All arrays should be 1024 x 1024 in size.
Array 1 should be Int16, 2 should be Float32 and 3 should be Int16
Verify that the first array does indeed have a mean of 100 and a standard deviation of 10.
Write out all 3 arrays to FITS file with array 1 in extension 1, array 2 in extension 2 and array 3 in extension 3. Include a keyword in the primary header MYNAME and set it equal to a string with your name.
import numpy as np
import pyfits
The first thing I did was google "numpy normal", and it suggested "numpy normal distribution" for me. Clicking on this link led me to this page:
http://docs.scipy.org/doc/numpy/reference/generated/numpy.random.normal.html
array1 = np.random.normal(loc=100.0, scale=10.0, size=(1024,1024))
array1
array([[ 93.20480607, 112.63396859, 115.16644969, ..., 120.56414716, 87.26477235, 99.42564914], [ 100.14444837, 112.73230282, 116.33273322, ..., 104.40872596, 103.16695148, 109.89391216], [ 103.15694836, 118.16964819, 96.30378699, ..., 85.79469168, 124.45615219, 101.44336637], ..., [ 84.43204005, 101.39462375, 109.19216879, ..., 112.15308713, 89.88616791, 97.76715757], [ 123.33547627, 102.2967618 , 109.40524982, ..., 109.68107542, 83.53726608, 113.18064322], [ 87.47161471, 93.94638559, 95.95080684, ..., 91.56742938, 103.94496298, 102.15600182]])
array1.mean()
100.00329592509874
array1.std()
10.006176661263446
This is floating point of course, and I want short integer type. I don't want to just do integer truncation, because that'll bias the mean. What I want is the nearest integer. Google was my friend again, pointing me to this page
http://docs.scipy.org/doc/numpy/reference/routines.math.html
that mentions the nearest integer function. I use the 'astype' method of numpy arrays to cast the array to int16.
a1 = np.rint(array1).astype(np.int16)
a1
array([[ 93, 113, 115, ..., 121, 87, 99], [100, 113, 116, ..., 104, 103, 110], [103, 118, 96, ..., 86, 124, 101], ..., [ 84, 101, 109, ..., 112, 90, 98], [123, 102, 109, ..., 110, 84, 113], [ 87, 94, 96, ..., 92, 104, 102]], dtype=int16)
a1.mean()
100.00308418273926
a1.std()
10.009972941083355
Check to see if there's any negative values (there shouldn't be...)
np.where(a1<0)
(array([], dtype=int64), array([], dtype=int64))
a2 = np.sqrt(a1)
a2.mean()
9.9802083969116211
This isn't equal to 10.0 - why?
a2
array([[ 9.64365101, 10.63014603, 10.72380543, ..., 11. , 9.32737923, 9.94987392], [ 10. , 10.63014603, 10.77032948, ..., 10.19803905, 10.14889145, 10.48808861], [ 10.14889145, 10.86278057, 9.79795933, ..., 9.2736187 , 11.13552856, 10.04987526], ..., [ 9.1651516 , 10.04987526, 10.44030666, ..., 10.58300495, 9.48683262, 9.89949512], [ 11.09053612, 10.09950447, 10.44030666, ..., 10.48808861, 9.1651516 , 10.63014603], [ 9.32737923, 9.69536018, 9.79795933, ..., 9.59166336, 10.19803905, 10.09950447]], dtype=float32)
a3 = np.zeros((1024,1024)).astype(np.int16)
a3
array([[0, 0, 0, ..., 0, 0, 0], [0, 0, 0, ..., 0, 0, 0], [0, 0, 0, ..., 0, 0, 0], ..., [0, 0, 0, ..., 0, 0, 0], [0, 0, 0, ..., 0, 0, 0], [0, 0, 0, ..., 0, 0, 0]], dtype=int16)
a3[np.where(a1 <= (a1.mean() - 2.0*a1.std()))] = 4
a3[np.where(a1 >= (a1.mean() + 2.0*a1.std()))] = 2
np.where(a3==2)[0].size
21077
np.where(a3==4)[0].size
21402
These should both be about 2.3% of the total number of pixels, seems a little high...
Now to make the FITS file. Start by making an empty HDUList.
f1 = pyfits.HDUList()
f1
[]
Add a Primary HDU
f1.append(pyfits.PrimaryHDU())
And three ImageHDUs, with the appropriate data
f1.append(pyfits.ImageHDU(data=a1))
f1.append(pyfits.ImageHDU(data=a2))
f1.append(pyfits.ImageHDU(data=a3))
The header is minimal
f1[0].header
SIMPLE = T / conforms to FITS standard BITPIX = 8 / array data type NAXIS = 0 / number of array dimensions EXTEND = T
Add the required keyword/value pair
f1[0].header['MYNAME'] = 'Robert Jedrzejewski'
And write out to a FITS file
f1.writeto('Session2_Q1.fits',clobber=True)
Overwriting existing file 'Session2_Q1.fits'.
Check that everything seems OK
pyfits.info('Session2_Q1.fits')
Filename: Session2_Q1.fits No. Name Type Cards Dimensions Format 0 PRIMARY PrimaryHDU 5 () uint8 1 ImageHDU 7 (1024, 1024) int16 2 ImageHDU 7 (1024, 1024) float32 3 ImageHDU 7 (1024, 1024) int16
Googling 'matplotlib subplot' points us to the 'gridspec' command in the first hit, but that's a bit complicated to use. What I neglected to mention during the talk (although it is in the worksheet) is the gallery of matplotlib plots, at
http://matplotlib.org/gallery.html
where you can see huge numbers of example of different types of plots, with source code. You will almost certainly find something similar to what you want to do there.
For example, the plot here:
http://matplotlib.org/examples/pylab_examples/anscombe.html
shows how to do more than 1 plot on a page. It uses the 'subplot' method of pylab.
pylab.subplot(121)
<matplotlib.axes.AxesSubplot at 0x30a41d0>
This gives the left-hand plot. To do an image display of the first extension of the image from problem #1, we use the 'imshow' method.
ext1 = pyfits.getdata('Session2_Q1.fits')
pyplot.imshow(ext1)
<matplotlib.image.AxesImage at 0x351d590>
import matplotlib.cm as cm
pylab.subplot(122)
pylab.imshow(ext1,cmap=cm.winter)
<matplotlib.image.AxesImage at 0x3510810>
Now lets try and figure out how to do the histogram. Googling matplotlib histogram takes us to this page
http://matplotlib.org/examples/api/histogram_demo.html
which indicates that there's a pylab.hist. Let's try it
pylab.hist(ext1)
([array([ 1, 1, 14, 104, 324, 337, 199, 36, 7, 1]), array([ 0, 1, 20, 115, 328, 346, 183, 28, 3, 0]), array([ 0, 1, 22, 127, 314, 360, 161, 36, 3, 0]), array([ 0, 1, 17, 123, 327, 322, 194, 36, 4, 0]), array([ 0, 4, 14, 98, 316, 349, 208, 33, 1, 1]), array([ 0, 2, 19, 108, 311, 330, 210, 38, 6, 0]), array([ 0, 1, 15, 116, 297, 339, 207, 45, 4, 0]), array([ 0, 0, 22, 95, 327, 359, 188, 27, 5, 1]), array([ 0, 1, 19, 110, 327, 339, 197, 27, 3, 1]), array([ 0, 2, 18, 105, 357, 313, 197, 28, 3, 1]), array([ 0, 0, 13, 106, 320, 350, 195, 36, 4, 0]), array([ 0, 0, 23, 110, 309, 333, 197, 46, 5, 1]), array([ 0, 0, 24, 95, 329, 353, 174, 47, 2, 0]), array([ 0, 1, 19, 102, 327, 355, 181, 35, 4, 0]), array([ 0, 2, 20, 115, 308, 347, 196, 36, 0, 0]), array([ 0, 1, 17, 114, 337, 337, 177, 36, 5, 0]), array([ 0, 0, 20, 115, 307, 345, 201, 31, 5, 0]), array([ 0, 1, 22, 115, 292, 347, 201, 38, 8, 0]), array([ 0, 2, 19, 115, 327, 339, 180, 36, 6, 0]), array([ 0, 0, 22, 125, 294, 352, 196, 31, 4, 0]), array([ 0, 0, 18, 100, 318, 370, 180, 37, 1, 0]), array([ 0, 1, 19, 86, 314, 349, 217, 32, 6, 0]), array([ 0, 1, 13, 110, 301, 346, 209, 40, 4, 0]), array([ 0, 2, 21, 115, 339, 318, 188, 39, 2, 0]), array([ 0, 0, 17, 116, 328, 348, 176, 35, 4, 0]), array([ 0, 0, 21, 110, 335, 316, 203, 32, 7, 0]), array([ 0, 1, 20, 103, 338, 334, 187, 37, 4, 0]), array([ 0, 1, 19, 110, 324, 337, 205, 27, 1, 0]), array([ 0, 0, 18, 115, 312, 335, 196, 41, 6, 1]), array([ 1, 1, 27, 125, 309, 324, 201, 34, 2, 0]), array([ 0, 0, 12, 107, 317, 348, 208, 31, 1, 0]), array([ 0, 2, 21, 114, 347, 306, 197, 29, 8, 0]), array([ 0, 3, 25, 102, 282, 362, 206, 40, 4, 0]), array([ 0, 0, 17, 123, 325, 331, 184, 38, 6, 0]), array([ 0, 2, 20, 98, 319, 389, 165, 27, 4, 0]), array([ 0, 4, 24, 105, 319, 343, 186, 41, 2, 0]), array([ 0, 3, 20, 96, 342, 344, 185, 30, 4, 0]), array([ 0, 1, 16, 107, 308, 344, 196, 47, 5, 0]), array([ 0, 0, 19, 112, 338, 311, 199, 38, 7, 0]), array([ 0, 1, 16, 119, 331, 346, 178, 30, 3, 0]), array([ 0, 2, 19, 114, 295, 360, 200, 32, 1, 1]), array([ 0, 5, 14, 104, 311, 343, 204, 38, 5, 0]), array([ 0, 2, 19, 120, 317, 333, 200, 29, 4, 0]), array([ 0, 3, 19, 124, 306, 344, 193, 32, 3, 0]), array([ 0, 0, 20, 111, 323, 320, 206, 42, 2, 0]), array([ 0, 1, 17, 100, 331, 321, 207, 46, 1, 0]), array([ 0, 7, 25, 99, 334, 314, 211, 30, 4, 0]), array([ 0, 0, 20, 92, 324, 354, 196, 34, 4, 0]), array([ 0, 0, 21, 112, 312, 348, 191, 37, 3, 0]), array([ 0, 1, 18, 98, 313, 365, 199, 28, 2, 0]), array([ 0, 3, 20, 120, 298, 337, 190, 48, 8, 0]), array([ 0, 1, 27, 104, 323, 349, 180, 31, 9, 0]), array([ 0, 0, 14, 107, 307, 354, 208, 32, 2, 0]), array([ 0, 1, 15, 107, 343, 347, 169, 38, 3, 1]), array([ 0, 1, 18, 103, 295, 374, 198, 32, 3, 0]), array([ 0, 1, 18, 119, 291, 355, 210, 27, 3, 0]), array([ 0, 2, 16, 88, 322, 361, 189, 43, 3, 0]), array([ 0, 1, 11, 90, 352, 349, 175, 41, 5, 0]), array([ 0, 1, 29, 93, 318, 331, 201, 48, 3, 0]), array([ 0, 2, 18, 98, 344, 337, 182, 35, 7, 1]), array([ 0, 2, 29, 100, 332, 330, 192, 37, 2, 0]), array([ 0, 0, 18, 97, 337, 333, 192, 38, 9, 0]), array([ 0, 2, 18, 99, 307, 358, 198, 38, 4, 0]), array([ 0, 0, 18, 102, 348, 331, 184, 38, 3, 0]), array([ 0, 2, 20, 109, 320, 334, 202, 35, 2, 0]), array([ 0, 1, 20, 124, 322, 329, 196, 32, 0, 0]), array([ 0, 0, 19, 102, 343, 322, 198, 34, 6, 0]), array([ 0, 1, 18, 117, 321, 352, 177, 33, 5, 0]), array([ 0, 2, 17, 129, 302, 348, 194, 29, 3, 0]), array([ 0, 0, 19, 111, 326, 362, 183, 23, 0, 0]), array([ 0, 2, 16, 113, 316, 332, 213, 29, 3, 0]), array([ 0, 0, 19, 102, 339, 315, 208, 35, 5, 1]), array([ 1, 2, 21, 86, 323, 350, 198, 39, 4, 0]), array([ 0, 0, 23, 98, 317, 363, 192, 29, 2, 0]), array([ 0, 4, 23, 98, 336, 327, 198, 33, 5, 0]), array([ 0, 0, 21, 107, 332, 346, 178, 36, 4, 0]), array([ 0, 2, 19, 127, 337, 302, 200, 36, 1, 0]), array([ 0, 0, 18, 114, 329, 347, 175, 37, 4, 0]), array([ 1, 2, 21, 107, 334, 328, 185, 35, 11, 0]), array([ 0, 0, 30, 113, 329, 328, 194, 26, 4, 0]), array([ 0, 3, 20, 95, 352, 334, 180, 36, 4, 0]), array([ 0, 2, 25, 90, 328, 352, 201, 23, 3, 0]), array([ 0, 1, 15, 113, 328, 347, 176, 41, 3, 0]), array([ 0, 2, 20, 102, 346, 306, 216, 30, 1, 1]), array([ 0, 0, 13, 123, 337, 335, 184, 29, 3, 0]), array([ 1, 0, 16, 123, 317, 331, 193, 42, 1, 0]), array([ 0, 1, 18, 94, 322, 359, 190, 36, 3, 1]), array([ 0, 2, 19, 104, 332, 348, 187, 25, 7, 0]), array([ 0, 2, 10, 101, 297, 399, 182, 28, 5, 0]), array([ 0, 1, 16, 118, 303, 342, 192, 49, 3, 0]), array([ 0, 1, 24, 111, 324, 290, 219, 49, 5, 1]), array([ 0, 1, 20, 113, 329, 314, 202, 39, 6, 0]), array([ 0, 0, 19, 111, 299, 341, 207, 42, 4, 1]), array([ 0, 0, 8, 95, 333, 349, 196, 40, 3, 0]), array([ 0, 0, 18, 111, 339, 328, 183, 41, 4, 0]), array([ 1, 2, 25, 137, 300, 356, 160, 42, 1, 0]), array([ 0, 0, 24, 92, 320, 340, 204, 42, 2, 0]), array([ 0, 3, 14, 99, 317, 360, 188, 39, 4, 0]), array([ 0, 2, 18, 106, 340, 355, 167, 32, 4, 0]), array([ 0, 5, 17, 107, 321, 349, 196, 29, 0, 0]), array([ 0, 1, 22, 124, 315, 322, 199, 37, 4, 0]), array([ 0, 1, 22, 98, 340, 337, 194, 28, 4, 0]), array([ 0, 1, 21, 112, 335, 358, 162, 33, 1, 1]), array([ 0, 1, 24, 116, 307, 321, 206, 46, 3, 0]), array([ 1, 8, 25, 105, 303, 364, 189, 29, 0, 0]), array([ 0, 1, 17, 112, 323, 337, 204, 28, 2, 0]), array([ 0, 1, 17, 112, 315, 335, 197, 41, 6, 0]), array([ 0, 0, 24, 99, 303, 354, 194, 46, 4, 0]), array([ 0, 0, 16, 106, 310, 345, 202, 39, 6, 0]), array([ 0, 1, 24, 117, 303, 339, 199, 36, 4, 1]), array([ 0, 0, 15, 97, 324, 341, 212, 29, 6, 0]), array([ 0, 0, 12, 112, 310, 340, 210, 36, 4, 0]), array([ 0, 1, 15, 114, 324, 340, 192, 32, 6, 0]), array([ 0, 2, 19, 103, 328, 352, 173, 40, 7, 0]), array([ 0, 0, 17, 116, 318, 329, 208, 31, 5, 0]), array([ 0, 0, 15, 111, 314, 330, 207, 42, 5, 0]), array([ 0, 2, 22, 99, 338, 329, 198, 30, 6, 0]), array([ 1, 0, 22, 95, 315, 340, 207, 41, 3, 0]), array([ 0, 0, 21, 126, 339, 319, 179, 37, 3, 0]), array([ 0, 2, 15, 100, 284, 370, 211, 36, 6, 0]), array([ 0, 1, 24, 109, 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319, 195, 36, 5, 0]), array([ 0, 2, 21, 111, 313, 322, 215, 34, 6, 0]), array([ 0, 2, 19, 103, 319, 351, 189, 37, 4, 0]), array([ 0, 0, 21, 103, 326, 338, 198, 31, 7, 0]), array([ 0, 3, 21, 99, 326, 337, 187, 49, 2, 0]), array([ 0, 1, 20, 112, 339, 347, 165, 35, 5, 0]), array([ 0, 2, 21, 124, 319, 319, 199, 37, 3, 0]), array([ 0, 0, 25, 102, 328, 341, 188, 38, 2, 0]), array([ 0, 1, 24, 114, 336, 289, 211, 48, 1, 0]), array([ 0, 0, 20, 94, 310, 359, 199, 36, 6, 0]), array([ 0, 2, 21, 109, 312, 340, 203, 32, 5, 0]), array([ 0, 1, 17, 108, 337, 329, 202, 26, 4, 0]), array([ 0, 0, 17, 113, 333, 339, 181, 38, 3, 0]), array([ 0, 0, 24, 108, 311, 343, 191, 43, 4, 0]), array([ 0, 1, 18, 111, 298, 371, 180, 39, 6, 0]), array([ 0, 2, 20, 117, 327, 315, 205, 36, 2, 0]), array([ 0, 1, 18, 129, 327, 342, 177, 28, 2, 0]), array([ 0, 0, 24, 108, 328, 327, 194, 41, 2, 0]), array([ 0, 0, 32, 107, 350, 299, 195, 36, 5, 0]), array([ 0, 2, 18, 111, 322, 344, 188, 32, 7, 0]), array([ 1, 2, 17, 85, 335, 354, 188, 36, 6, 0]), array([ 0, 1, 24, 105, 339, 332, 189, 29, 5, 0]), array([ 0, 0, 11, 100, 317, 364, 197, 30, 5, 0]), array([ 0, 0, 13, 103, 317, 350, 205, 34, 2, 0]), array([ 0, 0, 23, 103, 305, 343, 202, 45, 3, 0]), array([ 0, 1, 15, 108, 332, 339, 189, 35, 5, 0]), array([ 0, 0, 27, 113, 312, 354, 177, 34, 7, 0]), array([ 0, 0, 16, 108, 344, 338, 183, 33, 2, 0]), array([ 0, 0, 19, 105, 316, 353, 188, 36, 7, 0]), array([ 0, 0, 23, 109, 324, 340, 186, 38, 4, 0]), array([ 0, 1, 19, 100, 338, 331, 195, 40, 0, 0]), array([ 0, 2, 24, 110, 321, 317, 202, 41, 7, 0]), array([ 0, 0, 17, 112, 321, 328, 199, 45, 2, 0]), array([ 0, 0, 17, 118, 314, 319, 208, 46, 2, 0]), array([ 0, 0, 17, 90, 335, 353, 195, 32, 2, 0]), array([ 0, 2, 21, 107, 301, 347, 209, 32, 5, 0]), array([ 0, 0, 17, 108, 328, 339, 189, 39, 3, 1]), array([ 0, 0, 24, 104, 313, 342, 181, 52, 8, 0]), array([ 0, 0, 22, 126, 328, 330, 176, 37, 5, 0]), array([ 0, 1, 20, 110, 349, 331, 170, 39, 2, 2]), array([ 0, 0, 18, 98, 345, 333, 191, 36, 3, 0]), array([ 0, 0, 22, 109, 310, 367, 166, 48, 2, 0]), array([ 0, 2, 18, 102, 335, 330, 190, 41, 6, 0]), array([ 0, 0, 14, 103, 325, 362, 178, 37, 5, 0]), array([ 0, 1, 21, 99, 320, 335, 200, 43, 5, 0]), array([ 0, 1, 19, 103, 320, 339, 201, 37, 4, 0]), array([ 0, 0, 19, 97, 338, 334, 200, 28, 8, 0]), array([ 0, 0, 19, 110, 314, 352, 189, 37, 3, 0]), array([ 0, 1, 17, 114, 323, 359, 163, 44, 3, 0]), array([ 0, 2, 23, 112, 318, 332, 200, 34, 3, 0]), array([ 0, 1, 20, 122, 301, 344, 186, 42, 8, 0]), array([ 0, 2, 23, 119, 303, 334, 212, 31, 0, 0]), array([ 0, 1, 17, 96, 345, 341, 186, 33, 5, 0]), array([ 0, 4, 15, 95, 309, 348, 196, 53, 4, 0]), array([ 0, 3, 20, 103, 324, 333, 204, 32, 5, 0]), array([ 0, 2, 19, 115, 319, 333, 187, 40, 9, 0]), array([ 0, 2, 32, 96, 297, 369, 185, 41, 2, 0]), array([ 0, 0, 22, 117, 322, 355, 169, 34, 5, 0]), array([ 0, 3, 20, 103, 326, 342, 191, 31, 6, 2]), array([ 0, 0, 24, 98, 294, 353, 207, 42, 6, 0]), array([ 0, 1, 18, 103, 318, 358, 196, 27, 3, 0]), array([ 0, 1, 22, 95, 328, 328, 204, 42, 3, 1]), array([ 0, 1, 25, 97, 344, 317, 206, 30, 4, 0]), array([ 0, 2, 21, 108, 334, 328, 194, 34, 3, 0]), array([ 0, 5, 19, 104, 313, 325, 212, 42, 4, 0]), array([ 0, 0, 20, 111, 328, 344, 181, 35, 5, 0]), array([ 0, 1, 19, 110, 339, 327, 189, 33, 6, 0]), array([ 0, 0, 19, 109, 338, 306, 211, 36, 5, 0]), array([ 0, 0, 20, 115, 302, 344, 200, 40, 3, 0]), array([ 0, 3, 19, 104, 316, 329, 211, 41, 1, 0]), array([ 1, 0, 22, 105, 337, 323, 200, 35, 1, 0]), array([ 0, 0, 16, 96, 327, 342, 200, 37, 6, 0]), array([ 0, 1, 14, 119, 323, 302, 215, 47, 3, 0]), array([ 0, 2, 19, 115, 326, 329, 192, 38, 3, 0]), array([ 0, 2, 16, 119, 319, 345, 190, 29, 4, 0]), array([ 0, 0, 22, 101, 329, 324, 202, 42, 4, 0]), array([ 0, 3, 19, 98, 340, 334, 189, 38, 3, 0]), array([ 0, 2, 19, 101, 329, 345, 192, 33, 3, 0]), array([ 0, 1, 18, 111, 325, 342, 193, 29, 5, 0]), array([ 0, 1, 11, 96, 331, 362, 182, 37, 4, 0]), array([ 0, 0, 18, 112, 291, 353, 206, 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219, 28, 4, 0]), array([ 0, 1, 29, 115, 314, 325, 193, 43, 4, 0]), array([ 0, 0, 23, 113, 308, 345, 187, 39, 9, 0]), array([ 0, 1, 17, 105, 351, 322, 196, 29, 3, 0]), array([ 0, 1, 21, 103, 333, 319, 209, 33, 5, 0]), array([ 0, 2, 12, 124, 313, 354, 186, 31, 2, 0]), array([ 0, 0, 19, 107, 332, 298, 230, 33, 5, 0]), array([ 0, 3, 13, 109, 325, 333, 201, 38, 2, 0]), array([ 0, 1, 17, 98, 311, 331, 222, 41, 3, 0]), array([ 0, 4, 15, 99, 321, 348, 198, 36, 3, 0]), array([ 0, 1, 19, 104, 312, 359, 198, 30, 1, 0]), array([ 0, 2, 27, 106, 322, 338, 185, 42, 2, 0]), array([ 0, 1, 21, 95, 324, 359, 186, 36, 2, 0]), array([ 0, 0, 24, 118, 323, 331, 185, 39, 4, 0]), array([ 1, 0, 26, 99, 300, 354, 206, 38, 0, 0]), array([ 0, 1, 19, 99, 300, 341, 213, 50, 1, 0]), array([ 0, 2, 18, 82, 323, 362, 198, 37, 2, 0]), array([ 0, 0, 17, 121, 300, 343, 206, 32, 5, 0]), array([ 0, 0, 20, 95, 330, 374, 168, 33, 4, 0]), array([ 0, 0, 19, 102, 344, 341, 175, 39, 4, 0]), array([ 0, 1, 24, 78, 316, 356, 202, 42, 5, 0]), array([ 0, 1, 11, 112, 315, 352, 191, 34, 8, 0]), array([ 0, 3, 26, 93, 336, 339, 188, 34, 5, 0]), array([ 0, 0, 23, 117, 319, 336, 191, 35, 3, 0]), array([ 0, 1, 17, 118, 317, 322, 207, 39, 3, 0]), array([ 0, 0, 13, 96, 344, 329, 202, 33, 7, 0]), array([ 0, 1, 15, 113, 312, 346, 189, 45, 3, 0]), array([ 0, 2, 20, 107, 330, 340, 184, 38, 3, 0]), array([ 0, 1, 22, 105, 319, 354, 174, 46, 3, 0]), array([ 0, 0, 17, 109, 344, 336, 172, 44, 2, 0]), array([ 0, 0, 18, 120, 297, 353, 193, 38, 5, 0]), array([ 0, 1, 20, 120, 315, 343, 173, 46, 6, 0]), array([ 0, 1, 15, 103, 310, 346, 204, 39, 6, 0]), array([ 0, 0, 20, 111, 305, 355, 189, 40, 4, 0]), array([ 0, 0, 25, 113, 332, 318, 192, 40, 4, 0]), array([ 0, 1, 16, 92, 347, 332, 186, 45, 5, 0]), array([ 0, 0, 15, 110, 301, 336, 206, 54, 2, 0]), array([ 0, 1, 25, 106, 333, 331, 189, 33, 6, 0]), array([ 0, 4, 19, 113, 309, 349, 194, 32, 4, 0]), array([ 0, 0, 29, 93, 334, 338, 188, 38, 3, 1]), array([ 0, 0, 20, 100, 343, 333, 193, 33, 2, 0]), array([ 0, 1, 21, 101, 340, 330, 183, 42, 6, 0]), array([ 0, 1, 14, 100, 354, 339, 179, 35, 2, 0]), array([ 0, 0, 22, 100, 323, 351, 188, 38, 2, 0]), array([ 0, 1, 17, 110, 311, 350, 194, 36, 5, 0]), array([ 0, 3, 20, 110, 330, 322, 198, 38, 3, 0]), array([ 0, 0, 15, 107, 326, 329, 197, 46, 4, 0]), array([ 0, 1, 21, 114, 324, 334, 199, 29, 2, 0]), array([ 0, 2, 28, 105, 329, 345, 171, 40, 4, 0]), array([ 0, 1, 13, 120, 316, 357, 181, 33, 2, 1]), array([ 0, 1, 24, 112, 332, 342, 175, 34, 4, 0]), array([ 0, 2, 14, 96, 301, 363, 209, 36, 3, 0]), array([ 0, 0, 20, 110, 330, 318, 210, 30, 6, 0]), array([ 0, 1, 20, 100, 333, 345, 187, 32, 6, 0]), array([ 0, 0, 21, 106, 315, 350, 188, 40, 4, 0]), array([ 0, 1, 28, 122, 301, 323, 210, 34, 5, 0]), array([ 0, 2, 20, 103, 349, 330, 179, 35, 6, 0]), array([ 0, 0, 22, 112, 332, 353, 176, 26, 3, 0]), array([ 0, 1, 16, 100, 294, 352, 215, 41, 5, 0]), array([ 0, 1, 26, 101, 307, 354, 203, 28, 4, 0]), array([ 0, 2, 15, 110, 323, 353, 183, 36, 2, 0]), array([ 1, 0, 22, 109, 317, 336, 195, 40, 4, 0]), array([ 0, 0, 19, 116, 301, 373, 173, 38, 4, 0]), array([ 0, 0, 21, 118, 340, 304, 196, 41, 4, 0]), array([ 0, 2, 21, 114, 311, 348, 190, 32, 5, 1]), array([ 0, 2, 23, 112, 305, 325, 223, 29, 5, 0]), array([ 0, 0, 29, 90, 336, 327, 196, 43, 3, 0]), array([ 0, 0, 14, 114, 339, 337, 175, 40, 5, 0]), array([ 0, 0, 24, 104, 297, 366, 196, 35, 2, 0]), array([ 0, 1, 21, 103, 331, 353, 182, 33, 0, 0]), array([ 0, 2, 18, 101, 308, 360, 194, 36, 5, 0]), array([ 0, 1, 18, 89, 342, 343, 196, 29, 6, 0]), array([ 0, 0, 19, 91, 316, 348, 205, 40, 5, 0]), array([ 0, 2, 22, 92, 333, 352, 187, 29, 7, 0]), array([ 0, 1, 21, 106, 326, 343, 188, 36, 3, 0]), array([ 0, 0, 23, 94, 323, 351, 199, 31, 3, 0]), array([ 0, 1, 18, 102, 309, 366, 182, 40, 5, 1]), array([ 0, 1, 19, 117, 319, 340, 192, 35, 1, 0]), array([ 0, 0, 22, 96, 341, 344, 187, 32, 2, 0]), array([ 0, 1, 15, 123, 311, 337, 203, 34, 0, 0]), array([ 0, 0, 22, 111, 311, 354, 186, 39, 1, 0]), array([ 0, 1, 22, 101, 299, 383, 190, 25, 3, 0]), array([ 0, 2, 16, 131, 307, 337, 197, 27, 7, 0]), array([ 0, 2, 18, 104, 326, 345, 190, 39, 0, 0]), array([ 0, 3, 18, 114, 338, 316, 194, 41, 0, 0]), array([ 0, 3, 22, 114, 304, 343, 194, 37, 7, 0]), array([ 0, 1, 19, 94, 305, 375, 188, 41, 1, 0]), array([ 0, 0, 18, 103, 313, 355, 201, 32, 2, 0]), array([ 0, 2, 21, 107, 319, 351, 191, 31, 2, 0]), array([ 0, 1, 24, 107, 311, 347, 185, 42, 7, 0]), array([ 0, 2, 24, 115, 347, 308, 192, 34, 2, 0]), array([ 0, 3, 19, 116, 310, 347, 187, 39, 3, 0]), array([ 0, 1, 14, 95, 351, 322, 186, 48, 7, 0]), array([ 0, 1, 34, 93, 351, 320, 186, 34, 5, 0]), array([ 1, 1, 14, 92, 334, 340, 206, 33, 3, 0]), array([ 0, 3, 20, 96, 343, 342, 176, 38, 5, 1]), array([ 0, 3, 21, 103, 309, 360, 191, 33, 3, 1]), array([ 0, 0, 18, 113, 339, 332, 179, 38, 5, 0]), array([ 0, 1, 19, 119, 330, 336, 184, 34, 1, 0]), array([ 0, 1, 18, 116, 340, 321, 178, 43, 7, 0]), array([ 0, 2, 19, 113, 317, 360, 175, 36, 2, 0]), array([ 0, 0, 25, 119, 319, 345, 176, 37, 3, 0]), array([ 0, 2, 26, 94, 345, 321, 191, 40, 5, 0]), array([ 0, 1, 22, 108, 308, 353, 194, 34, 4, 0]), array([ 0, 3, 13, 112, 298, 380, 173, 35, 10, 0]), array([ 0, 0, 18, 98, 323, 331, 209, 37, 8, 0]), array([ 1, 1, 26, 104, 312, 339, 203, 36, 2, 0]), array([ 0, 0, 26, 110, 306, 342, 204, 33, 3, 0]), array([ 0, 1, 25, 107, 302, 346, 195, 46, 2, 0]), array([ 0, 3, 18, 121, 344, 307, 212, 16, 2, 1]), array([ 0, 1, 14, 118, 299, 344, 210, 32, 6, 0]), array([ 0, 1, 14, 90, 325, 338, 208, 39, 9, 0]), array([ 0, 0, 14, 101, 333, 329, 198, 44, 5, 0]), array([ 0, 1, 13, 107, 327, 327, 204, 42, 3, 0]), array([ 0, 2, 24, 89, 298, 374, 187, 48, 2, 0]), array([ 1, 0, 23, 104, 307, 354, 202, 29, 4, 0]), array([ 0, 2, 12, 102, 334, 329, 202, 42, 1, 0]), array([ 0, 1, 25, 107, 299, 362, 196, 33, 1, 0]), array([ 0, 1, 19, 109, 305, 360, 197, 29, 4, 0]), array([ 0, 1, 19, 101, 330, 350, 184, 34, 5, 0]), array([ 0, 0, 17, 109, 323, 354, 187, 30, 4, 0]), array([ 0, 2, 25, 101, 315, 356, 195, 28, 2, 0])], array([ 51. , 60.5, 70. , 79.5, 89. , 98.5, 108. , 117.5, 127. , 136.5, 146. ]), <a list of 1024 Lists of Patches objects>)
That doesn't look right. Notice it returned a list of 1024 Lists of Patches objects, which means that it probably did each row separately. Let's flatten the data first and see if that helps
pylab.hist(ext1.flatten())
(array([ 49, 1154, 20199, 109839, 330062, 349260, 196270, 37519, 4102, 122]), array([ 51. , 60.5, 70. , 79.5, 89. , 98.5, 108. , 117.5, 127. , 136.5, 146. ]), <a list of 10 Patch objects>)
Better, but let's have more bins.
nbins = ext1.max() - ext1.min()
pylab.hist(ext1.flatten(),bins=nbins)
(array([ 1, 0, 1, 2, 1, 2, 5, 10, 11, 16, 15, 36, 43, 63, 76, 134, 182, 267, 338, 470, 599, 817, 1117, 1460, 1858, 2400, 3059, 3696, 4723, 5613, 6949, 8388, 9755, 11719, 13433, 15919, 17845, 20218, 22854, 25320, 27854, 30426, 32549, 35143, 36877, 38475, 39749, 40815, 41461, 42124, 41334, 40971, 39849, 38789, 36816, 35011, 32905, 30309, 27950, 25425, 23052, 20570, 17774, 15744, 13702, 11711, 10033, 8248, 6752, 5666, 4582, 3622, 3014, 2365, 1791, 1479, 1112, 818, 649, 474, 336, 248, 174, 131, 96, 64, 44, 23, 17, 16, 11, 3, 4, 1, 3]), array([ 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146.]), <a list of 95 Patch objects>)
Much better, now lets put it all together
pylab.subplot(121)
pylab.imshow(ext1,cmap=cm.winter)
pylab.xlabel('X pixel')
pylab.ylabel('Y pixel')
pylab.title('Gaussian noise, mean=100, $\sigma = 10$')
pylab.subplot(122)
pylab.hist(ext1.flatten(),bins=nbins)
pylab.xlabel('Pixel Value')
pylab.ylabel('Number of pixels')
pylab.title('Histogram of pixel values')
<matplotlib.text.Text at 0x124590d0>
It's a bit quished up, so lets put an empty plot between them
pylab.subplot(131)
pylab.imshow(ext1,cmap=cm.winter)
pylab.xlabel('X pixel')
pylab.ylabel('Y pixel')
pylab.title('Gaussian noise, mean=100, $\sigma = 10$')
pylab.subplot(133)
pylab.hist(ext1.flatten(),bins=nbins)
pylab.xlabel('Pixel Value')
pylab.ylabel('Number of pixels')
pylab.title('Histogram of pixel values')
<matplotlib.text.Text at 0x13205b50>
Not perfect, but it'll do. We can play with this until it's just right.
Make a table with 8 columns:
Theta (degrees)
Theta (radians)
Sin(Theta)
Cos(Theta)
Tan(Theta)
Csc(Theta)
Sec(Theta)
Cot(Theta)
Populate this table with the correct values for Theta in degrees from 0 to 360.0 in increments of 1.0
If the data overflows, replace with 99999.0 or -99999.0
Write out the table in Latex form.
from astropy.io import ascii
First make an array for the x values
degrees = np.arange(361).astype(np.float32)
degrees
array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149., 150., 151., 152., 153., 154., 155., 156., 157., 158., 159., 160., 161., 162., 163., 164., 165., 166., 167., 168., 169., 170., 171., 172., 173., 174., 175., 176., 177., 178., 179., 180., 181., 182., 183., 184., 185., 186., 187., 188., 189., 190., 191., 192., 193., 194., 195., 196., 197., 198., 199., 200., 201., 202., 203., 204., 205., 206., 207., 208., 209., 210., 211., 212., 213., 214., 215., 216., 217., 218., 219., 220., 221., 222., 223., 224., 225., 226., 227., 228., 229., 230., 231., 232., 233., 234., 235., 236., 237., 238., 239., 240., 241., 242., 243., 244., 245., 246., 247., 248., 249., 250., 251., 252., 253., 254., 255., 256., 257., 258., 259., 260., 261., 262., 263., 264., 265., 266., 267., 268., 269., 270., 271., 272., 273., 274., 275., 276., 277., 278., 279., 280., 281., 282., 283., 284., 285., 286., 287., 288., 289., 290., 291., 292., 293., 294., 295., 296., 297., 298., 299., 300., 301., 302., 303., 304., 305., 306., 307., 308., 309., 310., 311., 312., 313., 314., 315., 316., 317., 318., 319., 320., 321., 322., 323., 324., 325., 326., 327., 328., 329., 330., 331., 332., 333., 334., 335., 336., 337., 338., 339., 340., 341., 342., 343., 344., 345., 346., 347., 348., 349., 350., 351., 352., 353., 354., 355., 356., 357., 358., 359., 360.], dtype=float32)
import math
radians = degrees * math.pi / 180.0
Now do the math
sintheta = sin(radians)
costheta = cos(radians)
tantheta = tan(radians)
sectheta = 1.0/cos(radians)
csctheta = 1.0/sin(radians)
cottheta = 1.0/tan(radians)
WARNING: RuntimeWarning: divide by zero encountered in divide [unknown] WARNING: RuntimeWarning: divide by zero encountered in divide [unknown]
We got a couple of divide by zero warnings. They are for csc and cot evaluated at 0. The other asymptotic values don't give an error because they would rely on the exact value of pi.
We can fix them by just setting values >99999.0 to 99999.0, and values less than -99999.0 to -99999.0.
tantheta[np.where(tantheta > 99999.0)] = 99999.0
tantheta[np.where(tantheta < -99999.0)] = -99999.0
sectheta[np.where(sectheta > 99999.0)] = 99999.0
sectheta[np.where(sectheta < -99999.0)] = -99999.0
csctheta[np.where(csctheta > 99999.0)] = 99999.0
csctheta[np.where(csctheta < -99999.0)] = -99999.0
cottheta[np.where(cottheta > 99999.0)] = 99999.0
cottheta[np.where(cottheta < -99999.0)] = -99999.0
Now write out the table. The astropy.ascii documentation tells us that to write out in Latex format, we just need to choose Writer=ascii.Latex in the ascii.write call
columns = [degrees, radians, sintheta, costheta, tantheta, csctheta, sectheta, cottheta]
names = ['Angle (degrees)', 'Angle (radians)', 'sin()', 'cos()', 'tan()', 'csc()', 'sec()', 'cot()']
ascii.write(columns, names=names, output='Session2_Q3.tex', Writer=ascii.Latex)
cat Session2_Q3.tex
\begin{table} \begin{tabular}{cccccccc} Angle (degrees) & Angle (radians) & sin() & cos() & tan() & csc() & sec() & cot() \\ 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 99999.0 & 1.0 & 99999.0 \\ 1.0 & 0.0174533 & 0.0174524 & 0.999848 & 0.0174551 & 57.2987 & 1.00015 & 57.29 \\ 2.0 & 0.0349066 & 0.0348995 & 0.999391 & 0.0349208 & 28.6537 & 1.00061 & 28.6363 \\ 3.0 & 0.0523599 & 0.052336 & 0.99863 & 0.0524078 & 19.1073 & 1.00137 & 19.0811 \\ 4.0 & 0.0698132 & 0.0697565 & 0.997564 & 0.0699268 & 14.3356 & 1.00244 & 14.3007 \\ 5.0 & 0.0872665 & 0.0871557 & 0.996195 & 0.0874887 & 11.4737 & 1.00382 & 11.4301 \\ 6.0 & 0.10472 & 0.104528 & 0.994522 & 0.105104 & 9.56677 & 1.00551 & 9.51436 \\ 7.0 & 0.122173 & 0.121869 & 0.992546 & 0.122785 & 8.20551 & 1.00751 & 8.14435 \\ 8.0 & 0.139626 & 0.139173 & 0.990268 & 0.140541 & 7.1853 & 1.00983 & 7.11537 \\ 9.0 & 0.15708 & 0.156434 & 0.987688 & 0.158384 & 6.39245 & 1.01247 & 6.31375 \\ 10.0 & 0.174533 & 0.173648 & 0.984808 & 0.176327 & 5.75877 & 1.01543 & 5.67128 \\ 11.0 & 0.191986 & 0.190809 & 0.981627 & 0.19438 & 5.24084 & 1.01872 & 5.14455 \\ 12.0 & 0.20944 & 0.207912 & 0.978148 & 0.212557 & 4.80973 & 1.02234 & 4.70463 \\ 13.0 & 0.226893 & 0.224951 & 0.97437 & 0.230868 & 4.44541 & 1.0263 & 4.33148 \\ 14.0 & 0.244346 & 0.241922 & 0.970296 & 0.249328 & 4.13356 & 1.03061 & 4.01078 \\ 15.0 & 0.261799 & 0.258819 & 0.965926 & 0.267949 & 3.8637 & 1.03528 & 3.73205 \\ 16.0 & 0.279253 & 0.275637 & 0.961262 & 0.286745 & 3.62796 & 1.0403 & 3.48741 \\ 17.0 & 0.296706 & 0.292372 & 0.956305 & 0.305731 & 3.4203 & 1.04569 & 3.27085 \\ 18.0 & 0.314159 & 0.309017 & 0.951056 & 0.32492 & 3.23607 & 1.05146 & 3.07768 \\ 19.0 & 0.331613 & 0.325568 & 0.945519 & 0.344328 & 3.07155 & 1.05762 & 2.90421 \\ 20.0 & 0.349066 & 0.34202 & 0.939693 & 0.36397 & 2.9238 & 1.06418 & 2.74748 \\ 21.0 & 0.366519 & 0.358368 & 0.93358 & 0.383864 & 2.79043 & 1.07115 & 2.60509 \\ 22.0 & 0.383972 & 0.374607 & 0.927184 & 0.404026 & 2.66947 & 1.07853 & 2.47509 \\ 23.0 & 0.401426 & 0.390731 & 0.920505 & 0.424475 & 2.5593 & 1.08636 & 2.35585 \\ 24.0 & 0.418879 & 0.406737 & 0.913545 & 0.445229 & 2.45859 & 1.09464 & 2.24604 \\ 25.0 & 0.436332 & 0.422618 & 0.906308 & 0.466308 & 2.3662 & 1.10338 & 2.14451 \\ 26.0 & 0.453786 & 0.438371 & 0.898794 & 0.487733 & 2.28117 & 1.1126 & 2.0503 \\ 27.0 & 0.471239 & 0.453991 & 0.891007 & 0.509525 & 2.20269 & 1.12233 & 1.96261 \\ 28.0 & 0.488692 & 0.469472 & 0.882948 & 0.531709 & 2.13005 & 1.13257 & 1.88073 \\ 29.0 & 0.506145 & 0.48481 & 0.87462 & 0.554309 & 2.06267 & 1.14335 & 1.80405 \\ 30.0 & 0.523599 & 0.5 & 0.866025 & 0.57735 & 2.0 & 1.1547 & 1.73205 \\ 31.0 & 0.541052 & 0.515038 & 0.857167 & 0.600861 & 1.9416 & 1.16663 & 1.66428 \\ 32.0 & 0.558505 & 0.529919 & 0.848048 & 0.624869 & 1.88708 & 1.17918 & 1.60033 \\ 33.0 & 0.575959 & 0.544639 & 0.838671 & 0.649408 & 1.83608 & 1.19236 & 1.53986 \\ 34.0 & 0.593412 & 0.559193 & 0.829038 & 0.674509 & 1.78829 & 1.20622 & 1.48256 \\ 35.0 & 0.610865 & 0.573577 & 0.819152 & 0.700208 & 1.74345 & 1.22077 & 1.42815 \\ 36.0 & 0.628319 & 0.587785 & 0.809017 & 0.726543 & 1.7013 & 1.23607 & 1.37638 \\ 37.0 & 0.645772 & 0.601815 & 0.798635 & 0.753554 & 1.66164 & 1.25214 & 1.32704 \\ 38.0 & 0.663225 & 0.615662 & 0.788011 & 0.781286 & 1.62427 & 1.26902 & 1.27994 \\ 39.0 & 0.680678 & 0.62932 & 0.777146 & 0.809784 & 1.58902 & 1.28676 & 1.2349 \\ 40.0 & 0.698132 & 0.642788 & 0.766044 & 0.8391 & 1.55572 & 1.30541 & 1.19175 \\ 41.0 & 0.715585 & 0.656059 & 0.75471 & 0.869287 & 1.52425 & 1.32501 & 1.15037 \\ 42.0 & 0.733038 & 0.669131 & 0.743145 & 0.900404 & 1.49448 & 1.34563 & 1.11061 \\ 43.0 & 0.750492 & 0.681998 & 0.731354 & 0.932515 & 1.46628 & 1.36733 & 1.07237 \\ 44.0 & 0.767945 & 0.694658 & 0.71934 & 0.965689 & 1.43956 & 1.39016 & 1.03553 \\ 45.0 & 0.785398 & 0.707107 & 0.707107 & 1.0 & 1.41421 & 1.41421 & 1.0 \\ 46.0 & 0.802851 & 0.71934 & 0.694658 & 1.03553 & 1.39016 & 1.43956 & 0.965689 \\ 47.0 & 0.820305 & 0.731354 & 0.681998 & 1.07237 & 1.36733 & 1.46628 & 0.932515 \\ 48.0 & 0.837758 & 0.743145 & 0.669131 & 1.11061 & 1.34563 & 1.49448 & 0.900404 \\ 49.0 & 0.855211 & 0.75471 & 0.656059 & 1.15037 & 1.32501 & 1.52425 & 0.869287 \\ 50.0 & 0.872665 & 0.766044 & 0.642788 & 1.19175 & 1.30541 & 1.55572 & 0.8391 \\ 51.0 & 0.890118 & 0.777146 & 0.62932 & 1.2349 & 1.28676 & 1.58902 & 0.809784 \\ 52.0 & 0.907571 & 0.788011 & 0.615661 & 1.27994 & 1.26902 & 1.62427 & 0.781286 \\ 53.0 & 0.925025 & 0.798636 & 0.601815 & 1.32704 & 1.25214 & 1.66164 & 0.753554 \\ 54.0 & 0.942478 & 0.809017 & 0.587785 & 1.37638 & 1.23607 & 1.7013 & 0.726542 \\ 55.0 & 0.959931 & 0.819152 & 0.573576 & 1.42815 & 1.22077 & 1.74345 & 0.700208 \\ 56.0 & 0.977384 & 0.829038 & 0.559193 & 1.48256 & 1.20622 & 1.78829 & 0.674508 \\ 57.0 & 0.994838 & 0.838671 & 0.544639 & 1.53987 & 1.19236 & 1.83608 & 0.649408 \\ 58.0 & 1.01229 & 0.848048 & 0.529919 & 1.60033 & 1.17918 & 1.88708 & 0.624869 \\ 59.0 & 1.02974 & 0.857167 & 0.515038 & 1.66428 & 1.16663 & 1.9416 & 0.600861 \\ 60.0 & 1.0472 & 0.866025 & 0.5 & 1.73205 & 1.1547 & 2.0 & 0.57735 \\ 61.0 & 1.06465 & 0.87462 & 0.48481 & 1.80405 & 1.14335 & 2.06267 & 0.554309 \\ 62.0 & 1.0821 & 0.882948 & 0.469472 & 1.88073 & 1.13257 & 2.13005 & 0.531709 \\ 63.0 & 1.09956 & 0.891007 & 0.45399 & 1.96261 & 1.12233 & 2.20269 & 0.509525 \\ 64.0 & 1.11701 & 0.898794 & 0.438371 & 2.0503 & 1.1126 & 2.28117 & 0.487733 \\ 65.0 & 1.13446 & 0.906308 & 0.422618 & 2.14451 & 1.10338 & 2.3662 & 0.466308 \\ 66.0 & 1.15192 & 0.913545 & 0.406737 & 2.24604 & 1.09464 & 2.45859 & 0.445229 \\ 67.0 & 1.16937 & 0.920505 & 0.390731 & 2.35585 & 1.08636 & 2.5593 & 0.424475 \\ 68.0 & 1.18682 & 0.927184 & 0.374607 & 2.47509 & 1.07853 & 2.66947 & 0.404026 \\ 69.0 & 1.20428 & 0.93358 & 0.358368 & 2.60509 & 1.07115 & 2.79043 & 0.383864 \\ 70.0 & 1.22173 & 0.939693 & 0.34202 & 2.74748 & 1.06418 & 2.92381 & 0.36397 \\ 71.0 & 1.23918 & 0.945519 & 0.325568 & 2.90421 & 1.05762 & 3.07155 & 0.344328 \\ 72.0 & 1.25664 & 0.951057 & 0.309017 & 3.07768 & 1.05146 & 3.23607 & 0.32492 \\ 73.0 & 1.27409 & 0.956305 & 0.292372 & 3.27085 & 1.04569 & 3.4203 & 0.305731 \\ 74.0 & 1.29154 & 0.961262 & 0.275637 & 3.48742 & 1.0403 & 3.62796 & 0.286745 \\ 75.0 & 1.309 & 0.965926 & 0.258819 & 3.73205 & 1.03528 & 3.8637 & 0.267949 \\ 76.0 & 1.32645 & 0.970296 & 0.241922 & 4.01078 & 1.03061 & 4.13357 & 0.249328 \\ 77.0 & 1.3439 & 0.97437 & 0.224951 & 4.33148 & 1.0263 & 4.44541 & 0.230868 \\ 78.0 & 1.36136 & 0.978148 & 0.207912 & 4.70463 & 1.02234 & 4.80974 & 0.212557 \\ 79.0 & 1.37881 & 0.981627 & 0.190809 & 5.14456 & 1.01872 & 5.24084 & 0.19438 \\ 80.0 & 1.39626 & 0.984808 & 0.173648 & 5.67128 & 1.01543 & 5.75877 & 0.176327 \\ 81.0 & 1.41372 & 0.987688 & 0.156434 & 6.31375 & 1.01247 & 6.39245 & 0.158384 \\ 82.0 & 1.43117 & 0.990268 & 0.139173 & 7.11537 & 1.00983 & 7.1853 & 0.140541 \\ 83.0 & 1.44862 & 0.992546 & 0.121869 & 8.14435 & 1.00751 & 8.20551 & 0.122785 \\ 84.0 & 1.46608 & 0.994522 & 0.104528 & 9.51437 & 1.00551 & 9.56678 & 0.105104 \\ 85.0 & 1.48353 & 0.996195 & 0.0871558 & 11.43 & 1.00382 & 11.4737 & 0.0874887 \\ 86.0 & 1.50098 & 0.997564 & 0.0697565 & 14.3007 & 1.00244 & 14.3356 & 0.0699269 \\ 87.0 & 1.51844 & 0.99863 & 0.0523359 & 19.0812 & 1.00137 & 19.1074 & 0.0524077 \\ 88.0 & 1.53589 & 0.999391 & 0.0348994 & 28.6364 & 1.00061 & 28.6538 & 0.0349206 \\ 89.0 & 1.55334 & 0.999848 & 0.0174524 & 57.29 & 1.00015 & 57.2988 & 0.017455 \\ 90.0 & 1.5708 & 1.0 & -4.37114e-08 & -99999.0 & 1.0 & -99999.0 & -4.37114e-08 \\ 91.0 & 1.58825 & 0.999848 & -0.0174525 & -57.2898 & 1.00015 & -57.2985 & -0.0174551 \\ 92.0 & 1.6057 & 0.999391 & -0.0348995 & -28.6363 & 1.00061 & -28.6537 & -0.0349207 \\ 93.0 & 1.62316 & 0.99863 & -0.0523359 & -19.0811 & 1.00137 & -19.1073 & -0.0524078 \\ 94.0 & 1.64061 & 0.997564 & -0.0697566 & -14.3006 & 1.00244 & -14.3356 & -0.0699269 \\ 95.0 & 1.65806 & 0.996195 & -0.0871559 & -11.43 & 1.00382 & -11.4737 & -0.0874888 \\ 96.0 & 1.67552 & 0.994522 & -0.104529 & -9.51436 & 1.00551 & -9.56677 & -0.105104 \\ 97.0 & 1.69297 & 0.992546 & -0.121869 & -8.14434 & 1.00751 & -8.2055 & -0.122785 \\ 98.0 & 1.71042 & 0.990268 & -0.139173 & -7.11537 & 1.00983 & -7.18529 & -0.140541 \\ 99.0 & 1.72788 & 0.987688 & -0.156434 & -6.31375 & 1.01247 & -6.39245 & -0.158384 \\ 100.0 & 1.74533 & 0.984808 & -0.173648 & -5.67128 & 1.01543 & -5.75877 & -0.176327 \\ 101.0 & 1.76278 & 0.981627 & -0.190809 & -5.14455 & 1.01872 & -5.24084 & -0.19438 \\ 102.0 & 1.78024 & 0.978148 & -0.207912 & -4.70463 & 1.02234 & -4.80973 & -0.212557 \\ 103.0 & 1.79769 & 0.97437 & -0.224951 & -4.33147 & 1.0263 & -4.44541 & -0.230868 \\ 104.0 & 1.81514 & 0.970296 & -0.241922 & -4.01078 & 1.03061 & -4.13356 & -0.249328 \\ 105.0 & 1.8326 & 0.965926 & -0.258819 & -3.73205 & 1.03528 & -3.8637 & -0.267949 \\ 106.0 & 1.85005 & 0.961262 & -0.275637 & -3.48741 & 1.0403 & -3.62796 & -0.286745 \\ 107.0 & 1.8675 & 0.956305 & -0.292372 & -3.27085 & 1.04569 & -3.4203 & -0.305731 \\ 108.0 & 1.88496 & 0.951056 & -0.309017 & -3.07768 & 1.05146 & -3.23607 & -0.32492 \\ 109.0 & 1.90241 & 0.945519 & -0.325568 & -2.90421 & 1.05762 & -3.07155 & -0.344328 \\ 110.0 & 1.91986 & 0.939693 & -0.34202 & -2.74748 & 1.06418 & -2.9238 & -0.36397 \\ 111.0 & 1.93732 & 0.93358 & -0.358368 & -2.60509 & 1.07115 & -2.79043 & -0.383864 \\ 112.0 & 1.95477 & 0.927184 & -0.374607 & -2.47509 & 1.07853 & -2.66947 & -0.404026 \\ 113.0 & 1.97222 & 0.920505 & -0.390731 & -2.35585 & 1.08636 & -2.5593 & -0.424475 \\ 114.0 & 1.98968 & 0.913545 & -0.406737 & -2.24604 & 1.09464 & -2.45859 & -0.445229 \\ 115.0 & 2.00713 & 0.906308 & -0.422618 & -2.14451 & 1.10338 & -2.3662 & -0.466308 \\ 116.0 & 2.02458 & 0.898794 & -0.438371 & -2.0503 & 1.1126 & -2.28117 & -0.487733 \\ 117.0 & 2.04204 & 0.891006 & -0.453991 & -1.96261 & 1.12233 & -2.20269 & -0.509526 \\ 118.0 & 2.05949 & 0.882948 & -0.469472 & -1.88073 & 1.13257 & -2.13005 & -0.531709 \\ 119.0 & 2.07694 & 0.87462 & -0.48481 & -1.80405 & 1.14335 & -2.06266 & -0.554309 \\ 120.0 & 2.0944 & 0.866025 & -0.5 & -1.73205 & 1.1547 & -2.0 & -0.57735 \\ 121.0 & 2.11185 & 0.857167 & -0.515038 & -1.66428 & 1.16663 & -1.9416 & -0.600861 \\ 122.0 & 2.1293 & 0.848048 & -0.529919 & -1.60033 & 1.17918 & -1.88708 & -0.624869 \\ 123.0 & 2.14675 & 0.838671 & -0.544639 & -1.53986 & 1.19236 & -1.83608 & -0.649408 \\ 124.0 & 2.16421 & 0.829037 & -0.559193 & -1.48256 & 1.20622 & -1.78829 & -0.674509 \\ 125.0 & 2.18166 & 0.819152 & -0.573576 & -1.42815 & 1.22077 & -1.74345 & -0.700208 \\ 126.0 & 2.19912 & 0.809017 & -0.587785 & -1.37638 & 1.23607 & -1.7013 & -0.726543 \\ 127.0 & 2.21657 & 0.798635 & -0.601815 & -1.32704 & 1.25214 & -1.66164 & -0.753554 \\ 128.0 & 2.23402 & 0.788011 & -0.615661 & -1.27994 & 1.26902 & -1.62427 & -0.781286 \\ 129.0 & 2.25147 & 0.777146 & -0.629321 & -1.2349 & 1.28676 & -1.58902 & -0.809784 \\ 130.0 & 2.26893 & 0.766044 & -0.642788 & -1.19175 & 1.30541 & -1.55572 & -0.8391 \\ 131.0 & 2.28638 & 0.75471 & -0.656059 & -1.15037 & 1.32501 & -1.52425 & -0.869287 \\ 132.0 & 2.30383 & 0.743145 & -0.669131 & -1.11061 & 1.34563 & -1.49448 & -0.900404 \\ 133.0 & 2.32129 & 0.731354 & -0.681998 & -1.07237 & 1.36733 & -1.46628 & -0.932516 \\ 134.0 & 2.33874 & 0.71934 & -0.694658 & -1.03553 & 1.39016 & -1.43956 & -0.965689 \\ 135.0 & 2.35619 & 0.707107 & -0.707107 & -1.0 & 1.41421 & -1.41421 & -1.0 \\ 136.0 & 2.37365 & 0.694658 & -0.71934 & -0.965688 & 1.43956 & -1.39016 & -1.03553 \\ 137.0 & 2.3911 & 0.681998 & -0.731354 & -0.932515 & 1.46628 & -1.36733 & -1.07237 \\ 138.0 & 2.40855 & 0.669131 & -0.743145 & -0.900404 & 1.49448 & -1.34563 & -1.11061 \\ 139.0 & 2.42601 & 0.656059 & -0.75471 & -0.869287 & 1.52425 & -1.32501 & -1.15037 \\ 140.0 & 2.44346 & 0.642787 & -0.766045 & -0.839099 & 1.55572 & -1.30541 & -1.19175 \\ 141.0 & 2.46091 & 0.62932 & -0.777146 & -0.809784 & 1.58902 & -1.28676 & -1.2349 \\ 142.0 & 2.47837 & 0.615661 & -0.788011 & -0.781286 & 1.62427 & -1.26902 & -1.27994 \\ 143.0 & 2.49582 & 0.601815 & -0.798636 & -0.753554 & 1.66164 & -1.25214 & -1.32705 \\ 144.0 & 2.51327 & 0.587785 & -0.809017 & -0.726542 & 1.7013 & -1.23607 & -1.37638 \\ 145.0 & 2.53073 & 0.573576 & -0.819152 & -0.700208 & 1.74345 & -1.22077 & -1.42815 \\ 146.0 & 2.54818 & 0.559193 & -0.829038 & -0.674508 & 1.78829 & -1.20622 & -1.48256 \\ 147.0 & 2.56563 & 0.544639 & -0.838671 & -0.649407 & 1.83608 & -1.19236 & -1.53987 \\ 148.0 & 2.58309 & 0.529919 & -0.848048 & -0.624869 & 1.88708 & -1.17918 & -1.60034 \\ 149.0 & 2.60054 & 0.515038 & -0.857167 & -0.600861 & 1.9416 & -1.16663 & -1.66428 \\ 150.0 & 2.61799 & 0.5 & -0.866026 & -0.57735 & 2.0 & -1.1547 & -1.73205 \\ 151.0 & 2.63545 & 0.48481 & -0.87462 & -0.554309 & 2.06267 & -1.14335 & -1.80405 \\ 152.0 & 2.6529 & 0.469472 & -0.882948 & -0.531709 & 2.13005 & -1.13257 & -1.88073 \\ 153.0 & 2.67035 & 0.45399 & -0.891007 & -0.509525 & 2.20269 & -1.12233 & -1.96261 \\ 154.0 & 2.68781 & 0.438371 & -0.898794 & -0.487733 & 2.28117 & -1.1126 & -2.0503 \\ 155.0 & 2.70526 & 0.422618 & -0.906308 & -0.466308 & 2.3662 & -1.10338 & -2.14451 \\ 156.0 & 2.72271 & 0.406737 & -0.913545 & -0.445229 & 2.45859 & -1.09464 & -2.24604 \\ 157.0 & 2.74017 & 0.390731 & -0.920505 & -0.424475 & 2.55931 & -1.08636 & -2.35585 \\ 158.0 & 2.75762 & 0.374606 & -0.927184 & -0.404026 & 2.66947 & -1.07853 & -2.47509 \\ 159.0 & 2.77507 & 0.358368 & -0.93358 & -0.383864 & 2.79043 & -1.07115 & -2.60509 \\ 160.0 & 2.79253 & 0.34202 & -0.939693 & -0.36397 & 2.92381 & -1.06418 & -2.74748 \\ 161.0 & 2.80998 & 0.325568 & -0.945519 & -0.344328 & 3.07155 & -1.05762 & -2.90421 \\ 162.0 & 2.82743 & 0.309017 & -0.951056 & -0.32492 & 3.23607 & -1.05146 & -3.07768 \\ 163.0 & 2.84489 & 0.292372 & -0.956305 & -0.305731 & 3.4203 & -1.04569 & -3.27085 \\ 164.0 & 2.86234 & 0.275637 & -0.961262 & -0.286745 & 3.62796 & -1.0403 & -3.48741 \\ 165.0 & 2.87979 & 0.258819 & -0.965926 & -0.267949 & 3.86371 & -1.03528 & -3.73205 \\ 166.0 & 2.89725 & 0.241922 & -0.970296 & -0.249328 & 4.13357 & -1.03061 & -4.01078 \\ 167.0 & 2.9147 & 0.224951 & -0.97437 & -0.230868 & 4.44542 & -1.0263 & -4.33148 \\ 168.0 & 2.93215 & 0.207912 & -0.978148 & -0.212556 & 4.80974 & -1.02234 & -4.70463 \\ 169.0 & 2.94961 & 0.190809 & -0.981627 & -0.19438 & 5.24085 & -1.01872 & -5.14456 \\ 170.0 & 2.96706 & 0.173648 & -0.984808 & -0.176327 & 5.75877 & -1.01543 & -5.67128 \\ 171.0 & 2.98451 & 0.156434 & -0.987688 & -0.158384 & 6.39245 & -1.01247 & -6.31375 \\ 172.0 & 3.00197 & 0.139173 & -0.990268 & -0.140541 & 7.18529 & -1.00983 & -7.11537 \\ 173.0 & 3.01942 & 0.121869 & -0.992546 & -0.122784 & 8.20551 & -1.00751 & -8.14435 \\ 174.0 & 3.03687 & 0.104528 & -0.994522 & -0.105104 & 9.56679 & -1.00551 & -9.51438 \\ 175.0 & 3.05433 & 0.0871556 & -0.996195 & -0.0874886 & 11.4737 & -1.00382 & -11.4301 \\ 176.0 & 3.07178 & 0.0697562 & -0.997564 & -0.0699266 & 14.3356 & -1.00244 & -14.3007 \\ 177.0 & 3.08923 & 0.052336 & -0.99863 & -0.0524079 & 19.1073 & -1.00137 & -19.0811 \\ 178.0 & 3.10669 & 0.0348995 & -0.999391 & -0.0349207 & 28.6537 & -1.00061 & -28.6363 \\ 179.0 & 3.12414 & 0.0174525 & -0.999848 & -0.0174551 & 57.2985 & -1.00015 & -57.2898 \\ 180.0 & 3.14159 & -8.74228e-08 & -1.0 & 8.74228e-08 & -99999.0 & -1.0 & 99999.0 \\ 181.0 & 3.15905 & -0.0174526 & -0.999848 & 0.0174553 & -57.2979 & -1.00015 & 57.2892 \\ 182.0 & 3.1765 & -0.0348996 & -0.999391 & 0.0349209 & -28.6536 & -1.00061 & 28.6361 \\ 183.0 & 3.19395 & -0.0523362 & -0.99863 & 0.052408 & -19.1072 & -1.00137 & 19.081 \\ 184.0 & 3.21141 & -0.0697564 & -0.997564 & 0.0699267 & -14.3356 & -1.00244 & 14.3007 \\ 185.0 & 3.22886 & -0.0871558 & -0.996195 & 0.0874887 & -11.4737 & -1.00382 & 11.43 \\ 186.0 & 3.24631 & -0.104528 & -0.994522 & 0.105104 & -9.56678 & -1.00551 & 9.51437 \\ 187.0 & 3.26377 & -0.121869 & -0.992546 & 0.122785 & -8.2055 & -1.00751 & 8.14434 \\ 188.0 & 3.28122 & -0.139173 & -0.990268 & 0.140541 & -7.18528 & -1.00983 & 7.11536 \\ 189.0 & 3.29867 & -0.156435 & -0.987688 & 0.158385 & -6.39245 & -1.01247 & 6.31375 \\ 190.0 & 3.31613 & -0.173648 & -0.984808 & 0.176327 & -5.75876 & -1.01543 & 5.67127 \\ 191.0 & 3.33358 & -0.190809 & -0.981627 & 0.19438 & -5.24084 & -1.01872 & 5.14456 \\ 192.0 & 3.35103 & -0.207912 & -0.978148 & 0.212557 & -4.80973 & -1.02234 & 4.70463 \\ 193.0 & 3.36849 & -0.224951 & -0.97437 & 0.230868 & -4.44541 & -1.0263 & 4.33148 \\ 194.0 & 3.38594 & -0.241922 & -0.970296 & 0.249328 & -4.13356 & -1.03061 & 4.01078 \\ 195.0 & 3.40339 & -0.258819 & -0.965926 & 0.267949 & -3.8637 & -1.03528 & 3.73205 \\ 196.0 & 3.42085 & -0.275638 & -0.961262 & 0.286746 & -3.62795 & -1.0403 & 3.48741 \\ 197.0 & 3.4383 & -0.292372 & -0.956305 & 0.305731 & -3.4203 & -1.04569 & 3.27085 \\ 198.0 & 3.45575 & -0.309017 & -0.951057 & 0.32492 & -3.23607 & -1.05146 & 3.07768 \\ 199.0 & 3.47321 & -0.325568 & -0.945519 & 0.344328 & -3.07155 & -1.05762 & 2.90421 \\ 200.0 & 3.49066 & -0.34202 & -0.939693 & 0.36397 & -2.9238 & -1.06418 & 2.74748 \\ 201.0 & 3.50811 & -0.358368 & -0.93358 & 0.383864 & -2.79043 & -1.07115 & 2.60509 \\ 202.0 & 3.52557 & -0.374607 & -0.927184 & 0.404026 & -2.66947 & -1.07853 & 2.47509 \\ 203.0 & 3.54302 & -0.390731 & -0.920505 & 0.424475 & -2.5593 & -1.08636 & 2.35585 \\ 204.0 & 3.56047 & -0.406737 & -0.913545 & 0.445229 & -2.45859 & -1.09464 & 2.24603 \\ 205.0 & 3.57792 & -0.422618 & -0.906308 & 0.466308 & -2.3662 & -1.10338 & 2.14451 \\ 206.0 & 3.59538 & -0.438371 & -0.898794 & 0.487733 & -2.28117 & -1.1126 & 2.0503 \\ 207.0 & 3.61283 & -0.453991 & -0.891007 & 0.509525 & -2.20269 & -1.12233 & 1.96261 \\ 208.0 & 3.63029 & -0.469472 & -0.882948 & 0.53171 & -2.13005 & -1.13257 & 1.88073 \\ 209.0 & 3.64774 & -0.48481 & -0.87462 & 0.554309 & -2.06266 & -1.14335 & 1.80405 \\ 210.0 & 3.66519 & -0.5 & -0.866025 & 0.577351 & -2.0 & -1.1547 & 1.73205 \\ 211.0 & 3.68265 & -0.515038 & -0.857167 & 0.600861 & -1.9416 & -1.16663 & 1.66428 \\ 212.0 & 3.7001 & -0.529919 & -0.848048 & 0.624869 & -1.88708 & -1.17918 & 1.60033 \\ 213.0 & 3.71755 & -0.544639 & -0.838671 & 0.649408 & -1.83608 & -1.19236 & 1.53987 \\ 214.0 & 3.735 & -0.559193 & -0.829038 & 0.674509 & -1.78829 & -1.20622 & 1.48256 \\ 215.0 & 3.75246 & -0.573577 & -0.819152 & 0.700208 & -1.74345 & -1.22077 & 1.42815 \\ 216.0 & 3.76991 & -0.587785 & -0.809017 & 0.726543 & -1.7013 & -1.23607 & 1.37638 \\ 217.0 & 3.78736 & -0.601815 & -0.798635 & 0.753554 & -1.66164 & -1.25214 & 1.32704 \\ 218.0 & 3.80482 & -0.615661 & -0.788011 & 0.781285 & -1.62427 & -1.26902 & 1.27994 \\ 219.0 & 3.82227 & -0.62932 & -0.777146 & 0.809784 & -1.58902 & -1.28676 & 1.2349 \\ 220.0 & 3.83972 & -0.642788 & -0.766044 & 0.8391 & -1.55572 & -1.30541 & 1.19175 \\ 221.0 & 3.85718 & -0.656059 & -0.75471 & 0.869287 & -1.52425 & -1.32501 & 1.15037 \\ 222.0 & 3.87463 & -0.669131 & -0.743145 & 0.900404 & -1.49448 & -1.34563 & 1.11061 \\ 223.0 & 3.89208 & -0.681998 & -0.731354 & 0.932515 & -1.46628 & -1.36733 & 1.07237 \\ 224.0 & 3.90954 & -0.694659 & -0.71934 & 0.965689 & -1.43956 & -1.39016 & 1.03553 \\ 225.0 & 3.92699 & -0.707107 & -0.707107 & 1.0 & -1.41421 & -1.41421 & 1.0 \\ 226.0 & 3.94444 & -0.71934 & -0.694658 & 1.03553 & -1.39016 & -1.43956 & 0.965689 \\ 227.0 & 3.9619 & -0.731354 & -0.681998 & 1.07237 & -1.36733 & -1.46628 & 0.932515 \\ 228.0 & 3.97935 & -0.743145 & -0.669131 & 1.11061 & -1.34563 & -1.49448 & 0.900404 \\ 229.0 & 3.9968 & -0.75471 & -0.656059 & 1.15037 & -1.32501 & -1.52425 & 0.869286 \\ 230.0 & 4.01426 & -0.766045 & -0.642788 & 1.19175 & -1.30541 & -1.55572 & 0.839099 \\ 231.0 & 4.03171 & -0.777146 & -0.62932 & 1.2349 & -1.28676 & -1.58902 & 0.809784 \\ 232.0 & 4.04916 & -0.788011 & -0.615662 & 1.27994 & -1.26902 & -1.62427 & 0.781286 \\ 233.0 & 4.06662 & -0.798635 & -0.601815 & 1.32704 & -1.25214 & -1.66164 & 0.753554 \\ 234.0 & 4.08407 & -0.809017 & -0.587785 & 1.37638 & -1.23607 & -1.7013 & 0.726542 \\ 235.0 & 4.10152 & -0.819152 & -0.573576 & 1.42815 & -1.22077 & -1.74345 & 0.700207 \\ 236.0 & 4.11898 & -0.829038 & -0.559193 & 1.48256 & -1.20622 & -1.78829 & 0.674508 \\ 237.0 & 4.13643 & -0.838671 & -0.544639 & 1.53987 & -1.19236 & -1.83608 & 0.649407 \\ 238.0 & 4.15388 & -0.848048 & -0.529919 & 1.60034 & -1.17918 & -1.88708 & 0.624869 \\ 239.0 & 4.17134 & -0.857167 & -0.515038 & 1.66428 & -1.16663 & -1.9416 & 0.600861 \\ 240.0 & 4.18879 & -0.866025 & -0.5 & 1.73205 & -1.1547 & -2.0 & 0.57735 \\ 241.0 & 4.20624 & -0.87462 & -0.48481 & 1.80405 & -1.14335 & -2.06267 & 0.554309 \\ 242.0 & 4.2237 & -0.882948 & -0.469472 & 1.88073 & -1.13257 & -2.13005 & 0.53171 \\ 243.0 & 4.24115 & -0.891007 & -0.45399 & 1.96261 & -1.12233 & -2.20269 & 0.509525 \\ 244.0 & 4.2586 & -0.898794 & -0.438371 & 2.0503 & -1.1126 & -2.28117 & 0.487732 \\ 245.0 & 4.27606 & -0.906308 & -0.422618 & 2.14451 & -1.10338 & -2.3662 & 0.466308 \\ 246.0 & 4.29351 & -0.913545 & -0.406737 & 2.24604 & -1.09464 & -2.45859 & 0.445229 \\ 247.0 & 4.31096 & -0.920505 & -0.390731 & 2.35585 & -1.08636 & -2.5593 & 0.424475 \\ 248.0 & 4.32842 & -0.927184 & -0.374606 & 2.47509 & -1.07853 & -2.66947 & 0.404026 \\ 249.0 & 4.34587 & -0.933581 & -0.358368 & 2.60509 & -1.07114 & -2.79043 & 0.383864 \\ 250.0 & 4.36332 & -0.939693 & -0.34202 & 2.74748 & -1.06418 & -2.9238 & 0.36397 \\ 251.0 & 4.38078 & -0.945519 & -0.325568 & 2.90421 & -1.05762 & -3.07155 & 0.344328 \\ 252.0 & 4.39823 & -0.951057 & -0.309017 & 3.07769 & -1.05146 & -3.23607 & 0.324919 \\ 253.0 & 4.41568 & -0.956305 & -0.292372 & 3.27085 & -1.04569 & -3.4203 & 0.305731 \\ 254.0 & 4.43314 & -0.961262 & -0.275637 & 3.48742 & -1.0403 & -3.62796 & 0.286745 \\ 255.0 & 4.45059 & -0.965926 & -0.258819 & 3.73205 & -1.03528 & -3.8637 & 0.267949 \\ 256.0 & 4.46804 & -0.970296 & -0.241922 & 4.01078 & -1.03061 & -4.13356 & 0.249328 \\ 257.0 & 4.4855 & -0.97437 & -0.224951 & 4.33148 & -1.0263 & -4.44542 & 0.230868 \\ 258.0 & 4.50295 & -0.978148 & -0.207911 & 4.70464 & -1.02234 & -4.80974 & 0.212556 \\ 259.0 & 4.5204 & -0.981627 & -0.190809 & 5.14456 & -1.01872 & -5.24085 & 0.19438 \\ 260.0 & 4.53786 & -0.984808 & -0.173648 & 5.67128 & -1.01543 & -5.75877 & 0.176327 \\ 261.0 & 4.55531 & -0.987688 & -0.156435 & 6.31375 & -1.01247 & -6.39245 & 0.158385 \\ 262.0 & 4.57276 & -0.990268 & -0.139173 & 7.11536 & -1.00983 & -7.18529 & 0.140541 \\ 263.0 & 4.59022 & -0.992546 & -0.121869 & 8.14436 & -1.00751 & -8.20552 & 0.122784 \\ 264.0 & 4.60767 & -0.994522 & -0.104528 & 9.51438 & -1.00551 & -9.56678 & 0.105104 \\ 265.0 & 4.62512 & -0.996195 & -0.0871557 & 11.4301 & -1.00382 & -11.4737 & 0.0874886 \\ 266.0 & 4.64258 & -0.997564 & -0.0697561 & 14.3007 & -1.00244 & -14.3357 & 0.0699264 \\ 267.0 & 4.66003 & -0.99863 & -0.0523361 & 19.0811 & -1.00137 & -19.1073 & 0.0524079 \\ 268.0 & 4.67748 & -0.999391 & -0.0348993 & 28.6364 & -1.00061 & -28.6539 & 0.0349206 \\ 269.0 & 4.69494 & -0.999848 & -0.0174523 & 57.2903 & -1.00015 & -57.2991 & 0.017455 \\ 270.0 & 4.71239 & -1.0 & 1.19249e-08 & -99999.0 & -1.0 & 99999.0 & -1.19249e-08 \\ 271.0 & 4.72984 & -0.999848 & 0.0174528 & -57.2887 & -1.00015 & 57.2974 & -0.0174555 \\ 272.0 & 4.7473 & -0.999391 & 0.0348998 & -28.636 & -1.00061 & 28.6535 & -0.0349211 \\ 273.0 & 4.76475 & -0.99863 & 0.0523361 & -19.0811 & -1.00137 & 19.1073 & -0.052408 \\ 274.0 & 4.7822 & -0.997564 & 0.0697566 & -14.3006 & -1.00244 & 14.3356 & -0.0699269 \\ 275.0 & 4.79966 & -0.996195 & 0.0871557 & -11.4301 & -1.00382 & 11.4737 & -0.0874887 \\ 276.0 & 4.81711 & -0.994522 & 0.104528 & -9.51437 & -1.00551 & 9.56678 & -0.105104 \\ 277.0 & 4.83456 & -0.992546 & 0.12187 & -8.14433 & -1.00751 & 8.20549 & -0.122785 \\ 278.0 & 4.85202 & -0.990268 & 0.139173 & -7.11536 & -1.00983 & 7.18529 & -0.140541 \\ 279.0 & 4.86947 & -0.987688 & 0.156435 & -6.31375 & -1.01247 & 6.39245 & -0.158385 \\ 280.0 & 4.88692 & -0.984808 & 0.173649 & -5.67127 & -1.01543 & 5.75876 & -0.176327 \\ 281.0 & 4.90438 & -0.981627 & 0.190809 & -5.14456 & -1.01872 & 5.24085 & -0.19438 \\ 282.0 & 4.92183 & -0.978148 & 0.207912 & -4.70462 & -1.02234 & 4.80973 & -0.212557 \\ 283.0 & 4.93928 & -0.97437 & 0.224951 & -4.33147 & -1.0263 & 4.44541 & -0.230868 \\ 284.0 & 4.95674 & -0.970296 & 0.241922 & -4.01078 & -1.03061 & 4.13356 & -0.249328 \\ 285.0 & 4.97419 & -0.965926 & 0.258819 & -3.73204 & -1.03528 & 3.8637 & -0.26795 \\ 286.0 & 4.99164 & -0.961262 & 0.275638 & -3.48741 & -1.0403 & 3.62795 & -0.286746 \\ 287.0 & 5.0091 & -0.956305 & 0.292372 & -3.27085 & -1.04569 & 3.4203 & -0.305731 \\ 288.0 & 5.02655 & -0.951056 & 0.309017 & -3.07768 & -1.05146 & 3.23607 & -0.32492 \\ 289.0 & 5.044 & -0.945519 & 0.325568 & -2.90421 & -1.05762 & 3.07155 & -0.344328 \\ 290.0 & 5.06145 & -0.939693 & 0.34202 & -2.74748 & -1.06418 & 2.9238 & -0.36397 \\ 291.0 & 5.07891 & -0.93358 & 0.358368 & -2.60509 & -1.07115 & 2.79043 & -0.383864 \\ 292.0 & 5.09636 & -0.927184 & 0.374607 & -2.47509 & -1.07853 & 2.66947 & -0.404026 \\ 293.0 & 5.11381 & -0.920505 & 0.390731 & -2.35585 & -1.08636 & 2.5593 & -0.424475 \\ 294.0 & 5.13127 & -0.913545 & 0.406737 & -2.24603 & -1.09464 & 2.45859 & -0.445229 \\ 295.0 & 5.14872 & -0.906308 & 0.422618 & -2.14451 & -1.10338 & 2.3662 & -0.466308 \\ 296.0 & 5.16617 & -0.898794 & 0.438371 & -2.0503 & -1.1126 & 2.28117 & -0.487733 \\ 297.0 & 5.18363 & -0.891006 & 0.453991 & -1.96261 & -1.12233 & 2.20269 & -0.509526 \\ 298.0 & 5.20108 & -0.882948 & 0.469472 & -1.88073 & -1.13257 & 2.13005 & -0.53171 \\ 299.0 & 5.21853 & -0.87462 & 0.48481 & -1.80405 & -1.14335 & 2.06267 & -0.554309 \\ 300.0 & 5.23599 & -0.866025 & 0.5 & -1.73205 & -1.1547 & 2.0 & -0.577351 \\ 301.0 & 5.25344 & -0.857167 & 0.515038 & -1.66428 & -1.16663 & 1.9416 & -0.60086 \\ 302.0 & 5.27089 & -0.848048 & 0.529919 & -1.60033 & -1.17918 & 1.88708 & -0.62487 \\ 303.0 & 5.28835 & -0.83867 & 0.544639 & -1.53986 & -1.19236 & 1.83608 & -0.649408 \\ 304.0 & 5.3058 & -0.829038 & 0.559193 & -1.48256 & -1.20622 & 1.78829 & -0.674509 \\ 305.0 & 5.32325 & -0.819152 & 0.573577 & -1.42815 & -1.22077 & 1.74345 & -0.700208 \\ 306.0 & 5.34071 & -0.809017 & 0.587785 & -1.37638 & -1.23607 & 1.7013 & -0.726543 \\ 307.0 & 5.35816 & -0.798635 & 0.601815 & -1.32704 & -1.25214 & 1.66164 & -0.753554 \\ 308.0 & 5.37561 & -0.788011 & 0.615662 & -1.27994 & -1.26902 & 1.62427 & -0.781286 \\ 309.0 & 5.39307 & -0.777146 & 0.62932 & -1.2349 & -1.28676 & 1.58902 & -0.809784 \\ 310.0 & 5.41052 & -0.766044 & 0.642788 & -1.19175 & -1.30541 & 1.55572 & -0.839099 \\ 311.0 & 5.42797 & -0.754709 & 0.656059 & -1.15037 & -1.32501 & 1.52425 & -0.869287 \\ 312.0 & 5.44543 & -0.743145 & 0.669131 & -1.11061 & -1.34563 & 1.49448 & -0.900404 \\ 313.0 & 5.46288 & -0.731354 & 0.681998 & -1.07237 & -1.36733 & 1.46628 & -0.932515 \\ 314.0 & 5.48033 & -0.719339 & 0.694659 & -1.03553 & -1.39016 & 1.43956 & -0.96569 \\ 315.0 & 5.49779 & -0.707107 & 0.707107 & -1.0 & -1.41421 & 1.41421 & -1.0 \\ 316.0 & 5.51524 & -0.694658 & 0.71934 & -0.965688 & -1.43956 & 1.39016 & -1.03553 \\ 317.0 & 5.53269 & -0.681998 & 0.731354 & -0.932515 & -1.46628 & 1.36733 & -1.07237 \\ 318.0 & 5.55015 & -0.669131 & 0.743145 & -0.900404 & -1.49448 & 1.34563 & -1.11061 \\ 319.0 & 5.5676 & -0.656059 & 0.75471 & -0.869286 & -1.52425 & 1.32501 & -1.15037 \\ 320.0 & 5.58505 & -0.642787 & 0.766045 & -0.839099 & -1.55572 & 1.30541 & -1.19175 \\ 321.0 & 5.60251 & -0.62932 & 0.777146 & -0.809784 & -1.58902 & 1.28676 & -1.2349 \\ 322.0 & 5.61996 & -0.615661 & 0.788011 & -0.781285 & -1.62427 & 1.26902 & -1.27994 \\ 323.0 & 5.63741 & -0.601815 & 0.798636 & -0.753554 & -1.66164 & 1.25214 & -1.32704 \\ 324.0 & 5.65487 & -0.587785 & 0.809017 & -0.726543 & -1.7013 & 1.23607 & -1.37638 \\ 325.0 & 5.67232 & -0.573576 & 0.819152 & -0.700207 & -1.74345 & 1.22077 & -1.42815 \\ 326.0 & 5.68977 & -0.559193 & 0.829037 & -0.674509 & -1.78829 & 1.20622 & -1.48256 \\ 327.0 & 5.70723 & -0.544639 & 0.838671 & -0.649407 & -1.83608 & 1.19236 & -1.53987 \\ 328.0 & 5.72468 & -0.529919 & 0.848048 & -0.624869 & -1.88708 & 1.17918 & -1.60033 \\ 329.0 & 5.74213 & -0.515038 & 0.857167 & -0.600861 & -1.9416 & 1.16663 & -1.66428 \\ 330.0 & 5.75959 & -0.5 & 0.866026 & -0.57735 & -2.0 & 1.1547 & -1.73205 \\ 331.0 & 5.77704 & -0.484809 & 0.87462 & -0.554309 & -2.06267 & 1.14335 & -1.80405 \\ 332.0 & 5.79449 & -0.469471 & 0.882948 & -0.531709 & -2.13005 & 1.13257 & -1.88073 \\ 333.0 & 5.81195 & -0.453991 & 0.891007 & -0.509525 & -2.20269 & 1.12233 & -1.96261 \\ 334.0 & 5.8294 & -0.438371 & 0.898794 & -0.487732 & -2.28117 & 1.1126 & -2.05031 \\ 335.0 & 5.84685 & -0.422618 & 0.906308 & -0.466307 & -2.3662 & 1.10338 & -2.14451 \\ 336.0 & 5.86431 & -0.406736 & 0.913546 & -0.445228 & -2.45859 & 1.09464 & -2.24604 \\ 337.0 & 5.88176 & -0.390731 & 0.920505 & -0.424474 & -2.55931 & 1.08636 & -2.35586 \\ 338.0 & 5.89921 & -0.374606 & 0.927184 & -0.404026 & -2.66947 & 1.07853 & -2.47509 \\ 339.0 & 5.91667 & -0.358368 & 0.933581 & -0.383864 & -2.79043 & 1.07114 & -2.60509 \\ 340.0 & 5.93412 & -0.34202 & 0.939693 & -0.36397 & -2.9238 & 1.06418 & -2.74748 \\ 341.0 & 5.95157 & -0.325568 & 0.945519 & -0.344327 & -3.07155 & 1.05762 & -2.90421 \\ 342.0 & 5.96903 & -0.309017 & 0.951057 & -0.32492 & -3.23607 & 1.05146 & -3.07768 \\ 343.0 & 5.98648 & -0.292372 & 0.956305 & -0.305731 & -3.4203 & 1.04569 & -3.27085 \\ 344.0 & 6.00393 & -0.275638 & 0.961262 & -0.286746 & -3.62795 & 1.0403 & -3.48741 \\ 345.0 & 6.02139 & -0.258819 & 0.965926 & -0.267949 & -3.86371 & 1.03528 & -3.73205 \\ 346.0 & 6.03884 & -0.241922 & 0.970296 & -0.249328 & -4.13357 & 1.03061 & -4.01078 \\ 347.0 & 6.05629 & -0.224951 & 0.97437 & -0.230868 & -4.44541 & 1.0263 & -4.33148 \\ 348.0 & 6.07375 & -0.207911 & 0.978148 & -0.212556 & -4.80974 & 1.02234 & -4.70464 \\ 349.0 & 6.0912 & -0.190809 & 0.981627 & -0.19438 & -5.24085 & 1.01872 & -5.14456 \\ 350.0 & 6.10865 & -0.173648 & 0.984808 & -0.176327 & -5.75878 & 1.01543 & -5.67129 \\ 351.0 & 6.12611 & -0.156434 & 0.987688 & -0.158384 & -6.39248 & 1.01247 & -6.31378 \\ 352.0 & 6.14356 & -0.139173 & 0.990268 & -0.14054 & -7.18532 & 1.00983 & -7.1154 \\ 353.0 & 6.16101 & -0.121869 & 0.992546 & -0.122785 & -8.2055 & 1.00751 & -8.14434 \\ 354.0 & 6.17847 & -0.104529 & 0.994522 & -0.105104 & -9.56676 & 1.00551 & -9.51435 \\ 355.0 & 6.19592 & -0.087156 & 0.996195 & -0.0874889 & -11.4737 & 1.00382 & -11.43 \\ 356.0 & 6.21337 & -0.0697564 & 0.997564 & -0.0699267 & -14.3356 & 1.00244 & -14.3007 \\ 357.0 & 6.23083 & -0.052336 & 0.99863 & -0.0524078 & -19.1073 & 1.00137 & -19.0811 \\ 358.0 & 6.24828 & -0.0348996 & 0.999391 & -0.0349209 & -28.6536 & 1.00061 & -28.6362 \\ 359.0 & 6.26573 & -0.0174521 & 0.999848 & -0.0174548 & -57.2996 & 1.00015 & -57.2909 \\ 360.0 & 6.28319 & 1.74846e-07 & 1.0 & 1.74846e-07 & 99999.0 & 1.0 & 99999.0 \\ \end{tabular} \end{table}