Grant PID2020-113887GB-I00 funded by MCIN/ AEI /10.13039/501100011033


The Diamond Ensemble



Our recipe to get N spherical points with low logarithmic energy:

  1. Choose a number of parallels in the sphere.
  2. On each parallel allocate a number of equally spaced points.
  3. Rotate the points on each parallel by a random phase.
  4. Add the north and south poles.

And... you already have your set! Watch the video for details.

Based on the papers
"The Diamond ensemble: A constructive set of spherical points with small logarithmic energy"
by Carlos Beltrán and Ujué Etayo, and
"Low energy points on the sphere and the real projective plane"
by Carlos Beltrán, Ujué Etayo and Pedro R. López-Gómez



Sensible choices of the parameters yield collections of points with small logarithmic energy.


You can download your set from the table below. Each file has \(N\) rows with the \(x,y,z\) coordinates of the corresponding \(N\) points.
The minimum energy is known to be of the form \(\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N + C N\) with \(C\approx -0.056\).

\(N\) Energy File
11              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.113099N$$            N000011.txt     
12              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.073502N$$            N000012.txt     
13              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.067480N$$            N000013.txt     
14              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.035641N$$            N000014.txt     
15              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.009535N$$            N000015.txt     
16              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.007453N$$            N000016.txt     
17              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.006563N$$            N000017.txt     
18              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.024114N$$            N000018.txt     
19              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.033485N$$            N000019.txt     
20              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.034022N$$            N000020.txt     
21              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.025596N$$            N000021.txt     
22              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.008372N$$            N000022.txt     
23              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037320N$$            N000023.txt     
24              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.026148N$$            N000024.txt     
25              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.007342N$$            N000025.txt     
26              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.018857N$$            N000026.txt     
27              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.014709N$$            N000027.txt     
28              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.005063N$$            N000028.txt     
29              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.031419N$$            N000029.txt     
30              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.064122N$$            N000030.txt     
31              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N +0.009659N$$            N000031.txt     
32              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.001055N$$            N000032.txt     
33              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.002712N$$            N000033.txt     
34              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.012852N$$            N000034.txt     
35              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.005099N$$            N000035.txt     
36              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.015532N$$            N000036.txt     
37              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.023261N$$            N000037.txt     
38              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.027818N$$            N000038.txt     
39              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.031431N$$            N000039.txt     
40              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036225N$$            N000040.txt     
41              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.030794N$$            N000041.txt     
42              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036378N$$            N000042.txt     
43              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039127N$$            N000043.txt     
44              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038801N$$            N000044.txt     
45              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.035235N$$            N000045.txt     
46              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.028318N$$            N000046.txt     
47              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.033127N$$            N000047.txt     
48              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.027950N$$            N000048.txt     
49              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041451N$$            N000049.txt     
50              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037232N$$            N000050.txt     
51              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.030036N$$            N000051.txt     
52              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.019802N$$            N000052.txt     
53              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.027639N$$            N000053.txt     
54              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.019147N$$            N000054.txt     
55              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.033047N$$            N000055.txt     
56              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.025680N$$            N000056.txt     
57              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.015575N$$            N000057.txt     
58              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.002702N$$            N000058.txt     
59              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.013158N$$            N000059.txt     
60              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.022058N$$            N000060.txt     
61              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.022345N$$            N000061.txt     
62              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.026228N$$            N000062.txt     
63              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.026072N$$            N000063.txt     
64              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.030034N$$            N000064.txt     
65              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.026790N$$            N000065.txt     
66              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.031026N$$            N000066.txt     
67              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.033895N$$            N000067.txt     
68              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.035244N$$            N000068.txt     
69              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037199N$$            N000069.txt     
70              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038714N$$            N000070.txt     
71              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039626N$$            N000071.txt     
72              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041357N$$            N000072.txt     
73              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039509N$$            N000073.txt     
74              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041601N$$            N000074.txt     
75              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042320N$$            N000075.txt     
76              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041567N$$            N000076.txt     
77              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039257N$$            N000077.txt     
78              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.035322N$$            N000078.txt     
79              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038180N$$            N000079.txt     
80              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.034899N$$            N000080.txt     
81              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040053N$$            N000081.txt     
82              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037213N$$            N000082.txt     
83              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044164N$$            N000083.txt     
84              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041648N$$            N000084.txt     
85              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037666N$$            N000085.txt     
86              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.032168N$$            N000086.txt     
87              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036463N$$            N000087.txt     
88              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.031613N$$            N000088.txt     
89              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037742N$$            N000089.txt     
90              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.033361N$$            N000090.txt     
91              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040278N$$            N000091.txt     
92              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036272N$$            N000092.txt     
93              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.030886N$$            N000093.txt     
94              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.024083N$$            N000094.txt     
95              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.029641N$$            N000095.txt     
96              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.023471N$$            N000096.txt     
97              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.030460N$$            N000097.txt     
98              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.024773N$$            N000098.txt     
99              $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.031869N$$            N000099.txt     
100             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.033624N$$            N000100.txt     
101             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.034576N$$            N000101.txt     
102             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036359N$$            N000102.txt     
103             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.034968N$$            N000103.txt     
104             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036816N$$            N000104.txt     
105             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036112N$$            N000105.txt     
106             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038044N$$            N000106.txt     
107             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036773N$$            N000107.txt     
108             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038842N$$            N000108.txt     
109             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040189N$$            N000109.txt     
110             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040748N$$            N000110.txt     
111             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042578N$$            N000111.txt     
112             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043208N$$            N000112.txt     
113             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042565N$$            N000113.txt     
114             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043298N$$            N000114.txt     
115             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043261N$$            N000115.txt     
116             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044112N$$            N000116.txt     
117             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043542N$$            N000117.txt     
118             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044552N$$            N000118.txt     
119             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044838N$$            N000119.txt     
120             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044353N$$            N000120.txt     
121             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043051N$$            N000121.txt     
122             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040895N$$            N000122.txt     
123             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042672N$$            N000123.txt     
124             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040783N$$            N000124.txt     
125             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042930N$$            N000125.txt     
126             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041244N$$            N000126.txt     
127             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042702N$$            N000127.txt     
128             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041184N$$            N000128.txt     
129             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045834N$$            N000129.txt     
130             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044434N$$            N000130.txt     
131             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042250N$$            N000131.txt     
132             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039252N$$            N000132.txt     
133             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041754N$$            N000133.txt     
134             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039023N$$            N000134.txt     
135             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041813N$$            N000135.txt     
136             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039291N$$            N000136.txt     
137             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041331N$$            N000137.txt     
138             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038989N$$            N000138.txt     
139             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043419N$$            N000139.txt     
140             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041217N$$            N000140.txt     
141             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038264N$$            N000141.txt     
142             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.034535N$$            N000142.txt     
143             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037694N$$            N000143.txt     
144             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.034228N$$            N000144.txt     
145             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037596N$$            N000145.txt     
146             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.034343N$$            N000146.txt     
147             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.036885N$$            N000147.txt     
148             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.037730N$$            N000148.txt     
149             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039082N$$            N000149.txt     
150             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038157N$$            N000150.txt     
151             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039530N$$            N000151.txt     
152             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.038242N$$            N000152.txt     
153             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039647N$$            N000153.txt     
154             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039250N$$            N000154.txt     
155             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040695N$$            N000155.txt     
156             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.039470N$$            N000156.txt     
157             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040983N$$            N000157.txt     
158             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042091N$$            N000158.txt     
159             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042757N$$            N000159.txt     
160             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043538N$$            N000160.txt     
161             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044229N$$            N000161.txt     
162             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043732N$$            N000162.txt     
163             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044461N$$            N000163.txt     
164             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043632N$$            N000164.txt     
165             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044409N$$            N000165.txt     
166             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044371N$$            N000166.txt     
167             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045200N$$            N000167.txt     
168             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044392N$$            N000168.txt     
169             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045298N$$            N000169.txt     
170             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045792N$$            N000170.txt     
171             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045845N$$            N000171.txt     
172             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045432N$$            N000172.txt     
173             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044527N$$            N000173.txt     
174             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044956N$$            N000174.txt     
175             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044176N$$            N000175.txt     
176             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045348N$$            N000176.txt     
177             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044659N$$            N000177.txt     
178             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044976N$$            N000178.txt     
179             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044367N$$            N000179.txt     
180             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045072N$$            N000180.txt     
181             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044528N$$            N000181.txt     
182             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047114N$$            N000182.txt     
183             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046616N$$            N000183.txt     
184             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045662N$$            N000184.txt     
185             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044231N$$            N000185.txt     
186             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045114N$$            N000186.txt     
187             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043809N$$            N000187.txt     
188             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045362N$$            N000188.txt     
189             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044152N$$            N000189.txt     
190             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044897N$$            N000190.txt     
191             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043773N$$            N000191.txt     
192             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044791N$$            N000192.txt     
193             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043738N$$            N000193.txt     
194             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046114N$$            N000194.txt     
195             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045119N$$            N000195.txt     
196             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043680N$$            N000196.txt     
197             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041780N$$            N000197.txt     
198             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043082N$$            N000198.txt     
199             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041307N$$            N000199.txt     
200             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043213N$$            N000200.txt     
201             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041536N$$            N000201.txt     
202             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042665N$$            N000202.txt     
203             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041078N$$            N000203.txt     
204             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042365N$$            N000204.txt     
205             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.040855N$$            N000205.txt     
206             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041044N$$            N000206.txt     
207             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041837N$$            N000207.txt     
208             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041348N$$            N000208.txt     
209             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042156N$$            N000209.txt     
210             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.041741N$$            N000210.txt     
211             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042565N$$            N000211.txt     
212             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042367N$$            N000212.txt     
213             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043212N$$            N000213.txt     
214             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042389N$$            N000214.txt     
215             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043267N$$            N000215.txt     
216             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042492N$$            N000216.txt     
217             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043413N$$            N000217.txt     
218             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044065N$$            N000218.txt     
219             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044429N$$            N000219.txt     
220             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044970N$$            N000220.txt     
221             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045351N$$            N000221.txt     
222             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045147N$$            N000222.txt     
223             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045550N$$            N000223.txt     
224             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045422N$$            N000224.txt     
225             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045849N$$            N000225.txt     
226             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045904N$$            N000226.txt     
227             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046357N$$            N000227.txt     
228             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045818N$$            N000228.txt     
229             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046309N$$            N000229.txt     
230             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045807N$$            N000230.txt     
231             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046344N$$            N000231.txt     
232             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046610N$$            N000232.txt     
233             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046589N$$            N000233.txt     
234             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046267N$$            N000234.txt     
235             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045628N$$            N000235.txt     
236             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045911N$$            N000236.txt     
237             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045341N$$            N000237.txt     
238             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045582N$$            N000238.txt     
239             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045068N$$            N000239.txt     
240             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045876N$$            N000240.txt     
241             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045406N$$            N000241.txt     
242             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046004N$$            N000242.txt     
243             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045573N$$            N000243.txt     
244             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046151N$$            N000244.txt     
245             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045753N$$            N000245.txt     
246             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047553N$$            N000246.txt     
247             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047180N$$            N000247.txt     
248             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046512N$$            N000248.txt     
249             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045534N$$            N000249.txt     
250             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046106N$$            N000250.txt     
251             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045198N$$            N000251.txt     
252             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045726N$$            N000252.txt     
253             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044876N$$            N000253.txt     
254             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045929N$$            N000254.txt     
255             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045125N$$            N000255.txt     
256             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045973N$$            N000256.txt     
257             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045211N$$            N000257.txt     
258             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045978N$$            N000258.txt     
259             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045253N$$            N000259.txt     
260             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046868N$$            N000260.txt     
261             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046175N$$            N000261.txt     
262             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045191N$$            N000262.txt     
263             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043907N$$            N000263.txt     
264             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044748N$$            N000264.txt     
265             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043533N$$            N000265.txt     
266             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044326N$$            N000266.txt     
267             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043170N$$            N000267.txt     
268             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044449N$$            N000268.txt     
269             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043341N$$            N000269.txt     
270             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044413N$$            N000270.txt     
271             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043349N$$            N000271.txt     
272             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044273N$$            N000272.txt     
273             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043250N$$            N000273.txt     
274             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.042654N$$            N000274.txt     
275             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043149N$$            N000275.txt     
276             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043479N$$            N000276.txt     
277             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043980N$$            N000277.txt     
278             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043883N$$            N000278.txt     
279             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044393N$$            N000279.txt     
280             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043662N$$            N000280.txt     
281             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044184N$$            N000281.txt     
282             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.043967N$$            N000282.txt     
283             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044502N$$            N000283.txt     
284             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044177N$$            N000284.txt     
285             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044728N$$            N000285.txt     
286             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044333N$$            N000286.txt     
287             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044905N$$            N000287.txt     
288             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044411N$$            N000288.txt     
289             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045009N$$            N000289.txt     
290             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045424N$$            N000290.txt     
291             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045645N$$            N000291.txt     
292             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046212N$$            N000292.txt     
293             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046444N$$            N000293.txt     
294             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046518N$$            N000294.txt     
295             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046762N$$            N000295.txt     
296             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046264N$$            N000296.txt     
297             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046523N$$            N000297.txt     
298             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046493N$$            N000298.txt     
299             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046768N$$            N000299.txt     
300             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046625N$$            N000300.txt     
301             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046919N$$            N000301.txt     
302             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046702N$$            N000302.txt     
303             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047019N$$            N000303.txt     
304             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046706N$$            N000304.txt     
305             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047051N$$            N000305.txt     
306             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047212N$$            N000306.txt     
307             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047179N$$            N000307.txt     
308             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046944N$$            N000308.txt     
309             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046498N$$            N000309.txt     
310             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046701N$$            N000310.txt     
311             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046295N$$            N000311.txt     
312             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046598N$$            N000312.txt     
313             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046225N$$            N000313.txt     
314             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046585N$$            N000314.txt     
315             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046240N$$            N000315.txt     
316             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046695N$$            N000316.txt     
317             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046373N$$            N000317.txt     
318             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046355N$$            N000318.txt     
319             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046056N$$            N000319.txt     
320             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046678N$$            N000320.txt     
321             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046396N$$            N000321.txt     
322             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047850N$$            N000322.txt     
323             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047582N$$            N000323.txt     
324             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047115N$$            N000324.txt     
325             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046441N$$            N000325.txt     
326             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046835N$$            N000326.txt     
327             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046201N$$            N000327.txt     
328             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046686N$$            N000328.txt     
329             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046085N$$            N000329.txt     
330             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046625N$$            N000330.txt     
331             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046054N$$            N000331.txt     
332             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046682N$$            N000332.txt     
333             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046135N$$            N000333.txt     
334             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046313N$$            N000334.txt     
335             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045791N$$            N000335.txt     
336             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046513N$$            N000336.txt     
337             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046011N$$            N000337.txt     
338             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047289N$$            N000338.txt     
339             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046805N$$            N000339.txt     
340             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046124N$$            N000340.txt     
341             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045239N$$            N000341.txt     
342             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045813N$$            N000342.txt     
343             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044969N$$            N000343.txt     
344             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045625N$$            N000344.txt     
345             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044816N$$            N000345.txt     
346             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045522N$$            N000346.txt     
347             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044742N$$            N000347.txt     
348             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045529N$$            N000348.txt     
349             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044776N$$            N000349.txt     
350             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045126N$$            N000350.txt     
351             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044398N$$            N000351.txt     
352             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044680N$$            N000352.txt     
353             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044982N$$            N000353.txt     
354             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044995N$$            N000354.txt     
355             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045303N$$            N000355.txt     
356             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044905N$$            N000356.txt     
357             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045222N$$            N000357.txt     
358             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044837N$$            N000358.txt     
359             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045163N$$            N000359.txt     
360             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.044913N$$            N000360.txt     
361             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045250N$$            N000361.txt     
362             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045164N$$            N000362.txt     
363             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045513N$$            N000363.txt     
364             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045265N$$            N000364.txt     
365             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045628N$$            N000365.txt     
366             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045564N$$            N000366.txt     
367             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045944N$$            N000367.txt     
368             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046191N$$            N000368.txt     
369             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046297N$$            N000369.txt     
370             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046776N$$            N000370.txt     
371             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046890N$$            N000371.txt     
372             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047022N$$            N000372.txt     
373             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047144N$$            N000373.txt     
374             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046909N$$            N000374.txt     
375             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047041N$$            N000375.txt     
376             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046813N$$            N000376.txt     
377             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046956N$$            N000377.txt     
378             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046845N$$            N000378.txt     
379             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047000N$$            N000379.txt     
380             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047038N$$            N000380.txt     
381             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047206N$$            N000381.txt     
382             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047086N$$            N000382.txt     
383             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047270N$$            N000383.txt     
384             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047321N$$            N000384.txt     
385             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047522N$$            N000385.txt     
386             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047590N$$            N000386.txt     
387             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047518N$$            N000387.txt     
388             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047301N$$            N000388.txt     
389             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046931N$$            N000389.txt     
390             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047357N$$            N000390.txt     
391             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047012N$$            N000391.txt     
392             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047264N$$            N000392.txt     
393             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046941N$$            N000393.txt     
394             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047343N$$            N000394.txt     
395             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047038N$$            N000395.txt     
396             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047276N$$            N000396.txt     
397             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046988N$$            N000397.txt     
398             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047101N$$            N000398.txt     
399             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046828N$$            N000399.txt     
400             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046942N$$            N000400.txt     
401             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046683N$$            N000401.txt     
402             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047217N$$            N000402.txt     
403             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046970N$$            N000403.txt     
404             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.048121N$$            N000404.txt     
405             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047883N$$            N000405.txt     
406             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047501N$$            N000406.txt     
407             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046969N$$            N000407.txt     
408             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047517N$$            N000408.txt     
409             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047010N$$            N000409.txt     
410             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047391N$$            N000410.txt     
411             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046907N$$            N000411.txt     
412             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047430N$$            N000412.txt     
413             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046965N$$            N000413.txt     
414             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047335N$$            N000414.txt     
415             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046887N$$            N000415.txt     
416             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047139N$$            N000416.txt     
417             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046707N$$            N000417.txt     
418             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046953N$$            N000418.txt     
419             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046536N$$            N000419.txt     
420             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047133N$$            N000420.txt     
421             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046729N$$            N000421.txt     
422             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047726N$$            N000422.txt     
423             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047333N$$            N000423.txt     
424             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046798N$$            N000424.txt     
425             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046116N$$            N000425.txt     
426             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046779N$$            N000426.txt     
427             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046123N$$            N000427.txt     
428             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046626N$$            N000428.txt     
429             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045992N$$            N000429.txt     
430             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046630N$$            N000430.txt     
431             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046015N$$            N000431.txt     
432             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046508N$$            N000432.txt     
433             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045911N$$            N000433.txt     
434             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046290N$$            N000434.txt     
435             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045710N$$            N000435.txt     
436             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046072N$$            N000436.txt     
437             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045507N$$            N000437.txt     
438             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046153N$$            N000438.txt     
439             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045379N$$            N000439.txt     
440             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045639N$$            N000440.txt     
441             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045842N$$            N000441.txt     
442             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045888N$$            N000442.txt     
443             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046095N$$            N000443.txt     
444             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045862N$$            N000444.txt     
445             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046075N$$            N000445.txt     
446             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045923N$$            N000446.txt     
447             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046142N$$            N000447.txt     
448             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.045857N$$            N000448.txt     
449             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046083N$$            N000449.txt     
450             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046078N$$            N000450.txt     
451             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046311N$$            N000451.txt     
452             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046076N$$            N000452.txt     
453             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046318N$$            N000453.txt     
454             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046167N$$            N000454.txt     
455             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046419N$$            N000455.txt     
456             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046367N$$            N000456.txt     
457             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046631N$$            N000457.txt     
458             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046796N$$            N000458.txt     
459             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.046858N$$            N000459.txt     
460             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047243N$$            N000460.txt     
461             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047310N$$            N000461.txt     
462             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047442N$$            N000462.txt     
463             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047514N$$            N000463.txt     
464             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047400N$$            N000464.txt     
465             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047479N$$            N000465.txt     
466             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047438N$$            N000466.txt     
467             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047524N$$            N000467.txt     
468             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047353N$$            N000468.txt     
469             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047446N$$            N000469.txt     
470             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047533N$$            N000470.txt     
471             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047634N$$            N000471.txt     
472             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047499N$$            N000472.txt     
473             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047610N$$            N000473.txt     
474             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047551N$$            N000474.txt     
475             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047673N$$            N000475.txt     
476             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047707N$$            N000476.txt     
477             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047841N$$            N000477.txt     
478             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047876N$$            N000478.txt     
479             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047809N$$            N000479.txt     
480             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047633N$$            N000480.txt     
481             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047347N$$            N000481.txt     
482             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047652N$$            N000482.txt     
483             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047382N$$            N000483.txt     
484             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047595N$$            N000484.txt     
485             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047340N$$            N000485.txt     
486             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047471N$$            N000486.txt     
487             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047229N$$            N000487.txt     
488             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047577N$$            N000488.txt     
489             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047346N$$            N000489.txt     
490             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047424N$$            N000490.txt     
491             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047203N$$            N000491.txt     
492             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047413N$$            N000492.txt     
493             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047201N$$            N000493.txt     
494             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047344N$$            N000494.txt     
495             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047141N$$            N000495.txt     
496             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047575N$$            N000496.txt     
497             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047379N$$            N000497.txt     
498             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.048287N$$            N000498.txt     
499             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.048098N$$            N000499.txt     
500             $$\left(\frac{1}{2}-\mathrm{ln}\, 2\right)N^2-\frac{1}{2}N\;\mathrm{ln}\,N -0.047802N$$            N000500.txt