Mean effective pressure: Difference between revisions

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The '''Thomson problem''' is to determine the minimum energy configuration of ''N'' [[electron]]s on the surface of a sphere that repel each other with a force given by [[Coulomb's law]]. The physicist [[J. J. Thomson]] posed the problem in 1904<ref>J. J. Thomson, "On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a number of Corpuscles arranged at equal intervals around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure", ''Philosophical Magazine'' Series 6, Volume 7, Number 39, pp. 237–265, March 1904</ref> after creating his so-called  [[plum pudding model]] of the [[atom]]. 
Greetings! I am Myrtle Shroyer. I am a meter reader but I strategy on changing it. California is where I've usually been residing and I love each day living right here. Doing ceramics is what her family members and her appreciate.<br><br>Also visit my homepage ... [http://www.animecontent.com/blog/461505 www.animecontent.com]
Related problems include the study of the geometry of the minimum energy configuration and the study of the large N behavior of the minimum energy.
 
== Mathematical statement ==
Let <math> \mathbf{r}_1, \mathbf{r}_2, \ldots, \mathbf{r}_N </math> be a collection of <math>N</math> distinct points on the [[unit sphere]] centered at the origin.
The '' energy '' of this configuration of points is defined to be  <math> \sum_{i < j} \frac{1}{|\mathbf{r}_i-\mathbf{r}_j|}  </math>. 
Thomson's problem is to minimize this energy over all possible collections of <math>N</math> distinct points
on the unit sphere.
 
== Known solutions ==
Minimal energy configurations have been rigorously identified in only a handful of cases.
In the case of two points, the optimal configuration consists of [[antipodal point]]s.
For N=3, three equidistant points on a [[great circle]] realize the minimum energy configuration.
.<ref>L. Foppl, "Stabile anordnungen von elektronen im atom", ''J. Reine Angew. Math'', 141 (1912), 251–301.</ref> The vertices of a regular [[tetrahedron]] minimize the energy in the case of 4 points. Yudin <ref>V.A. Yudin, "The minimum of potential energy of a system of point charges", ''Discretnaya Matematika'' 4(2) (1992), 115–121 (in Russian); Discrete Math. Appl., 3(1) (1993), 75–81</ref> showed that the vertices of the regular [[octahedron]] solve the problem in the case of 6 vertices. N.N. Andreev <ref>N.N. Andreev, "An extremal property of the icosahedron", ''East J. Approximation'', 2(4) (1996), 459-462, MR 97m:52022, Zbl 0877.51021</ref> provides a method to prove that the vertex set of the regular [[icosahedron]] provides a solution in the case of 12 vertices.
In 2010, Richard Schwartz announced a mathematically rigorous computer-aided solution for 5 points.<ref>http://arxiv.org/abs/1001.3702</ref>
 
{{pquote|No fact discovered about the atom can be trivial, nor fail to accelerate the progress of physical science, for the greater part of natural philosophy is the outcome of the structure and mechanism of the atom.|Sir J. J. Thomson|<ref>Sir J.J. Thomson, The Romanes Lecture, 1914 (The Atomic Theory)</ref>}}
 
== Generalizations ==
One can also ask for ground states of particles interacting with arbitrary potentials.
To be mathematically precise, let f be a decreasing real-valued function, and define the energy functional <math> \sum_{i < j} f(|x_i-x_j|)</math>
 
Traditionally, one considers <math> f(x)=x^{-\alpha} </math>.  Notable cases include ''α''&nbsp;=&nbsp;∞, the [[Tammes problem]] (packing); ''α''&nbsp;=&nbsp;1, the Thomson problem; ''α''&nbsp;=&nbsp;0, [[Whyte's problem]] (to maximize the product of distances).
 
One may also consider configurations of ''N'' points on a [[n-sphere|sphere of higher dimension]].
 
== Relations to other scientific problems ==
Though experimental evidence led to the abandonment of Thomson's [[plum pudding model]], Thomson's problem has since found
a role in the study of other physical models.  These include [[multi-electron bubble]]s and the surface ordering of liquid metal drops confined in [[Pauli traps]].
 
The generalized Thomson problem arises, for example, in determining the arrangements of the protein subunits which comprise the shells of spherical [[virus]]es. The "particles" in this application are clusters of protein subunits arranged on a shell. Other realizations include regular arrangements of [[colloid]] particles in ''colloidosomes'', proposed for encapsulation of active ingredients such as drugs, nutrients or living cells, [[fullerene]] patterns of carbon atoms, and [[VSEPR Theory]]. An example with long-range logarithmic interactions is provided by the [[Abrikosov vortices]] which would form at low temperatures in a [[superconductivity|superconducting]] metal shell with a large monopole at the center.
 
== Configurations of smallest known energy ==
In the following table '''<math>N</math>''' is the number of points (charges) in a configuration.  '''<math>E_1</math>''' is the energy. The symmetry type is given in [[Schönflies notation]] (see [[Point groups in three dimensions]]). '''<math>r_i</math>''' are the positions of the charges. Most symmetry types require the vector sum of the positions (and thus the [[electric dipole moment]]) to be zero.
 
It is customary to also consider the polyhedron formed by the [[convex hull]] of the points. Thus '''<math>v_i</math>''' is the number of vertices where the given number of edges meet. '''<math>e</math>''' is the total number of edges and '''<math>f_3</math>''' and '''<math>f_4</math>''' are the number of triangle and quadrilateral faces. '''<math>\theta_1</math>''' is the smallest angle between any two points.
 
{| class="wikitable"
|-
! ''N''
! <math>E_{1}</math>
! [[Point groups in three dimensions|Symmetry]]
! <math>\left| \sum \mathbf{r}_{i} \right| </math>
! <math>v_{3}</math>
! <math>v_{4}</math>
! <math>v_{5}</math>
! <math>v_{6}</math>
! <math>v_{7}</math>
! <math>v_{8}</math>
! <math>e</math>
! <math>f_{3}</math>
! <math>f_{4}</math>
! <math>\theta_{1}</math>
! Equivalent Polyhedron
|-
| align=right | 2
| align=right | 0.500000000
| align=center | <math>D_{\infty h}</math>
| align=center | 0
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=right | 180.000°
|-
| align=right | 3
| align=right | 1.732050808
| align=center | <math>D_{3h}</math>
| align=center | 0
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=center | –
| align=right | 120.000°
|-
| align=right | 4
| align=right | 3.674234614
| align=center | <math>T_{d}</math>
| align=center | 0
| align=right | 4
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 6
| align=right | 4
| align=right | 0
| align=right | 109.471°
| [[tetrahedron]]
|-
| align=right | 5
| align=right | 6.474691495
| align=center | <math>D_{3h}</math>
| align=center | 0
| align=right | 2
| align=right | 3
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 9
| align=right | 6
| align=right | 0
| align=right | 90.000°
| [[triangular dipyramid]]
|-
| align=right | 6
| align=right | 9.985281374
| align=center | <math>O_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 6
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 8
| align=right | 0
| align=right | 90.000°
| [[octahedron]]
|-
| align=right | 7
| align=right | 14.452977414
| align=center | <math>D_{5h}</math>
| align=center | 0
| align=right | 0
| align=right | 5
| align=right | 2
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 15
| align=right | 10
| align=right | 0
| align=right | 72.000°
| [[pentagonal dipyramid]]
|-
| align=right | 8
| align=right | 19.675287861
| align=center | <math>D_{4d}</math>
| align=center | 0
| align=right | 0
| align=right | 8
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 16
| align=right | 8
| align=right | 2
| align=right | 71.694°
| [[square antiprism]]
|-
| align=right | 9
| align=right | 25.759986531
| align=center | <math>D_{3h}</math>
| align=center | 0
| align=right | 0
| align=right | 3
| align=right | 6
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 21
| align=right | 14
| align=right | 0
| align=right | 61.190°
| [[triaugmented triangular prism]]
|-
| align=right | 10
| align=right | 32.716949460
| align=center | <math>D_{4d}</math>
| align=center | 0
| align=right | 0
| align=right | 2
| align=right | 8
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 16
| align=right | 0
| align=right | 64.996°
| [[gyroelongated square dipyramid]]
|-
| align=right | 11
| align=right | 40.596450510
| align=center | <math>C_{2v}</math>
| align=center | 0.013219635
| align=right | 0
| align=right | 2
| align=right | 8
| align=right | 1
| align=right | 0
| align=right | 0
| align=right | 27
| align=right | 18
| align=right | 0
| align=right | 58.540°
|-
| align=right | 12
| align=right | 49.165253058
| align=center | <math>I_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 30
| align=right | 20
| align=right | 0
| align=right | 63.435°
| [[icosahedron]]
|-
| align=right | 13
| align=right | 58.853230612
| align=center | <math>C_{2v}</math>
| align=center | 0.008820367
| align=right | 0
| align=right | 1
| align=right | 10
| align=right | 2
| align=right | 0
| align=right | 0
| align=right | 33
| align=right | 22
| align=right | 0
| align=right | 52.317°
|-
| align=right | 14
| align=right | 69.306363297
| align=center | <math>D_{6d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 2
| align=right | 0
| align=right | 0
| align=right | 36
| align=right | 24
| align=right | 0
| align=right | 52.866°
| gyroelongated hexagonal dipyramid
|-
| align=right | 15
| align=right | 80.670244114
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 3
| align=right | 0
| align=right | 0
| align=right | 39
| align=right | 26
| align=right | 0
| align=right | 49.225°
|-
| align=right | 16
| align=right | 92.911655302
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 4
| align=right | 0
| align=right | 0
| align=right | 42
| align=right | 28
| align=right | 0
| align=right | 48.936°
|-
| align=right | 17
| align=right | 106.050404829
| align=center | <math>D_{5h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 5
| align=right | 0
| align=right | 0
| align=right | 45
| align=right | 30
| align=right | 0
| align=right | 50.108°
|-
| align=right | 18
| align=right | 120.084467447
| align=center | <math>D_{4d}</math>
| align=center | 0
| align=right | 0
| align=right | 2
| align=right | 8
| align=right | 8
| align=right | 0
| align=right | 0
| align=right | 48
| align=right | 32
| align=right | 0
| align=right | 47.534°
|-
| align=right | 19
| align=right | 135.089467557
| align=center | <math>C_{2v}</math>
| align=center | 0.000135163
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 5
| align=right | 0
| align=right | 0
| align=right | 50
| align=right | 32
| align=right | 1
| align=right | 44.910°
|-
| align=right | 20
| align=right | 150.881568334
| align=center | <math>D_{3h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 8
| align=right | 0
| align=right | 0
| align=right | 54
| align=right | 36
| align=right | 0
| align=right | 46.093°
|-
| align=right | 21
| align=right | 167.641622399
| align=center | <math>C_{2v}</math>
| align=center | 0.001406124
| align=right | 0
| align=right | 1
| align=right | 10
| align=right | 10
| align=right | 0
| align=right | 0
| align=right | 57
| align=right | 38
| align=right | 0
| align=right | 44.321°
|-
| align=right | 22
| align=right | 185.287536149
| align=center | <math>T_{d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 10
| align=right | 0
| align=right | 0
| align=right | 60
| align=right | 40
| align=right | 0
| align=right | 43.302°
|-
| align=right | 23
| align=right | 203.930190663
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 11
| align=right | 0
| align=right | 0
| align=right | 63
| align=right | 42
| align=right | 0
| align=right | 41.481°
|-
| align=right | 24
| align=right | 223.347074052
| align=center | <math>O</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 0
| align=right | 0
| align=right | 0
| align=right | 60
| align=right | 32
| align=right | 6
| align=right | 42.065°
| [[snub cube]]
|-
| align=right | 25
| align=right | 243.812760299
| align=center | <math>C_{s}</math>
| align=center | 0.001021305
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 11
| align=right | 0
| align=right | 0
| align=right | 68
| align=right | 44
| align=right | 1
| align=right | 39.610°
|-
| align=right | 26
| align=right | 265.133326317
| align=center | <math>C_{2}</math>
| align=center | 0.001919065
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 14
| align=right | 0
| align=right | 0
| align=right | 72
| align=right | 48
| align=right | 0
| align=right | 38.842°
|-
| align=right | 27
| align=right | 287.302615033
| align=center | <math>D_{5h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 15
| align=right | 0
| align=right | 0
| align=right | 75
| align=right | 50
| align=right | 0
| align=right | 39.940°
|-
| align=right | 28
| align=right | 310.491542358
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 16
| align=right | 0
| align=right | 0
| align=right | 78
| align=right | 52
| align=right | 0
| align=right | 37.824°
|-
| align=right | 29
| align=right | 334.634439920
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 17
| align=right | 0
| align=right | 0
| align=right | 81
| align=right | 54
| align=right | 0
| align=right | 36.391°
|-
| align=right | 30
| align=right | 359.603945904
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 18
| align=right | 0
| align=right | 0
| align=right | 84
| align=right | 56
| align=right | 0
| align=right | 36.942°
|-
| align=right | 31
| align=right | 385.530838063
| align=center | <math>C_{3v}</math>
| align=center | 0.003204712
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 19
| align=right | 0
| align=right | 0
| align=right | 87
| align=right | 58
| align=right | 0
| align=right | 36.373°
|-
| align=right | 32
| align=right | 412.261274651
| align=center | <math>I_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 20
| align=right | 0
| align=right | 0
| align=right | 90
| align=right | 60
| align=right | 0
| align=right | 37.377°
|-
| align=right | 33
| align=right | 440.204057448
| align=center | <math>C_{s}</math>
| align=center | 0.004356481
| align=right | 0
| align=right | 0
| align=right | 15
| align=right | 17
| align=right | 1
| align=right | 0
| align=right | 92
| align=right | 60
| align=right | 1
| align=right | 33.700°
|-
| align=right | 34
| align=right | 468.904853281
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 22
| align=right | 0
| align=right | 0
| align=right | 96
| align=right | 64
| align=right | 0
| align=right | 33.273°
|-
| align=right | 35
| align=right | 498.569872491
| align=center | <math>C_{2}</math>
| align=center | 0.000419208
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 23
| align=right | 0
| align=right | 0
| align=right | 99
| align=right | 66
| align=right | 0
| align=right | 33.100°
|-
| align=right | 36
| align=right | 529.122408375
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 24
| align=right | 0
| align=right | 0
| align=right | 102
| align=right | 68
| align=right | 0
| align=right | 33.229°
|-
| align=right | 37
| align=right | 560.618887731
| align=center | <math>D_{5h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 25
| align=right | 0
| align=right | 0
| align=right | 105
| align=right | 70
| align=right | 0
| align=right | 32.332°
|-
| align=right | 38
| align=right | 593.038503566
| align=center | <math>D_{6d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 26
| align=right | 0
| align=right | 0
| align=right | 108
| align=right | 72
| align=right | 0
| align=right | 33.236°
|-
| align=right | 39
| align=right | 626.389009017
| align=center | <math>D_{3h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 27
| align=right | 0
| align=right | 0
| align=right | 111
| align=right | 74
| align=right | 0
| align=right | 32.053°
|-
| align=right | 40
| align=right | 660.675278835
| align=center | <math>T_{d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 28
| align=right | 0
| align=right | 0
| align=right | 114
| align=right | 76
| align=right | 0
| align=right | 31.916°
|-
| align=right | 41
| align=right | 695.916744342
| align=center | <math>D_{3h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 29
| align=right | 0
| align=right | 0
| align=right | 117
| align=right | 78
| align=right | 0
| align=right | 31.528°
|-
| align=right | 42
| align=right | 732.078107544
| align=center | <math>D_{5h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 30
| align=right | 0
| align=right | 0
| align=right | 120
| align=right | 80
| align=right | 0
| align=right | 31.245°
|-
| align=right | 43
| align=right | 769.190846459
| align=center | <math>C_{2v}</math>
| align=center | 0.000399668
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 31
| align=right | 0
| align=right | 0
| align=right | 123
| align=right | 82
| align=right | 0
| align=right | 30.867°
|-
| align=right | 44
| align=right | 807.174263085
| align=center | <math>O_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 20
| align=right | 0
| align=right | 0
| align=right | 120
| align=right | 72
| align=right | 6
| align=right | 31.258°
|-
| align=right | 45
| align=right | 846.188401061
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 33
| align=right | 0
| align=right | 0
| align=right | 129
| align=right | 86
| align=right | 0
| align=right | 30.207°
|-
| align=right | 46
| align=right | 886.167113639
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 34
| align=right | 0
| align=right | 0
| align=right | 132
| align=right | 88
| align=right | 0
| align=right | 29.790°
|-
| align=right | 47
| align=right | 927.059270680
| align=center | <math>C_{s}</math>
| align=center | 0.002482914
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 33
| align=right | 0
| align=right | 0
| align=right | 134
| align=right | 88
| align=right | 1
| align=right | 28.787°
|-
| align=right | 48
| align=right | 968.713455344
| align=center | <math>O</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 24
| align=right | 0
| align=right | 0
| align=right | 132
| align=right | 80
| align=right | 6
| align=right | 29.690°
|-
| align=right | 49
| align=right | 1011.557182654
| align=center | <math>C_{3}</math>
| align=center | 0.001529341
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 37
| align=right | 0
| align=right | 0
| align=right | 141
| align=right | 94
| align=right | 0
| align=right | 28.387°
|-
| align=right | 50
| align=right | 1055.182314726
| align=center | <math>D_{6d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 38
| align=right | 0
| align=right | 0
| align=right | 144
| align=right | 96
| align=right | 0
| align=right | 29.231°
|-
| align=right | 51
| align=right | 1099.819290319
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 39
| align=right | 0
| align=right | 0
| align=right | 147
| align=right | 98
| align=right | 0
| align=right | 28.165°
|-
| align=right | 52
| align=right | 1145.418964319
| align=center | <math>C_{3}</math>
| align=center | 0.000457327
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 40
| align=right | 0
| align=right | 0
| align=right | 150
| align=right | 100
| align=right | 0
| align=right | 27.670°
|-
| align=right | 53
| align=right | 1191.922290416
| align=center | <math>C_{2v}</math>
| align=center | 0.000278469
| align=right | 0
| align=right | 0
| align=right | 18
| align=right | 35
| align=right | 0
| align=right | 0
| align=right | 150
| align=right | 96
| align=right | 3
| align=right | 27.137°
|-
| align=right | 54
| align=right | 1239.361474729
| align=center | <math>C_{2}</math>
| align=center | 0.000137870
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 42
| align=right | 0
| align=right | 0
| align=right | 156
| align=right | 104
| align=right | 0
| align=right | 27.030°
|-
| align=right | 55
| align=right | 1287.772720783
| align=center | <math>C_{2}</math>
| align=center | 0.000391696
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 43
| align=right | 0
| align=right | 0
| align=right | 159
| align=right | 106
| align=right | 0
| align=right | 26.615°
|-
| align=right | 56
| align=right | 1337.094945276
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 44
| align=right | 0
| align=right | 0
| align=right | 162
| align=right | 108
| align=right | 0
| align=right | 26.683°
|-
| align=right | 57
| align=right | 1387.383229253
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 45
| align=right | 0
| align=right | 0
| align=right | 165
| align=right | 110
| align=right | 0
| align=right | 26.702°
|-
| align=right | 58
| align=right | 1438.618250640
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 46
| align=right | 0
| align=right | 0
| align=right | 168
| align=right | 112
| align=right | 0
| align=right | 26.155°
|-
| align=right | 59
| align=right | 1490.773335279
| align=center | <math>C_{2}</math>
| align=center | 0.000154286
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 43
| align=right | 2
| align=right | 0
| align=right | 171
| align=right | 114
| align=right | 0
| align=right | 26.170°
|-
| align=right | 60
| align=right | 1543.830400976
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 48
| align=right | 0
| align=right | 0
| align=right | 174
| align=right | 116
| align=right | 0
| align=right | 25.958°
|-
| align=right | 61
| align=right | 1597.941830199
| align=center | <math>C_{1}</math>
| align=center | 0.001091717
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 49
| align=right | 0
| align=right | 0
| align=right | 177
| align=right | 118
| align=right | 0
| align=right | 25.392°
|-
| align=right | 62
| align=right | 1652.909409898
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 50
| align=right | 0
| align=right | 0
| align=right | 180
| align=right | 120
| align=right | 0
| align=right | 25.880°
|-
| align=right | 63
| align=right | 1708.879681503
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 51
| align=right | 0
| align=right | 0
| align=right | 183
| align=right | 122
| align=right | 0
| align=right | 25.257°
|-
| align=right | 64
| align=right | 1765.802577927
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 52
| align=right | 0
| align=right | 0
| align=right | 186
| align=right | 124
| align=right | 0
| align=right | 24.920°
|-
| align=right | 65
| align=right | 1823.667960264
| align=center | <math>C_{2}</math>
| align=center | 0.000399515
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 53
| align=right | 0
| align=right | 0
| align=right | 189
| align=right | 126
| align=right | 0
| align=right | 24.527°
|-
| align=right | 66
| align=right | 1882.441525304
| align=center | <math>C_{2}</math>
| align=center | 0.000776245
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 54
| align=right | 0
| align=right | 0
| align=right | 192
| align=right | 128
| align=right | 0
| align=right | 24.765°
|-
| align=right | 67
| align=right | 1942.122700406
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 55
| align=right | 0
| align=right | 0
| align=right | 195
| align=right | 130
| align=right | 0
| align=right | 24.727°
|-
| align=right | 68
| align=right | 2002.874701749
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 56
| align=right | 0
| align=right | 0
| align=right | 198
| align=right | 132
| align=right | 0
| align=right | 24.433°
|-
| align=right | 69
| align=right | 2064.533483235
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 57
| align=right | 0
| align=right | 0
| align=right | 201
| align=right | 134
| align=right | 0
| align=right | 24.137°
|-
| align=right | 70
| align=right | 2127.100901551
| align=center | <math>D_{2d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 50
| align=right | 0
| align=right | 0
| align=right | 200
| align=right | 128
| align=right | 4
| align=right | 24.291°
|-
| align=right | 71
| align=right | 2190.649906425
| align=center | <math>C_{2}</math>
| align=center | 0.001256769
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 55
| align=right | 2
| align=right | 0
| align=right | 207
| align=right | 138
| align=right | 0
| align=right | 23.803°
|-
| align=right | 72
| align=right | 2255.001190975
| align=center | <math>I</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 60
| align=right | 0
| align=right | 0
| align=right | 210
| align=right | 140
| align=right | 0
| align=right | 24.492°
|-
| align=right | 73
| align=right | 2320.633883745
| align=center | <math>C_{2}</math>
| align=center | 0.001572959
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 61
| align=right | 0
| align=right | 0
| align=right | 213
| align=right | 142
| align=right | 0
| align=right | 22.810°
|-
| align=right | 74
| align=right | 2387.072981838
| align=center | <math>C_{2}</math>
| align=center | 0.000641539
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 62
| align=right | 0
| align=right | 0
| align=right | 216
| align=right | 144
| align=right | 0
| align=right | 22.966°
|-
| align=right | 75
| align=right | 2454.369689040
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 63
| align=right | 0
| align=right | 0
| align=right | 219
| align=right | 146
| align=right | 0
| align=right | 22.736°
|-
| align=right | 76
| align=right | 2522.674871841
| align=center | <math>C_{2}</math>
| align=center | 0.000943474
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 64
| align=right | 0
| align=right | 0
| align=right | 222
| align=right | 148
| align=right | 0
| align=right | 22.886°
|-
| align=right | 77
| align=right | 2591.850152354
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 65
| align=right | 0
| align=right | 0
| align=right | 225
| align=right | 150
| align=right | 0
| align=right | 23.286°
|-
| align=right | 78
| align=right | 2662.046474566
| align=center | <math>T_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 66
| align=right | 0
| align=right | 0
| align=right | 228
| align=right | 152
| align=right | 0
| align=right | 23.426°
|-
| align=right | 79
| align=right | 2733.248357479
| align=center | <math>C_{s}</math>
| align=center | 0.000702921
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 63
| align=right | 1
| align=right | 0
| align=right | 230
| align=right | 152
| align=right | 1
| align=right | 22.636°
|-
| align=right | 80
| align=right | 2805.355875981
| align=center | <math>D_{4d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 16
| align=right | 64
| align=right | 0
| align=right | 0
| align=right | 232
| align=right | 152
| align=right | 2
| align=right | 22.778°
|-
| align=right | 81
| align=right | 2878.522829664
| align=center | <math>C_{2}</math>
| align=center | 0.000194289
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 69
| align=right | 0
| align=right | 0
| align=right | 237
| align=right | 158
| align=right | 0
| align=right | 21.892°
|-
| align=right | 82
| align=right | 2952.569675286
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 70
| align=right | 0
| align=right | 0
| align=right | 240
| align=right | 160
| align=right | 0
| align=right | 22.206°
|-
| align=right | 83
| align=right | 3027.528488921
| align=center | <math>C_{2}</math>
| align=center | 0.000339815
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 67
| align=right | 2
| align=right | 0
| align=right | 243
| align=right | 162
| align=right | 0
| align=right | 21.646°
|-
| align=right | 84
| align=right | 3103.465124431
| align=center | <math>C_{2}</math>
| align=center | 0.000401973
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 72
| align=right | 0
| align=right | 0
| align=right | 246
| align=right | 164
| align=right | 0
| align=right | 21.513°
|-
| align=right | 85
| align=right | 3180.361442939
| align=center | <math>C_{2}</math>
| align=center | 0.000416581
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 73
| align=right | 0
| align=right | 0
| align=right | 249
| align=right | 166
| align=right | 0
| align=right | 21.498°
|-
| align=right | 86
| align=right | 3258.211605713
| align=center | <math>C_{2}</math>
| align=center | 0.001378932
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 74
| align=right | 0
| align=right | 0
| align=right | 252
| align=right | 168
| align=right | 0
| align=right | 21.522°
|-
| align=right | 87
| align=right | 3337.000750014
| align=center | <math>C_{2}</math>
| align=center | 0.000754863
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 75
| align=right | 0
| align=right | 0
| align=right | 255
| align=right | 170
| align=right | 0
| align=right | 21.456°
|-
| align=right | 88
| align=right | 3416.720196758
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 76
| align=right | 0
| align=right | 0
| align=right | 258
| align=right | 172
| align=right | 0
| align=right | 21.486°
|-
| align=right | 89
| align=right | 3497.439018625
| align=center | <math>C_{2}</math>
| align=center | 0.000070891
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 77
| align=right | 0
| align=right | 0
| align=right | 261
| align=right | 174
| align=right | 0
| align=right | 21.182°
|-
| align=right | 90
| align=right | 3579.091222723
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 78
| align=right | 0
| align=right | 0
| align=right | 264
| align=right | 176
| align=right | 0
| align=right | 21.230°
|-
| align=right | 91
| align=right | 3661.713699320
| align=center | <math>C_{2}</math>
| align=center | 0.000033221
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 79
| align=right | 0
| align=right | 0
| align=right | 267
| align=right | 178
| align=right | 0
| align=right | 21.105°
|-
| align=right | 92
| align=right | 3745.291636241
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 80
| align=right | 0
| align=right | 0
| align=right | 270
| align=right | 180
| align=right | 0
| align=right | 21.026°
|-
| align=right | 93
| align=right | 3829.844338421
| align=center | <math>C_{2}</math>
| align=center | 0.000213246
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 81
| align=right | 0
| align=right | 0
| align=right | 273
| align=right | 182
| align=right | 0
| align=right | 20.751°
|-
| align=right | 94
| align=right | 3915.309269620
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 82
| align=right | 0
| align=right | 0
| align=right | 276
| align=right | 184
| align=right | 0
| align=right | 20.952°
|-
| align=right | 95
| align=right | 4001.771675565
| align=center | <math>C_{2}</math>
| align=center | 0.000116638
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 83
| align=right | 0
| align=right | 0
| align=right | 279
| align=right | 186
| align=right | 0
| align=right | 20.711°
|-
| align=right | 96
| align=right | 4089.154010060
| align=center | <math>C_{2}</math>
| align=center | 0.000036310
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 84
| align=right | 0
| align=right | 0
| align=right | 282
| align=right | 188
| align=right | 0
| align=right | 20.687°
|-
| align=right | 97
| align=right | 4177.533599622
| align=center | <math>C_{2}</math>
| align=center | 0.000096437
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 85
| align=right | 0
| align=right | 0
| align=right | 285
| align=right | 190
| align=right | 0
| align=right | 20.450°
|-
| align=right | 98
| align=right | 4266.822464156
| align=center | <math>C_{2}</math>
| align=center | 0.000112916
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 86
| align=right | 0
| align=right | 0
| align=right | 288
| align=right | 192
| align=right | 0
| align=right | 20.422°
|-
| align=right | 99
| align=right | 4357.139163132
| align=center | <math>C_{2}</math>
| align=center | 0.000156508
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 87
| align=right | 0
| align=right | 0
| align=right | 291
| align=right | 194
| align=right | 0
| align=right | 20.284°
|-
| align=right | 100
| align=right | 4448.350634331
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 88
| align=right | 0
| align=right | 0
| align=right | 294
| align=right | 196
| align=right | 0
| align=right | 20.297°
|-
| align=right | 101
| align=right | 4540.590051694
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 89
| align=right | 0
| align=right | 0
| align=right | 297
| align=right | 198
| align=right | 0
| align=right | 20.011°
|-
| align=right | 102
| align=right | 4633.736565899
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 90
| align=right | 0
| align=right | 0
| align=right | 300
| align=right | 200
| align=right | 0
| align=right | 20.040°
|-
| align=right | 103
| align=right | 4727.836616833
| align=center | <math>C_{2}</math>
| align=center | 0.000201245
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 91
| align=right | 0
| align=right | 0
| align=right | 303
| align=right | 202
| align=right | 0
| align=right | 19.907°
|-
| align=right | 104
| align=right | 4822.876522746
| align=center | <math>D_{6}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 92
| align=right | 0
| align=right | 0
| align=right | 306
| align=right | 204
| align=right | 0
| align=right | 19.957°
|-
| align=right | 105
| align=right | 4919.000637616
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 93
| align=right | 0
| align=right | 0
| align=right | 309
| align=right | 206
| align=right | 0
| align=right | 19.842°
|-
| align=right | 106
| align=right | 5015.984595705
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 94
| align=right | 0
| align=right | 0
| align=right | 312
| align=right | 208
| align=right | 0
| align=right | 19.658°
|-
| align=right | 107
| align=right | 5113.953547724
| align=center | <math>C_{2}</math>
| align=center | 0.000064137
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 95
| align=right | 0
| align=right | 0
| align=right | 315
| align=right | 210
| align=right | 0
| align=right | 19.327°
|-
| align=right | 108
| align=right | 5212.813507831
| align=center | <math>C_{2}</math>
| align=center | 0.000432525
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 96
| align=right | 0
| align=right | 0
| align=right | 318
| align=right | 212
| align=right | 0
| align=right | 19.327°
|-
| align=right | 109
| align=right | 5312.735079920
| align=center | <math>C_{2}</math>
| align=center | 0.000647299
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 93
| align=right | 2
| align=right | 0
| align=right | 321
| align=right | 214
| align=right | 0
| align=right | 19.103°
|-
| align=right | 110
| align=right | 5413.549294192
| align=center | <math>D_{6}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 98
| align=right | 0
| align=right | 0
| align=right | 324
| align=right | 216
| align=right | 0
| align=right | 19.476°
|-
| align=right | 111
| align=right | 5515.293214587
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 99
| align=right | 0
| align=right | 0
| align=right | 327
| align=right | 218
| align=right | 0
| align=right | 19.255°
|-
| align=right | 112
| align=right | 5618.044882327
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 100
| align=right | 0
| align=right | 0
| align=right | 330
| align=right | 220
| align=right | 0
| align=right | 19.351°
|-
| align=right | 113
| align=right | 5721.824978027
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 101
| align=right | 0
| align=right | 0
| align=right | 333
| align=right | 222
| align=right | 0
| align=right | 18.978°
|-
| align=right | 114
| align=right | 5826.521572163
| align=center | <math>C_{2}</math>
| align=center | 0.000149772
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 102
| align=right | 0
| align=right | 0
| align=right | 336
| align=right | 224
| align=right | 0
| align=right | 18.836°
|-
| align=right | 115
| align=right | 5932.181285777
| align=center | <math>C_{3}</math>
| align=center | 0.000049972
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 103
| align=right | 0
| align=right | 0
| align=right | 339
| align=right | 226
| align=right | 0
| align=right | 18.458°
|-
| align=right | 116
| align=right | 6038.815593579
| align=center | <math>C_{2}</math>
| align=center | 0.000259726
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 104
| align=right | 0
| align=right | 0
| align=right | 342
| align=right | 228
| align=right | 0
| align=right | 18.386°
|-
| align=right | 117
| align=right | 6146.342446579
| align=center | <math>C_{2}</math>
| align=center | 0.000127609
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 105
| align=right | 0
| align=right | 0
| align=right | 345
| align=right | 230
| align=right | 0
| align=right | 18.566°
|-
| align=right | 118
| align=right | 6254.877027790
| align=center | <math>C_{2}</math>
| align=center | 0.000332475
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 106
| align=right | 0
| align=right | 0
| align=right | 348
| align=right | 232
| align=right | 0
| align=right | 18.455°
|-
| align=right | 119
| align=right | 6364.347317479
| align=center | <math>C_{2}</math>
| align=center | 0.000685590
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 107
| align=right | 0
| align=right | 0
| align=right | 351
| align=right | 234
| align=right | 0
| align=right | 18.336°
|-
| align=right | 120
| align=right | 6474.756324980
| align=center | <math>C_{s}</math>
| align=center | 0.001373062
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 108
| align=right | 0
| align=right | 0
| align=right | 354
| align=right | 236
| align=right | 0
| align=right | 18.418°
|-
| align=right | 121
| align=right | 6586.121949584
| align=center | <math>C_{3}</math>
| align=center | 0.000838863
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 109
| align=right | 0
| align=right | 0
| align=right | 357
| align=right | 238
| align=right | 0
| align=right | 18.199°
|-
| align=right | 122
| align=right | 6698.374499261
| align=center | <math>I_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 110
| align=right | 0
| align=right | 0
| align=right | 360
| align=right | 240
| align=right | 0
| align=right | 18.612°
|-
| align=right | 123
| align=right | 6811.827228174
| align=center | <math>C_{2v}</math>
| align=center | 0.001939754
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 107
| align=right | 2
| align=right | 0
| align=right | 363
| align=right | 242
| align=right | 0
| align=right | 17.840°
|-
| align=right | 124
| align=right | 6926.169974193
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 112
| align=right | 0
| align=right | 0
| align=right | 366
| align=right | 244
| align=right | 0
| align=right | 18.111°
|-
| align=right | 125
| align=right | 7041.473264023
| align=center | <math>C_{2}</math>
| align=center | 0.000088274
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 113
| align=right | 0
| align=right | 0
| align=right | 369
| align=right | 246
| align=right | 0
| align=right | 17.867°
|-
| align=right | 126
| align=right | 7157.669224867
| align=center | <math>D_{4}</math>
| align=center | 0
| align=right | 0
| align=right | 2
| align=right | 16
| align=right | 100
| align=right | 8
| align=right | 0
| align=right | 372
| align=right | 248
| align=right | 0
| align=right | 17.920°
|-
| align=right | 127
| align=right | 7274.819504675
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 115
| align=right | 0
| align=right | 0
| align=right | 375
| align=right | 250
| align=right | 0
| align=right | 17.877°
|-
| align=right | 128
| align=right | 7393.007443068
| align=center | <math>C_{2}</math>
| align=center | 0.000054132
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 116
| align=right | 0
| align=right | 0
| align=right | 378
| align=right | 252
| align=right | 0
| align=right | 17.814°
|-
| align=right | 129
| align=right | 7512.107319268
| align=center | <math>C_{2}</math>
| align=center | 0.000030099
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 117
| align=right | 0
| align=right | 0
| align=right | 381
| align=right | 254
| align=right | 0
| align=right | 17.743°
|-
| align=right | 130
| align=right | 7632.167378912
| align=center | <math>C_{2}</math>
| align=center | 0.000025622
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 118
| align=right | 0
| align=right | 0
| align=right | 384
| align=right | 256
| align=right | 0
| align=right | 17.683°
|-
| align=right | 131
| align=right | 7753.205166941
| align=center | <math>C_{2}</math>
| align=center | 0.000305133
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 119
| align=right | 0
| align=right | 0
| align=right | 387
| align=right | 258
| align=right | 0
| align=right | 17.511°
|-
| align=right | 132
| align=right | 7875.045342797
| align=center | <math>I</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 120
| align=right | 0
| align=right | 0
| align=right | 390
| align=right | 260
| align=right | 0
| align=right | 17.958°
|-
| align=right | 133
| align=right | 7998.179212898
| align=center | <math>C_{3}</math>
| align=center | 0.000591438
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 121
| align=right | 0
| align=right | 0
| align=right | 393
| align=right | 262
| align=right | 0
| align=right | 17.133°
|-
| align=right | 134
| align=right | 8122.089721194
| align=center | <math>C_{2}</math>
| align=center | 0.000470268
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 122
| align=right | 0
| align=right | 0
| align=right | 396
| align=right | 264
| align=right | 0
| align=right | 17.214°
|-
| align=right | 135
| align=right | 8246.909486992
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 123
| align=right | 0
| align=right | 0
| align=right | 399
| align=right | 266
| align=right | 0
| align=right | 17.431°
|-
| align=right | 136
| align=right | 8372.743302539
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 124
| align=right | 0
| align=right | 0
| align=right | 402
| align=right | 268
| align=right | 0
| align=right | 17.485°
|-
| align=right | 137
| align=right | 8499.534494782
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 125
| align=right | 0
| align=right | 0
| align=right | 405
| align=right | 270
| align=right | 0
| align=right | 17.560°
|-
| align=right | 138
| align=right | 8627.406389880
| align=center | <math>C_{2}</math>
| align=center | 0.000473576
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 126
| align=right | 0
| align=right | 0
| align=right | 408
| align=right | 272
| align=right | 0
| align=right | 16.924°
|-
| align=right | 139
| align=right | 8756.227056057
| align=center | <math>C_{2}</math>
| align=center | 0.000404228
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 127
| align=right | 0
| align=right | 0
| align=right | 411
| align=right | 274
| align=right | 0
| align=right | 16.673°
|-
| align=right | 140
| align=right | 8885.980609041
| align=center | <math>C_{1}</math>
| align=center | 0.000630351
| align=right | 0
| align=right | 0
| align=right | 13
| align=right | 126
| align=right | 1
| align=right | 0
| align=right | 414
| align=right | 276
| align=right | 0
| align=right | 16.773°
|-
| align=right | 141
| align=right | 9016.615349190
| align=center | <math>C_{2v}</math>
| align=center | 0.000376365
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 126
| align=right | 0
| align=right | 1
| align=right | 417
| align=right | 278
| align=right | 0
| align=right | 16.962°
|-
| align=right | 142
| align=right | 9148.271579993
| align=center | <math>C_{2}</math>
| align=center | 0.000550138
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 130
| align=right | 0
| align=right | 0
| align=right | 420
| align=right | 280
| align=right | 0
| align=right | 16.840°
|-
| align=right | 143
| align=right | 9280.839851192
| align=center | <math>C_{2}</math>
| align=center | 0.000255449
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 131
| align=right | 0
| align=right | 0
| align=right | 423
| align=right | 282
| align=right | 0
| align=right | 16.782°
|-
| align=right | 144
| align=right | 9414.371794460
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 132
| align=right | 0
| align=right | 0
| align=right | 426
| align=right | 284
| align=right | 0
| align=right | 16.953°
|-
| align=right | 145
| align=right | 9548.928837232
| align=center | <math>C_{s}</math>
| align=center | 0.000094938
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 133
| align=right | 0
| align=right | 0
| align=right | 429
| align=right | 286
| align=right | 0
| align=right | 16.841°
|-
| align=right | 146
| align=right | 9684.381825575
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 134
| align=right | 0
| align=right | 0
| align=right | 432
| align=right | 288
| align=right | 0
| align=right | 16.905°
|-
| align=right | 147
| align=right | 9820.932378373
| align=center | <math>C_{2}</math>
| align=center | 0.000636651
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 135
| align=right | 0
| align=right | 0
| align=right | 435
| align=right | 290
| align=right | 0
| align=right | 16.458°
|-
| align=right | 148
| align=right | 9958.406004270
| align=center | <math>C_{2}</math>
| align=center | 0.000203701
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 136
| align=right | 0
| align=right | 0
| align=right | 438
| align=right | 292
| align=right | 0
| align=right | 16.627°
|-
| align=right | 149
| align=right | 10096.859907397
| align=center | <math>C_{1}</math>
| align=center | 0.000638186
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 133
| align=right | 2
| align=right | 0
| align=right | 441
| align=right | 294
| align=right | 0
| align=right | 16.344°
|-
| align=right | 150
| align=right | 10236.196436701
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 138
| align=right | 0
| align=right | 0
| align=right | 444
| align=right | 296
| align=right | 0
| align=right | 16.405°
|-
| align=right | 151
| align=right | 10376.571469275
| align=center | <math>C_{2}</math>
| align=center | 0.000153836
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 139
| align=right | 0
| align=right | 0
| align=right | 447
| align=right | 298
| align=right | 0
| align=right | 16.163°
|-
| align=right | 152
| align=right | 10517.867592878
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 140
| align=right | 0
| align=right | 0
| align=right | 450
| align=right | 300
| align=right | 0
| align=right | 16.117°
|-
| align=right | 153
| align=right | 10660.082748237
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 141
| align=right | 0
| align=right | 0
| align=right | 453
| align=right | 302
| align=right | 0
| align=right | 16.390°
|-
| align=right | 154
| align=right | 10803.372421141
| align=center | <math>C_{2}</math>
| align=center | 0.000735800
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 142
| align=right | 0
| align=right | 0
| align=right | 456
| align=right | 304
| align=right | 0
| align=right | 16.078°
|-
| align=right | 155
| align=right | 10947.574692279
| align=center | <math>C_{2}</math>
| align=center | 0.000603670
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 143
| align=right | 0
| align=right | 0
| align=right | 459
| align=right | 306
| align=right | 0
| align=right | 15.990°
|-
| align=right | 156
| align=right | 11092.798311456
| align=center | <math>C_{2}</math>
| align=center | 0.000508534
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 144
| align=right | 0
| align=right | 0
| align=right | 462
| align=right | 308
| align=right | 0
| align=right | 15.822°
|-
| align=right | 157
| align=right | 11238.903041156
| align=center | <math>C_{2}</math>
| align=center | 0.000357679
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 145
| align=right | 0
| align=right | 0
| align=right | 465
| align=right | 310
| align=right | 0
| align=right | 15.948°
|-
| align=right | 158
| align=right | 11385.990186197
| align=center | <math>C_{2}</math>
| align=center | 0.000921918
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 146
| align=right | 0
| align=right | 0
| align=right | 468
| align=right | 312
| align=right | 0
| align=right | 15.987°
|-
| align=right | 159
| align=right | 11534.023960956
| align=center | <math>C_{2}</math>
| align=center | 0.000381457
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 147
| align=right | 0
| align=right | 0
| align=right | 471
| align=right | 314
| align=right | 0
| align=right | 15.960°
|-
| align=right | 160
| align=right | 11683.054805549
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 148
| align=right | 0
| align=right | 0
| align=right | 474
| align=right | 316
| align=right | 0
| align=right | 15.961°
|-
| align=right | 161
| align=right | 11833.084739465
| align=center | <math>C_{2}</math>
| align=center | 0.000056447
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 149
| align=right | 0
| align=right | 0
| align=right | 477
| align=right | 318
| align=right | 0
| align=right | 15.810°
|-
| align=right | 162
| align=right | 11984.050335814
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 150
| align=right | 0
| align=right | 0
| align=right | 480
| align=right | 320
| align=right | 0
| align=right | 15.813°
|-
| align=right | 163
| align=right | 12136.013053220
| align=center | <math>C_{2}</math>
| align=center | 0.000120798
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 151
| align=right | 0
| align=right | 0
| align=right | 483
| align=right | 322
| align=right | 0
| align=right | 15.675°
|-
| align=right | 164
| align=right | 12288.930105320
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 152
| align=right | 0
| align=right | 0
| align=right | 486
| align=right | 324
| align=right | 0
| align=right | 15.655°
|-
| align=right | 165
| align=right | 12442.804451373
| align=center | <math>C_{2}</math>
| align=center | 0.000091119
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 153
| align=right | 0
| align=right | 0
| align=right | 489
| align=right | 326
| align=right | 0
| align=right | 15.651°
|-
| align=right | 166
| align=right | 12597.649071323
| align=center | <math>D_{2d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 16
| align=right | 146
| align=right | 4
| align=right | 0
| align=right | 492
| align=right | 328
| align=right | 0
| align=right | 15.607°
|-
| align=right | 167
| align=right | 12753.469429750
| align=center | <math>C_{2}</math>
| align=center | 0.000097382
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 155
| align=right | 0
| align=right | 0
| align=right | 495
| align=right | 330
| align=right | 0
| align=right | 15.600°
|-
| align=right | 168
| align=right | 12910.212672268
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 156
| align=right | 0
| align=right | 0
| align=right | 498
| align=right | 332
| align=right | 0
| align=right | 15.655°
|-
| align=right | 169
| align=right | 13068.006451127
| align=center | <math>C_{s}</math>
| align=center | 0.000068102
| align=right | 0
| align=right | 0
| align=right | 13
| align=right | 155
| align=right | 1
| align=right | 0
| align=right | 501
| align=right | 334
| align=right | 0
| align=right | 15.537°
|-
| align=right | 170
| align=right | 13226.681078541
| align=center | <math>D_{2d}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 158
| align=right | 0
| align=right | 0
| align=right | 504
| align=right | 336
| align=right | 0
| align=right | 15.569°
|-
| align=right | 171
| align=right | 13386.355930717
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 159
| align=right | 0
| align=right | 0
| align=right | 507
| align=right | 338
| align=right | 0
| align=right | 15.497°
|-
| align=right | 172
| align=right | 13547.018108787
| align=center | <math>C_{2v}</math>
| align=center | 0.000547291
| align=right | 0
| align=right | 0
| align=right | 14
| align=right | 156
| align=right | 2
| align=right | 0
| align=right | 510
| align=right | 340
| align=right | 0
| align=right | 15.292°
|-
| align=right | 173
| align=right | 13708.635243034
| align=center | <math>C_{s}</math>
| align=center | 0.000286544
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 161
| align=right | 0
| align=right | 0
| align=right | 513
| align=right | 342
| align=right | 0
| align=right | 15.225°
|-
| align=right | 174
| align=right | 13871.187092292
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 162
| align=right | 0
| align=right | 0
| align=right | 516
| align=right | 344
| align=right | 0
| align=right | 15.366°
|-
| align=right | 175
| align=right | 14034.781306929
| align=center | <math>C_{2}</math>
| align=center | 0.000026686
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 163
| align=right | 0
| align=right | 0
| align=right | 519
| align=right | 346
| align=right | 0
| align=right | 15.252°
|-
| align=right | 176
| align=right | 14199.354775632
| align=center | <math>C_{1}</math>
| align=center | 0.000283978
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 164
| align=right | 0
| align=right | 0
| align=right | 522
| align=right | 348
| align=right | 0
| align=right | 15.101°
|-
| align=right | 177
| align=right | 14364.837545298
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 165
| align=right | 0
| align=right | 0
| align=right | 525
| align=right | 350
| align=right | 0
| align=right | 15.269°
|-
| align=right | 178
| align=right | 14531.309552587
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 166
| align=right | 0
| align=right | 0
| align=right | 528
| align=right | 352
| align=right | 0
| align=right | 15.145°
|-
| align=right | 179
| align=right | 14698.754594220
| align=center | <math>C_{1}</math>
| align=center | 0.000125113
| align=right | 0
| align=right | 0
| align=right | 13
| align=right | 165
| align=right | 1
| align=right | 0
| align=right | 531
| align=right | 354
| align=right | 0
| align=right | 14.968°
|-
| align=right | 180
| align=right | 14867.099927525
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 168
| align=right | 0
| align=right | 0
| align=right | 534
| align=right | 356
| align=right | 0
| align=right | 15.067°
|-
| align=right | 181
| align=right | 15036.467239769
| align=center | <math>C_{2}</math>
| align=center | 0.000304193
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 169
| align=right | 0
| align=right | 0
| align=right | 537
| align=right | 358
| align=right | 0
| align=right | 15.002°
|-
| align=right | 182
| align=right | 15206.730610906
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 170
| align=right | 0
| align=right | 0
| align=right | 540
| align=right | 360
| align=right | 0
| align=right | 15.155°
|-
| align=right | 183
| align=right | 15378.166571028
| align=center | <math>C_{1}</math>
| align=center | 0.000467899
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 171
| align=right | 0
| align=right | 0
| align=right | 543
| align=right | 362
| align=right | 0
| align=right | 14.747°
|-
| align=right | 184
| align=right | 15550.421450311
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 172
| align=right | 0
| align=right | 0
| align=right | 546
| align=right | 364
| align=right | 0
| align=right | 14.932°
|-
| align=right | 185
| align=right | 15723.720074072
| align=center | <math>C_{2}</math>
| align=center | 0.000389762
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 173
| align=right | 0
| align=right | 0
| align=right | 549
| align=right | 366
| align=right | 0
| align=right | 14.775°
|-
| align=right | 186
| align=right | 15897.897437048
| align=center | <math>C_{1}</math>
| align=center | 0.000389762
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 174
| align=right | 0
| align=right | 0
| align=right | 552
| align=right | 368
| align=right | 0
| align=right | 14.739°
|-
| align=right | 187
| align=right | 16072.975186320
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 175
| align=right | 0
| align=right | 0
| align=right | 555
| align=right | 370
| align=right | 0
| align=right | 14.848°
|-
| align=right | 188
| align=right | 16249.222678879
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 176
| align=right | 0
| align=right | 0
| align=right | 558
| align=right | 372
| align=right | 0
| align=right | 14.740°
|-
| align=right | 189
| align=right | 16426.371938862
| align=center | <math>C_{2}</math>
| align=center | 0.000020732
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 177
| align=right | 0
| align=right | 0
| align=right | 561
| align=right | 374
| align=right | 0
| align=right | 14.671°
|-
| align=right | 190
| align=right | 16604.428338501
| align=center | <math>C_{3}</math>
| align=center | 0.000586804
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 178
| align=right | 0
| align=right | 0
| align=right | 564
| align=right | 376
| align=right | 0
| align=right | 14.501°
|-
| align=right | 191
| align=right | 16783.452219362
| align=center | <math>C_{1}</math>
| align=center | 0.001129202
| align=right | 0
| align=right | 0
| align=right | 13
| align=right | 177
| align=right | 1
| align=right | 0
| align=right | 567
| align=right | 378
| align=right | 0
| align=right | 14.195°
|-
| align=right | 192
| align=right | 16963.338386460
| align=center | <math>I</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 180
| align=right | 0
| align=right | 0
| align=right | 570
| align=right | 380
| align=right | 0
| align=right | 14.819°
|-
| align=right | 193
| align=right | 17144.564740880
| align=center | <math>C_{2}</math>
| align=center | 0.000985192
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 181
| align=right | 0
| align=right | 0
| align=right | 573
| align=right | 382
| align=right | 0
| align=right | 14.144°
|-
| align=right | 194
| align=right | 17326.616136471
| align=center | <math>C_{1}</math>
| align=center | 0.000322358
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 182
| align=right | 0
| align=right | 0
| align=right | 576
| align=right | 384
| align=right | 0
| align=right | 14.350°
|-
| align=right | 195
| align=right | 17509.489303930
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 183
| align=right | 0
| align=right | 0
| align=right | 579
| align=right | 386
| align=right | 0
| align=right | 14.375°
|-
| align=right | 196
| align=right | 17693.460548082
| align=center | <math>C_{2}</math>
| align=center | 0.000315907
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 184
| align=right | 0
| align=right | 0
| align=right | 582
| align=right | 388
| align=right | 0
| align=right | 14.251°
|-
| align=right | 197
| align=right | 17878.340162571
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 185
| align=right | 0
| align=right | 0
| align=right | 585
| align=right | 390
| align=right | 0
| align=right | 14.147°
|-
| align=right | 198
| align=right | 18064.262177195
| align=center | <math>C_{2}</math>
| align=center | 0.000011149
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 186
| align=right | 0
| align=right | 0
| align=right | 588
| align=right | 392
| align=right | 0
| align=right | 14.237°
|-
| align=right | 199
| align=right | 18251.082495640
| align=center | <math>C_{1}</math>
| align=center | 0.000534779
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 187
| align=right | 0
| align=right | 0
| align=right | 591
| align=right | 394
| align=right | 0
| align=right | 14.153°
|-
| align=right | 200
| align=right | 18438.842717530
| align=center | <math>D_{2}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 188
| align=right | 0
| align=right | 0
| align=right | 594
| align=right | 396
| align=right | 0
| align=right | 14.222°
|-
| align=right | 201
| align=right | 18627.591226244
| align=center | <math>C_{1}</math>
| align=center | 0.001048859
| align=right | 0
| align=right | 0
| align=right | 13
| align=right | 187
| align=right | 1
| align=right | 0
| align=right | 597
| align=right | 398
| align=right | 0
| align=right | 13.830°
|-
| align=right | 202
| align=right | 18817.204718262
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 190
| align=right | 0
| align=right | 0
| align=right | 600
| align=right | 400
| align=right | 0
| align=right | 14.189°
|-
| align=right | 203
| align=right | 19007.981204580
| align=center | <math>C_{s}</math>
| align=center | 0.000600343
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 191
| align=right | 0
| align=right | 0
| align=right | 603
| align=right | 402
| align=right | 0
| align=right | 13.977°
|-
| align=right | 204
| align=right | 19199.540775603
| align=center | <math>T_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 192
| align=right | 0
| align=right | 0
| align=right | 606
| align=right | 404
| align=right | 0
| align=right | 14.291°
|-
| align=right | 212
| align=right | 20768.053085964
| align=center | <math>I</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 200
| align=right | 0
| align=right | 0
| align=right | 630
| align=right | 420
| align=right | 0
| align=right | 14.118°
|-
| align=right | 214
| align=right | 21169.910410375
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 202
| align=right | 0
| align=right | 0
| align=right | 636
| align=right | 424
| align=right | 0
| align=right | 13.771°
|-
| align=right | 216
| align=right | 21575.596377869
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 204
| align=right | 0
| align=right | 0
| align=right | 642
| align=right | 428
| align=right | 0
| align=right | 13.735°
|-
| align=right | 217
| align=right | 21779.856080418
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 205
| align=right | 0
| align=right | 0
| align=right | 645
| align=right | 430
| align=right | 0
| align=right | 13.902°
|-
| align=right | 232
| align=right | 24961.252318934
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 220
| align=right | 0
| align=right | 0
| align=right | 690
| align=right | 460
| align=right | 0
| align=right | 13.260°
|-
| align=right | 255
| align=right | 30264.424251281
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 243
| align=right | 0
| align=right | 0
| align=right | 759
| align=right | 506
| align=right | 0
| align=right | 12.565°
|-
| align=right | 256
| align=right | 30506.687515847
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 244
| align=right | 0
| align=right | 0
| align=right | 762
| align=right | 508
| align=right | 0
| align=right | 12.572°
|-
| align=right | 257
| align=right | 30749.941417346
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 245
| align=right | 0
| align=right | 0
| align=right | 765
| align=right | 510
| align=right | 0
| align=right | 12.672°
|-
| align=right | 272
| align=right | 34515.193292681
| align=center | <math>I_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 260
| align=right | 0
| align=right | 0
| align=right | 810
| align=right | 540
| align=right | 0
| align=right | 12.335°
|-
| align=right | 282
| align=right | 37147.294418462
| align=center | <math>I</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 270
| align=right | 0
| align=right | 0
| align=right | 840
| align=right | 560
| align=right | 0
| align=right | 12.166°
|-
| align=right | 292
| align=right | 39877.008012909
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 280
| align=right | 0
| align=right | 0
| align=right | 870
| align=right | 580
| align=right | 0
| align=right | 11.857°
|-
| align=right | 306
| align=right | 43862.569780797
| align=center | <math>T_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 294
| align=right | 0
| align=right | 0
| align=right | 912
| align=right | 608
| align=right | 0
| align=right | 11.628°
|-
| align=right | 312
| align=right | 45629.313804002
| align=center | <math>C_{2}</math>
| align=center | 0.000306163
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 300
| align=right | 0
| align=right | 0
| align=right | 930
| align=right | 620
| align=right | 0
| align=right | 11.299°
|-
| align=right | 315
| align=right | 46525.825643432
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 303
| align=right | 0
| align=right | 0
| align=right | 939
| align=right | 626
| align=right | 0
| align=right | 11.337°
|-
| align=right | 317
| align=right | 47128.310344520
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 305
| align=right | 0
| align=right | 0
| align=right | 945
| align=right | 630
| align=right | 0
| align=right | 11.423°
|-
| align=right | 318
| align=right | 47431.056020043
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 306
| align=right | 0
| align=right | 0
| align=right | 948
| align=right | 632
| align=right | 0
| align=right | 11.219°
|-
| align=right | 334
| align=right | 52407.728127822
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 322
| align=right | 0
| align=right | 0
| align=right | 996
| align=right | 664
| align=right | 0
| align=right | 11.058°
|-
| align=right | 348
| align=right | 56967.472454334
| align=center | <math>T_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 336
| align=right | 0
| align=right | 0
| align=right | 1038
| align=right | 692
| align=right | 0
| align=right | 10.721°
|-
| align=right | 357
| align=right | 59999.922939598
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 345
| align=right | 0
| align=right | 0
| align=right | 1065
| align=right | 710
| align=right | 0
| align=right | 10.728°
|-
| align=right | 358
| align=right | 60341.830924588
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 346
| align=right | 0
| align=right | 0
| align=right | 1068
| align=right | 712
| align=right | 0
| align=right | 10.647°
|-
| align=right | 372
| align=right | 65230.027122557
| align=center | <math>I</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 360
| align=right | 0
| align=right | 0
| align=right | 1110
| align=right | 740
| align=right | 0
| align=right | 10.531°
|-
| align=right | 382
| align=right | 68839.426839215
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 370
| align=right | 0
| align=right | 0
| align=right | 1140
| align=right | 760
| align=right | 0
| align=right | 10.379°
|-
| align=right | 390
| align=right | 71797.035335953
| align=center | <math>T_{h}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 378
| align=right | 0
| align=right | 0
| align=right | 1164
| align=right | 776
| align=right | 0
| align=right | 10.222°
|-
| align=right | 392
| align=right | 72546.258370889
| align=center | <math>I</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 380
| align=right | 0
| align=right | 0
| align=right | 1170
| align=right | 780
| align=right | 0
| align=right | 10.278°
|-
| align=right | 400
| align=right | 75582.448512213
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 388
| align=right | 0
| align=right | 0
| align=right | 1194
| align=right | 796
| align=right | 0
| align=right | 10.068°
|-
| align=right | 402
| align=right | 76351.192432673
| align=center | <math>D_{5}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 12
| align=right | 390
| align=right | 0
| align=right | 0
| align=right | 1200
| align=right | 800
| align=right | 0
| align=right | 10.099°
|-
| align=right | 432
| align=right | 88353.709681956
| align=center | <math>D_{3}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 396
| align=right | 12
| align=right | 0
| align=right | 1290
| align=right | 860
| align=right | 0
| align=right | 9.556°
|-
| align=right | 448
| align=right | 95115.546986209
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 412
| align=right | 12
| align=right | 0
| align=right | 1338
| align=right | 892
| align=right | 0
| align=right | 9.322°
|-
| align=right | 460
| align=right | 100351.763108673
| align=center | <math>T</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 424
| align=right | 12
| align=right | 0
| align=right | 1374
| align=right | 916
| align=right | 0
| align=right | 9.297°
|-
| align=right | 468
| align=right | 103920.871715127
| align=center | <math>S_{6}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 432
| align=right | 12
| align=right | 0
| align=right | 1398
| align=right | 932
| align=right | 0
| align=right | 9.120°
|-
| align=right | 470
| align=right | 104822.886324279
| align=center | <math>S_{6}</math>
| align=center | 0
| align=right | 0
| align=right | 0
| align=right | 24
| align=right | 434
| align=right | 12
| align=right | 0
| align=right | 1404
| align=right | 936
| align=right | 0
| align=right | 9.059°
|}
 
==References==
 
<references/>
 
==Notes==
 
*Henry Cohn and Abhinav Kumar, "Universally optimal distribution of points on spheres".  J. Amer. Math. Soc.  20  (2007),  no. 1, 99—148
 
*P. D. Dragnev, D. A.  Legg, and D. W. Townsend, "Discrete logarithmic energy on the sphere". Pacific J. Math. 207 (2002), no. 2, 345—358.
 
*T. Erber and G. M. Hockney, "Complex Systems: Equilibrium Configurations of <math>N</math> Equal Charges on a Sphere <math>(2\leq N\leq 112)</math>", Advances in Chemical Physics, Volume 98, pp.&nbsp;495–594, 1997.
 
*Cris Cecka, Mark J. Bowick, and Alan A. Middleton: http://thomson.phy.syr.edu/
 
*David J. Wales and Sidika Ulker: http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html and also http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson2/table.html
 
{{DEFAULTSORT:Thomson Problem}}
[[Category:Electron]]
[[Category:Circle packing]]

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