088590455,2.93758839149645
+4.4,0.720465281131124,-2.63413817732492,-3.30905701113038,2.33966877156705
+4.5,0.443118721263638,-2.88581866922071,-1.7019965436784,1.64847394096703
+4.6,0.148752195959367,-2.9721968288911,-0.0363712415656969,0.891559656400984
+4.7,-0.145978041760561,-2.89314281403451,1.60780240616761,0.0991017018134311
+4.8,-0.424630255418812,-2.6573248762253,3.05425204912372,-0.697307124891926
+4.9,-0.672739948585826,-2.28475882540464,4.28045566687232,-1.46591651700771
+5,-0.878045085084117,-1.80273599561743,5.25923148399143,-2.17608444355748
+5.1,-1.03075790674249,-1.24353668430421,5.82481140361651,-2.79949875037417
+5.2,-1.12522261436471,-0.643004409169855,6.04748257510137,-3.31130587634261
+5.3,-1.1592124962359,-0.0379409362849684,5.93663216000357,-3.69110168645123
+5.4,-1.13383605650707,0.536222156936191,5.44971725872656,-3.92374492026596
+5.5,-1.05396244419096,1.0488134681975,4.70608941857451,-3.99996082620281
+5.6,-0.927027937689114,1.47376030771876,3.73555922576492,-3.91671091660527
+5.7,-0.762737838929616,1.79264354239405,2.61355404944852,-3.6773141026587
+5.8,-0.572312199675633,1.99548574983561,1.42458709467841,-3.29131437987484
+5.9,-0.367640689474866,2.07886112031207,0.262305797895423,-2.77410033910849
+6,-0.160346121295144,2.04848897718534,-0.810850096629428,-2.14629167200174
+6.1,0.0388399459182828,1.91690138358474,-1.77355404228442,-1.43291712894731
+6.2,0.220290472708866,1.70086688471167,-2.4993835921759,-0.662416701793245
+6.3,0.37674716357769,1.42178996137362,-2.98924153660423,0.134492188884547
+6.4,0.503311439080471,1.10348685128045,-3.29015849694185,0.926039300406156
+6.5,0.596974129613834,0.769202496718443,-3.33640210419521,1.68066814730656
+6.6,0.657272799105245,0.440521180295969,-3.17264695963287,2.36829405882889
+6.7,0.685844999000327,0.135894667251947,-2.86638329348033,2.96150355980979
+6.8,0.685753365960606,-0.130056648987914,-2.4258467093915,3.43664725942598
+6.9,0.66140326582697,-0.348319746055368,-1.92261772520869,3.77478267777642
+7,0.617826988441247,-0.514598278935145,-1.40501807933374,3.96242942277948
+7.1,0.560200530262187,-0.629615801215412,-0.916072884584751,3.99210661086545
+7.2,0.493413343237279,-0.69879973855337,-0.492918132824716,3.86263110619711
+7.3,0.421696974884124,-0.730300222058687,-0.171396746594032,3.57916468856202
+7.4,0.348266639065028,-0.734788651043527,0.0391562230663889,3.15300826950127
+7.5,0.275227865476597,-0.723747007930665,0.146209239141237,2.60115136062847
+7.6,0.203651184279578,-0.707781762836823,0.149580300874402,1.9455947554152
+7.7,0.133570306091302,-0.695777792179926,0.0729875409504199,1.21247342698282
+7.8,0.0642193033125314,-0.693970566176326,-0.0528266102662545,0.431014609197776
+7.9,-0.00565996556890208,-0.705189843622758,-0.176774620509094,-0.367627400910727
+8,-0.0773069806554265,-0.728754337147554,-0.272236743211374,-1.15161326666026
+8.1,-0.151676363174065,-0.760025340521132,-0.320431798418802,-1.88968794559386
+8.2,-0.229250063676891,-0.791068874381492,-0.26944342019663,-2.55242672939179
+8.3,-0.309518198381683,-0.812020729944363,-0.116985223730676,-3.11340831413719
+8.4,-0.390956185323783,-0.811937896451692,0.150000908551928,-3.55026813432602
+8.5,-0.470894163180363,-0.780014211551689,0.506511756278782,-3.84558996751823
+8.6,-0.545767023474155,-0.706877423058831,0.987756481582302,-3.98760026416638
+8.7,-0.610762318952124,-0.584754897081681,1.49232424767703,-3.97063752188253
+8.8,-0.660834371953323,-0.410270182511013,1.99274911516525,-3.7953779916725
+8.9,-0.690978933802869,-0.185167021665459,2.4515939666655,-3.46880871794233
+9,-0.69660755598576,0.0846502421423621,2.89889571627953,-3.0039489870867
+9.1,-0.673247221005856,0.38886209853353,3.18600736796181,-2.41933128962514
+9.2,-0.618026812346334,0.712716882427263,3.24837904850636,-1.73826248828759
+9.3,-0.530322613201749,1.03769639917485,3.14927230108912,-0.987894646946484
+9.4,-0.411125691046272,1.34339406863417,2.88048334532758,-0.19814256351347
+9.5,-0.263123935437519,1.60779762342013,2.3619797807729,0.599508838651809
+9.6,-0.0915023820210375,1.81056496541802,1.637461432577,1.37325971527958
+9.7,0.0964937857212142,1.93408194004453,0.767273551172426,2.09226306063079
+9.8,0.29216268897519,1.96313670409293,-0.221801959469345,2.72785448027254
+9.9,0.485613572634473,1.88840380409875,-1.27624885849323,3.25469495002842
+10,0.666301967708823,1.707692915511,0,3.65178100291051

Work 1/scripts/problem3_data_T20s.csv

@@ -0,0 +1,202 @@
+t,q,dq,ddq,u
+0,0,0,0,0
+0.1,0.00112730370377742,0.0336536743050961,0.657669343872878,0.794677323180245
+0.2,0.00883130084628362,0.130095105060834,1.23031152735571,1.5576733692346
+0.3,0.0288384132623469,0.277086967848714,1.6472957578342,2.25856989358014
+0.4,0.0653184832567522,0.456177260208145,1.85826392239339,2.86942436359809
+0.5,0.120381192475091,0.64441963262565,1.82183441394098,3.36588393923159
+0.6,0.19366224583284,0.816729955124557,1.5387129073771,3.72815634386891
+0.7,0.28233042826436,0.947731422726794,1.01198704123085,3.94179891995384
+0.8,0.381118481108189,1.01514724688817,0.281130829714293,3.99829441216602
+0.9,0.48271784224916,1.00127150126433,-0.606890939324855,3.89539052351278
+1,0.578248293996883,0.894322024572221,-1.54403616041735,3.63718970730273
+1.1,0.658338384140432,0.691502504394097,-2.46777849195839,3.23398561527836
+1.2,0.713750689364397,0.398398200996943,-3.35626893527373,2.7018527222046
+1.3,0.735600305235625,0.0284599263544737,-4.00825914367234,2.06200548728586
+1.4,0.71736732967013,-0.396782279453475,-4.38489881755735,1.33995260062362
+1.5,0.655285365929061,-0.849118356836855,-4.531083639236,0.564480032239469
+1.6,0.547892565795632,-1.29622623806606,-4.3244857319699,-0.23349657371032
+1.7,0.397254908342504,-1.70407791327366,-3.73168898607231,-1.02216440810733
+1.8,0.209300361028653,-2.04006080855522,-2.86613213766537,-1.77008177317941
+1.9,-0.00731550766185135,-2.27387198043844,-1.72922293231809,-2.44743156377088
+2,-0.241223605675537,-2.38106324008954,-0.381252753564326,-3.02720998123171
+2.1,-0.478944231224866,-2.34680237646659,1.08356113140267,-3.48630308965435
+2.2,-0.705829245460168,-2.16426570569947,2.58237734005865,-3.80640829555806
+2.3,-0.906890486294884,-1.83629821096442,3.93455844050654,-3.97476401453386
+2.4,-1.06860614272453,-1.37787653165824,5.11374520668299,-3.98465843534336
+2.5,-1.17918434708735,-0.81284329382283,6.09389607575295,-3.83569709865255
+2.6,-1.22882359069265,-0.17295878351365,6.62469772469187,-3.53381862288061
+2.7,-1.21221585705102,0.503754630673891,6.74037610639779,-3.09105795022395
+2.8,-1.12820436234541,1.17582411838087,6.533191358181,-2.52506655148928
+2.9,-0.978860954057995,1.79981035847128,5.85182622072886,-1.85840871765503
+3,-0.770999283563291,2.33562906493079,4.75245091059759,-1.1176619927957
+3.1,-0.515613103962611,2.74891875894459,3.39005668287868,-0.332357611269986
+3.2,-0.226326357533143,3.01046279160286,1.78219595985548,0.466196819401975
+3.3,0.0807823484948785,3.10169417161173,0.0444195098736388,1.24616545405351
+3.4,0.388335249621637,3.01614941528424,-1.75393602905129,1.97645340455444
+3.5,0.678348790457882,2.7560797824945,-3.43408611860293,2.62794639487516
+3.6,0.934021470108098,2.33567935225527,-4.86907935984763,3.17467145539661
+3.7,1.14100335615984,1.78100950577136,-6.08628991994047,3.59483238324651
+3.8,1.28712234301217,1.12495585256584,-6.94253943286844,3.87167868812595
+3.9,1.36381593553582,0.406902302885183,-7.28297214851448,3.99417338149842
+4,1.36767980657433,-0.330174021755641,-7.26531793532952,3.95743298649353
+4.1,1.29889049825954,-1.04224588166547,-6.8546938160307,3.76292222671909
+4.2,1.16155425178444,-1.68650054567169,-5.94967344220412,3.41839563235312
+4.3,0.964721270887307,-2.22697247599071,-4.74230088590455,2.93758839149645
+4.4,0.720465281131124,-2.63413817732492,-3.30905701113038,2.33966877156705
+4.5,0.443118721263638,-2.88581866922071,-1.7019965436784,1.64847394096703
+4.6,0.148752195959367,-2.9721968288911,-0.0363712415656969,0.891559656400984
+4.7,-0.145978041760561,-2.89314281403451,1.60780240616761,0.0991017018134311
+4.8,-0.424630255418812,-2.6573248762253,3.05425204912372,-0.697307124891926
+4.9,-0.672739948585826,-2.28475882540464,4.28045566687232,-1.46591651700771
+5,-0.878045085084117,-1.80273599561743,5.25923148399132,-2.17608444355748
+5.1,-1.0307579067425,-1.24353668430421,5.82481140361667,-2.79949875037417
+5.2,-1.12522261436471,-0.64300440916985,6.04748257510137,-3.31130587634261
+5.3,-1.1592124962359,-0.0379409362849631,5.93663216000362,-3.69110168645123
+5.4,-1.13383605650707,0.536222156936198,5.4497172587264,-3.92374492026597
+5.5,-1.05396244419096,1.0488134681975,4.70608941857471,-3.99996082620281
+5.6,-0.927027937689112,1.47376030771876,3.73555922576465,-3.91671091660527
+5.7,-0.762737838929616,1.79264354239405,2.61355404944882,-3.6773141026587
+5.8,-0.572312199675631,1.99548574983561,1.42458709467826,-3.29131437987483
+5.9,-0.367640689474864,2.07886112031207,0.262305797895213,-2.77410033910849
+6,-0.160346121295144,2.04848897718534,-0.810850096629073,-2.14629167200174
+6.1,0.0388399459182844,1.91690138358474,-1.7735540422846,-1.43291712894731
+6.2,0.220290472708867,1.70086688471167,-2.49938359217591,-0.662416701793238
+6.3,0.376747163577691,1.42178996137362,-2.98924153660433,0.134492188884554
+6.4,0.503311439080471,1.10348685128045,-3.29015849694172,0.926039300406156
+6.5,0.596974129613834,0.769202496718443,-3.33640210419518,1.68066814730656
+6.6,0.657272799105245,0.440521180295967,-3.17264695963293,2.3682940588289
+6.7,0.685844999000327,0.135894667251945,-2.86638329348033,2.96150355980979
+6.8,0.685753365960606,-0.130056648987916,-2.42584670939147,3.43664725942599
+6.9,0.66140326582697,-0.348319746055368,-1.9226177252087,3.77478267777642
+7,0.617826988441247,-0.514598278935145,-1.4050180793338,3.96242942277948
+7.1,0.560200530262186,-0.629615801215413,-0.916072884584706,3.99210661086545
+7.2,0.493413343237278,-0.698799738553371,-0.492918132824704,3.86263110619711
+7.3,0.421696974884123,-0.730300222058687,-0.171396746593982,3.57916468856201
+7.4,0.348266639065028,-0.734788651043527,0.0391562230663334,3.15300826950127
+7.5,0.275227865476597,-0.723747007930665,0.146209239141171,2.60115136062847
+7.6,0.203651184279577,-0.707781762836823,0.149580300874469,1.94559475541519
+7.7,0.133570306091302,-0.695777792179925,0.0729875409504171,1.21247342698281
+7.8,0.0642193033125308,-0.693970566176327,-0.0528266102661962,0.431014609197769
+7.9,-0.00565996556890208,-0.705189843622758,-0.176774620509154,-0.367627400910727
+8,-0.0773069806554265,-0.728754337147554,-0.272236743211374,-1.15161326666026
+8.1,-0.151676363174065,-0.760025340521132,-0.320431798418941,-1.88968794559386
+8.2,-0.229250063676892,-0.791068874381493,-0.269443420196352,-2.5524267293918
+8.3,-0.309518198381683,-0.812020729944363,-0.116985223730814,-3.11340831413719
+8.4,-0.390956185323783,-0.811937896451692,0.150000908551928,-3.55026813432602
+8.5,-0.470894163180363,-0.780014211551689,0.506511756278782,-3.84558996751823
+8.6,-0.545767023474155,-0.706877423058831,0.987756481582191,-3.98760026416638
+8.7,-0.610762318952125,-0.584754897081678,1.49232424767726,-3.97063752188253
+8.8,-0.660834371953323,-0.410270182511013,1.99274911516514,-3.7953779916725
+8.9,-0.690978933802869,-0.185167021665459,2.4515939666655,-3.46880871794233
+9,-0.69660755598576,0.0846502421423621,2.89889571627953,-3.0039489870867
+9.1,-0.673247221005856,0.38886209853353,3.18600736796194,-2.41933128962514
+9.2,-0.618026812346333,0.712716882427269,3.24837904850609,-1.73826248828757
+9.3,-0.530322613201749,1.03769639917485,3.14927230108926,-0.987894646946484
+9.4,-0.411125691046272,1.34339406863417,2.88048334532758,-0.19814256351347
+9.5,-0.263123935437519,1.60779762342013,2.36197978077322,0.599508838651809
+9.6,-0.0915023820210343,1.81056496541803,1.63746143257671,1.37325971527959
+9.7,0.0964937857212176,1.93408194004453,0.767273551172054,2.0922630606308
+9.8,0.29216268897519,1.96313670409293,-0.221801959468998,2.72785448027254
+9.9,0.485613572634473,1.88840380409875,-1.26370594814139,3.25469495002842
+10,0.666427396812341,1.70781029255568,-2.32502138310778,3.65178100291051
+10.1,0.823991007159132,1.42465365235776,-3.33319403023266,3.9032820710679
+10.2,0.948222677203596,1.04894121731209,-4.13865076550263,3.99917160057068
+10.3,1.03106783959303,0.598156775647966,-4.76046725558521,3.93562677847447
+10.4,1.06630832942662,0.0947352695087426,-5.2178509060175,3.71518093630897
+10.5,1.04937031020003,-0.434312443933761,-5.31641723595164,3.34662255414422
+10.6,0.979268118613925,-0.959752129511336,-5.08241943079766,2.84464489162393
+10.7,0.858341732719843,-1.45161171663342,-4.62975436959168,2.22926021407065
+10.8,0.691117803129844,-1.88025259648709,-3.867248155187,1.52500196661977
+10.9,0.485221391987975,-2.21970646439723,-2.85754093317886,0.759946703181751
+11,0.250749571514318,-2.44943291557137,-1.67161013024184,-0.0354052371616155
+11.1,-0.000438350261758313,-2.55312745846465,-0.375763795189948,-0.829345682427035
+11.2,-0.255383909989734,-2.52309987678432,0.952965679522388,-1.59022273248573
+11.3,-0.500799812922485,-2.36022031937371,2.28511009480977,-2.28770262043824
+11.4,-0.723364614907139,-2.07139984431106,3.47086400980713,-2.89397902417698
+11.5,-0.911220776793722,-1.6717298045001,4.42872084424201,-3.38488161670068
+11.6,-1.05478973023788,-1.18365614859635,5.21919831200576,-3.74083966077816
+11.7,-1.14616670056199,-0.633909431993279,5.71312747678929,-3.9476622324826
+11.8,-1.1804123961182,-0.0529039972742618,5.81110139261212,-3.99710396854651
+11.9,-1.15654707774829,0.527556150777705,5.65764025054154,-3.88719378297545
+12,-1.07610535687297,1.07571672648671,5.2163127831585,-3.6223134480265
+12.1,-0.943500508166058,1.56146712848275,4.43697105900003,-3.21302290677582
+12.2,-0.766525948869148,1.96035615835787,3.4609293991261,-2.6756392815121
+12.3,-0.554942095580977,2.25250630665306,2.3272368398947,-2.03158636156249
+12.4,-0.32008587389386,2.42370796171182,1.08931263730755,-1.3065405044189
+12.5,-0.0743365258336663,2.46879082652308,-0.1770192409213,-0.529407000391092
+12.6,0.169642629817314,2.38887320745735,-1.41378215966272,0.2688322901019
+12.7,0.399483963871667,2.19126967373951,-2.49538473357942,1.05635408553788
+12.8,0.604371450590226,1.89125156271722,-3.41634101074438,1.80176237710156
+12.9,0.775095527201341,1.50871959992942,-4.16363340087401,2.47534008848015
+13,0.904183269803716,1.06691912927852,-4.60578356433584,3.05023380191841
+13.1,0.987213176762733,0.591483046925517,-4.80212576778471,3.50352431924356
+13.2,1.0222218260439,0.108629047861588,-4.76881448780202,3.81714037797079
+13.3,1.00954233044705,-0.356205183827859,-4.45876635868854,3.97857909551135
+13.4,0.952275171263315,-0.780824415768228,-3.96220376540242,3.98140441964624
+13.5,0.855385974425555,-1.14594637692938,-3.2952486798697,3.82550371361801
+13.6,0.725544290789098,-1.4371149546949,-2.50230123302698,3.5170922466029
+13.7,0.570679594822371,-1.64564000854823,-1.64702732564788,3.06846541054212
+13.8,0.399344625599165,-1.76678408803482,-0.780867714276601,2.49750854166557
+13.9,0.220200979233193,-1.80188062145097,0.0469489535935452,1.82698388857678
+14,0.0415268224031566,-1.75709452297478,0.824257478983237,1.08362315323148
+14.1,-0.128904759637047,-1.64114478327725,1.4702707582532,0.297061782337445
+14.2,-0.284633634094719,-1.46622301139372,1.97079614706245,-0.501342504385716
+14.3,-0.420654547081767,-1.24683654154735,2.3617661103195,-1.27975984753679
+14.4,-0.533057798965619,-0.997314523257609,2.5931017548774,-2.00715720408228
+14.5,-0.619530033300698,-0.731801275213912,2.66333555853092,-2.65453553685187
+14.6,-0.679368912050467,-0.462916466781307,2.66219437240927,-3.19608591463845
+14.7,-0.712585847076143,-0.20205757711387,2.55190149362584,-3.61021843284074
+14.8,-0.720283767165562,0.0418838528707965,2.32163308146018,-3.88042293482874
+14.9,-0.704765356440378,0.263312972330474,2.07883133331249,-3.9959272197878
+15,-0.668458632382069,0.458661712399707,1.81834120086973,-3.95212649637145
+15.1,-0.613968496315063,0.62613158162342,1.53630267476219,-3.75076696120112
+15.2,-0.544115333500436,0.766427475271895,1.27216427812542,-3.39987618351731
+15.3,-0.461540527904553,0.881036343301911,1.02622940697853,-2.91344307132637
+15.4,-0.368703428238886,0.971781415266678,0.797298150514092,-2.31086017778294
+15.5,-0.267893347068078,1.04105962463048,0.592183486473996,-1.61615058129226
+15.6,-0.16116143103253,1.09030538050508,0.394598168220228,-0.857010161183551
+15.7,-0.0504835333147792,1.11987929835739,0.196387416210717,-0.0637034504004072
+15.8,0.0621582385650784,1.12950638006746,-0.00542612113233337,0.732142915922352
+15.9,0.174745749233613,1.11775704891626,-0.239453023627634,1.49880105459783
+16,0.284938729665871,1.08162158397329,-0.499980045730242,2.20570672496676
+16.1,0.390131909640826,1.01802771910313,-0.781014098836352,2.82467782872134
+16.2,0.487514948627418,0.92408182259519,-1.081230681301,3.33103794123112
+16.3,0.574085680801,0.797145817515727,-1.46172506984881,3.70460008272211
+16.4,0.646039162276094,0.635051860971208,-1.81897397838919,3.93047150945656
+16.5,0.699802903967296,0.437977095267359,-2.13057734233654,3.99964744042907
+16.6,0.732260872235133,0.208731503507477,-2.39893781212285,3.90937004956903
+16.7,0.740729462381741,-0.0478983366353404,-2.68422717530223,3.66323841156328
+16.8,0.722355780775327,-0.324577270594466,-2.85733049764952,3.27106501810577
+16.9,0.675408794192417,-0.611199331914063,-2.86159329006487,2.74848458481898
+17,0.599845874708859,-0.895577408933868,-2.75462306175829,2.1163307444801
+17.1,0.496736724607718,-1.16413733097779,-2.55068385730742,1.39980547582665
+17.2,0.368120735933503,-1.40174697538996,-2.16745299394969,0.62747438019364
+17.3,0.217830217319791,-1.59394033340686,-1.63449153404535,-0.169872138867806
+17.4,0.0511947833656253,-1.72774820042218,-0.990788498984157,-0.960446391815098
+17.5,-0.125348535578382,-1.79095853322587,-0.244208088454018,-1.7127306779846
+17.6,-0.304333935406929,-1.77494222941117,0.565762756929766,-2.39673379685706
+17.7,-0.477661707666179,-1.67577850449359,1.41246201984706,-2.98518670257967
+17.8,-0.636864859726958,-1.49279172650053,2.25451472115851,-3.45462963477182
+17.9,-0.773522864576152,-1.22990903082874,2.9824331051199,-3.78634738513984
+18,-0.880356538374148,-0.896795339672411,3.59912160219564,-3.96711541377246
+18.1,-0.951198996150186,-0.507078295983122,4.13585113634964,-3.98972706981459
+18.2,-0.980682942562729,-0.0782624790182752,4.41974070040262,-3.85328089789504
+18.3,-0.965969481971245,0.369209230986198,4.44685044666184,-3.56321657630745
+18.4,-0.906787516913142,0.813039716275539,4.32412725327608,-3.13109805420262
+18.5,-0.804364279322279,1.22992832619715,3.95418668923767,-2.574152533428
+18.6,-0.662399174839039,1.59732144999188,3.33450271279904,-1.91458367435366
+18.7,-0.487089043227809,1.89570309190105,2.56072149023441,-1.17868640600103
+18.8,-0.286171696714235,2.10752289091859,1.63380699481198,-0.395798630201158
+18.9,-0.0689162802525407,2.2197528765431,0.60117181028112,0.402868387970002
+19,0.154350854311965,2.22590557055069,-0.484649769110557,1.18547431483754
+19.1,0.372771491185364,2.12370409200131,-1.56606702536783,1.92081912175304
+19.2,0.575531457805086,1.91658596997832,-2.54192275532618,2.57958693177947
+19.3,0.752872196871545,1.61513069870749,-3.41107769073975,3.13551475119317
+19.4,0.896102159030608,1.23422981873053,-4.15639887813154,3.56643949216576
+19.5,0.997768132408354,0.792893829276582,-4.62323032183498,3.85518154513635
+19.6,1.05320180256775,0.313605645687501,-4.84812446443323,3.99022967563122
+19.7,1.06015422808282,-0.17954698751638,-4.91488492044845,3.96619994085656
+19.8,1.0179578043934,-0.660879466111878,-4.68136281855116,3.78405033050763
+19.9,0.928947752518464,-1.10636537743868,-4.16245180252246,3.45104257474272
+20,0.798313182618308,-1.49461244763109,0,2.9804526419174

Work 1/scripts/problem3_data_T40s.csv

@@ -0,0 +1,402 @@
+t,q,dq,ddq,u
+0,0,0,0,0
+0.1,0.00112730370377742,0.0336536743050961,0.657669343872878,0.794677323180245
+0.2,0.00883130084628362,0.130095105060834,1.23031152735571,1.5576733692346
+0.3,0.0288384132623469,0.277086967848714,1.6472957578342,2.25856989358014
+0.4,0.0653184832567522,0.456177260208145,1.85826392239339,2.86942436359809
+0.5,0.120381192475091,0.64441963262565,1.82183441394098,3.36588393923159
+0.6,0.19366224583284,0.816729955124557,1.5387129073771,3.72815634386891
+0.7,0.28233042826436,0.947731422726794,1.01198704123085,3.94179891995384
+0.8,0.381118481108189,1.01514724688817,0.281130829714293,3.99829441216602
+0.9,0.48271784224916,1.00127150126433,-0.606890939324855,3.89539052351278
+1,0.578248293996883,0.894322024572221,-1.54403616041735,3.63718970730273
+1.1,0.658338384140432,0.691502504394097,-2.46777849195839,3.23398561527836
+1.2,0.713750689364397,0.398398200996943,-3.35626893527373,2.7018527222046
+1.3,0.735600305235625,0.0284599263544737,-4.00825914367234,2.06200548728586
+1.4,0.71736732967013,-0.396782279453475,-4.38489881755735,1.33995260062362
+1.5,0.655285365929061,-0.849118356836855,-4.531083639236,0.564480032239469
+1.6,0.547892565795632,-1.29622623806606,-4.3244857319699,-0.23349657371032
+1.7,0.397254908342504,-1.70407791327366,-3.73168898607231,-1.02216440810733
+1.8,0.209300361028653,-2.04006080855522,-2.86613213766537,-1.77008177317941
+1.9,-0.00731550766185135,-2.27387198043844,-1.72922293231809,-2.44743156377088
+2,-0.241223605675537,-2.38106324008954,-0.381252753564326,-3.02720998123171
+2.1,-0.478944231224866,-2.34680237646659,1.08356113140267,-3.48630308965435
+2.2,-0.705829245460168,-2.16426570569947,2.58237734005865,-3.80640829555806
+2.3,-0.906890486294884,-1.83629821096442,3.93455844050654,-3.97476401453386
+2.4,-1.06860614272453,-1.37787653165824,5.11374520668299,-3.98465843534336
+2.5,-1.17918434708735,-0.81284329382283,6.09389607575295,-3.83569709865255
+2.6,-1.22882359069265,-0.17295878351365,6.62469772469187,-3.53381862288061
+2.7,-1.21221585705102,0.503754630673891,6.74037610639779,-3.09105795022395
+2.8,-1.12820436234541,1.17582411838087,6.533191358181,-2.52506655148928
+2.9,-0.978860954057995,1.79981035847128,5.85182622072886,-1.85840871765503
+3,-0.770999283563291,2.33562906493079,4.75245091059759,-1.1176619927957
+3.1,-0.515613103962611,2.74891875894459,3.39005668287868,-0.332357611269986
+3.2,-0.226326357533143,3.01046279160286,1.78219595985548,0.466196819401975
+3.3,0.0807823484948785,3.10169417161173,0.0444195098736388,1.24616545405351
+3.4,0.388335249621637,3.01614941528424,-1.75393602905129,1.97645340455444
+3.5,0.678348790457882,2.7560797824945,-3.43408611860293,2.62794639487516
+3.6,0.934021470108098,2.33567935225527,-4.86907935984763,3.17467145539661
+3.7,1.14100335615984,1.78100950577136,-6.08628991994047,3.59483238324651
+3.8,1.28712234301217,1.12495585256584,-6.94253943286844,3.87167868812595
+3.9,1.36381593553582,0.406902302885183,-7.28297214851448,3.99417338149842
+4,1.36767980657433,-0.330174021755641,-7.26531793532952,3.95743298649353
+4.1,1.29889049825954,-1.04224588166547,-6.8546938160307,3.76292222671909
+4.2,1.16155425178444,-1.68650054567169,-5.94967344220412,3.41839563235312
+4.3,0.964721270887307,-2.22697247599071,-4.74230088590455,2.93758839149645
+4.4,0.720465281131124,-2.63413817732492,-3.30905701113038,2.33966877156705
+4.5,0.443118721263638,-2.88581866922071,-1.7019965436784,1.64847394096703
+4.6,0.148752195959367,-2.9721968288911,-0.0363712415656969,0.891559656400984
+4.7,-0.145978041760561,-2.89314281403451,1.60780240616761,0.0991017018134311
+4.8,-0.424630255418812,-2.6573248762253,3.05425204912372,-0.697307124891926
+4.9,-0.672739948585826,-2.28475882540464,4.28045566687232,-1.46591651700771
+5,-0.878045085084117,-1.80273599561743,5.25923148399132,-2.17608444355748
+5.1,-1.0307579067425,-1.24353668430421,5.82481140361667,-2.79949875037417
+5.2,-1.12522261436471,-0.64300440916985,6.04748257510137,-3.31130587634261
+5.3,-1.1592124962359,-0.0379409362849631,5.93663216000362,-3.69110168645123
+5.4,-1.13383605650707,0.536222156936198,5.4497172587264,-3.92374492026597
+5.5,-1.05396244419096,1.0488134681975,4.70608941857471,-3.99996082620281
+5.6,-0.927027937689112,1.47376030771876,3.73555922576465,-3.91671091660527
+5.7,-0.762737838929616,1.79264354239405,2.61355404944882,-3.6773141026587
+5.8,-0.572312199675631,1.99548574983561,1.42458709467826,-3.29131437987483
+5.9,-0.367640689474864,2.07886112031207,0.262305797895213,-2.77410033910849
+6,-0.160346121295144,2.04848897718534,-0.810850096629073,-2.14629167200174
+6.1,0.0388399459182844,1.91690138358474,-1.7735540422846,-1.43291712894731
+6.2,0.220290472708867,1.70086688471167,-2.49938359217591,-0.662416701793238
+6.3,0.376747163577691,1.42178996137362,-2.98924153660433,0.134492188884554
+6.4,0.503311439080471,1.10348685128045,-3.29015849694172,0.926039300406156
+6.5,0.596974129613834,0.769202496718443,-3.33640210419518,1.68066814730656
+6.6,0.657272799105245,0.440521180295967,-3.17264695963293,2.3682940588289
+6.7,0.685844999000327,0.135894667251945,-2.86638329348033,2.96150355980979
+6.8,0.685753365960606,-0.130056648987916,-2.42584670939147,3.43664725942599
+6.9,0.66140326582697,-0.348319746055368,-1.9226177252087,3.77478267777642
+7,0.617826988441247,-0.514598278935145,-1.4050180793338,3.96242942277948
+7.1,0.560200530262186,-0.629615801215413,-0.916072884584706,3.99210661086545
+7.2,0.493413343237278,-0.698799738553371,-0.492918132824704,3.86263110619711
+7.3,0.421696974884123,-0.730300222058687,-0.171396746593982,3.57916468856201
+7.4,0.348266639065028,-0.734788651043527,0.0391562230663334,3.15300826950127
+7.5,0.275227865476597,-0.723747007930665,0.146209239141171,2.60115136062847
+7.6,0.203651184279577,-0.707781762836823,0.149580300874469,1.94559475541519
+7.7,0.133570306091302,-0.695777792179925,0.0729875409504171,1.21247342698281
+7.8,0.0642193033125308,-0.693970566176327,-0.0528266102661962,0.431014609197769
+7.9,-0.00565996556890208,-0.705189843622758,-0.176774620509154,-0.367627400910727
+8,-0.0773069806554265,-0.728754337147554,-0.272236743211374,-1.15161326666026
+8.1,-0.151676363174065,-0.760025340521132,-0.320431798418941,-1.88968794559386
+8.2,-0.229250063676892,-0.791068874381493,-0.269443420196352,-2.5524267293918
+8.3,-0.309518198381683,-0.812020729944363,-0.116985223730814,-3.11340831413719
+8.4,-0.390956185323783,-0.811937896451692,0.150000908551928,-3.55026813432602
+8.5,-0.470894163180363,-0.780014211551689,0.506511756278782,-3.84558996751823
+8.6,-0.545767023474155,-0.706877423058831,0.987756481582191,-3.98760026416638
+8.7,-0.610762318952125,-0.584754897081678,1.49232424767726,-3.97063752188253
+8.8,-0.660834371953323,-0.410270182511013,1.99274911516514,-3.7953779916725
+8.9,-0.690978933802869,-0.185167021665459,2.4515939666655,-3.46880871794233
+9,-0.69660755598576,0.0846502421423621,2.89889571627953,-3.0039489870867
+9.1,-0.673247221005856,0.38886209853353,3.18600736796194,-2.41933128962514
+9.2,-0.618026812346333,0.712716882427269,3.24837904850609,-1.73826248828757
+9.3,-0.530322613201749,1.03769639917485,3.14927230108926,-0.987894646946484
+9.4,-0.411125691046272,1.34339406863417,2.88048334532758,-0.19814256351347
+9.5,-0.263123935437519,1.60779762342013,2.36197978077322,0.599508838651809
+9.6,-0.0915023820210343,1.81056496541803,1.63746143257671,1.37325971527959
+9.7,0.0964937857212176,1.93408194004453,0.767273551172054,2.0922630606308
+9.8,0.29216268897519,1.96313670409293,-0.221801959468998,2.72785448027254
+9.9,0.485613572634473,1.88840380409875,-1.26370594814139,3.25469495002842
+10,0.666427396812341,1.70781029255568,-2.32502138310754,3.65178100291051
+10.1,0.823991007159134,1.42465365235776,-3.33319403023297,3.90328207106791
+10.2,0.948222677203598,1.04894121731208,-4.13865076550263,3.99917160057068
+10.3,1.03106783959304,0.598156775647957,-4.76046725558523,3.93562677847446
+10.4,1.06630832942662,0.0947352695087333,-5.21785090601743,3.71518093630896
+10.5,1.04937031020003,-0.434312443933761,-5.31641723595177,3.34662255414422
+10.6,0.979268118613924,-0.959752129511345,-5.08241943079759,2.84464489162392
+10.7,0.858341732719841,-1.45161171663343,-4.62975436959169,2.22926021407063
+10.8,0.691117803129841,-1.8802525964871,-3.86724815518654,1.52500196661976
+10.9,0.485221391987975,-2.21970646439723,-2.85754093317921,0.759946703181751
+11,0.250749571514318,-2.44943291557137,-1.6716101302423,-0.0354052371616155
+11.1,-0.000438350261762848,-2.55312745846465,-0.375763795189493,-0.829345682427049
+11.2,-0.255383909989738,-2.52309987678432,0.952965679522412,-1.59022273248574
+11.3,-0.50079981292249,-2.3602203193737,2.28511009481016,-2.28770262043826
+11.4,-0.723364614907139,-2.07139984431106,3.47086400980671,-2.89397902417698
+11.5,-0.911220776793722,-1.6717298045001,4.42872084424178,-3.38488161670068
+11.6,-1.05478973023789,-1.18365614859634,5.21919831200609,-3.74083966077816
+11.7,-1.14616670056199,-0.633909431993268,5.71312747678929,-3.9476622324826
+11.8,-1.1804123961182,-0.052903997274252,5.811101392612,-3.99710396854651
+11.9,-1.15654707774829,0.527556150777705,5.65764025054154,-3.88719378297545
+12,-1.07610535687297,1.07571672648671,5.21631278315875,-3.6223134480265
+12.1,-0.943500508166056,1.56146712848275,4.43697105899985,-3.21302290677581
+12.2,-0.766525948869145,1.96035615835788,3.46092939912567,-2.67563928151209
+12.3,-0.554942095580977,2.25250630665306,2.32723683989551,-2.03158636156249
+12.4,-0.320085873893855,2.42370796171182,1.08931263730662,-1.30654050441889
+12.5,-0.0743365258336663,2.46879082652308,-0.177019240920412,-0.529407000391092
+12.6,0.169642629817318,2.38887320745735,-1.41378215966316,0.268832290101914
+12.7,0.399483963871671,2.1912696737395,-2.4953847335798,1.05635408553789
+12.8,0.604371450590226,1.89125156271722,-3.41634101074372,1.80176237710156
+12.9,0.775095527201344,1.50871959992941,-4.16363340087454,2.47534008848016
+13,0.904183269803716,1.06691912927852,-4.60578356433547,3.05023380191841
+13.1,0.987213176762734,0.591483046925509,-4.80212576778489,3.50352431924356
+13.2,1.0222218260439,0.108629047861579,-4.76881448780196,3.81714037797079
+13.3,1.00954233044705,-0.356205183827859,-4.45876635868865,3.97857909551135
+13.4,0.952275171263314,-0.780824415768235,-3.96220376540213,3.98140441964624
+13.5,0.855385974425555,-1.14594637692938,-3.2952486798701,3.82550371361801
+13.6,0.725544290789095,-1.4371149546949,-2.50230123302676,3.51709224660289
+13.7,0.570679594822368,-1.64564000854823,-1.64702732564755,3.06846541054211
+13.8,0.399344625599165,-1.76678408803482,-0.7808677142772,2.49750854166557
+13.9,0.22020097923319,-1.80188062145097,0.0469489535941892,1.82698388857677
+14,0.0415268224031566,-1.75709452297478,0.824257478982615,1.08362315323148
+14.1,-0.12890475963705,-1.64114478327725,1.47027075825354,0.297061782337431
+14.2,-0.284633634094722,-1.46622301139371,1.97079614706269,-0.501342504385731
+14.3,-0.420654547081767,-1.24683654154735,2.36176611031907,-1.27975984753679
+14.4,-0.533057798965621,-0.997314523257605,2.59310175487771,-2.0071572040823
+14.5,-0.619530033300698,-0.731801275213912,2.66333555853069,-2.65453553685187
+14.6,-0.679368912050468,-0.462916466781302,2.66219437240939,-3.19608591463846
+14.7,-0.712585847076144,-0.202057577113865,2.55190149362583,-3.61021843284075
+14.8,-0.720283767165562,0.0418838528707965,2.32163308146019,-3.88042293482874
+14.9,-0.704765356440377,0.263312972330478,2.0788313333124,-3.9959272197878
+15,-0.668458632382069,0.458661712399707,1.81834120086989,-3.95212649637145
+15.1,-0.613968496315062,0.626131581623423,1.5363026747621,-3.75076696120112
+15.2,-0.544115333500434,0.766427475271897,1.27216427812526,-3.3998761835173
+15.3,-0.461540527904553,0.881036343301911,1.02622940697884,-2.91344307132637
+15.4,-0.368703428238884,0.97178141526668,0.797298150513748,-2.31086017778293
+15.5,-0.267893347068078,1.04105962463048,0.592183486474357,-1.61615058129226
+15.6,-0.161161431032528,1.09030538050508,0.394598168220051,-0.857010161183537
+15.7,-0.0504835333147771,1.11987929835739,0.196387416210489,-0.063703450400393
+15.8,0.0621582385650784,1.12950638006746,-0.00542612113192259,0.732142915922352
+15.9,0.174745749233615,1.11775704891626,-0.239453023628034,1.49880105459785
+16,0.284938729665871,1.08162158397329,-0.499980045730042,2.20570672496676
+16.1,0.390131909640826,1.01802771910313,-0.781014098836352,2.82467782872134
+16.2,0.487514948627418,0.92408182259519,-1.081230681301,3.33103794123112
+16.3,0.574085680801,0.797145817515727,-1.46172506984858,3.70460008272211
+16.4,0.646039162276096,0.635051860971201,-1.81897397838964,3.93047150945656
+16.5,0.699802903967296,0.437977095267359,-2.13057734233631,3.99964744042907
+16.6,0.732260872235133,0.208731503507477,-2.39893781212285,3.90937004956903
+16.7,0.740729462381741,-0.0478983366353404,-2.68422717530223,3.66323841156328
+16.8,0.722355780775327,-0.324577270594466,-2.85733049764975,3.27106501810577
+16.9,0.675408794192415,-0.611199331914073,-2.86159329006442,2.74848458481896
+17,0.599845874708859,-0.895577408933868,-2.75462306175851,2.1163307444801
+17.1,0.496736724607718,-1.16413733097779,-2.55068385730742,1.39980547582665
+17.2,0.368120735933503,-1.40174697538996,-2.16745299394969,0.62747438019364
+17.3,0.217830217319791,-1.59394033340686,-1.63449153404597,-0.169872138867806
+17.4,0.0511947833656191,-1.72774820042218,-0.990788498982925,-0.960446391815126
+17.5,-0.125348535578382,-1.79095853322587,-0.244208088454634,-1.7127306779846
+17.6,-0.304333935406929,-1.77494222941117,0.565762756929766,-2.39673379685706
+17.7,-0.477661707666179,-1.67577850449359,1.41246201984706,-2.98518670257967
+17.8,-0.636864859726958,-1.49279172650053,2.25451472115812,-3.45462963477182
+17.9,-0.773522864576156,-1.22990903082873,2.98243310512067,-3.78634738513985
+18,-0.880356538374148,-0.896795339672411,3.59912160219525,-3.96711541377246
+18.1,-0.951198996150186,-0.507078295983122,4.13585113634964,-3.98972706981459
+18.2,-0.980682942562729,-0.0782624790182752,4.41974070040262,-3.85328089789504
+18.3,-0.965969481971245,0.369209230986198,4.44685044666215,-3.56321657630745
+18.4,-0.906787516913139,0.813039716275554,4.32412725327548,-3.1310980542026
+18.5,-0.804364279322279,1.22992832619715,3.95418668923797,-2.574152533428
+18.6,-0.662399174839039,1.59732144999188,3.33450271279904,-1.91458367435366
+18.7,-0.487089043227809,1.89570309190105,2.56072149023441,-1.17868640600103
+18.8,-0.286171696714235,2.10752289091859,1.63380699481278,-0.395798630201158
+18.9,-0.0689162802525327,2.21975287654311,0.601171810279521,0.40286838797003
+19,0.154350854311965,2.22590557055069,-0.484649769109757,1.18547431483754
+19.1,0.372771491185364,2.12370409200131,-1.56606702536715,1.92081912175304
+19.2,0.575531457805093,1.91658596997831,-2.54192275532754,2.57958693177949
+19.3,0.752872196871545,1.61513069870749,-3.41107769073864,3.13551475119317
+19.4,0.896102159030612,1.23422981873052,-4.15639887813241,3.56643949216578
+19.5,0.997768132408354,0.792893829276582,-4.62323032183455,3.85518154513635
+19.6,1.05320180256775,0.313605645687501,-4.8481244644333,3.99022967563122
+19.7,1.06015422808282,-0.179546987516398,-4.91488492044831,3.96619994085656
+19.8,1.0179578043934,-0.660879466111878,-4.68136281855165,3.78405033050763
+19.9,0.92894775251846,-1.10636537743869,-4.16180978968383,3.4510425747427
+20,0.798319602746686,-1.49481248709571,-3.51517542213668,2.9804526419174
+20.1,0.632539698753545,-1.80722433110446,-2.68738958893209,2.39104146762104
+20.2,0.439885898871083,-2.02917282735088,-1.73208782361014,1.70630701537829
+20.3,0.22991122075252,-2.15237819552754,-0.710795377392193,0.953547486995596
+20.4,0.012828588860035,-2.17230006411957,0.315922489801301,0.162773029399459
+20.5,-0.201094818134437,-2.0903027376454,1.28748934567219,-0.634490675218836
+20.6,-0.402143331672187,-1.91412015001226,2.19263638615833,-1.40645923886724
+20.7,-0.581265481348354,-1.6547701833087,2.9635186130253,-2.12235671100081
+20.8,-0.730752444894268,-1.32724438029782,3.52120350121379,-2.75364251855066
+20.9,-0.845027373428044,-0.949786544885419,3.93849985790889,-3.27514928850737
+21,-0.919917303382731,-0.542076550670578,4.17036962574386,-3.66608619166254
+21.1,-0.95310353707998,-0.124594019434549,4.13445653213561,-3.91086780736008
+21.2,-0.944945205455872,0.283218914722046,3.93971722599954,-3.99973546503521
+21.3,-0.897389701571769,0.663372154026642,3.6052377817895,-3.92914629161454
+21.4,-0.813781819869771,0.999468590505024,3.08953900601842,-3.70191445468532
+21.5,-0.699278548107589,1.27936657263204,2.47384718357586,-3.32709897051439
+21.6,-0.560036804509648,1.49417578796122,1.79612332768816,-2.81964254965701
+21.7,-0.402833827634826,1.63778391118715,1.07609516888514,-2.19977587824139
+21.8,-0.234869899071152,1.70891730570789,0.356936923752682,-1.49221108435449
+21.9,-0.0633366012699514,1.70932239145856,-0.342855223246863,-0.725156543478779
+22,0.104768144298781,1.64296382408564,-0.965614133653403,0.0708077004216543
+22.1,0.263216748530978,1.5172688187972,-1.50576113296801,0.863949064752869
+22.2,0.406607741433496,1.3414083745033,-1.97934131219715,1.62264750622134
+22.3,0.530205321214043,1.12521365347596,-2.32218932107076,2.31665611217708
+22.4,0.630581007783881,0.879321210604183,-2.54362052236839,2.91830694957141
+22.5,0.705520489130036,0.614202224639568,-2.71503029066132,3.40361409813647
+22.6,0.753309667569578,0.340232064407701,-2.76348454329707,3.75322989333421
+22.7,0.773464000576149,0.0667830029912097,-2.68306683484107,3.95321625668655
+22.8,0.766787665234309,-0.198274692895016,-2.57432067434318,3.99560036298008
+22.9,0.734368123149037,-0.447839416471281,-2.40086929997348,3.87869249164768
+23,0.67793988806403,-0.675675555199043,-2.14740377403967,3.60715339059524
+23.1,0.600037615238627,-0.877441627681105,-1.86836117031645,3.19180846689054
+23.2,0.50345173071006,-1.04925827423152,-1.55673369364595,2.64921621194497
+23.3,0.391298509245033,-1.187710197628,-1.20786651505222,2.00100806671435
+23.4,0.267066622629483,-1.29073839348898,-0.843475158509443,1.27302604440995
+23.5,0.134399984428839,-1.35621124674887,-0.458344239344627,0.494292490980896
+23.6,-0.00285009616525078,-1.38214313844087,-0.059791542750473,-0.304146944233386
+23.7,-0.140698092186846,-1.3677196718212,0.341594495654124,-1.0904610005723
+23.8,-0.275130143251899,-1.31238820970223,0.770356233531033,-1.83330181796706
+23.9,-0.401858631981642,-1.21551167499635,1.17996208449757,-2.50305467719789
+24,-0.51678749986641,-1.07789083789226,1.55645817174586,-3.07301864529467
+24.1,-0.616151786033719,-0.901726454358557,1.93499979117093,-3.52047105747465
+24.2,-0.696166074289319,-0.689790388407546,2.30402555498439,-3.82757339808195
+24.3,-0.753140106995074,-0.446498125688537,2.57237301210501,-3.98208246591406
+24.4,-0.78439040957978,-0.178077175731741,2.74876254517949,-3.97783847201806
+24.5,-0.788153086712691,0.107866400078127,2.91170359449568,-3.81501061103789
+24.6,-0.762798727900644,0.402050475566698,2.96456315632156,-3.50009031595779
+24.7,-0.707798737525383,0.693630398800405,2.85190257152932,-3.04563246515416
+24.8,-0.624279721434828,0.971304193936907,2.64308988309186,-2.46975485901387
+24.9,-0.514329806513354,1.22328068584775,2.34451262244754,-1.79541592040682
+25,-0.380934765367405,1.43702202626802,1.90223637397218,-1.04949941481572
+25.1,-0.228517360481734,1.60149980165784,1.35594955479583,-0.261742679442828
+25.2,-0.0625404600481052,1.70723298786561,0.723133207198251,0.536448910582629
+25.3,0.110667772457506,1.74556047096408,0.0261212037458214,1.31325397540559
+25.4,0.284137217000576,1.71138436459486,-0.702396267614064,2.03770374844172
+25.5,0.450582698867505,1.60324447735729,-1.45665282973397,2.6809167033735
+25.6,0.602461652437094,1.42199564129162,-2.17168076835038,3.21724996946366
+25.7,0.73262379832318,1.17251988262275,-2.78130028813425,3.62532163189065
+25.8,0.834972941327923,0.863894630807964,-3.32404433153258,3.88886316121815
+25.9,0.90408164101734,0.50794798942584,-3.76548217913518,3.99736798832524
+26,0.935535518915406,0.119619850397707,-3.97697025045044,3.94651036816194
+26.1,0.927219694308967,-0.283974659455778,-4.01013233041617,3.73831783355366
+26.2,0.878802546398366,-0.684574312503813,-3.9209073068845,3.38109036386571
+26.3,0.79117632541892,-1.06264825147563,-3.60298721598925,2.88906949101807
+26.4,0.667520232279582,-1.39984544914497,-3.08592312380012,2.28187053454951
+26.5,0.513004907902243,-1.679919724776,-2.45030807640039,1.58370060072734
+26.6,0.3339865027609,-1.88772854049162,-1.67365749636832,0.822393521610405
+26.7,0.138231522655873,-2.01209796539562,-0.80239794157676,0.0283002079997237
+26.8,-0.0655474368649209,-2.04669857780043,0.126830216926732,-0.766921345597435
+26.9,-0.268058094216448,-1.98802224163351,1.05467818633128,-1.53156816530591
+27,-0.460021969704661,-1.83763743815858,1.92000064433629,-2.23515619540647
+27.1,-0.632785838749512,-1.60281733897742,2.72602455029305,-2.84963560143942
+27.2,-0.778289462291433,-1.29399367347152,3.42299758092881,-3.35050902858811
+27.3,-0.889563110024065,-0.925382622971186,3.90393914283342,-3.71780823390965
+27.4,-0.961797366328363,-0.514567052029249,4.22975916071577,-3.93689015716755
+27.5,-0.991734031025504,-0.0809896783122246,4.3752536849365,-3.99902069343448
+27.6,-0.977918158873279,0.354662984202197,4.27513858004718,-3.90172289429372
+27.7,-0.921350900920583,0.772303187247982,4.00331506900962,-3.64887571595608
+27.8,-0.824750492277791,1.15227144713477,3.54344441665955,-3.25055937751645
+27.9,-0.692715639468403,1.47707858133418,2.90903247588473,-2.72265349442851
+28,-0.531590461900168,1.73295598865354,2.16297022301366,-2.08620400834765
+28.1,-0.348835582101796,1.90836515002523,1.3253836757788,-1.36658415185141
+28.2,-0.152826865545637,1.99657879079477,0.444346544124202,-0.592482897726545
+28.3,0.0476253164517652,1.99593687673925,-0.457232296479337,0.20523877984277
+28.4,0.243505175484374,1.90752289430776,-1.30752221312575,0.994778234928204
+28.5,0.426309812385724,1.73707263783885,-2.05807086992117,1.7446590209913
+28.6,0.588533740587864,1.49496636703473,-2.72923130396795,2.42498575747738
+28.7,0.723465355750323,1.19356066928054,-3.26803294249315,3.0086359642979
+28.8,0.825716641487851,0.847708232410037,-3.60138730156748,3.47234134952167
+28.9,0.891954054209705,0.473915621149842,-3.80278598247599,3.7976154427468
+29,0.920163607106798,0.0892582853721786,-3.83846668158522,3.97149059233815
+29.1,0.90998849318804,-0.289273251774021,-3.68180244808219,3.98703494477626
+29.2,0.862995354788459,-0.646216017130072,-3.40204140508072,3.84362879578248
+29.3,0.781981802338071,-0.96702706652218,-2.97987483490012,3.54698929597293
+29.4,0.671169501538682,-1.23980910243003,-2.44599336584111,3.10894252610491
+29.5,0.535897267080882,-1.45566247228799,-1.84328405672255,2.54695202855655
+29.6,0.382192192055856,-1.60748410878641,-1.18578618848679,1.88342259100155
+29.7,0.216629255145962,-1.69206266514918,-0.511346158493853,1.14480703822701
+29.8,0.0459528566511302,-1.70920750774921,0.168978693211841,0.36055164148589
+29.9,-0.123033754911584,-1.66029756109788,0.802595009824025,-0.438077811414805
+30,-0.283994416376057,-1.54991941587693,1.37150481295061,-1.21924248440887
+30.1,-0.431240029711024,-1.38511987597607,1.89468407300439,-1.9517998070917
+30.2,-0.559538802315948,-1.17369589413942,2.31726561265243,-2.60654503072622
+30.3,-0.664664918794347,-0.924925405622006,2.61248066855307,-3.15737552941419
+30.4,-0.743666228587216,-0.648804211695891,2.85767812786022,-3.58233142941908
+30.5,-0.794090757101482,-0.355774421770125,2.99505212150768,-3.86447108003357
+30.6,-0.814564764400671,-0.0564059192369974,2.97664744413729,-3.99254646373082
+30.7,-0.805272297258488,0.239453298470098,2.88897549734178,-3.96145161912805
+30.8,-0.767090075142887,0.522508836684332,2.73692186229009,-3.77242619955414
+30.9,-0.701538634404384,0.783550236553299,2.46927421363637,-3.43300605198327
+31,-0.611294451529519,1.01504086865001,2.133860444651,-2.95672278659689
+31.1,-0.499711664208143,1.21045072857571,1.7497252126068,-2.3625643141872
+31.2,-0.370631624760699,1.36354449245871,1.30223532286136,-1.6742178580737
+31.3,-0.228529232084641,1.4700838568005,0.819781869089858,-0.91912561925878
+31.4,-0.0782290207176851,1.52703812494592,0.306584930313733,-0.1273907424726
+31.5,0.0751370399524083,1.531787600798,-0.215459272375862,0.669422801211228
+31.6,0.226348507898743,1.48387842999012,-0.728680800790782,1.43954857029657
+31.7,0.37027316783717,1.38457740147688,-1.24943206404431,2.15228408064237
+31.8,0.501703507135154,1.23577321485867,-1.72988446314417,2.77921481661814
+31.9,0.615835001801696,1.04127656610021,-2.13411763174848,3.29534702817487
+32,0.708625320150753,0.806740623731863,-2.51113103064477,3.68010415278716
+32.1,0.776304328193363,0.538928425627184,-2.83525831397685,3.91814713806804
+32.2,0.815630753096204,0.246289597031347,-3.01442210716902,3.99998596138243
+32.3,0.824812956927355,-0.0614832041052607,-3.08514279515983,3.92235796710214
+32.4,0.803143732806908,-0.373953763378354,-3.10816394670644,3.68835793838981
+32.5,0.750392869219396,-0.679329683368414,-2.98300067341966,3.30731471796041
+32.6,0.667811998897687,-0.965743410289283,-2.7098985121046,2.79441929656106
+32.7,0.558132143454933,-1.22203951643419,-2.36311438054805,2.17011919610783
+32.8,0.424821144206698,-1.43679570783077,-1.90211716826572,1.45930329151297
+32.9,0.272488973275806,-1.59976602467912,-1.33692849357445,0.690309569783273
+33,0.106787517409169,-1.70323241104461,-0.70617188786401,-0.106204616095867
+33.1,-0.0659756573361076,-1.74057266142648,-0.0216437982321987,-0.898484759079311
+33.2,-0.238955270063706,-1.70760761208279,0.677855840379698,-1.65494515005088
+33.3,-0.405156324387508,-1.60409141022083,1.37337952492993,-2.34542810037129
+33.4,-0.55762358346201,-1.43218349305218,2.05864794649168,-2.94240623375632
+33.5,-0.689504363071596,-1.19677480937801,2.63653537950597,-3.42207991590129
+33.6,-0.795019788886122,-0.906397820743869,3.10637308940034,-3.76532607079692
+33.7,-0.869471483806644,-0.572125020994657,3.52607802983197,-3.9584605574234
+33.8,-0.908662398428847,-0.207466729894084,3.75847084135373,-3.99378371327005
+33.9,-0.910268604637512,0.172329063105214,3.78364594574693,-3.86988731558193
+34,-0.874038351388709,0.551043728729605,3.70730958140954,-3.59171072275717
+34.1,-0.800735002325809,0.911843293529007,3.462546695685,-3.17034395771468
+34.2,-0.69280618630606,1.2380304567007,3.02150651590785,-2.62258558367701
+34.3,-0.554662305127232,1.51513403950297,2.46529157048396,-1.97027299846557
+34.4,-0.391865508243565,1.72989200358458,1.79284593257342,-1.23941184636124
+34.5,-0.211140252034164,1.87134905910922,1.0224227437125,-0.459139255132749
+34.6,-0.0201907683876373,1.93304167745406,0.201316606686122,0.339437769300183
+34.7,0.17277188132575,1.91129652978029,-0.648139675181787,1.12448248102894
+34.8,0.35925313428732,1.80570813044315,-1.45233206451472,1.86469762474869
+34.9,0.531211066603743,1.62101702973504,-2.19455896368278,2.53057315856339
+35,0.681223409283338,1.36533053691152,-2.88666680642853,3.09556272623156
+35.1,0.802369083898647,1.04954661371724,-3.4078011327733,3.53714197661794
+35.2,0.889436747186224,0.687764662682182,-3.76304505955219,3.83770653849353
+35.3,0.938873959878278,0.296247049655655,-3.99874894552199,3.98527385126268
+35.4,0.948323683115113,-0.107364629541952,-4.02322700601408,3.97396087184089
+35.5,0.917541136291807,-0.505194341924379,-3.86939968501233,3.8042186130175
+35.6,0.848064592618377,-0.879763975447483,-3.56503709982814,3.48281416299914
+35.7,0.742937677946667,-1.21418116424588,-3.08195949524438,3.02256090295765
+35.8,0.606991168322512,-1.49449590034631,-2.47889763532513,2.44180767795777
+35.9,0.446255682345106,-1.70874321653988,-1.77590849689744,1.7637072864074
+36,0.267761111398726,-1.84777496274074,-0.997414460222523,1.01529345104815
+36.1,0.07929239585012,-1.90718391726351,-0.186330696744008,0.226403069739362
+36.2,-0.111039626665926,-1.88525704648404,0.630111207414466,-0.571513287503728
+36.3,-0.295070537107827,-1.78354266072464,1.38566357854265,-1.34664521348846
+36.4,-0.465244811764301,-1.6082803973491,2.07391978207209,-2.06809064439617
+36.5,-0.614679888600055,-1.36831260602331,2.69485483067931,-2.70708782754923
+36.6,-0.737166417129015,-1.07474666364329,3.14810891491782,-3.23816196172753
+36.7,-0.828171856508797,-0.741051886076848,3.45108459628095,-3.64014079710274
+36.8,-0.88466644992577,-0.38182626405947,3.67265584971046,-3.89699870602599
+36.9,-0.904434484845638,-0.0128887645268788,3.69593348277025,-3.99849557423056
+37,-0.887243184937804,0.350344816324664,3.52264605656962,-3.94058504187299
+37.1,-0.834825424464273,0.693549135233025,3.27238319371003,-3.72557581913113
+37.2,-0.749683832053642,1.0030828793926,2.88353046471858,-3.36203964521487
+37.3,-0.635706934995826,1.26711503201759,2.37075122760643,-2.86446956017354
+37.4,-0.498022525661945,1.47686524786982,1.79277878594835,-2.25270211312447
+37.5,-0.34241032846858,1.62491777600676,1.15500798497955,-1.55112654163772
+37.6,-0.17524805142542,1.70682041750501,0.487842785115999,-0.787712449798735
+37.7,-0.00320734653110058,1.72170840933805,-0.188696676619238,0.00710525164334786
+37.8,0.166946391597027,1.67012580326579,-0.843888961271191,0.801639689124273
+37.9,0.328661240112442,1.55520926928202,-1.4322575280005,1.56421528192019
+38,0.476053513347853,1.38325936469567,-1.96659982465404,2.26443054759272
+38.1,0.603779788336723,1.16177591759149,-2.44227413655749,2.87437011315654
+38.2,0.707083321960019,0.899741186376182,-2.77931879403386,3.36971761290822
+38.3,0.782593667642975,0.607525301838271,-3.01565056522867,3.73072510519206
+38.4,0.827947507673646,0.29612556642821,-3.17098460444728,3.94300036051579
+38.5,0.841591501659843,-0.0228236964901042,-3.17840872140722,3.99808063432293
+38.6,0.823451408431968,-0.338083127822773,-3.08272901289559,3.89377004991262
+38.7,0.774484025075137,-0.638662477046212,-2.89429625230196,3.63422714111424
+38.8,0.696573679195287,-0.913766683083364,-2.58252129179651,3.22979906466659
+38.9,0.592838120397471,-1.15437300793856,-2.19617503169354,2.69660909173098
+39,0.46714081128272,-1.35218731640368,-1.73740345119955,2.05591382395014
+39.1,0.324069467655974,-1.50004908950298,-1.20942502050285,1.33325575981964
+39.2,0.168903873824199,-1.59339207660848,-0.644612589870452,0.557444995876983
+39.3,0.00729215409371936,-1.6287237235411,-0.0504596333345764,-0.240589340931828
+39.4,-0.154824161970106,-1.60407523394882,0.539910892241158,-1.02903213994131
+39.5,-0.311541369111519,-1.52043812062031,1.11362092021049,-1.77645067483003
+39.6,-0.457122367050828,-1.38043358340667,1.67776539023491,-2.45304772722756
+39.7,-0.585925711087788,-1.18816658929153,2.1597729437701,-3.03184950778026
+39.8,-0.693131325687046,-0.950080460475161,2.56955698034681,-3.48978101601211
+39.9,-0.774641370482837,-0.674309404759449,2.90992197271254,-3.80858596777642
+40,-0.827052195551502,-0.370360257262315,0,-3.9755546156935

Work 1/scripts/problem3_data_T60s.csv

@@ -0,0 +1,602 @@
+t,q,dq,ddq,u
+0,0,0,0,0
+0.1,0.00112730370377742,0.0336536743050961,0.657669343872878,0.794677323180245
+0.2,0.00883130084628362,0.130095105060834,1.23031152735571,1.5576733692346
+0.3,0.0288384132623469,0.277086967848714,1.6472957578342,2.25856989358014
+0.4,0.0653184832567522,0.456177260208145,1.85826392239339,2.86942436359809
+0.5,0.120381192475091,0.64441963262565,1.82183441394098,3.36588393923159
+0.6,0.19366224583284,0.816729955124557,1.5387129073771,3.72815634386891
+0.7,0.28233042826436,0.947731422726794,1.01198704123085,3.94179891995384
+0.8,0.381118481108189,1.01514724688817,0.281130829714293,3.99829441216602
+0.9,0.48271784224916,1.00127150126433,-0.606890939324855,3.89539052351278
+1,0.578248293996883,0.894322024572221,-1.54403616041735,3.63718970730273
+1.1,0.658338384140432,0.691502504394097,-2.46777849195839,3.23398561527836
+1.2,0.713750689364397,0.398398200996943,-3.35626893527373,2.7018527222046
+1.3,0.735600305235625,0.0284599263544737,-4.00825914367234,2.06200548728586
+1.4,0.71736732967013,-0.396782279453475,-4.38489881755735,1.33995260062362
+1.5,0.655285365929061,-0.849118356836855,-4.531083639236,0.564480032239469
+1.6,0.547892565795632,-1.29622623806606,-4.3244857319699,-0.23349657371032
+1.7,0.397254908342504,-1.70407791327366,-3.73168898607231,-1.02216440810733
+1.8,0.209300361028653,-2.04006080855522,-2.86613213766537,-1.77008177317941
+1.9,-0.00731550766185135,-2.27387198043844,-1.72922293231809,-2.44743156377088
+2,-0.241223605675537,-2.38106324008954,-0.381252753564326,-3.02720998123171
+2.1,-0.478944231224866,-2.34680237646659,1.08356113140267,-3.48630308965435
+2.2,-0.705829245460168,-2.16426570569947,2.58237734005865,-3.80640829555806
+2.3,-0.906890486294884,-1.83629821096442,3.93455844050654,-3.97476401453386
+2.4,-1.06860614272453,-1.37787653165824,5.11374520668299,-3.98465843534336
+2.5,-1.17918434708735,-0.81284329382283,6.09389607575295,-3.83569709865255
+2.6,-1.22882359069265,-0.17295878351365,6.62469772469187,-3.53381862288061
+2.7,-1.21221585705102,0.503754630673891,6.74037610639779,-3.09105795022395
+2.8,-1.12820436234541,1.17582411838087,6.533191358181,-2.52506655148928
+2.9,-0.978860954057995,1.79981035847128,5.85182622072886,-1.85840871765503
+3,-0.770999283563291,2.33562906493079,4.75245091059759,-1.1176619927957
+3.1,-0.515613103962611,2.74891875894459,3.39005668287868,-0.332357611269986
+3.2,-0.226326357533143,3.01046279160286,1.78219595985548,0.466196819401975
+3.3,0.0807823484948785,3.10169417161173,0.0444195098736388,1.24616545405351
+3.4,0.388335249621637,3.01614941528424,-1.75393602905129,1.97645340455444
+3.5,0.678348790457882,2.7560797824945,-3.43408611860293,2.62794639487516
+3.6,0.934021470108098,2.33567935225527,-4.86907935984763,3.17467145539661
+3.7,1.14100335615984,1.78100950577136,-6.08628991994047,3.59483238324651
+3.8,1.28712234301217,1.12495585256584,-6.94253943286844,3.87167868812595
+3.9,1.36381593553582,0.406902302885183,-7.28297214851448,3.99417338149842
+4,1.36767980657433,-0.330174021755641,-7.26531793532952,3.95743298649353
+4.1,1.29889049825954,-1.04224588166547,-6.8546938160307,3.76292222671909
+4.2,1.16155425178444,-1.68650054567169,-5.94967344220412,3.41839563235312
+4.3,0.964721270887307,-2.22697247599071,-4.74230088590455,2.93758839149645
+4.4,0.720465281131124,-2.63413817732492,-3.30905701113038,2.33966877156705
+4.5,0.443118721263638,-2.88581866922071,-1.7019965436784,1.64847394096703
+4.6,0.148752195959367,-2.9721968288911,-0.0363712415656969,0.891559656400984
+4.7,-0.145978041760561,-2.89314281403451,1.60780240616761,0.0991017018134311
+4.8,-0.424630255418812,-2.6573248762253,3.05425204912372,-0.697307124891926
+4.9,-0.672739948585826,-2.28475882540464,4.28045566687232,-1.46591651700771
+5,-0.878045085084117,-1.80273599561743,5.25923148399132,-2.17608444355748
+5.1,-1.0307579067425,-1.24353668430421,5.82481140361667,-2.79949875037417
+5.2,-1.12522261436471,-0.64300440916985,6.04748257510137,-3.31130587634261
+5.3,-1.1592124962359,-0.0379409362849631,5.93663216000362,-3.69110168645123
+5.4,-1.13383605650707,0.536222156936198,5.4497172587264,-3.92374492026597
+5.5,-1.05396244419096,1.0488134681975,4.70608941857471,-3.99996082620281
+5.6,-0.927027937689112,1.47376030771876,3.73555922576465,-3.91671091660527
+5.7,-0.762737838929616,1.79264354239405,2.61355404944882,-3.6773141026587
+5.8,-0.572312199675631,1.99548574983561,1.42458709467826,-3.29131437987483
+5.9,-0.367640689474864,2.07886112031207,0.262305797895213,-2.77410033910849
+6,-0.160346121295144,2.04848897718534,-0.810850096629073,-2.14629167200174
+6.1,0.0388399459182844,1.91690138358474,-1.7735540422846,-1.43291712894731
+6.2,0.220290472708867,1.70086688471167,-2.49938359217591,-0.662416701793238
+6.3,0.376747163577691,1.42178996137362,-2.98924153660433,0.134492188884554
+6.4,0.503311439080471,1.10348685128045,-3.29015849694172,0.926039300406156
+6.5,0.596974129613834,0.769202496718443,-3.33640210419518,1.68066814730656
+6.6,0.657272799105245,0.440521180295967,-3.17264695963293,2.3682940588289
+6.7,0.685844999000327,0.135894667251945,-2.86638329348033,2.96150355980979
+6.8,0.685753365960606,-0.130056648987916,-2.42584670939147,3.43664725942599
+6.9,0.66140326582697,-0.348319746055368,-1.9226177252087,3.77478267777642
+7,0.617826988441247,-0.514598278935145,-1.4050180793338,3.96242942277948
+7.1,0.560200530262186,-0.629615801215413,-0.916072884584706,3.99210661086545
+7.2,0.493413343237278,-0.698799738553371,-0.492918132824704,3.86263110619711
+7.3,0.421696974884123,-0.730300222058687,-0.171396746593982,3.57916468856201
+7.4,0.348266639065028,-0.734788651043527,0.0391562230663334,3.15300826950127
+7.5,0.275227865476597,-0.723747007930665,0.146209239141171,2.60115136062847
+7.6,0.203651184279577,-0.707781762836823,0.149580300874469,1.94559475541519
+7.7,0.133570306091302,-0.695777792179925,0.0729875409504171,1.21247342698281
+7.8,0.0642193033125308,-0.693970566176327,-0.0528266102661962,0.431014609197769
+7.9,-0.00565996556890208,-0.705189843622758,-0.176774620509154,-0.367627400910727
+8,-0.0773069806554265,-0.728754337147554,-0.272236743211374,-1.15161326666026
+8.1,-0.151676363174065,-0.760025340521132,-0.320431798418941,-1.88968794559386
+8.2,-0.229250063676892,-0.791068874381493,-0.269443420196352,-2.5524267293918
+8.3,-0.309518198381683,-0.812020729944363,-0.116985223730814,-3.11340831413719
+8.4,-0.390956185323783,-0.811937896451692,0.150000908551928,-3.55026813432602
+8.5,-0.470894163180363,-0.780014211551689,0.506511756278782,-3.84558996751823
+8.6,-0.545767023474155,-0.706877423058831,0.987756481582191,-3.98760026416638
+8.7,-0.610762318952125,-0.584754897081678,1.49232424767726,-3.97063752188253
+8.8,-0.660834371953323,-0.410270182511013,1.99274911516514,-3.7953779916725
+8.9,-0.690978933802869,-0.185167021665459,2.4515939666655,-3.46880871794233
+9,-0.69660755598576,0.0846502421423621,2.89889571627953,-3.0039489870867
+9.1,-0.673247221005856,0.38886209853353,3.18600736796194,-2.41933128962514
+9.2,-0.618026812346333,0.712716882427269,3.24837904850609,-1.73826248828757
+9.3,-0.530322613201749,1.03769639917485,3.14927230108926,-0.987894646946484
+9.4,-0.411125691046272,1.34339406863417,2.88048334532758,-0.19814256351347
+9.5,-0.263123935437519,1.60779762342013,2.36197978077322,0.599508838651809
+9.6,-0.0915023820210343,1.81056496541803,1.63746143257671,1.37325971527959
+9.7,0.0964937857212176,1.93408194004453,0.767273551172054,2.0922630606308
+9.8,0.29216268897519,1.96313670409293,-0.221801959468998,2.72785448027254
+9.9,0.485613572634473,1.88840380409875,-1.26370594814139,3.25469495002842
+10,0.666427396812341,1.70781029255568,-2.32502138310754,3.65178100291051
+10.1,0.823991007159134,1.42465365235776,-3.33319403023297,3.90328207106791
+10.2,0.948222677203598,1.04894121731208,-4.13865076550263,3.99917160057068
+10.3,1.03106783959304,0.598156775647957,-4.76046725558523,3.93562677847446
+10.4,1.06630832942662,0.0947352695087333,-5.21785090601743,3.71518093630896
+10.5,1.04937031020003,-0.434312443933761,-5.31641723595177,3.34662255414422
+10.6,0.979268118613924,-0.959752129511345,-5.08241943079759,2.84464489162392
+10.7,0.858341732719841,-1.45161171663343,-4.62975436959169,2.22926021407063
+10.8,0.691117803129841,-1.8802525964871,-3.86724815518654,1.52500196661976
+10.9,0.485221391987975,-2.21970646439723,-2.85754093317921,0.759946703181751
+11,0.250749571514318,-2.44943291557137,-1.6716101302423,-0.0354052371616155
+11.1,-0.000438350261762848,-2.55312745846465,-0.375763795189493,-0.829345682427049
+11.2,-0.255383909989738,-2.52309987678432,0.952965679522412,-1.59022273248574
+11.3,-0.50079981292249,-2.3602203193737,2.28511009481016,-2.28770262043826
+11.4,-0.723364614907139,-2.07139984431106,3.47086400980671,-2.89397902417698
+11.5,-0.911220776793722,-1.6717298045001,4.42872084424178,-3.38488161670068
+11.6,-1.05478973023789,-1.18365614859634,5.21919831200609,-3.74083966077816
+11.7,-1.14616670056199,-0.633909431993268,5.71312747678929,-3.9476622324826
+11.8,-1.1804123961182,-0.052903997274252,5.811101392612,-3.99710396854651
+11.9,-1.15654707774829,0.527556150777705,5.65764025054154,-3.88719378297545
+12,-1.07610535687297,1.07571672648671,5.21631278315875,-3.6223134480265
+12.1,-0.943500508166056,1.56146712848275,4.43697105899985,-3.21302290677581
+12.2,-0.766525948869145,1.96035615835788,3.46092939912567,-2.67563928151209
+12.3,-0.554942095580977,2.25250630665306,2.32723683989551,-2.03158636156249
+12.4,-0.320085873893855,2.42370796171182,1.08931263730662,-1.30654050441889
+12.5,-0.0743365258336663,2.46879082652308,-0.177019240920412,-0.529407000391092
+12.6,0.169642629817318,2.38887320745735,-1.41378215966316,0.268832290101914
+12.7,0.399483963871671,2.1912696737395,-2.4953847335798,1.05635408553789
+12.8,0.604371450590226,1.89125156271722,-3.41634101074372,1.80176237710156
+12.9,0.775095527201344,1.50871959992941,-4.16363340087454,2.47534008848016
+13,0.904183269803716,1.06691912927852,-4.60578356433547,3.05023380191841
+13.1,0.987213176762734,0.591483046925509,-4.80212576778489,3.50352431924356
+13.2,1.0222218260439,0.108629047861579,-4.76881448780196,3.81714037797079
+13.3,1.00954233044705,-0.356205183827859,-4.45876635868865,3.97857909551135
+13.4,0.952275171263314,-0.780824415768235,-3.96220376540213,3.98140441964624
+13.5,0.855385974425555,-1.14594637692938,-3.2952486798701,3.82550371361801
+13.6,0.725544290789095,-1.4371149546949,-2.50230123302676,3.51709224660289
+13.7,0.570679594822368,-1.64564000854823,-1.64702732564755,3.06846541054211
+13.8,0.399344625599165,-1.76678408803482,-0.7808677142772,2.49750854166557
+13.9,0.22020097923319,-1.80188062145097,0.0469489535941892,1.82698388857677
+14,0.0415268224031566,-1.75709452297478,0.824257478982615,1.08362315323148
+14.1,-0.12890475963705,-1.64114478327725,1.47027075825354,0.297061782337431
+14.2,-0.284633634094722,-1.46622301139371,1.97079614706269,-0.501342504385731
+14.3,-0.420654547081767,-1.24683654154735,2.36176611031907,-1.27975984753679
+14.4,-0.533057798965621,-0.997314523257605,2.59310175487771,-2.0071572040823
+14.5,-0.619530033300698,-0.731801275213912,2.66333555853069,-2.65453553685187
+14.6,-0.679368912050468,-0.462916466781302,2.66219437240939,-3.19608591463846
+14.7,-0.712585847076144,-0.202057577113865,2.55190149362583,-3.61021843284075
+14.8,-0.720283767165562,0.0418838528707965,2.32163308146019,-3.88042293482874
+14.9,-0.704765356440377,0.263312972330478,2.0788313333124,-3.9959272197878
+15,-0.668458632382069,0.458661712399707,1.81834120086989,-3.95212649637145
+15.1,-0.613968496315062,0.626131581623423,1.5363026747621,-3.75076696120112
+15.2,-0.544115333500434,0.766427475271897,1.27216427812526,-3.3998761835173
+15.3,-0.461540527904553,0.881036343301911,1.02622940697884,-2.91344307132637
+15.4,-0.368703428238884,0.97178141526668,0.797298150513748,-2.31086017778293
+15.5,-0.267893347068078,1.04105962463048,0.592183486474357,-1.61615058129226
+15.6,-0.161161431032528,1.09030538050508,0.394598168220051,-0.857010161183537
+15.7,-0.0504835333147771,1.11987929835739,0.196387416210489,-0.063703450400393
+15.8,0.0621582385650784,1.12950638006746,-0.00542612113192259,0.732142915922352
+15.9,0.174745749233615,1.11775704891626,-0.239453023628034,1.49880105459785
+16,0.284938729665871,1.08162158397329,-0.499980045730042,2.20570672496676
+16.1,0.390131909640826,1.01802771910313,-0.781014098836352,2.82467782872134
+16.2,0.487514948627418,0.92408182259519,-1.081230681301,3.33103794123112
+16.3,0.574085680801,0.797145817515727,-1.46172506984858,3.70460008272211
+16.4,0.646039162276096,0.635051860971201,-1.81897397838964,3.93047150945656
+16.5,0.699802903967296,0.437977095267359,-2.13057734233631,3.99964744042907
+16.6,0.732260872235133,0.208731503507477,-2.39893781212285,3.90937004956903
+16.7,0.740729462381741,-0.0478983366353404,-2.68422717530223,3.66323841156328
+16.8,0.722355780775327,-0.324577270594466,-2.85733049764975,3.27106501810577
+16.9,0.675408794192415,-0.611199331914073,-2.86159329006442,2.74848458481896
+17,0.599845874708859,-0.895577408933868,-2.75462306175851,2.1163307444801
+17.1,0.496736724607718,-1.16413733097779,-2.55068385730742,1.39980547582665
+17.2,0.368120735933503,-1.40174697538996,-2.16745299394969,0.62747438019364
+17.3,0.217830217319791,-1.59394033340686,-1.63449153404597,-0.169872138867806
+17.4,0.0511947833656191,-1.72774820042218,-0.990788498982925,-0.960446391815126
+17.5,-0.125348535578382,-1.79095853322587,-0.244208088454634,-1.7127306779846
+17.6,-0.304333935406929,-1.77494222941117,0.565762756929766,-2.39673379685706
+17.7,-0.477661707666179,-1.67577850449359,1.41246201984706,-2.98518670257967
+17.8,-0.636864859726958,-1.49279172650053,2.25451472115812,-3.45462963477182
+17.9,-0.773522864576156,-1.22990903082873,2.98243310512067,-3.78634738513985
+18,-0.880356538374148,-0.896795339672411,3.59912160219525,-3.96711541377246
+18.1,-0.951198996150186,-0.507078295983122,4.13585113634964,-3.98972706981459
+18.2,-0.980682942562729,-0.0782624790182752,4.41974070040262,-3.85328089789504
+18.3,-0.965969481971245,0.369209230986198,4.44685044666215,-3.56321657630745
+18.4,-0.906787516913139,0.813039716275554,4.32412725327548,-3.1310980542026
+18.5,-0.804364279322279,1.22992832619715,3.95418668923797,-2.574152533428
+18.6,-0.662399174839039,1.59732144999188,3.33450271279904,-1.91458367435366
+18.7,-0.487089043227809,1.89570309190105,2.56072149023441,-1.17868640600103
+18.8,-0.286171696714235,2.10752289091859,1.63380699481278,-0.395798630201158
+18.9,-0.0689162802525327,2.21975287654311,0.601171810279521,0.40286838797003
+19,0.154350854311965,2.22590557055069,-0.484649769109757,1.18547431483754
+19.1,0.372771491185364,2.12370409200131,-1.56606702536715,1.92081912175304
+19.2,0.575531457805093,1.91658596997831,-2.54192275532754,2.57958693177949
+19.3,0.752872196871545,1.61513069870749,-3.41107769073864,3.13551475119317
+19.4,0.896102159030612,1.23422981873052,-4.15639887813241,3.56643949216578
+19.5,0.997768132408354,0.792893829276582,-4.62323032183455,3.85518154513635
+19.6,1.05320180256775,0.313605645687501,-4.8481244644333,3.99022967563122
+19.7,1.06015422808282,-0.179546987516398,-4.91488492044831,3.96619994085656
+19.8,1.0179578043934,-0.660879466111878,-4.68136281855165,3.78405033050763
+19.9,0.92894775251846,-1.10636537743869,-4.16180978968383,3.4510425747427
+20,0.798319602746686,-1.49481248709571,-3.51517542213731,2.9804526419174
+20.1,0.632539698753539,-1.80722433110447,-2.68738958893158,2.39104146762102
+20.2,0.439885898871076,-2.02917282735089,-1.73208782361008,1.70630701537827
+20.3,0.229911220752512,-2.15237819552755,-0.710795377392154,0.953547486995568
+20.4,0.0128285888600272,-2.17230006411957,0.315922489802078,0.162773029399431
+20.5,-0.201094818134437,-2.0903027376454,1.28748934567074,-0.634490675218836
+20.6,-0.402143331672194,-1.91412015001225,2.1926363861591,-1.40645923886727
+20.7,-0.58126548134836,-1.65477018330869,2.96351861302532,-2.12235671100084
+20.8,-0.730752444894273,-1.32724438029781,3.52120350121381,-2.75364251855068
+20.9,-0.845027373428048,-0.949786544885405,3.9384998579091,-3.27514928850739
+21,-0.919917303382731,-0.542076550670578,4.17036962574346,-3.66608619166254
+21.1,-0.953103537079981,-0.124594019434533,4.13445653213582,-3.91086780736008
+21.2,-0.944945205455871,0.28321891472206,3.93971722599928,-3.99973546503522
+21.3,-0.897389701571769,0.663372154026642,3.60523778178998,-3.92914629161454
+21.4,-0.813781819869767,0.999468590505036,3.08953900601766,-3.70191445468531
+21.5,-0.699278548107589,1.27936657263204,2.47384718357677,-3.32709897051439
+21.6,-0.560036804509643,1.49417578796122,1.79612332768767,-2.81964254965699
+21.7,-0.40283382763482,1.63778391118715,1.07609516888449,-2.19977587824137
+21.8,-0.234869899071152,1.70891730570789,0.356936923753887,-1.49221108435449
+21.9,-0.0633366012699452,1.70932239145856,-0.342855223248106,-0.725156543478751
+22,0.104768144298781,1.64296382408564,-0.965614133652237,0.0708077004216543
+22.1,0.263216748530984,1.51726881879719,-1.50576113296862,0.863949064752896
+22.2,0.406607741433501,1.3414083745033,-1.97934131219756,1.62264750622137
+22.3,0.530205321214043,1.12521365347596,-2.32218932106997,2.31665611217708
+22.4,0.630581007783884,0.879321210604174,-2.54362052236902,2.91830694957143
+22.5,0.705520489130036,0.614202224639568,-2.71503029066088,3.40361409813647
+22.6,0.753309667569579,0.340232064407692,-2.7634845432973,3.75322989333422
+22.7,0.773464000576149,0.0667830029911999,-2.68306683484101,3.95321625668655
+22.8,0.766787665234309,-0.198274692895016,-2.5743206743433,3.99560036298008
+22.9,0.734368123149035,-0.447839416471289,-2.40086929997317,3.87869249164768
+23,0.67793988806403,-0.675675555199043,-2.14740377404013,3.60715339059524
+23.1,0.600037615238624,-0.877441627681111,-1.8683611703162,3.19180846689052
+23.2,0.503451730710056,-1.04925827423153,-1.55673369364551,2.64921621194495
+23.3,0.391298509245033,-1.187710197628,-1.20786651505307,2.00100806671435
+23.4,0.267066622629479,-1.29073839348898,-0.843475158508522,1.27302604440993
+23.5,0.134399984428839,-1.35621124674887,-0.45834423934557,0.494292490980896
+23.6,-0.00285009616525561,-1.38214313844087,-0.0597915427499929,-0.304146944233414
+23.7,-0.14069809218685,-1.3677196718212,0.341594495654612,-1.09046100057232
+23.8,-0.275130143251899,-1.31238820970223,0.770356233530126,-1.83330181796706
+23.9,-0.401858631981647,-1.21551167499635,1.17996208449841,-2.50305467719792
+24,-0.51678749986641,-1.07789083789226,1.55645817174543,-3.07301864529467
+24.1,-0.616151786033719,-0.901726454358557,1.93499979117069,-3.52047105747465
+24.2,-0.696166074289321,-0.689790388407538,2.3040255549847,-3.82757339808196
+24.3,-0.753140106995076,-0.446498125688527,2.57237301210506,-3.98208246591406
+24.4,-0.784390409579781,-0.178077175731731,2.74876254517945,-3.97783847201806
+24.5,-0.788153086712691,0.107866400078127,2.91170359449562,-3.81501061103789
+24.6,-0.762798727900644,0.402050475566698,2.96456315632181,-3.50009031595779
+24.7,-0.70779873752538,0.693630398800415,2.85190257152917,-3.04563246515414
+24.8,-0.624279721434824,0.971304193936916,2.64308988309184,-2.46975485901385
+24.9,-0.51432980651335,1.22328068584776,2.34451262244704,-1.79541592040679
+25,-0.380934765367405,1.43702202626802,1.9022363739726,-1.04949941481572
+25.1,-0.228517360481734,1.60149980165784,1.35594955479644,-0.261742679442828
+25.2,-0.0625404600480991,1.70723298786561,0.723133207197657,0.536448910582657
+25.3,0.110667772457513,1.74556047096408,0.0261212037457797,1.31325397540561
+25.4,0.284137217000582,1.71138436459485,-0.702396267614652,2.03770374844174
+25.5,0.450582698867505,1.60324447735729,-1.45665282973336,2.6809167033735
+25.6,0.602461652437094,1.42199564129162,-2.17168076834996,3.21724996946366
+25.7,0.732623798323184,1.17251988262274,-2.78130028813478,3.62532163189067
+25.8,0.834972941327926,0.863894630807952,-3.32404433153262,3.88886316121816
+25.9,0.904081641017342,0.507947989425826,-3.7654821791352,3.99736798832524
+26,0.935535518915406,0.119619850397707,-3.97697025045027,3.94651036816194
+26.1,0.927219694308967,-0.283974659455778,-4.01013233041642,3.73831783355366
+26.2,0.878802546398364,-0.684574312503827,-3.92090730688439,3.38109036386569
+26.3,0.791176325418917,-1.06264825147564,-3.60298721598927,2.88906949101805
+26.4,0.667520232279577,-1.39984544914498,-3.08592312379943,2.28187053454949
+26.5,0.513004907902243,-1.679919724776,-2.45030807640092,1.58370060072734
+26.6,0.3339865027609,-1.88772854049162,-1.67365749636903,0.822393521610405
+26.7,0.138231522655866,-2.01209796539562,-0.802397941576066,0.0283002079996953
+26.8,-0.0655474368649281,-2.04669857780043,0.126830216926765,-0.766921345597463
+26.9,-0.268058094216455,-1.98802224163351,1.05467818633196,-1.53156816530593
+27,-0.460021969704661,-1.83763743815858,1.92000064433559,-2.23515619540647
+27.1,-0.632785838749512,-1.60281733897742,2.7260245502926,-2.84963560143942
+27.2,-0.778289462291437,-1.29399367347151,3.42299758092934,-3.35050902858813
+27.3,-0.889563110024069,-0.925382622971171,3.90393914283351,-3.71780823390966
+27.4,-0.961797366328365,-0.514567052029234,4.22975916071577,-3.93689015716755
+27.5,-0.991734031025504,-0.0809896783122246,4.37525368493632,-3.99902069343448
+27.6,-0.977918158873279,0.354662984202197,4.27513858004744,-3.90172289429372
+27.7,-0.92135090092058,0.772303187247996,4.00331506900946,-3.64887571595607
+27.8,-0.824750492277787,1.15227144713478,3.54344441665955,-3.25055937751643
+27.9,-0.692715639468398,1.47707858133419,2.90903247588405,-2.72265349442849
+28,-0.531590461900168,1.73295598865354,2.1629702230142,-2.08620400834765
+28.1,-0.348835582101796,1.90836515002523,1.32538367577951,-1.36658415185141
+28.2,-0.152826865545629,1.99657879079477,0.444346544123486,-0.592482897726517
+28.3,0.0476253164517723,1.99593687673925,-0.457232296479376,0.205238779842798
+28.4,0.24350517548438,1.90752289430775,-1.30752221312637,0.994778234928231
+28.5,0.426309812385724,1.73707263783885,-2.05807086992051,1.7446590209913
+28.6,0.588533740587864,1.49496636703473,-2.72923130396753,2.42498575747738
+28.7,0.723465355750327,1.19356066928053,-3.26803294249371,3.00863596429792
+28.8,0.825716641487854,0.847708232410025,-3.60138730156745,3.47234134952169
+28.9,0.891954054209706,0.473915621149829,-3.80278598247604,3.79761544274681
+29,0.920163607106798,0.0892582853721786,-3.83846668158505,3.97149059233815
+29.1,0.90998849318804,-0.289273251774021,-3.68180244808243,3.98703494477626
+29.2,0.862995354788457,-0.646216017130084,-3.4020414050806,3.84362879578247
+29.3,0.781981802338068,-0.967027066522191,-2.97987483490011,3.54698929597291
+29.4,0.671169501538677,-1.23980910243004,-2.44599336584057,3.10894252610489
+29.5,0.535897267080882,-1.45566247228799,-1.84328405672299,2.54695202855655
+29.6,0.382192192055856,-1.60748410878641,-1.18578618848739,1.88342259100155
+29.7,0.216629255145956,-1.69206266514918,-0.511346158493259,1.14480703822699
+29.8,0.0459528566511241,-1.70920750774921,0.168978693211869,0.360551641485862
+29.9,-0.123033754911589,-1.66029756109787,0.802595009824594,-0.438077811414833
+30,-0.283994416376057,-1.54991941587693,1.37150481295052,-1.21924248440887
+30.1,-0.431240029711019,-1.38511987597608,1.89468407300339,-1.95179980709167
+30.2,-0.559538802315948,-1.17369589413942,2.31726561265293,-2.60654503072622
+30.3,-0.664664918794347,-0.924925405622006,2.61248066855307,-3.15737552941419
+30.4,-0.743666228587216,-0.648804211695891,2.85767812786022,-3.58233142941908
+30.5,-0.794090757101482,-0.355774421770125,2.99505212150771,-3.86447108003357
+30.6,-0.814564764400671,-0.0564059192370084,2.97664744413723,-3.99254646373081
+30.7,-0.805272297258488,0.239453298470098,2.88897549734182,-3.96145161912805
+30.8,-0.767090075142887,0.522508836684332,2.73692186229009,-3.77242619955414
+30.9,-0.701538634404384,0.783550236553299,2.46927421363637,-3.43300605198327
+31,-0.611294451529519,1.01504086865001,2.13386044465057,-2.95672278659689
+31.1,-0.499711664208147,1.2104507285757,1.74972521260767,-2.36256431418722
+31.2,-0.370631624760699,1.36354449245871,1.30223532286092,-1.6742178580737
+31.3,-0.228529232084641,1.4700838568005,0.819781869089858,-0.91912561925878
+31.4,-0.0782290207176851,1.52703812494592,0.306584930313733,-0.1273907424726
+31.5,0.0751370399524083,1.531787600798,-0.215459272376339,0.669422801211228
+31.6,0.226348507898738,1.48387842999012,-0.728680800789827,1.43954857029654
+31.7,0.37027316783717,1.38457740147688,-1.24943206404479,2.15228408064237
+31.8,0.501703507135154,1.23577321485867,-1.72988446314417,2.77921481661814
+31.9,0.615835001801696,1.04127656610021,-2.13411763174848,3.29534702817487
+32,0.708625320150753,0.806740623731863,-2.51113103064517,3.68010415278716
+32.1,0.776304328193359,0.538928425627204,-2.83525831397605,3.91814713806803
+32.2,0.815630753096204,0.246289597031347,-3.01442210716942,3.99998596138243
+32.3,0.824812956927355,-0.0614832041052607,-3.08514279515983,3.92235796710214
+32.4,0.803143732806908,-0.373953763378354,-3.10816394670644,3.68835793838981
+32.5,0.750392869219396,-0.679329683368414,-2.98300067341897,3.30731471796041
+32.6,0.667811998897694,-0.965743410289264,-2.70989851210598,2.7944192965611
+32.7,0.558132143454933,-1.22203951643419,-2.36311438054736,2.17011919610783
+32.8,0.424821144206698,-1.43679570783077,-1.90211716826572,1.45930329151297
+32.9,0.272488973275806,-1.59976602467912,-1.33692849357445,0.690309569783273
+33,0.106787517409169,-1.70323241104461,-0.70617188786275,-0.106204616095867
+33.1,-0.065975657336095,-1.74057266142648,-0.021643798234719,-0.898484759079256
+33.2,-0.238955270063706,-1.70760761208279,0.677855840380959,-1.65494515005088
+33.3,-0.405156324387508,-1.60409141022083,1.37337952492993,-2.34542810037129
+33.4,-0.55762358346201,-1.43218349305218,2.05864794649168,-2.94240623375632
+33.5,-0.689504363071596,-1.19677480937801,2.63653537950661,-3.42207991590129
+33.6,-0.795019788886115,-0.906397820743891,3.10637308939905,-3.7653260707969
+33.7,-0.869471483806644,-0.572125020994657,3.52607802983261,-3.9584605574234
+33.8,-0.908662398428847,-0.207466729894084,3.75847084135373,-3.99378371327005
+33.9,-0.910268604637512,0.172329063105214,3.78364594574693,-3.86988731558193
+34,-0.874038351388709,0.551043728729605,3.7073095814089,-3.59171072275717
+34.1,-0.800735002325816,0.911843293528983,3.46254669568629,-3.17034395771472
+34.2,-0.69280618630606,1.2380304567007,3.0215065159072,-2.62258558367701
+34.3,-0.554662305127232,1.51513403950297,2.46529157048396,-1.97027299846557
+34.4,-0.391865508243565,1.72989200358458,1.79284593257342,-1.23941184636124
+34.5,-0.211140252034164,1.87134905910922,1.02242274371113,-0.459139255132749
+34.6,-0.020190768387651,1.93304167745406,0.201316606688867,0.339437769300127
+34.7,0.17277188132575,1.91129652978029,-0.64813967518316,1.12448248102894
+34.8,0.35925313428732,1.80570813044315,-1.45233206451472,1.86469762474869
+34.9,0.531211066603743,1.62101702973504,-2.19455896368278,2.53057315856339
+35,0.681223409283338,1.36533053691152,-2.88666680642924,3.09556272623156
+35.1,0.80236908389864,1.04954661371726,-3.40780113277188,3.53714197661791
+35.2,0.889436747186224,0.687764662682182,-3.7630450595529,3.83770653849353
+35.3,0.938873959878278,0.296247049655655,-3.99874894552199,3.98527385126268
+35.4,0.948323683115113,-0.107364629541952,-4.02322700601408,3.97396087184089
+35.5,0.917541136291807,-0.505194341924379,-3.86939968501171,3.8042186130175
+35.6,0.848064592618384,-0.879763975447457,-3.56503709982938,3.48281416299917
+35.7,0.742937677946667,-1.21418116424588,-3.08195949524376,3.02256090295765
+35.8,0.606991168322512,-1.49449590034631,-2.47889763532513,2.44180767795777
+35.9,0.446255682345106,-1.70874321653988,-1.77590849689744,1.7637072864074
+36,0.267761111398726,-1.84777496274074,-0.997414460221169,1.01529345104815
+36.1,0.0792923958501336,-1.90718391726351,-0.186330696746723,0.226403069739419
+36.2,-0.111039626665926,-1.88525704648404,0.630111207415823,-0.571513287503728
+36.3,-0.295070537107827,-1.78354266072464,1.38566357854265,-1.34664521348846
+36.4,-0.465244811764301,-1.6082803973491,2.07391978207209,-2.06809064439617
+36.5,-0.614679888600055,-1.36831260602331,2.69485483068012,-2.70708782754923
+36.6,-0.737166417129007,-1.07474666364332,3.1481089149162,-3.2381619617275
+36.7,-0.828171856508797,-0.741051886076848,3.45108459628176,-3.64014079710274
+36.8,-0.88466644992577,-0.38182626405947,3.67265584971046,-3.89699870602599
+36.9,-0.904434484845638,-0.0128887645268788,3.69593348277025,-3.99849557423056
+37,-0.887243184937804,0.350344816324664,3.52264605656913,-3.94058504187299
+37.1,-0.834825424464278,0.693549135233001,3.272383193711,-3.72557581913115
+37.2,-0.749683832053642,1.0030828793926,2.88353046471809,-3.36203964521487
+37.3,-0.635706934995826,1.26711503201759,2.37075122760643,-2.86446956017354
+37.4,-0.498022525661945,1.47686524786982,1.79277878594835,-2.25270211312447
+37.5,-0.34241032846858,1.62491777600676,1.15500798497832,-1.55112654163772
+37.6,-0.175248051425433,1.70682041750501,0.487842785118464,-0.787712449798791
+37.7,-0.00320734653110058,1.72170840933805,-0.18869667662047,0.00710525164334786
+37.8,0.166946391597027,1.67012580326579,-0.843888961271191,0.801639689124273
+37.9,0.328661240112442,1.55520926928202,-1.4322575280005,1.56421528192019
+38,0.476053513347853,1.38325936469567,-1.96659982465486,2.26443054759272
+38.1,0.603779788336715,1.16177591759151,-2.44227413655584,2.8743701131565
+38.2,0.707083321960019,0.899741186376182,-2.77931879403468,3.36971761290822
+38.3,0.782593667642975,0.607525301838271,-3.01565056522867,3.73072510519206
+38.4,0.827947507673646,0.29612556642821,-3.17098460444728,3.94300036051579
+38.5,0.841591501659843,-0.0228236964901042,-3.17840872140699,3.99808063432293
+38.6,0.82345140843197,-0.338083127822751,-3.08272901289606,3.89377004991263
+38.7,0.774484025075137,-0.638662477046212,-2.89429625230173,3.63422714111424
+38.8,0.696573679195287,-0.913766683083364,-2.58252129179651,3.22979906466659
+38.9,0.592838120397471,-1.15437300793856,-2.19617503169354,2.69660909173098
+39,0.46714081128272,-1.35218731640368,-1.73740345119844,2.05591382395014
+39.1,0.324069467655985,-1.50004908950297,-1.20942502050506,1.3332557598197
+39.2,0.168903873824199,-1.59339207660848,-0.644612589869348,0.557444995876983
+39.3,0.00729215409371936,-1.6287237235411,-0.0504596333345764,-0.240589340931828
+39.4,-0.154824161970106,-1.60407523394882,0.539910892241158,-1.02903213994131
+39.5,-0.311541369111519,-1.52043812062031,1.11362092021148,-1.77645067483003
+39.6,-0.457122367050818,-1.38043358340668,1.67776539023294,-2.45304772722751
+39.7,-0.585925711087788,-1.18816658929153,2.15937196968577,-3.03184950778026
+39.8,-0.6931353354279,-0.950078576059937,2.55348393031962,-3.48978101601211
+39.9,-0.774810120464815,-0.674197279687546,2.9231683855248,-3.80858596777642
+40,-0.827253221646483,-0.370110426775568,3.15895013097687,-3.9755546156935
+40.1,-0.848106821518381,-0.0486766531971985,3.23445689440821,-3.98403044667095
+40.2,-0.836615852446198,0.278502255254705,3.24165566581991,-3.8336755560747
+40.3,-0.792708326715816,0.59923023824791,3.13735071239722,-3.53048411892058
+40.4,-0.717427293861461,0.900713277579412,2.86778810791144,-3.08654342103197
+40.5,-0.613468379927992,1.1713770060556,2.49887731441831,-2.51955197709782
+40.6,-0.48452069285034,1.40027068753456,2.03984625582534,-1.85211394674286
+40.7,-0.335174543214434,1.57697677846239,1.47493661787668,-1.11083797801471
+40.8,-0.171079027399762,1.69386957789449,0.845782642626996,-0.325276404555161
+40.9,0.0014743148411803,1.74530920133054,0.163078442825801,0.473252912685002
+41,0.175658441510381,1.7271707902529,-0.530469967063099,1.25291512973234
+41.1,0.34453786850895,1.63911391412412,-1.2080807628052,1.98262757435953
+41.2,0.501336487879467,1.48383979420031,-1.8817402834238,2.6332989141402
+41.3,0.639317704415747,1.26600989720324,-2.46887297572844,3.17898893606928
+41.4,0.752610191194741,0.99349479377947,-2.93156237918081,3.59794270099701
+41.5,0.836587054181928,0.676857880071494,-3.33771841628174,3.87345784440074
+41.6,0.887186733006297,0.328521749092758,-3.61176035387193,3.99455044695128
+41.7,0.901668808291948,-0.0372447805776948,-3.67464750617001,3.95639292871475
+41.8,0.879404408515897,-0.405377003719039,-3.61243041277279,3.76050650953023
+41.9,0.821015704612119,-0.760520486439642,-3.43189250011703,3.41470056277525
+42,0.728308075707171,-1.08688353024557,-3.06300864127107,2.93276128029317
+42.1,0.604970360389512,-1.37057409391292,-2.56459684013355,2.33390206042924
+42.2,0.455986676670518,-1.59936970349085,-1.96810538217936,1.64199753046976
+42.3,0.287321939129729,-1.76222885845629,-1.2705912876146,0.884631740593388
+42.4,0.105951288712795,-1.85198707181431,-0.518045479609941,0.0919984748363959
+42.5,-0.0805998165002384,-1.86469283234785,0.276966808203408,-0.704302479794348
+42.6,-0.264381253631238,-1.79850783039594,1.04798164088306,-1.47252511711064
+42.7,-0.437682874353407,-1.65602412655844,1.76514898006245,-2.18204282482954
+42.8,-0.593333005274951,-1.44368736666515,2.44679575619648,-2.80456937095672
+42.9,-0.724515178634531,-1.17003082861093,3.01146321286949,-3.31528658659434
+43,-0.825582719865415,-0.846657404461907,3.40918111281701,-3.69383378801624
+43.1,-0.89255844996813,-0.487618524852169,3.7049886379205,-3.9251194928765
+43.2,-0.92248429369164,-0.108328812324347,3.83555700406456,-3.99992306998662
+43.3,-0.914054567374504,0.274832613509358,3.77343286224894,-3.91526233678354
+43.4,-0.867890512434878,0.645819586064217,3.58450321522623,-3.67451244953766
+43.5,-0.785881425342991,0.98845470678921,3.22821838628318,-3.28727134652329
+43.6,-0.671590154388271,1.28831305016719,2.72827411086255,-2.76897710850768
+43.7,-0.530016142324926,1.53339045354134,2.13188063144624,-2.14029249118834
+43.8,-0.367123323947119,1.71299545610142,1.44171709946236,-1.42628116632893
+43.9,-0.189813334574688,1.82026053532874,0.69946390455336,-0.655408512258436
+44,-0.00550870615672311,1.85184854908476,-0.0780011523648399,0.141593210934643
+44.1,0.178015910737593,1.80636949539041,-0.831971370478446,0.932950059630973
+44.2,0.353220813927125,1.68653295057571,-1.53165247692894,1.68711313354398
+44.3,0.513109192347367,1.49879400146259,-2.18968954936057,2.37401633081589
+44.4,0.651100675274004,1.25134375605879,-2.74198157494212,2.96627498861998
+44.5,0.761672342451219,0.955041704860805,-3.13373251041401,3.44027762324981
+44.6,0.840906684524295,0.622744969754559,-3.44026095559188,3.7771272454645
+44.7,0.885738417041451,0.268452252908571,-3.61920649435553,3.9633947238168
+44.8,0.894378084615052,-0.0928752373167027,-3.58631071476322,3.99165416174583
+44.9,0.867154645041021,-0.446740112113128,-3.42603769654021,3.86077894463917
+45,0.805670828501588,-0.77929900547202,-3.16947353721776,3.57598665440223
+45.1,0.712492276589978,-1.07706526231834,-2.75852211776298,3.14863106093272
+45.2,0.591728503500737,-1.32904142533005,-2.24793185521147,2.5957494831437
+45.3,0.448485411859382,-1.5262616323709,-1.66669664330515,1.93938356482296
+45.4,0.288575353784975,-1.66113018752898,-1.02155179851006,1.20570054385143
+45.5,0.118449777725468,-1.72965373523755,-0.350581405776218,0.423950047004627
+45.6,-0.0551816123918014,-1.73045331533023,0.339956459965621,-0.374702000364513
+45.7,-0.225413437909415,-1.66370371348195,0.992729726012073,-1.15841586141966
+45.8,-0.385717966166907,-1.53298446871734,1.58757040068614,-1.89594733767259
+45.9,-0.530146790417538,-1.3445985702692,2.14927769201669,-2.55789337658038
+46,-0.653082837748003,-1.10602028643508,2.61092289010357,-3.11786427846322
+46.1,-0.749909656177431,-0.826777564332173,2.92999883406695,-3.55353577055342
+46.2,-0.81743648626619,-0.517823535591006,3.18337258994613,-3.84753900530223
+46.3,-0.853129590455488,-0.190939721870919,3.33373059948677,-3.98815300152108
+46.4,-0.855485388649918,0.141213300794342,3.29861061565979,-3.96977192291387
+46.5,-0.82485508068775,0.466395569085696,3.14946177748914,-3.79312856507979
+46.6,-0.762730154950691,0.772861436756366,2.92730117892511,-3.46526514126534
+46.7,-0.67133221742438,1.04887844906443,2.56779566760511,-2.99925253154515
+46.8,-0.554256323222019,1.2845552352877,2.11549882699935,-2.41366918808098
+46.9,-0.416025440749664,1.47158357768813,1.59610652204643,-1.73186047086155
+47,-0.261833493056844,1.60245331670383,1.01017363616006,-0.981007941870617
+47.1,-0.0975398090024244,1.6725978672,0.391326694679062,-0.191045721986883
+47.2,0.0706671419987862,1.67974171373244,-0.257302205918064,0.60653288795283
+47.3,0.236301070940816,1.62274006627912,-0.885858489810576,1.37993094567502
+47.4,0.39307641498474,1.50352915918103,-1.47079979651948,2.09831551121711
+47.5,0.53514376106347,1.32683559415889,-2.03447633157524,2.73304685894448
+47.6,0.656866343826447,1.09859013935702,-2.52343989786452,3.25882025303383
+47.7,0.753354527610778,0.826961290868237,-2.88113047921192,3.65467476743671
+47.8,0.821031406602991,0.522064866600595,-3.16367556000285,3.90482893185501
+47.9,0.857071529995175,0.195144999936506,-3.33852289056371,3.99930988916053
+48,0.859726424481722,-0.141361214136604,-3.35294930604232,3.93435098173738
+48.1,0.828851825907845,-0.47491067671471,-3.26547775812467,3.71254191623483
+48.2,0.765322449752722,-0.792435435880653,-3.0493230065179,3.34272552013549
+48.3,0.67129984353242,-1.08121495053563,-2.69108303880927,2.83964520612875
+48.4,0.550366406924026,-1.33016714697112,-2.24508646867104,2.22335719877226
+48.5,0.406982105628921,-1.52863895598114,-1.6999882512328,1.51843095611009
+48.6,0.246597921821487,-1.66803959115883,-1.07528270461655,0.75296966291377
+48.7,0.0754609109678888,-1.7428127970588,-0.402160169202614,-0.0425101546097433
+48.8,-0.0996977015777361,-1.74868370053188,0.296069439692642,-0.836295226417461
+48.9,-0.271895619726434,-1.68427246455358,0.979000930667079,-1.59673984663017
+49,-0.434303528568462,-1.55201174024934,1.64065210271234,-2.29352748796169
+49.1,-0.580304916383366,-1.35630366846649,2.26262104513159,-2.8988794259927
+49.2,-0.703680093746955,-1.10411023205786,2.75802557402407,-3.3886621892524
+49.3,-0.799475015370302,-0.805283627006006,3.15147943178919,-3.7433496845685
+49.4,-0.863755142675758,-0.47143099098312,3.48113154356732,-3.9488016407839
+49.5,-0.89322395454554,-0.116102662176094,3.61826606958167,-3.99682733674541
+49.6,-0.886510105719506,0.246307056265723,3.57412672641375,-3.8855121395089
+49.7,-0.844054989629334,0.601155085828559,3.4491971576467,-3.61929383471276
+49.8,-0.767107901962696,0.933445334022424,3.16133312625995,-3.2087857060688
+49.9,-0.658547483033457,1.22902859096356,2.71406577839811,-2.6703534172327
+50,-0.522846406320238,1.47599861331902,2.17827388109442,-2.02546256443904
+50.1,-0.365362590796075,1.66332722193662,1.54299366087101,-1.29982291091792
+50.2,-0.192448838663201,1.78260912900088,0.834898318539234,-0.522363419766889
+50.3,-0.0111861033449351,1.82926765527414,0.08775950480015,0.275921052517094
+50.4,0.170954227021332,1.8005990260342,-0.669746783674122,1.06320542315651
+50.5,0.346397089550858,1.69708879825367,-1.38281268443853,1.8081031487134
+50.6,0.508011825235999,1.52350461969101,-2.04909609447533,2.48091750753052
+50.7,0.649135599976387,1.28690519529887,-2.66131388694573,3.05482551431032
+50.8,0.763646235847317,0.996843657614496,-3.11766501761506,3.5069472678939
+50.9,0.846980221542097,0.665538395935895,-3.44804709719959,3.81925810071865
+51,0.89583373626488,0.306817848364173,-3.67213013526945,3.97930716543363
+51.1,0.90796594963497,-0.0641498251783784,-3.70553650600914,3.98071381089268
+51.2,0.883042797944968,-0.432076053543659,-3.59404442317057,3.82342195858028
+51.3,0.82217920202326,-0.781739478436288,-3.35074327223127,3.513702338285
+51.4,0.727808173379239,-1.09822294652437,-2.94278720260547,3.06390249389121
+51.5,0.604009272709164,-1.36898709935135,-2.42889446544867,2.4919545257694
+51.6,0.455921427384602,-1.58287756638715,-1.81947477450373,1.8206601945224
+51.7,0.289638834315003,-1.73086393694655,-1.12980356383395,1.07678188674528
+51.8,0.112058205607064,-1.8078607315018,-0.400513136803832,0.28997568312542
+51.9,-0.0695275544689131,-1.81092561689091,0.348365731734744,-0.508390935909523
+52,-0.247629657227543,-1.73981471238967,1.06183783381403,-1.28648961265012
+52.1,-0.415113381648032,-1.59849852414307,1.72895669107996,-2.0133000082871
+52.2,-0.565307539157722,-1.3933576180508,2.35153312555216,-2.65984648592923
+52.3,-0.69198636541189,-1.13292320136315,2.83591003583148,-3.2003532778083
+52.4,-0.790306091307743,-0.828294459156285,3.1897643713546,-3.61327208379996
+52.5,-0.856728173490051,-0.492037157899832,3.48007779377536,-3.88214113414994
+52.6,-0.888349477734604,-0.138215524438144,3.58850244619645,-3.99624146828613
+52.7,-0.884085757517194,0.218778561436833,3.50643877092035,-3.95102426595095
+52.8,-0.84475764959058,0.564918195159538,3.34590257813575,-3.74829219431038
+52.9,-0.771970515882608,0.886355718513012,3.04635347496687,-3.39612754130267
+53,-0.668719847424967,1.17023150528947,2.60164063243097,-2.90857000032341
+53.1,-0.539452772643017,1.40624764221344,2.07966340121862,-2.30505695195465
+53.2,-0.389389063848881,1.58521373431672,1.47795864791239,-1.60964855693931
+53.3,-0.224545768575621,1.70024628258955,0.818393583228316,-0.850068553498602
+53.4,-0.0515185374700774,1.74806924063227,0.1327492859825,-0.0565989993762971
+53.5,0.122836186495291,1.72706370007543,-0.559122340400846,0.73912697824267
+53.6,0.291599687056651,1.63810066323702,-1.20602249035494,1.50538629568916
+53.7,0.448302962714461,1.48569806112928,-1.80542076002075,2.21163061204768
+53.8,0.586952030772064,1.27624247341797,-2.36271484815132,2.82970419510781
+53.9,0.701973950348154,1.01794163969271,-2.78670286650151,3.33496640155699
+54,0.789128841259229,0.721128542156945,-3.08635746717625,3.70727402167114
+54.1,0.845420157498541,0.397281165709151,-3.33582429704656,3.93178432552095
+54.2,0.868353230767387,0.059205027169321,-3.42191322258949,3.99954679577516
+54.3,0.857067171810339,-0.280006283852881,-3.32706332473397,3.90785995658159
+54.4,0.812510479605951,-0.607663131950302,-3.16051852758853,3.66037907288432
+54.5,0.736348602125678,-0.911221471414874,-2.87297579422971,3.26697042654527
+54.6,0.631456966703107,-1.17881227656261,-2.45111512249235,2.7433179788212
+54.7,0.502054180055613,-1.40082637574421,-1.95336045736763,2.11029810032202
+54.8,0.353117788834443,-1.56857370238091,-1.38014308261943,1.3931472959938
+54.9,0.190379966787078,-1.67528574200807,-0.748978456540289,0.620456105304778
+55,0.0201523601743106,-1.71751062158304,-0.0903099544153046,-0.176970712340284
+55.1,-0.15097834598261,-1.69333464248243,0.581956364118825,-0.967342266147715
+55.2,-0.316289488498342,-1.60302464105252,1.21483289086554,-1.71914893642888
+55.3,-0.469452302105419,-1.4503716042302,1.80162038092841,-2.40241856370276
+55.4,-0.604598911903212,-1.2411756787352,2.36034018597741,-2.98991134411205
+55.5,-0.716142119841231,-0.982991529221922,2.7937894365975,-3.45820579444243
+55.6,-0.799747433413274,-0.685639195666135,3.1057771958249,-3.78863249274784
+55.7,-0.852294975027069,-0.360501784164729,3.34521843626646,-3.96801836928859
+55.8,-0.871390332278199,-0.020122804225618,3.42929268226182,-3.98921187525186
+55.9,-0.856192762706711,0.322375215408923,3.37181476678984,-3.85136809243487
+56,-0.807277045467324,0.653905016150409,3.21042691776193,-3.55998241746733
+56.1,-0.726257059050318,0.960969964910205,2.89843987938975,-3.12667147768952
+56.2,-0.616252673839415,1.23161283661252,2.47453053670337,-2.56871001287864
+56.3,-0.481502983261478,1.45513253833522,1.96109733118294,-1.90834218588752
+56.4,-0.327142319371711,1.62176908117505,1.35533740548058,-1.17189477806704
+56.5,-0.159228281427139,1.72495069224455,0.69664406625593,-0.388727623572836
+56.6,0.0156521971799928,1.76034766042739,-0.00394706194363215,0.40993687457226
+56.7,0.190493205167688,1.72532378789641,-0.697492155823548,1.19225848315877
+56.8,0.358359291597148,1.62106553427138,-1.36008978891856,1.92704850841091
+56.9,0.512624480137422,1.45170010781882,-2.00667572041944,2.58501319078597
+57,0.646822911473502,1.22316697278945,-2.55474954452363,3.13992155472524
+57.1,0.755473847364345,0.944275873780184,-2.97109058157938,3.56965115487306
+57.2,0.834413877439395,0.626071867257521,-3.32960893269238,3.85707002816171
+57.3,0.880057818187521,0.281164571767317,-3.55286974773665,3.99071969111587
+57.4,0.89017306145828,-0.0764461264672943,-3.57164015089442,3.96527195342947
+57.5,0.864571903220095,-0.43244062076451,-3.47708902247902,3.78174133609908
+57.6,0.80419985475712,-0.772484035858681,-3.27032618961769,3.44744462567331
+57.7,0.711124544397968,-1.08210424555491,-2.89205906992255,2.97570917706255
+57.8,0.589128643339591,-1.34888933040631,-2.40193412647461,2.38534159395568
+57.9,0.443113401016467,-1.56199333510426,-1.82357344282523,1.69987796887844
+58,0.278862424265091,-1.71181032819441,-1.15830454536157,0.946645573457144
+58.1,0.1030284020601,-1.79241151649161,-0.448569669726739,0.155673406334965
+58.2,-0.0772913168421593,-1.80060338151221,0.295966544709038,-0.641504968241948
+58.3,-0.254651370297328,-1.73509834550598,1.01370093350801,-1.41310856412099
+58.4,-0.421874414417416,-1.5986436338331,1.68015724746413,-2.12837598087053
+58.5,-0.572295886062864,-1.39725378878568,2.31691771686564,-2.75879176374156
+58.6,-0.699548180539655,-1.13873444813981,2.84150443595326,-3.27922322486305
+58.7,-0.798385430656913,-0.833628172298409,3.20900679549124,-3.66892240419654
+58.8,-0.865132612819259,-0.494540170353653,3.4990697493315,-3.91235322522886
+58.9,-0.89688909748829,-0.13534926180238,3.65965780655267,-3.99981086931586
+59,-0.892049004091794,0.228898066442701,3.60511637826204,-3.92780867617633
+59.1,-0.851157746912678,0.583466067688855,3.42033840518923,-3.69921714603469
+59.2,-0.776063105681669,0.914092603510251,3.13383759890993,-3.32314950183539
+59.3,-0.669630088461561,1.20681510966502,2.68936638826144,-2.81459837380262
+59.4,-0.536303407358839,1.45011532638389,2.14148226186807,-2.19383809058509
+59.5,-0.381561903637436,1.63440964991718,1.51448548449103,-1.48561640575236
+59.6,-0.211675545071123,1.75171261509378,0.822613563492086,-0.718167882955955
+59.7,-0.0335630508698891,1.79794866905546,0.104815448160761,0.0779117270240975
+59.8,0.145597597812953,1.77179484226075,-0.632802274174623,0.870885242312316
+59.9,0.318430223754048,1.6739003038524,-1.32142279586259,1.6291393112269
+60,0.478048621736518,1.50874053812944,0,2.32244473684926

Work 1/scripts/problem3_data_T90s.csv

@@ -0,0 +1,902 @@
+t,q,dq,ddq,u
+0,0,0,0,0
+0.1,0.00112730370377742,0.0336536743050961,0.657669343872878,0.794677323180245
+0.2,0.00883130084628362,0.130095105060834,1.23031152735571,1.5576733692346
+0.3,0.0288384132623469,0.277086967848714,1.6472957578342,2.25856989358014
+0.4,0.0653184832567522,0.456177260208145,1.85826392239339,2.86942436359809
+0.5,0.120381192475091,0.64441963262565,1.82183441394098,3.36588393923159
+0.6,0.19366224583284,0.816729955124557,1.5387129073771,3.72815634386891
+0.7,0.28233042826436,0.947731422726794,1.01198704123085,3.94179891995384
+0.8,0.381118481108189,1.01514724688817,0.281130829714293,3.99829441216602
+0.9,0.48271784224916,1.00127150126433,-0.606890939324855,3.89539052351278
+1,0.578248293996883,0.894322024572221,-1.54403616041735,3.63718970730273
+1.1,0.658338384140432,0.691502504394097,-2.46777849195839,3.23398561527836
+1.2,0.713750689364397,0.398398200996943,-3.35626893527373,2.7018527222046
+1.3,0.735600305235625,0.0284599263544737,-4.00825914367234,2.06200548728586
+1.4,0.71736732967013,-0.396782279453475,-4.38489881755735,1.33995260062362
+1.5,0.655285365929061,-0.849118356836855,-4.531083639236,0.564480032239469
+1.6,0.547892565795632,-1.29622623806606,-4.3244857319699,-0.23349657371032
+1.7,0.397254908342504,-1.70407791327366,-3.73168898607231,-1.02216440810733
+1.8,0.209300361028653,-2.04006080855522,-2.86613213766537,-1.77008177317941
+1.9,-0.00731550766185135,-2.27387198043844,-1.72922293231809,-2.44743156377088
+2,-0.241223605675537,-2.38106324008954,-0.381252753564326,-3.02720998123171
+2.1,-0.478944231224866,-2.34680237646659,1.08356113140267,-3.48630308965435
+2.2,-0.705829245460168,-2.16426570569947,2.58237734005865,-3.80640829555806
+2.3,-0.906890486294884,-1.83629821096442,3.93455844050654,-3.97476401453386
+2.4,-1.06860614272453,-1.37787653165824,5.11374520668299,-3.98465843534336
+2.5,-1.17918434708735,-0.81284329382283,6.09389607575295,-3.83569709865255
+2.6,-1.22882359069265,-0.17295878351365,6.62469772469187,-3.53381862288061
+2.7,-1.21221585705102,0.503754630673891,6.74037610639779,-3.09105795022395
+2.8,-1.12820436234541,1.17582411838087,6.533191358181,-2.52506655148928
+2.9,-0.978860954057995,1.79981035847128,5.85182622072886,-1.85840871765503
+3,-0.770999283563291,2.33562906493079,4.75245091059759,-1.1176619927957
+3.1,-0.515613103962611,2.74891875894459,3.39005668287868,-0.332357611269986
+3.2,-0.226326357533143,3.01046279160286,1.78219595985548,0.466196819401975
+3.3,0.0807823484948785,3.10169417161173,0.0444195098736388,1.24616545405351
+3.4,0.388335249621637,3.01614941528424,-1.75393602905129,1.97645340455444
+3.5,0.678348790457882,2.7560797824945,-3.43408611860293,2.62794639487516
+3.6,0.934021470108098,2.33567935225527,-4.86907935984763,3.17467145539661
+3.7,1.14100335615984,1.78100950577136,-6.08628991994047,3.59483238324651
+3.8,1.28712234301217,1.12495585256584,-6.94253943286844,3.87167868812595
+3.9,1.36381593553582,0.406902302885183,-7.28297214851448,3.99417338149842
+4,1.36767980657433,-0.330174021755641,-7.26531793532952,3.95743298649353
+4.1,1.29889049825954,-1.04224588166547,-6.8546938160307,3.76292222671909
+4.2,1.16155425178444,-1.68650054567169,-5.94967344220412,3.41839563235312
+4.3,0.964721270887307,-2.22697247599071,-4.74230088590455,2.93758839149645
+4.4,0.720465281131124,-2.63413817732492,-3.30905701113038,2.33966877156705
+4.5,0.443118721263638,-2.88581866922071,-1.7019965436784,1.64847394096703
+4.6,0.148752195959367,-2.9721968288911,-0.0363712415656969,0.891559656400984
+4.7,-0.145978041760561,-2.89314281403451,1.60780240616761,0.0991017018134311
+4.8,-0.424630255418812,-2.6573248762253,3.05425204912372,-0.697307124891926
+4.9,-0.672739948585826,-2.28475882540464,4.28045566687232,-1.46591651700771
+5,-0.878045085084117,-1.80273599561743,5.25923148399132,-2.17608444355748
+5.1,-1.0307579067425,-1.24353668430421,5.82481140361667,-2.79949875037417
+5.2,-1.12522261436471,-0.64300440916985,6.04748257510137,-3.31130587634261
+5.3,-1.1592124962359,-0.0379409362849631,5.93663216000362,-3.69110168645123
+5.4,-1.13383605650707,0.536222156936198,5.4497172587264,-3.92374492026597
+5.5,-1.05396244419096,1.0488134681975,4.70608941857471,-3.99996082620281
+5.6,-0.927027937689112,1.47376030771876,3.73555922576465,-3.91671091660527
+5.7,-0.762737838929616,1.79264354239405,2.61355404944882,-3.6773141026587
+5.8,-0.572312199675631,1.99548574983561,1.42458709467826,-3.29131437987483
+5.9,-0.367640689474864,2.07886112031207,0.262305797895213,-2.77410033910849
+6,-0.160346121295144,2.04848897718534,-0.810850096629073,-2.14629167200174
+6.1,0.0388399459182844,1.91690138358474,-1.7735540422846,-1.43291712894731
+6.2,0.220290472708867,1.70086688471167,-2.49938359217591,-0.662416701793238
+6.3,0.376747163577691,1.42178996137362,-2.98924153660433,0.134492188884554
+6.4,0.503311439080471,1.10348685128045,-3.29015849694172,0.926039300406156
+6.5,0.596974129613834,0.769202496718443,-3.33640210419518,1.68066814730656
+6.6,0.657272799105245,0.440521180295967,-3.17264695963293,2.3682940588289
+6.7,0.685844999000327,0.135894667251945,-2.86638329348033,2.96150355980979
+6.8,0.685753365960606,-0.130056648987916,-2.42584670939147,3.43664725942599
+6.9,0.66140326582697,-0.348319746055368,-1.9226177252087,3.77478267777642
+7,0.617826988441247,-0.514598278935145,-1.4050180793338,3.96242942277948
+7.1,0.560200530262186,-0.629615801215413,-0.916072884584706,3.99210661086545
+7.2,0.493413343237278,-0.698799738553371,-0.492918132824704,3.86263110619711
+7.3,0.421696974884123,-0.730300222058687,-0.171396746593982,3.57916468856201
+7.4,0.348266639065028,-0.734788651043527,0.0391562230663334,3.15300826950127
+7.5,0.275227865476597,-0.723747007930665,0.146209239141171,2.60115136062847
+7.6,0.203651184279577,-0.707781762836823,0.149580300874469,1.94559475541519
+7.7,0.133570306091302,-0.695777792179925,0.0729875409504171,1.21247342698281
+7.8,0.0642193033125308,-0.693970566176327,-0.0528266102661962,0.431014609197769
+7.9,-0.00565996556890208,-0.705189843622758,-0.176774620509154,-0.367627400910727
+8,-0.0773069806554265,-0.728754337147554,-0.272236743211374,-1.15161326666026
+8.1,-0.151676363174065,-0.760025340521132,-0.320431798418941,-1.88968794559386
+8.2,-0.229250063676892,-0.791068874381493,-0.269443420196352,-2.5524267293918
+8.3,-0.309518198381683,-0.812020729944363,-0.116985223730814,-3.11340831413719
+8.4,-0.390956185323783,-0.811937896451692,0.150000908551928,-3.55026813432602
+8.5,-0.470894163180363,-0.780014211551689,0.506511756278782,-3.84558996751823
+8.6,-0.545767023474155,-0.706877423058831,0.987756481582191,-3.98760026416638
+8.7,-0.610762318952125,-0.584754897081678,1.49232424767726,-3.97063752188253
+8.8,-0.660834371953323,-0.410270182511013,1.99274911516514,-3.7953779916725
+8.9,-0.690978933802869,-0.185167021665459,2.4515939666655,-3.46880871794233
+9,-0.69660755598576,0.0846502421423621,2.89889571627953,-3.0039489870867
+9.1,-0.673247221005856,0.38886209853353,3.18600736796194,-2.41933128962514
+9.2,-0.618026812346333,0.712716882427269,3.24837904850609,-1.73826248828757
+9.3,-0.530322613201749,1.03769639917485,3.14927230108926,-0.987894646946484
+9.4,-0.411125691046272,1.34339406863417,2.88048334532758,-0.19814256351347
+9.5,-0.263123935437519,1.60779762342013,2.36197978077322,0.599508838651809
+9.6,-0.0915023820210343,1.81056496541803,1.63746143257671,1.37325971527959
+9.7,0.0964937857212176,1.93408194004453,0.767273551172054,2.0922630606308
+9.8,0.29216268897519,1.96313670409293,-0.221801959468998,2.72785448027254
+9.9,0.485613572634473,1.88840380409875,-1.26370594814139,3.25469495002842
+10,0.666427396812341,1.70781029255568,-2.32502138310754,3.65178100291051
+10.1,0.823991007159134,1.42465365235776,-3.33319403023297,3.90328207106791
+10.2,0.948222677203598,1.04894121731208,-4.13865076550263,3.99917160057068
+10.3,1.03106783959304,0.598156775647957,-4.76046725558523,3.93562677847446
+10.4,1.06630832942662,0.0947352695087333,-5.21785090601743,3.71518093630896
+10.5,1.04937031020003,-0.434312443933761,-5.31641723595177,3.34662255414422
+10.6,0.979268118613924,-0.959752129511345,-5.08241943079759,2.84464489162392
+10.7,0.858341732719841,-1.45161171663343,-4.62975436959169,2.22926021407063
+10.8,0.691117803129841,-1.8802525964871,-3.86724815518654,1.52500196661976
+10.9,0.485221391987975,-2.21970646439723,-2.85754093317921,0.759946703181751
+11,0.250749571514318,-2.44943291557137,-1.6716101302423,-0.0354052371616155
+11.1,-0.000438350261762848,-2.55312745846465,-0.375763795189493,-0.829345682427049
+11.2,-0.255383909989738,-2.52309987678432,0.952965679522412,-1.59022273248574
+11.3,-0.50079981292249,-2.3602203193737,2.28511009481016,-2.28770262043826
+11.4,-0.723364614907139,-2.07139984431106,3.47086400980671,-2.89397902417698
+11.5,-0.911220776793722,-1.6717298045001,4.42872084424178,-3.38488161670068
+11.6,-1.05478973023789,-1.18365614859634,5.21919831200609,-3.74083966077816
+11.7,-1.14616670056199,-0.633909431993268,5.71312747678929,-3.9476622324826
+11.8,-1.1804123961182,-0.052903997274252,5.811101392612,-3.99710396854651
+11.9,-1.15654707774829,0.527556150777705,5.65764025054154,-3.88719378297545
+12,-1.07610535687297,1.07571672648671,5.21631278315875,-3.6223134480265
+12.1,-0.943500508166056,1.56146712848275,4.43697105899985,-3.21302290677581
+12.2,-0.766525948869145,1.96035615835788,3.46092939912567,-2.67563928151209
+12.3,-0.554942095580977,2.25250630665306,2.32723683989551,-2.03158636156249
+12.4,-0.320085873893855,2.42370796171182,1.08931263730662,-1.30654050441889
+12.5,-0.0743365258336663,2.46879082652308,-0.177019240920412,-0.529407000391092
+12.6,0.169642629817318,2.38887320745735,-1.41378215966316,0.268832290101914
+12.7,0.399483963871671,2.1912696737395,-2.4953847335798,1.05635408553789
+12.8,0.604371450590226,1.89125156271722,-3.41634101074372,1.80176237710156
+12.9,0.775095527201344,1.50871959992941,-4.16363340087454,2.47534008848016
+13,0.904183269803716,1.06691912927852,-4.60578356433547,3.05023380191841
+13.1,0.987213176762734,0.591483046925509,-4.80212576778489,3.50352431924356
+13.2,1.0222218260439,0.108629047861579,-4.76881448780196,3.81714037797079
+13.3,1.00954233044705,-0.356205183827859,-4.45876635868865,3.97857909551135
+13.4,0.952275171263314,-0.780824415768235,-3.96220376540213,3.98140441964624
+13.5,0.855385974425555,-1.14594637692938,-3.2952486798701,3.82550371361801
+13.6,0.725544290789095,-1.4371149546949,-2.50230123302676,3.51709224660289
+13.7,0.570679594822368,-1.64564000854823,-1.64702732564755,3.06846541054211
+13.8,0.399344625599165,-1.76678408803482,-0.7808677142772,2.49750854166557
+13.9,0.22020097923319,-1.80188062145097,0.0469489535941892,1.82698388857677
+14,0.0415268224031566,-1.75709452297478,0.824257478982615,1.08362315323148
+14.1,-0.12890475963705,-1.64114478327725,1.47027075825354,0.297061782337431
+14.2,-0.284633634094722,-1.46622301139371,1.97079614706269,-0.501342504385731
+14.3,-0.420654547081767,-1.24683654154735,2.36176611031907,-1.27975984753679
+14.4,-0.533057798965621,-0.997314523257605,2.59310175487771,-2.0071572040823
+14.5,-0.619530033300698,-0.731801275213912,2.66333555853069,-2.65453553685187
+14.6,-0.679368912050468,-0.462916466781302,2.66219437240939,-3.19608591463846
+14.7,-0.712585847076144,-0.202057577113865,2.55190149362583,-3.61021843284075
+14.8,-0.720283767165562,0.0418838528707965,2.32163308146019,-3.88042293482874
+14.9,-0.704765356440377,0.263312972330478,2.0788313333124,-3.9959272197878
+15,-0.668458632382069,0.458661712399707,1.81834120086989,-3.95212649637145
+15.1,-0.613968496315062,0.626131581623423,1.5363026747621,-3.75076696120112
+15.2,-0.544115333500434,0.766427475271897,1.27216427812526,-3.3998761835173
+15.3,-0.461540527904553,0.881036343301911,1.02622940697884,-2.91344307132637
+15.4,-0.368703428238884,0.97178141526668,0.797298150513748,-2.31086017778293
+15.5,-0.267893347068078,1.04105962463048,0.592183486474357,-1.61615058129226
+15.6,-0.161161431032528,1.09030538050508,0.394598168220051,-0.857010161183537
+15.7,-0.0504835333147771,1.11987929835739,0.196387416210489,-0.063703450400393
+15.8,0.0621582385650784,1.12950638006746,-0.00542612113192259,0.732142915922352
+15.9,0.174745749233615,1.11775704891626,-0.239453023628034,1.49880105459785
+16,0.284938729665871,1.08162158397329,-0.499980045730042,2.20570672496676
+16.1,0.390131909640826,1.01802771910313,-0.781014098836352,2.82467782872134
+16.2,0.487514948627418,0.92408182259519,-1.081230681301,3.33103794123112
+16.3,0.574085680801,0.797145817515727,-1.46172506984858,3.70460008272211
+16.4,0.646039162276096,0.635051860971201,-1.81897397838964,3.93047150945656
+16.5,0.699802903967296,0.437977095267359,-2.13057734233631,3.99964744042907
+16.6,0.732260872235133,0.208731503507477,-2.39893781212285,3.90937004956903
+16.7,0.740729462381741,-0.0478983366353404,-2.68422717530223,3.66323841156328
+16.8,0.722355780775327,-0.324577270594466,-2.85733049764975,3.27106501810577
+16.9,0.675408794192415,-0.611199331914073,-2.86159329006442,2.74848458481896
+17,0.599845874708859,-0.895577408933868,-2.75462306175851,2.1163307444801
+17.1,0.496736724607718,-1.16413733097779,-2.55068385730742,1.39980547582665
+17.2,0.368120735933503,-1.40174697538996,-2.16745299394969,0.62747438019364
+17.3,0.217830217319791,-1.59394033340686,-1.63449153404597,-0.169872138867806
+17.4,0.0511947833656191,-1.72774820042218,-0.990788498982925,-0.960446391815126
+17.5,-0.125348535578382,-1.79095853322587,-0.244208088454634,-1.7127306779846
+17.6,-0.304333935406929,-1.77494222941117,0.565762756929766,-2.39673379685706
+17.7,-0.477661707666179,-1.67577850449359,1.41246201984706,-2.98518670257967
+17.8,-0.636864859726958,-1.49279172650053,2.25451472115812,-3.45462963477182
+17.9,-0.773522864576156,-1.22990903082873,2.98243310512067,-3.78634738513985
+18,-0.880356538374148,-0.896795339672411,3.59912160219525,-3.96711541377246
+18.1,-0.951198996150186,-0.507078295983122,4.13585113634964,-3.98972706981459
+18.2,-0.980682942562729,-0.0782624790182752,4.41974070040262,-3.85328089789504
+18.3,-0.965969481971245,0.369209230986198,4.44685044666215,-3.56321657630745
+18.4,-0.906787516913139,0.813039716275554,4.32412725327548,-3.1310980542026
+18.5,-0.804364279322279,1.22992832619715,3.95418668923797,-2.574152533428
+18.6,-0.662399174839039,1.59732144999188,3.33450271279904,-1.91458367435366
+18.7,-0.487089043227809,1.89570309190105,2.56072149023441,-1.17868640600103
+18.8,-0.286171696714235,2.10752289091859,1.63380699481278,-0.395798630201158
+18.9,-0.0689162802525327,2.21975287654311,0.601171810279521,0.40286838797003
+19,0.154350854311965,2.22590557055069,-0.484649769109757,1.18547431483754
+19.1,0.372771491185364,2.12370409200131,-1.56606702536715,1.92081912175304
+19.2,0.575531457805093,1.91658596997831,-2.54192275532754,2.57958693177949
+19.3,0.752872196871545,1.61513069870749,-3.41107769073864,3.13551475119317
+19.4,0.896102159030612,1.23422981873052,-4.15639887813241,3.56643949216578
+19.5,0.997768132408354,0.792893829276582,-4.62323032183455,3.85518154513635
+19.6,1.05320180256775,0.313605645687501,-4.8481244644333,3.99022967563122
+19.7,1.06015422808282,-0.179546987516398,-4.91488492044831,3.96619994085656
+19.8,1.0179578043934,-0.660879466111878,-4.68136281855165,3.78405033050763
+19.9,0.92894775251846,-1.10636537743869,-4.16180978968383,3.4510425747427
+20,0.798319602746686,-1.49481248709571,-3.51517542213731,2.9804526419174
+20.1,0.632539698753539,-1.80722433110447,-2.68738958893158,2.39104146762102
+20.2,0.439885898871076,-2.02917282735089,-1.73208782361008,1.70630701537827
+20.3,0.229911220752512,-2.15237819552755,-0.710795377392154,0.953547486995568
+20.4,0.0128285888600272,-2.17230006411957,0.315922489802078,0.162773029399431
+20.5,-0.201094818134437,-2.0903027376454,1.28748934567074,-0.634490675218836
+20.6,-0.402143331672194,-1.91412015001225,2.1926363861591,-1.40645923886727
+20.7,-0.58126548134836,-1.65477018330869,2.96351861302532,-2.12235671100084
+20.8,-0.730752444894273,-1.32724438029781,3.52120350121381,-2.75364251855068
+20.9,-0.845027373428048,-0.949786544885405,3.9384998579091,-3.27514928850739
+21,-0.919917303382731,-0.542076550670578,4.17036962574346,-3.66608619166254
+21.1,-0.953103537079981,-0.124594019434533,4.13445653213582,-3.91086780736008
+21.2,-0.944945205455871,0.28321891472206,3.93971722599928,-3.99973546503522
+21.3,-0.897389701571769,0.663372154026642,3.60523778178998,-3.92914629161454
+21.4,-0.813781819869767,0.999468590505036,3.08953900601766,-3.70191445468531
+21.5,-0.699278548107589,1.27936657263204,2.47384718357677,-3.32709897051439
+21.6,-0.560036804509643,1.49417578796122,1.79612332768767,-2.81964254965699
+21.7,-0.40283382763482,1.63778391118715,1.07609516888449,-2.19977587824137
+21.8,-0.234869899071152,1.70891730570789,0.356936923753887,-1.49221108435449
+21.9,-0.0633366012699452,1.70932239145856,-0.342855223248106,-0.725156543478751
+22,0.104768144298781,1.64296382408564,-0.965614133652237,0.0708077004216543
+22.1,0.263216748530984,1.51726881879719,-1.50576113296862,0.863949064752896
+22.2,0.406607741433501,1.3414083745033,-1.97934131219756,1.62264750622137
+22.3,0.530205321214043,1.12521365347596,-2.32218932106997,2.31665611217708
+22.4,0.630581007783884,0.879321210604174,-2.54362052236902,2.91830694957143
+22.5,0.705520489130036,0.614202224639568,-2.71503029066088,3.40361409813647
+22.6,0.753309667569579,0.340232064407692,-2.7634845432973,3.75322989333422
+22.7,0.773464000576149,0.0667830029911999,-2.68306683484101,3.95321625668655
+22.8,0.766787665234309,-0.198274692895016,-2.5743206743433,3.99560036298008
+22.9,0.734368123149035,-0.447839416471289,-2.40086929997317,3.87869249164768
+23,0.67793988806403,-0.675675555199043,-2.14740377404013,3.60715339059524
+23.1,0.600037615238624,-0.877441627681111,-1.8683611703162,3.19180846689052
+23.2,0.503451730710056,-1.04925827423153,-1.55673369364551,2.64921621194495
+23.3,0.391298509245033,-1.187710197628,-1.20786651505307,2.00100806671435
+23.4,0.267066622629479,-1.29073839348898,-0.843475158508522,1.27302604440993
+23.5,0.134399984428839,-1.35621124674887,-0.45834423934557,0.494292490980896
+23.6,-0.00285009616525561,-1.38214313844087,-0.0597915427499929,-0.304146944233414
+23.7,-0.14069809218685,-1.3677196718212,0.341594495654612,-1.09046100057232
+23.8,-0.275130143251899,-1.31238820970223,0.770356233530126,-1.83330181796706
+23.9,-0.401858631981647,-1.21551167499635,1.17996208449841,-2.50305467719792
+24,-0.51678749986641,-1.07789083789226,1.55645817174543,-3.07301864529467
+24.1,-0.616151786033719,-0.901726454358557,1.93499979117069,-3.52047105747465
+24.2,-0.696166074289321,-0.689790388407538,2.3040255549847,-3.82757339808196
+24.3,-0.753140106995076,-0.446498125688527,2.57237301210506,-3.98208246591406
+24.4,-0.784390409579781,-0.178077175731731,2.74876254517945,-3.97783847201806
+24.5,-0.788153086712691,0.107866400078127,2.91170359449562,-3.81501061103789
+24.6,-0.762798727900644,0.402050475566698,2.96456315632181,-3.50009031595779
+24.7,-0.70779873752538,0.693630398800415,2.85190257152917,-3.04563246515414
+24.8,-0.624279721434824,0.971304193936916,2.64308988309184,-2.46975485901385
+24.9,-0.51432980651335,1.22328068584776,2.34451262244704,-1.79541592040679
+25,-0.380934765367405,1.43702202626802,1.9022363739726,-1.04949941481572
+25.1,-0.228517360481734,1.60149980165784,1.35594955479644,-0.261742679442828
+25.2,-0.0625404600480991,1.70723298786561,0.723133207197657,0.536448910582657
+25.3,0.110667772457513,1.74556047096408,0.0261212037457797,1.31325397540561
+25.4,0.284137217000582,1.71138436459485,-0.702396267614652,2.03770374844174
+25.5,0.450582698867505,1.60324447735729,-1.45665282973336,2.6809167033735
+25.6,0.602461652437094,1.42199564129162,-2.17168076834996,3.21724996946366
+25.7,0.732623798323184,1.17251988262274,-2.78130028813478,3.62532163189067
+25.8,0.834972941327926,0.863894630807952,-3.32404433153262,3.88886316121816
+25.9,0.904081641017342,0.507947989425826,-3.7654821791352,3.99736798832524
+26,0.935535518915406,0.119619850397707,-3.97697025045027,3.94651036816194
+26.1,0.927219694308967,-0.283974659455778,-4.01013233041642,3.73831783355366
+26.2,0.878802546398364,-0.684574312503827,-3.92090730688439,3.38109036386569
+26.3,0.791176325418917,-1.06264825147564,-3.60298721598927,2.88906949101805
+26.4,0.667520232279577,-1.39984544914498,-3.08592312379943,2.28187053454949
+26.5,0.513004907902243,-1.679919724776,-2.45030807640092,1.58370060072734
+26.6,0.3339865027609,-1.88772854049162,-1.67365749636903,0.822393521610405
+26.7,0.138231522655866,-2.01209796539562,-0.802397941576066,0.0283002079996953
+26.8,-0.0655474368649281,-2.04669857780043,0.126830216926765,-0.766921345597463
+26.9,-0.268058094216455,-1.98802224163351,1.05467818633196,-1.53156816530593
+27,-0.460021969704661,-1.83763743815858,1.92000064433559,-2.23515619540647
+27.1,-0.632785838749512,-1.60281733897742,2.7260245502926,-2.84963560143942
+27.2,-0.778289462291437,-1.29399367347151,3.42299758092934,-3.35050902858813
+27.3,-0.889563110024069,-0.925382622971171,3.90393914283351,-3.71780823390966
+27.4,-0.961797366328365,-0.514567052029234,4.22975916071577,-3.93689015716755
+27.5,-0.991734031025504,-0.0809896783122246,4.37525368493632,-3.99902069343448
+27.6,-0.977918158873279,0.354662984202197,4.27513858004744,-3.90172289429372
+27.7,-0.92135090092058,0.772303187247996,4.00331506900946,-3.64887571595607
+27.8,-0.824750492277787,1.15227144713478,3.54344441665955,-3.25055937751643
+27.9,-0.692715639468398,1.47707858133419,2.90903247588405,-2.72265349442849
+28,-0.531590461900168,1.73295598865354,2.1629702230142,-2.08620400834765
+28.1,-0.348835582101796,1.90836515002523,1.32538367577951,-1.36658415185141
+28.2,-0.152826865545629,1.99657879079477,0.444346544123486,-0.592482897726517
+28.3,0.0476253164517723,1.99593687673925,-0.457232296479376,0.205238779842798
+28.4,0.24350517548438,1.90752289430775,-1.30752221312637,0.994778234928231
+28.5,0.426309812385724,1.73707263783885,-2.05807086992051,1.7446590209913
+28.6,0.588533740587864,1.49496636703473,-2.72923130396753,2.42498575747738
+28.7,0.723465355750327,1.19356066928053,-3.26803294249371,3.00863596429792
+28.8,0.825716641487854,0.847708232410025,-3.60138730156745,3.47234134952169
+28.9,0.891954054209706,0.473915621149829,-3.80278598247604,3.79761544274681
+29,0.920163607106798,0.0892582853721786,-3.83846668158505,3.97149059233815
+29.1,0.90998849318804,-0.289273251774021,-3.68180244808243,3.98703494477626
+29.2,0.862995354788457,-0.646216017130084,-3.4020414050806,3.84362879578247
+29.3,0.781981802338068,-0.967027066522191,-2.97987483490011,3.54698929597291
+29.4,0.671169501538677,-1.23980910243004,-2.44599336584057,3.10894252610489
+29.5,0.535897267080882,-1.45566247228799,-1.84328405672299,2.54695202855655
+29.6,0.382192192055856,-1.60748410878641,-1.18578618848739,1.88342259100155
+29.7,0.216629255145956,-1.69206266514918,-0.511346158493259,1.14480703822699
+29.8,0.0459528566511241,-1.70920750774921,0.168978693211869,0.360551641485862
+29.9,-0.123033754911589,-1.66029756109787,0.802595009824594,-0.438077811414833
+30,-0.283994416376057,-1.54991941587693,1.37150481295002,-1.21924248440887
+30.1,-0.431240029711024,-1.38511987597607,1.89468407300399,-1.9517998070917
+30.2,-0.559538802315952,-1.17369589413942,2.31726561265291,-2.60654503072624
+30.3,-0.66466491879435,-0.924925405621996,2.61248066855309,-3.1573755294142
+30.4,-0.743666228587218,-0.648804211695881,2.85767812786036,-3.58233142941909
+30.5,-0.794090757101482,-0.355774421770125,2.99505212150745,-3.86447108003357
+30.6,-0.814564764400671,-0.0564059192369974,2.97664744413738,-3.99254646373082
+30.7,-0.805272297258487,0.239453298470109,2.88897549734179,-3.96145161912805
+30.8,-0.767090075142885,0.522508836684342,2.73692186229008,-3.77242619955413
+30.9,-0.701538634404382,0.783550236553308,2.46927421363601,-3.43300605198326
+31,-0.611294451529519,1.01504086865001,2.13386044465128,-2.95672278659689
+31.1,-0.499711664208143,1.21045072857571,1.74972521260727,-2.3625643141872
+31.2,-0.370631624760694,1.36354449245872,1.30223532286094,-1.67421785807368
+31.3,-0.228529232084636,1.4700838568005,0.819781869089819,-0.919125619258752
+31.4,-0.0782290207176797,1.52703812494592,0.306584930313178,-0.127390742472572
+31.5,0.0751370399524083,1.531787600798,-0.215459272375323,0.669422801211228
+31.6,0.226348507898743,1.48387842999012,-0.728680800790293,1.43954857029657
+31.7,0.370273167837175,1.38457740147688,-1.24943206404484,2.1522840806424
+31.8,0.501703507135158,1.23577321485867,-1.72988446314417,2.77921481661816
+31.9,0.6158350018017,1.0412765661002,-2.13411763174883,3.29534702817489
+32,0.708625320150753,0.806740623731863,-2.51113103064438,3.68010415278716
+32.1,0.776304328193363,0.538928425627184,-2.83525831397685,3.91814713806804
+32.2,0.815630753096204,0.246289597031347,-3.01442210716907,3.99998596138243
+32.3,0.824812956927355,-0.0614832041052829,-3.08514279515974,3.92235796710212
+32.4,0.803143732806908,-0.373953763378354,-3.10816394670649,3.68835793838981
+32.5,0.750392869219396,-0.679329683368414,-2.98300067341966,3.30731471796041
+32.6,0.667811998897687,-0.965743410289283,-2.7098985121046,2.79441929656106
+32.7,0.558132143454933,-1.22203951643419,-2.36311438054907,2.17011919610783
+32.8,0.424821144206687,-1.43679570783078,-1.90211716826367,1.45930329151292
+32.9,0.272488973275806,-1.59976602467912,-1.33692849357547,0.690309569783273
+33,0.106787517409169,-1.70323241104461,-0.70617188786401,-0.106204616095867
+33.1,-0.0659756573361076,-1.74057266142648,-0.0216437982321987,-0.898484759079311
+33.2,-0.238955270063706,-1.70760761208279,0.677855840378555,-1.65494515005088
+33.3,-0.405156324387519,-1.60409141022082,1.37337952493222,-2.34542810037133
+33.4,-0.55762358346201,-1.43218349305218,2.05864794649053,-2.94240623375632
+33.5,-0.689504363071596,-1.19677480937801,2.63653537950597,-3.42207991590129
+33.6,-0.795019788886122,-0.906397820743869,3.10637308940034,-3.76532607079692
+33.7,-0.869471483806644,-0.572125020994657,3.52607802983182,-3.9584605574234
+33.8,-0.908662398428848,-0.207466729894057,3.75847084135402,-3.99378371327004
+33.9,-0.910268604637512,0.172329063105214,3.78364594574678,-3.86988731558193
+34,-0.874038351388709,0.551043728729605,3.70730958140954,-3.59171072275717
+34.1,-0.800735002325809,0.911843293529007,3.462546695685,-3.17034395771468
+34.2,-0.69280618630606,1.2380304567007,3.02150651590891,-2.62258558367701
+34.3,-0.554662305127222,1.51513403950299,2.46529157048183,-1.97027299846552
+34.4,-0.391865508243565,1.72989200358458,1.79284593257448,-1.23941184636124
+34.5,-0.211140252034164,1.87134905910922,1.0224227437125,-0.459139255132749
+34.6,-0.0201907683876373,1.93304167745406,0.201316606686122,0.339437769300183
+34.7,0.17277188132575,1.91129652978029,-0.648139675180505,1.12448248102894
+34.8,0.359253134287333,1.80570813044314,-1.45233206451728,1.86469762474874
+34.9,0.531211066603743,1.62101702973504,-2.1945589636815,2.53057315856339
+35,0.681223409283338,1.36533053691152,-2.88666680642853,3.09556272623156
+35.1,0.802369083898647,1.04954661371724,-3.4078011327733,3.53714197661794
+35.2,0.889436747186224,0.687764662682182,-3.76304505955198,3.83770653849353
+35.3,0.93887395987828,0.296247049655626,-3.99874894552241,3.98527385126269
+35.4,0.948323683115113,-0.107364629541952,-4.02322700601387,3.97396087184089
+35.5,0.917541136291807,-0.505194341924379,-3.86939968501233,3.8042186130175
+35.6,0.848064592618377,-0.879763975447483,-3.56503709982814,3.48281416299914
+35.7,0.742937677946667,-1.21418116424588,-3.08195949524544,3.02256090295765
+35.8,0.606991168322501,-1.49449590034632,-2.478897635323,2.44180767795773
+35.9,0.446255682345106,-1.70874321653988,-1.7759084968985,1.7637072864074
+36,0.267761111398726,-1.84777496274074,-0.997414460222523,1.01529345104815
+36.1,0.07929239585012,-1.90718391726351,-0.186330696744008,0.226403069739362
+36.2,-0.111039626665926,-1.88525704648404,0.630111207413222,-0.571513287503728
+36.3,-0.295070537107839,-1.78354266072463,1.38566357854514,-1.34664521348851
+36.4,-0.465244811764301,-1.6082803973491,2.07391978207085,-2.06809064439617
+36.5,-0.614679888600055,-1.36831260602331,2.69485483067931,-2.70708782754923
+36.6,-0.737166417129015,-1.07474666364329,3.14810891491782,-3.23816196172753
+36.7,-0.828171856508797,-0.741051886076848,3.45108459628067,-3.64014079710274
+36.8,-0.884666449925773,-0.381826264059444,3.67265584971101,-3.896998706026
+36.9,-0.904434484845638,-0.0128887645268788,3.69593348276997,-3.99849557423056
+37,-0.887243184937804,0.350344816324664,3.52264605656962,-3.94058504187299
+37.1,-0.834825424464273,0.693549135233025,3.27238319371003,-3.72557581913113
+37.2,-0.749683832053642,1.0030828793926,2.88353046471946,-3.36203964521487
+37.3,-0.635706934995817,1.26711503201761,2.37075122760465,-2.8644695601735
+37.4,-0.498022525661945,1.47686524786982,1.79277878594923,-2.25270211312447
+37.5,-0.34241032846858,1.62491777600676,1.15500798497955,-1.55112654163772
+37.6,-0.17524805142542,1.70682041750501,0.487842785115999,-0.787712449798735
+37.7,-0.00320734653110058,1.72170840933805,-0.188696676618061,0.00710525164334786
+37.8,0.166946391597039,1.67012580326578,-0.843888961273545,0.801639689124329
+37.9,0.328661240112442,1.55520926928202,-1.43225752799932,1.56421528192019
+38,0.476053513347853,1.38325936469567,-1.96659982465404,2.26443054759272
+38.1,0.603779788336723,1.16177591759149,-2.44227413655749,2.87437011315654
+38.2,0.707083321960019,0.899741186376182,-2.77931879403342,3.36971761290822
+38.3,0.78259366764298,0.607525301838249,-3.01565056522932,3.73072510519208
+38.4,0.827947507673648,0.296125566428187,-3.17098460444727,3.9430003605158
+38.5,0.841591501659843,-0.0228236964901042,-3.17840872140701,3.99808063432293
+38.6,0.823451408431968,-0.338083127822773,-3.08272901289559,3.89377004991262
+38.7,0.774484025075137,-0.638662477046212,-2.89429625230264,3.63422714111424
+38.8,0.69657367919528,-0.913766683083382,-2.58252129179597,3.22979906466655
+38.9,0.592838120397463,-1.15437300793858,-2.19617503169259,2.69660909173094
+39,0.46714081128272,-1.35218731640368,-1.73740345120036,2.05591382395014
+39.1,0.324069467655974,-1.50004908950298,-1.20942502050285,1.33325575981964
+39.2,0.168903873824199,-1.59339207660848,-0.644612589871618,0.557444995876983
+39.3,0.0072921540937077,-1.6287237235411,-0.0504596333333829,-0.240589340931885
+39.4,-0.154824161970117,-1.60407523394881,0.539910892242268,-1.02903213994137
+39.5,-0.311541369111519,-1.52043812062031,1.11362092020935,-1.77645067483003
+39.6,-0.457122367050828,-1.38043358340667,1.67776539023491,-2.45304772722756
+39.7,-0.585925711087788,-1.18816658929153,2.15937196968411,-3.03184950778026
+39.8,-0.693135335427906,-0.950078576059918,2.55348393032049,-3.48978101601214
+39.9,-0.77481012046482,-0.674197279687526,2.9231683855251,-3.80858596777644
+40,-0.827253221646483,-0.370110426775568,3.15895013097636,-3.9755546156935
+40.1,-0.848106821518382,-0.0486766531971755,3.23445689440825,-3.98403044667094
+40.2,-0.836615852446198,0.278502255254705,3.24165566582032,-3.8336755560747
+40.3,-0.792708326715811,0.599230238247933,3.13735071239699,-3.53048411892055
+40.4,-0.717427293861455,0.900713277579433,2.86778810791061,-3.08654342103193
+40.5,-0.613468379927992,1.1713770060556,2.49887731441993,-2.51955197709782
+40.6,-0.48452069285033,1.40027068753457,2.03984625582336,-1.85211394674281
+40.7,-0.335174543214434,1.57697677846239,1.47493661787887,-1.11083797801471
+40.8,-0.17107902739975,1.6938695778945,0.845782642625831,-0.325276404555104
+40.9,0.0014743148411927,1.74530920133054,0.163078442824524,0.473252912685059
+41,0.175658441510381,1.7271707902529,-0.530469967060693,1.25291512973234
+41.1,0.344537868508962,1.63911391412411,-1.20808076280753,1.98262757435958
+41.2,0.501336487879467,1.48383979420031,-1.88174028342174,2.6332989141402
+41.3,0.639317704415756,1.26600989720322,-2.46887297572954,3.17898893606931
+41.4,0.752610191194748,0.993494793779449,-2.93156237918131,3.59794270099703
+41.5,0.836587054181928,0.676857880071494,-3.3377184162808,3.87345784440074
+41.6,0.8871867330063,0.328521749092733,-3.61176035387242,3.99455044695128
+41.7,0.901668808291948,-0.0372447805776948,-3.67464750617006,3.95639292871475
+41.8,0.879404408515895,-0.405377003719065,-3.61243041277276,3.76050650953021
+41.9,0.821015704612114,-0.760520486439666,-3.43189250011623,3.41470056277522
+42,0.728308075707171,-1.08688353024557,-3.06300864127259,2.93276128029317
+42.1,0.604970360389502,-1.37057409391294,-2.56459684013159,2.3339020604292
+42.2,0.455986676670518,-1.59936970349085,-1.96810538218161,1.64199753046976
+42.3,0.287321939129717,-1.7622288584563,-1.27059128761339,0.884631740593333
+42.4,0.105951288712782,-1.85198707181431,-0.518045479608575,0.091998474836339
+42.5,-0.0805998165002384,-1.86469283234785,0.276966808200808,-0.704302479794348
+42.6,-0.264381253631251,-1.79850783039594,1.04798164088563,-1.47252511711069
+42.7,-0.437682874353407,-1.65602412655844,1.76514898006013,-2.18204282482954
+42.8,-0.593333005274961,-1.44368736666513,2.44679575619771,-2.80456937095676
+42.9,-0.724515178634539,-1.17003082861091,3.01146321287012,-3.31528658659437
+43,-0.825582719865415,-0.846657404461907,3.40918111281582,-3.69383378801624
+43.1,-0.892558449968134,-0.487618524852142,3.70498863792121,-3.92511949287651
+43.2,-0.92248429369164,-0.108328812324347,3.83555700406439,-3.99992306998662
+43.3,-0.914054567374502,0.274832613509385,3.77343286224901,-3.91526233678353
+43.4,-0.867890512434874,0.645819586064243,3.58450321522551,-3.67451244953764
+43.5,-0.785881425342991,0.98845470678921,3.22821838628455,-3.28727134652329
+43.6,-0.671590154388262,1.28831305016721,2.72827411086071,-2.76897710850764
+43.7,-0.530016142324926,1.53339045354134,2.13188063144838,-2.14029249118834
+43.8,-0.367123323947107,1.71299545610143,1.44171709946124,-1.42628116632888
+43.9,-0.189813334574675,1.82026053532874,0.699463904551983,-0.65540851225838
+44,-0.00550870615672311,1.85184854908476,-0.0780011523635465,0.141593210934643
+44.1,0.178015910737593,1.80636949539041,-0.831971370478446,0.932950059630973
+44.2,0.353220813927125,1.68653295057571,-1.53165247692787,1.68711313354398
+44.3,0.513109192347378,1.49879400146258,-2.18968954936181,2.37401633081594
+44.4,0.651100675274013,1.25134375605877,-2.74198157494283,2.96627498862002
+44.5,0.761672342451219,0.955041704860805,-3.13373251041312,3.44027762324981
+44.6,0.840906684524295,0.622744969754559,-3.44026095559188,3.7771272454645
+44.7,0.885738417041451,0.268452252908571,-3.6192064943556,3.9633947238168
+44.8,0.894378084615052,-0.0928752373167281,-3.58631071476341,3.99165416174582
+44.9,0.867154645041018,-0.446740112113153,-3.42603769653963,3.86077894463916
+45,0.805670828501588,-0.77929900547202,-3.16947353721734,3.57598665440223
+45.1,0.712492276589985,-1.07706526231832,-2.75852211776353,3.14863106093275
+45.2,0.591728503500747,-1.32904142533003,-2.24793185521261,2.59574948314374
+45.3,0.448485411859382,-1.5262616323709,-1.66669664330421,1.93938356482296
+45.4,0.288575353784975,-1.66113018752898,-1.02155179851006,1.20570054385143
+45.5,0.118449777725468,-1.72965373523755,-0.350581405774991,0.423950047004627
+45.6,-0.0551816123917891,-1.73045331533024,0.339956459964338,-0.374702000364456
+45.7,-0.225413437909403,-1.66370371348195,0.992729726010949,-1.1584158614196
+45.8,-0.385717966166907,-1.53298446871734,1.58757040068732,-1.89594733767259
+45.9,-0.530146790417538,-1.3445985702692,2.14927769201669,-2.55789337658038
+46,-0.653082837748003,-1.10602028643508,2.61092289010416,-3.11786427846322
+46.1,-0.749909656177425,-0.826777564332194,2.92999883406614,-3.55353577055339
+46.2,-0.817436486266187,-0.517823535591029,3.18337258994599,-3.84753900530222
+46.3,-0.853129590455488,-0.190939721870919,3.33373059948714,-3.98815300152108
+46.4,-0.855485388649918,0.141213300794342,3.29861061565979,-3.96977192291387
+46.5,-0.82485508068775,0.466395569085696,3.14946177748858,-3.79312856507979
+46.6,-0.762730154950696,0.772861436756346,2.92730117892547,-3.46526514126537
+46.7,-0.671332217424388,1.04887844906441,2.56779566760606,-2.99925253154519
+46.8,-0.554256323222019,1.2845552352877,2.1154988269986,-2.41366918808098
+46.9,-0.416025440749664,1.47158357768813,1.59610652204643,-1.73186047086155
+47,-0.261833493056844,1.60245331670383,1.01017363615887,-0.981007941870617
+47.1,-0.0975398090024363,1.6725978672,0.391326694680244,-0.19104572198694
+47.2,0.0706671419987742,1.67974171373244,-0.257302205916865,0.606532887952774
+47.3,0.236301070940816,1.62274006627912,-0.885858489811769,1.37993094567502
+47.4,0.39307641498474,1.50352915918103,-1.47079979651948,2.09831551121711
+47.5,0.53514376106347,1.32683559415889,-2.03447633157601,2.73304685894448
+47.6,0.656866343826439,1.09859013935704,-2.52343989786358,3.2588202530338
+47.7,0.753354527610772,0.826961290868258,-2.88113047921148,3.65467476743668
+47.8,0.821031406602991,0.522064866600595,-3.16367556000346,3.90482893185501
+47.9,0.857071529995175,0.195144999936506,-3.33852289056371,3.99930988916053
+48,0.859726424481722,-0.141361214136604,-3.35294930604197,3.93435098173738
+48.1,0.828851825907849,-0.474910676714686,-3.2654777581248,3.71254191623485
+48.2,0.765322449752728,-0.792435435880631,-3.04932300651867,3.34272552013552
+48.3,0.67129984353242,-1.08121495053563,-2.69108303880872,2.83964520612875
+48.4,0.550366406924026,-1.33016714697112,-2.24508646867104,2.22335719877226
+48.5,0.406982105628921,-1.52863895598114,-1.69998825123161,1.51843095611009
+48.6,0.246597921821499,-1.66803959115883,-1.07528270461769,0.752969662913826
+48.7,0.0754609109679011,-1.74281279705879,-0.402160169203905,-0.0425101546096864
+48.8,-0.0996977015777361,-1.74868370053188,0.29606943969388,-0.836295226417461
+48.9,-0.271895619726434,-1.68427246455358,0.979000930667079,-1.59673984663017
+49,-0.434303528568462,-1.55201174024934,1.64065210271331,-2.29352748796169
+49.1,-0.580304916383357,-1.35630366846651,2.26262104513046,-2.89887942599266
+49.2,-0.703680093746947,-1.10411023205788,2.75802557402344,-3.38866218925237
+49.3,-0.799475015370302,-0.805283627006006,3.15147943178999,-3.7433496845685
+49.4,-0.863755142675758,-0.47143099098312,3.48113154356732,-3.9488016407839
+49.5,-0.89322395454554,-0.116102662176094,3.61826606958149,-3.99682733674541
+49.6,-0.886510105719508,0.246307056265698,3.57412672641367,-3.88551213950891
+49.7,-0.844054989629339,0.601155085828534,3.44919715764739,-3.61929383471278
+49.8,-0.767107901962696,0.933445334022424,3.16133312625951,-3.2087857060688
+49.9,-0.658547483033457,1.22902859096356,2.71406577839811,-2.6703534172327
+50,-0.522846406320238,1.47599861331902,2.17827388109323,-2.02546256443904
+50.1,-0.365362590796086,1.66332722193661,1.54299366087207,-1.29982291091797
+50.2,-0.192448838663214,1.78260912900088,0.834898318540672,-0.522363419766945
+50.3,-0.0111861033449351,1.82926765527414,0.08775950479884,0.275921052517094
+50.4,0.170954227021332,1.8005990260342,-0.669746783674122,1.06320542315651
+50.5,0.346397089550858,1.69708879825367,-1.38281268443962,1.8081031487134
+50.6,0.508011825235988,1.52350461969102,-2.04909609447408,2.48091750753048
+50.7,0.649135599976378,1.28690519529889,-2.66131388694497,3.05482551431029
+50.8,0.763646235847317,0.996843657614496,-3.11766501761598,3.5069472678939
+50.9,0.846980221542097,0.665538395935895,-3.44804709719959,3.81925810071865
+51,0.89583373626488,0.306817848364173,-3.6721301352694,3.97930716543363
+51.1,0.90796594963497,-0.064149825178352,-3.70553650600892,3.98071381089268
+51.2,0.883042797944971,-0.432076053543634,-3.59404442317115,3.82342195858029
+51.3,0.82217920202326,-0.781739478436288,-3.35074327223096,3.513702338285
+51.4,0.727808173379239,-1.09822294652437,-2.94278720260547,3.06390249389121
+51.5,0.604009272709164,-1.36898709935135,-2.42889446544754,2.4919545257694
+51.6,0.455921427384613,-1.58287756638714,-1.81947477450474,1.82066019452245
+51.7,0.289638834315015,-1.73086393694655,-1.1298035638353,1.07678188674534
+51.8,0.112058205607064,-1.8078607315018,-0.400513136802594,0.28997568312542
+51.9,-0.0695275544689131,-1.81092561689091,0.348365731734744,-0.508390935909523
+52,-0.247629657227543,-1.73981471238967,1.06183783381403,-1.28648961265012
+52.1,-0.415113381648032,-1.59849852414307,1.72895669108096,-2.0133000082871
+52.2,-0.565307539157712,-1.39335761805082,2.35153312555016,-2.65984648592919
+52.3,-0.69198636541189,-1.13292320136315,2.83591003583248,-3.2003532778083
+52.4,-0.790306091307743,-0.828294459156285,3.1897643713546,-3.61327208379996
+52.5,-0.856728173490051,-0.492037157899832,3.48007779377536,-3.88214113414994
+52.6,-0.888349477734604,-0.138215524438144,3.58850244619627,-3.99624146828613
+52.7,-0.884085757517196,0.21877856143681,3.5064387709207,-3.95102426595096
+52.8,-0.84475764959058,0.564918195159538,3.34590257813557,-3.74829219431038
+52.9,-0.771970515882608,0.886355718513012,3.04635347496687,-3.39612754130267
+53,-0.668719847424967,1.17023150528947,2.60164063243097,-2.90857000032341
+53.1,-0.539452772643017,1.40624764221344,2.07966340121748,-2.30505695195465
+53.2,-0.389389063848892,1.58521373431671,1.47795864791468,-1.60964855693936
+53.3,-0.224545768575621,1.70024628258955,0.818393583227173,-0.850068553498602
+53.4,-0.0515185374700774,1.74806924063227,0.1327492859825,-0.0565989993762971
+53.5,0.122836186495291,1.72706370007543,-0.559122340400846,0.73912697824267
+53.6,0.291599687056651,1.63810066323702,-1.206022490356,1.50538629568916
+53.7,0.448302962714451,1.48569806112929,-1.80542076001864,2.21163061204764
+53.8,0.586952030772064,1.27624247341797,-2.36271484815237,2.82970419510781
+53.9,0.701973950348154,1.01794163969271,-2.78670286650151,3.33496640155699
+54,0.789128841259229,0.721128542156945,-3.08635746717625,3.70727402167114
+54.1,0.845420157498541,0.397281165709151,-3.3358242970466,3.93178432552095
+54.2,0.868353230767387,0.0592050271693455,-3.42191322258942,3.99954679577517
+54.3,0.857067171810339,-0.280006283852881,-3.327063324734,3.90785995658159
+54.4,0.812510479605951,-0.607663131950302,-3.16051852758853,3.66037907288432
+54.5,0.736348602125678,-0.911221471414874,-2.87297579422971,3.26697042654527
+54.6,0.631456966703107,-1.17881227656261,-2.45111512249136,2.7433179788212
+54.7,0.502054180055623,-1.4008263757442,-1.9533604573696,2.11029810032207
+54.8,0.353117788834443,-1.56857370238091,-1.38014308261845,1.3931472959938
+54.9,0.190379966787078,-1.67528574200807,-0.748978456540289,0.620456105304778
+55,0.0201523601743106,-1.71751062158304,-0.0903099544153046,-0.176970712340284
+55.1,-0.15097834598261,-1.69333464248243,0.581956364119997,-0.967342266147715
+55.2,-0.316289488498331,-1.60302464105253,1.2148328908632,-1.71914893642883
+55.3,-0.469452302105419,-1.4503716042302,1.80162038092959,-2.40241856370276
+55.4,-0.604598911903212,-1.2411756787352,2.36034018597741,-2.98991134411205
+55.5,-0.716142119841231,-0.982991529221922,2.7937894365975,-3.45820579444243
+55.6,-0.799747433413274,-0.685639195666135,3.10577719582515,-3.78863249274784
+55.7,-0.852294975027066,-0.360501784164753,3.34521843626595,-3.96801836928858
+55.8,-0.871390332278199,-0.020122804225618,3.42929268226207,-3.98921187525186
+55.9,-0.856192762706711,0.322375215408923,3.37181476678984,-3.85136809243487
+56,-0.807277045467324,0.653905016150409,3.21042691776193,-3.55998241746733
+56.1,-0.726257059050318,0.960969964910205,2.89843987938888,-3.12667147768952
+56.2,-0.616252673839423,1.2316128366125,2.4745305367051,-2.56871001287868
+56.3,-0.481502983261478,1.45513253833522,1.96109733118207,-1.90834218588752
+56.4,-0.327142319371711,1.62176908117505,1.35533740548058,-1.17189477806704
+56.5,-0.159228281427139,1.72495069224455,0.69664406625593,-0.388727623572836
+56.6,0.0156521971799928,1.76034766042739,-0.00394706194483119,0.40993687457226
+56.7,0.190493205167676,1.72532378789642,-0.69749215582115,1.19225848315872
+56.8,0.358359291597148,1.62106553427138,-1.36008978891975,1.92704850841091
+56.9,0.512624480137422,1.45170010781882,-2.00667572041944,2.58501319078597
+57,0.646822911473502,1.22316697278945,-2.55474954452363,3.13992155472524
+57.1,0.755473847364345,0.944275873780184,-2.97109058157983,3.56965115487306
+57.2,0.834413877439391,0.626071867257545,-3.3296089326915,3.8570700281617
+57.3,0.880057818187521,0.281164571767317,-3.5528697477371,3.99071969111587
+57.4,0.89017306145828,-0.0764461264672943,-3.57164015089442,3.96527195342947
+57.5,0.864571903220095,-0.43244062076451,-3.47708902247902,3.78174133609908
+57.6,0.80419985475712,-0.772484035858681,-3.2703261896169,3.44744462567331
+57.7,0.711124544397976,-1.08210424555489,-2.89205906992412,2.97570917706259
+57.8,0.589128643339591,-1.34888933040631,-2.40193412647383,2.38534159395568
+57.9,0.443113401016467,-1.56199333510426,-1.82357344282523,1.69987796887844
+58,0.278862424265091,-1.71181032819441,-1.15830454536029,0.946645573457144
+58.1,0.103028402060112,-1.79241151649161,-0.448569669729293,0.155673406335022
+58.2,-0.0772913168421593,-1.80060338151221,0.295966544710313,-0.641504968241948
+58.3,-0.254651370297328,-1.73509834550598,1.01370093350801,-1.41310856412099
+58.4,-0.421874414417416,-1.5986436338331,1.68015724746413,-2.12837598087053
+58.5,-0.572295886062864,-1.39725378878568,2.31691771686646,-2.75879176374156
+58.6,-0.699548180539646,-1.13873444813983,2.84150443595161,-3.27922322486302
+58.7,-0.798385430656913,-0.833628172298409,3.20900679549206,-3.66892240419654
+58.8,-0.865132612819259,-0.494540170353653,3.4990697493315,-3.91235322522886
+58.9,-0.89688909748829,-0.13534926180238,3.65965780655267,-3.99981086931586
+59,-0.892049004091794,0.228898066442701,3.60511637826163,-3.92780867617633
+59.1,-0.851157746912682,0.583466067688831,3.42033840519005,-3.69921714603471
+59.2,-0.776063105681669,0.914092603510251,3.13383759890952,-3.32314950183539
+59.3,-0.669630088461561,1.20681510966502,2.68936638826144,-2.81459837380262
+59.4,-0.536303407358839,1.45011532638389,2.14148226186807,-2.19383809058509
+59.5,-0.381561903637436,1.63440964991718,1.51448548448984,-1.48561640575236
+59.6,-0.211675545071135,1.75171261509377,0.822674697287773,-0.718167882956011
+59.7,-0.0335624395319564,1.79795118079259,0.105272943885676,0.0779117270240975
+59.8,0.145603395446079,1.77181700124349,-0.633044303203257,0.870885242312316
+59.9,0.318438787392082,1.67392491200152,-1.32206562848165,1.6291393112269
+60,0.478053523053269,1.50872707049773,-1.94083867960993,2.32244473684926
+60.1,0.618259871918356,1.28372287179706,-2.5210942619317,2.92316161971157
+60.2,0.733255278164126,1.007920428946,-2.98222669976409,3.40734127336597
+60.3,0.818428417412256,0.692635699334109,-3.28224159885494,3.75568098293837
+60.4,0.870779140671835,0.350838340422314,-3.49209482806476,3.95429354345774
+60.5,0.888208915650768,-0.00365207065730211,-3.55660476941427,3.99526089889432
+60.6,0.870072642935557,-0.356499447911588,-3.45436210512656,3.87694981006682
+60.7,0.817392749169081,-0.693998983233751,-3.24368034178574,3.60407696673453
+60.8,0.732276051984748,-1.00244257756959,-2.89138170848037,3.18752094806113
+60.9,0.618245537715611,-1.26980853671036,-2.42163646642758,2.64388852799253
+61,0.479998658782198,-1.48613472720379,-1.87085221163101,1.99485261558558
+61.1,0.323043257732475,-1.64248752957452,-1.24171268161645,1.26628822451673
+61.2,0.153670729866587,-1.73324739611503,-0.570683323642357,0.487240917939871
+61.3,-0.0214086312357242,-1.7556553739203,0.132075810988314,-0.311231146457515
+61.4,-0.195167234228152,-1.70841538977275,0.814518197224268,-1.09729540719237
+61.5,-0.360780655248338,-1.59372793310199,1.44992147774153,-1.83961396275836
+61.6,-0.511894861491108,-1.41698581370035,2.05513333965577,-2.50859291486669
+61.7,-0.64245773433732,-1.18498571093336,2.57331266229078,-3.07756218378209
+61.8,-0.747287480560625,-0.906917365450411,2.94750955527372,-3.52383876023909
+61.9,-0.822642131231192,-0.593894706202393,3.24460970694956,-3.82963100544165
+62,-0.865550684832264,-0.258113858455356,3.4436614514219,-3.98274794755672
+62.1,-0.874022623919116,0.086986697486057,3.44713662490139,-3.97708529729064
+62.2,-0.848023196756955,0.428078647110953,3.31617914318372,-3.81286880663997
+62.3,-0.788861978162957,0.752210015979107,3.10732347598444,-3.4966452688719
+62.4,-0.698627524809114,1.04634502982007,2.74728167633251,-3.04102151853611
+62.5,-0.580920254691946,1.29923578775445,2.27765615857632,-2.46416183675463
+62.6,-0.440436422989015,1.50152107427933,1.73402773221718,-1.78906379865412
+62.7,-0.282612313963912,1.64468206614394,1.11517852920017,-1.04264143261847
+62.8,-0.113636419646808,1.72334897580679,0.456873388249374,-0.254652242909727
+62.9,0.0599082085527906,1.73496001367328,-0.233363014548438,0.543489128122257
+63,0.231119206606905,1.67827604103361,-0.903996628836753,1.31996330269513
+63.1,0.393290238372651,1.55538126206712,-1.52573637840625,2.04381470577457
+63.2,0.540203906354335,1.37158868203444,-2.11718377966373,2.68618566616513
+63.3,0.665945736539381,1.1336179045427,-2.63112148351747,3.22146688079466
+63.4,0.765376351889253,0.850539760762407,-3.00118052592424,3.62831837681356
+63.5,0.834795161979883,0.533478158187111,-3.28346169566921,3.89052026896963
+63.6,0.87137935511382,0.194704316017418,-3.45150004568411,3.99761939524855
+63.7,0.873448547790916,-0.152393787500329,-3.44973054152711,3.9453460514564
+63.8,0.841020435052742,-0.494492653204448,-3.33802087204594,3.73578421085213
+63.9,0.775212113594107,-0.817947073921015,-3.09371920389757,3.37728844270996
+64,0.678466600096497,-1.10970320634918,-2.70612773068833,2.88415084200693
+64.1,0.554659809292004,-1.35863214953483,-2.23044817688341,2.27603124869741
+64.2,0.408548536718677,-1.55426128932647,-1.65903803786449,1.57717347193417
+64.3,0.245846883766704,-1.68845796023457,-1.01460507838338,0.815438765903723
+64.4,0.072999180030898,-1.75631305442138,-0.327098059469905,0.0211950895424105
+64.5,-0.103119504299607,-1.75429489970722,0.37655024073342,-0.773893568153874
+64.6,-0.275472686222778,-1.68187886484902,1.05567283670884,-1.53812953145024
+64.7,-0.437269139778861,-1.54232903049152,1.70766311871543,-2.24104512417621
+64.8,-0.581988962147789,-1.34076703665266,2.3108855666203,-2.85461731982802
+64.9,-0.703599928850515,-1.08478550870394,2.78228587890101,-3.35438493120424
+65,-0.79738803676423,-0.784616370420079,3.15394289910997,-3.72042380074705
+65.1,-0.859636715686846,-0.45202409859475,3.45634289294472,-3.9381411138303
+65.2,-0.887321965680014,-0.100515587946381,3.56651436168787,-3.99885716822809
+65.3,-0.879342072056304,0.255841508576896,3.50477197267484,-3.90015140645214
+65.4,-0.836314458705845,0.602955651070934,3.36735084519769,-3.64595891574039
+65.5,-0.759613336903409,0.926470311435319,3.07086192737352,-3.2464135485468
+65.6,-0.652203595827239,1.2130898452876,2.62689147031516,-2.71744391782303
+65.7,-0.518524940047916,1.45173782463998,2.10200300033868,-2.08013837348574
+65.8,-0.363826254265207,1.63213926075353,1.48385545431434,-1.3599042764539
+65.9,-0.194289013939354,1.74667731549734,0.800628984365104,-0.585455087345836
+66,-0.0167454837698504,1.79130375184852,0.08145994309397,0.212334348584233
+66.1,0.161612645830593,1.76358241347358,-0.643435040827431,1.00165868409603
+66.2,0.333536425022762,1.66417653285585,-1.32587302725473,1.7510500487898
+66.3,0.492201473942384,1.4977035345273,-1.96714384126307,2.43063257379617
+66.4,0.631195084449375,1.27075031715964,-2.55377227870154,3.01331344839002
+66.5,0.744650972169351,0.992272223711825,-2.99195713818354,3.47586302485694
+66.6,0.828187288507491,0.673693580287197,-3.30814897552433,3.7998409112429
+66.7,0.878642115090388,0.327779843039949,-3.55730833306869,3.97233113158903
+66.8,0.893523858342598,-0.0311041644151168,-3.61430812507019,3.98645704513447
+66.9,0.872262520344107,-0.388400054976224,-3.48379619699269,3.84165549628304
+67,0.816163220375688,-0.72994548448544,-3.27652976824464,3.54369926583979
+67.1,0.727298622724823,-1.0417127321338,-2.92181937993847,3.10446692845723
+67.2,0.609215831274573,-1.31093820016729,-2.43106807256906,2.54146929134891
+67.3,0.466822359098633,-1.52741159855802,-1.86065791766998,1.87715129366471
+67.4,0.305822307745992,-1.68197797691172,-1.21212900554831,1.13799719759546
+67.5,0.132700966337869,-1.76836089391502,-0.515068233586735,0.353474744416006
+67.6,-0.0455710574061217,-1.78397208838733,0.206751909165825,-0.445139631369254
+67.7,-0.221775562058454,-1.7278646986198,0.92057276181042,-1.22600769477127
+67.8,-0.388774339092682,-1.60210780425387,1.57366292838407,-1.95799870027365
+67.9,-0.54003648684307,-1.41257639842215,2.17338960913735,-2.61193047641842
+68,-0.669564738502084,-1.16698268841021,2.71573211872443,-3.16173282689155
+68.1,-0.771935668973854,-0.875149436878042,3.10166684534414,-3.58548686698143
+68.2,-0.843289930992182,-0.54899756229563,3.3648047615386,-3.86629886034291
+68.3,-0.880996145395124,-0.201649105439839,3.529535333593,-3.99297371895406
+68.4,-0.883407006462137,0.152790516398461,3.51977493411013,-3.96046131594775
+68.5,-0.850620118188048,0.500373539225723,3.37969290577503,-3.770057818233
+68.6,-0.784036300856208,0.82732812983038,3.11693363825366,-3.42935401241075
+68.7,-0.686283147141832,1.12037703429806,2.71051782944095,-2.951932684066
+68.8,-0.561424815133047,1.36848509823692,2.21251652159172,-2.35682711496987
+68.9,-0.414441317908344,1.56167487798603,1.6276412163999,-1.66776228619785
+69,-0.251181408519642,1.69215106720094,0.974025718323312,-0.912209038003445
+69.1,-0.0781812419477073,1.75562875378977,0.285330767795461,-0.120288894105933
+69.2,0.0976722323021821,1.74943935641501,-0.417465397810343,0.676426788406137
+69.3,0.269351052573968,1.67355610322251,-1.08652725549734,1.44617546945251
+69.4,0.430164600290781,1.53175231816914,-1.71683475245824,2.15826969820251
+69.5,0.573809800483011,1.32976569364504,-2.30520353566983,2.78432052489897
+69.6,0.694402965318543,1.07541832559104,-2.7620251478678,3.29936927869922
+69.7,0.787375878675397,0.778949763552511,-3.10231305823039,3.68288259111963
+69.8,0.849325661449947,0.45197073765426,-3.38685011273987,3.91957099664013
+69.9,0.877406943097099,0.107628658397102,-3.49534804385867,3.99999847544615
+70,0.870534744305663,-0.240495647722759,-3.42304595946551,3.92095863776125
+70.1,0.829432085919573,-0.578996835725448,-3.27801772214069,3.68560255248931
+70.2,0.755549250312076,-0.894445817333564,-2.99542269223284,3.30331312404099
+70.3,0.65171218778225,-1.17418735104859,-2.56914126145692,2.78933102554458
+70.4,0.522183712637855,-1.40784912149648,-2.06406137783213,2.16414710130268
+70.5,0.372014623715139,-1.58594914282649,-1.47522935839307,1.45268546149304
+70.6,0.207093241208492,-1.70116530368055,-0.822930068678856,0.683309836547733
+70.7,0.0339425580150563,-1.74964677316692,-0.139072090187844,-0.113307195271957
+70.8,-0.140598846080258,-1.72914791404423,0.557314869020971,-0.905407026777573
+70.9,-0.309567101485362,-1.63993294019836,1.214490742577,-1.66141113730277
+71,-0.466390449464696,-1.48600867142785,1.82771103530678,-2.35118002866963
+71.1,-0.604936687090963,-1.27340703628169,2.4039884244115,-2.94721479187107
+71.2,-0.719443040473114,-1.01014613912757,2.84660779768263,-3.42575340179477
+71.3,-0.805483315878439,-0.706620774061068,3.15967244413637,-3.76771803417886
+71.4,-0.859926866842401,-0.374619507780197,3.42131778811038,-3.95947563826207
+71.5,-0.880157239925259,-0.0274206262666834,3.51667293613063,-3.99338144349567
+71.6,-0.86522088364681,0.321180795529319,3.42010268902932,-3.86808373242099
+71.7,-0.816083500478068,0.657675202464539,3.24135485396344,-3.58857772937872
+71.8,-0.734532568769692,0.968684012718607,2.93655958319097,-3.16600645667805
+71.9,-0.623616041229406,1.24147283244468,2.48910238239535,-2.61721649746067
+72,-0.487808489865167,1.4656785024833,1.95754586118619,-1.96408637559388
+72.1,-0.332425479889065,1.63202318794197,1.34627595628929,-1.23265432796513
+72.2,-0.163579710350071,1.73334936222111,0.675397693203666,-0.452080242145981
+72.3,0.0120200361209602,1.76614185413624,-0.0229711181447156,0.34651685630572
+72.4,0.187390071410544,1.7287189225769,-0.733101579882617,1.1312994211938
+72.5,0.355429090901302,1.6218254440388,-1.39425311216866,1.87098064818053
+72.6,0.509525579270373,1.45004532166679,-1.99937325247279,2.53607178094518
+72.7,0.643628335114716,1.22023561959202,-2.5697174850711,3.10005773484092
+72.8,0.752033916108348,0.941164968517483,-3.0004305025413,3.54045416964637
+72.9,0.830435192076567,0.623930467555974,-3.29358917145713,3.83970386925727
+73,0.875900576330215,0.28122858058577,-3.50325560587965,3.98587669248709
+73.1,0.886333404525067,-0.0731814851660592,-3.54678102608955,3.97314519014873
+73.2,0.861298422459023,-0.425154483829152,-3.44194573816827,3.8020169270638
+73.3,0.801843983011296,-0.760789264577941,-3.22200126551642,3.47931424705509
+73.4,0.710169530908405,-1.06612803584162,-2.85038465339911,3.01790228762725
+73.5,0.589991232271523,-1.32918831756576,-2.37102981954322,2.43617608753317
+73.6,0.446102635439208,-1.53937714365824,-1.80179933559489,1.75732723462736
+73.7,0.284196045250945,-1.68760611608031,-1.15041140584695,1.00841929044362
+73.8,0.110785341004212,-1.76838705276335,-0.456705481234676,0.219308851401098
+73.9,-0.0671924180548676,-1.77844480005903,0.266999476015925,-0.578544739477799
+74,-0.242500182353788,-1.71661883372389,0.964894851261072,-1.35333357729711
+74.1,-0.408158998140097,-1.58574474131032,1.6186313988391,-2.07416927608065
+74.2,-0.557631499938016,-1.39136455999553,2.24511109336758,-2.7123143912466
+74.3,-0.684652890802259,-1.14092079195072,2.75126716216083,-3.24232809083647
+74.4,-0.784161610044893,-0.844527590954028,3.11777048623119,-3.64308040120272
+74.5,-0.852492624425216,-0.514136844185805,3.42579810902106,-3.89859459237798
+74.6,-0.886565657715328,-0.163142595656793,3.58138592152491,-3.99868411988181
+74.7,-0.884824831790191,0.194146462232816,3.53339874313571,-3.93935873010338
+74.8,-0.847750018433697,0.543560230548348,3.38497805543955,-3.72298353912108
+74.9,-0.776825424522807,0.871129083314836,3.1180873077896,-3.35818474298792
+75,-0.674719957534021,1.16322831972589,2.69400183767585,-2.85950571851666
+75.1,-0.545674472168477,1.40862530353534,2.17517811062365,-2.24682722474026
+75.2,-0.394877205696696,1.59752060869378,1.57407357649347,-1.54457481978668
+75.3,-0.228339203459981,1.72182542110112,0.903407080463519,-0.780745090956018
+75.4,-0.0527671304186303,1.7772092199056,0.201600768741719,0.0142104808675659
+75.5,0.124820950310138,1.76162054992602,-0.521496423218488,0.808599525662615
+75.6,0.297194066806721,1.67510785285486,-1.2032217214736,1.57075225905286
+75.7,0.457534966088568,1.52161093286497,-1.82747406611388,2.27028405667015
+75.8,0.599601124709276,1.30773131103383,-2.42037884773852,2.87930679324354
+75.9,0.717463494852599,1.04179841536323,-2.88699119767325,3.3735406541484
+76,0.806455953019189,0.734543661753757,-3.21113893825066,3.73328209499545
+76.1,0.863337021803273,0.398427117976952,-3.4536436510416,3.94418935976795
+76.2,0.885681654076941,0.0469512239517909,-3.53909977690924,3.9978542413758
+76.3,0.872635288581516,-0.305816072519307,-3.46713722293336,3.89213729033859
+76.4,0.824917550856758,-0.646135613272601,-3.2876144544083,3.63125310788502
+76.5,0.744323668587917,-0.960045630106469,-2.95719096532533,3.22560232310195
+76.6,0.634157876665822,-1.23529729736555,-2.50974419216992,2.69135695267356
+76.7,0.498894642822029,-1.46132608441826,-1.97578631580025,2.04981567360998
+76.8,0.343873545820232,-1.62861557971305,-1.35458766850162,1.32655471220708
+76.9,0.17530657213342,-1.73100091622222,-0.685182398112338,0.55040820061385
+77,-0.00011222553451587,-1.76486392524594,0.020700949655475,-0.247681349024229
+77.1,-0.175324013705897,-1.72822770676942,0.71240122152281,-1.03589662488041
+77.2,-0.34341178966205,-1.62285999623483,1.36613856455146,-1.78281397126355
+77.3,-0.497838179972688,-1.45353891855965,1.99665465166177,-2.45865615060712
+77.4,-0.632298023766709,-1.22665508499655,2.53004598355376,-3.03647946796423
+77.5,-0.741457407725192,-0.951237041440915,2.92858899872631,-3.49324793109859
+77.6,-0.821330901696412,-0.638325351990068,3.26645138389969,-3.81075162280137
+77.7,-0.868539881828635,-0.300303527920258,3.47740123617026,-3.97633267282524
+77.8,-0.880974849599155,0.0492546619341351,3.48987970392309,-3.98338988722691
+77.9,-0.858511020330444,0.396678726260356,3.3913721144438,-3.83164191713852
+78,-0.802133469917296,0.728444499198624,3.19186492212077,-3.52713847525912
+78.1,-0.71383727028294,1.03093401669136,2.8305855268136,-3.08201915290027
+78.2,-0.597235215380447,1.29254362250368,2.36330184337726,-2.51402945278905
+78.3,-0.457000142044182,1.50323967798442,1.81586788181494,-1.84581333187393
+78.4,-0.298606389889768,1.65404344011265,1.1865071312686,-1.1040104582177
+78.5,-0.128347566422668,1.73936629810716,0.515039439897069,-0.318194171498888
+78.6,0.0470616514434032,1.75617132227653,-0.189947994197465,0.480307512717804
+78.7,0.2205713893675,1.70302181137868,-0.873676653067215,1.25966085210055
+78.8,0.385344360760924,1.58215006353304,-1.51255268877244,1.98879548839963
+78.9,0.534991805266623,1.39882985754068,-2.12633481285709,2.6386431245834
+79,0.663375901643752,1.15987558440453,-2.64274932983904,3.18329638610982
+79.1,0.765332504722491,0.874655079921723,-3.01551152619679,3.60104166619471
+79.2,0.837133992539261,0.554523176840765,-3.31851340874344,3.87522477879256
+79.3,0.875750346268597,0.212053206321813,-3.50789184702045,3.99491490843888
+79.4,0.879287781527729,-0.138927015907329,-3.49538617128943,3.95534038736874
+79.5,0.847871355073966,-0.48465775165889,-3.35627347364279,3.75807892685259
+79.6,0.782892193883776,-0.811675144718545,-3.12647995851953,3.41099471882669
+79.7,0.68664823310839,-1.10647921006564,-2.74017341945275,2.92792491537739
+79.8,0.563002538138477,-1.35757179196317,-2.24637744471371,2.32812798515344
+79.9,0.416893068721426,-1.55523672411733,-1.67363092918974,1.63551593899403
+80,0.254047290012478,-1.69084908910804,-1.02578659106898,0.877701033516019
+80.1,0.0809436453928406,-1.75925033563335,-0.3413635841505,0.0848949575775101
+80.2,-0.095573635068302,-1.75803858798687,0.374083182447907,-0.711295612418195
+80.3,-0.268350083704966,-1.68640095862005,1.0601760838952,-1.47912907096978
+80.4,-0.430524771502677,-1.5471641570194,1.69105986642802,-2.1879943211236
+80.5,-0.575788860636109,-1.34637513142765,2.29058596003201,-2.80963114230948
+80.6,-0.69814709016922,-1.09159059052653,2.79392337945926,-3.31925683615528
+80.7,-0.792566085907739,-0.79284416904215,3.14550776994555,-3.69655423446428
+80.8,-0.855530003946802,-0.462174290565884,3.4085779891393,-3.92648168059658
+80.9,-0.884408142094472,-0.112721043749619,3.53925789389154,-3.99987269285298
+81,-0.877893701303226,0.241431414976542,3.49869910362126,-3.91380140317352
+81.1,-0.836392269475768,0.586442744162633,3.34714872829968,-3.67169920226408
+81.2,-0.761419350365313,0.908203643206626,3.05153957219552,-3.28321794087717
+81.3,-0.655931035532904,1.19374443142173,2.62235847322106,-2.7638451409809
+81.4,-0.524219135968283,1.43207472393608,2.10467265514755,-2.13428655713134
+81.5,-0.371460509852187,1.61298768286235,1.49408821106584,-1.41964070337974
+81.6,-0.203761001625432,1.72928631955722,0.824350315679978,-0.6483982547197
+81.7,-0.0278179902418781,1.77685685364484,0.113230568230774,0.148693786217111
+81.8,0.149257326823984,1.7530217282407,-0.595096038601109,0.939857875127711
+81.9,0.320381683503835,1.6586291027919,-1.26847649267758,1.69355279645011
+82,0.47882127525691,1.49810581887659,-1.91434162303154,2.37973111209283
+82.1,0.618117450779669,1.27752787028591,-2.48524471059019,2.97103705797221
+82.2,0.732561179196527,1.00560961470737,-2.91471181586218,3.44389713199991
+82.3,0.817857789454763,0.693413358010213,-3.2605300768843,3.77945989522057
+82.4,0.870549098944156,0.353347723029781,-3.50997053784603,3.9643475191942
+82.5,0.888140703055088,-0.000676532510593408,-3.55724242017723,3.99118911779956
+82.6,0.870159882964249,-0.354548450484297,-3.458080309597,3.85891460120386
+82.7,0.817598259777439,-0.694378075789427,-3.27523627809036,3.57279733696734
+82.8,0.732284273809725,-1.00607177785371,-2.9294480518975,3.14424391751995
+82.9,0.617675807323037,-1.27725066184689,-2.45860082407674,2.59033941531642
+83,0.478481332595581,-1.49759890326713,-1.90928109028055,1.93316625491303
+83.1,0.32019404696532,-1.65765691387826,-1.27498213194849,1.19892385638515
+83.2,0.149156940015574,-1.75118274284316,-0.592690454203076,0.416884147126094
+83.3,-0.0278070714762033,-1.77510058405102,0.124042683457826,-0.381775417524764
+83.4,-0.203530656133402,-1.72780237213343,0.826065857031391,-1.16521480104102
+83.5,-0.370993582220287,-1.61115152161943,1.47965433154557,-1.9022007474876
+83.6,-0.523659964991716,-1.43055084155996,2.09852107102708,-2.56335195287343
+83.7,-0.655341137052874,-1.19297515556978,2.63938340115499,-3.12231040502314
+83.8,-0.760628475102482,-0.907852094814912,3.02851045583886,-3.55679219434475
+83.9,-0.835630708593702,-0.586749052178804,3.32110187197717,-3.84947590298472
+84,-0.87742192336515,-0.242362177048916,3.52808772987565,-3.98869315509632
+84.1,-0.883932260837841,0.111190802814395,3.5356118445498,-3.96889379816337
+84.2,-0.855086479865035,0.45989588308956,3.38322838824879,-3.79086717006627
+84.3,-0.79240841500974,0.79019193332069,3.15738456697009,-3.46171063067178
+84.4,-0.698156504484745,1.08857007398338,2.77869021797965,-2.99454661249194
+84.5,-0.576117691779953,1.34322381220308,2.2825214091015,-2.40799947071042
+84.6,-0.431253664984146,1.54459020157824,1.71007388227539,-1.72545298891343
+84.7,-0.269288899365585,1.68405670509154,1.06452212793054,-0.974118141430129
+84.8,-0.0966789124677192,1.75625196664369,0.380765815318013,-0.183948277655674
+84.9,0.0797387325833271,1.75901469858262,-0.33127596794417,0.613555023466667
+85,0.252843617954932,1.69161851323529,-1.02064926623846,1.38659782198812
+85.1,0.415742010664152,1.55665724000592,-1.65045327534641,2.10436134100937
+85.2,0.562135870619908,1.36020671092838,-2.23886554962769,2.7382306140609
+85.3,0.686141075079387,1.10985119036809,-2.75243794826031,3.26293527351611
+85.4,0.782621900056262,0.815439972840438,-3.10993393739265,3.65755700040399
+85.5,0.848003385659212,0.488812758070017,-3.36448878227514,3.90636347177426
+85.6,0.87973998343941,0.1428911919735,-3.50735803862404,3.9994355587677
+85.7,0.876403000833367,-0.208432064745552,-3.47786672448579,3.9330627709818
+85.8,0.838287350982467,-0.551515608957932,-3.33107147397857,3.70989118201416
+85.9,0.76686098639178,-0.872635741324414,-3.05276798432997,3.33881793885819
+86,0.664906941957795,-1.15887101393682,-2.63710814171683,2.83463656072929
+86.1,0.53658181610664,-1.39940129292507,-2.13411502126558,2.21744716813707
+86.2,0.38691554004283,-1.58420512602557,-1.54126292566027,1.51185515451031
+86.3,0.221836634722418,-1.70587379050884,-0.884723618900024,0.745990246808149
+86.4,0.047910493213005,-1.76025921066023,-0.190080156910255,-0.0496149379260034
+86.5,-0.12791644986551,-1.74459433974361,0.510424723661815,-0.843242131653925
+86.6,-0.298639145707408,-1.65923023583867,1.17740166933769,-1.60325192259723
+86.7,-0.457587824855928,-1.50820212822025,1.81335605302134,-2.2993451187407
+86.8,-0.598402943474235,-1.29725549660743,2.39212074850056,-2.90377068100299
+86.9,-0.715296854607536,-1.03453708695483,2.83367150759354,-3.39243206959204
+87,-0.803854050664902,-0.730604462559656,3.17700994967833,-3.74584789700485
+87.1,-0.860641147225485,-0.397356182511217,3.44783273989282,-3.94992858947069
+87.2,-0.88294991638714,-0.0482838964814454,3.52692486061391,-3.99653809379481
+87.3,-0.869989436942655,0.302799635855015,3.4400476280988,-3.88381823612458
+87.4,-0.822628481217182,0.642235209840036,3.28097782935298,-3.61626280147721
+87.5,-0.74245774719818,0.956191129646175,2.96714485198778,-3.20453838071216
+87.6,-0.6326155646593,1.23205820510038,2.51689408902562,-2.66505912721377
+87.7,-0.497604441230163,1.45943025389423,1.98967665289129,-2.01933237639369
+87.8,-0.342696551272114,1.62867000555469,1.37557013648773,-1.29310121609869
+87.9,-0.174032959949187,1.73287996401899,0.704228986681227,-0.515318190934587
+88,0.00167292124055196,1.7685538402267,-0.000232228427526904,0.283008944321381
+88.1,0.177376480146016,1.73364192461621,-0.704655757715383,1.07005340605362
+88.2,0.346033481474326,1.62916780265181,-1.36450647712554,1.81443821523541
+88.3,0.50104541803138,1.4598928088801,-1.98505586595346,2.48648709856654
+88.4,0.6362067959289,1.23234967815111,-2.54917387878788,3.0594075878417
+88.5,0.745876435038541,0.955364921846097,-2.96671108434836,3.51035915110846
+88.6,0.825878963304699,0.640086081857378,-3.26822930838148,3.82136377259943
+88.7,0.873199198487041,0.298895722323901,-3.50515953064528,3.98002267948761
+88.8,0.885467838362931,-0.0542648134714709,-3.55353683762112,3.98001064183246
+88.9,0.86220110986261,-0.405297343460045,-3.42035016638842,3.82132813953729
+89,0.804730879698405,-0.740488441875841,-3.21444016361511,3.51030134321708
+89.1,0.715116247898048,-1.04620999213951,-2.86393252397064,3.05932990973927
+89.2,0.596862290857985,-1.3100476115398,-2.38160660840003,2.48639264703389
+89.3,0.454792267733922,-1.52201740902586,-1.82075573841189,1.81433075575708
+89.4,0.29451468722574,-1.67309023772605,-1.18255524491913,1.06993722269992
+89.5,0.122411554268366,-1.75705098984509,-0.495946128010488,0.282888668955965
+89.6,-0.0546510399691118,-1.77124353178625,0.216705571241521,-0.515437763312442
+89.7,-0.229546578494175,-1.71456818919395,0.922567771642638,-1.29321531851561
+89.8,-0.395216439302812,-1.58891123413296,1.57425987588677,-2.01943645994639
+89.9,-0.545143701352581,-1.39991273118759,2.17516076997459,-2.66514904241946
+90,-0.673319355702604,-1.15506149641353,0,-3.20461054293532