由相同的玻色子系集组成的力学系统等效于由一组振子组成的力学系统—这两个系统恰恰是从两种不同观点来看待的同一个系统,它使光的波动理论与微粒理论的統一得以实现。①
假设神经网络系统相当于振子系统,制作玻色子力学系统与制作振子力学系统是同一个问题。如果神经网络是谐振子那同时也可以看作是一种玻色子。
假设一个场景
如图 按照公式
可以得到
如果ωa,ωb,ωc是已知的情况下ma,mb,mc是可以求出来的,而图C和图D是等价的。有理由相信如果神经网络符合这组公式应该就可以被看作是可以用谐振子来近似的。
再假设
可以得到
只要ω09,ωx0, ωx9是已知的ωx,ω0,ω9就都可以解出来。
现在假设弹簧并联过程就是分类的过程。
让一个二分类的网络模拟这个并联的过程。
制作一个带有1个3*3卷积核网络三层节点数分别是49*30*2的网络,分类minst的0和9,将28*28的图片缩小到9*9,让0向1,0收敛,让9向0,1收敛。将这个网络简写成
d2(minst0,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
就相当于
A:m09=m0+m9
B:mx0=mx+m0
C:mx9=mx+m9
具体进样顺序 |
|||
δ=0.1 |
|||
初始化权重 |
|||
迭代次数 |
|||
minst 0-1 |
1 |
判断是否达到收敛 |
|
minst 9-1 |
2 |
判断是否达到收敛 |
|
梯度下降 |
|||
minst 0-2 |
3 |
判断是否达到收敛 |
|
minst 9-2 |
4 |
判断是否达到收敛 |
|
梯度下降 |
|||
…… |
|||
minst 0-4999 |
9997 |
判断是否达到收敛 |
|
minst 9-4999 |
9998 |
判断是否达到收敛 |
|
梯度下降 |
|||
…… |
|||
如果4999图片内没有达到收敛标准再次从头循环 |
|||
minst 0-1 |
9999 |
判断是否达到收敛 |
|
minst 9-1 |
10000 |
判断是否达到收敛 |
|
梯度下降 |
|||
…… |
|||
每当网路达到收敛标准记录迭代次数和对应的准确率测试结果 |
|||
将这一过程重复199次 |
|||
δ=0.01 |
|||
… |
|||
δ=1e-7 |
收敛条件是
if (Math.abs(f2[0]-y[0])< δ && Math.abs(f2[1]-y[1])< δ )
因为对应每个δ都有一个n与之对应,所以可以得到一条稳定的n(δ)曲线,这条曲线已经在《计算神经网络准确率实例二分类minst0,9》2019-2-8的文中测出来了。
再用同样的办法做另外的两个网络
d2(minstx,0)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
意思是用同样的网络分类minst的0和一张x图片,让0向1,0收敛,让x向0,1收敛
d2(minstx,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
意思是用同样的网络分类minst的9和一张x图片,让x向1,0收敛,让9向0,1收敛
这张图片x就是一个9*9的二维数组是固定不变的
double [][]x=new double[9][9];
for(int n=0 ;n<9;n++){
for(int m=0 ;m<9 ;m++){
x[n][m]=((double)(n+1)*(m+1)/100);
}}
相当于让三个对象两两分类,使其中的任何一个都成为其他两个的参照物。
A,B,C分别对应三个网络
d2(minst0,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
d2(minstx,0)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
d2(minstx,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
ωx0,ωx9都可以用实验的办法测出来。未知数ωx,ω0,ω9可以被解出来。
得到的具体数据是
δ |
实测ω09 |
实测ωx0 |
实测ωx9 |
计算ωx |
计算ω0 |
计算ω9 |
0.1 |
2362.90452 |
2472.38693 |
2904.67337 |
3115.69296 |
2112.06017 |
2731.43692 |
0.01 |
3377.82412 |
3167.76382 |
3803.26633 |
3510.5585 |
2909.07317 |
4183.99025 |
0.001 |
4638.89447 |
4400.33668 |
4757.46734 |
4501.15066 |
4306.00668 |
5063.23345 |
1.00E-04 |
7127.50251 |
6164.71859 |
7442.24121 |
6364.98122 |
5982.2422 |
9355.13754 |
9.00E-05 |
7156.28643 |
6342.79899 |
7431.69849 |
6532.18998 |
6168.98039 |
8847.0741 |
8.00E-05 |
7367.8593 |
6398.79899 |
7796.70352 |
6673.71357 |
6155.28019 |
9783.06651 |
7.00E-05 |
7518.49246 |
6637.88442 |
7991.43719 |
6956.59709 |
6359.31156 |
9688.48997 |
6.00E-05 |
7833.10553 |
6804.88945 |
8491.47739 |
7223.28744 |
6451.67759 |
10801.3082 |
5.00E-05 |
8203.9799 |
7217 |
8554.46231 |
7452.14541 |
7002.79568 |
10356.4536 |
4.00E-05 |
8463.40201 |
7507.39196 |
8887.58794 |
7798.7203 |
7246.44858 |
10613.1273 |
3.00E-05 |
9201.8392 |
7946.28643 |
9326.41206 |
8026.09448 |
7868.81273 |
11570.395 |
2.00E-05 |
10848.196 |
8857.38191 |
10088.8241 |
8429.36547 |
9358.00654 |
13392.2472 |
1.00E-05 |
13375.7136 |
10095.7136 |
12178.9648 |
9550.38505 |
10746.5733 |
19920.566 |
9.00E-06 |
13466.4121 |
10820.3769 |
12143.4774 |
10097.3698 |
11724.8624 |
16320.012 |
8.00E-06 |
14629.7236 |
10830.608 |
12512.2211 |
9882.00453 |
12118.0853 |
19862.3411 |
7.00E-06 |
14828.5377 |
11451.1809 |
13638.5327 |
10875.8035 |
12128.7434 |
20861.2315 |
6.00E-06 |
15859.3467 |
11989.7337 |
13834.804 |
11039.7143 |
13236.5305 |
21109.481 |
5.00E-06 |
18927.2362 |
12050.6683 |
14346.2513 |
10568.2732 |
14405.4861 |
36179.0406 |
4.00E-06 |
19663.6382 |
13025.0905 |
15675.0251 |
11642.0648 |
15057.1888 |
36231.5706 |
3.00E-06 |
26072.9548 |
14325.3719 |
16518.2714 |
11895.6128 |
19320.4428 |
61652.2599 |
2.00E-06 |
34811.5477 |
15382.9698 |
18210.9548 |
12484.3622 |
22163.391 |
#NUM! |
1.00E-06 |
70131.8543 |
19339.2412 |
22626.201 |
15035.0068 |
32902.3542 |
#NUM! |
9.00E-07 |
77841.005 |
20197.5528 |
22949.3065 |
15457.9335 |
37328.7161 |
#NUM! |
8.00E-07 |
108462.04 |
19328.6583 |
25960.6131 |
15664.329 |
27973.7654 |
#NUM! |
7.00E-07 |
123232.583 |
21669.5729 |
27226.9849 |
17117.8607 |
34370.7668 |
#NUM! |
6.00E-07 |
140167.92 |
23628.8191 |
29224.6935 |
18534.3118 |
38600.6748 |
#NUM! |
5.00E-07 |
149534.352 |
24159.4422 |
29883.2362 |
18937.6249 |
39584.7289 |
#NUM! |
4.00E-07 |
164962.131 |
24202.1357 |
29714.4925 |
18887.939 |
40441.954 |
#NUM! |
3.00E-07 |
249506.065 |
30488.2161 |
35897.5879 |
23339.518 |
56266.811 |
#NUM! |
2.00E-07 |
289655.658 |
35339.0101 |
44208.5829 |
27729.8175 |
57639.8005 |
#NUM! |
1.00E-07 |
|
41935.7035 |
61469.5075 |
#VALUE! |
#VALUE! |
#VALUE! |
#NUM!是由测量误差造成的
将计算到的ω0和ω9画成曲线
所以这个网络d2(minst0,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)的迭代次数n可以理解成是由参与分类的对象的频率决定的,n的精确的表达式为
因为ω0和ω9是特征的彼此区分的所以可以被分类。
再由质量可以得到方程组
所以如果假设mx=1则m0,m9,mx0,mx9,m09都可以解出来得到的数据是
δ |
mx |
m0 |
m9 |
mxo |
mx9 |
m09 |
0.1 |
1 |
2.17619 |
1.301149 |
3.17619 |
2.301149 |
3.477338 |
0.01 |
1 |
1.456274 |
0.703997 |
2.456274 |
1.703997 |
2.160272 |
0.001 |
1 |
1.092692 |
0.790299 |
2.092692 |
1.790299 |
1.88299 |
1.00E-04 |
1 |
1.132052 |
0.462907 |
2.132052 |
1.462907 |
1.594959 |
9.00E-05 |
1 |
1.12122 |
0.545153 |
2.12122 |
1.545153 |
1.666373 |
8.00E-05 |
1 |
1.175546 |
0.465356 |
2.175546 |
1.465356 |
1.640901 |
7.00E-05 |
1 |
1.196667 |
0.515563 |
2.196667 |
1.515563 |
1.71223 |
6.00E-05 |
1 |
1.2535 |
0.447216 |
2.2535 |
1.447216 |
1.700716 |
5.00E-05 |
1 |
1.132452 |
0.517774 |
2.132452 |
1.517774 |
1.650226 |
4.00E-05 |
1 |
1.158234 |
0.539958 |
2.158234 |
1.539958 |
1.698192 |
3.00E-05 |
1 |
1.040376 |
0.481185 |
2.040376 |
1.481185 |
1.521561 |
2.00E-05 |
1 |
0.811378 |
0.396171 |
1.811378 |
1.396171 |
1.207549 |
1.00E-05 |
1 |
0.789772 |
0.229847 |
1.789772 |
1.229847 |
1.019619 |
9.00E-06 |
1 |
0.741653 |
0.382803 |
1.741653 |
1.382803 |
1.124457 |
8.00E-06 |
1 |
0.665001 |
0.247531 |
1.665001 |
1.247531 |
0.912531 |
7.00E-06 |
1 |
0.804065 |
0.271796 |
1.804065 |
1.271796 |
1.075861 |
6.00E-06 |
1 |
0.695612 |
0.273502 |
1.695612 |
1.273502 |
0.969114 |
5.00E-06 |
1 |
0.538211 |
0.085328 |
1.538211 |
1.085328 |
0.623539 |
4.00E-06 |
1 |
0.597822 |
0.103249 |
1.597822 |
1.103249 |
0.701071 |
3.00E-06 |
1 |
0.379088 |
0.037229 |
1.379088 |
1.037229 |
0.416316 |
2.00E-06 |
1 |
0.317293 |
#NUM! |
1.317293 |
#NUM! |
#NUM! |
1.00E-06 |
1 |
0.208811 |
#NUM! |
1.208811 |
#NUM! |
#NUM! |
9.00E-07 |
1 |
0.171481 |
#NUM! |
1.171481 |
#NUM! |
#NUM! |
8.00E-07 |
1 |
0.313561 |
#NUM! |
1.313561 |
#NUM! |
#NUM! |
7.00E-07 |
1 |
0.248039 |
#NUM! |
1.248039 |
#NUM! |
#NUM! |
6.00E-07 |
1 |
0.230549 |
#NUM! |
1.230549 |
#NUM! |
#NUM! |
5.00E-07 |
1 |
0.228874 |
#NUM! |
1.228874 |
#NUM! |
#NUM! |
4.00E-07 |
1 |
0.218125 |
#NUM! |
1.218125 |
#NUM! |
#NUM! |
3.00E-07 |
1 |
0.17206 |
#NUM! |
1.17206 |
#NUM! |
#NUM! |
2.00E-07 |
1 |
0.231446 |
#NUM! |
1.231446 |
#NUM! |
#NUM! |
1.00E-07 |
1 |
#VALUE! |
#VALUE! |
#VALUE! |
#VALUE! |
#VALUE! |
比较计算出来的m0和m9的曲线
这个结果表明被分类对象的质量也是特征分开的。
所以现在已经从数学上证明了将神经网络理解成是振子系统是可能的。很难用弹簧模型理解为什么一组有规则的图片有质量,所以将神经网络系统理解成玻色子系统,这三个网络
d2(minst0,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
d2(minstx,0)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
d2(minstx,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
看起来像是三个微观粒子,mx,m0,m9相互作用生成了另外三个微观粒子,mx0,mx9,m09,当δ=0.1时这个6个粒子的质量分别是
δ |
mx |
m0 |
m9 |
mxo |
mx9 |
m09 |
0.1 |
1 |
2.17619 |
1.301149 |
3.17619 |
2.301149 |
3.477338 |
mx,m0,m9三个粒子两两作用只产生确定的频率但没有确定的质量,只有三个粒子共同作用的情况下才会获得确定的质量。
参考书籍
- 狄拉克《量子力学原理》
实验数据 |
学习率 0.1 |
权重初始化方式 |
Random rand1 =new Random(); |
int ti1=rand1.nextInt(98)+1; |
int xx=1; |
if(ti1%2==0) |
{ xx=-1;} |
tw[a][b]=xx*((double)ti1/x); |
第一层第二层和卷积核的权重的初始化的x分别为1000,1000,200 |
d2(minst0,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
的数据在《计算神经网络准确率实例二分类minst0,9》2019-2-8已经给出了
d2(minstx,0)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)的数据已经在《神经网络与并联的弹簧》2019-2-2中给出了
d2(minstx,9)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)的数据
x9 |
||||||||
f2[0] |
f2[1] |
迭代次数n |
平均准确率p-ave |
δ |
耗时ms/次 |
耗时ms/199次 |
耗时 min/199 |
最大准确率p-max |
0.498139657 |
0.500639115 |
17.74372 |
0.505996549 |
0.5 |
755.0804 |
150261 |
2.50435 |
0.780794 |
0.390807874 |
0.609657762 |
1995.286 |
0.737359497 |
0.4 |
1128.477 |
224568 |
3.7428 |
0.895425 |
0.282098228 |
0.71779138 |
2269.729 |
0.738968851 |
0.3 |
1172.864 |
233416 |
3.8902667 |
0.902966 |
0.18149788 |
0.818163396 |
2605.286 |
0.746917089 |
0.2 |
593.2864 |
118066 |
1.9677667 |
0.910508 |
0.085215516 |
0.914988471 |
2904.673 |
0.744703912 |
0.1 |
1281.704 |
255060 |
4.251 |
0.892408 |
0.007571533 |
0.992414357 |
3803.266 |
0.69892196 |
0.01 |
1454.377 |
289422 |
4.8237 |
0.906486 |
7.14E-04 |
0.999283614 |
4757.467 |
0.673005551 |
0.001 |
1643.317 |
327020 |
5.4503333 |
0.907491 |
6.84E-05 |
0.999931679 |
7442.241 |
0.659415731 |
1.00E-04 |
2137.769 |
425417 |
7.0902833 |
0.892911 |
6.28E-05 |
0.999937215 |
7431.698 |
0.658127238 |
9.00E-05 |
2127.136 |
423300 |
7.055 |
0.888889 |
5.48E-05 |
0.999945191 |
7796.704 |
0.655242022 |
8.00E-05 |
2179.347 |
433706 |
7.2284333 |
0.906988 |
4.62E-05 |
0.999953855 |
7991.437 |
0.672629108 |
7.00E-05 |
2220.698 |
441919 |
7.3653167 |
0.879336 |
4.02E-05 |
0.999959868 |
8491.477 |
0.658657794 |
6.00E-05 |
2323.256 |
462328 |
7.7054667 |
0.873806 |
3.34E-05 |
0.999966593 |
8554.462 |
0.668465505 |
5.00E-05 |
2334.352 |
464552 |
7.7425333 |
0.889392 |
2.74E-05 |
0.999972618 |
8887.588 |
0.665168477 |
4.00E-05 |
1748.241 |
347917 |
5.7986167 |
0.924082 |
1.99E-05 |
0.999980097 |
9326.412 |
0.649428641 |
3.00E-05 |
2444.322 |
486422 |
8.1070333 |
0.88185 |
1.33E-05 |
0.99998669 |
10088.82 |
0.665279641 |
2.00E-05 |
2557.312 |
508905 |
8.48175 |
0.895928 |
6.76E-06 |
0.999993225 |
12178.96 |
0.638501709 |
1.00E-05 |
2939.317 |
584940 |
9.749 |
0.887883 |
6.11E-06 |
0.999993885 |
12143.48 |
0.654463873 |
9.00E-06 |
2932.889 |
583645 |
9.7274167 |
0.870789 |
5.51E-06 |
0.999994488 |
12512.22 |
0.653832258 |
8.00E-06 |
3008.106 |
598613 |
9.9768833 |
0.906988 |
4.69E-06 |
0.999995312 |
13638.53 |
0.637003519 |
7.00E-06 |
2961.266 |
589292 |
9.8215333 |
0.862242 |
4.03E-06 |
0.999995968 |
13834.8 |
0.631786383 |
6.00E-06 |
3233.638 |
643494 |
10.7249 |
0.869281 |
3.42E-06 |
0.999996585 |
14346.25 |
0.630813696 |
5.00E-06 |
3373.543 |
671335 |
11.188917 |
0.86727 |
2.83E-06 |
0.999997165 |
15675.03 |
0.644355513 |
4.00E-06 |
3694.774 |
735260 |
12.254333 |
0.866264 |
2.13E-06 |
0.999997867 |
16518.27 |
0.619889291 |
3.00E-06 |
3857.106 |
767564 |
12.792733 |
0.892408 |
1.33E-06 |
0.999998674 |
18210.95 |
0.634962141 |
2.00E-06 |
3756.452 |
747534 |
12.4589 |
0.879839 |
6.87E-07 |
0.999999313 |
22626.2 |
0.618752384 |
1.00E-06 |
5255.593 |
1045873 |
17.431217 |
0.873303 |
6.11E-07 |
0.999999389 |
22949.31 |
0.620222783 |
9.00E-07 |
5065.628 |
1008068 |
16.801133 |
0.865259 |
5.44E-07 |
0.999999456 |
25960.61 |
0.617067237 |
8.00E-07 |
5595.648 |
1113534 |
18.5589 |
0.858723 |
4.86E-07 |
0.999999515 |
27226.98 |
0.623226742 |
7.00E-07 |
5647.839 |
1123926 |
18.7321 |
0.865762 |
4.31E-07 |
0.999999568 |
29224.69 |
0.617794857 |
6.00E-07 |
6046.739 |
1203305 |
20.055083 |
0.865762 |
3.62E-07 |
0.999999637 |
29883.24 |
0.610450442 |
5.00E-07 |
6089.095 |
1211738 |
20.195633 |
0.826546 |
2.80E-07 |
0.99999972 |
29714.49 |
0.612643408 |
4.00E-07 |
6126.884 |
1219254 |
20.3209 |
0.863751 |
2.21E-07 |
0.999999779 |
35897.59 |
0.610356963 |
3.00E-07 |
7195.874 |
1431986 |
23.866433 |
0.858723 |
1.50E-07 |
0.99999985 |
44208.58 |
0.611597454 |
2.00E-07 |
8500.035 |
1691507 |
28.191783 |
0.863751 |
7.60E-08 |
0.999999924 |
61469.51 |
0.600589675 |
1.00E-07 |
11332.24 |
2255132 |
37.585533 |
0.86174 |
f2[0] f2[1] 迭代次数n 平均准确率p-ave δ 耗时ms/次
0.51060173 0.469918755 1 0.492709904 0.5 1788
0.504361511 0.49971626 19 0.492709904 0.5 900
0.500031553 0.498096327 33 0.492709904 0.5 863
0.500249575 0.499971377 51 0.492709904 0.5 861
0.497166709 0.500033228 30 0.501759678 0.5 798
0.497710273 0.500188656 42 0.521870287 0.5 839
0.500581015 0.499919359 33 0.492709904 0.5 750
0.500849616 0.499930994 49 0.492709904 0.5 805
0.499872419 0.502546005 30 0.507290096 0.5 728
0.444794271 0.510460632 2 0.507290096 0.5 763
0.499384568 0.500128722 44 0.418803419 0.5 747
0.479117415 0.51296932 2 0.507290096 0.5 737
0.490931445 0.57438072 2 0.507290096 0.5 719
0.455914485 0.516614624 2 0.507290096 0.5 755
0.54464122 0.460992067 1 0.492709904 0.5 704
0.505668079 0.492995776 1 0.492709904 0.5 750
0.400368 0.505051669 2 0.507290096 0.5 734
0.500108665 0.49909793 43 0.492709904 0.5 768
0.505929971 0.426796182 1 0.492709904 0.5 720
0.58494026 0.478849633 1 0.492709904 0.5 791
0.499552165 0.540351549 4 0.507290096 0.5 737
0.45709587 0.557875039 2 0.507290096 0.5 739
0.496199266 0.500031372 6 0.533433886 0.5 761
0.437908871 0.524044688 2 0.507290096 0.5 757
0.522031761 0.498720888 1 0.492709904 0.5 737
0.498199436 0.50022038 32 0.486173957 0.5 745
0.496707084 0.500811485 28 0.507290096 0.5 743
0.499666937 0.50016238 36 0.611865259 0.5 748
0.463715697 0.594141086 2 0.507290096 0.5 764
0.498144733 0.500112548 38 0.544997486 0.5 733
0.499388702 0.500050829 54 0.247360483 0.5 768
0.528710545 0.479302064 1 0.492709904 0.5 752
0.539740062 0.488078171 1 0.492709904 0.5 735
0.527229832 0.480020199 1 0.492709904 0.5 758
0.540801056 0.483311335 1 0.492709904 0.5 756
0.460077852 0.527897466 2 0.507290096 0.5 733
0.523743381 0.499027245 1 0.492709904 0.5 758
0.470601302 0.539028496 2 0.507290096 0.5 706
0.499855971 0.501028133 46 0.557063851 0.5 778
0.47728593 0.508430838 2 0.507290096 0.5 735
0.501165559 0.446592759 1 0.492709904 0.5 727
0.541657252 0.49251106 1 0.492709904 0.5 798
0.560420143 0.492025621 1 0.492709904 0.5 745
0.507907526 0.452946306 1 0.492709904 0.5 740
0.445465877 0.506996591 2 0.507290096 0.5 733
0.475792841 0.528921681 2 0.507290096 0.5 734
0.480250453 0.500484838 2 0.507290096 0.5 783
0.491432579 0.500190343 22 0.507290096 0.5 754
0.452532032 0.525994178 2 0.507290096 0.5 727
0.499798283 0.500365415 42 0.592760181 0.5 763
0.499854858 0.500836747 54 0.75967823 0.5 739
0.500110742 0.499334446 27 0.492709904 0.5 739
0.507446995 0.499729621 23 0.492709904 0.5 768
0.493408417 0.507564936 2 0.507290096 0.5 743
0.503125593 0.499913884 25 0.492709904 0.5 719
0.498005746 0.549677644 2 0.507290096 0.5 756
0.500069768 0.49076551 23 0.492709904 0.5 719
0.474104341 0.522873143 2 0.507290096 0.5 742
0.500129438 0.498637365 41 0.492709904 0.5 722
0.540424141 0.469832675 1 0.492709904 0.5 749
0.47741202 0.533998169 2 0.507290096 0.5 720
0.499055711 0.500208395 40 0.473102061 0.5 764
0.499948043 0.500976059 32 0.712418301 0.5 734
0.485132888 0.597575449 2 0.507290096 0.5 788
0.513866568 0.480864476 1 0.492709904 0.5 753
0.523556376 0.478567969 1 0.492709904 0.5 726
0.465394834 0.5431315 2 0.507290096 0.5 749
0.500010041 0.498776325 37 0.492709904 0.5 772
0.499685659 0.501207414 52 0.511814982 0.5 774
0.500081095 0.498910766 29 0.492709904 0.5 744
0.524712789 0.44497972 1 0.492709904 0.5 744
0.501324407 0.499954367 37 0.492709904 0.5 748
0.521427772 0.485793364 1 0.492709904 0.5 719
0.499989671 0.500198865 108 0.393665158 0.5 802
0.469366742 0.510704896 2 0.507290096 0.5 738
0.499807229 0.502215007 34 0.507290096 0.5 736
0.556541848 0.463173365 1 0.492709904 0.5 766
0.580539078 0.45330076 1 0.492709904 0.5 747
0.499764902 0.50045551 50 0.555555556 0.5 753
0.500024021 0.497846144 41 0.492709904 0.5 759
0.515523414 0.494854858 1 0.492709904 0.5 800
0.486457389 0.511976874 2 0.507290096 0.5 708
0.48623306 0.50496137 2 0.507290096 0.5 774
0.485686832 0.520858316 2 0.507290096 0.5 734
0.499915253 0.500230196 48 0.453494218 0.5 771
0.498903044 0.500884582 34 0.507290096 0.5 737
0.500004183 0.499639426 53 0.492709904 0.5 758
0.511922346 0.480879327 1 0.492709904 0.5 705
0.519284492 0.472107707 1 0.492709904 0.5 752
0.425885225 0.503210896 2 0.507290096 0.5 705
0.498855843 0.500266496 42 0.509301156 0.5 755
0.500157019 0.498447781 41 0.492709904 0.5 727
0.500110849 0.499094096 43 0.492709904 0.5 753
0.499979535 0.50152958 48 0.668174962 0.5 775
0.499792284 0.500205837 52 0.780794369 0.5 752
0.50114349 0.499846841 41 0.492709904 0.5 763
0.505336441 0.454397825 1 0.492709904 0.5 734
0.521893146 0.458615268 1 0.492709904 0.5 760
0.531213587 0.382281474 1 0.492709904 0.5 713
0.525310192 0.46753712 1 0.492709904 0.5 746
0.505116216 0.499914683 27 0.492709904 0.5 714
0.493841267 0.526428255 2 0.507290096 0.5 739
0.49971133 0.502174336 34 0.507290096 0.5 747
0.467107196 0.540167857 2 0.507290096 0.5 719
0.475835289 0.504847423 2 0.507290096 0.5 739
0.500779438 0.49990075 51 0.492709904 0.5 766
0.498858449 0.527213163 2 0.507290096 0.5 739
0.496027926 0.500263017 16 0.507290096 0.5 779
0.497731187 0.559723904 2 0.507290096 0.5 728
0.498429166 0.50085493 40 0.489693313 0.5 794
0.49776156 0.500078921 26 0.579688286 0.5 712
0.512987868 0.449095429 1 0.492709904 0.5 765
0.437582336 0.532056006 2 0.507290096 0.5 725
0.500011476 0.498492044 47 0.492709904 0.5 762
0.453705515 0.52305216 2 0.507290096 0.5 746
0.467701766 0.513156092 2 0.507290096 0.5 731
0.437672925 0.510163856 2 0.507290096 0.5 738
0.417333761 0.590150011 2 0.507290096 0.5 749
0.499868413 0.50121845 26 0.579688286 0.5 740
0.496084974 0.53963516 2 0.507290096 0.5 769
0.50119812 0.499816556 39 0.492709904 0.5 739
0.578156865 0.448821225 1 0.492709904 0.5 757
0.503431459 0.487643037 1 0.492709904 0.5 752
0.500094355 0.49567559 15 0.492709904 0.5 743
0.492349326 0.500121124 20 0.507290096 0.5 738
0.465636067 0.527708804 2 0.507290096 0.5 739
0.500149679 0.495791423 31 0.492709904 0.5 789
0.501439206 0.499722494 27 0.492709904 0.5 759
0.555260536 0.491178113 1 0.492709904 0.5 754
0.484785594 0.55156791 2 0.507290096 0.5 751
0.375615987 0.531977978 2 0.507290096 0.5 732
0.541907512 0.425081972 1 0.492709904 0.5 752
0.434381785 0.525468346 2 0.507290096 0.5 765
0.499712141 0.500547911 52 0.475113122 0.5 709
0.500030482 0.498245935 37 0.492709904 0.5 786
0.549643282 0.470443634 1 0.492709904 0.5 705
0.519084358 0.499033995 1 0.492709904 0.5 749
0.496556679 0.534675474 2 0.507290096 0.5 754
0.519735827 0.473948707 1 0.492709904 0.5 736
0.450206616 0.525566367 2 0.507290096 0.5 744
0.496556874 0.500011617 28 0.507290096 0.5 756
0.498652423 0.500134955 46 0.731523379 0.5 774
0.543302746 0.477348419 1 0.492709904 0.5 744
0.499925629 0.53314019 2 0.507290096 0.5 748
0.547188418 0.468794333 1 0.492709904 0.5 717
0.508929132 0.49990989 15 0.492709904 0.5 765
0.510371702 0.461047924 1 0.492709904 0.5 735
0.499633494 0.50008425 38 0.533936652 0.5 764
0.534390793 0.467457684 1 0.492709904 0.5 751
0.499719931 0.56607049 2 0.507290096 0.5 740
0.473738033 0.514905726 2 0.507290096 0.5 746
0.502368317 0.499981073 35 0.492709904 0.5 724
0.498983459 0.50000484 38 0.550025138 0.5 729
0.539710497 0.470939125 1 0.492709904 0.5 770
0.500012325 0.498877717 45 0.492709904 0.5 719
0.499222644 0.501116582 38 0.648567119 0.5 782
0.49981747 0.504208347 16 0.507290096 0.5 719
0.50684211 0.422976754 1 0.492709904 0.5 741
0.50128628 0.499989008 25 0.492709904 0.5 738
0.498914823 0.500121874 44 0.480140774 0.5 760
0.49445244 0.551881144 2 0.507290096 0.5 720
0.500105586 0.498183441 23 0.492709904 0.5 758
0.49682115 0.51612087 2 0.507290096 0.5 766
0.427039074 0.505880718 2 0.507290096 0.5 726
0.500272723 0.499995755 43 0.492709904 0.5 742
0.518157906 0.447819596 1 0.492709904 0.5 763
0.515022154 0.440927866 1 0.492709904 0.5 767
0.505890293 0.48170838 1 0.492709904 0.5 741
0.478072875 0.541127452 2 0.507290096 0.5 743
0.496170155 0.500440185 32 0.507290096 0.5 759
0.498530876 0.500762992 34 0.532428356 0.5 730
0.500865271 0.499919219 39 0.492709904 0.5 732
0.500075651 0.49985236 43 0.492709904 0.5 734
0.499350394 0.500094737 42 0.37254902 0.5 749
0.493783224 0.500040998 22 0.507290096 0.5 748
0.500906741 0.492182032 1 0.492709904 0.5 739
0.470475317 0.551417603 2 0.507290096 0.5 797
0.499891811 0.500687803 34 0.49321267 0.5 744
0.482474855 0.552579112 2 0.507290096 0.5 771
0.516653245 0.435390925 1 0.492709904 0.5 745
0.48639443 0.515817217 2 0.507290096 0.5 772
0.479825196 0.549451838 2 0.507290096 0.5 720
0.499449262 0.503270001 30 0.507290096 0.5 761
0.500002297 0.499635849 45 0.492709904 0.5 749
0.507729693 0.476875323 1 0.492709904 0.5 743
0.538057455 0.453422095 1 0.492709904 0.5 729
0.550233214 0.456541338 1 0.492709904 0.5 731
0.500060332 0.499417836 47 0.492709904 0.5 780
0.500065759 0.499588679 61 0.492709904 0.5 737
0.469532765 0.576897617 2 0.507290096 0.5 755
0.499445668 0.500096917 50 0.525389643 0.5 737
0.49850414 0.502338587 40 0.512317748 0.5 746
0.454260077 0.516214205 2 0.507290096 0.5 754
0.499922487 0.500412737 66 0.413273002 0.5 755
0.499753262 0.502566207 8 0.509803922 0.5 747
0.504431423 0.464510572 1 0.492709904 0.5 760
0.499889023 0.502117702 20 0.576168929 0.5 743
0.500482026 0.499950144 47 0.492709904 0.5 743
0.499419289 0.500138498 48 0.508798391 0.5 728
150261
0.399988799 0.603228518 1608 0.714429361 0.4 1218
0.395993408 0.604977168 1860 0.626948215 0.4 1137
0.377716379 0.621752977 1058 0.66314731 0.4 973
0.384992384 0.615159058 2212 0.850175968 0.4 1205
0.386732267 0.615000647 1884 0.591754651 0.4 1091
0.39204928 0.604277687 1424 0.646053293 0.4 1004
0.393646491 0.604437244 1924 0.667672197 0.4 1116
0.399090469 0.603372365 4074 0.732026144 0.4 1707
0.388673598 0.607043537 1334 0.703871292 0.4 963
0.384723724 0.615832507 3206 0.527903469 0.4 1329
0.391945093 0.603598605 2954 0.81950729 0.4 1274
0.395693343 0.606035458 1564 0.816993464 0.4 1035
0.392959537 0.605358451 1608 0.537958773 0.4 1065
0.389192208 0.616093467 2652 0.815987934 0.4 1267
0.396729969 0.600582973 2330 0.79436903 0.4 1171
0.399464518 0.601956913 2658 0.841126194 0.4 1252
0.39421193 0.611605915 1692 0.593262946 0.4 1070
0.375010144 0.628797176 1860 0.773252891 0.4 1082
0.391753204 0.602673117 2294 0.780794369 0.4 1168
0.397807367 0.60490918 1582 0.802916038 0.4 1018
0.373053296 0.626521856 1686 0.683257919 0.4 1078
0.394927827 0.60566407 1582 0.749120161 0.4 1048
0.386402517 0.619764224 2598 0.826043238 0.4 1274
0.394501534 0.607953431 1334 0.529411765 0.4 1009
0.377289843 0.618547114 2954 0.750125691 0.4 1330
0.395717759 0.605180236 2122 0.861236802 0.4 1161
0.397054743 0.605737092 2218 0.815987934 0.4 1181
0.398049625 0.606445865 3446 0.799899447 0.4 1372
0.395044913 0.609484743 1598 0.609351433 0.4 1072
0.373007521 0.624062233 1700 0.575666164 0.4 1079
0.390823611 0.607570444 3912 0.768728004 0.4 1452
0.396459928 0.602514474 1582 0.753142283 0.4 1026
0.391408029 0.604016684 946 0.659627954 0.4 901
0.388223707 0.615376969 1700 0.895424837 0.4 1082
0.383939686 0.609921869 998 0.790849673 0.4 943
0.397748775 0.600326069 2338 0.67571644 0.4 1213
0.376817887 0.624024434 2598 0.762694822 0.4 1258
0.393944275 0.606473536 1518 0.772750126 0.4 1025
0.386775755 0.618223882 2316 0.811463047 0.4 1151
0.382698561 0.609196527 1058 0.576671694 0.4 938
0.386627152 0.608176392 1374 0.734037205 0.4 980
0.388970698 0.614413584 2748 0.783308195 0.4 1252
0.394932304 0.602800482 1338 0.821518351 0.4 999
0.377917517 0.62601519 1468 0.725992961 0.4 990
0.39883441 0.600222456 1300 0.648064354 0.4 980
0.399131955 0.600869842 2528 0.656108597 0.4 1219
0.360231404 0.644842333 1700 0.853192559 0.4 1057
0.382798603 0.621272907 2380 0.600301659 0.4 1214
0.393925566 0.601952631 2338 0.702865762 0.4 1151
0.395453447 0.601106691 2338 0.690296631 0.4 1183
0.394659149 0.610506251 1426 0.876822524 0.4 990
0.381443832 0.623050832 3684 0.569130216 0.4 1417
0.391701567 0.607214198 1940 0.868275515 0.4 1118
0.395554534 0.605161123 1700 0.615384615 0.4 1068
0.39458993 0.60581905 1914 0.821015586 0.4 1086
0.380848904 0.616002953 1860 0.761186526 0.4 1101
0.386299373 0.611648599 2212 0.825540473 0.4 1144
0.399540043 0.602059954 1780 0.530417295 0.4 1079
0.384892632 0.613485157 1334 0.655103067 0.4 1015
0.381494512 0.618161927 2598 0.719959779 0.4 1239
0.395502034 0.603657036 954 0.827048768 0.4 955
0.385334454 0.620226419 3626 0.7239819 0.4 1404
0.386129376 0.613735552 2294 0.526897939 0.4 1197
0.3970948 0.605526297 1974 0.770739065 0.4 1149
0.395973632 0.602360553 1986 0.656108597 0.4 1130
0.396031707 0.603065187 2366 0.808446456 0.4 1190
0.374310893 0.626524411 1686 0.84263449 0.4 1063
0.390884484 0.607627899 1914 0.684263449 0.4 1122
0.397947967 0.604582066 1368 0.646556058 0.4 1023
0.378549156 0.625886397 3274 0.690296631 0.4 1352
0.395288352 0.604071231 2598 0.804424334 0.4 1268
0.393508061 0.611841266 3736 0.836098542 0.4 1461
0.387101828 0.614571092 2122 0.69984917 0.4 1196
0.399816048 0.601097502 2598 0.604826546 0.4 1239
0.394553749 0.602962857 2218 0.670186023 0.4 1169
0.396950438 0.603304362 2076 0.67370538 0.4 1163
0.394812565 0.601736108 1290 0.614379085 0.4 1006
0.39700045 0.602561174 2528 0.679738562 0.4 1220
0.393049344 0.606993664 1232 0.62745098 0.4 968
0.390654788 0.609992897 1518 0.784816491 0.4 1062
0.390188405 0.603184647 1878 0.808446456 0.4 1114
0.386414559 0.619584707 2466 0.822021116 0.4 1188
0.385800066 0.612084982 1860 0.817998994 0.4 1105
0.391454491 0.612578206 1994 0.812971342 0.4 1137
0.384992586 0.61055817 4202 0.813474108 0.4 1564
0.382117801 0.619144367 1894 0.75967823 0.4 1107
0.394349521 0.608832936 2652 0.80693816 0.4 1255
0.395866039 0.60335152 1348 0.599296129 0.4 1032
0.393348889 0.612835989 1518 0.739064857 0.4 1041
0.396535528 0.601601031 1196 0.550527903 0.4 1006
0.393710322 0.604625741 1058 0.685771745 0.4 955
0.393281468 0.604462755 2104 0.723479135 0.4 1116
0.396757419 0.600406117 2294 0.595274007 0.4 1210
0.396267447 0.614660859 2022 0.768728004 0.4 1143
0.395071408 0.609598796 2430 0.733031674 0.4 1196
0.391410373 0.601313088 2122 0.853192559 0.4 1099
0.396344936 0.601614597 1620 0.741578683 0.4 1014
0.387042488 0.619041633 1312 0.787833082 0.4 1008
0.382291963 0.619633076 1334 0.655103067 0.4 1004
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224568
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233416
0.176893058 0.823550331 4000 0.815485168 0.2 1512
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5.27E-04 0.999481731 4120 0.690296631 0.001 1563
8.79E-04 0.999114739 4550 0.643539467 0.001 1578
8.96E-04 0.999093174 5140 0.811463047 0.001 1672
6.70E-04 0.999351536 6732 0.786827552 0.001 1989
7.45E-04 0.999230723 5910 0.802916038 0.001 1870
3.86E-04 0.999612755 4488 0.527903469 0.001 1587
5.54E-04 0.999464719 6496 0.78381096 0.001 1945
6.81E-04 0.999325837 3634 0.558069382 0.001 1438
8.97E-04 0.99903684 3810 0.683760684 0.001 1460
6.76E-04 0.999332795 4550 0.736551031 0.001 1605
9.68E-04 0.999063675 5172 0.600804424 0.001 1706
8.50E-04 0.999138064 5522 0.597285068 0.001 1778
6.08E-04 0.999409496 6078 0.666163901 0.001 1877
7.18E-04 0.999288745 4314 0.741578683 0.001 1572
2.83E-04 0.999719971 4550 0.576168929 0.001 1596
8.49E-04 0.999148716 4120 0.602815485 0.001 1574
9.76E-04 0.99906618 4120 0.527400704 0.001 1580
8.83E-04 0.999096954 2766 0.708898944 0.001 1252
9.63E-04 0.999019862 4550 0.75967823 0.001 1575
1.15E-04 0.999888028 5882 0.852689794 0.001 1880
9.47E-04 0.999055288 4740 0.523881347 0.001 1638
3.68E-04 0.999631922 6472 0.744595274 0.001 1935
8.36E-04 0.999157199 3972 0.535947712 0.001 1452
8.92E-04 0.999121671 3972 0.559577677 0.001 1456
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9.10E-04 0.999083483 4074 0.648064354 0.001 1486
1.39E-04 0.999861509 5882 0.863750628 0.001 1901
9.81E-04 0.999008105 3298 0.660130719 0.001 1378
6.08E-04 0.999399177 4488 0.746606335 0.001 1579
8.39E-04 0.999167785 3428 0.714429361 0.001 1373
9.29E-04 0.999064044 3814 0.834087481 0.001 1454
8.48E-04 0.999152198 7476 0.584715938 0.001 2151
9.42E-04 0.999036937 3810 0.560080442 0.001 1513
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4.56E-04 0.999555895 5244 0.827551533 0.001 1700
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2.30E-04 0.99977611 4550 0.833081951 0.001 1616
7.87E-04 0.999199609 4550 0.539467069 0.001 1624
7.89E-04 0.999222002 3810 0.600301659 0.001 1491
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1.42E-04 0.999858403 7252 0.883358472 0.001 2064
5.54E-04 0.999447097 3810 0.580693816 0.001 1467
5.54E-04 0.999430659 6078 0.593765711 0.001 1925
7.64E-04 0.999199286 3912 0.729512318 0.001 1510
8.03E-04 0.999162624 4314 0.733031674 0.001 1558
5.41E-04 0.999474902 4550 0.740573152 0.001 1565
6.57E-04 0.999332825 4314 0.840623429 0.001 1527
7.42E-04 0.999277702 3410 0.780794369 0.001 1389
8.87E-04 0.999108061 4550 0.778280543 0.001 1649
8.67E-04 0.999139325 5492 0.787833082 0.001 1799
4.78E-04 0.999536675 4074 0.699346405 0.001 1504
9.45E-04 0.999056095 4314 0.558572147 0.001 1502
6.78E-04 0.999290985 4314 0.620915033 0.001 1538
8.80E-04 0.99913239 4202 0.555555556 0.001 1551
9.80E-04 0.999030705 5684 0.808446456 0.001 1849
8.42E-04 0.999170381 4156 0.526897939 0.001 1522
6.19E-04 0.999361273 4550 0.746606335 0.001 1619
3.84E-04 0.999615181 6078 0.806435395 0.001 1912
4.89E-04 0.999500119 4202 0.798893917 0.001 1563
7.45E-04 0.999247225 4084 0.531422826 0.001 1510
4.09E-04 0.999587931 5882 0.79537456 0.001 1891
8.16E-04 0.999186452 4550 0.519859226 0.001 1600
8.57E-04 0.999137947 4326 0.588235294 0.001 1565
5.10E-04 0.999500637 4558 0.812468577 0.001 1605
3.49E-04 0.999662949 4550 0.7239819 0.001 1611
6.74E-04 0.999297246 3814 0.69984917 0.001 1454
7.23E-04 0.999268727 5368 0.720965309 0.001 1762
2.33E-04 0.999754437 5684 0.65057818 0.001 1801
6.09E-04 0.999364105 4954 0.794871795 0.001 1678
7.50E-04 0.999229192 3814 0.681749623 0.001 1463
7.12E-04 0.999238788 5882 0.852689794 0.001 1901
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4.62E-04 0.999556863 4074 0.714429361 0.001 1509
4.07E-04 0.999594238 4314 0.519859226 0.001 1579
3.62E-04 0.999629418 4488 0.66314731 0.001 1620
4.89E-04 0.999526322 5318 0.686777275 0.001 1747
5.55E-04 0.99941965 6078 0.699346405 0.001 1894
7.11E-04 0.999282702 6974 0.820010055 0.001 2037
3.41E-04 0.999650248 4550 0.693313223 0.001 1590
5.61E-04 0.99943769 5882 0.762192056 0.001 1861
9.89E-04 0.9990097 4326 0.706887883 0.001 1572
9.66E-04 0.999041142 4202 0.717948718 0.001 1524
9.77E-04 0.999015292 3810 0.54248366 0.001 1459
6.05E-04 0.999421545 4074 0.567621921 0.001 1559
4.94E-04 0.999512535 5684 0.57918552 0.001 1850
7.80E-04 0.999231477 3292 0.563097034 0.001 1352
9.94E-04 0.9990295 3428 0.734037205 0.001 1393
9.62E-04 0.999030612 4314 0.688788336 0.001 1557
8.60E-04 0.999142932 5872 0.744595274 0.001 1831
6.97E-04 0.999309761 5244 0.743589744 0.001 1770
9.24E-04 0.999035898 4316 0.550527903 0.001 1581
9.84E-04 0.999015816 3682 0.600301659 0.001 1439
9.31E-04 0.999074965 4202 0.679738562 0.001 1545
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6.99E-04 0.999293653 3810 0.534942182 0.001 1463
4.48E-04 0.999540319 3810 0.629964806 0.001 1467
8.00E-04 0.999207819 5530 0.507792861 0.001 1837
8.87E-04 0.999070279 5368 0.753142283 0.001 1777
7.80E-04 0.999209087 5876 0.854198089 0.001 1859
7.71E-04 0.999226108 4488 0.507290096 0.001 1581
8.28E-04 0.999180407 4550 0.791855204 0.001 1639
7.94E-04 0.999205825 6078 0.602815485 0.001 1865
4.56E-04 0.999536381 5684 0.800402212 0.001 1853
5.62E-04 0.999442074 7118 0.565108095 0.001 2074
5.21E-04 0.999475446 4550 0.67571644 0.001 1621
4.86E-04 0.999491845 4550 0.792860734 0.001 1600
8.91E-04 0.999116086 5684 0.799899447 0.001 1848
7.49E-04 0.999240006 5692 0.751633987 0.001 1813
9.43E-04 0.999050274 3292 0.554550025 0.001 1427
7.04E-04 0.999267742 2766 0.762694822 0.001 1237
6.42E-04 0.999375654 6974 0.861236802 0.001 2045
7.00E-04 0.99929135 6158 0.734037205 0.001 1896
4.09E-04 0.999603307 4488 0.581699346 0.001 1609
8.30E-04 0.999170218 4202 0.557063851 0.001 1546
8.99E-04 0.999100041 4084 0.510306687 0.001 1502
6.55E-04 0.999343399 7006 0.737053796 0.001 2116
7.42E-04 0.999242939 4314 0.522373052 0.001 1538
6.78E-04 0.999329172 3292 0.584715938 0.001 1368
4.09E-04 0.999598988 6496 0.798391151 0.001 1942
9.01E-04 0.999075318 5244 0.554550025 0.001 1748
7.26E-04 0.999263642 7510 0.73453997 0.001 2170
9.11E-04 0.999097074 4156 0.527400704 0.001 1585
8.73E-04 0.999144379 6322 0.562594268 0.001 1916
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7.85E-04 0.999217041 4488 0.717948718 0.001 1580
7.19E-04 0.999270453 3810 0.580693816 0.001 1489
7.55E-04 0.999236817 3130 0.605329311 0.001 1382
8.38E-04 0.999185619 3810 0.661639015 0.001 1436
9.87E-04 0.999016377 4074 0.513323278 0.001 1513
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7.90E-04 0.999215241 4314 0.739567622 0.001 1540
9.24E-04 0.999073938 4120 0.706887883 0.001 1523
5.73E-04 0.999417065 9546 0.861236802 0.001 2500
9.04E-04 0.999096469 4740 0.66314731 0.001 1666
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8.37E-04 0.999162063 3912 0.573655103 0.001 1502
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4.18E-04 0.999577668 4550 0.813976873 0.001 1559
8.01E-04 0.999195335 5040 0.512317748 0.001 1709
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9.24E-04 0.999050751 3812 0.515837104 0.001 1474
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6.79E-04 0.999300392 7010 0.686777275 0.001 2070
8.49E-04 0.999144781 4954 0.65158371 0.001 1688
6.24E-04 0.99938364 4314 0.510306687 0.001 1576
8.99E-04 0.999086918 3912 0.521870287 0.001 1480
7.89E-04 0.999208426 6430 0.563097034 0.001 1991
7.39E-04 0.999251236 4074 0.767219708 0.001 1496
8.92E-04 0.999101999 3410 0.809954751 0.001 1358
5.61E-04 0.999430556 4488 0.719959779 0.001 1558
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9.30E-04 0.999089078 3832 0.742584213 0.001 1500
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3.85E-04 0.999622097 3810 0.547008547 0.001 1454
9.71E-04 0.999060022 3810 0.633986928 0.001 1454
5.92E-04 0.999407391 4488 0.573152338 0.001 1578
8.49E-04 0.999133473 4326 0.610859729 0.001 1539
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327020
9.31E-05 0.999909121 13206 0.574157868 1.00E-04 3286
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9.54E-05 0.99990371 8546 0.525389643 1.00E-04 2377
3.83E-05 0.999963601 5882 0.761186526 1.00E-04 1908
6.03E-05 0.999940899 7252 0.706385118 1.00E-04 2078
2.72E-05 0.99997292 7252 0.593765711 1.00E-04 2076
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4.57E-05 0.999952968 8474 0.829562594 1.00E-04 2363
7.29E-05 0.999925999 8928 0.827048768 1.00E-04 2370
5.57E-05 0.999943295 9146 0.558572147 1.00E-04 2508
3.51E-05 0.99996574 5882 0.568627451 1.00E-04 1843
9.78E-05 0.999901962 9576 0.534439417 1.00E-04 2517
7.29E-05 0.999927899 6078 0.773252891 1.00E-04 1922
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3.62E-05 0.999965109 5976 0.513323278 1.00E-04 1865
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5.91E-05 0.999939164 6974 0.667169432 1.00E-04 2057
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3.92E-05 0.9999612 7952 0.527903469 1.00E-04 2240
9.54E-05 0.999904516 8838 0.836601307 1.00E-04 2421
7.52E-05 0.999928301 4550 0.692810458 1.00E-04 1609
5.52E-05 0.999945967 8508 0.718954248 1.00E-04 2337
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8.73E-05 0.999912649 8344 0.892911011 1.00E-04 2281
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2.97E-05 0.999970243 9146 0.697335344 1.00E-04 2486
6.83E-05 0.999932154 6732 0.825540473 1.00E-04 1981
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2.43E-05 0.999976243 8086 0.805932629 1.00E-04 2282
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425417
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423300
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441919
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347917
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486422
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508905
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1211738
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9.42E-08 0.999999907 61030 0.509803922 1.00E-07 11500
8.19E-08 0.999999918 47536 0.622423328 1.00E-07 9371
9.30E-08 0.999999906 125946 0.523881347 1.00E-07 23241
9.66E-08 0.999999904 20074 0.522373052 1.00E-07 4313
8.65E-08 0.999999914 24542 0.59074912 1.00E-07 5042
9.78E-08 0.999999904 24542 0.610859729 1.00E-07 5085
8.77E-08 0.999999915 49968 0.592257416 1.00E-07 9470
7.80E-08 0.999999922 34476 0.696329814 1.00E-07 6922
4.98E-08 0.999999951 34302 0.648567119 1.00E-07 6872
9.22E-08 0.999999907 30070 0.592760181 1.00E-07 6166
5.25E-08 0.999999946 14546 0.528406234 1.00E-07 3374
9.51E-08 0.999999905 29538 0.752136752 1.00E-07 6001
7.07E-08 0.999999927 58488 0.635495224 1.00E-07 11033
7.52E-08 0.999999927 24542 0.637003519 1.00E-07 5189
9.45E-08 0.999999906 14546 0.777777778 1.00E-07 3304
8.34E-08 0.999999916 77992 0.507290096 1.00E-07 14764
9.77E-08 0.999999903 55974 0.512820513 1.00E-07 11588
9.29E-08 0.999999908 34476 0.516339869 1.00E-07 6934
8.03E-08 0.999999919 85962 0.508295626 1.00E-07 16107
9.76E-08 0.999999901 69030 0.525892408 1.00E-07 13025
6.38E-08 0.999999934 31902 0.640020111 1.00E-07 6521
9.66E-08 0.999999906 402698 0.521870287 1.00E-07 73076
9.04E-08 0.999999911 194364 0.508295626 1.00E-07 35632
6.53E-08 0.999999932 14546 0.631473102 1.00E-07 3405
9.89E-08 0.999999902 75584 0.546505782 1.00E-07 14157
4.17E-08 0.999999959 22758 0.725992961 1.00E-07 4817
5.97E-08 0.99999994 28078 0.661136249 1.00E-07 5699
6.73E-08 0.999999933 31768 0.754147813 1.00E-07 6459
9.85E-08 0.999999902 115950 0.515837104 1.00E-07 21405
9.60E-08 0.999999905 43412 0.659627954 1.00E-07 8673
8.42E-08 0.999999913 105954 0.512820513 1.00E-07 19935
7.32E-08 0.999999927 131006 0.507290096 1.00E-07 24470
8.27E-08 0.999999916 62742 0.791855204 1.00E-07 12062
7.99E-08 0.999999918 64526 0.72297637 1.00E-07 12427
9.70E-08 0.999999905 45978 0.512317748 1.00E-07 9000
2.89E-08 0.999999971 24542 0.669683258 1.00E-07 5130
5.21E-08 0.999999949 22758 0.861739568 1.00E-07 4878
9.57E-08 0.999999905 150994 0.512317748 1.00E-07 27869
7.57E-08 0.999999926 42750 0.78381096 1.00E-07 8511
8.62E-08 0.999999913 33432 0.669180493 1.00E-07 6740
3.42E-08 0.999999967 26748 0.53092006 1.00E-07 5615
8.96E-08 0.999999909 43394 0.679738562 1.00E-07 8605
4.90E-08 0.999999951 24798 0.665158371 1.00E-07 5240
8.49E-08 0.999999914 64260 0.569632981 1.00E-07 12386
9.96E-08 0.999999901 60996 0.519859226 1.00E-07 11676
9.16E-08 0.999999906 32846 0.524886878 1.00E-07 6583
8.55E-08 0.999999914 31902 0.705379588 1.00E-07 6501
7.29E-08 0.999999928 55974 0.524384113 1.00E-07 10951
9.16E-08 0.999999907 115950 0.510306687 1.00E-07 21578
9.54E-08 0.999999905 144494 0.512820513 1.00E-07 26928
5.82E-08 0.999999942 38496 0.510809452 1.00E-07 7626
6.55E-08 0.999999936 34728 0.520864756 1.00E-07 7046
3.75E-08 0.999999962 27544 0.604826546 1.00E-07 5738
6.32E-08 0.999999937 35964 0.569130216 1.00E-07 7266
7.30E-08 0.999999925 34538 0.72197084 1.00E-07 6920
7.88E-08 0.999999923 33690 0.591754651 1.00E-07 6795
9.40E-08 0.999999906 54530 0.833584716 1.00E-07 10638
9.45E-08 0.999999903 25032 0.580191051 1.00E-07 5220
6.38E-08 0.999999936 22758 0.641025641 1.00E-07 4835
9.92E-08 0.9999999 44724 0.675213675 1.00E-07 8827
9.81E-08 0.9999999 131416 0.508295626 1.00E-07 24692
6.55E-08 0.999999934 44472 0.510809452 1.00E-07 8890
9.75E-08 0.999999903 252838 0.515334339 1.00E-07 47273
6.35E-08 0.999999937 32754 0.711915535 1.00E-07 6644
9.67E-08 0.999999903 295252 0.508295626 1.00E-07 55672
6.06E-08 0.99999994 12762 0.695324284 1.00E-07 2977
7.34E-08 0.999999927 44724 0.586224233 1.00E-07 8626
9.48E-08 0.999999905 241372 0.507792861 1.00E-07 43571
6.61E-08 0.999999934 30496 0.563599799 1.00E-07 6184
8.84E-08 0.999999912 141002 0.508295626 1.00E-07 25779
5.38E-08 0.999999947 37540 0.537456008 1.00E-07 7404
3.99E-08 0.99999996 22758 0.77124183 1.00E-07 4791
2.51E-08 0.999999975 33690 0.574157868 1.00E-07 6654
9.48E-08 0.999999904 34476 0.599296129 1.00E-07 6941
8.57E-08 0.999999914 114506 0.507792861 1.00E-07 21152
6.23E-08 0.999999939 45960 0.507290096 1.00E-07 8890
2.48E-08 0.999999976 24542 0.606334842 1.00E-07 5507
9.49E-08 0.999999905 22758 0.69884364 1.00E-07 4880
7.38E-08 0.999999926 14546 0.709904475 1.00E-07 3344
9.60E-08 0.999999903 62914 0.517848165 1.00E-07 12084
9.62E-08 0.999999905 131006 0.507290096 1.00E-07 24182
4.09E-08 0.999999959 22758 0.548014077 1.00E-07 4838
9.14E-08 0.999999906 31902 0.574157868 1.00E-07 6362
7.96E-08 0.999999919 22786 0.580191051 1.00E-07 4782
8.78E-08 0.99999991 201134 0.507792861 1.00E-07 36081
9.75E-08 0.999999904 212774 0.514831574 1.00E-07 38266
9.08E-08 0.999999909 36744 0.757667169 1.00E-07 7279
4.38E-08 0.999999956 24732 0.670688788 1.00E-07 5147
9.54E-08 0.999999901 431296 0.507792861 1.00E-07 76764
6.42E-08 0.999999936 17952 0.602815485 1.00E-07 3876
7.08E-08 0.999999929 18082 0.705882353 1.00E-07 3898
8.65E-08 0.999999911 27544 0.735042735 1.00E-07 5557
9.11E-08 0.99999991 173530 0.5173454 1.00E-07 31319
6.71E-08 0.999999931 24542 0.791855204 1.00E-07 4989
9.68E-08 0.999999907 195918 0.511312217 1.00E-07 35134
9.74E-08 0.999999902 275886 0.509301156 1.00E-07 49489
9.34E-08 0.999999907 79548 0.518853695 1.00E-07 14830
6.27E-08 0.999999936 34538 0.576671694 1.00E-07 6826
8.57E-08 0.999999915 30870 0.632981398 1.00E-07 6121
9.47E-08 0.999999909 35964 0.514328808 1.00E-07 7141
4.54E-08 0.999999954 24732 0.653594771 1.00E-07 5229
5.85E-08 0.99999994 30870 0.624434389 1.00E-07 6153
8.86E-08 0.999999911 75966 0.534942182 1.00E-07 14080
8.82E-08 0.999999911 95940 0.507290096 1.00E-07 17578
4.56E-08 0.999999954 25968 0.511814982 1.00E-07 5323
9.14E-08 0.999999907 65952 0.507290096 1.00E-07 12446
4.78E-08 0.999999951 45978 0.595776772 1.00E-07 8940
4.97E-08 0.999999952 41898 0.645047763 1.00E-07 8141
4.23E-08 0.999999958 25874 0.519859226 1.00E-07 5244
4.79E-08 0.999999953 24480 0.513323278 1.00E-07 5025
9.75E-08 0.999999903 145312 0.507792861 1.00E-07 26518
9.83E-08 0.999999902 44938 0.529411765 1.00E-07 8611
5.78E-08 0.99999994 44724 0.560080442 1.00E-07 8649
7.85E-08 0.99999992 81026 0.507792861 1.00E-07 15063
9.02E-08 0.99999991 34302 0.536953243 1.00E-07 6752
8.69E-09 0.999999991 20074 0.74811463 1.00E-07 4211
6.64E-08 0.999999933 34476 0.615887381 1.00E-07 6823
9.25E-08 0.999999911 50876 0.534942182 1.00E-07 9695
9.38E-08 0.999999906 45960 0.523378582 1.00E-07 8959
2.02E-08 0.99999998 30070 0.839115133 1.00E-07 6105
3.56E-08 0.999999963 19542 0.660130719 1.00E-07 4142
9.98E-08 0.9999999 53408 0.606837607 1.00E-07 10159
8.27E-08 0.999999916 134498 0.515837104 1.00E-07 -52545
5.44E-08 0.999999946 44724 0.657616893 1.00E-07 8517
9.37E-08 0.999999906 25968 0.54147813 1.00E-07 5250
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