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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"# <p style=\"text-align: center;\">PHYS 134L Spring 2024 Lab 1</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-danger\"><b>Due date:</b> Sunday, April 14th, 2024 by 11:59pm, submitted through Canvas.</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Names: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Enter your name and your partner's name here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This lab will introduce you to **ds9**, a venerable (if not fantastic) image viewer that is a common way astronomers look at images; and you will continue to use **jupyter**. While **ds9** will have limited usefulness beyond this class (unless you continue in astronomical research!), **python** and **jupyter** are very widely used across fields. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">ds9 Fundamentals</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The program ds9 allows you to display astronomical images, measure many of their properties, and much more. Unfortunately, the\n",
"manual for ds9 is particularly terse and unhelpful. The only way to understand the program’s capabilities is to try things, or to consult a\n",
"guru (perhaps your own lab partner). Do the following few first steps."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Download _object.fits_ and _object.cat_ from Gauchospace. You may right-click _object.fits_ (if you associated fits files with ds9) and open with ds9, or you my load ds9 by clicking on the icon pinned to the taskbar and then using the open function (you can do this with both the GUI button and from the \"File\" menu) to find the file _object.fits_.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Image Scaling\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once you have opened the image, About how many stars do you see?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Left click on “scale”, on “more. . . ” if necessary to make “zscale” visible, and on “zscale”.\n",
"Changing the scale parameters adjusts how the 2D image array in ds9 is display to the user,\n",
"but doens’t actually change the data itself. About how many stars now?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Right click inside the image window, and drag the cursor around. Describe the effect of moving it left-right? Describe the effect of moving the (right-clicked) cursor up-down?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Experiment with different scale options (there are many!) to get a feel for how this functionality works. Try different colormaps (in the ”color” menu). Describe the settings that\n",
"you find best display the image and why."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Header Data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Astronomical images ordinarily come with “metadata” = (data about the data). In images in FITS format, the metadata appear in a ”header” that can be displayed separately from the data. In the ds9 window, click on “File/Display Fits Header. . . ” Answer the following questions, based on the header."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What are the x- and y- dimensions of the image (in pixels)?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What was the image exposure time (in s)?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What filter was used? (We will go into what this means later)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What was the name of the object being observed?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What was the right ascension object being observed?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Google the object name you found above, and find an image of it on the web. Match this image to your ds9 display of object.fits. Adjust the scaling so you get a recognizable picture of the object (which is a supernova) and its host galaxy. (Try clicking “scale”, then “min/max” and then various scalings. Then play with right-click-and-drag-the-cursor to get a good-looking image. This is as much art as science!)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What are the x,y coordinates of the supernova?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the signal in the central pixel of the supernova? (units of counts)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the signal in the central pixel of the host galaxy?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Type Your Answer Here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Fits Files and Python</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While ds9 can be powerful, sometimes you'll want to have a more flexible and customizable way to interact with your data. To do this, we'll read the data into python. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First import the necessary libraries"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import os #This package allows you to interact with your operating system\n",
"import numpy as np #This is a standard \n",
"from astropy.io import fits #Astropy is a multi-purpose python package made by astronomers\n",
"import matplotlib.pyplot as plt #You've already used this in your bootcamp!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When we type `import numpy as np`, this means that we are importing a package called `numpy`, and that in\n",
"the future we will refer to it as `np`. We can call functions, classes, and objects defined within\n",
"numpy using syntax like `np.sin(x)`. The first thing we will do here is to read in the same image file as earlier\n",
"and try to make a pretty plot in python. You will use lines similar to the following, first defining a string\n",
"containing the path to your image file, and then opening the image."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"imagefile = \"object.fits\" #The file has automatically been downloaded to the appropriate location in your JupyterHub drive\n",
"image = fits.open(imagefile)[0].data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first line is to tell the program where to find the image file. Don’t worry at the moment why we have to use `[0].data` when we open\n",
"the file: this is due to how fits files are structured. Feel free to read up on the astropy documentation to learn a bit more. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we will plot the image. Use the following at first:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.imshow(image, origin='lower')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This creates and displays a plot of the same image as before. It is inverted vertically relative to what you\n",
"saw in ds9 unless we force origin to be ’lower’. Try it leaving this argument out and see for yourself!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now it is up to you to make the figure look better (leave the output of these commands as\n",
"they are; create a new cell to make your new figure). Try changing the size of the figure (e.g. with\n",
"`plt.figure(figsize=(10, 10)`) before `plt.imshow`), the color map, the minimum and maximum values\n",
"to show, and the scaling (you can plot any function of the values in image). **Read the documentation\n",
"pages.** Try square root scales, log scales, linear scales, other scales, and see what looks good! To plot with\n",
"some other scale, you may plot, e.g., `np.log(image)` or `np.exp(image)` instead of just `image`, or you could try using different [image normalizations](https://matplotlib.org/stable/tutorials/colors/colormapnorms.html). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Also, it’s a good idea to read [this](https://matplotlib.org/users/colormaps.html) page on color maps."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, you may\n",
"turn off the axes labeling pixel values with another line\n",
"```\n",
"plt.axis(’off’)\n",
"```\n",
"before\n",
"```\n",
"plt.show()\n",
"```\n",
"You may also save your figure to a png file using `plt.savefig` so that you can print it out and tape it to your door or wall. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"## Put the code for your nicer looking figure here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Stellar Photometry</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this final section of Lab 1 we'll move on to a catalog of stellar photometry (i.e. how bright the stars are) based on your ``object.fits`` files that was extracted using a program called Source Extractor (sometimes known as SExtractor). Yes, the name is crass, and no, you should not choose a similar name when you write your own useful pieces of software. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The catalog of extracted stars is in a file called `object.cat`. We will visualize this catalog a few ways,\n",
"getting a little practice with python arrays along the way. The first step is to load in the catalog. You will\n",
"define the catalog filename in exactly the same way you did before. You will then read it into python with the syntax\n",
"```\n",
"catalog = np.loadtxt(catalogfile)\n",
"```\n",
"where `catalogfile` is a string giving the filename of the catalog. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Open the catalog in the text editor of your choice (notepad, wordpad, word, emacs, etc.) and\n",
"take a look: the first few lines show what each column represents. For now, focus on three columns:\n",
"x-position, y-position, and flags. Note that you can download files off the JupyterHub onto any computer you're using. \n",
"\n",
"\n",
"Set a new variable x equal to the array of x-positions from the\n",
"catalog, a new variable y equal to the array of y-positions, and flags equal to the flag entry.\n",
"When you do this, remember that the first array element is indexed with a zero. Play around to see what to do, use a search\n",
"engine, and don’t immediately ask for the answer. For example, what would the following lines give?\n",
"```\n",
"x = catalog[0, 0]\n",
"x = catalog[:, 0]\n",
"x = catalog[0]\n",
"x = catalog[0, :]\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"## Your code to read in the file goes here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you have never programmed before, this sort of indexing varies between programming languages but the\n",
"basic idea is very standard. Now plot the extracted stars atop your pretty image of `object.fits` using plt.plot(x,\n",
"y) (use a new cell). Use dots/markers rather than lines, and consult the [manual](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.html) for guidance if you need it. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"## Your code goes here. Overplot the catalog positions on top of the image of object.fits"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, change the plot a bit: plot those stars that have flag == 0 in one color/marker style, and stars that have flag != 0 in a different color/marker style. Hint: the easiest way to do this will involve either `numpy.where` or boolean indexing. You might want to go back to the indexing tutorial.\n",
"Also, there is a very important difference between = and ==. The statement\n",
"```\n",
"x = 5\n",
"```\n",
"sets the variable x equal to the value 5. The statement\n",
"```\n",
"x == 5\n",
"```\n",
"will not change the value of x. It will evaluate to True if, indeed, x is the integer 5, and False otherwise. If\n",
"x is an array, this statement will return an array of True and False values (a boolean array). The statement\n",
"will return an error if x is not defined."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once you have extracted arrays like `x_flagged` and `y_flagged` and have plotted them atop\n",
"your image, comment on any differences that you notice between the flagged (flag != 0) and\n",
"unflagged (flag == 0) stars. As usual, this comment should appear in a markdown cell below\n",
"the figure. If you need insight or are curious, go search for what the flags represent in the\n",
"SExtractor manual and use this to help inform your comments."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"##Your code goes Here##"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your comments go here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The exact factor relating the peak intensity and total flux will vary from star to star. Part of the reason why is that the flux in any one pixel is subject to photon noise (also called shot noise or Poisson noise). If we have a lot of photons, the scatter in the count rate scales roughly as the square root of the number of counts (refereed to below as the \"square root rule\"). Remind yourself of why this is the case for Poisson statistics!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Choose the eight stars with fluxes between 1990 and 2010 as reported by SExtractor. If you haven’t already played with\n",
"boolean indexing and/or `np.where`, now is the time. You probably don’t want to do this by hand. Hint: You can combine logical expressions with the python and (&) and or operators."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using your newfound ability to select elements from arrays, find the x and y coordinates of\n",
"these eight stars. Then compute the standard deviation of the eight peak pixel values. You\n",
"may compute the peak pixel values either by hand in ds9 or directly in python. Either way, be explicit\n",
"about what you are doing in your jupyter notebook. When you compute the standard deviation, you\n",
"may also do that as you like, but again be clear. What would you expect for the standard deviation\n",
"according to the square root rule? Is this what you find? If your standard deviation was larger\n",
"or smaller than this expectation, try to come up with possible explanations, and write these\n",
"in a markdown cell in your jupyter notebook."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"## Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your reponse here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have one, last, easy task for this lab. You will make histograms of the fluxes returned by\n",
"SExtractor. Use the function `plt.hist()` for this purpose. Make two separate histograms: one\n",
"of the fluxes, and one of the log of the fluxes (either base ten or natural log, your choice).\n",
"Comment on which of these looks more informative and why. As before, use your judgment and the\n",
"manual pages to make a figure with labeled axes that looks nice. We will work in logarithmic units of flux\n",
"called magnitudes for the rest of the course, and indeed, this is another column of the catalog file returned\n",
"by SExtractor."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"## Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your reponse here*"
]
}
],
"metadata": {
"interpreter": {
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# <p style=\"text-align: center;\">PHYS 134L Spring 2022 Lab 2</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-danger\"><b>Due date:</b> Sunday, April 17th, 2022 by 11:59pm, submitted through Gradescope.</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Names: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Enter your name and your partner's name here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Read through this entire lab before you start. This lab will introduce you to the idea of astronomical coordinate systems, sidereal time, focal length and image scale. To complete this lab you should have already read textbook Chapter 1 and Section 2.2. You may also find it useful to read the Wikipedia entries for \"Right ascension\", \"Declination,\" and \"Sidereal time.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 1: Celestial Coordinates</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Objects in the sky have ''equatorial'' coordinates just as objects on the Earth. But instead of ''longitude'' for the\n",
"east-west coordinate, astronomers say ''right ascension'' (or ''RA''), and instead of ''latitude'' for the north-south coordinate, they say ''declination'' (or ''$\\delta$''). Right ascension is typically measured in hours, not degrees. Dividing the full circle of the celestial equator into 24 hours, each hour corresponds to 15 degrees.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll begin by revisiting the same datafile that we used in Lab 1: ```object.fits```.\n",
"**In ds9, open \\texttt{object.fits}. Click on ''file/display\\_header'' to display the header.** The entries ''RA'' and ''Dec'' give the coordinates in the sky where the telescope was pointing while taking the image. Also notice the entry\n",
"commented ``start time of the observation.'' This is the time (in Universal Time, or UT) when the shutter opened for the CCD image. UT corresponds to the local time on the prime meridian (longitude = 0 degrees), which passes through the observatory at Greenwich, England. This time zone is 8 hours ahead of Pacific Std Time, and 7 hours ahead of Pacific Daylight Time.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**On a certain day, the Sun crossed the meridian at 12:00 noon UT in Greenwich, England. Santa Barbara lies at 119.7 degrees W longitude. On that same day, what is the UT time when the Sun crosses the meridian in Santa Barbara?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Using ds9 to get information from the headers, list the RA, $\\delta$, date, and UT for the file ```object.fits```**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**On a sheet of paper, sketch a map of the part of the sky where the image was taken large enough to include a couple of bright, named stars (please label them). Check out the [Stellarium website](https://stellarium-web.org/) if you need some help. Note that RA is defined so that as the Earth turns, the RA of objects on the meridian increases with time. Draw your map with N up and E to the left (as it would appear if you were facing the southern horizon). Attach the drawing to the end of this lab report before you submit it to gradescope**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Does RA increase to the right, or to the left?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Positions on the Earth stay fixed in the planet's rotating reference frame. For example, as time passes, Los Angeles always remains about 100 miles, or 160 km, east-southeast of us here in Santa Barbara. Positions in the sky are different. The stars remain basically fixed in their current positions in the sky (they do move across the celestial sphere, but very slowly). As the Earth rotates about its axis, the entire sky appears to rotate from the perspective of someone fixed on the Earth's surface.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 2: Sidereal Time</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The word ''sidereal'' means ''with respect to the stars.'' The current Local Sidereal Time (LST) is the value of the RA in the equatorial\n",
"coordinate system that is crossing your meridian at the moment. Since the coordinates of stars are essentially constant over very long times,\n",
"at a given LST you will always find the stars in the same apparent positions in the sky. Sidereal time is not the same as solar time (which we normally use) -- at a given solar time (such as noon), we find the {\\it Sun} in the same position, not the stars. Because the Earth orbits the Sun once per year, the sidereal day is about 4 minutes shorter than the solar day. Thus, measuring by solar time, a given star rises and sets about 4 minutes earlier every day."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Explain, with words, a sketch (appended to the end of the lab) and/or a calculation, why the solar day is about 4 minutes longer than the sidereal day.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answere here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**You are in Goleta (long = 120 degrees W, lat = +34:30) and the LST is 07:30. At the same instant, what is the LST in New York City (long = 74 degrees W, lat = +40:00)? (hint: remember 15 degrees per hour)**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What bright star (bright as in ''with a name, not a catalog number'') is most nearly overhead in Goleta at midnght tonight? (Check a star map on the web or the celestial globe.)**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What bright star is the most nearly overhead in Goleta over the whole year?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**You are in Urumqi, China (long = 87 degrees E, lat = +44:00) and the LST is 07:30. What bright star is most nearly tonight?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What bright star is the most nearly overhead in Urumqi over the whole year?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we will explore the use of ```astropy``` to calculate local sidereal time and the apparent positions of objects in the sky. Here we'll continue to use the file ```object.fits``` from the first lab. Recall from last time that (after importing the standard libraries, such as \\texttt{numpy, matplotlib, astropy, etc.}) you can read the image using\n",
"```\n",
"image = fits.open(imfile)[0].data\n",
"```\n",
"where ```imfile``` is the name of the file we want to open. As we discussed briefly in the introduction to fits files last lab, indexing the file by ```[0]``` opens the *first* file extension (this file only has one). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To read the header in python, you simply use \n",
"```\n",
"header = fits.open(imfile)[0].header\n",
"```\n",
"\n",
"The header is read in as a python dictionary, which you now have experience with from the Python Bootcamp.\n",
"\n",
"**Open the file here and print out the contents of the header**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your Code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One of the first listings should read\n",
"```\n",
"\\MJD-OBS = 56365.29978605324 / [UTC days] Start date/time (Modified Julian Dat\n",
"```\n",
"\n",
"There are three components to this. The first, ```MJD-OBS```, is called the keyword. It is how we access the information. The second component, ```56365.29978605324``` is the value. The third component is a comment. You may create a new variable and set it equal to a header value using, e.g.,\n",
"```\n",
"mjd = header['MJD-OBS']}\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we'll try a bit of astropy's machinery to deal with coordinates and observations. We'll use the astropy [coordinates](https://docs.astropy.org/en/stable/coordinates/index.html)coordinates, [time](https://docs.astropy.org/en/stable/time/index.html) and [units](https://docs.astropy.org/en/stable/units/index.html) packages. Check out their documentation pages for some examples on how to use them. **To use them, we first need to import the relevant bits, so put these lines in a notebook cell:**\n",
"```\n",
"from astropy import coordinates, time\n",
"from astropy import units as u\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we want to create a coordinate object with the sky position of the observation, a location object with the location of our observation, and a time object. We do that as follows (with ```imfile``` being the path to ````object.fits``` as you did last time):\n",
"```\n",
"header = fits.open(imfile)[0].header \n",
"radec = coordinates.SkyCoord(header['RA'], header['DEC'], unit=(u.hourangle, u.deg)) \n",
"location = coordinates.EarthLocation(lon=header['LONGITUD'], lat=header['LATITUDE']) \n",
"t = time.Time(header['MJD-OBS'], format='mjd')\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Copy and paste the above code into the cell below to create a time object ```t```.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An observer needs to know both their location and the time in order to compute the position of the stars. These two objects together define the reference frame:\n",
"```\n",
"frame_altaz = coordinates.AltAz(obstime=t, location=location)\n",
"```\n",
"\n",
"MJD, the modified Julian date, is a unit of time, the (fractional) number of days since a certain date (midnight on November 17, 1858). For example, Tuesday, Oct 5, 2021 at noon UTC is MJD 59492.50000. Tuesday at 9:30 Pacific, (16:30 UTC; the start of class) is MJD 59492.68750, etc. We are using an altitude-azimuth reference frame, which gives the cardinal direction (east-west-north-south) toward which I need to point my telescope, and the elevation or altitude, how high an angle above the horizon I should point. With a location on the Earth, a time of observation, and a location on the sky, we can compute other quantities. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Now compute the local sidereal time at the time of observation.** This calls a *method* of our time *object*. We also need to specify our longitude on the Earth.\n",
"```\n",
"lst = t.sidereal\\_time('apparent', header['LONGITUD'])\n",
"```\n",
"**Compare this computed value to the local sidereal time that you can find in the fits header.**\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Now compute the altitude, or the elevation, of our telescope pointing.** We'll transform to the altitude-azimuth frame that we defined a few lines prior:\n",
"```\n",
"coord_altaz = radec.transform_to(frame_altaz)\n",
"altitude = coord_altaz.alt\n",
"```\n",
"\n",
"In that last line, ```coord_altaz.alt`` fetches the value ```alt`` held within the object ```coord_altaz```. \n",
"**Compare this altitude with the value you obtain from the header.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Now is your turn to dig into the code a bit. Don't forget to read up on the documentation for how to use the astropy packages.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What was the altitude one hour before this image was taken (hint: what was the mjd one hour before)?**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*You answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What will be the altitude two hours after the time this image was taken?**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Approximately when (local time)did the object pass through zenith (maximum elevation), and what was the local sidereal time when this happened?** (hint: recall the relationship between RA and local sidereal time)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(Skip these next two questions and jump to the next section if you're short on time)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Approximately how long after this image was taken did the object reach an elevation of 40 $^\\circ$?**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"vscode": {
"languageId": "plaintext"
}
},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**If you have time and are feeling ambitious, make a plot of the elevation vs. time from when the object rises to when it sets. (optional, not part of grade)**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"vscode": {
"languageId": "plaintext"
}
},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## <p style=\"text-align: center;\">Part 3: Focal Length and Image Scale</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The size of an astronomical image on the CCD detector depends on the effective focal length (usually abbreviated ''focal length'') of\n",
"the telescope. Here is a link to a quick primary on focal length: [Focal length and f/# explained](https://www.paragon-press.com/lens/lenchart.html). This part of the lab will use a fits file called ```cluster.fits``` that should have been downloaded to your JupyterHub account when you clicked the link for this notebook, but it can also be found on the Lab 2 tab on the Gauchospace site. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**To get quantitative, an angle of 1 arcsec on the sky maps into a distance $d = fl / 206264.80$ measured in the focal plane of a\n",
"telescope having focal length $fl$.\n",
"Explain the origin of the magic number 206264.80. If you get stuck here, read the the primer above and think about the relationship between radians and arcseconds.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**The header of the image ```cluster.fits``` has a keyword ```FOCALLEN``` that gives an estimate of the telescope’s\n",
"focal length. The mean angular diameter of the Moon is about $\\frac{1}{2}$ degree, or 1800 arcsec. What is the diameter of an image of the Moon\n",
"made by this telescope, in mm?**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"vscode": {
"languageId": "plaintext"
}
},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Other keywords give the widths and the number of detector pixels, in the x- and y- directions. What is the (x,y) size of the detector as\n",
"projected on the sky, in arcsec? Will the entire image of the full Moon fit on it?**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How do we know if the header value for the image scale of the telescope is correct? We will measure it. **Use ds9 to open the image ```cluster.fits```. Click on ''scale'' and ''zscale'' so you can see faint stars. Display the header, and write down the RA, $\\delta$ coordinates to which the telescope is pointing.**\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After doing a Y-invert (see below), your image should look like this, except for the little circles and numbers, and the color scheme I used to make the numbers show up better.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![test](M67_circled.jpeg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

807
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# <p style=\"text-align: center;\">PHYS 134L Spring 2022 Lab 3</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-danger\"><b>Due date:</b> Sunday, April 24th, 2022 by 11:59pm, submitted through Gradescope.</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Names: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Enter your name and your partner's name here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Read through this entire lab before you start. In this lab, we will look at the brightness of stars as measured in astronomical units called ''magnitudes.'' To complete this lab you should have already read textbook Chapter 3 and Sections 2.3 and 2.4. In this lab, you will be asked to type out some equations. In a jupyter notebook you can do this using standard LATEX math notation. If you're new to LATEX you can use [this online equation editor](https://latex.codecogs.com/) to help you along to start. Later in this course you'll be using La"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 1: Astronomical Magnitudes</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**We'll begin by making a two-dimensional plot of ```cluster1.fits``` and overplotting the locations of the stars given in ```cluster1.cat.```** Refer to the first lab if you have forgotten how to do this. As in that lab, please use a scale that shows the full dynamic range of the image and that looks nice: no garish color schemes, and few (if any) pixels beyond the limits of your color scale. The $x$ and $y$ pixel locations might be in different locations than they were in ```object.cat``` from Lab 1, so please check and make sure that you are reading the correct column. You may open ```cluster1.cat``` in a text editor (like notepad) or on JupyterHub to double-check the contents of each column.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The file ```cluster1.cat``` has many columns besides the $x$ and $y$ positions. We will now look at the information in the columns ```MAG_ISOCOR``` and ```MAGERR_ISOCOR```. **First, make a scatter plot showing ```MAG_ISOCOR``` as a function of ```NUMBER```, i.e., simply plot the magnitudes as a function of the order in which they appear in the catalog. Overplot the error bars given by ```MAGERR_ISOCOR```.** Check the documentation for ```pyplot.errorbar``` if you are unsure of how to get started."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's hard to interpret that previous plot; it looks like a bit of a mess. To make it easier to see what is going on, let's sort the stars by magnitude. You'll want to sort the magnitudes and their uncertainties in the same way. In other words, you want the same uncertainty to remain associated with each measured magnitude. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Assume that you have read in the catalog file and set an array called ```mags``` equal to the column ```MAG_ISOCOR``` and an array called ```mag_errs``` equal to the column ```MAGERR_ISOCOR```. Explain why the following code will produce nonsense if you use the array ```mag_errs_sorted``` for the error bars of ```mags_sorted```:\n",
"```\n",
"mags_sorted = np.sort(mags)\n",
"mag_errs_sorted = np.sort(mag_errs)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To sort the arrays in the same way, try ```np.argsort```. Experiment yourself a bit to get it working, and read the documentation page. \n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Now remake your plot of magnitudes with error bars, but sorted by magnitude on the horizontal axis.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Do the estimated errors varay with magnitude in a systematic way? Explain"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So far we have used catalogs output by Source Extractor to obtain only the most minimal information about the objects in the detector field of view--the positions and fluxes from each detected object. We will now look at Source Extractor output files for which we have asked the program to do a more thorough job. Typically we want more kinds of information about each object for one of three reasons: to represent the data in a more convenient way, to display the result of a different way to estimate a number (such as the flux) for which we already have a value, or to give information about the reliability of the results displayed in other columns.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will continue to work with the catalog given by ```cluster1.cat```, but now will load the columns corresponding to ```FLUX_ISOCOR``` and ```FLUXERR_ISOCOR```. Open the catalog file in a text editor like notepad if you cannot find them. As usual, remember that Source Extractor counts from 1, while python indexes from 0. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we will check the relationship between flux and magnitude, if you need a reminder, check out Section 3.2 of the Burns. **Make a scatter plot with ```MAG_ISOCOR``` on the $x$-axis and ```FLUX_ISOCOR``` on the $y$-axis. Once you have done this, adjust the vertical axis to have a logarithmic scaling (check ```pyplot.yscale```).** "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once you have this scatter plot, try fitting a line by eye. The mechanics of how to actually do this properly are beyond the scope of this class. For now, please define a variable $x$ by\n",
"```\n",
"x = np.linspace(np.amin(mags,np.amax(mags)),10)\n",
"```\n",
"and a variable $y$ by\n",
"```\n",
"y = a*x + b\n",
"```\n",
"where you determine the best-fit ceofficients ```a``` and ```b``` by eye. Depending on how you have implemented your logarithmic vertical scale you may need to plot either \n",
"```\n",
"y = np.exp(a*x+b)\n",
"```\n",
"or \n",
"```\n",
"y = 10**(a*x+b)\n",
"```\n",
"for it to appear as a line on your plot. **Please overplot your best-fit line on the scatter plot of magnitudes against logarithmic flux.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#You code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Write down the definition of astronomical magnitudes in the space below.**\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**How closely does your fitted constant ```a``` match expectations?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Approximately what magnitude would yield a flux of 1 given your values of ```a``` and ```b```? Please show your work.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 2: The Sizes of (Images of) Stars</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The catalog file has a column entitled ```FWHM_IMAGE``` (meaning Full Width at Half Maximum of the star image). This parameter is a measure of the width of the star images in units of pixels -- smaller numbers mean sharper images. You can also estimate these values yourself by looking at the image in ds9. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Open the image in ds9, set the “scale” option to “zscale,” and estimate the size of the images\n",
"of stars (in pixels). How do these sizes compare with the FWHM IMAGE values in the catalog\n",
"file?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Now try setting the ds9 ``scale'' to ``min/max'' and ``linear'' and estimate the sizes of a few of the star images (necessarily the brightest ones, since those are all you can see this way). Use the cursor to read the pixel values. How do the sizes you estimate in this way compare to the FWHM_IMAGE values in the catalog file?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Set the ``Horizontal Graph'' option in the ``View'' tab, and estimate the FWHM of a bright star from this graph. How does this estimate compare with the other two estimates you gave above?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Last lab, you estimated the angular sizes of a few stars; the largest size you should have computed was around 2~mas. You also computed the pixel scale in these images; you should have gotten a scale of around $0.\\!\\!^{\\prime \\prime}58$ arcsec/pixel. **Use these two numbers to estimate the angular size of a star in units of pixels. Please show your work for the unit conversion.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The angular size of a star (in units of pixels) divided by the image FWHM gives a dimensionless number. If this number is larger than 1, the star is said to be resolved: a larger star makes a larger image. If this number is much less than 1, the star is said to be unresolved, because the size of the star on the image is set almost entirely by something other than its physical size. **What is this dimensionless number, angular size/FWHM, for the current image? Roughly how small would the FWHM have to be for any of the stars to be resolved at all?**\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your anwer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**To see if all stars have the same size on the image, make a plot of FWHM ($y$-axis) against stellar magnitude ($x$-axis). As usual, please label your axes and make the plot look nice. Do you see evidence for a dependence of FWHM on magnitude?**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For telescopes on the ground, the FWHM is usually set by atmospheric turbulence and is called ''seeing.'' A better site gives a shaper image. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 3: Backgrounds and Photon Noise</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ```BACKGROUND``` column in ```cluster1.cat``` contains estimates of the sky background flux (per pixel) in the neighborhood of each identified object. **Make a scatter plot of the sky background as a function of ```X_IMAGE```, using any plot symbols you like, but without lines connecting the points.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What happens if you do use lines to connect the data points? **Explain what the program is doing to generate this unusable plot.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What is a typical value for the sky background? What is the approximate scatter in the reported values?**"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Within Python you can calculate simple statistics (min, max, mean, standard deviation) for data sets using ```numpy``` functions. Ordinarily, your visual impression of the typical value of a bunch of plotted data points will closely approximate the mean value, and your visual estimate of the peak-to-peak scatter (ignoring rare outliers) will be roughly 4 times the standard deviation. How do mean and standard deviation computed with Python compare with the visual estimates you just made?"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"**Now, make a scatter plot ```MAGERR_ISOCOR``` as a function of ```MAG_ISOCOR```.** ```MAGERR_ISOCOR``` is an estimate of the error in ```MAG_ISOCOR```, based on square-root-rule counting error for the number of detected photons in the object plus the underlying sky background (derived from the Poisson distribution). The total number of sky+object photons is\n",
"$$\n",
"N_{\\rm phot} = {\\tt GAIN} \\cdot ({\\tt FLUX\\_ISOCOR} + {\\tt BACKGROUND} \\cdot N_{\\rm pix})\n",
"$$\n",
"Where ````GAIN```` is the number of detected photo-electrons per signal count (2.36 $e^-$/count for this image, determined from the ```EGAIN```\n",
"keyword in the FITS header). $N_{\\rm pix}$ is the number of pixels occupied by the object image. With ```ISOCOR``` photometry this number is hard to know for sure, but a reasonable guess is $\\pi ({\\rm FWHM}/2)^2$. **Use this guess, the ```GAIN``` value just given, and your estimate of ```BACKGROUND``` to write an expression for $N_{\\rm phot}$ as a function of ```FLUX_ISOCOR```.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Now use the flux-vs-magnitude expression from page 2 to write an expression for $N_{\\rm phot}$ as a function of ```MAG_ISOCOR```.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The expected counting error (measured in photo-electrons) is the square root of $N_{\\rm phot}$. To get the noise in units of counts, we must\n",
"divide by the ```GAIN```. **Write an expression for this counting error as a function of MAG_ISOCOR}.**\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now the tricky part. **What error (in magnitudes) is implied by this error in the measured value of $N_{\\rm phot}$?** Assume that the error is small\n",
"compared to $N_{\\rm phot}$ itself (i.e., that $N_{\\rm phot} \\ll 1$), and show that if\n",
"$$\n",
"{\\rm mag} = m_1 - 2.5 \\log_{10}({\\rm flux})\n",
"$$\n",
"(where $m_1$ is the magnitude that yields ${\\rm flux} = 1$), then\n",
"$$\n",
"\\delta {\\rm mag} \\approx 1.086 \\frac{\\delta {\\rm flux}}{\\rm flux}.\n",
"$$\n",
"Derive this expression below. You may use standard propagation of uncertainties and take the square root."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your equation here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Now combine this expression and the one for counting error to write an expression for the expected error in magnitudes as a function of the object magnitude.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your equation here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Finally, define integer magnitudes covering the range of magnitudes in ```cluster1.cat```:**\n",
"\n",
"```x = np.arange(int(np.amin(mags)), int(np.amax(mags)) + 1)```\n",
"\n",
"**and evaluate your expression for magnitude uncertainties at these integer ```x``` values. Overplot this on your plot of ```MAGERR_ISOCOR``` vs.~```MAG_ISOCOR``` using a thick, red line.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 4: Consistency and Systematic Errors</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we know how to use Source Extractor output to estimate the fluxes and magnitudes of stars, and also the precision that simple physics says we should be achieving. But how well do we know our errors, really? Might effects other than photon counting statistics be dominant? And what about systematic errors, which give us consistent and repeatable wrong answers? How can we test for these?\n",
"\n",
"\n",
"Source Extractor can estimate source fluxes in several ways – two of these are isophotal photometry (which deals well with objects having funny shapes) and aperture photometry (which works well for perfectly round objects, as star images are supposed to be). Check section 7.4 of *Source Extractor for Dummies* for an explanation of what these things mean. The picture on p.~41 is particularly helpful.\n",
"\n",
"\n",
"Since there are different ways to estimate what ought to be the same quantities, let’s see if we get the same answers with aperture photometry as we did with isophotal photometry. If not, the differences tell us something about our errors. \n",
"\n",
"Make a figure with two graphs, one on top of the other. For this task, you'll want to use subplots sharing the $x$-axis (read the documentation page for ```pyplot.subplots```). On the top axes, plot ```MAG_ISOCOR``` on the $x$-axis and ```MAG_APER``` on the $y$-axis. You should expect a tight but not perfect correlation between the two measurements, with a few dramatic outliers. The wide range in plotted magnitudes makes it hard to see the errors. **On the lower graph plot ```MAG_ISOCOR``` on the $x$-axis and, on the $y$-axis, plot (```MAG_ISOCOR – MAG_APER```). Choose your y-axis plot range carefully, to show the most information.\n",
"If necessary, sacrifice a few outliers to show the typical scatter better.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the peak-to-peak scatter in the difference (```MAG_ISOCOR - MAG_APER```), if you ignore extreme outliers? How does this compare with the tabulated uncertainties ```MAGERR_ISOCOR``` and ```MAGERR_APER```? What do you conclude from this?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Identify the stars corresponding to 3 of the most extreme outliers in your upper plot, and look at them using ds9. Can you describe the potential source(s) of these systematic errors?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.8"
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},
"nbformat": 4,
"nbformat_minor": 2
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BIN
Lab 3/cluster.fits
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486
Lab 3/cluster1.cat
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@ -1,486 +0,0 @@
# 1 NUMBER Running object number
# 2 X_IMAGE Object position along x [pixel]
# 3 Y_IMAGE Object position along y [pixel]
# 4 FLUX_ISOCOR Corrected isophotal flux [count]
# 5 FLUXERR_ISOCOR RMS error for corrected isophotal flux [count]
# 6 MAG_ISOCOR Corrected isophotal magnitude [mag]
# 7 MAGERR_ISOCOR RMS error for corrected isophotal magnitude [mag]
# 8 FLUX_APER Flux vector within fixed circular aperture(s) [count]
# 9 FLUXERR_APER RMS error vector for aperture flux(es) [count]
# 10 MAG_APER Fixed aperture magnitude vector [mag]
# 11 MAGERR_APER RMS error vector for fixed aperture mag. [mag]
# 12 ELONGATION A_IMAGE/B_IMAGE
# 13 FWHM_IMAGE FWHM assuming a gaussian core [pixel]
# 14 BACKGROUND Background at centroid position [count]
# 15 FLAGS Extraction flags
1 389.0368 71.6170 306479.9 449.4477 -13.7160 0.0016 221860.5 321.6074 -13.3652 0.0016 1.031 7.25 570.4601 0
2 535.8401 72.3356 111624.2 312.1177 -12.6194 0.0030 81540.21 209.6749 -12.2784 0.0028 1.039 7.31 570.7159 2
3 705.8304 58.6026 897266.8 695.18 -14.8823 0.0008 650860.2 534.042 -14.5337 0.0009 1.027 6.15 571.3956 2
4 659.9183 45.8076 184636.1 373.7914 -13.1658 0.0022 133710 257.0073 -12.8154 0.0021 1.034 7.52 571.569 2
5 672.6502 15.1796 161059.9 357.9897 -13.0175 0.0024 116081.1 242.0871 -12.6619 0.0023 1.047 7.32 571.9493 10
6 1203.9077 50.1429 22185.08 200.8275 -10.8652 0.0098 16619.72 128.3285 -10.5516 0.0084 1.085 11.62 571.1428 2
7 1002.1099 48.1919 19659.39 196.8211 -10.7339 0.0109 15186.5 125.8607 -10.4536 0.0090 1.060 7.24 571.392 2
8 656.1636 24.0052 22719.3 202.8197 -10.8910 0.0097 16519.26 128.1105 -10.5450 0.0084 1.126 13.64 571.6312 2
9 356.5015 35.1145 3813.68 161.5075 -8.9534 0.0460 3057.215 103.5923 -8.7133 0.0368 1.086 14.57 570.3051 0
10 94.4035 32.7588 9606.526 171.344 -9.9564 0.0194 7652.083 112.465 -9.7094 0.0160 1.109 8.26 572.4567 2
11 893.1217 26.2778 56846.22 254.468 -11.8868 0.0049 42039.12 165.1033 -11.5591 0.0043 1.048 8.83 571.5414 0
12 1507.4277 17.3794 325051.8 454.1195 -13.7799 0.0015 237964.2 332.0415 -13.4413 0.0015 1.034 7.32 584.3629 2
13 1506.0000 5.0173 4980.516 54.35657 -9.2432 0.0119 5294.731 104.7538 -9.3096 0.0215 1.005 0.00 584.6544 18
14 1.2756 20.1721 352.0092 45.47412 -6.3664 0.1403 373.6361 75.03796 -6.4311 0.2181 1.750 -0.99 574.8361 24
15 1444.3497 5.3484 122885.2 296.4996 -12.7237 0.0026 99819.45 226.3685 -12.4980 0.0025 1.245 8.24 577.5316 24
16 1535.6854 12.0019 431.8897 32.13369 -6.5884 0.0808 324.9601 75.07807 -6.2796 0.2509 1.497 3.34 587.8103 24
17 1320.4512 2.7629 6273.627 127.1033 -9.4938 0.0220 5292.692 95.6935 -9.3092 0.0196 2.124 13.09 573.1546 24
18 1296.6378 3.0893 4602.483 133.719 -9.1575 0.0316 3723.802 93.74911 -8.9275 0.0273 1.921 9.88 572.8157 24
19 1271.3274 2.8810 14518.22 148.8741 -10.4048 0.0111 12181.67 110.4817 -10.2143 0.0098 2.055 9.57 572.4188 24
20 1411.0084 1.8239 311.4857 42.12267 -6.2336 0.1469 204.5039 78.15753 -5.7768 0.4150 1.047 3.83 575.6845 24
21 1463.8964 1.9485 330.5657 48.8313 -6.2981 0.1604 499.7827 79.77227 -6.7470 0.1733 1.180 4.07 579.8969 24
22 1139.9670 2.0064 526.8016 41.37827 -6.8041 0.0853 577.7314 80.27001 -6.9043 0.1509 1.017 0.00 571.1617 24
23 1090.6235 2.1652 203.4737 39.61199 -5.7713 0.2114 331.8169 80.5127 -6.3022 0.2635 1.558 3.25 571.0824 24
24 1035.9690 1.8887 584.1646 40.19136 -6.9163 0.0747 685.5258 79.84801 -7.0901 0.1265 1.028 1.11 571.1794 24
25 983.9792 2.0576 411.6134 46.73682 -6.5362 0.1233 362.5716 80.01291 -6.3985 0.2397 1.015 4.23 571.5439 24
26 717.8780 2.1685 248.9239 42.04086 -5.9902 0.1834 229.4858 80.26372 -5.9019 0.3798 1.270 3.59 572.3331 24
27 527.1032 1.4904 695.3176 36.29724 -7.1055 0.0567 815.3862 77.80977 -7.2784 0.1036 1.182 1.00 569.946 24
28 447.8138 1.8790 241.7663 44.33751 -5.9585 0.1992 252.848 78.52211 -6.0071 0.3373 1.258 0.87 570.1091 24
29 435.0042 2.0222 231.634 34.51355 -5.9120 0.1618 253.9699 79.53661 -6.0120 0.3401 1.029 3.39 570.1216 24
30 358.1033 1.8874 363.3374 44.29612 -6.4008 0.1324 354.3787 79.0488 -6.3737 0.2422 1.151 0.00 570.2073 24
31 275.0032 1.7940 648.4477 39.34929 -7.0297 0.0659 739.7831 79.19677 -7.1728 0.1163 1.015 1.54 570.3818 24
32 1345.9760 1.2237 178.8039 31.72073 -5.6309 0.1927 132.2047 74.06143 -5.3031 0.6084 1.512 0.00 573.5095 24
33 1307.0096 1.3946 297.7979 36.23338 -6.1848 0.1321 416.0429 75.8414 -6.5478 0.1980 1.483 3.50 572.9758 24
34 1495.1985 50.5526 27914.38 209.7055 -11.1146 0.0082 21062.47 135.3664 -10.8088 0.0070 1.073 14.24 581.9782 2
35 639.9816 1.1932 216.37 28.40033 -5.8380 0.1425 356.9218 74.41113 -6.3814 0.2264 1.596 2.91 571.4084 24
36 616.0170 1.1981 183.7082 31.06188 -5.6603 0.1836 10.61068 73.44116 -2.5644 7.5167 1.558 2.90 570.9252 24
37 535.0229 1.3363 475.2159 31.70255 -6.6922 0.0724 557.8524 75.93008 -6.8663 0.1478 1.506 0.00 569.9243 24
38 506.9860 1.2328 166.3176 34.21916 -5.5523 0.2234 197.0305 74.3811 -5.7363 0.4100 1.508 0.00 570.0002 24
39 456.0171 1.3341 817.851 31.69455 -7.2817 0.0421 876.3889 76.81374 -7.3567 0.0952 1.507 3.40 570.0954 24
40 367.1576 1.3138 239.0407 33.80391 -5.9462 0.1536 347.8513 75.29762 -6.3535 0.2351 1.508 3.20 570.1935 24
41 317.0129 1.7687 166.7218 43.88645 -5.5550 0.2859 598.6397 78.81828 -6.9429 0.1430 1.660 3.18 570.2615 24
42 200.1788 1.3060 273.1656 31.62398 -6.0911 0.1257 411.6056 75.34428 -6.5362 0.1988 1.582 3.23 570.925 24
43 101.0173 1.2231 192.3715 30.1251 -5.7104 0.1701 369.4842 74.78168 -6.4190 0.2198 1.530 3.01 572.5365 24
44 571.1406 843.8476 693.754 92.48909 -7.1030 0.1448 868.277 98.91342 -7.3466 0.1237 1.241 6.59 566.5977 0
45 1480.8933 1024.0000 176.5775 23.84674 -5.6173 0.1467 64.14983 72.27107 -4.5180 1.2235 2.971 1.29 578.8329 24
46 1378.5719 1023.5145 198.4511 29.59098 -5.7441 0.1619 -80.5513 75.38045 99.0000 99.0000 1.083 0.23 571.181 24
47 1331.5981 1023.4440 188.5104 30.51293 -5.6883 0.1758 -77.16092 75.75509 99.0000 99.0000 1.080 0.44 570.5027 24
48 1147.0376 1023.4218 256.1931 40.56774 -6.0214 0.1720 -86.93473 76.04034 99.0000 99.0000 1.477 0.00 567.348 24
49 1099.9960 1023.2465 290.3186 45.43005 -6.1572 0.1699 -34.99454 77.06281 99.0000 99.0000 1.044 0.00 567.1688 24
50 977.0167 1023.0481 1158.141 38.62954 -7.6594 0.0362 900.8903 80.76871 -7.3867 0.0974 1.018 0.00 566.9571 24
51 959.9641 1022.5631 5586.261 116.963 -9.3678 0.0227 4799.314 93.0327 -9.2029 0.0211 2.324 10.61 566.972 24
52 911.9476 1024.0000 210.2598 22.82982 -5.8069 0.1179 -43.82784 72.08277 99.0000 99.0000 2.646 0.00 566.6826 24
53 722.5679 1022.2255 2171.332 111.8442 -8.3418 0.0559 1875.761 87.86003 -8.1829 0.0509 1.432 11.31 566.1988 24
54 668.9771 1023.8237 257.1691 26.8563 -6.0255 0.1134 -24.38488 73.34245 99.0000 99.0000 1.699 0.00 566.1174 24
55 625.0696 1023.8542 217.4814 28.3406 -5.8436 0.1415 -21.94512 73.16058 99.0000 99.0000 1.898 0.00 565.7858 24
56 618.0152 1023.2153 355.4968 38.66916 -6.3771 0.1181 27.4378 77.33227 -3.5959 3.0608 1.046 0.00 565.7391 24
57 609.9766 1023.8417 258.8605 26.81335 -6.0327 0.1125 -95.94534 73.20609 99.0000 99.0000 1.811 2.86 565.6727 24
58 603.9647 1023.0606 553.2466 40.76528 -6.8573 0.0800 225.543 78.89294 -5.8831 0.3799 1.021 0.00 565.6498 24
59 408.0154 1023.5025 6393.519 123.8021 -9.5143 0.0210 5669.829 89.93337 -9.3839 0.0172 1.575 16.56 567.3068 26
60 404.2147 1023.6516 2047.724 50.12054 -8.2782 0.0266 2390.589 81.00583 -8.4463 0.0368 1.849 0.77 567.3087 26
61 300.0554 1024.0000 194.529 23.21 -5.7225 0.1296 9.612668 72.13411 -2.4571 8.1494 2.741 2.78 567.0597 24
62 159.9874 1023.6769 195.0727 29.87731 -5.7255 0.1663 -84.56991 74.29002 99.0000 99.0000 1.332 3.16 569.3026 24
63 58.0101 1023.7108 395.1473 32.70463 -6.4919 0.0899 294.483 74.90314 -6.1727 0.2762 1.551 3.32 572.1126 24
64 4.0389 1023.5570 317.7219 35.10119 -6.2551 0.1200 168.747 69.57799 -5.5681 0.4478 1.446 1.04 574.1973 24
65 92.0124 835.0628 2892.752 154.7811 -8.6533 0.0581 2222 101.739 -8.3669 0.0497 1.186 9.09 570.2118 0
66 946.0488 830.3796 14789.75 187.1461 -10.4249 0.0137 10951.07 118.5871 -10.0986 0.0118 1.106 12.69 568.6592 0
67 314.3318 834.2944 2243.109 157.834 -8.3771 0.0764 1853.114 101.0997 -8.1698 0.0592 1.260 7.78 568.1591 0
68 982.8816 824.6236 88428.16 289.3284 -12.3665 0.0036 64634.99 191.8254 -12.0262 0.0032 1.043 8.41 568.9642 0
69 1360.3040 830.3319 122.617 36.99383 -5.2214 0.3276 653.2732 98.57016 -7.0377 0.1639 1.658 2.53 572.0346 0
70 1028.8444 816.2819 29138.28 229.3314 -11.1612 0.0085 17979.26 130.541 -10.6369 0.0079 1.423 23.62 569.2427 2
71 1031.7109 807.2930 1652.074 44.86493 -8.0451 0.0295 2057.618 101.5438 -8.2834 0.0536 1.579 0.00 569.4155 2
72 185.6552 810.6270 29178.74 215.8286 -11.1627 0.0080 21562.37 136.22 -10.8342 0.0069 1.074 7.88 569.6203 2
73 193.9553 815.0057 456.0123 28.61519 -6.6474 0.0681 818.3894 98.78965 -7.2824 0.1311 1.028 3.48 569.6991 2
74 831.9339 814.3178 1702.223 136.373 -8.0775 0.0870 1597.302 100.5456 -8.0085 0.0684 1.277 10.72 567.916 0
75 719.0699 845.1190 16637.08 197.6402 -10.5527 0.0129 12202.93 120.858 -10.2162 0.0108 1.017 8.91 567.0499 0
76 77.5644 797.0984 25463.77 210.824 -11.0148 0.0090 18983.89 132.1236 -10.6960 0.0076 1.061 7.69 569.5073 0
77 341.9962 791.5062 23339.69 200.8374 -10.9202 0.0093 17869.51 130.286 -10.6303 0.0079 1.052 7.47 567.426 0
78 1535.7051 798.2408 152.9125 25.26869 -5.4611 0.1795 108.7093 74.51004 -5.0907 0.7444 1.473 0.00 580.6508 24
79 204.7318 783.5220 159438.3 358.6378 -13.0065 0.0024 114413.1 240.6576 -12.6462 0.0023 1.119 7.43 569.4357 0
80 114.5093 782.7014 159062.3 362.3949 -13.0039 0.0025 97669.65 225.436 -12.4744 0.0025 1.269 11.93 569.3098 0
81 1031.8646 775.4187 945937.1 717.8205 -14.9397 0.0008 638931.2 529.2821 -14.5136 0.0009 1.137 8.37 569.5766 0
82 253.5605 777.4815 100357.3 303.6525 -12.5039 0.0033 73121.68 201.0051 -12.1601 0.0030 1.040 7.42 568.9042 0
83 1309.7655 771.3724 622381.6 595.9546 -14.4851 0.0010 446218.7 445.5315 -14.1239 0.0011 1.041 8.95 570.9946 0
84 1.7065 787.2881 145.4647 25.96159 -5.4069 0.1938 -8.030077 76.95468 99.0000 99.0000 1.546 0.84 569.9659 24
85 866.9930 773.4222 121961.1 322.2259 -12.7156 0.0029 89747.38 217.81 -12.3826 0.0026 1.032 7.64 568.5294 2
86 860.0238 769.0179 5351.41 55.76167 -9.3212 0.0113 5503.967 108.4042 -9.3517 0.0214 1.023 4.34 568.4647 2
87 386.8057 776.8505 15680.58 187.8443 -10.4884 0.0130 11931.57 120.2568 -10.1917 0.0109 1.139 9.83 566.7452 2
88 378.2201 777.0212 598.3875 33.99408 -6.9425 0.0617 863.1305 98.9024 -7.3402 0.1244 1.047 3.95 566.8578 2
89 149.9731 768.0416 14740.43 194.7258 -10.4213 0.0143 10706.93 118.136 -10.0742 0.0120 1.058 13.96 569.2845 0
90 637.3253 767.3802 1498.14 131.4086 -7.9389 0.0953 1292.797 99.7685 -7.7788 0.0838 1.197 10.16 566.9343 0
91 586.5219 763.3857 13218.75 179.3087 -10.3030 0.0147 10240.15 117.2249 -10.0258 0.0124 1.036 11.04 566.7806 2
92 586.0002 756.0030 23330.59 103.462 -10.9198 0.0048 23843.89 139.5684 -10.9434 0.0064 1.000 4.19 566.7729 2
93 279.2478 753.7066 129564.3 339.9291 -12.7812 0.0028 92597.57 220.6329 -12.4165 0.0026 1.097 7.36 568.2382 0
94 1535.0524 762.9042 335.7802 47.79423 -6.3151 0.1546 211.3919 79.00263 -5.8127 0.4059 1.190 0.00 579.4632 24
95 1098.0483 738.3636 2050370 1011.655 -15.7796 0.0005 1470165 795.2153 -15.4184 0.0006 1.024 7.31 569.2079 0
96 968.7756 704.7058 54220.5 280.0743 -11.8354 0.0056 34485.18 154.9677 -11.3441 0.0049 1.088 9.10 569.5555 2
97 951.8831 737.8629 2877208 1171.293 -16.1474 0.0004 2068290 941.1783 -15.7890 0.0005 1.068 7.29 569.8163 2
98 971.9218 726.1238 245697.1 397.9074 -13.4760 0.0018 173297.8 287.884 -13.0970 0.0018 1.065 7.40 569.727 2
99 899.2938 755.8594 4527.937 153.0861 -9.1398 0.0367 3850.797 105.1395 -8.9639 0.0297 1.023 5.75 569.137 2
100 897.4845 751.4378 500.723 42.12727 -6.7490 0.0914 881.5577 98.94186 -7.3631 0.1219 1.178 -0.37 569.1727 2
101 1496.3372 748.2548 6391.317 169.5444 -9.5140 0.0288 4932.04 107.3117 -9.2326 0.0236 1.128 8.88 576.7207 0
102 1347.0923 742.8418 21225.65 200.4461 -10.8172 0.0103 15873.92 127.0912 -10.5017 0.0087 1.027 9.75 571.7237 0
103 252.5567 746.0145 10461.51 89.15668 -10.0490 0.0093 10336.42 117.4555 -10.0359 0.0123 2.517 7.88 568.4484 0
104 647.7886 730.2021 150412.2 343.9447 -12.9432 0.0025 109921.5 236.5647 -12.6027 0.0023 1.015 7.37 566.9549 2
105 668.9844 719.3401 11668.54 184.2906 -10.1675 0.0172 8640.732 114.3414 -9.8414 0.0144 1.068 18.26 567.0324 2
106 870.3569 733.5926 9646.822 174.5925 -9.9610 0.0197 7519.082 112.2438 -9.6904 0.0162 1.139 13.94 568.9334 0
107 1.5910 736.6395 225.3193 27.95505 -5.8820 0.1347 81.07081 76.30955 -4.7722 1.0222 1.024 2.83 568.7809 24
108 1535.1375 732.8823 260.4868 39.87928 -6.0395 0.1663 118.0934 78.26414 -5.1806 0.7197 1.239 3.59 578.6476 24
109 274.5451 714.7672 6389.943 166.8334 -9.5137 0.0284 5049.103 107.4806 -9.2580 0.0231 1.090 8.55 567.9453 0
110 506.6902 714.3842 884.6818 103.6956 -7.3670 0.1273 1023.11 99.19415 -7.5248 0.1053 1.380 7.58 566.5515 0
111 759.5422 703.0983 48092.64 245.6235 -11.7052 0.0055 35572.86 156.5434 -11.3778 0.0048 1.045 8.00 567.0292 0
112 1.6210 713.8533 198.8546 42.60148 -5.7463 0.2327 123.1838 76.68742 -5.2264 0.6761 1.692 1.43 568.8441 24
113 1316.1206 693.5350 180819.7 368.9051 -13.1431 0.0022 131409.8 255.1759 -12.7966 0.0021 1.051 7.29 570.4988 0
114 1215.8433 701.2114 9154.539 171.2209 -9.9041 0.0203 7222.528 111.6826 -9.6467 0.0168 1.038 9.03 568.8199 0
115 716.9677 702.5513 2833.355 157.3204 -8.6308 0.0603 2219.288 101.7497 -8.3655 0.0498 1.251 11.36 566.9985 0
116 599.4573 690.2487 192601.3 379.7938 -13.2116 0.0021 140026.1 262.1941 -12.8655 0.0020 1.028 7.26 567.1793 0
117 878.7529 686.2391 121071.6 320.4928 -12.7076 0.0029 85641.12 213.7941 -12.3317 0.0027 1.019 9.55 568.9286 2
118 873.0854 664.4724 119499.7 316.0713 -12.6934 0.0029 83149.25 211.3654 -12.2996 0.0028 1.074 13.53 568.9153 2
119 872.5131 644.5047 152817.8 351.6819 -12.9604 0.0025 107927.9 234.8931 -12.5828 0.0024 1.065 7.93 569.2052 2
120 855.9648 685.6813 270684.3 419.5621 -13.5812 0.0017 194517.4 303.0488 -13.2224 0.0017 1.040 7.32 568.4662 2
121 847.1931 662.3392 581310.8 571.3052 -14.4110 0.0011 420077.9 432.9031 -14.0583 0.0011 1.021 7.29 568.4235 2
122 954.7587 667.2405 58716.28 263.7987 -11.9219 0.0049 42058.05 165.0772 -11.5596 0.0043 1.052 9.87 569.4413 2
123 934.0070 692.9849 5242.795 55.35353 -9.2989 0.0115 5692.074 108.664 -9.3882 0.0207 1.008 0.00 569.7808 2
124 938.6715 682.9146 170716.3 355.3527 -13.0807 0.0023 125515.4 250.2474 -12.7467 0.0022 1.053 7.30 569.7128 2
125 525.9485 685.9960 7689.264 73.31499 -9.7147 0.0104 8317.622 113.6972 -9.8000 0.0148 1.046 0.00 566.9208 2
126 522.5003 685.4977 20539.31 201.4312 -10.7815 0.0107 17004.74 128.9626 -10.5764 0.0082 1.140 12.40 566.8902 2
127 1104.0127 691.7571 579.6447 34.08554 -6.9079 0.0639 1068.364 99.3243 -7.5718 0.1010 1.069 0.00 568.7316 2
128 1103.2250 683.6935 20277.34 199.2345 -10.7675 0.0107 15406.17 126.2299 -10.4692 0.0089 1.053 19.48 568.6555 2
129 1107.8810 676.1071 541.3816 31.36313 -6.8338 0.0629 820.3095 98.92854 -7.2849 0.1310 1.271 3.67 568.5802 2
130 1425.0533 684.9311 6591.957 139.4514 -9.5475 0.0230 5790.149 108.9926 -9.4067 0.0204 1.233 13.88 572.6516 0
131 1275.8137 677.1052 88928.13 289.6272 -12.3726 0.0035 64964.09 192.1626 -12.0317 0.0032 1.054 7.65 569.4414 0
132 309.6055 676.8823 13127.72 184.1904 -10.2955 0.0152 9934.206 116.6278 -9.9928 0.0127 1.074 8.00 567.1455 0
133 113.5566 663.4138 1139480 778.2751 -15.1418 0.0007 815402.6 595.7563 -14.7784 0.0008 1.022 7.33 568.8038 0
134 547.9919 669.0195 4577.742 52.79301 -9.1516 0.0125 4925.515 107.2056 -9.2311 0.0236 1.011 4.24 567.3125 2
135 545.1306 674.7978 17312.71 187.8304 -10.5959 0.0118 13372.86 122.7834 -10.3156 0.0100 1.072 8.32 567.2858 2
136 1193.7474 695.0914 819.1385 95.83013 -7.2834 0.1270 1030.688 99.311 -7.5328 0.1046 1.503 8.07 568.7092 0
137 1178.1858 651.4692 88835.96 288.1526 -12.3715 0.0035 65545.04 192.8193 -12.0413 0.0032 1.048 9.39 568.5361 2
138 1188.7242 653.0130 571.064 34.1343 -6.8917 0.0649 1119.296 99.39938 -7.6224 0.0964 1.081 0.00 568.562 2
139 1418.9794 648.5443 85598.11 286.4098 -12.3312 0.0036 62822.8 189.8485 -11.9953 0.0033 1.043 7.46 572.0171 0
140 497.4454 653.8682 3982.452 159.2191 -9.0004 0.0434 3229.183 103.8793 -8.7727 0.0349 1.121 11.32 566.7216 0
141 1145.3861 642.5230 30944.45 217.7573 -11.2265 0.0076 23207.8 138.6955 -10.9141 0.0065 1.049 7.59 568.5324 0
142 1306.7957 641.5597 6773.157 173.5098 -9.5770 0.0278 5180.646 107.7086 -9.2860 0.0226 1.047 10.66 569.6579 0
143 1.3138 648.0190 341.467 34.11103 -6.3334 0.1085 416.0694 75.42311 -6.5479 0.1969 1.576 3.42 569.0836 24
144 1084.4985 635.1830 109440.4 307.9083 -12.5979 0.0031 80291.55 208.3774 -12.2617 0.0028 1.035 7.45 568.3456 0
145 535.6158 645.8846 376.3221 68.20155 -6.4389 0.1968 833.6094 98.77172 -7.3024 0.1287 2.554 5.29 567.231 0
146 272.1246 632.1758 173055.3 365.7697 -13.0955 0.0023 125086 249.8236 -12.7430 0.0022 1.037 7.33 567.5929 0
147 210.5425 628.6658 94973.73 293.6758 -12.4440 0.0034 70485.36 198.2405 -12.1202 0.0031 1.049 7.31 568.5956 2
148 204.0284 624.0238 3900.172 48.05275 -8.9777 0.0134 4365.78 106.1564 -9.1002 0.0264 1.024 3.99 568.6294 2
149 437.8864 636.5464 750.4542 93.12788 -7.1883 0.1348 1100.349 99.50972 -7.6038 0.0982 1.286 7.29 566.4881 0
150 631.3391 631.8169 910.4944 105.7646 -7.3982 0.1262 1094.991 99.39783 -7.5985 0.0986 1.542 8.05 567.3303 0
151 1.3299 632.9932 1770.147 36.54151 -8.1200 0.0224 1763.107 79.22169 -8.1157 0.0488 1.507 0.00 569.1593 24
152 575.8073 626.9306 5784.55 169.4362 -9.4057 0.0318 4482.449 106.3421 -9.1288 0.0258 1.060 8.12 567.3551 0
153 1210.6587 623.2158 14748.29 189.6943 -10.4219 0.0140 11243.65 119.0667 -10.1273 0.0115 1.050 7.87 568.7001 0
154 476.9905 615.7000 183450.8 369.7404 -13.1588 0.0022 133396.9 256.7685 -12.8129 0.0021 1.033 7.28 566.8321 0
155 306.0975 611.2288 242455.6 414.3528 -13.4616 0.0019 174310.9 288.5651 -13.1033 0.0018 1.052 7.47 566.9442 0
156 1535.7252 624.9125 298.7418 30.64093 -6.1882 0.1114 117.8701 74.53609 -5.1785 0.6867 1.591 0.00 579.3865 24
157 1.7554 622.9925 290.9472 45.29123 -6.1595 0.1691 92.56979 77.31689 -4.9162 0.9071 1.067 3.88 569.2062 24
158 21.6285 615.3055 15691.27 195.4853 -10.4891 0.0135 11586.33 119.661 -10.1599 0.0112 1.137 12.27 569.1669 0
159 363.1283 608.8676 54596.75 248.0771 -11.8429 0.0049 46140.98 170.2367 -11.6602 0.0040 1.042 7.12 566.5079 2
160 360.3043 606.3028 10751.24 85.04531 -10.0786 0.0086 14736 125.2065 -10.4209 0.0092 1.928 0.99 566.5179 2
161 48.6502 618.8121 502.2541 28.53945 -6.7523 0.0617 862.8392 98.90177 -7.3398 0.1245 1.564 3.28 569.0497 2
162 44.6211 613.0625 8629.592 176.7796 -9.8400 0.0222 6661.83 110.5988 -9.5590 0.0180 1.150 8.56 569.0812 2
163 1493.5818 610.8138 6553.139 169.9273 -9.5411 0.0282 5004.657 107.3929 -9.2484 0.0233 1.243 9.73 576.2265 0
164 883.9446 600.2039 166946.1 358.0286 -13.0564 0.0023 120720.4 246.1002 -12.7045 0.0022 1.062 7.86 569.5296 2
165 889.3654 567.4880 302030.2 447.3039 -13.7001 0.0016 218027.3 319.0618 -13.3463 0.0016 1.033 7.35 569.0577 2
166 920.4991 563.5016 199800.6 387.2326 -13.2515 0.0021 145332.7 266.4663 -12.9059 0.0020 1.026 7.29 568.9343 2
167 253.3248 594.7138 146539 347.7894 -12.9149 0.0026 105289.6 232.5013 -12.5560 0.0024 1.046 7.70 568.0712 0
168 569.7487 594.1737 32437.46 231.1921 -11.2776 0.0077 22989.71 138.4101 -10.9038 0.0065 1.066 11.62 567.5294 2
169 574.5621 577.5217 6572.086 176.5748 -9.5443 0.0292 4928.134 107.2263 -9.2317 0.0236 1.153 9.31 567.7083 2
170 1535.1311 601.8925 261.7513 39.69443 -6.0447 0.1647 -8.92977 78.00787 99.0000 99.0000 1.256 0.00 579.4667 24
171 673.2163 587.4077 21028.77 198.2325 -10.8070 0.0102 15771.91 126.8292 -10.4947 0.0087 1.041 9.50 567.9054 0
172 1.7910 593.9964 303.3369 43.15304 -6.2048 0.1545 69.85355 77.36233 -4.6105 1.2027 1.089 3.85 569.4634 24
173 445.2023 577.1520 54804.7 253.6697 -11.8470 0.0050 40060.82 162.4117 -11.5068 0.0044 1.027 8.70 566.9033 0
174 525.3393 576.7914 45086.12 234.8142 -11.6351 0.0057 33716.04 153.9342 -11.3196 0.0050 1.016 7.61 567.4961 0
175 938.9756 580.9537 2274.719 61.22087 -8.3923 0.0292 2580.053 102.5144 -8.5291 0.0432 1.980 7.21 569.0106 2
176 945.4011 577.1667 8331.748 127.2485 -9.8018 0.0166 8661.494 114.3653 -9.8440 0.0143 1.090 9.95 568.9703 2
177 954.7986 566.9867 125254.4 327.3867 -12.7445 0.0028 90420.57 218.4104 -12.3907 0.0026 1.037 7.30 568.8921 2
178 834.4672 601.7120 112088.2 309.4975 -12.6239 0.0030 82902.12 211.0939 -12.2964 0.0028 1.030 7.15 569.0584 0
179 633.1782 539.7517 3040759 1216.327 -16.2075 0.0004 2185858 967.2816 -15.8491 0.0005 1.016 7.20 568.6135 2
180 776.6585 519.2133 27565.23 260.8065 -11.1009 0.0103 16776.25 128.5478 -10.5617 0.0083 1.738 25.49 569.0828 2
181 782.3267 550.4127 151439.7 327.3777 -12.9506 0.0023 108977.8 235.7604 -12.5933 0.0023 1.106 9.70 568.7622 2
182 789.1563 540.8710 161217.5 327.1824 -13.0185 0.0022 123899.5 248.822 -12.7327 0.0022 1.091 7.06 568.8199 2
183 1184.2992 546.1727 234231.5 405.5146 -13.4241 0.0019 170637.4 285.8495 -13.0802 0.0018 1.025 7.19 568.0508 2
184 1177.0184 541.0120 21763.38 100.2037 -10.8443 0.0050 21754.89 136.4703 -10.8439 0.0068 1.009 4.24 568.0671 2
185 184.4795 553.5676 40334.72 230.9237 -11.5142 0.0062 29990.64 148.7297 -11.1925 0.0054 1.044 9.08 568.7677 0
186 1081.2974 557.0922 1486.595 130.1057 -7.9305 0.0950 1360.901 100.0296 -7.8346 0.0798 1.293 9.85 567.8113 0
187 138.4052 554.0659 2516.375 147.6268 -8.5019 0.0637 2032.632 101.3438 -8.2701 0.0541 1.027 11.64 568.8465 0
188 1085.9260 541.6534 18845.88 198.1295 -10.6880 0.0114 14376.8 124.5705 -10.3942 0.0094 1.068 8.90 567.7946 0
189 1.2823 544.1592 331.4366 29.81122 -6.3010 0.0977 200.6826 74.65966 -5.7563 0.4040 1.609 3.20 570.0832 24
190 1003.4260 513.0878 181146.8 365.0528 -13.1451 0.0022 131123.8 254.8795 -12.7942 0.0021 1.034 7.28 568.7896 2
191 1020.9795 525.9935 157575 348.1346 -12.9937 0.0024 113961.4 240.2111 -12.6419 0.0023 1.033 7.69 568.4249 2
192 1010.0092 525.9988 13096.1 79.83015 -10.2929 0.0066 13198.73 122.4009 -10.3013 0.0101 1.005 0.00 568.5955 2
193 749.1982 508.9486 206878.9 389.7599 -13.2893 0.0020 150001.1 270.1094 -12.9402 0.0020 1.023 7.23 569.4791 0
194 1235.6732 515.3381 4529.084 145.8737 -9.1400 0.0350 3554.825 104.5732 -8.8770 0.0319 1.732 12.97 568.7115 2
195 1238.1975 510.5745 1946.188 85.2217 -8.2230 0.0476 2062.13 101.3726 -8.2858 0.0534 1.531 4.48 568.7632 2
196 699.8337 511.3173 25601.59 203.0016 -11.0207 0.0086 19618.6 133.15 -10.7317 0.0074 1.035 9.36 569.3909 2
197 692.2857 514.7178 496.5755 31.55862 -6.7400 0.0690 1099.815 99.54205 -7.6033 0.0983 1.510 3.69 569.3143 2
198 336.2180 506.8369 49848.85 245.5969 -11.7441 0.0054 36443.48 157.6751 -11.4040 0.0047 1.074 11.75 566.8962 0
199 457.7266 520.9659 409.2845 67.68867 -6.5301 0.1796 754.728 98.60237 -7.1945 0.1419 2.309 6.61 567.239 0
200 152.4362 508.5069 26095.93 206.608 -11.0414 0.0086 19909.87 133.6126 -10.7477 0.0073 1.055 7.62 568.9182 0
201 642.9609 544.9823 17960.27 90.81291 -10.6358 0.0055 18817.75 131.8822 -10.6864 0.0076 1.025 0.00 568.6691 2
202 239.0035 476.0161 2258.615 42.99911 -8.3846 0.0207 2731.964 102.7306 -8.5912 0.0408 1.011 4.30 568.3884 2
203 244.4041 490.2019 557736.1 569.7789 -14.3661 0.0011 403029 424.4576 -14.0133 0.0011 1.022 7.31 568.3071 2
204 244.0059 479.0661 5332.545 55.69098 -9.3173 0.0113 5336.321 108.0452 -9.3181 0.0220 1.001 4.35 568.2805 2
205 657.1502 493.9525 10952.2 184.4618 -10.0988 0.0183 8175.511 113.4761 -9.7813 0.0151 1.024 17.08 569.3169 0
206 392.8562 494.0174 2755.374 154.6475 -8.6005 0.0610 2234.791 101.8147 -8.3731 0.0495 1.035 11.05 566.8086 0
207 474.9600 487.4564 35293.62 228.5145 -11.3692 0.0070 25973.49 142.8811 -11.0363 0.0060 1.024 8.13 567.3862 0
208 93.2091 490.1264 9661.538 171.0606 -9.9626 0.0192 7701.645 112.5879 -9.7165 0.0159 1.067 17.53 569.3828 0
209 567.8943 477.8943 193489.2 366.5658 -13.2166 0.0021 140501.1 262.6156 -12.8692 0.0020 1.086 7.32 568.595 2
210 569.0291 462.7141 170902.5 349.9643 -13.0819 0.0022 125748 250.3844 -12.7488 0.0022 1.094 7.30 568.7151 2
211 1294.3748 489.5649 4244.179 77.80367 -9.0695 0.0199 4073.742 105.572 -9.0250 0.0281 2.369 4.54 569.2574 0
212 614.7700 486.5844 9494.841 175.4781 -9.9437 0.0201 7251.458 111.7971 -9.6511 0.0167 1.095 10.98 569.3324 0
213 1358.7886 479.1590 81275.4 284.2853 -12.2749 0.0038 59606.88 186.1982 -11.9382 0.0034 1.042 7.30 570.9054 2
214 1339.2848 476.1683 12961.59 191.6511 -10.2816 0.0161 9241.751 115.4496 -9.9144 0.0136 1.084 19.36 570.2587 2
215 802.1502 486.1475 6608.885 189.7197 -9.5503 0.0312 4601.733 106.5951 -9.1573 0.0252 1.220 9.97 569.0273 2
216 814.8317 460.7858 1420245 853.6215 -15.3809 0.0007 1022885 665.4686 -15.0246 0.0007 1.024 7.23 569.5461 2
217 1.3353 490.9694 494.8762 31.56871 -6.7362 0.0693 482.3161 75.78497 -6.7083 0.1706 1.523 0.00 569.9128 24
218 298.3986 487.2194 213.6877 50.38371 -5.8244 0.2561 294.8155 97.60917 -6.1739 0.3596 1.712 3.45 567.2378 0
219 398.7540 473.2307 71146.46 272.0713 -12.1304 0.0042 51918.61 177.2344 -11.7883 0.0037 1.034 8.96 566.9072 0
220 906.9934 482.9700 2522.278 44.16702 -8.5045 0.0190 2820.28 103.0096 -8.6257 0.0397 1.002 4.25 569.1108 2
221 907.5663 472.7889 69804.25 266.7199 -12.1097 0.0041 51851.18 177.182 -11.7869 0.0037 1.007 7.40 569.0699 2
222 1535.8125 480.0054 203.5318 29.20293 -5.7716 0.1558 57.33055 73.4172 -4.3960 1.3907 1.634 2.91 578.9084 24
223 145.2426 462.1636 35147.31 230.5307 -11.3647 0.0071 25964.89 142.9383 -11.0360 0.0060 1.052 8.94 569.0937 0
224 663.8979 460.5441 62826.33 259.5395 -11.9954 0.0045 47049.61 171.3735 -11.6814 0.0040 1.030 7.25 569.4373 0
225 762.4770 456.8458 32948.66 218.7867 -11.2946 0.0072 24531.29 140.7737 -10.9743 0.0062 1.036 8.39 570.1227 2
226 751.6163 440.4321 44347.18 235.6285 -11.6172 0.0058 33233.08 153.3115 -11.3039 0.0050 1.081 7.40 570.5086 2
227 1198.5684 446.2457 498183.2 545.233 -14.2435 0.0012 361409 403.1815 -13.8950 0.0012 1.013 7.27 568.7339 0
228 1.9529 458.9642 223.7527 35.43246 -5.8744 0.1720 128.5742 78.75908 -5.2729 0.6652 1.045 0.00 570.2826 24
229 1535.8220 457.9392 198.1385 29.61646 -5.7424 0.1623 13.28338 73.40351 -2.8083 6.0012 1.653 2.86 578.6463 24
230 1438.2441 450.0635 10462.37 182.9217 -10.0491 0.0190 7873.783 112.9408 -9.7405 0.0156 1.147 8.85 572.9673 2
231 1426.3929 428.1570 63816.04 263.4797 -12.0123 0.0045 46272.47 170.3514 -11.6633 0.0040 1.114 9.34 573.1825 2
232 1423.4384 411.2955 7554.672 170.4117 -9.6955 0.0245 5964.761 109.3011 -9.4390 0.0199 1.222 4.33 573.341 2
233 960.8632 435.1900 1653721 918.1796 -15.5462 0.0006 1189394 716.5146 -15.1883 0.0007 1.031 7.22 568.8812 2
234 700.8220 446.9313 1555.374 136.5259 -7.9796 0.0953 1242.823 99.64561 -7.7360 0.0871 1.250 10.44 569.9025 0
235 995.4854 435.4116 81574.7 270.4897 -12.2789 0.0036 70116.84 197.7704 -12.1146 0.0031 1.099 15.88 568.9448 2
236 32.2357 429.8874 181419.6 372.3817 -13.1467 0.0022 130854.7 254.6819 -12.7920 0.0021 1.054 7.39 570.454 0
237 1161.8766 426.7566 92863.61 295.1726 -12.4196 0.0035 67921.02 195.4466 -12.0800 0.0031 1.058 7.26 568.6226 0
238 781.8557 425.5675 160736.9 355.235 -13.0153 0.0024 115604.4 241.649 -12.6574 0.0023 1.049 7.30 570.6792 2
239 802.5657 417.7780 42548.41 233.0482 -11.5722 0.0059 31220.35 150.4933 -11.2361 0.0052 1.048 11.23 570.8036 2
240 810.9788 422.9886 2840.001 45.5655 -8.6333 0.0174 3300.061 103.9597 -8.7963 0.0342 1.005 -19.21 570.4293 2
241 564.5262 422.6582 47083.86 242.6338 -11.6822 0.0056 34664.4 155.2984 -11.3497 0.0049 1.110 7.35 568.935 2
242 571.9675 416.0224 1419.365 39.46109 -7.8802 0.0302 1865.187 101.0426 -8.1768 0.0588 1.017 0.00 569.0518 2
243 1367.2023 424.6882 3735.087 153.5798 -8.9308 0.0447 3038.459 103.3769 -8.7066 0.0369 1.319 8.97 571.564 0
244 1090.5992 416.0958 23976.4 195.2232 -10.9495 0.0088 18779.25 131.7445 -10.6842 0.0076 1.103 15.61 568.752 2
245 1085.5693 402.4745 57652.69 254.1403 -11.9020 0.0048 42224.75 165.2104 -11.5639 0.0042 1.057 7.30 568.8077 2
246 831.7541 414.9341 11039.82 182.4255 -10.1074 0.0179 8196.661 113.5596 -9.7841 0.0150 1.099 18.34 569.8548 0
247 1074.3198 451.4497 3831.49 147.4924 -8.9584 0.0418 3206.203 103.8164 -8.7650 0.0352 1.075 8.78 568.6868 0
248 732.5168 416.2176 1549.591 138.3827 -7.9755 0.0970 1400.423 99.98013 -7.8656 0.0775 1.445 10.10 570.7856 0
249 907.7534 417.2511 346.9641 64.5695 -6.3507 0.2021 860.5858 98.86326 -7.3370 0.1248 1.483 4.70 568.7692 0
250 711.3885 393.5685 1364846 838.5897 -15.3377 0.0007 977822.8 650.9692 -14.9757 0.0007 1.011 7.31 569.9722 2
251 736.8256 384.7282 8860.46 193.6435 -9.8686 0.0237 6082.245 109.4829 -9.4602 0.0195 1.064 10.53 570.1913 2
252 217.6064 407.2765 8858.327 173.1173 -9.8684 0.0212 6928.146 111.1078 -9.6015 0.0174 1.071 9.65 568.5673 0
253 208.3666 454.0331 357.7236 58.98864 -6.3839 0.1791 323.6797 97.77405 -6.2753 0.3280 1.882 4.89 568.6995 0
254 1170.4919 396.6587 51402.02 244.4799 -11.7775 0.0052 38623.3 160.5981 -11.4671 0.0045 1.048 7.34 568.8523 0
255 889.1747 397.5316 3684.913 166.21 -8.9161 0.0490 2879.372 103.0826 -8.6482 0.0389 1.115 9.74 568.9166 0
256 1.1751 401.0359 242.7468 27.27782 -5.9629 0.1220 67.24962 73.58174 -4.5692 1.1883 1.694 2.88 570.961 24
257 1189.6937 389.5130 2875.329 157.9382 -8.6467 0.0597 2297.169 102.0587 -8.4030 0.0482 1.202 9.95 569.0104 0
258 811.7170 377.7045 177848.5 367.8935 -13.1251 0.0022 129516.2 253.6119 -12.7808 0.0021 1.035 7.25 569.8939 0
259 547.8994 375.2592 181846.6 349.5311 -13.1493 0.0021 134666.3 257.8654 -12.8231 0.0021 1.119 7.97 568.8017 2
260 1534.8395 391.1724 255.8132 40.63386 -6.0198 0.1725 134.4803 80.01255 -5.3216 0.6461 1.262 3.60 578.1884 24
261 1436.5868 385.0678 11243.42 178.4281 -10.1272 0.0172 8773.057 114.5718 -9.8579 0.0142 1.149 7.88 573.7438 0
262 1100.3826 374.7240 64256.14 269.967 -12.0198 0.0046 46837.13 171.0133 -11.6765 0.0040 1.120 7.37 568.8514 2
263 1102.9727 364.0503 1087.556 38.46878 -7.5911 0.0384 1645.986 100.5654 -8.0411 0.0664 1.017 4.29 568.8864 2
264 480.7602 375.0351 78609.08 280.5967 -12.2387 0.0039 57937.47 184.3521 -11.9074 0.0035 1.054 7.78 568.4489 2
265 482.9031 364.1710 530.5693 34.43391 -6.8119 0.0705 600.8499 98.30507 -6.9469 0.1777 1.572 1.46 568.5609 2
266 615.4128 336.8404 180890.3 370.3799 -13.1435 0.0022 131124.7 254.9064 -12.7942 0.0021 1.016 7.27 569.5464 2
267 617.8385 364.4600 436379.6 522.1233 -14.0997 0.0013 269405.6 351.517 -13.5760 0.0014 1.255 9.82 569.4128 2
268 628.9664 354.0240 1460.982 39.61598 -7.9116 0.0294 1759.754 100.8213 -8.1136 0.0622 1.016 4.33 569.3725 2
269 285.4190 374.7091 10895.07 188.902 -10.0931 0.0188 8068.655 113.2029 -9.7670 0.0152 1.042 8.47 568.2696 0
270 1377.7532 369.9927 28045.46 211.2512 -11.1197 0.0082 21302.69 135.7787 -10.8211 0.0069 1.064 8.10 572.4717 0
271 1023.7278 374.8381 2088.633 153.0091 -8.2997 0.0796 1594.151 100.423 -8.0063 0.0684 1.278 12.90 569.0493 2
272 1013.3053 370.1889 2671.93 175.8889 -8.5671 0.0715 1712.699 100.6231 -8.0842 0.0638 1.262 14.59 569.1161 2
273 1022.7167 364.7001 445.9181 31.97025 -6.6231 0.0779 1252.126 99.84902 -7.7441 0.0866 1.689 0.00 569.0895 2
274 1019.2045 358.3472 15106.4 188.3152 -10.4479 0.0135 11575.32 119.6137 -10.1588 0.0112 1.024 19.17 569.1374 2
275 1338.3918 368.8807 4386.3 122.1571 -9.1052 0.0302 4504.04 106.3224 -9.1340 0.0256 1.180 8.05 570.9123 2
276 1343.9404 355.2447 99384.16 306.3449 -12.4933 0.0033 70730.46 198.4435 -12.1240 0.0030 1.054 10.09 571.2734 2
277 1422.9534 361.1173 83330.1 287.369 -12.3020 0.0037 59944.61 186.591 -11.9444 0.0034 1.093 7.76 573.4723 0
278 759.2888 358.0734 108543.5 321.1349 -12.5890 0.0032 78283.44 206.4305 -12.2342 0.0029 1.065 9.72 569.5952 2
279 733.7847 343.8413 109413.1 314.6581 -12.5977 0.0031 78997.13 207.0974 -12.2440 0.0028 1.040 7.24 569.4623 2
280 719.1465 324.1569 85956.32 289.5103 -12.3357 0.0037 62678.29 189.6608 -11.9928 0.0033 1.042 7.27 569.406 2
281 1118.8661 365.8265 526.3643 34.47257 -6.8032 0.0711 981.6555 99.13918 -7.4799 0.1097 1.546 3.92 568.8647 2
282 1119.0170 360.1693 8536.745 174.5052 -9.8282 0.0222 6640.842 110.6038 -9.5556 0.0181 1.060 17.46 568.893 2
283 844.8472 354.6751 16563.23 191.5363 -10.5479 0.0126 12698.18 121.6547 -10.2594 0.0104 1.051 7.75 569.4832 0
284 976.0650 358.2110 1135.64 117.0833 -7.6381 0.1120 979.5918 99.13477 -7.4776 0.1099 1.361 8.70 569.179 0
285 353.1110 350.8444 64952.19 262.6889 -12.0315 0.0044 47865.64 172.3601 -11.7001 0.0039 1.056 8.76 568.0709 0
286 796.7365 349.0502 7564.784 182.1021 -9.6970 0.0261 5495.489 108.3876 -9.3500 0.0214 1.029 9.27 569.4794 2
287 812.9947 347.9868 2880.34 45.74181 -8.6486 0.0172 3409.593 104.1027 -8.8318 0.0332 1.001 0.00 569.4793 2
288 810.3277 336.3240 103828.5 306.249 -12.5408 0.0032 76241.59 204.316 -12.2055 0.0029 1.029 7.32 569.4651 2
289 513.1359 347.9854 14550.69 173.8364 -10.4072 0.0130 11714.78 119.8882 -10.1718 0.0111 1.135 17.73 568.8051 0
290 164.9871 321.0194 1750.191 40.78201 -8.1077 0.0253 2258.42 101.8311 -8.3845 0.0490 1.004 0.00 570.0052 2
291 152.7275 333.9623 967580 723.5369 -14.9642 0.0008 689550.7 549.1677 -14.5964 0.0009 1.044 7.33 569.9282 2
292 563.7424 373.7921 804740.8 658.7786 -14.7641 0.0009 579714.4 505.0291 -14.4080 0.0009 1.073 7.25 568.9684 2
293 923.4663 321.3381 184923.3 368.6769 -13.1675 0.0022 134805.4 257.9797 -12.8243 0.0021 1.050 7.23 569.222 2
294 906.1515 316.4818 61724.25 256.9528 -11.9761 0.0045 45131.22 168.9458 -11.6362 0.0041 1.054 7.10 569.3285 2
295 52.7376 328.2247 3178.323 173.441 -8.7555 0.0593 2289.099 101.9113 -8.3992 0.0483 1.108 10.84 570.6279 0
296 1013.0151 321.7200 45613.11 238.2446 -11.6477 0.0057 33699.19 153.8786 -11.3190 0.0050 1.066 12.37 569.3107 0
297 677.4539 311.6614 166634.5 356.0636 -13.0544 0.0023 121893.5 247.1216 -12.7150 0.0022 1.043 8.74 569.3425 0
298 139.6216 285.3202 190621.8 387.9835 -13.2004 0.0022 136355.2 259.1915 -12.8367 0.0021 1.012 8.00 570.6309 2
299 115.0030 294.0279 1384.718 39.3357 -7.8534 0.0309 1912.935 101.0768 -8.2043 0.0574 1.003 4.28 570.6147 2
300 121.9895 296.0339 3054.5 46.49905 -8.7123 0.0165 3300.094 104.0238 -8.7963 0.0342 1.002 4.29 570.5864 2
301 128.9980 312.0324 72562.78 178.674 -12.1518 0.0027 72936.48 200.7849 -12.1574 0.0030 1.058 0.00 570.426 6
302 119.2280 306.9764 199994.7 379.1064 -13.2525 0.0021 145090.4 266.2673 -12.9041 0.0020 1.070 11.43 570.5252 2
303 1179.9917 297.0321 829.5106 29.61928 -7.2971 0.0388 1308.128 99.88445 -7.7916 0.0829 1.002 0.00 569.519 2
304 1358.4225 299.0651 202844.7 397.0564 -13.2679 0.0021 126344.2 250.8751 -12.7539 0.0022 1.434 9.30 571.9699 0
305 1264.0242 298.2581 65749.29 267.6499 -12.0447 0.0044 47681.85 172.1147 -11.6959 0.0039 1.026 7.84 570.118 2
306 1276.4452 294.9617 10426.65 155.0993 -10.0454 0.0162 9215.116 115.444 -9.9113 0.0136 1.149 8.81 570.163 2
307 1176.1322 303.9489 26919.94 216.1402 -11.0752 0.0087 19232.68 132.5722 -10.7101 0.0075 1.050 9.00 569.4788 2
308 466.2436 301.3683 2154.187 137.4185 -8.3332 0.0693 1852.551 101.0491 -8.1694 0.0592 1.010 11.69 569.3735 0
309 325.1265 294.9048 23842.98 216.8451 -10.9434 0.0099 17060.08 129.0921 -10.5800 0.0082 1.140 21.41 569.0575 2
310 311.0523 270.1046 211589.1 395.894 -13.3137 0.0020 151300.1 271.2001 -12.9496 0.0019 1.036 7.36 569.3192 2
311 313.7943 242.7544 492948.3 545.214 -14.2320 0.0012 352365.7 398.3928 -13.8675 0.0012 1.028 7.58 569.5616 2
312 894.1555 290.7959 11031.85 178.5293 -10.1066 0.0176 8546.412 114.1373 -9.8295 0.0145 1.086 11.07 569.4784 0
313 966.5088 291.4034 6475.713 158.1146 -9.5282 0.0265 5326.547 107.9644 -9.3161 0.0220 1.038 15.59 569.4783 0
314 520.3867 283.6607 153902.1 346.2231 -12.9681 0.0024 113079.5 239.432 -12.6335 0.0023 1.044 7.26 569.9358 0
315 788.8865 273.1897 551448.3 576.9519 -14.3538 0.0011 383958.8 414.8498 -13.9607 0.0012 1.227 7.52 569.3985 2
316 1189.0786 280.1242 11758.17 178.7383 -10.1758 0.0165 9116.692 115.3499 -9.8996 0.0137 1.079 8.00 569.6844 0
317 36.5474 278.7976 8536.089 172.5201 -9.8281 0.0219 6617.764 110.4842 -9.5518 0.0181 1.100 16.87 570.6779 0
318 1.3234 284.0191 437.1339 32.06957 -6.6015 0.0797 398.7043 75.41849 -6.5016 0.2054 1.514 0.00 570.6367 24
319 1.9320 279.9697 582.9242 40.21189 -6.9140 0.0749 397.1719 79.31053 -6.4974 0.2169 1.020 0.00 570.6588 24
320 597.5209 271.0217 4408.013 154.1752 -9.1106 0.0380 3604.448 104.5463 -8.8921 0.0315 1.107 10.03 570.262 0
321 731.1889 262.5690 26773.21 209.3516 -11.0693 0.0085 20092.54 133.9268 -10.7576 0.0072 1.044 9.83 569.3985 0
322 1483.4398 261.6202 27310.42 213.6566 -11.0908 0.0085 20504.99 134.553 -10.7796 0.0071 1.042 7.99 576.5723 0
323 1348.4666 264.9120 1394.505 125.2177 -7.8611 0.0975 1296.196 99.90916 -7.7817 0.0837 1.149 9.93 571.7993 0
324 1193.5824 260.2585 12899.72 178.7833 -10.2765 0.0151 10308.98 117.4202 -10.0330 0.0124 1.078 17.68 569.9075 0
325 1046.4960 255.6492 39379.19 229.6317 -11.4882 0.0063 29103.74 147.5738 -11.1599 0.0055 1.018 11.01 569.6838 0
326 456.9798 257.0255 30054.88 271.2838 -11.1948 0.0098 10341.09 117.4781 -10.0364 0.0123 2.108 42.33 569.8321 2
327 451.9934 244.0021 9757.63 70.44401 -9.9734 0.0078 10191.41 117.0799 -10.0206 0.0125 1.002 4.21 569.9363 2
328 440.2356 246.5394 177785.4 334.1463 -13.1247 0.0020 146835 267.6394 -12.9171 0.0020 1.082 7.42 569.746 2
329 435.2433 246.9858 21099.26 98.79065 -10.8107 0.0051 21072.84 135.4442 -10.8093 0.0070 1.023 4.44 569.6832 2
330 393.5028 249.1606 275009.5 431.1631 -13.5984 0.0017 198574.8 305.8777 -13.2448 0.0017 1.043 7.27 569.4543 0
331 797.9958 260.0139 2107.441 42.33088 -8.3094 0.0218 2780.44 102.8305 -8.6103 0.0402 1.002 0.00 569.3985 2
332 574.8161 248.9913 189423.4 374.2015 -13.1936 0.0021 137804.3 260.3733 -12.8482 0.0021 1.038 7.30 570.5038 0
333 943.6876 244.2561 86054.28 294.3093 -12.3369 0.0037 61322.85 188.2025 -11.9691 0.0033 1.094 14.64 570.4471 2
334 963.0655 237.6504 114299 312.7988 -12.6451 0.0030 82845.09 211.0051 -12.2957 0.0028 1.068 11.95 570.7387 2
335 911.1133 244.2430 204272.2 386.5289 -13.2755 0.0021 147975 268.5651 -12.9255 0.0020 1.026 7.26 570.2999 2
336 922.7039 229.1774 10821.01 140.2647 -10.0857 0.0141 10160.08 117.0801 -10.0172 0.0125 1.261 8.56 570.5997 2
337 929.9926 227.7715 1299.844 35.67518 -7.7847 0.0298 1530.189 100.3212 -7.9619 0.0712 1.051 4.00 570.6433 2
338 930.1562 220.0732 42571.76 236.9654 -11.5728 0.0060 30931.96 150.0646 -11.2260 0.0053 1.047 22.11 570.709 2
339 1096.6111 250.3318 14695.78 181.2898 -10.4180 0.0134 11651.03 119.7755 -10.1659 0.0112 1.116 18.14 569.7451 0
340 1512.2275 249.4871 8107.574 175.0377 -9.7722 0.0234 6265.945 109.8075 -9.4925 0.0190 1.061 8.43 578.4499 0
341 1183.3364 239.7057 76746.91 279.5199 -12.2127 0.0040 56157.15 182.2764 -11.8735 0.0035 1.050 7.81 570.0289 0
342 619.6721 244.7971 9895.577 177.5409 -9.9886 0.0195 7646.876 112.4551 -9.7087 0.0160 1.057 7.91 570.4999 0
343 1370.8412 233.6943 167184.3 360.2471 -13.0580 0.0023 121536.9 246.8291 -12.7118 0.0022 1.042 7.27 572.6031 0
344 1.2118 246.0035 174.974 32.32819 -5.6074 0.2006 212.4916 74.13367 -5.8184 0.3789 1.596 0.00 570.8431 24
345 682.3170 234.0578 37518.34 235.8787 -11.4356 0.0068 26890.65 144.327 -11.0740 0.0058 1.080 9.61 569.3985 0
346 1005.0590 228.9340 158891.4 351.4758 -13.0028 0.0024 116547.8 242.5227 -12.6663 0.0023 1.037 7.27 570.9686 0
347 882.7033 213.8188 55399.46 251.6355 -11.8588 0.0049 41455.98 164.2114 -11.5440 0.0043 1.046 8.70 570.5965 0
348 632.9984 215.0914 40316.77 238.7078 -11.5137 0.0064 28575.26 146.6542 -11.1400 0.0056 1.039 15.25 570.6185 2
349 655.6232 197.3575 1331284 831.4123 -15.3107 0.0007 956413.2 643.9558 -14.9516 0.0007 1.028 7.29 570.5131 2
350 1170.0375 211.3203 844.2399 94.70972 -7.3162 0.1218 649.8874 98.42762 -7.0321 0.1645 3.910 7.05 570.2296 2
351 555.0073 204.9922 2823.515 45.49335 -8.6270 0.0175 3269.146 103.8005 -8.7861 0.0345 1.007 4.23 570.8909 2
352 561.3152 201.1822 10761.79 160.0405 -10.0797 0.0162 9178.183 115.304 -9.9069 0.0136 1.252 17.50 570.9749 2
353 563.6866 184.4685 273904.9 428.7455 -13.5940 0.0017 197445.8 305.122 -13.2386 0.0017 1.038 7.36 571.1664 2
354 1028.2812 183.5516 96340.16 309.1154 -12.4595 0.0035 67876.23 195.3981 -12.0793 0.0031 1.068 8.01 570.9269 2
355 1085.3414 195.9940 21030.13 177.4152 -10.8071 0.0092 18111.39 130.717 -10.6449 0.0078 1.098 8.00 570.3177 2
356 1073.3975 193.4199 78665.51 286.0262 -12.2395 0.0039 55514.94 181.4642 -11.8610 0.0035 1.070 7.40 570.3591 2
357 1042.1340 194.8650 2850.893 43.2994 -8.6375 0.0165 2950.613 103.3579 -8.6748 0.0380 1.525 3.88 570.5707 2
358 1049.4741 187.3801 270744.7 419.1121 -13.5814 0.0017 198394 305.7361 -13.2438 0.0017 1.055 7.49 570.5953 2
359 1044.0171 178.0286 6012.234 58.18803 -9.4476 0.0105 6055.064 109.5064 -9.4553 0.0196 1.009 4.28 570.8115 2
360 978.9670 182.0029 2377.048 43.52391 -8.4401 0.0199 2803.515 102.959 -8.6193 0.0399 1.009 0.00 571.2549 2
361 967.9719 185.9064 93792.54 241.3515 -12.4304 0.0028 88977.67 217.0523 -12.3732 0.0026 1.200 7.51 571.1441 2
362 961.5632 173.1210 769791.1 659.3442 -14.7159 0.0009 539952.6 488.0602 -14.3309 0.0010 1.080 7.22 571.0978 2
363 182.9546 191.1445 1010.256 111.5285 -7.5111 0.1199 1311.215 99.84097 -7.7942 0.0827 2.123 9.13 570.6021 0
364 1535.7856 211.9845 196.3294 29.76791 -5.7325 0.1647 -22.86891 73.65966 99.0000 99.0000 1.504 2.94 580.1351 24
365 820.1038 168.4550 5655.899 155.1218 -9.3813 0.0298 4663.142 106.8262 -9.1717 0.0249 1.165 7.31 570.3076 2
366 818.2520 162.4496 2899.06 69.94952 -8.6556 0.0262 3144.796 103.6589 -8.7440 0.0358 2.748 7.88 570.3539 2
367 1178.3666 160.8956 63389.95 265.1758 -12.0051 0.0045 46524.98 170.6652 -11.6692 0.0040 1.033 8.94 570.3905 2
368 1171.2831 166.7194 608.9612 26.1894 -6.9615 0.0467 1733.387 100.898 -8.0972 0.0632 2.186 0.00 570.3835 2
369 550.8932 122.7173 18722.64 222.6585 -10.6809 0.0129 12853.71 122.0208 -10.2726 0.0103 1.365 8.70 571.1688 2
370 520.6047 160.6883 82103.02 299.5721 -12.2859 0.0040 54531.83 180.2942 -11.8416 0.0036 1.116 25.02 571.0353 2
371 519.0179 132.5739 912884.3 698.5983 -14.9010 0.0008 655347.8 535.8287 -14.5412 0.0009 1.033 7.28 570.9686 2
372 509.0086 142.9893 8305.811 65.95502 -9.7985 0.0086 8452.188 113.9038 -9.8174 0.0146 1.001 0.00 570.9144 2
373 1286.2076 169.4518 971.8323 106.8517 -7.4690 0.1194 1042.715 99.2528 -7.5454 0.1034 1.438 7.78 571.1672 0
374 428.6366 156.2078 98740.4 299.8264 -12.4862 0.0033 72222.85 200.0471 -12.1467 0.0030 1.054 7.06 570.544 0
375 997.4131 155.9517 136362.3 336.0184 -12.8367 0.0027 98063.78 225.7618 -12.4788 0.0025 1.025 9.58 571.372 2
376 994.0093 146.0387 3277.538 47.45849 -8.7889 0.0157 3717.086 104.822 -8.9255 0.0306 1.010 -9.58 571.3903 2
377 34.0099 155.5276 894.6991 104.5387 -7.3792 0.1269 967.5167 99.09215 -7.4641 0.1112 1.462 5.92 572.3236 2
378 884.7037 146.8082 38697.22 226.8561 -11.4692 0.0064 29084.44 147.4106 -11.1592 0.0055 1.044 8.58 570.7449 0
379 1.3610 154.9976 440.6593 32.02853 -6.6103 0.0789 556.3204 76.05729 -6.8633 0.1485 1.507 0.00 572.9769 24
380 1338.3982 147.5683 2066.436 138.7165 -8.2881 0.0729 1827.728 100.9146 -8.1548 0.0600 1.283 7.48 572.5853 0
381 293.4906 146.4948 1583.06 135.1851 -7.9987 0.0927 1316.641 99.96916 -7.7987 0.0825 2.073 8.32 570.2275 2
382 160.2618 131.1067 216017.2 395.7352 -13.3362 0.0020 155502.3 274.4389 -12.9793 0.0019 1.051 7.39 570.8848 0
383 613.0306 109.0300 1181.71 38.69101 -7.6813 0.0356 1604.092 100.4937 -8.0131 0.0680 1.008 0.00 571.5841 2
384 621.3865 111.8925 25946.74 214.3995 -11.0352 0.0090 19093.69 132.2744 -10.7022 0.0075 1.202 20.76 571.5451 2
385 633.0207 98.3087 100855.7 298.9932 -12.5093 0.0032 74268.09 202.1604 -12.1770 0.0030 1.029 7.30 571.44 2
386 630.5546 134.8887 47423.39 236.0201 -11.6900 0.0054 36015.05 157.1196 -11.3912 0.0047 1.066 9.29 571.538 2
387 635.9630 131.0171 3031.827 45.27918 -8.7043 0.0162 3322.637 104.0697 -8.8037 0.0340 1.200 0.00 571.4925 2
388 1531.2736 131.1324 69678.58 248.3193 -12.1077 0.0039 55227.28 180.4648 -11.8554 0.0035 1.201 9.72 581.8389 24
389 1245.1403 131.1902 95807.49 296.3319 -12.4535 0.0034 70150.93 197.8407 -12.1151 0.0031 1.035 8.09 570.9893 0
390 1376.2397 139.1044 1076.569 110.9689 -7.5801 0.1119 1135.228 99.51704 -7.6377 0.0952 1.186 7.86 573.8674 0
391 1402.4619 125.9489 23896.74 208.0053 -10.9458 0.0095 17813.17 130.2583 -10.6269 0.0079 1.045 11.57 574.4122 0
392 1.0000 133.4642 166.2103 34.25 -5.5516 0.2238 234.0493 72.81319 -5.9233 0.3379 4.013 3.40 573.178 24
393 580.3881 121.6143 52148.96 247.0223 -11.7931 0.0051 38764.68 160.712 -11.4711 0.0045 1.047 7.59 571.4103 0
394 312.8781 111.2738 690662.3 625.6754 -14.5982 0.0010 496446.8 468.8263 -14.2397 0.0010 1.035 7.34 570.3502 2
395 325.9893 103.0016 6505.127 59.93805 -9.5331 0.0100 6716.45 110.6131 -9.5678 0.0179 1.001 0.00 570.3976 2
396 655.8513 126.4709 1311.536 112.8107 -7.7945 0.0934 1433.575 100.1668 -7.8911 0.0759 1.104 6.37 571.3436 0
397 916.9801 116.9675 130770 328.1771 -12.7913 0.0027 95265.2 223.1275 -12.4473 0.0025 1.029 8.05 570.8182 0
398 1048.9640 117.2508 73612.95 270.6054 -12.1674 0.0040 55331.83 181.287 -11.8574 0.0036 1.022 7.27 571.0632 2
399 1056.9581 114.0051 1363.645 34.34037 -7.8368 0.0273 1896.536 101.0589 -8.1949 0.0579 1.253 3.73 571.0162 2
400 84.7752 124.9567 1266.644 118.8581 -7.7566 0.1019 1130.283 99.47303 -7.6330 0.0956 1.451 8.12 571.7458 2
401 840.4144 76.6228 50576.98 254.4429 -11.7599 0.0055 36624.43 157.9075 -11.4094 0.0047 1.023 7.40 570.9312 2
402 823.8599 98.9064 103374 310.4949 -12.5360 0.0033 74622.38 202.5889 -12.1822 0.0029 1.020 7.25 570.5626 2
403 1523.5181 108.3286 15290.81 194.584 -10.4611 0.0138 11470.31 119.5808 -10.1489 0.0113 1.042 17.63 582.5868 0
404 1330.0009 95.2369 468.1632 48.45803 -6.6760 0.1124 880.7438 98.87276 -7.3621 0.1219 1.155 0.00 573.067 2
405 1326.9956 110.9447 2715.5 45.01939 -8.5846 0.0180 3260.097 103.8782 -8.7831 0.0346 1.006 0.00 572.7901 2
406 1326.1752 103.7468 29883.56 212.8726 -11.1886 0.0077 22858.96 138.2098 -10.8976 0.0066 1.070 7.80 572.8781 2
407 1.4900 108.9697 240.1104 45.23544 -5.9510 0.2046 476.8479 76.79576 -6.6959 0.1749 1.525 1.47 573.3975 24
408 1491.5389 96.6756 45703.91 238.2865 -11.6499 0.0057 33464.83 153.6748 -11.3115 0.0050 1.046 11.90 580.2938 0
409 102.5414 97.3220 10481.43 173.0098 -10.0511 0.0179 8397.62 113.9631 -9.8104 0.0147 1.127 9.35 571.8409 0
410 1535.6304 117.0065 309.192 35.54433 -6.2256 0.1248 501.4726 75.97015 -6.7506 0.1645 1.522 -0.55 583.0645 24
411 1040.4235 98.1706 827.0355 100.9159 -7.2938 0.1325 973.799 99.13918 -7.4712 0.1106 1.499 7.23 571.1197 0
412 1055.5858 79.1706 85886.88 292.7718 -12.3348 0.0037 62530.26 189.5217 -11.9902 0.0033 1.045 7.21 571.0261 0
413 496.9105 82.1701 16291.8 187.4628 -10.5299 0.0125 12377.43 121.0811 -10.2316 0.0106 1.067 19.00 570.6656 0
414 205.3543 1015.6260 4226.593 167.546 -9.0650 0.0431 3021.728 103.4553 -8.7006 0.0372 1.302 9.34 569.0291 8
415 501.4073 1011.4348 3163.192 163.8322 -8.7503 0.0562 2373.049 102.0856 -8.4383 0.0467 1.084 12.00 565.4015 0
416 538.9880 60.2298 600.8334 33.98357 -6.9469 0.0614 1012.544 99.27229 -7.5135 0.1065 1.048 3.96 570.5885 2
417 1306.4246 78.2114 3535.864 183.1233 -8.8712 0.0562 2327.208 101.9905 -8.4171 0.0476 1.324 15.29 572.6646 0
418 684.1806 69.7900 33353.44 229.3654 -11.3079 0.0075 23104.09 138.537 -10.9092 0.0065 1.105 18.32 571.3856 2
419 1.9238 1013.7868 210.0515 28.76742 -5.8058 0.1487 -180.6892 78.15717 99.0000 99.0000 1.515 0.00 574.033 24
420 1282.5294 68.1601 49204.11 244.4585 -11.7300 0.0054 36616.36 157.8861 -11.4092 0.0047 1.054 7.59 572.2349 0
421 820.4248 117.1983 7615.113 173.1951 -9.7042 0.0247 5826.044 108.9555 -9.4134 0.0203 1.099 17.26 570.4926 2
422 1.1980 65.0146 165.2792 34.53007 -5.5455 0.2269 269.6117 74.18457 -6.0768 0.2988 1.719 1.28 574.0594 24
423 650.9710 1009.9269 1019.505 111.3722 -7.5210 0.1186 861.2838 98.84791 -7.3379 0.1246 1.363 8.17 566.0403 0
424 936.8433 996.0051 104504.7 306.6453 -12.5478 0.0032 76366.87 204.3725 -12.2073 0.0029 1.042 7.40 567.0234 0
425 1491.2788 57.6946 354.6474 25.63309 -6.3745 0.0785 1139.83 99.59374 -7.6421 0.0949 2.161 0.00 581.3596 2
426 377.0147 1002.9818 10916.38 73.83514 -10.0952 0.0073 11066.12 118.7784 -10.1100 0.0117 1.009 4.25 567.256 2
427 1197.0377 54.9860 442.4348 32.00846 -6.6146 0.0786 861.293 98.89846 -7.3379 0.1247 1.258 3.73 571.0234 2
428 589.1859 50.1661 23394.89 205.1717 -10.9228 0.0095 17537.61 129.8222 -10.6099 0.0080 1.098 10.57 570.9639 0
429 1001.0854 56.9053 524.0023 37.81151 -6.7983 0.0784 597.5091 98.46714 -6.9409 0.1790 1.150 4.09 571.3897 2
430 380.6473 998.3588 39402.54 227.1328 -11.4888 0.0063 29787.21 148.4508 -11.1851 0.0054 1.091 13.21 567.2253 2
431 1.8559 54.8980 365.1693 44.12769 -6.4062 0.1312 376.5965 78.91862 -6.4397 0.2276 1.140 0.00 574.2112 24
432 768.2953 976.8056 27158.29 207.7526 -11.0848 0.0083 21180.84 135.5639 -10.8149 0.0070 1.136 8.37 566.233 2
433 1535.0048 39.4898 479.8795 38.71117 -6.7028 0.0876 255.3535 79.28865 -6.0179 0.3372 1.066 0.08 586.5837 24
434 959.4097 36.7140 1779.281 138.9529 -8.1256 0.0848 1450.212 100.1022 -7.9036 0.0750 1.369 11.06 571.4473 0
435 772.9701 975.0129 9038.422 68.25625 -9.8902 0.0082 9325.734 115.6613 -9.9242 0.0135 1.008 0.00 566.2313 2
436 1.1504 983.0304 227.233 27.86953 -5.8912 0.1332 126.1798 73.50242 -5.2525 0.6326 1.847 0.00 573.3109 24
437 88.1465 29.1702 520.6266 34.52795 -6.7913 0.0720 642.0872 98.42775 -7.0190 0.1665 1.526 3.87 572.6284 2
438 659.8459 972.4583 14567.6 198.4455 -10.4085 0.0148 10406.72 117.5681 -10.0433 0.0123 1.117 10.72 566.2397 0
439 1.7105 32.0964 395.9899 36.92375 -6.4942 0.1013 427.3461 78.10104 -6.5769 0.1985 1.140 1.86 574.6057 24
440 122.4400 973.8329 246.0232 52.5806 -5.9774 0.2321 568.968 98.338 -6.8877 0.1877 1.698 4.59 570.1951 0
441 841.0043 956.0942 34144.66 225.252 -11.3333 0.0072 25276.79 141.8208 -11.0068 0.0061 1.033 7.80 566.5067 0
442 45.3218 26.2681 958.7429 107.5031 -7.4543 0.1218 959.4084 99.20919 -7.4550 0.1123 1.875 6.50 573.6808 2
443 1534.9882 960.0451 453.8096 44.00692 -6.6422 0.1053 345.3012 79.67508 -6.3455 0.2506 1.031 4.21 583.0381 24
444 573.7265 957.2314 437.9861 62.64963 -6.6037 0.1553 508.0921 98.071 -6.7649 0.2096 1.943 5.49 565.9006 0
445 165.1780 957.2151 831.5047 97.83089 -7.2997 0.1278 1136.04 99.50203 -7.6385 0.0951 1.823 7.66 569.3137 0
446 930.7224 943.0375 91258.63 291.0279 -12.4007 0.0035 66738.76 194.1265 -12.0609 0.0032 1.023 7.38 567.0641 0
447 17.2526 942.0139 7071.583 170.9299 -9.6238 0.0263 5435.622 108.2552 -9.3381 0.0216 1.141 9.60 572.0671 0
448 1535.7031 945.1575 242.7091 33.49449 -5.9627 0.1499 235.5076 74.89196 -5.9300 0.3454 1.601 0.00 583.1658 24
449 730.7506 943.6141 332.6407 61.88263 -6.3049 0.2020 659.4673 98.46515 -7.0480 0.1622 1.671 4.11 566.2906 0
450 156.4838 934.3063 2985.51 163.8574 -8.6875 0.0596 2283.285 102.0299 -8.3964 0.0485 1.200 11.06 569.4579 0
451 325.7133 923.8927 181777.8 370.1347 -13.1489 0.0022 132298.1 255.9318 -12.8039 0.0021 1.023 7.28 567.8268 0
452 393.7177 926.7001 5606.012 164.8685 -9.3716 0.0319 4468.123 106.4544 -9.1253 0.0259 1.243 15.86 566.8171 0
453 145.5013 919.8887 17029.11 196.3743 -10.5780 0.0125 12678.93 121.6896 -10.2577 0.0104 1.121 7.83 569.8 0
454 723.1345 899.0394 669788.9 619.2785 -14.5648 0.0010 481245.6 461.8769 -14.2059 0.0010 1.024 7.30 566.6635 0
455 628.3530 900.8157 120589.8 319.6886 -12.7033 0.0029 88367.04 216.4785 -12.3657 0.0027 1.063 7.34 566.5408 0
456 837.1782 908.3299 4010.753 155.5362 -9.0081 0.0421 3275.799 103.8942 -8.7883 0.0344 1.094 8.32 566.9343 0
457 516.3662 901.8062 31368.43 219.9729 -11.2412 0.0076 23330.52 138.9308 -10.9198 0.0065 1.059 7.39 566.1391 0
458 1.2684 908.9004 273.2072 31.62204 -6.0912 0.1257 196.3385 74.69193 -5.7325 0.4131 1.645 0.00 571.8723 24
459 1252.7832 903.8932 51281.44 246.8483 -11.7749 0.0052 37278.74 158.7305 -11.4287 0.0046 1.042 9.21 569.3575 0
460 603.3322 886.5198 1678.697 139.886 -8.0624 0.0905 1415.1 100.1776 -7.8770 0.0769 1.095 8.42 566.5366 0
461 842.5924 873.8029 50785.86 280.223 -11.7644 0.0060 33316.79 153.3186 -11.3067 0.0050 1.526 7.49 567.341 2
462 829.3594 867.0640 2838.523 88.99777 -8.6327 0.0340 3218.747 103.8099 -8.7692 0.0350 1.319 8.87 567.4587 2
463 825.4636 867.4711 690.4557 44.81046 -7.0978 0.0705 1060.704 99.39177 -7.5640 0.1018 1.199 0.06 567.4709 2
464 222.3049 868.3086 103594.5 306.8633 -12.5383 0.0032 76833.48 204.9207 -12.2139 0.0029 1.031 22.25 569.9885 0
465 44.9636 871.8757 12457.84 179.3246 -10.2386 0.0156 9645.13 116.1589 -9.9608 0.0131 1.066 18.24 571.3076 0
466 1408.2908 875.7048 553.3074 48.71286 -6.8574 0.0956 874.0866 99.02682 -7.3539 0.1230 1.333 0.00 573.408 2
467 1417.2190 866.9792 855.8945 38.32928 -7.3311 0.0486 1391.751 100.0284 -7.8589 0.0781 2.623 4.75 573.611 2
468 1413.9711 871.9753 3984.324 50.41391 -9.0009 0.0137 4527.437 106.4629 -9.1396 0.0255 1.013 4.26 573.5486 2
469 1408.8536 866.5915 28416.21 209.3476 -11.1339 0.0080 21565.12 136.1998 -10.8344 0.0069 1.040 9.35 573.4162 2
470 1533.5531 855.3389 1589.414 121.8982 -8.0031 0.0833 1374.105 90.1277 -7.8450 0.0712 1.297 10.28 581.638 24
471 284.4399 838.0594 1110582 771.53 -15.1139 0.0008 796227.3 588.8948 -14.7526 0.0008 1.023 7.28 568.7106 0

465
Lab 4/Lab 4.ipynb
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@ -1,465 +0,0 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# <p style=\"text-align: center;\">PHYS 134L Spring 2022 Lab 4</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-danger\"><b>Due date:</b> Sunday, May 1st, 2022 by 11:59pm, submitted through Gradescope.</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Names: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Enter your name and your partner's name here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The previous lab explored the systematic differences that result from doing a measurement in two slightly different ways. Next, we will try to replicate the measurements made by Source Extractor using ```Astropy``` packages. The main new package we will use is called ```photutils```, an astropy package used for photometry--the measurement of the brightness of astronomical objects. You can find all the documentation for ```photutils``` [here.](https://photutils.readthedocs.io/en/stable/)\n",
"\n",
"We'll again be using ```cluster.fits``` from our previous labs. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 1: Background Estimation</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first step will be determining the background level, so that we don't overestimate the amount of light coming from any given star. We can do this in several ways. First, open ```cluster.fits``` in DS9. **Hover your mouse around the background and try to estimate by eye what you think the background level is, enter it here:**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Another way to estimate the background here is by looking at the median of the image. **Load the fits file into a new jupyter notebook and get the median value of the whole array.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What kind of probablems can you think that might make a simple median a poor estimate?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Read the photutils background estimation [documentation](https://photutils.readthedocs.io/en/stable/background.html) to determine the best method to use on this data. Play with image scaling and colorbars to help determine if a 2D background estimation is needed. Describe below your final decision on the best method here and why"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 2: Source Identification</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've settled on a method to extract the background we can move on to automatically detecting the sources. ```photutils``` has two options for this: ```DAOStarFinder``` and ```IRAFStarFinder```. See the [documentation here](https://photutils.readthedocs.io/en/stable/detection.html). We'll stick with ```DAOStarFinder```, but feel free to read up both methods and experiment with them. \n",
"\n",
"**Follow the example in the documentation and generate a list of detected sources.** There are several knobs you can easily turn to change your results: the FWHM, threshhold (i.e. how many ```stds``` above the background a source needs to be before being considered real) and how the ```std``` is calculated. Play with these until you are satisfied. Try to maximize the number of detected sources. **Display the cluster image and overplot the locations of the stars that you found to confirm that things are behaving as you expect.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You'll notice some obviously bright stars don't get identified. Go look at the image in DS9. Do the unidentified stars have anything in common? "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Do these same stars get picked up by the Source Extractor? If so, how reliable do you think their aperture photometry will be?"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"#Your code here (if need be)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Source Extractor may have methods to compensate for these kinds of issues (such as the \"FLAG\" column), but this kind of thing should raise your suspicion and motivate you to read the documentation to find out. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 3: Aperture Photometry</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we're moving on to extracting the photometry. Here we'll be carrying out photometry using a technique called \"aperture photometry\", where we simply add up all the counts within a circular aperture. See the ```photutils``` documentation [here](https://photutils.readthedocs.io/en/stable/aperture.html). **Read up on the documentation and try it out yourself.** There are other types of photometry, such as \"weighted PSF\" photometry, that may be useful in your final project. \n",
"\n",
"To get started quickly you can ignore some of these sections in the documentation: sky apertures, pixel masking, aperture masks, aperture photometry using Sky Coordinates. \n",
"\n",
"**Extract photometry using circular apertures for all the sources you found using the DAOStarFinder. Don't forget to subtract off the background (using whatever method you settled on earlier) before calculating the photometry. What do you think the radius of your circular apertures should be and why?**"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Match your star list with the Source Extractor star list (```cluster1.cat```) by matching the closest x and y positions from the two catalogs. Plot your newly extracted photometry against the ```FLUX_APER``` value from Source Extractor. If they don't match, try to explain a few reasons you think this might be the case.**"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"#Your Code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Play with the various input parameters to the photometric extraction funtion until you get the two catalogs to match as well as you can. One key parameter you can change is the aperture radius, especially if the background isn't sufficiently subtracted. What radius did you have to choose to match the two catalogs? "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If changing the radius has such an important impact on the final answer, how does one choose an optimal radius? \n",
"\n",
"One way to do this is by optimizing the radius to maximize the signal to noise ratio (SNR) in your extracted photometry. To do this we need to estimate the noise in our apertures. The simplest way to do this is to pass to the ```aperture_photometry``` function a map of the expected noise in our image. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To calculate the noise, we'll first assume that the entire image is limited by the photon noise from our stars and background. This might not be strictly true, as the fainter parts of the image might be limited by the read-out noise of the detector. \n",
"\n",
"To create the error map, you'll want to manipulate the original data array, before background subtraction. Discuss with your partner why you want to do this before background subtraction. To calculate the error at each pixel, consider the value at that pixel to be the mean of a Poisson distribution, and the error at that pixel will be the square root of the variance of that distribution. Keep in mind that the Poisson distribution applies to the number of *photons* the detector sees, not the number of counts in your image (recall the previous lab's discussion of the detector gain). **Write down the equation for calculating the error in each pixel here:**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using that equation create an error map for the whole data array and pass that into the ```aperture_photometry``` function so that you can get an estimate of the flux error on each star. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pick 3 random stars from your list and make plots of the SNR as a function of aperture radius (i.e. the aperture sum divided by its error). At what radius do these stars maximize their SNRs?"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If they are different, why do you think that is the case?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**For each star calculate its optimal aperture sum and error by maximizing the signal to noise. Convert this to a magnitude as: $$m = -2.5log_{10}(N_{aperture\\_sum}),$$ where $N_{aperture\\_sum}$ is the optimal aperture sum. For each magnitude calculate an error.**"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 4: Photometric Calibration</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Leaving aside the issues of error and uncertainty, we still have to put our measured magnitudes on a standard scale, such that the numbers we derive can be directly compared with other work. This comes down to measuring the constant $m_1$:\n",
"${\\rm mag} = m_1 - 2.5 \\log_{10}({\\rm flux}),$\n",
"so that it is reasonably consistent with other work. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use the website [sky-map](http://www.sky-map.org/) to determine the magnitudes of the same 4 stars that you used for the image-scale calculation in the previous lab. Make a table below that shows the star number from the Figure in Lab 3, its magnitude from *sky-map*, and (by matching $\\{x,y\\}$ coordinates) the magnitude that you calculated with ```photutils```. Calculate the average difference between your magnitudes and those from *sky-map*, and the standard deviation of this difference:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Star| sky-map Mag | ```photutils``` Mag | difference \n",
"---|---|---|---\n",
"1 |---|---|---\n",
"2 |---|---|---\n",
"3 |---|---|---\n",
"4 |---|---|---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Write an expression for magnitudes in the *sky-map* system (assumed here to be the true on-sky magnitudes) in terms of your derived magnitudes.** This expression will convert your measured magnitudes (based on image counts) into on-sky magnitudes. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Assume the brightest of the stars in your list of 4 has an **absolute** magnitude of 2.75. What is its distance (in parsecs) based on its apparent magnitude? What uncertainty do you assign to this distance estimate, given only the uncertainty that you just calculated in estimating *sky-map* magnitudes from the magnitudes you calculated? Justify your answers."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

BIN
Lab 4/cluster.fits
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Lab 4/cluster1.cat
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@ -1,486 +0,0 @@
# 1 NUMBER Running object number
# 2 X_IMAGE Object position along x [pixel]
# 3 Y_IMAGE Object position along y [pixel]
# 4 FLUX_ISOCOR Corrected isophotal flux [count]
# 5 FLUXERR_ISOCOR RMS error for corrected isophotal flux [count]
# 6 MAG_ISOCOR Corrected isophotal magnitude [mag]
# 7 MAGERR_ISOCOR RMS error for corrected isophotal magnitude [mag]
# 8 FLUX_APER Flux vector within fixed circular aperture(s) [count]
# 9 FLUXERR_APER RMS error vector for aperture flux(es) [count]
# 10 MAG_APER Fixed aperture magnitude vector [mag]
# 11 MAGERR_APER RMS error vector for fixed aperture mag. [mag]
# 12 ELONGATION A_IMAGE/B_IMAGE
# 13 FWHM_IMAGE FWHM assuming a gaussian core [pixel]
# 14 BACKGROUND Background at centroid position [count]
# 15 FLAGS Extraction flags
1 389.0368 71.6170 306479.9 449.4477 -13.7160 0.0016 221860.5 321.6074 -13.3652 0.0016 1.031 7.25 570.4601 0
2 535.8401 72.3356 111624.2 312.1177 -12.6194 0.0030 81540.21 209.6749 -12.2784 0.0028 1.039 7.31 570.7159 2
3 705.8304 58.6026 897266.8 695.18 -14.8823 0.0008 650860.2 534.042 -14.5337 0.0009 1.027 6.15 571.3956 2
4 659.9183 45.8076 184636.1 373.7914 -13.1658 0.0022 133710 257.0073 -12.8154 0.0021 1.034 7.52 571.569 2
5 672.6502 15.1796 161059.9 357.9897 -13.0175 0.0024 116081.1 242.0871 -12.6619 0.0023 1.047 7.32 571.9493 10
6 1203.9077 50.1429 22185.08 200.8275 -10.8652 0.0098 16619.72 128.3285 -10.5516 0.0084 1.085 11.62 571.1428 2
7 1002.1099 48.1919 19659.39 196.8211 -10.7339 0.0109 15186.5 125.8607 -10.4536 0.0090 1.060 7.24 571.392 2
8 656.1636 24.0052 22719.3 202.8197 -10.8910 0.0097 16519.26 128.1105 -10.5450 0.0084 1.126 13.64 571.6312 2
9 356.5015 35.1145 3813.68 161.5075 -8.9534 0.0460 3057.215 103.5923 -8.7133 0.0368 1.086 14.57 570.3051 0
10 94.4035 32.7588 9606.526 171.344 -9.9564 0.0194 7652.083 112.465 -9.7094 0.0160 1.109 8.26 572.4567 2
11 893.1217 26.2778 56846.22 254.468 -11.8868 0.0049 42039.12 165.1033 -11.5591 0.0043 1.048 8.83 571.5414 0
12 1507.4277 17.3794 325051.8 454.1195 -13.7799 0.0015 237964.2 332.0415 -13.4413 0.0015 1.034 7.32 584.3629 2
13 1506.0000 5.0173 4980.516 54.35657 -9.2432 0.0119 5294.731 104.7538 -9.3096 0.0215 1.005 0.00 584.6544 18
14 1.2756 20.1721 352.0092 45.47412 -6.3664 0.1403 373.6361 75.03796 -6.4311 0.2181 1.750 -0.99 574.8361 24
15 1444.3497 5.3484 122885.2 296.4996 -12.7237 0.0026 99819.45 226.3685 -12.4980 0.0025 1.245 8.24 577.5316 24
16 1535.6854 12.0019 431.8897 32.13369 -6.5884 0.0808 324.9601 75.07807 -6.2796 0.2509 1.497 3.34 587.8103 24
17 1320.4512 2.7629 6273.627 127.1033 -9.4938 0.0220 5292.692 95.6935 -9.3092 0.0196 2.124 13.09 573.1546 24
18 1296.6378 3.0893 4602.483 133.719 -9.1575 0.0316 3723.802 93.74911 -8.9275 0.0273 1.921 9.88 572.8157 24
19 1271.3274 2.8810 14518.22 148.8741 -10.4048 0.0111 12181.67 110.4817 -10.2143 0.0098 2.055 9.57 572.4188 24
20 1411.0084 1.8239 311.4857 42.12267 -6.2336 0.1469 204.5039 78.15753 -5.7768 0.4150 1.047 3.83 575.6845 24
21 1463.8964 1.9485 330.5657 48.8313 -6.2981 0.1604 499.7827 79.77227 -6.7470 0.1733 1.180 4.07 579.8969 24
22 1139.9670 2.0064 526.8016 41.37827 -6.8041 0.0853 577.7314 80.27001 -6.9043 0.1509 1.017 0.00 571.1617 24
23 1090.6235 2.1652 203.4737 39.61199 -5.7713 0.2114 331.8169 80.5127 -6.3022 0.2635 1.558 3.25 571.0824 24
24 1035.9690 1.8887 584.1646 40.19136 -6.9163 0.0747 685.5258 79.84801 -7.0901 0.1265 1.028 1.11 571.1794 24
25 983.9792 2.0576 411.6134 46.73682 -6.5362 0.1233 362.5716 80.01291 -6.3985 0.2397 1.015 4.23 571.5439 24
26 717.8780 2.1685 248.9239 42.04086 -5.9902 0.1834 229.4858 80.26372 -5.9019 0.3798 1.270 3.59 572.3331 24
27 527.1032 1.4904 695.3176 36.29724 -7.1055 0.0567 815.3862 77.80977 -7.2784 0.1036 1.182 1.00 569.946 24
28 447.8138 1.8790 241.7663 44.33751 -5.9585 0.1992 252.848 78.52211 -6.0071 0.3373 1.258 0.87 570.1091 24
29 435.0042 2.0222 231.634 34.51355 -5.9120 0.1618 253.9699 79.53661 -6.0120 0.3401 1.029 3.39 570.1216 24
30 358.1033 1.8874 363.3374 44.29612 -6.4008 0.1324 354.3787 79.0488 -6.3737 0.2422 1.151 0.00 570.2073 24
31 275.0032 1.7940 648.4477 39.34929 -7.0297 0.0659 739.7831 79.19677 -7.1728 0.1163 1.015 1.54 570.3818 24
32 1345.9760 1.2237 178.8039 31.72073 -5.6309 0.1927 132.2047 74.06143 -5.3031 0.6084 1.512 0.00 573.5095 24
33 1307.0096 1.3946 297.7979 36.23338 -6.1848 0.1321 416.0429 75.8414 -6.5478 0.1980 1.483 3.50 572.9758 24
34 1495.1985 50.5526 27914.38 209.7055 -11.1146 0.0082 21062.47 135.3664 -10.8088 0.0070 1.073 14.24 581.9782 2
35 639.9816 1.1932 216.37 28.40033 -5.8380 0.1425 356.9218 74.41113 -6.3814 0.2264 1.596 2.91 571.4084 24
36 616.0170 1.1981 183.7082 31.06188 -5.6603 0.1836 10.61068 73.44116 -2.5644 7.5167 1.558 2.90 570.9252 24
37 535.0229 1.3363 475.2159 31.70255 -6.6922 0.0724 557.8524 75.93008 -6.8663 0.1478 1.506 0.00 569.9243 24
38 506.9860 1.2328 166.3176 34.21916 -5.5523 0.2234 197.0305 74.3811 -5.7363 0.4100 1.508 0.00 570.0002 24
39 456.0171 1.3341 817.851 31.69455 -7.2817 0.0421 876.3889 76.81374 -7.3567 0.0952 1.507 3.40 570.0954 24
40 367.1576 1.3138 239.0407 33.80391 -5.9462 0.1536 347.8513 75.29762 -6.3535 0.2351 1.508 3.20 570.1935 24
41 317.0129 1.7687 166.7218 43.88645 -5.5550 0.2859 598.6397 78.81828 -6.9429 0.1430 1.660 3.18 570.2615 24
42 200.1788 1.3060 273.1656 31.62398 -6.0911 0.1257 411.6056 75.34428 -6.5362 0.1988 1.582 3.23 570.925 24
43 101.0173 1.2231 192.3715 30.1251 -5.7104 0.1701 369.4842 74.78168 -6.4190 0.2198 1.530 3.01 572.5365 24
44 571.1406 843.8476 693.754 92.48909 -7.1030 0.1448 868.277 98.91342 -7.3466 0.1237 1.241 6.59 566.5977 0
45 1480.8933 1024.0000 176.5775 23.84674 -5.6173 0.1467 64.14983 72.27107 -4.5180 1.2235 2.971 1.29 578.8329 24
46 1378.5719 1023.5145 198.4511 29.59098 -5.7441 0.1619 -80.5513 75.38045 99.0000 99.0000 1.083 0.23 571.181 24
47 1331.5981 1023.4440 188.5104 30.51293 -5.6883 0.1758 -77.16092 75.75509 99.0000 99.0000 1.080 0.44 570.5027 24
48 1147.0376 1023.4218 256.1931 40.56774 -6.0214 0.1720 -86.93473 76.04034 99.0000 99.0000 1.477 0.00 567.348 24
49 1099.9960 1023.2465 290.3186 45.43005 -6.1572 0.1699 -34.99454 77.06281 99.0000 99.0000 1.044 0.00 567.1688 24
50 977.0167 1023.0481 1158.141 38.62954 -7.6594 0.0362 900.8903 80.76871 -7.3867 0.0974 1.018 0.00 566.9571 24
51 959.9641 1022.5631 5586.261 116.963 -9.3678 0.0227 4799.314 93.0327 -9.2029 0.0211 2.324 10.61 566.972 24
52 911.9476 1024.0000 210.2598 22.82982 -5.8069 0.1179 -43.82784 72.08277 99.0000 99.0000 2.646 0.00 566.6826 24
53 722.5679 1022.2255 2171.332 111.8442 -8.3418 0.0559 1875.761 87.86003 -8.1829 0.0509 1.432 11.31 566.1988 24
54 668.9771 1023.8237 257.1691 26.8563 -6.0255 0.1134 -24.38488 73.34245 99.0000 99.0000 1.699 0.00 566.1174 24
55 625.0696 1023.8542 217.4814 28.3406 -5.8436 0.1415 -21.94512 73.16058 99.0000 99.0000 1.898 0.00 565.7858 24
56 618.0152 1023.2153 355.4968 38.66916 -6.3771 0.1181 27.4378 77.33227 -3.5959 3.0608 1.046 0.00 565.7391 24
57 609.9766 1023.8417 258.8605 26.81335 -6.0327 0.1125 -95.94534 73.20609 99.0000 99.0000 1.811 2.86 565.6727 24
58 603.9647 1023.0606 553.2466 40.76528 -6.8573 0.0800 225.543 78.89294 -5.8831 0.3799 1.021 0.00 565.6498 24
59 408.0154 1023.5025 6393.519 123.8021 -9.5143 0.0210 5669.829 89.93337 -9.3839 0.0172 1.575 16.56 567.3068 26
60 404.2147 1023.6516 2047.724 50.12054 -8.2782 0.0266 2390.589 81.00583 -8.4463 0.0368 1.849 0.77 567.3087 26
61 300.0554 1024.0000 194.529 23.21 -5.7225 0.1296 9.612668 72.13411 -2.4571 8.1494 2.741 2.78 567.0597 24
62 159.9874 1023.6769 195.0727 29.87731 -5.7255 0.1663 -84.56991 74.29002 99.0000 99.0000 1.332 3.16 569.3026 24
63 58.0101 1023.7108 395.1473 32.70463 -6.4919 0.0899 294.483 74.90314 -6.1727 0.2762 1.551 3.32 572.1126 24
64 4.0389 1023.5570 317.7219 35.10119 -6.2551 0.1200 168.747 69.57799 -5.5681 0.4478 1.446 1.04 574.1973 24
65 92.0124 835.0628 2892.752 154.7811 -8.6533 0.0581 2222 101.739 -8.3669 0.0497 1.186 9.09 570.2118 0
66 946.0488 830.3796 14789.75 187.1461 -10.4249 0.0137 10951.07 118.5871 -10.0986 0.0118 1.106 12.69 568.6592 0
67 314.3318 834.2944 2243.109 157.834 -8.3771 0.0764 1853.114 101.0997 -8.1698 0.0592 1.260 7.78 568.1591 0
68 982.8816 824.6236 88428.16 289.3284 -12.3665 0.0036 64634.99 191.8254 -12.0262 0.0032 1.043 8.41 568.9642 0
69 1360.3040 830.3319 122.617 36.99383 -5.2214 0.3276 653.2732 98.57016 -7.0377 0.1639 1.658 2.53 572.0346 0
70 1028.8444 816.2819 29138.28 229.3314 -11.1612 0.0085 17979.26 130.541 -10.6369 0.0079 1.423 23.62 569.2427 2
71 1031.7109 807.2930 1652.074 44.86493 -8.0451 0.0295 2057.618 101.5438 -8.2834 0.0536 1.579 0.00 569.4155 2
72 185.6552 810.6270 29178.74 215.8286 -11.1627 0.0080 21562.37 136.22 -10.8342 0.0069 1.074 7.88 569.6203 2
73 193.9553 815.0057 456.0123 28.61519 -6.6474 0.0681 818.3894 98.78965 -7.2824 0.1311 1.028 3.48 569.6991 2
74 831.9339 814.3178 1702.223 136.373 -8.0775 0.0870 1597.302 100.5456 -8.0085 0.0684 1.277 10.72 567.916 0
75 719.0699 845.1190 16637.08 197.6402 -10.5527 0.0129 12202.93 120.858 -10.2162 0.0108 1.017 8.91 567.0499 0
76 77.5644 797.0984 25463.77 210.824 -11.0148 0.0090 18983.89 132.1236 -10.6960 0.0076 1.061 7.69 569.5073 0
77 341.9962 791.5062 23339.69 200.8374 -10.9202 0.0093 17869.51 130.286 -10.6303 0.0079 1.052 7.47 567.426 0
78 1535.7051 798.2408 152.9125 25.26869 -5.4611 0.1795 108.7093 74.51004 -5.0907 0.7444 1.473 0.00 580.6508 24
79 204.7318 783.5220 159438.3 358.6378 -13.0065 0.0024 114413.1 240.6576 -12.6462 0.0023 1.119 7.43 569.4357 0
80 114.5093 782.7014 159062.3 362.3949 -13.0039 0.0025 97669.65 225.436 -12.4744 0.0025 1.269 11.93 569.3098 0
81 1031.8646 775.4187 945937.1 717.8205 -14.9397 0.0008 638931.2 529.2821 -14.5136 0.0009 1.137 8.37 569.5766 0
82 253.5605 777.4815 100357.3 303.6525 -12.5039 0.0033 73121.68 201.0051 -12.1601 0.0030 1.040 7.42 568.9042 0
83 1309.7655 771.3724 622381.6 595.9546 -14.4851 0.0010 446218.7 445.5315 -14.1239 0.0011 1.041 8.95 570.9946 0
84 1.7065 787.2881 145.4647 25.96159 -5.4069 0.1938 -8.030077 76.95468 99.0000 99.0000 1.546 0.84 569.9659 24
85 866.9930 773.4222 121961.1 322.2259 -12.7156 0.0029 89747.38 217.81 -12.3826 0.0026 1.032 7.64 568.5294 2
86 860.0238 769.0179 5351.41 55.76167 -9.3212 0.0113 5503.967 108.4042 -9.3517 0.0214 1.023 4.34 568.4647 2
87 386.8057 776.8505 15680.58 187.8443 -10.4884 0.0130 11931.57 120.2568 -10.1917 0.0109 1.139 9.83 566.7452 2
88 378.2201 777.0212 598.3875 33.99408 -6.9425 0.0617 863.1305 98.9024 -7.3402 0.1244 1.047 3.95 566.8578 2
89 149.9731 768.0416 14740.43 194.7258 -10.4213 0.0143 10706.93 118.136 -10.0742 0.0120 1.058 13.96 569.2845 0
90 637.3253 767.3802 1498.14 131.4086 -7.9389 0.0953 1292.797 99.7685 -7.7788 0.0838 1.197 10.16 566.9343 0
91 586.5219 763.3857 13218.75 179.3087 -10.3030 0.0147 10240.15 117.2249 -10.0258 0.0124 1.036 11.04 566.7806 2
92 586.0002 756.0030 23330.59 103.462 -10.9198 0.0048 23843.89 139.5684 -10.9434 0.0064 1.000 4.19 566.7729 2
93 279.2478 753.7066 129564.3 339.9291 -12.7812 0.0028 92597.57 220.6329 -12.4165 0.0026 1.097 7.36 568.2382 0
94 1535.0524 762.9042 335.7802 47.79423 -6.3151 0.1546 211.3919 79.00263 -5.8127 0.4059 1.190 0.00 579.4632 24
95 1098.0483 738.3636 2050370 1011.655 -15.7796 0.0005 1470165 795.2153 -15.4184 0.0006 1.024 7.31 569.2079 0
96 968.7756 704.7058 54220.5 280.0743 -11.8354 0.0056 34485.18 154.9677 -11.3441 0.0049 1.088 9.10 569.5555 2
97 951.8831 737.8629 2877208 1171.293 -16.1474 0.0004 2068290 941.1783 -15.7890 0.0005 1.068 7.29 569.8163 2
98 971.9218 726.1238 245697.1 397.9074 -13.4760 0.0018 173297.8 287.884 -13.0970 0.0018 1.065 7.40 569.727 2
99 899.2938 755.8594 4527.937 153.0861 -9.1398 0.0367 3850.797 105.1395 -8.9639 0.0297 1.023 5.75 569.137 2
100 897.4845 751.4378 500.723 42.12727 -6.7490 0.0914 881.5577 98.94186 -7.3631 0.1219 1.178 -0.37 569.1727 2
101 1496.3372 748.2548 6391.317 169.5444 -9.5140 0.0288 4932.04 107.3117 -9.2326 0.0236 1.128 8.88 576.7207 0
102 1347.0923 742.8418 21225.65 200.4461 -10.8172 0.0103 15873.92 127.0912 -10.5017 0.0087 1.027 9.75 571.7237 0
103 252.5567 746.0145 10461.51 89.15668 -10.0490 0.0093 10336.42 117.4555 -10.0359 0.0123 2.517 7.88 568.4484 0
104 647.7886 730.2021 150412.2 343.9447 -12.9432 0.0025 109921.5 236.5647 -12.6027 0.0023 1.015 7.37 566.9549 2
105 668.9844 719.3401 11668.54 184.2906 -10.1675 0.0172 8640.732 114.3414 -9.8414 0.0144 1.068 18.26 567.0324 2
106 870.3569 733.5926 9646.822 174.5925 -9.9610 0.0197 7519.082 112.2438 -9.6904 0.0162 1.139 13.94 568.9334 0
107 1.5910 736.6395 225.3193 27.95505 -5.8820 0.1347 81.07081 76.30955 -4.7722 1.0222 1.024 2.83 568.7809 24
108 1535.1375 732.8823 260.4868 39.87928 -6.0395 0.1663 118.0934 78.26414 -5.1806 0.7197 1.239 3.59 578.6476 24
109 274.5451 714.7672 6389.943 166.8334 -9.5137 0.0284 5049.103 107.4806 -9.2580 0.0231 1.090 8.55 567.9453 0
110 506.6902 714.3842 884.6818 103.6956 -7.3670 0.1273 1023.11 99.19415 -7.5248 0.1053 1.380 7.58 566.5515 0
111 759.5422 703.0983 48092.64 245.6235 -11.7052 0.0055 35572.86 156.5434 -11.3778 0.0048 1.045 8.00 567.0292 0
112 1.6210 713.8533 198.8546 42.60148 -5.7463 0.2327 123.1838 76.68742 -5.2264 0.6761 1.692 1.43 568.8441 24
113 1316.1206 693.5350 180819.7 368.9051 -13.1431 0.0022 131409.8 255.1759 -12.7966 0.0021 1.051 7.29 570.4988 0
114 1215.8433 701.2114 9154.539 171.2209 -9.9041 0.0203 7222.528 111.6826 -9.6467 0.0168 1.038 9.03 568.8199 0
115 716.9677 702.5513 2833.355 157.3204 -8.6308 0.0603 2219.288 101.7497 -8.3655 0.0498 1.251 11.36 566.9985 0
116 599.4573 690.2487 192601.3 379.7938 -13.2116 0.0021 140026.1 262.1941 -12.8655 0.0020 1.028 7.26 567.1793 0
117 878.7529 686.2391 121071.6 320.4928 -12.7076 0.0029 85641.12 213.7941 -12.3317 0.0027 1.019 9.55 568.9286 2
118 873.0854 664.4724 119499.7 316.0713 -12.6934 0.0029 83149.25 211.3654 -12.2996 0.0028 1.074 13.53 568.9153 2
119 872.5131 644.5047 152817.8 351.6819 -12.9604 0.0025 107927.9 234.8931 -12.5828 0.0024 1.065 7.93 569.2052 2
120 855.9648 685.6813 270684.3 419.5621 -13.5812 0.0017 194517.4 303.0488 -13.2224 0.0017 1.040 7.32 568.4662 2
121 847.1931 662.3392 581310.8 571.3052 -14.4110 0.0011 420077.9 432.9031 -14.0583 0.0011 1.021 7.29 568.4235 2
122 954.7587 667.2405 58716.28 263.7987 -11.9219 0.0049 42058.05 165.0772 -11.5596 0.0043 1.052 9.87 569.4413 2
123 934.0070 692.9849 5242.795 55.35353 -9.2989 0.0115 5692.074 108.664 -9.3882 0.0207 1.008 0.00 569.7808 2
124 938.6715 682.9146 170716.3 355.3527 -13.0807 0.0023 125515.4 250.2474 -12.7467 0.0022 1.053 7.30 569.7128 2
125 525.9485 685.9960 7689.264 73.31499 -9.7147 0.0104 8317.622 113.6972 -9.8000 0.0148 1.046 0.00 566.9208 2
126 522.5003 685.4977 20539.31 201.4312 -10.7815 0.0107 17004.74 128.9626 -10.5764 0.0082 1.140 12.40 566.8902 2
127 1104.0127 691.7571 579.6447 34.08554 -6.9079 0.0639 1068.364 99.3243 -7.5718 0.1010 1.069 0.00 568.7316 2
128 1103.2250 683.6935 20277.34 199.2345 -10.7675 0.0107 15406.17 126.2299 -10.4692 0.0089 1.053 19.48 568.6555 2
129 1107.8810 676.1071 541.3816 31.36313 -6.8338 0.0629 820.3095 98.92854 -7.2849 0.1310 1.271 3.67 568.5802 2
130 1425.0533 684.9311 6591.957 139.4514 -9.5475 0.0230 5790.149 108.9926 -9.4067 0.0204 1.233 13.88 572.6516 0
131 1275.8137 677.1052 88928.13 289.6272 -12.3726 0.0035 64964.09 192.1626 -12.0317 0.0032 1.054 7.65 569.4414 0
132 309.6055 676.8823 13127.72 184.1904 -10.2955 0.0152 9934.206 116.6278 -9.9928 0.0127 1.074 8.00 567.1455 0
133 113.5566 663.4138 1139480 778.2751 -15.1418 0.0007 815402.6 595.7563 -14.7784 0.0008 1.022 7.33 568.8038 0
134 547.9919 669.0195 4577.742 52.79301 -9.1516 0.0125 4925.515 107.2056 -9.2311 0.0236 1.011 4.24 567.3125 2
135 545.1306 674.7978 17312.71 187.8304 -10.5959 0.0118 13372.86 122.7834 -10.3156 0.0100 1.072 8.32 567.2858 2
136 1193.7474 695.0914 819.1385 95.83013 -7.2834 0.1270 1030.688 99.311 -7.5328 0.1046 1.503 8.07 568.7092 0
137 1178.1858 651.4692 88835.96 288.1526 -12.3715 0.0035 65545.04 192.8193 -12.0413 0.0032 1.048 9.39 568.5361 2
138 1188.7242 653.0130 571.064 34.1343 -6.8917 0.0649 1119.296 99.39938 -7.6224 0.0964 1.081 0.00 568.562 2
139 1418.9794 648.5443 85598.11 286.4098 -12.3312 0.0036 62822.8 189.8485 -11.9953 0.0033 1.043 7.46 572.0171 0
140 497.4454 653.8682 3982.452 159.2191 -9.0004 0.0434 3229.183 103.8793 -8.7727 0.0349 1.121 11.32 566.7216 0
141 1145.3861 642.5230 30944.45 217.7573 -11.2265 0.0076 23207.8 138.6955 -10.9141 0.0065 1.049 7.59 568.5324 0
142 1306.7957 641.5597 6773.157 173.5098 -9.5770 0.0278 5180.646 107.7086 -9.2860 0.0226 1.047 10.66 569.6579 0
143 1.3138 648.0190 341.467 34.11103 -6.3334 0.1085 416.0694 75.42311 -6.5479 0.1969 1.576 3.42 569.0836 24
144 1084.4985 635.1830 109440.4 307.9083 -12.5979 0.0031 80291.55 208.3774 -12.2617 0.0028 1.035 7.45 568.3456 0
145 535.6158 645.8846 376.3221 68.20155 -6.4389 0.1968 833.6094 98.77172 -7.3024 0.1287 2.554 5.29 567.231 0
146 272.1246 632.1758 173055.3 365.7697 -13.0955 0.0023 125086 249.8236 -12.7430 0.0022 1.037 7.33 567.5929 0
147 210.5425 628.6658 94973.73 293.6758 -12.4440 0.0034 70485.36 198.2405 -12.1202 0.0031 1.049 7.31 568.5956 2
148 204.0284 624.0238 3900.172 48.05275 -8.9777 0.0134 4365.78 106.1564 -9.1002 0.0264 1.024 3.99 568.6294 2
149 437.8864 636.5464 750.4542 93.12788 -7.1883 0.1348 1100.349 99.50972 -7.6038 0.0982 1.286 7.29 566.4881 0
150 631.3391 631.8169 910.4944 105.7646 -7.3982 0.1262 1094.991 99.39783 -7.5985 0.0986 1.542 8.05 567.3303 0
151 1.3299 632.9932 1770.147 36.54151 -8.1200 0.0224 1763.107 79.22169 -8.1157 0.0488 1.507 0.00 569.1593 24
152 575.8073 626.9306 5784.55 169.4362 -9.4057 0.0318 4482.449 106.3421 -9.1288 0.0258 1.060 8.12 567.3551 0
153 1210.6587 623.2158 14748.29 189.6943 -10.4219 0.0140 11243.65 119.0667 -10.1273 0.0115 1.050 7.87 568.7001 0
154 476.9905 615.7000 183450.8 369.7404 -13.1588 0.0022 133396.9 256.7685 -12.8129 0.0021 1.033 7.28 566.8321 0
155 306.0975 611.2288 242455.6 414.3528 -13.4616 0.0019 174310.9 288.5651 -13.1033 0.0018 1.052 7.47 566.9442 0
156 1535.7252 624.9125 298.7418 30.64093 -6.1882 0.1114 117.8701 74.53609 -5.1785 0.6867 1.591 0.00 579.3865 24
157 1.7554 622.9925 290.9472 45.29123 -6.1595 0.1691 92.56979 77.31689 -4.9162 0.9071 1.067 3.88 569.2062 24
158 21.6285 615.3055 15691.27 195.4853 -10.4891 0.0135 11586.33 119.661 -10.1599 0.0112 1.137 12.27 569.1669 0
159 363.1283 608.8676 54596.75 248.0771 -11.8429 0.0049 46140.98 170.2367 -11.6602 0.0040 1.042 7.12 566.5079 2
160 360.3043 606.3028 10751.24 85.04531 -10.0786 0.0086 14736 125.2065 -10.4209 0.0092 1.928 0.99 566.5179 2
161 48.6502 618.8121 502.2541 28.53945 -6.7523 0.0617 862.8392 98.90177 -7.3398 0.1245 1.564 3.28 569.0497 2
162 44.6211 613.0625 8629.592 176.7796 -9.8400 0.0222 6661.83 110.5988 -9.5590 0.0180 1.150 8.56 569.0812 2
163 1493.5818 610.8138 6553.139 169.9273 -9.5411 0.0282 5004.657 107.3929 -9.2484 0.0233 1.243 9.73 576.2265 0
164 883.9446 600.2039 166946.1 358.0286 -13.0564 0.0023 120720.4 246.1002 -12.7045 0.0022 1.062 7.86 569.5296 2
165 889.3654 567.4880 302030.2 447.3039 -13.7001 0.0016 218027.3 319.0618 -13.3463 0.0016 1.033 7.35 569.0577 2
166 920.4991 563.5016 199800.6 387.2326 -13.2515 0.0021 145332.7 266.4663 -12.9059 0.0020 1.026 7.29 568.9343 2
167 253.3248 594.7138 146539 347.7894 -12.9149 0.0026 105289.6 232.5013 -12.5560 0.0024 1.046 7.70 568.0712 0
168 569.7487 594.1737 32437.46 231.1921 -11.2776 0.0077 22989.71 138.4101 -10.9038 0.0065 1.066 11.62 567.5294 2
169 574.5621 577.5217 6572.086 176.5748 -9.5443 0.0292 4928.134 107.2263 -9.2317 0.0236 1.153 9.31 567.7083 2
170 1535.1311 601.8925 261.7513 39.69443 -6.0447 0.1647 -8.92977 78.00787 99.0000 99.0000 1.256 0.00 579.4667 24
171 673.2163 587.4077 21028.77 198.2325 -10.8070 0.0102 15771.91 126.8292 -10.4947 0.0087 1.041 9.50 567.9054 0
172 1.7910 593.9964 303.3369 43.15304 -6.2048 0.1545 69.85355 77.36233 -4.6105 1.2027 1.089 3.85 569.4634 24
173 445.2023 577.1520 54804.7 253.6697 -11.8470 0.0050 40060.82 162.4117 -11.5068 0.0044 1.027 8.70 566.9033 0
174 525.3393 576.7914 45086.12 234.8142 -11.6351 0.0057 33716.04 153.9342 -11.3196 0.0050 1.016 7.61 567.4961 0
175 938.9756 580.9537 2274.719 61.22087 -8.3923 0.0292 2580.053 102.5144 -8.5291 0.0432 1.980 7.21 569.0106 2
176 945.4011 577.1667 8331.748 127.2485 -9.8018 0.0166 8661.494 114.3653 -9.8440 0.0143 1.090 9.95 568.9703 2
177 954.7986 566.9867 125254.4 327.3867 -12.7445 0.0028 90420.57 218.4104 -12.3907 0.0026 1.037 7.30 568.8921 2
178 834.4672 601.7120 112088.2 309.4975 -12.6239 0.0030 82902.12 211.0939 -12.2964 0.0028 1.030 7.15 569.0584 0
179 633.1782 539.7517 3040759 1216.327 -16.2075 0.0004 2185858 967.2816 -15.8491 0.0005 1.016 7.20 568.6135 2
180 776.6585 519.2133 27565.23 260.8065 -11.1009 0.0103 16776.25 128.5478 -10.5617 0.0083 1.738 25.49 569.0828 2
181 782.3267 550.4127 151439.7 327.3777 -12.9506 0.0023 108977.8 235.7604 -12.5933 0.0023 1.106 9.70 568.7622 2
182 789.1563 540.8710 161217.5 327.1824 -13.0185 0.0022 123899.5 248.822 -12.7327 0.0022 1.091 7.06 568.8199 2
183 1184.2992 546.1727 234231.5 405.5146 -13.4241 0.0019 170637.4 285.8495 -13.0802 0.0018 1.025 7.19 568.0508 2
184 1177.0184 541.0120 21763.38 100.2037 -10.8443 0.0050 21754.89 136.4703 -10.8439 0.0068 1.009 4.24 568.0671 2
185 184.4795 553.5676 40334.72 230.9237 -11.5142 0.0062 29990.64 148.7297 -11.1925 0.0054 1.044 9.08 568.7677 0
186 1081.2974 557.0922 1486.595 130.1057 -7.9305 0.0950 1360.901 100.0296 -7.8346 0.0798 1.293 9.85 567.8113 0
187 138.4052 554.0659 2516.375 147.6268 -8.5019 0.0637 2032.632 101.3438 -8.2701 0.0541 1.027 11.64 568.8465 0
188 1085.9260 541.6534 18845.88 198.1295 -10.6880 0.0114 14376.8 124.5705 -10.3942 0.0094 1.068 8.90 567.7946 0
189 1.2823 544.1592 331.4366 29.81122 -6.3010 0.0977 200.6826 74.65966 -5.7563 0.4040 1.609 3.20 570.0832 24
190 1003.4260 513.0878 181146.8 365.0528 -13.1451 0.0022 131123.8 254.8795 -12.7942 0.0021 1.034 7.28 568.7896 2
191 1020.9795 525.9935 157575 348.1346 -12.9937 0.0024 113961.4 240.2111 -12.6419 0.0023 1.033 7.69 568.4249 2
192 1010.0092 525.9988 13096.1 79.83015 -10.2929 0.0066 13198.73 122.4009 -10.3013 0.0101 1.005 0.00 568.5955 2
193 749.1982 508.9486 206878.9 389.7599 -13.2893 0.0020 150001.1 270.1094 -12.9402 0.0020 1.023 7.23 569.4791 0
194 1235.6732 515.3381 4529.084 145.8737 -9.1400 0.0350 3554.825 104.5732 -8.8770 0.0319 1.732 12.97 568.7115 2
195 1238.1975 510.5745 1946.188 85.2217 -8.2230 0.0476 2062.13 101.3726 -8.2858 0.0534 1.531 4.48 568.7632 2
196 699.8337 511.3173 25601.59 203.0016 -11.0207 0.0086 19618.6 133.15 -10.7317 0.0074 1.035 9.36 569.3909 2
197 692.2857 514.7178 496.5755 31.55862 -6.7400 0.0690 1099.815 99.54205 -7.6033 0.0983 1.510 3.69 569.3143 2
198 336.2180 506.8369 49848.85 245.5969 -11.7441 0.0054 36443.48 157.6751 -11.4040 0.0047 1.074 11.75 566.8962 0
199 457.7266 520.9659 409.2845 67.68867 -6.5301 0.1796 754.728 98.60237 -7.1945 0.1419 2.309 6.61 567.239 0
200 152.4362 508.5069 26095.93 206.608 -11.0414 0.0086 19909.87 133.6126 -10.7477 0.0073 1.055 7.62 568.9182 0
201 642.9609 544.9823 17960.27 90.81291 -10.6358 0.0055 18817.75 131.8822 -10.6864 0.0076 1.025 0.00 568.6691 2
202 239.0035 476.0161 2258.615 42.99911 -8.3846 0.0207 2731.964 102.7306 -8.5912 0.0408 1.011 4.30 568.3884 2
203 244.4041 490.2019 557736.1 569.7789 -14.3661 0.0011 403029 424.4576 -14.0133 0.0011 1.022 7.31 568.3071 2
204 244.0059 479.0661 5332.545 55.69098 -9.3173 0.0113 5336.321 108.0452 -9.3181 0.0220 1.001 4.35 568.2805 2
205 657.1502 493.9525 10952.2 184.4618 -10.0988 0.0183 8175.511 113.4761 -9.7813 0.0151 1.024 17.08 569.3169 0
206 392.8562 494.0174 2755.374 154.6475 -8.6005 0.0610 2234.791 101.8147 -8.3731 0.0495 1.035 11.05 566.8086 0
207 474.9600 487.4564 35293.62 228.5145 -11.3692 0.0070 25973.49 142.8811 -11.0363 0.0060 1.024 8.13 567.3862 0
208 93.2091 490.1264 9661.538 171.0606 -9.9626 0.0192 7701.645 112.5879 -9.7165 0.0159 1.067 17.53 569.3828 0
209 567.8943 477.8943 193489.2 366.5658 -13.2166 0.0021 140501.1 262.6156 -12.8692 0.0020 1.086 7.32 568.595 2
210 569.0291 462.7141 170902.5 349.9643 -13.0819 0.0022 125748 250.3844 -12.7488 0.0022 1.094 7.30 568.7151 2
211 1294.3748 489.5649 4244.179 77.80367 -9.0695 0.0199 4073.742 105.572 -9.0250 0.0281 2.369 4.54 569.2574 0
212 614.7700 486.5844 9494.841 175.4781 -9.9437 0.0201 7251.458 111.7971 -9.6511 0.0167 1.095 10.98 569.3324 0
213 1358.7886 479.1590 81275.4 284.2853 -12.2749 0.0038 59606.88 186.1982 -11.9382 0.0034 1.042 7.30 570.9054 2
214 1339.2848 476.1683 12961.59 191.6511 -10.2816 0.0161 9241.751 115.4496 -9.9144 0.0136 1.084 19.36 570.2587 2
215 802.1502 486.1475 6608.885 189.7197 -9.5503 0.0312 4601.733 106.5951 -9.1573 0.0252 1.220 9.97 569.0273 2
216 814.8317 460.7858 1420245 853.6215 -15.3809 0.0007 1022885 665.4686 -15.0246 0.0007 1.024 7.23 569.5461 2
217 1.3353 490.9694 494.8762 31.56871 -6.7362 0.0693 482.3161 75.78497 -6.7083 0.1706 1.523 0.00 569.9128 24
218 298.3986 487.2194 213.6877 50.38371 -5.8244 0.2561 294.8155 97.60917 -6.1739 0.3596 1.712 3.45 567.2378 0
219 398.7540 473.2307 71146.46 272.0713 -12.1304 0.0042 51918.61 177.2344 -11.7883 0.0037 1.034 8.96 566.9072 0
220 906.9934 482.9700 2522.278 44.16702 -8.5045 0.0190 2820.28 103.0096 -8.6257 0.0397 1.002 4.25 569.1108 2
221 907.5663 472.7889 69804.25 266.7199 -12.1097 0.0041 51851.18 177.182 -11.7869 0.0037 1.007 7.40 569.0699 2
222 1535.8125 480.0054 203.5318 29.20293 -5.7716 0.1558 57.33055 73.4172 -4.3960 1.3907 1.634 2.91 578.9084 24
223 145.2426 462.1636 35147.31 230.5307 -11.3647 0.0071 25964.89 142.9383 -11.0360 0.0060 1.052 8.94 569.0937 0
224 663.8979 460.5441 62826.33 259.5395 -11.9954 0.0045 47049.61 171.3735 -11.6814 0.0040 1.030 7.25 569.4373 0
225 762.4770 456.8458 32948.66 218.7867 -11.2946 0.0072 24531.29 140.7737 -10.9743 0.0062 1.036 8.39 570.1227 2
226 751.6163 440.4321 44347.18 235.6285 -11.6172 0.0058 33233.08 153.3115 -11.3039 0.0050 1.081 7.40 570.5086 2
227 1198.5684 446.2457 498183.2 545.233 -14.2435 0.0012 361409 403.1815 -13.8950 0.0012 1.013 7.27 568.7339 0
228 1.9529 458.9642 223.7527 35.43246 -5.8744 0.1720 128.5742 78.75908 -5.2729 0.6652 1.045 0.00 570.2826 24
229 1535.8220 457.9392 198.1385 29.61646 -5.7424 0.1623 13.28338 73.40351 -2.8083 6.0012 1.653 2.86 578.6463 24
230 1438.2441 450.0635 10462.37 182.9217 -10.0491 0.0190 7873.783 112.9408 -9.7405 0.0156 1.147 8.85 572.9673 2
231 1426.3929 428.1570 63816.04 263.4797 -12.0123 0.0045 46272.47 170.3514 -11.6633 0.0040 1.114 9.34 573.1825 2
232 1423.4384 411.2955 7554.672 170.4117 -9.6955 0.0245 5964.761 109.3011 -9.4390 0.0199 1.222 4.33 573.341 2
233 960.8632 435.1900 1653721 918.1796 -15.5462 0.0006 1189394 716.5146 -15.1883 0.0007 1.031 7.22 568.8812 2
234 700.8220 446.9313 1555.374 136.5259 -7.9796 0.0953 1242.823 99.64561 -7.7360 0.0871 1.250 10.44 569.9025 0
235 995.4854 435.4116 81574.7 270.4897 -12.2789 0.0036 70116.84 197.7704 -12.1146 0.0031 1.099 15.88 568.9448 2
236 32.2357 429.8874 181419.6 372.3817 -13.1467 0.0022 130854.7 254.6819 -12.7920 0.0021 1.054 7.39 570.454 0
237 1161.8766 426.7566 92863.61 295.1726 -12.4196 0.0035 67921.02 195.4466 -12.0800 0.0031 1.058 7.26 568.6226 0
238 781.8557 425.5675 160736.9 355.235 -13.0153 0.0024 115604.4 241.649 -12.6574 0.0023 1.049 7.30 570.6792 2
239 802.5657 417.7780 42548.41 233.0482 -11.5722 0.0059 31220.35 150.4933 -11.2361 0.0052 1.048 11.23 570.8036 2
240 810.9788 422.9886 2840.001 45.5655 -8.6333 0.0174 3300.061 103.9597 -8.7963 0.0342 1.005 -19.21 570.4293 2
241 564.5262 422.6582 47083.86 242.6338 -11.6822 0.0056 34664.4 155.2984 -11.3497 0.0049 1.110 7.35 568.935 2
242 571.9675 416.0224 1419.365 39.46109 -7.8802 0.0302 1865.187 101.0426 -8.1768 0.0588 1.017 0.00 569.0518 2
243 1367.2023 424.6882 3735.087 153.5798 -8.9308 0.0447 3038.459 103.3769 -8.7066 0.0369 1.319 8.97 571.564 0
244 1090.5992 416.0958 23976.4 195.2232 -10.9495 0.0088 18779.25 131.7445 -10.6842 0.0076 1.103 15.61 568.752 2
245 1085.5693 402.4745 57652.69 254.1403 -11.9020 0.0048 42224.75 165.2104 -11.5639 0.0042 1.057 7.30 568.8077 2
246 831.7541 414.9341 11039.82 182.4255 -10.1074 0.0179 8196.661 113.5596 -9.7841 0.0150 1.099 18.34 569.8548 0
247 1074.3198 451.4497 3831.49 147.4924 -8.9584 0.0418 3206.203 103.8164 -8.7650 0.0352 1.075 8.78 568.6868 0
248 732.5168 416.2176 1549.591 138.3827 -7.9755 0.0970 1400.423 99.98013 -7.8656 0.0775 1.445 10.10 570.7856 0
249 907.7534 417.2511 346.9641 64.5695 -6.3507 0.2021 860.5858 98.86326 -7.3370 0.1248 1.483 4.70 568.7692 0
250 711.3885 393.5685 1364846 838.5897 -15.3377 0.0007 977822.8 650.9692 -14.9757 0.0007 1.011 7.31 569.9722 2
251 736.8256 384.7282 8860.46 193.6435 -9.8686 0.0237 6082.245 109.4829 -9.4602 0.0195 1.064 10.53 570.1913 2
252 217.6064 407.2765 8858.327 173.1173 -9.8684 0.0212 6928.146 111.1078 -9.6015 0.0174 1.071 9.65 568.5673 0
253 208.3666 454.0331 357.7236 58.98864 -6.3839 0.1791 323.6797 97.77405 -6.2753 0.3280 1.882 4.89 568.6995 0
254 1170.4919 396.6587 51402.02 244.4799 -11.7775 0.0052 38623.3 160.5981 -11.4671 0.0045 1.048 7.34 568.8523 0
255 889.1747 397.5316 3684.913 166.21 -8.9161 0.0490 2879.372 103.0826 -8.6482 0.0389 1.115 9.74 568.9166 0
256 1.1751 401.0359 242.7468 27.27782 -5.9629 0.1220 67.24962 73.58174 -4.5692 1.1883 1.694 2.88 570.961 24
257 1189.6937 389.5130 2875.329 157.9382 -8.6467 0.0597 2297.169 102.0587 -8.4030 0.0482 1.202 9.95 569.0104 0
258 811.7170 377.7045 177848.5 367.8935 -13.1251 0.0022 129516.2 253.6119 -12.7808 0.0021 1.035 7.25 569.8939 0
259 547.8994 375.2592 181846.6 349.5311 -13.1493 0.0021 134666.3 257.8654 -12.8231 0.0021 1.119 7.97 568.8017 2
260 1534.8395 391.1724 255.8132 40.63386 -6.0198 0.1725 134.4803 80.01255 -5.3216 0.6461 1.262 3.60 578.1884 24
261 1436.5868 385.0678 11243.42 178.4281 -10.1272 0.0172 8773.057 114.5718 -9.8579 0.0142 1.149 7.88 573.7438 0
262 1100.3826 374.7240 64256.14 269.967 -12.0198 0.0046 46837.13 171.0133 -11.6765 0.0040 1.120 7.37 568.8514 2
263 1102.9727 364.0503 1087.556 38.46878 -7.5911 0.0384 1645.986 100.5654 -8.0411 0.0664 1.017 4.29 568.8864 2
264 480.7602 375.0351 78609.08 280.5967 -12.2387 0.0039 57937.47 184.3521 -11.9074 0.0035 1.054 7.78 568.4489 2
265 482.9031 364.1710 530.5693 34.43391 -6.8119 0.0705 600.8499 98.30507 -6.9469 0.1777 1.572 1.46 568.5609 2
266 615.4128 336.8404 180890.3 370.3799 -13.1435 0.0022 131124.7 254.9064 -12.7942 0.0021 1.016 7.27 569.5464 2
267 617.8385 364.4600 436379.6 522.1233 -14.0997 0.0013 269405.6 351.517 -13.5760 0.0014 1.255 9.82 569.4128 2
268 628.9664 354.0240 1460.982 39.61598 -7.9116 0.0294 1759.754 100.8213 -8.1136 0.0622 1.016 4.33 569.3725 2
269 285.4190 374.7091 10895.07 188.902 -10.0931 0.0188 8068.655 113.2029 -9.7670 0.0152 1.042 8.47 568.2696 0
270 1377.7532 369.9927 28045.46 211.2512 -11.1197 0.0082 21302.69 135.7787 -10.8211 0.0069 1.064 8.10 572.4717 0
271 1023.7278 374.8381 2088.633 153.0091 -8.2997 0.0796 1594.151 100.423 -8.0063 0.0684 1.278 12.90 569.0493 2
272 1013.3053 370.1889 2671.93 175.8889 -8.5671 0.0715 1712.699 100.6231 -8.0842 0.0638 1.262 14.59 569.1161 2
273 1022.7167 364.7001 445.9181 31.97025 -6.6231 0.0779 1252.126 99.84902 -7.7441 0.0866 1.689 0.00 569.0895 2
274 1019.2045 358.3472 15106.4 188.3152 -10.4479 0.0135 11575.32 119.6137 -10.1588 0.0112 1.024 19.17 569.1374 2
275 1338.3918 368.8807 4386.3 122.1571 -9.1052 0.0302 4504.04 106.3224 -9.1340 0.0256 1.180 8.05 570.9123 2
276 1343.9404 355.2447 99384.16 306.3449 -12.4933 0.0033 70730.46 198.4435 -12.1240 0.0030 1.054 10.09 571.2734 2
277 1422.9534 361.1173 83330.1 287.369 -12.3020 0.0037 59944.61 186.591 -11.9444 0.0034 1.093 7.76 573.4723 0
278 759.2888 358.0734 108543.5 321.1349 -12.5890 0.0032 78283.44 206.4305 -12.2342 0.0029 1.065 9.72 569.5952 2
279 733.7847 343.8413 109413.1 314.6581 -12.5977 0.0031 78997.13 207.0974 -12.2440 0.0028 1.040 7.24 569.4623 2
280 719.1465 324.1569 85956.32 289.5103 -12.3357 0.0037 62678.29 189.6608 -11.9928 0.0033 1.042 7.27 569.406 2
281 1118.8661 365.8265 526.3643 34.47257 -6.8032 0.0711 981.6555 99.13918 -7.4799 0.1097 1.546 3.92 568.8647 2
282 1119.0170 360.1693 8536.745 174.5052 -9.8282 0.0222 6640.842 110.6038 -9.5556 0.0181 1.060 17.46 568.893 2
283 844.8472 354.6751 16563.23 191.5363 -10.5479 0.0126 12698.18 121.6547 -10.2594 0.0104 1.051 7.75 569.4832 0
284 976.0650 358.2110 1135.64 117.0833 -7.6381 0.1120 979.5918 99.13477 -7.4776 0.1099 1.361 8.70 569.179 0
285 353.1110 350.8444 64952.19 262.6889 -12.0315 0.0044 47865.64 172.3601 -11.7001 0.0039 1.056 8.76 568.0709 0
286 796.7365 349.0502 7564.784 182.1021 -9.6970 0.0261 5495.489 108.3876 -9.3500 0.0214 1.029 9.27 569.4794 2
287 812.9947 347.9868 2880.34 45.74181 -8.6486 0.0172 3409.593 104.1027 -8.8318 0.0332 1.001 0.00 569.4793 2
288 810.3277 336.3240 103828.5 306.249 -12.5408 0.0032 76241.59 204.316 -12.2055 0.0029 1.029 7.32 569.4651 2
289 513.1359 347.9854 14550.69 173.8364 -10.4072 0.0130 11714.78 119.8882 -10.1718 0.0111 1.135 17.73 568.8051 0
290 164.9871 321.0194 1750.191 40.78201 -8.1077 0.0253 2258.42 101.8311 -8.3845 0.0490 1.004 0.00 570.0052 2
291 152.7275 333.9623 967580 723.5369 -14.9642 0.0008 689550.7 549.1677 -14.5964 0.0009 1.044 7.33 569.9282 2
292 563.7424 373.7921 804740.8 658.7786 -14.7641 0.0009 579714.4 505.0291 -14.4080 0.0009 1.073 7.25 568.9684 2
293 923.4663 321.3381 184923.3 368.6769 -13.1675 0.0022 134805.4 257.9797 -12.8243 0.0021 1.050 7.23 569.222 2
294 906.1515 316.4818 61724.25 256.9528 -11.9761 0.0045 45131.22 168.9458 -11.6362 0.0041 1.054 7.10 569.3285 2
295 52.7376 328.2247 3178.323 173.441 -8.7555 0.0593 2289.099 101.9113 -8.3992 0.0483 1.108 10.84 570.6279 0
296 1013.0151 321.7200 45613.11 238.2446 -11.6477 0.0057 33699.19 153.8786 -11.3190 0.0050 1.066 12.37 569.3107 0
297 677.4539 311.6614 166634.5 356.0636 -13.0544 0.0023 121893.5 247.1216 -12.7150 0.0022 1.043 8.74 569.3425 0
298 139.6216 285.3202 190621.8 387.9835 -13.2004 0.0022 136355.2 259.1915 -12.8367 0.0021 1.012 8.00 570.6309 2
299 115.0030 294.0279 1384.718 39.3357 -7.8534 0.0309 1912.935 101.0768 -8.2043 0.0574 1.003 4.28 570.6147 2
300 121.9895 296.0339 3054.5 46.49905 -8.7123 0.0165 3300.094 104.0238 -8.7963 0.0342 1.002 4.29 570.5864 2
301 128.9980 312.0324 72562.78 178.674 -12.1518 0.0027 72936.48 200.7849 -12.1574 0.0030 1.058 0.00 570.426 6
302 119.2280 306.9764 199994.7 379.1064 -13.2525 0.0021 145090.4 266.2673 -12.9041 0.0020 1.070 11.43 570.5252 2
303 1179.9917 297.0321 829.5106 29.61928 -7.2971 0.0388 1308.128 99.88445 -7.7916 0.0829 1.002 0.00 569.519 2
304 1358.4225 299.0651 202844.7 397.0564 -13.2679 0.0021 126344.2 250.8751 -12.7539 0.0022 1.434 9.30 571.9699 0
305 1264.0242 298.2581 65749.29 267.6499 -12.0447 0.0044 47681.85 172.1147 -11.6959 0.0039 1.026 7.84 570.118 2
306 1276.4452 294.9617 10426.65 155.0993 -10.0454 0.0162 9215.116 115.444 -9.9113 0.0136 1.149 8.81 570.163 2
307 1176.1322 303.9489 26919.94 216.1402 -11.0752 0.0087 19232.68 132.5722 -10.7101 0.0075 1.050 9.00 569.4788 2
308 466.2436 301.3683 2154.187 137.4185 -8.3332 0.0693 1852.551 101.0491 -8.1694 0.0592 1.010 11.69 569.3735 0
309 325.1265 294.9048 23842.98 216.8451 -10.9434 0.0099 17060.08 129.0921 -10.5800 0.0082 1.140 21.41 569.0575 2
310 311.0523 270.1046 211589.1 395.894 -13.3137 0.0020 151300.1 271.2001 -12.9496 0.0019 1.036 7.36 569.3192 2
311 313.7943 242.7544 492948.3 545.214 -14.2320 0.0012 352365.7 398.3928 -13.8675 0.0012 1.028 7.58 569.5616 2
312 894.1555 290.7959 11031.85 178.5293 -10.1066 0.0176 8546.412 114.1373 -9.8295 0.0145 1.086 11.07 569.4784 0
313 966.5088 291.4034 6475.713 158.1146 -9.5282 0.0265 5326.547 107.9644 -9.3161 0.0220 1.038 15.59 569.4783 0
314 520.3867 283.6607 153902.1 346.2231 -12.9681 0.0024 113079.5 239.432 -12.6335 0.0023 1.044 7.26 569.9358 0
315 788.8865 273.1897 551448.3 576.9519 -14.3538 0.0011 383958.8 414.8498 -13.9607 0.0012 1.227 7.52 569.3985 2
316 1189.0786 280.1242 11758.17 178.7383 -10.1758 0.0165 9116.692 115.3499 -9.8996 0.0137 1.079 8.00 569.6844 0
317 36.5474 278.7976 8536.089 172.5201 -9.8281 0.0219 6617.764 110.4842 -9.5518 0.0181 1.100 16.87 570.6779 0
318 1.3234 284.0191 437.1339 32.06957 -6.6015 0.0797 398.7043 75.41849 -6.5016 0.2054 1.514 0.00 570.6367 24
319 1.9320 279.9697 582.9242 40.21189 -6.9140 0.0749 397.1719 79.31053 -6.4974 0.2169 1.020 0.00 570.6588 24
320 597.5209 271.0217 4408.013 154.1752 -9.1106 0.0380 3604.448 104.5463 -8.8921 0.0315 1.107 10.03 570.262 0
321 731.1889 262.5690 26773.21 209.3516 -11.0693 0.0085 20092.54 133.9268 -10.7576 0.0072 1.044 9.83 569.3985 0
322 1483.4398 261.6202 27310.42 213.6566 -11.0908 0.0085 20504.99 134.553 -10.7796 0.0071 1.042 7.99 576.5723 0
323 1348.4666 264.9120 1394.505 125.2177 -7.8611 0.0975 1296.196 99.90916 -7.7817 0.0837 1.149 9.93 571.7993 0
324 1193.5824 260.2585 12899.72 178.7833 -10.2765 0.0151 10308.98 117.4202 -10.0330 0.0124 1.078 17.68 569.9075 0
325 1046.4960 255.6492 39379.19 229.6317 -11.4882 0.0063 29103.74 147.5738 -11.1599 0.0055 1.018 11.01 569.6838 0
326 456.9798 257.0255 30054.88 271.2838 -11.1948 0.0098 10341.09 117.4781 -10.0364 0.0123 2.108 42.33 569.8321 2
327 451.9934 244.0021 9757.63 70.44401 -9.9734 0.0078 10191.41 117.0799 -10.0206 0.0125 1.002 4.21 569.9363 2
328 440.2356 246.5394 177785.4 334.1463 -13.1247 0.0020 146835 267.6394 -12.9171 0.0020 1.082 7.42 569.746 2
329 435.2433 246.9858 21099.26 98.79065 -10.8107 0.0051 21072.84 135.4442 -10.8093 0.0070 1.023 4.44 569.6832 2
330 393.5028 249.1606 275009.5 431.1631 -13.5984 0.0017 198574.8 305.8777 -13.2448 0.0017 1.043 7.27 569.4543 0
331 797.9958 260.0139 2107.441 42.33088 -8.3094 0.0218 2780.44 102.8305 -8.6103 0.0402 1.002 0.00 569.3985 2
332 574.8161 248.9913 189423.4 374.2015 -13.1936 0.0021 137804.3 260.3733 -12.8482 0.0021 1.038 7.30 570.5038 0
333 943.6876 244.2561 86054.28 294.3093 -12.3369 0.0037 61322.85 188.2025 -11.9691 0.0033 1.094 14.64 570.4471 2
334 963.0655 237.6504 114299 312.7988 -12.6451 0.0030 82845.09 211.0051 -12.2957 0.0028 1.068 11.95 570.7387 2
335 911.1133 244.2430 204272.2 386.5289 -13.2755 0.0021 147975 268.5651 -12.9255 0.0020 1.026 7.26 570.2999 2
336 922.7039 229.1774 10821.01 140.2647 -10.0857 0.0141 10160.08 117.0801 -10.0172 0.0125 1.261 8.56 570.5997 2
337 929.9926 227.7715 1299.844 35.67518 -7.7847 0.0298 1530.189 100.3212 -7.9619 0.0712 1.051 4.00 570.6433 2
338 930.1562 220.0732 42571.76 236.9654 -11.5728 0.0060 30931.96 150.0646 -11.2260 0.0053 1.047 22.11 570.709 2
339 1096.6111 250.3318 14695.78 181.2898 -10.4180 0.0134 11651.03 119.7755 -10.1659 0.0112 1.116 18.14 569.7451 0
340 1512.2275 249.4871 8107.574 175.0377 -9.7722 0.0234 6265.945 109.8075 -9.4925 0.0190 1.061 8.43 578.4499 0
341 1183.3364 239.7057 76746.91 279.5199 -12.2127 0.0040 56157.15 182.2764 -11.8735 0.0035 1.050 7.81 570.0289 0
342 619.6721 244.7971 9895.577 177.5409 -9.9886 0.0195 7646.876 112.4551 -9.7087 0.0160 1.057 7.91 570.4999 0
343 1370.8412 233.6943 167184.3 360.2471 -13.0580 0.0023 121536.9 246.8291 -12.7118 0.0022 1.042 7.27 572.6031 0
344 1.2118 246.0035 174.974 32.32819 -5.6074 0.2006 212.4916 74.13367 -5.8184 0.3789 1.596 0.00 570.8431 24
345 682.3170 234.0578 37518.34 235.8787 -11.4356 0.0068 26890.65 144.327 -11.0740 0.0058 1.080 9.61 569.3985 0
346 1005.0590 228.9340 158891.4 351.4758 -13.0028 0.0024 116547.8 242.5227 -12.6663 0.0023 1.037 7.27 570.9686 0
347 882.7033 213.8188 55399.46 251.6355 -11.8588 0.0049 41455.98 164.2114 -11.5440 0.0043 1.046 8.70 570.5965 0
348 632.9984 215.0914 40316.77 238.7078 -11.5137 0.0064 28575.26 146.6542 -11.1400 0.0056 1.039 15.25 570.6185 2
349 655.6232 197.3575 1331284 831.4123 -15.3107 0.0007 956413.2 643.9558 -14.9516 0.0007 1.028 7.29 570.5131 2
350 1170.0375 211.3203 844.2399 94.70972 -7.3162 0.1218 649.8874 98.42762 -7.0321 0.1645 3.910 7.05 570.2296 2
351 555.0073 204.9922 2823.515 45.49335 -8.6270 0.0175 3269.146 103.8005 -8.7861 0.0345 1.007 4.23 570.8909 2
352 561.3152 201.1822 10761.79 160.0405 -10.0797 0.0162 9178.183 115.304 -9.9069 0.0136 1.252 17.50 570.9749 2
353 563.6866 184.4685 273904.9 428.7455 -13.5940 0.0017 197445.8 305.122 -13.2386 0.0017 1.038 7.36 571.1664 2
354 1028.2812 183.5516 96340.16 309.1154 -12.4595 0.0035 67876.23 195.3981 -12.0793 0.0031 1.068 8.01 570.9269 2
355 1085.3414 195.9940 21030.13 177.4152 -10.8071 0.0092 18111.39 130.717 -10.6449 0.0078 1.098 8.00 570.3177 2
356 1073.3975 193.4199 78665.51 286.0262 -12.2395 0.0039 55514.94 181.4642 -11.8610 0.0035 1.070 7.40 570.3591 2
357 1042.1340 194.8650 2850.893 43.2994 -8.6375 0.0165 2950.613 103.3579 -8.6748 0.0380 1.525 3.88 570.5707 2
358 1049.4741 187.3801 270744.7 419.1121 -13.5814 0.0017 198394 305.7361 -13.2438 0.0017 1.055 7.49 570.5953 2
359 1044.0171 178.0286 6012.234 58.18803 -9.4476 0.0105 6055.064 109.5064 -9.4553 0.0196 1.009 4.28 570.8115 2
360 978.9670 182.0029 2377.048 43.52391 -8.4401 0.0199 2803.515 102.959 -8.6193 0.0399 1.009 0.00 571.2549 2
361 967.9719 185.9064 93792.54 241.3515 -12.4304 0.0028 88977.67 217.0523 -12.3732 0.0026 1.200 7.51 571.1441 2
362 961.5632 173.1210 769791.1 659.3442 -14.7159 0.0009 539952.6 488.0602 -14.3309 0.0010 1.080 7.22 571.0978 2
363 182.9546 191.1445 1010.256 111.5285 -7.5111 0.1199 1311.215 99.84097 -7.7942 0.0827 2.123 9.13 570.6021 0
364 1535.7856 211.9845 196.3294 29.76791 -5.7325 0.1647 -22.86891 73.65966 99.0000 99.0000 1.504 2.94 580.1351 24
365 820.1038 168.4550 5655.899 155.1218 -9.3813 0.0298 4663.142 106.8262 -9.1717 0.0249 1.165 7.31 570.3076 2
366 818.2520 162.4496 2899.06 69.94952 -8.6556 0.0262 3144.796 103.6589 -8.7440 0.0358 2.748 7.88 570.3539 2
367 1178.3666 160.8956 63389.95 265.1758 -12.0051 0.0045 46524.98 170.6652 -11.6692 0.0040 1.033 8.94 570.3905 2
368 1171.2831 166.7194 608.9612 26.1894 -6.9615 0.0467 1733.387 100.898 -8.0972 0.0632 2.186 0.00 570.3835 2
369 550.8932 122.7173 18722.64 222.6585 -10.6809 0.0129 12853.71 122.0208 -10.2726 0.0103 1.365 8.70 571.1688 2
370 520.6047 160.6883 82103.02 299.5721 -12.2859 0.0040 54531.83 180.2942 -11.8416 0.0036 1.116 25.02 571.0353 2
371 519.0179 132.5739 912884.3 698.5983 -14.9010 0.0008 655347.8 535.8287 -14.5412 0.0009 1.033 7.28 570.9686 2
372 509.0086 142.9893 8305.811 65.95502 -9.7985 0.0086 8452.188 113.9038 -9.8174 0.0146 1.001 0.00 570.9144 2
373 1286.2076 169.4518 971.8323 106.8517 -7.4690 0.1194 1042.715 99.2528 -7.5454 0.1034 1.438 7.78 571.1672 0
374 428.6366 156.2078 98740.4 299.8264 -12.4862 0.0033 72222.85 200.0471 -12.1467 0.0030 1.054 7.06 570.544 0
375 997.4131 155.9517 136362.3 336.0184 -12.8367 0.0027 98063.78 225.7618 -12.4788 0.0025 1.025 9.58 571.372 2
376 994.0093 146.0387 3277.538 47.45849 -8.7889 0.0157 3717.086 104.822 -8.9255 0.0306 1.010 -9.58 571.3903 2
377 34.0099 155.5276 894.6991 104.5387 -7.3792 0.1269 967.5167 99.09215 -7.4641 0.1112 1.462 5.92 572.3236 2
378 884.7037 146.8082 38697.22 226.8561 -11.4692 0.0064 29084.44 147.4106 -11.1592 0.0055 1.044 8.58 570.7449 0
379 1.3610 154.9976 440.6593 32.02853 -6.6103 0.0789 556.3204 76.05729 -6.8633 0.1485 1.507 0.00 572.9769 24
380 1338.3982 147.5683 2066.436 138.7165 -8.2881 0.0729 1827.728 100.9146 -8.1548 0.0600 1.283 7.48 572.5853 0
381 293.4906 146.4948 1583.06 135.1851 -7.9987 0.0927 1316.641 99.96916 -7.7987 0.0825 2.073 8.32 570.2275 2
382 160.2618 131.1067 216017.2 395.7352 -13.3362 0.0020 155502.3 274.4389 -12.9793 0.0019 1.051 7.39 570.8848 0
383 613.0306 109.0300 1181.71 38.69101 -7.6813 0.0356 1604.092 100.4937 -8.0131 0.0680 1.008 0.00 571.5841 2
384 621.3865 111.8925 25946.74 214.3995 -11.0352 0.0090 19093.69 132.2744 -10.7022 0.0075 1.202 20.76 571.5451 2
385 633.0207 98.3087 100855.7 298.9932 -12.5093 0.0032 74268.09 202.1604 -12.1770 0.0030 1.029 7.30 571.44 2
386 630.5546 134.8887 47423.39 236.0201 -11.6900 0.0054 36015.05 157.1196 -11.3912 0.0047 1.066 9.29 571.538 2
387 635.9630 131.0171 3031.827 45.27918 -8.7043 0.0162 3322.637 104.0697 -8.8037 0.0340 1.200 0.00 571.4925 2
388 1531.2736 131.1324 69678.58 248.3193 -12.1077 0.0039 55227.28 180.4648 -11.8554 0.0035 1.201 9.72 581.8389 24
389 1245.1403 131.1902 95807.49 296.3319 -12.4535 0.0034 70150.93 197.8407 -12.1151 0.0031 1.035 8.09 570.9893 0
390 1376.2397 139.1044 1076.569 110.9689 -7.5801 0.1119 1135.228 99.51704 -7.6377 0.0952 1.186 7.86 573.8674 0
391 1402.4619 125.9489 23896.74 208.0053 -10.9458 0.0095 17813.17 130.2583 -10.6269 0.0079 1.045 11.57 574.4122 0
392 1.0000 133.4642 166.2103 34.25 -5.5516 0.2238 234.0493 72.81319 -5.9233 0.3379 4.013 3.40 573.178 24
393 580.3881 121.6143 52148.96 247.0223 -11.7931 0.0051 38764.68 160.712 -11.4711 0.0045 1.047 7.59 571.4103 0
394 312.8781 111.2738 690662.3 625.6754 -14.5982 0.0010 496446.8 468.8263 -14.2397 0.0010 1.035 7.34 570.3502 2
395 325.9893 103.0016 6505.127 59.93805 -9.5331 0.0100 6716.45 110.6131 -9.5678 0.0179 1.001 0.00 570.3976 2
396 655.8513 126.4709 1311.536 112.8107 -7.7945 0.0934 1433.575 100.1668 -7.8911 0.0759 1.104 6.37 571.3436 0
397 916.9801 116.9675 130770 328.1771 -12.7913 0.0027 95265.2 223.1275 -12.4473 0.0025 1.029 8.05 570.8182 0
398 1048.9640 117.2508 73612.95 270.6054 -12.1674 0.0040 55331.83 181.287 -11.8574 0.0036 1.022 7.27 571.0632 2
399 1056.9581 114.0051 1363.645 34.34037 -7.8368 0.0273 1896.536 101.0589 -8.1949 0.0579 1.253 3.73 571.0162 2
400 84.7752 124.9567 1266.644 118.8581 -7.7566 0.1019 1130.283 99.47303 -7.6330 0.0956 1.451 8.12 571.7458 2
401 840.4144 76.6228 50576.98 254.4429 -11.7599 0.0055 36624.43 157.9075 -11.4094 0.0047 1.023 7.40 570.9312 2
402 823.8599 98.9064 103374 310.4949 -12.5360 0.0033 74622.38 202.5889 -12.1822 0.0029 1.020 7.25 570.5626 2
403 1523.5181 108.3286 15290.81 194.584 -10.4611 0.0138 11470.31 119.5808 -10.1489 0.0113 1.042 17.63 582.5868 0
404 1330.0009 95.2369 468.1632 48.45803 -6.6760 0.1124 880.7438 98.87276 -7.3621 0.1219 1.155 0.00 573.067 2
405 1326.9956 110.9447 2715.5 45.01939 -8.5846 0.0180 3260.097 103.8782 -8.7831 0.0346 1.006 0.00 572.7901 2
406 1326.1752 103.7468 29883.56 212.8726 -11.1886 0.0077 22858.96 138.2098 -10.8976 0.0066 1.070 7.80 572.8781 2
407 1.4900 108.9697 240.1104 45.23544 -5.9510 0.2046 476.8479 76.79576 -6.6959 0.1749 1.525 1.47 573.3975 24
408 1491.5389 96.6756 45703.91 238.2865 -11.6499 0.0057 33464.83 153.6748 -11.3115 0.0050 1.046 11.90 580.2938 0
409 102.5414 97.3220 10481.43 173.0098 -10.0511 0.0179 8397.62 113.9631 -9.8104 0.0147 1.127 9.35 571.8409 0
410 1535.6304 117.0065 309.192 35.54433 -6.2256 0.1248 501.4726 75.97015 -6.7506 0.1645 1.522 -0.55 583.0645 24
411 1040.4235 98.1706 827.0355 100.9159 -7.2938 0.1325 973.799 99.13918 -7.4712 0.1106 1.499 7.23 571.1197 0
412 1055.5858 79.1706 85886.88 292.7718 -12.3348 0.0037 62530.26 189.5217 -11.9902 0.0033 1.045 7.21 571.0261 0
413 496.9105 82.1701 16291.8 187.4628 -10.5299 0.0125 12377.43 121.0811 -10.2316 0.0106 1.067 19.00 570.6656 0
414 205.3543 1015.6260 4226.593 167.546 -9.0650 0.0431 3021.728 103.4553 -8.7006 0.0372 1.302 9.34 569.0291 8
415 501.4073 1011.4348 3163.192 163.8322 -8.7503 0.0562 2373.049 102.0856 -8.4383 0.0467 1.084 12.00 565.4015 0
416 538.9880 60.2298 600.8334 33.98357 -6.9469 0.0614 1012.544 99.27229 -7.5135 0.1065 1.048 3.96 570.5885 2
417 1306.4246 78.2114 3535.864 183.1233 -8.8712 0.0562 2327.208 101.9905 -8.4171 0.0476 1.324 15.29 572.6646 0
418 684.1806 69.7900 33353.44 229.3654 -11.3079 0.0075 23104.09 138.537 -10.9092 0.0065 1.105 18.32 571.3856 2
419 1.9238 1013.7868 210.0515 28.76742 -5.8058 0.1487 -180.6892 78.15717 99.0000 99.0000 1.515 0.00 574.033 24
420 1282.5294 68.1601 49204.11 244.4585 -11.7300 0.0054 36616.36 157.8861 -11.4092 0.0047 1.054 7.59 572.2349 0
421 820.4248 117.1983 7615.113 173.1951 -9.7042 0.0247 5826.044 108.9555 -9.4134 0.0203 1.099 17.26 570.4926 2
422 1.1980 65.0146 165.2792 34.53007 -5.5455 0.2269 269.6117 74.18457 -6.0768 0.2988 1.719 1.28 574.0594 24
423 650.9710 1009.9269 1019.505 111.3722 -7.5210 0.1186 861.2838 98.84791 -7.3379 0.1246 1.363 8.17 566.0403 0
424 936.8433 996.0051 104504.7 306.6453 -12.5478 0.0032 76366.87 204.3725 -12.2073 0.0029 1.042 7.40 567.0234 0
425 1491.2788 57.6946 354.6474 25.63309 -6.3745 0.0785 1139.83 99.59374 -7.6421 0.0949 2.161 0.00 581.3596 2
426 377.0147 1002.9818 10916.38 73.83514 -10.0952 0.0073 11066.12 118.7784 -10.1100 0.0117 1.009 4.25 567.256 2
427 1197.0377 54.9860 442.4348 32.00846 -6.6146 0.0786 861.293 98.89846 -7.3379 0.1247 1.258 3.73 571.0234 2
428 589.1859 50.1661 23394.89 205.1717 -10.9228 0.0095 17537.61 129.8222 -10.6099 0.0080 1.098 10.57 570.9639 0
429 1001.0854 56.9053 524.0023 37.81151 -6.7983 0.0784 597.5091 98.46714 -6.9409 0.1790 1.150 4.09 571.3897 2
430 380.6473 998.3588 39402.54 227.1328 -11.4888 0.0063 29787.21 148.4508 -11.1851 0.0054 1.091 13.21 567.2253 2
431 1.8559 54.8980 365.1693 44.12769 -6.4062 0.1312 376.5965 78.91862 -6.4397 0.2276 1.140 0.00 574.2112 24
432 768.2953 976.8056 27158.29 207.7526 -11.0848 0.0083 21180.84 135.5639 -10.8149 0.0070 1.136 8.37 566.233 2
433 1535.0048 39.4898 479.8795 38.71117 -6.7028 0.0876 255.3535 79.28865 -6.0179 0.3372 1.066 0.08 586.5837 24
434 959.4097 36.7140 1779.281 138.9529 -8.1256 0.0848 1450.212 100.1022 -7.9036 0.0750 1.369 11.06 571.4473 0
435 772.9701 975.0129 9038.422 68.25625 -9.8902 0.0082 9325.734 115.6613 -9.9242 0.0135 1.008 0.00 566.2313 2
436 1.1504 983.0304 227.233 27.86953 -5.8912 0.1332 126.1798 73.50242 -5.2525 0.6326 1.847 0.00 573.3109 24
437 88.1465 29.1702 520.6266 34.52795 -6.7913 0.0720 642.0872 98.42775 -7.0190 0.1665 1.526 3.87 572.6284 2
438 659.8459 972.4583 14567.6 198.4455 -10.4085 0.0148 10406.72 117.5681 -10.0433 0.0123 1.117 10.72 566.2397 0
439 1.7105 32.0964 395.9899 36.92375 -6.4942 0.1013 427.3461 78.10104 -6.5769 0.1985 1.140 1.86 574.6057 24
440 122.4400 973.8329 246.0232 52.5806 -5.9774 0.2321 568.968 98.338 -6.8877 0.1877 1.698 4.59 570.1951 0
441 841.0043 956.0942 34144.66 225.252 -11.3333 0.0072 25276.79 141.8208 -11.0068 0.0061 1.033 7.80 566.5067 0
442 45.3218 26.2681 958.7429 107.5031 -7.4543 0.1218 959.4084 99.20919 -7.4550 0.1123 1.875 6.50 573.6808 2
443 1534.9882 960.0451 453.8096 44.00692 -6.6422 0.1053 345.3012 79.67508 -6.3455 0.2506 1.031 4.21 583.0381 24
444 573.7265 957.2314 437.9861 62.64963 -6.6037 0.1553 508.0921 98.071 -6.7649 0.2096 1.943 5.49 565.9006 0
445 165.1780 957.2151 831.5047 97.83089 -7.2997 0.1278 1136.04 99.50203 -7.6385 0.0951 1.823 7.66 569.3137 0
446 930.7224 943.0375 91258.63 291.0279 -12.4007 0.0035 66738.76 194.1265 -12.0609 0.0032 1.023 7.38 567.0641 0
447 17.2526 942.0139 7071.583 170.9299 -9.6238 0.0263 5435.622 108.2552 -9.3381 0.0216 1.141 9.60 572.0671 0
448 1535.7031 945.1575 242.7091 33.49449 -5.9627 0.1499 235.5076 74.89196 -5.9300 0.3454 1.601 0.00 583.1658 24
449 730.7506 943.6141 332.6407 61.88263 -6.3049 0.2020 659.4673 98.46515 -7.0480 0.1622 1.671 4.11 566.2906 0
450 156.4838 934.3063 2985.51 163.8574 -8.6875 0.0596 2283.285 102.0299 -8.3964 0.0485 1.200 11.06 569.4579 0
451 325.7133 923.8927 181777.8 370.1347 -13.1489 0.0022 132298.1 255.9318 -12.8039 0.0021 1.023 7.28 567.8268 0
452 393.7177 926.7001 5606.012 164.8685 -9.3716 0.0319 4468.123 106.4544 -9.1253 0.0259 1.243 15.86 566.8171 0
453 145.5013 919.8887 17029.11 196.3743 -10.5780 0.0125 12678.93 121.6896 -10.2577 0.0104 1.121 7.83 569.8 0
454 723.1345 899.0394 669788.9 619.2785 -14.5648 0.0010 481245.6 461.8769 -14.2059 0.0010 1.024 7.30 566.6635 0
455 628.3530 900.8157 120589.8 319.6886 -12.7033 0.0029 88367.04 216.4785 -12.3657 0.0027 1.063 7.34 566.5408 0
456 837.1782 908.3299 4010.753 155.5362 -9.0081 0.0421 3275.799 103.8942 -8.7883 0.0344 1.094 8.32 566.9343 0
457 516.3662 901.8062 31368.43 219.9729 -11.2412 0.0076 23330.52 138.9308 -10.9198 0.0065 1.059 7.39 566.1391 0
458 1.2684 908.9004 273.2072 31.62204 -6.0912 0.1257 196.3385 74.69193 -5.7325 0.4131 1.645 0.00 571.8723 24
459 1252.7832 903.8932 51281.44 246.8483 -11.7749 0.0052 37278.74 158.7305 -11.4287 0.0046 1.042 9.21 569.3575 0
460 603.3322 886.5198 1678.697 139.886 -8.0624 0.0905 1415.1 100.1776 -7.8770 0.0769 1.095 8.42 566.5366 0
461 842.5924 873.8029 50785.86 280.223 -11.7644 0.0060 33316.79 153.3186 -11.3067 0.0050 1.526 7.49 567.341 2
462 829.3594 867.0640 2838.523 88.99777 -8.6327 0.0340 3218.747 103.8099 -8.7692 0.0350 1.319 8.87 567.4587 2
463 825.4636 867.4711 690.4557 44.81046 -7.0978 0.0705 1060.704 99.39177 -7.5640 0.1018 1.199 0.06 567.4709 2
464 222.3049 868.3086 103594.5 306.8633 -12.5383 0.0032 76833.48 204.9207 -12.2139 0.0029 1.031 22.25 569.9885 0
465 44.9636 871.8757 12457.84 179.3246 -10.2386 0.0156 9645.13 116.1589 -9.9608 0.0131 1.066 18.24 571.3076 0
466 1408.2908 875.7048 553.3074 48.71286 -6.8574 0.0956 874.0866 99.02682 -7.3539 0.1230 1.333 0.00 573.408 2
467 1417.2190 866.9792 855.8945 38.32928 -7.3311 0.0486 1391.751 100.0284 -7.8589 0.0781 2.623 4.75 573.611 2
468 1413.9711 871.9753 3984.324 50.41391 -9.0009 0.0137 4527.437 106.4629 -9.1396 0.0255 1.013 4.26 573.5486 2
469 1408.8536 866.5915 28416.21 209.3476 -11.1339 0.0080 21565.12 136.1998 -10.8344 0.0069 1.040 9.35 573.4162 2
470 1533.5531 855.3389 1589.414 121.8982 -8.0031 0.0833 1374.105 90.1277 -7.8450 0.0712 1.297 10.28 581.638 24
471 284.4399 838.0594 1110582 771.53 -15.1139 0.0008 796227.3 588.8948 -14.7526 0.0008 1.023 7.28 568.7106 0

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Lab 4/cluster1.fits
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Lab 5/Bfilt.dat
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# <p style=\"text-align: center;\">PHYS 134L Spring 2022 Lab 5</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-danger\"><b>Due date:</b> Sunday, May 8th, 2022 by 11:59pm, submitted through Gradescope.</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Names: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Enter your name and your partner's name here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this lab we will start exploring how photometry can teach us about the fundamental properties of stars. To do this we'll start by considering their spectra, and what we can learn about the spectra from two images in different filters. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 1: Stellar Spectra</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first part of this lab will be an introduction to spectra. Astronomical data comes in two basic forms: images and spectra. You have already seen images. Spectra are a bit different: we lose at least some of our ability to resolve an object and see its shape, but we spread out its light into its colors, or wavelengths. The intro slides to this lab included a spectrum as it appears on a detector. It is a colored spectrum of the Sun, showing many black parts where there is less light. These are absorption lines and give a whole lot of information about the physics of the Sun. \n",
"\n",
"Just like Source Extractor takes the images and extracts the positions and brightnesses of stars, we can extract the flux of a star as a function of wavelength. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this part of the lab, you will use three spectra contained in the files ```spectrum1.dat```, ```spectrum2.dat```, and ```spectrum3.dat```. The spectra are of three stars. The data files have two columns: the first is wavelength in Angstroms ($1~{\\rm \\AA}=10^{-10}$~m), and the second is flux density in units of erg/s/cm<sup>2</sup>/$\\AA$. \n",
"You may read the files using, e.g.,\n",
"```\n",
"spectrum = np.loadtxt(specfile)\n",
"lam = spectrum[:, 0]\n",
"flam = spectrum[:, 1]\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Please be aware that ```lambda``` has a special meaning within python, so don't try to define it as a variable!\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Make a plot of each star's spectrum as a function of wavelength. Please label the figures nicely using appropriate labels. For example: \n",
"```\n",
"plt.xlabel(r'Wavelength ( $ \\AA $ )'\n",
"```\n",
"\n",
"The ```r``` before the string tells matplotlib that it should use Latex to render this. Please get the units right for the vertical axis. Hint: if you are unsure of how to write a symbol in Latex, try [http://detexify.kirelabs.org](http://detexify.kirelabs.org). "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's try to learn something about these stars. We can try to approximate the stars as blackbodies using the Planck function (look it up in Wikipedia). **Write down the Planck function in a markdown cell in your notebook so that it has as close as possible to the same units as the flux density of your spectra (i.e.~make sure it's per Angstrom, not per Hertz or per nm).** The units won't be completely identical: the Planck function will still be per steradian. This will be important soon."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**By eye, find the temperature and normalization of the Planck function that best fits each stellar spectrum.** You should choose the temperature that gives a good fit to the peak wavelength (a blackbody isn't a great fit to ```spectrum2.dat``` for reasons that we will discuss later), and multiply the Planck function by a number to put it on the same scale as your spectrum. This number will be very small. Make a plot with the three stellar spectra again, with your best-fit Planck functions overplotted. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You have fit two parameters by eye to each star's spectrum: the temperature and a normalization factor to the Planck function. What units does your normalization constant need to have in order for the units to work out? What is the physical meaning of this value?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 2: Stellar Colors</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Many factors influence the appearance of a star’s emitted energy spectrum, but the most important is the stellar temperature. You already saw this in Part 1: the three stars have almost the same chemical composition, but their spectra look very different. Their surface temperatures range from around 4000K to around 10000K: Spectrum 1 is from a $\\sim$ 5000K star, Spectrum 2 is from a $\\sim$ 9500K star, and Spectrum 3 is from a $\\sim$ 6200K star."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The cluster images that you have been looking at, however, are not spectra. The telescope takes the light from the stars, focuses it, and uses a filter to let only some colors through. Only photons within a specified wavelength range actually make it onto the detector. Here we will investigate how the visible-light spectrum changes with temperature, and how these changes are manifested in the stars’ photometric colors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Lab 5 directory contains three filter files and three additional stellar spectra. The stars are at three different temperatures:\n",
"\n",
"```f05.dat``` = 9550K\n",
"\n",
"```f10.dat``` = 6110K\n",
"\n",
"```f15.dat``` = 4350K\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These new files contain the energy flux $F_\\lambda$ (proportional to ${\\rm erg}\\,{\\rm s}^{-1}\\,{\\rm cm}^{-2}\\,{\\rm \\AA}^{-1}$), where wavelength $\\lambda$ is measured in Angstroms (${\\rm \\AA}$), and $1~{\\rm Angstrom} = 0.1~{\\rm nm}$. The flux values have been arbitrarily normalized so they have a value of 100 units near 5500\\,${\\rm \\AA}$. Remember from Part 1 that the normalization of the stellar spectrum told you the angular diameter of the star on the sky. The shape of the spectrum tells you about the physical conditions of the star, mainly its temperature and chemical composition. \n",
"\n",
"Take the spectra of the three stars ```f05.dat```, ```f10.dat```, and ```f15.dat```, and plot them together on the same graph, using different colors. Also plot the Planck functions at these three temperatures on the same axes. You will notice that the hottest star is a particularly poor match to the blackbody; this is due to the hydrogen in the star's atmosphere."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using a CCD detector with colored filters, we measure the energy flux from stars integrated over the bandpass of each filter:\n",
"\n",
"\\begin{equation*}\n",
" F = \\int_0^\\infty T[\\lambda] F_\\lambda d\\lambda,\n",
"\\end{equation*}\n",
"\n",
"where $T[\\lambda]$ is called the *transfer function* and describes how efficiently we record energy from photons of a given wavelength. $T[\\lambda] = 1$ means that our instrument records every photon at a given wavelength, while $T[\\lambda] = 0$ means that it never records a single photon. **We will do the integrals for the filters $B$ and $V$.** It's worth spending a bit of time on how to do an integral numerically, as this is something many of you will have to do again and again."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The integral is defined as the limit of the Riemann sum,\n",
"\n",
"\\begin{equation*}\n",
" \\int_a^b f(x) dx = \\lim_{N \\rightarrow \\infty} \\sum_{i = 0}^{N - 1} f[x_i] \\Delta x_i,\n",
"\\end{equation*}\n",
"where $\\Delta x_i$ is the spacing between values of $x_i$, $x_0 = a$, and $x_N = b$. Let's see how we can write this in python. First, we'll define $x$ to run from $a$ to $b$ with $N + 1$ points in total. For now, define $a = 0$, $b = 1$, and $N = 1000$ (we'll change these later when we actually integrate over the band passes).\n",
"```\n",
"x = np.linspace(a, b, N + 1)\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now check: use the print function to verify that ```x[0] = a``` and ```x[N] = b```. In your case, the spacing is uniform, so $\\Delta x_i$ is the same for all points $i$. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now use your value for $\\Delta x$, the ```numpy``` function ```sum```, and your values of ```x``` to numerically evaluate the integral\n",
"\n",
"\\begin{equation*}\n",
" \\int_0^1 \\sin x dx\n",
"\\end{equation*}\n",
"\n",
"and compare to the actual value of the integral. Remember that your (left) Riemann sum should stop at $N - 1$, which you can write using index notation as ```[:N]```. Show that your answer is closer to the truth if $N = 2000$, but is farther from the truth if $N = 500$.\n",
"\n",
"Now we can do an integral numerically, but how do we integrate \n",
"\n",
"\\begin{equation*}\n",
" F = \\int_0^\\infty T[\\lambda] F_\\lambda d\\lambda? \n",
"\\end{equation*}\n",
"\n",
"We need to define a wavelength array, and then be able to call $T[\\lambda]$ and $F[\\lambda]$ just as we did above with sine. We can do this by first reading in the data files and then *interpolating* between the data points. We will use the package ```scipy.interpolate```, and we will use cubic polynomials (called *splines*) to interpolate:\n",
"\n",
"```from scipy import interpolate```\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From this point, ```python``` actually makes our lives pretty easy. First, let's read in one of the spectral files (first column is wavelength, second column is flux density $F_\\lambda$):\n",
"```\n",
"spec_data = np.loadtxt('f05.dat')\n",
"```\n",
"and then\n",
"```\n",
"Flam = interpolate.interp1d(spec_data[:, 0], spec_data[:, 1], kind='cubic')\n",
"```\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now ```Flam``` is a function that you can call just like ```np.sin```. Calling this function will return an error if you ask it for the value outside the range of $x$-values you supplied to ```interpolate.interp1d```. **For the transfer function, we may assume that it is zero outside of the wavelength range given. Read the documentation page (check the keywords ```bounds_error``` and ```fill_value```) to make the function behave in this way.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we are ready to compute magnitudes. **Use the tools you have developed above to integrate the three spectra over the transfer functions given by ```Bfilt.dat``` and ```Vfilt.dat```.** The definition of magnitude includes a zero point:\n",
"\n",
"\\begin{equation*}\n",
" M = -2.5 \\log_{10} F - Z.\n",
"\\end{equation*}\n",
"\n",
"For now, ignore the zero points $Z$ (let $Z=0$). What are the magnitudes of the three stars in the two bands? Please fill in the following table. Also, please compute the difference between the $B$ and $V$ band magnitudes (the $B-V$ color). This is the ratio between the flux in the $B$ band and the flux in the $V$ band."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---| ```f05.dat``` | ```f10.dat``` | ```f15.dat1```\n",
"---|---|---|---\n",
"B |---|---|---\n",
"V |---|---|---\n",
"B-V |---|---|---\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Does a high value of $B-V$ indicate a star that is very blue (puts out lots of blue light relative to yellow/green light), or a star that is very red?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the qualitative relation between temperature and B − V color?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now you can image that only using images of a star in two filters, we can learn a lot about its fundamental properties! "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So colors provide a way to estimate stellar temperatures. Suppose we know the temperature -- then what else do we know? Stellar evolution theory provides relations between the characteristics of stars at the time they are born (mass and composition), and their properties (including temperature and luminosity) at any time in their later lives. We'll explore this more in Lab 6. For a quick introduction to (or refresher on)\n",
"many of the basic notions, see [here](http://www.tim-thompson.com/hr.html). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

24
Lab 5/Vfilt.dat
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@ -1,24 +0,0 @@
4700.0 0.0000000000
4800.0 0.0300000000
4900.0 0.1630000000
5000.0 0.4580000000
5100.0 0.7800000000
5200.0 0.9670000000
5300.0 1.0000000000
5400.0 0.9730000000
5500.0 0.8980000000
5600.0 0.7920000000
5700.0 0.6840000000
5800.0 0.5740000000
5900.0 0.4610000000
6000.0 0.3590000000
6100.0 0.2700000000
6200.0 0.1970000000
6300.0 0.1350000000
6400.0 0.0810000000
6500.0 0.0450000000
6600.0 0.0250000000
6700.0 0.0170000000
6800.0 0.0130000000
6900.0 0.0090000000
7000.0 0.0000000000

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Lab 5/f05.dat
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Lab 5/f10.dat
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Lab 5/f15.dat
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2468
Lab 5/spectrum1.dat
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Lab 5/spectrum2.dat
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Lab 6/Lab 6.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# <p style=\"text-align: center;\">PHYS 134L Spring 2022 Lab 6</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-danger\"><b>Due date:</b> Sunday, May 15th, 2022 by 11:59pm, submitted through Gradescope.</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Names: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Enter your name and your partner's name here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From last lab, we now know that colors provide a way to estimate stellar temperatures. Suppose we know the temperature -- then what else do we know? Stellar evolution theory provides relations between the characteristics of stars at the time they are born (mass and composition), and their properties (including temperature and luminosity) at any time in their later lives. \n",
"\n",
"In this lab, we will explore how we can learn even more about a set of stars just using two-color photometry, the Hertzsprung Russell diagram and stellar evolutionary models. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 1: Stellar Evolutionary Tracks</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For a quick introduction to (or refresher on) many of the basic notions, see [here](http://www.tim-thompson.com/hr.html). \n",
"\n",
"For a more quantitative picture of stellar evolution, consider the files ```evol_M0.8.dat```, ```evol_M1.0.dat```, ```evol_M1.3.dat```,```evol_M1.8.dat```, and ```evol_M2.6.dat. These contain evolutionary tracks for stars with compositions similar to the Sun's and with masses of 0.8, 1.0, 1.3, 1.8, and 2.5 times the mass of the\n",
"Sun. The columns of the tables contain $\\log_{10}(Temperature~(K))$, $\\log_{10}(Luminosity~(solar~units)$), and Age (in Gyr). Notice (by opening one of the files in a text editor) that the range of ages in the various tables is fairly wide -- massive stars live for much shorter times than low-mass ones, though they are much more luminous. They burn brightly but burn out quickly."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Make a plot that shows the evolutionary tracks for all 5 stars overplotted on one graph. Use different colors to distinguish the different masses, and (for once) connect the points with straight lines, using no symbols. Make the x-axis log(Temperature), but make Temperature increase from right to left. (Because that’s the way astronomers do it. Don’t ask.) Make the y-axis log(Luminosity), increasing from bottom to top. On the track for the 1-solar-mass star mark the following points with text integers 1-5 the following locations: (1) Arrival on the main sequence. (2) Turnoff from the main sequence. (3) Beginning of the subgiant branch. (4) Base of the giant branch. (5) Tip of the giant branch.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Now make the same plot again, only make all of the curves black, and do not provide any annotating integers. In each of the five data files, identify the point at which the age of the star is 10 million years old (0.01 Gyr). Create two arrays, giving log(Temperature) and log(Luminosity) for each of the stars at this age. Overplot this (jagged, because there are not very many points on it) curve, using a heavy green line. This is the 10-million-year isochrone (line of constant age). If you start with a group of stars (the members of a star cluster, say) that have the same initial composition and are formed at nearly the same time, then 10 million years later, you will see the stars of different masses strung out along this isochrone. In the same way, plot isochrones for ages of 0.1 Gyr, 0.6 Gyr, and 5.0 Gyr.**"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What do you think it means if the oldest age in a table is smaller than one of these isochrone ages?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Do a similar plot, but this time use only the data for the 1-solar-mass star (```evol_M1.0.dat```). Create an array that contains only the lines that lie as close as you can come to ages that are integer multiples of 1 Gyr, up to 12 Gyr. Overplot this table onto the original curve, using suitable symbols, but no lines connecting the points.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your Answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**About what fraction of this star’s life is spent on the main sequence? What fraction on the giant branch?**\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## <p style=\"text-align: center;\">Part 2: Make you own HR Diagram</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we’re going to process some real data. We'll be using data on M67 found in the lab directory: ```M67_B.fits``` and ```M67_V.fits```. The files contain images of the Messier 67 object in the *B* and *V* filters, respectively. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Google around a bit to learn about the Messier catalog. **Describe it in your own words:**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What kind of object is Messier 67?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I highly recommend you spend some time browsing some images of the Messier Catalog (look up the Hubble Space Telescope Messier Catalog) just for fun! They are gorgeous astronomical objects!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Use ```photutils``` like you did in Lab 4 to extract the photometry from the B and V-band images.**"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once you have extracted photometry for each of the images you now need to associate the stars between each image. The B and V-band images might be slightly offset from each other and may contain differential distortions between the filters. Open your final image in DS9 and pick 4 or 5 of the brightest stars. In the table below, for each image note their x and y positions and the difference."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Star| $B_x$ | $B_y$ | $V_x$ | $V_y$ | $\\Delta_{x}$ | $\\Delta_{y}$\n",
"---|---|---|--- |--- |--- |--- \n",
"1 |---|---|---|--- |--- |--- \n",
"2 |---|---|---|--- |--- |--- \n",
"3 |---|---|---|--- |--- |--- \n",
"4 |---|---|---|--- |--- |--- \n",
"5 |---|---|---|--- |--- |--- \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**What is the average $\\Delta_x$ and $\\Delta_y?**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Use this offset to match up stars from your two lists, much like you did before matching your stars to the Source Extractor Catalog, but not taking advantage of the average delta x and delta y you just measured.** Just as before, you may find that some stars don't exist in both catalogs. Set a maximum $r$ value as a threshold above which you can say there is no reasonable match. **Make a list of indices that match one magnitude list (B or V magnitude) to the other.**"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we need to calibrate our B and V magnitudes using the sky-map website. Use 5 stars in the field to do an absolute calibration of the $B$ and $V$ magnitudes (we did this in Lab 4!). **Please state which stars you used and what zero points (ZP) you obtained in the table below.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Star| Star Name | $B_{mag}$ | $B_{skymap}$ | $B_{ZP}$ |$V_{mag}$ | $V_{skymap}$ | $V_{ZP}$ \n",
"---|---|---|--- |--- |--- |--- |--- \n",
"1 |---|---|---|--- |--- |--- |--- \n",
"2 |---|---|---|--- |--- |--- |--- \n",
"3 |---|---|---|--- |--- |--- |--- \n",
"4 |---|---|---|--- |--- |--- |--- \n",
"5 |---|---|---|--- |--- |--- |--- "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Make an HR Diagram with (calibrated) $B-V$ color plotted on the $x$-axis (make sure to follow astronomical convention on the direction of this axis!), and (calibrated) $V$ magnitude on the $y$-axis. Label the various important features of the HR Diagram in a plot in your notebook (see Part 1).**"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now download the solar metallicity (```lj98m01757.txt```) isochrones (recall isochrones from Part 1!) from [here](https://www.astronomy.ohio-state.edu/terndrup.1/iso/pl.html). Plot the solar metallicity isochrone that best fits your data on top of your HR diagram. You will have to manually adjust the V-magnitude by a certain offset to match the isochrone to your data. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the physical meaning of this offset? What does it tell you about the cluster (be quantitative)?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answer here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The age of this isochrone corresponds to your estimate of the age of the cluster. What is your estimate? How close is your estimate to the published value of age and distance (look this up)? What do you think are the largest sources of error in your estimate?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Your answers here*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

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Lab 6/M67_B.fits
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Lab 6/M67_V.fits
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353
Lab 6/evol_M0.8.dat
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@ -1,353 +0,0 @@
3.6272 -0.2786 0.0039811
3.627 -0.2862 0.0040738
3.6267 -0.294 0.0041687
3.6265 -0.3014 0.0042658
3.6263 -0.3079 0.0043652
3.6262 -0.3146 0.0044668
3.626 -0.3215 0.0045709
3.6258 -0.3285 0.0046774
3.6256 -0.3356 0.0047863
3.6254 -0.3429 0.0048978
3.6252 -0.3504 0.0050119
3.625 -0.358 0.0051286
3.6248 -0.3642 0.0052481
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3.6243 -0.3836 0.0056234
3.6241 -0.3904 0.0057544
3.624 -0.3973 0.0058884
3.6238 -0.4044 0.0060256
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3.6224 -0.4863 0.0081283
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3.6223 -0.4985 0.0085114
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3.6222 -0.5112 0.0089125
3.6223 -0.5159 0.0091201
3.6223 -0.5207 0.0093325
3.6224 -0.5257 0.0095499
3.6225 -0.5307 0.0097724
3.6226 -0.5359 0.01
3.6227 -0.5411 0.010233
3.6227 -0.5465 0.010471
3.6228 -0.5521 0.010715
3.6229 -0.5577 0.010965
3.6231 -0.5619 0.01122
3.6233 -0.5658 0.011482
3.6235 -0.5698 0.011749
3.6237 -0.5739 0.012023
3.6239 -0.5782 0.012303
3.6242 -0.5825 0.012589
3.6244 -0.5869 0.012882
3.6246 -0.5914 0.013183
3.6249 -0.596 0.01349
3.6251 -0.6007 0.013804
3.6254 -0.6044 0.014125
3.6258 -0.6068 0.014454
3.6262 -0.6093 0.014791
3.6266 -0.6118 0.015136
3.627 -0.6144 0.015488
3.6274 -0.617 0.015849
3.6278 -0.6197 0.016218
3.6283 -0.6225 0.016596
3.6287 -0.6253 0.016982
3.6292 -0.6282 0.017378
3.6297 -0.6312 0.017783
3.6302 -0.6342 0.018197
3.6306 -0.6373 0.018621
3.6312 -0.6405 0.019055
3.6319 -0.641 0.019498
3.6327 -0.6411 0.019953
3.6335 -0.6411 0.020417
3.6343 -0.6411 0.020893
3.6351 -0.6412 0.02138
3.636 -0.6412 0.021878
3.6369 -0.6412 0.022387
3.6378 -0.6413 0.022909
3.6387 -0.6413 0.023442
3.6396 -0.6414 0.023988
3.6406 -0.6414 0.024547
3.6416 -0.6414 0.025119
3.6429 -0.6388 0.025704
3.6444 -0.6353 0.026303
3.646 -0.6316 0.026915
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347
Lab 6/evol_M1.0.dat
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306
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Lab 6/evol_M2.6.dat
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@ -1,226 +0,0 @@
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