Xây dựng thang thời gian quốc gia UTC (VMI)
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BỘ KHOA HỌC VÀ CÔNG NGHỆ
TỔNG CỤC TC-ĐL-CL VIỆT NAM
VIỆN ĐO LƯỜNG VIỆT NAM
_______________________________________________
ĐỀ TÀI ĐỘC LẬP CẤP NHÀ NƯỚC
XÂY DỰNG THANG
THỜI GIAN QUỐC GIA UTC (VMI)
Mã số : ĐTĐL 2008G/11
Chủ nhiệm đề tài: Lê Văn Ninh
PHỤ LỤC
7672-1
04/02/2010
Hà Nội, 2009
Bé khoa häc vµ c«ng nghÖ
ViÖn ®o l−êng viÖt nam
B¸o c¸o khoa häc
Tæng kÕt ®Ò tµi
x©y dùng thang thêi gian quèc gia utc(VMI)
Phô lôc
1. bµi b¸o “the establishment of the Vietnam atomic
time scale”
2
. sè liÖu tÝnh to¸n trung gian x©y dùng thang thêi
gian quèc gia utc(VMI)
3. kÕt qu¶ ®o, hiÖu chuÈn cho hÖ thèng cung cÊp thêi
gian m¸y tÝnh tù ®éng ACTS
4. kÕt qu¶ ®o, hiÖu chuÈn cho hÖ thèng hiÖu chuÈn
timeserver
Hµ Néi - 2009
Phô lôc 1
BµI b¸o
“the establishment of the
vietnam atomic time scale”
1
Abstract - The national metrology institutes always
establish their time scale UTC(k) (UTC of k laboratory )
based on the atomic clocks. Atomic clocks and a time scale
algorithm provides an ensemble time which is better than
any component clock in the system. This paper introduces
establishing of Vietnam time scale UTC(VMI) (UTC of
Vietnam Metrology Institute) using the comparison data of
commercial ceasium atomic clocks. We applied the time scale
algorithm named AT1 and an own our method and present
instrument at the time and frequency laboratory – VMI.
UTC(VMI) data has appeared on the BIPM website since
2008.
I. Introduction
Time is one of seven of basic quantities so creating and
maintaining the national time scale is one of the task
which are belong to the national metrology institutes. In
order to creating and maintaining a national time scale the
time and frequency laboratory in a national metrology
institute always operates a time system which includes
many atomic clocks (which are commercial or created by
themselves) and a lot of measurement, comparison
instruments. Furthermore a time scale algorithm must be
studied based on the data which are from the comparison
of separated atomic clocks. The time scale algorithm
processes clock comparison data resulting in a ensemble
time which is more stable than any component atomic
clock. At present time community in the world has been
using algorithm named ALGOS and AT1 [2]. ALGOS has
been using by Bureau International des Poids et Mesures
(BIPM) for establishing International Atomic Time (TAI)
which has good long stability. AT1 has been using by
National Institute of Standards and Technology (NIST) for
creating AT1 which is a real time scale. As recommended
by BIPM the national metrology institutes should keep the
time difference between their own the time scale UTC(k)
and Coordinated Universal Time (UTC) to be smaller than
100 ns, the national metrology institutes always apply AT1
algorithm for its own time scale. However, the time and
frequency laboratories have different clock total and the
different kind of atomic clock so they employ different
measurement instruments and clock comparison methods
so that a time and frequency laboratory must study its own
method for establishing its own the national time scale
based on its present instruments.
This paper describes briefly the general time scale
algorithm and describes our method based on a time
system which has three commercial atomic clocks at
Vietnam Metrology Institute.
As usually, in order to establish a real time scale, we must
have the comparison data from at least three atomic clocks
and TA (Average Time) is derived from a reference clock.
However, VMI has only three atomic clocks so we have to
compare clocks and TA is derived from one of them but
insure the independence of clock comparison data which
is the most important factor in data processing.
The successfulness of creating Vietnam average time scale
not only to combines three of atomic clocks in order to
have time scale which is more stable but also to create the
foundation of creating a time scale with more clocks and
more stable in the near future.
The paper is organized as following : section II describes
briefly the general algorithm for creating a time scale then
section III describes operating and maintaining atomic
clocks and comparison system at VMI. In section IV the
method and operation of establishing the average time
scale of VMI with three clocks is described and the
conclusion is section V.
II. Time scale algorithm general
Hereinafter, time is discussed in reference to "ideal
time," referring to a perfectly steady time scale, and to the
simple term "time," which refers to actual time, which is
offset from ideal time. Ideal time is purely conceptual and
cannot be obtained in actual calculations or measurement.
Below,
is the time of clock , and TA is the average
time. The average time scale is theoretically defined as
follows:
0
∑
,
∑
1
(1)
Here, i is the index that identifies each clock,
is the weighting of clock i.
is the total number of clocks
When each clock is independent, the weighted average
(with optimum weighting) gives a more stable time scale
than any of the component clocks alone. In Equation (1), if
clock 1 is removed at point
, time
falls out of the
calculation entirely, causing significant time offset in the
summation result. What is to be done in this case? The
purpose of Equation (1) is initially to reduce fluctuation.
Therefore, it must be sufficient to extract the fluctuations
and average them alone. Based on this premise, the
average time scale may be calculated with the following
expression:
∑
,
∑
1
(2)
In other words, subtract the predictable variation
of
clock i from the actual time
of the same clock, treat
the difference as the fluctuation, and average all
fluctuations, with weighting. This procedure yields the
average time scale TA. The weight
and the
predictable variation
are determined according to
various models.
We cannot know the absolute value of
because the
ideal reference time is unknowable. In other words, we
cannot calculate an absolute value for
from
Equation (2). What we can calculate is the time difference
between clock i and the average time scale:
(3)
The establishment of the Vietnam atomic time scale
Le Van Ninh, Nguyen Bang, Nguyen Thi Hang, Trieu Viet Phuong, Nguyen Đuc Trung
Time and fre
q
uenc
y
laborator
y
– Vietnam Metrolo
gy
Institute (VMI)
2
can be calculated from the time difference
between
clocks i and j.
is the only value that can be measured
and is used as data in the TA calculation:
t
t
1…, (4)
Equations (2), (3), and (4) yield the following
simultaneous equations, which uniquely determine xi(t):
5
, 1,…, ,
Equation (4) gives N-1 independent relations containing N
clocks; thus, with Equation (5), we have N equations. The
unknown quantities are
for i = 1 to N, with N is the
total number of clocks. Therefore,
can be determined
uniquely from Equations (4) and (5). The explicit
expression is as follows:
∑
(6)
Generally,
is predicted with a linear expression:
(7)
Here,
is the last period at which
is calculated,
is the time difference between the time given by clock i
and at
, and
is the predicted drift rate
(predicted frequency) of clock i.
To summarize, calculating involves calculating the
time difference
between each clock and the average
time scale. The value
can be calculated from the time
difference
between the clocks, the epoch
at
which the calculation was conducted, the value
calculated at
, the weight
for each clock, and the
predicted frequency
for each clock. As the time
is unknowable, the numerical value of
cannot
be obtained, but it is possible to calculate the variation in
. In addition, time comparison with the of
another station can define local using their time
difference.
III. Controlling the atomic clock performance
As with the national time scales the Vietnam time scale
is based on some atomic clocks which are combined into a
system clock providing a single time scale. At present
VMI has been keeping atomic clocks to work continuously
for 24 hours a day in every day and atomic clocks have
been comparing every second to provide data for creating
UTC(VMI). One of the important problem during
maintaining a time system is to control the clocks
performance. Ofcouse when it calculates the average time
scale the calculating procedure of weight will values
automatically the clock performances by assigning the
weights for them. These clock weights will be applied to
predict the time of clocks at the next measurement. During
a period of prediction/estimation if the stability of a clock
is reduced (compared to the other clocks) then its weight is
also reduced then its contribution to the ensemble average
time to be reduced also. It means that the algorithm
lightens automatically the role of clocks which have bad
performance or even removes their data from data
processing although there is not any removing of the
physical link between the clocks and general system.
However, it means that the clock performances are not
compared to a threshold that through it we can know if the
clock performance is meet its technical characteristic
pronounced by its manufacturer. It is clearly that if there is
a trouble with a clock or its performance is reduced for
working for a long time then it must be removed from the
general system and to be replaced by a new one. Several
methods can be applied to control the clock performance.
One of them is to measure the spectrum of clock output by
a spectrum analyzer but this method does not give us the
information of its long stability. Another way to control
the clock performance is to compare the clock output to a
primary frequency standard as a hydro maser but this way
also does not value clock’s long stability and it is also not
realizable because we do not have any hydro maser.
Fortunately, there is one way to do it. We can control the
clock performance by the three-corner hat method [1]
based on processing of comparison data which are from
measurement system. This method allows us to estimate
continuously the clock performance then to compared to
noise characteristics pronounced by the manufacturer.
With this way, firstly the comparison data between clocks
with tau of 1 s, 10 s, .v.v. , 100,000 s are stored
continuously for at least 4 months. After that it applies the
three-corner hat method to process data which provides the
stability of each which are corresponding to tau of 1 s, 10
s,…, 100,000 s. Finally, those stabilities are compared to
clock noise characteristics to value the clock performance.
One of the results of three-corner hat processing is
presented on figures 1, 2, 3.
Figure 1. The noise characteristic of the
high performance clock
Figure 2. The noise characteristic of the newest clock
which has normal performance
3
Figure 3. The noise characteristic of the oldest clock
The figures above shows the curves of the noise
characteristics (or Allan deviation) of clocks for the time
to February of 2009. We see that all the noise
characteristic curves are below reference noise
characteristics of manufacturer. It means that the clocks
have good stability although clock HP5071A (the oldest
one) has been operating since 1998.
IV. Creating Vietnam time scale UTC(VMI)
In the choice of the algorithm to calculated TA(VMI) we
have consider that the optimum algorithm with a small
group of clocks is not obvious and very difficult to find. In
general a time scale algorithm takes the time difference
measurements between clocks and combines them
mathematically to produce an average time scale [4, 5].
The algorithm that generates TA(VMI) follows the same
steps of the main ensemble algorithm used successfully in
the NIST [2] and is outlined here shortly.
Here we must set forth two essential premises in any
discussion of an algorithm of ensemble atomic time:
1. The measurement errors of the time difference
between the clocks must be negligibly small compared to
the noise of the clocks.
2. Each clock must be independent, with no correlation
between measured time differences between the clocks.
If these conditions are not satisfied, the method described
in Section II to calculate the average time scale will not be
valid.
The ideal algorithm changes according to the type of time
scale (standard frequency) required. For instance, is a real-
time time scale needed or is an ex post facto report
sufficient? What time interval of stability is thought as
important? These factors influence the selection of the
calculation interval and prediction method for the given
frequency.
The inputs to the algorithm are the time difference
measurements
between all of the clock pairs, with the
time intervals between measurements of 3 hours. This
interval is long enough to eliminate the influence of the
measurement noise.
A first prediction of the time offset for each clock against
the ensemble is given by
τ
τ
)()()(
ˆ
tYtxtx
iii
+=+ (8)
The best estimate of the time offset of each clock
at time
given the measurements
)(
τ
+tX
ij
is
∑
=
+−+=+
N
i
ijiij
tXtxwtx
1
)]()(
ˆ
)[()(
ττττ
(9)
Once the
)(
τ
+
tx
i
are known the average frequency of
each clock over the last interval can be estimate by
τ
τ
τ
)()(
)(
ˆ
txtx
tY
ii
i
−
+
=+
(10)
An exponentially filtered estimate of the current average
frequency of clock i that will be used in the next prediction
interval is given by
[
]
)()(
ˆ
1
1
)( tYmtY
m
tY
iii
i
i
++
+
=+
ττ
(11)
where
mi is an exponential time constant determined from
the relative levels of white noise and random walk FM,
that is
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
++−=
2/1
2
2
min
3
4
3
1
1
2
1
τ
τ
i
i
m
(12)
is the period in which each clock is the most stable.
The clock weights
i
w
appear in (2) are calculated from
the variances of the time residuals
2
i
ε
by
)(
1
)(
1
1
2
1
2
τε
τε
i
N
i
i
i
w
∑
=
=
(13)
The prediction error of clock
i
over the interval
τ
+
t
is
estimated by
[
]
iiii
Ktxtx
2
2
)(
ˆ
)(
ˆ
ττε
+−+=
(14)
Because ensemble time is a weighted average of each
clock times, the prediction error estimate (14) is biased,
because each clock is a member of the ensemble, so it is
necessary to correct this biasing [6] by
)1(
1
i
i
w
K
−
=
(15)
Since the noise characteristics of a cesium clock may not
be stationary, the current prediction error of each clock is
exponentially filter where the past prediction error are
deweighted in the process, that is
(16)
the time constant for the filter is typically chosen to be
= 20 days and the initial value of
2
i
ε
is estimated as
)(
22
τστ
y
.
Vietnam time scale has been based on a system which is
described in figure 4. The clock measurements is
[
]
)()(
1
1
)(
222
tNt
N
t
iii
ετετε
τ
τ
++
+
=+
4
Figure 4. System block diagram of UTC(VMI)
continuous every second for 24 hours a day. From that the
data which are corresponding to tau of 1 s, 10 s, 100 s,
1000 s, 10,000 s, 100,000 s to be used for calculating
Allan deviation then clock performance to be value as
described above.
Here measurement interval of 1 day (86400 s) is used for
calculating the average time so the values at 00:0:00 UTC
have great significance because they are used for creating
UTC(VMI)
From Equation (3), atomic time is obtained as an
actual signal by correcting the output of clock
by the
calculated value
. However, we cannot artificially
adjust the frequency of the cesium atomic clocks, as these
clocks serve as the basis for the ensemble calculation.
Thus, we modify the output of the frequency adjuster
corresponding to a cesium clock and regard this adjusted
output as the signal . Maintaining this signal to trace
UTC, we regard this signal as the actual signal of
UTC(VMI). Denoting the output of the frequency adjuster
as
([as noted, this value represents UTC(VMI)] and
the time difference relative to the reference clock s as
, is expressed as:
(17)
Because TA is calculated and the frequency is adjusted
daily, a correction value is given to maintain the present
value for
until the following day. The frequency
adjuster drifts in accordance with the rate of its referred
oscillator, cesium clock a;
thus, taking the adjustment
value
into consideration as well, the output of the
frequency adjuster for the next day is expressed as
follows:
(18)
Here,
′
is the rate of clock a, and is from BIPM
website. The value for
is determined such that the
value of
in Equation (18) equals the value of
in Equation (17):
(19)
In actual operation, we adjust the frequency whenever
necessary using the UTC-UTC(VMI) time-difference
value included in the Circular-T report published monthly
by the BIPM, in order to minimize time discrepancies
relative to the UTC.
Every month time and frequency laboratory send clock
comparison data to BIPM which contributes to creating the
International Time Scale (TAI) so we can not have a clock
UTC(VMI) - TA(VMI)
VFS
Frequency adjusting (Realize ensemble time)
1 PPS
5 MHz
5 MHz
UTC(VMI
)
Atomic clock set
Time differences
between clocks
(TSC12030)
Cs Clock
Cs Clock
Cs Clock
Cs Clock
Frequency
adjuster
(AOG110)
Pulse amplifier
(6602
)
RF
amplifier
(6502)
Algorithm
Ensemble atomic
time
Frequency
adjusting
(UTC-trace as
required)
UTC(VMI)
data from
Circular-T
UTC(VMI) data
( send to BIPM)
Time GPS
receiver
(EURO-80)
Clock data (Send to
BIPM)
5
reserved as reference for establishing TA(VMI) and
UTC(VMI). We have been using best clock for this
purpose. It is not only for creating TA(VMI) but also for
realization of TA(VMI) and UTC(VMI) using a high
performance phase/frequency adjuster.
The realization of TA(VMI) every day using a
phase/frequency adjuster is implemented by software on
steps as follows:
1. To set clock and measurement parameters as
MJD, date, clock index.
2. To connect to SQL data base on which clock
comparison is stored.
3. To get comparison data between clocks and
between UTC(VMI) and reference frequency
source.
4. To calculate TA(VMI).
5. To calculate UTC(VMI)-TA(VMI).
6. To calculate theoretically frequency offset for the
phase/frequency adjuster at 00:00 UTC which is
needed to track the theoretical ideal time.
7. To calculate the real frequency offset quantity for
phase/frequency adjuster at 00:00 UTC. By
applying this one the adjuster output will track
TA(VMI).
The frequency offset quantity in clause 7 above can be
explained as follows: adjusting phase/frequency adjuster
output to follow the ideal time scale is not needed because
it does not know the ideal time scale. Here adjusting is
only to make UTC(VMI) to follow TA(VMI) it means that
UTC(VMI) has the stability which is nearly the same
TA(VMI)’s stability. But absolute time difference between
UTC(VMI) and UTC is added when needed (for example,
when we want to keep /UTC-UTC(VMI)/ < 100 ns).
However, in this case we must pay special attention to its
stability.
Adjusting on the phase/frequency adjuster is implemented
carefully by hand using adjuster keyboard first (after
getting data from the measurement system and following
steps from 1
st
to 7
th
as reminded above). Then the semi-
automatic adjust is implemented. The steps from 1
st
to 7
th
and adjusting are implemented by software which is active
by the operator when need. Finally, all those activations
are implemented automatically by software at a fixed time
every day.
A problem arisen during TA(VMI) calculating progress is
the clock weight value. VMI have been operating three of
ceasium atomic clocks. The first one is normal
performance and begin to be operated on 1998. The
second is a high performance clock and begins to work
from 2006 and the last one is normal performance and
begins to work from 2007. It is known from Equation (1)
that the contribution of a clock depends on its weight. But
the weight of a clock depends on its performance or its
stability. Although at first clock weights set randomly but
then TA creating procedure calculates them using fact
data. We see that the oldest clock’s weight is about 0.01,
the high performance clock’s weight approximates to 0.9
and the last one’s weight is about 0.1. It is clearly that the
high performance clock contribution dominates on
creating TA(VMI). The problem we need to look at is that
we should set the limit value for clock weights or not. This
problem will be studied later in the next time.
After adjusting the phase/frequency adjuster output
follows TA(VMI) and UTC then we have UTC(VMI).
Through the GPS intermediate comparison the UTC(VMI)
data are send to BIPM to be valued then to be published on
the Circular-T of BIPM website. At the same time the
clock data are send to BIPM to contribute to the
international atomic time TAI. The data of UTC(VMI)
published on cirt.256, cirt.257 are shown on figure 5. The
error bar value is smaller than 33 ns.
Figure 5. UTC(VMI) published on BIPM website
V. Conclusion
A national metrology institute must create itself its own
time scale. In order to establish a real time scale the AT1
algorithm is always chosen as a basic algorithm for data
processing. Time and frequency laboratory – Vietnam
Metrology Institute created a procedure in detail to make a
time scale based on a atomic clock set. That is also the
base for the development of a ensemble time with more
clocks and other frequency primary standard. UTC(VMI)
data has been being valued and published on the website
of the Bureau International des Poids et Mesures (BIPM)
monthly. Our work in the near future is to improve
UTC(VMI) stability with more atomic clocks and consider
carefully the weight of atomic clocks in the procedure.
R
EFERENCES
[1] Allan, D.W., 1987, “Time and frequency (time domain)
characterization, estimation, and prediction of precision clocks
and oscillators,” IEEE Trans. Ultrasonic, Ferroelectrics, and
Frequency Control, vol. 34, n. 6, pp. 647-654.
[2] Weiss, M. A., Allan D. W., Peppler T. K., 1989, “A Study of
the NBS Time Scale Algorithm,” IEEE Transactions on
Instrumentation and Measurement, vol.38, n. 2, pp. 631-635.
[3] Tavella, P., and Thomas, C., 1991, “Comparative Study of
Time Scale Algorithms,” Metrologia, vol. 28, pp. 57-63.
[4] Weiss, M. A. and Weissert T., 1991, “AT2, A new time scale
algorithm: AT1 plus frequency variance,” Metrologia, vol. 28,
pp. 65-74.
[5] P. Tavella and C. Thomas, "Comparative study of time scale
algorithms", Metrologia, Vol. 28, pp.57- 63,1991.
[6]Tavella P., Azoubib J., Thomas C., “Study of the Clock
Ensemble Correlation in ALGOS Using Real Data,” in Proc. 5th
European Frequency and Time Forum, 1991, pp. 435-441.
[7] Hanado Yuko, Imae Michito, Aida Masanori, Hosokawa
Mizuhiko, Ito Hiroyuki, Nakagawa Fumimaru, and Shimisu
Yoshiyuki, “Algorithm of Ensemble Atomic Time”, NICT
website.
Phô lôc 2
sè liÖu tÝnh to¸n trung gian
x©y dùng thang thêi gian quèc
gia utc(VMI)
PHỤ LỤC 2
SỐ LIỆU TÍNH TOÁN TRUNG GIAN XÂY DỰNG THANG THỜI GIAN QUỐC GIA UTC(VMI)
x(1)_prediction
x(1)_estimate y(1)_estimate y(1)_update estimate_epsilon(1) estimate_epsilon(1)_update m_i(1) K w(1)
-1.06E-07 -8.18E-08 7.67E-14 -1.86E-13 2.41E-08 4.32E-10 16.822914 3.08E-10 0.89181064
-9.79E-08 -9.87E-08 -1.95E-13 -1.87E-13 1.09E-09 4.32E-10 16.822914 3.08E-10 0.89181199
-1.15E-07 -1.15E-07 -1.85E-13 -1.87E-13 4.40E-10 4.32E-10 16.822914 3.08E-10 0.89181195
-1.31E-07 -1.28E-07 -1.48E-13 -1.85E-13 3.66E-09 4.32E-10 16.822914 3.09E-10 0.89183679
-1.43E-07 -1.43E-07 -1.78E-13 -1.84E-13 9.08E-10 4.32E-10 16.822914 3.09E-10 0.89183729
-1.59E-07 -1.59E-07 -1.83E-13 -1.84E-13 3.85E-10 4.32E-10 16.822914 3.09E-10 0.89183726
-1.75E-07 -1.75E-07 -1.92E-13 -1.85E-13 9.62E-10 4.32E-10 16.822914 3.09E-10 0.89183811
-1.91E-07 -1.92E-07 -1.93E-13 -1.85E-13 1.02E-09 4.32E-10 16.822914 3.09E-10 0.89183926
-2.08E-07 -2.08E-07 -1.86E-13 -1.85E-13 4.16E-10 4.32E-10 16.822914 3.09E-10 0.89183923
-2.24E-07 -2.24E-07 -1.85E-13 -1.85E-13 3.27E-10 4.32E-10 16.822914 3.09E-10 0.89183924
-2.40E-07 -2.40E-07 -1.89E-13 -1.85E-13 6.39E-10 4.32E-10 16.822914 3.09E-10 0.89183946
-2.56E-07 -2.56E-07 -1.82E-13 -1.85E-13 5.81E-10 4.32E-10 16.822914 3.09E-10 0.89183949
-2.72E-07 -2.72E-07 -1.88E-13 -1.85E-13 5.86E-10 4.32E-10 16.822914 3.09E-10 0.8918397
-2.88E-07 -2.88E-07 -1.83E-13 -1.85E-13 4.91E-10 4.32E-10 16.822914 3.09E-10 0.8918398
-3.04E-07 -3.04E-07 -1.85E-13 -1.85E-13 3.50E-10 4.32E-10 16.822914 3.09E-10 0.89183977
-3.20E-07 -3.21E-07 -1.95E-13 -1.86E-13 1.13E-09 4.32E-10 16.822914 3.09E-10 0.89184112
-3.37E-07 -3.37E-07 -1.88E-13 -1.86E-13 4.99E-10 4.32E-10 16.822914 3.09E-10 0.89184124
-3.53E-07 -3.53E-07 -1.87E-13 -1.86E-13 4.45E-10 4.32E-10 16.822914 3.09E-10 0.89184123
-3.69E-07 -3.69E-07 -1.86E-13 -1.86E-13 3.39E-10 4.32E-10 16.822914 3.09E-10 0.8918412
-3.85E-07 -3.86E-07 -1.87E-13 -1.86E-13 3.66E-10 4.32E-10 16.822914 3.09E-10 0.89184118
-4.02E-07 -4.02E-07 -1.87E-13 -1.86E-13 4.09E-10 4.32E-10 16.822914 3.09E-10 0.89184117
1
-4.18E-07
-4.18E-07 -1.88E-13 -1.86E-13 4.95E-10 4.32E-10 16.822914 3.09E-10 0.89184115
-4.34E-07 -4.34E-07 -1.87E-13 -1.86E-13 4.20E-10 4.32E-10 16.822914 3.09E-10 0.89184111
-4.50E-07 -4.51E-07 -1.92E-13 -1.87E-13 7.78E-10 4.32E-10 16.822914 3.09E-10 0.89184153
-4.67E-07 -4.67E-07 -1.93E-13 -1.87E-13 8.94E-10 4.32E-10 16.822914 3.09E-10 0.89184208
-4.84E-07 -4.84E-07 -1.98E-13 -1.87E-13 1.23E-09 4.32E-10 16.822914 3.09E-10 0.89184366
-5.01E-07 -5.01E-07 -1.89E-13 -1.88E-13 4.44E-10 4.32E-10 16.822914 3.09E-10 0.89184363
-5.17E-07 -5.17E-07 -1.89E-13 -1.88E-13 4.49E-10 4.32E-10 16.822914 3.09E-10 0.8918436
-5.33E-07 -5.34E-07 -1.90E-13 -1.88E-13 5.48E-10 4.32E-10 16.822914 3.09E-10 0.89184361
-5.50E-07 -5.50E-07 -1.86E-13 -1.88E-13 4.49E-10 4.32E-10 16.822914 3.09E-10 0.89184369
-5.66E-07 -5.66E-07 -1.86E-13 -1.88E-13 4.56E-10 4.32E-10 16.822914 3.09E-10 0.8918437
-5.82E-07 -5.82E-07 -1.83E-13 -1.87E-13 7.01E-10 4.32E-10 16.822914 3.09E-10 0.89184403
-5.98E-07 -5.98E-07 -1.87E-13 -1.87E-13 3.25E-10 4.32E-10 16.822914 3.09E-10 0.89184401
-6.14E-07 -6.14E-07 -1.88E-13 -1.87E-13 4.01E-10 4.32E-10 16.822914 3.09E-10 0.89184403
-6.30E-07 -6.31E-07 -1.92E-13 -1.88E-13 7.15E-10 4.32E-10 16.822914 3.09E-10 0.89184428
-6.47E-07 -6.47E-07 -1.86E-13 -1.88E-13 4.29E-10 4.32E-10 16.822914 3.09E-10 0.89184426
-6.63E-07 -6.63E-07 -1.89E-13 -1.88E-13 4.43E-10 4.32E-10 16.822914 3.09E-10 0.89184424
-6.79E-07 -6.79E-07 -1.85E-13 -1.88E-13 5.66E-10 4.32E-10 16.822914 3.09E-10 0.89184433
-6.95E-07 -6.95E-07 -1.90E-13 -1.88E-13 5.20E-10 4.32E-10 16.822914 3.09E-10 0.89184433
-7.12E-07 -7.12E-07 -1.90E-13 -1.88E-13 5.22E-10 4.32E-10 16.822914 3.09E-10 0.89184443
-7.28E-07 -7.29E-07 -1.92E-13 -1.88E-13 7.06E-10 4.32E-10 16.822914 3.09E-10 0.89184477
-7.45E-07 -7.45E-07 -1.88E-13 -1.88E-13 3.55E-10 4.32E-10 16.822914 3.09E-10 0.89184475
-7.61E-07 -7.61E-07 -1.86E-13 -1.88E-13 4.77E-10 4.32E-10 16.822914 3.09E-10 0.89184473
-7.77E-07 -7.77E-07 -1.91E-13 -1.88E-13 5.92E-10 4.32E-10 16.822914 3.09E-10 0.89184482
-7.94E-07 -7.93E-07 -1.81E-13 -1.88E-13 9.00E-10 4.32E-10 16.822914 3.09E-10 0.89184541
-8.09E-07 -8.09E-07 -1.85E-13 -1.88E-13 5.60E-10 4.32E-10 16.822914 3.09E-10 0.89184549
2
-8.25E-07
-8.25E-07 -1.86E-13 -1.87E-13 4.69E-10 4.32E-10 16.822914 3.09E-10 0.89184554
-8.41E-07 -8.41E-07 -1.87E-13 -1.87E-13 3.57E-10 4.32E-10 16.822914 3.09E-10 0.89184551
-8.57E-07 -8.58E-07 -1.93E-13 -1.88E-13 7.99E-10 4.32E-10 16.822914 3.09E-10 0.89184577
-8.74E-07 -8.74E-07 -1.87E-13 -1.88E-13 3.95E-10 4.32E-10 16.822914 3.09E-10 0.89184574
-8.90E-07 -8.90E-07 -1.90E-13 -1.88E-13 5.30E-10 4.32E-10 16.822914 3.09E-10 0.89184575
-9.07E-07 -9.06E-07 -1.82E-13 -1.88E-13 7.88E-10 4.32E-10 16.822914 3.09E-10 0.89184611
-9.22E-07 -9.23E-07 -1.92E-13 -1.88E-13 6.73E-10 4.32E-10 16.822914 3.09E-10 0.89184626
-9.39E-07 -9.39E-07 -1.92E-13 -1.88E-13 6.77E-10 4.32E-10 16.822914 3.09E-10 0.8918464
-9.56E-07 -9.55E-07 -1.85E-13 -1.88E-13 5.84E-10 4.32E-10 16.822914 3.09E-10 0.89184643
-9.72E-07 -9.72E-07 -1.93E-13 -1.88E-13 7.32E-10 4.32E-10 16.822914 3.09E-10 0.89184683
-9.88E-07 -9.88E-07 -1.88E-13 -1.88E-13 3.15E-10 4.32E-10 16.822914 3.09E-10 0.8918468
-1.00E-06 -1.00E-06 -1.85E-13 -1.88E-13 5.92E-10 4.32E-10 16.822914 3.09E-10 0.89184685
-1.02E-06 -1.02E-06 -1.85E-13 -1.88E-13 5.85E-10 4.32E-10 16.822914 3.09E-10 0.89184698
-1.04E-06 -1.04E-06 -1.79E-13 -1.87E-13 1.03E-09 4.32E-10 16.822914 3.09E-10 0.89184808
-1.05E-06 -1.05E-06 -1.93E-13 -1.88E-13 8.03E-10 4.32E-10 16.822914 3.09E-10 0.89184855
-1.07E-06 -1.07E-06 -1.86E-13 -1.87E-13 4.72E-10 4.32E-10 16.822914 3.09E-10 0.89184853
-1.08E-06 -1.08E-06 -1.92E-13 -1.88E-13 6.79E-10 4.32E-10 16.822914 3.09E-10 0.8918488
-1.10E-06 -1.10E-06 -1.86E-13 -1.88E-13 4.33E-10 4.32E-10 16.822914 3.09E-10 0.89184877
-1.12E-06 -1.12E-06 -1.86E-13 -1.88E-13 4.85E-10 4.32E-10 16.822914 3.09E-10 0.89184885
-1.13E-06 -1.13E-06 -1.85E-13 -1.87E-13 5.24E-10 4.32E-10 16.822914 3.09E-10 0.89184885
-1.15E-06 -1.15E-06 -1.93E-13 -1.88E-13 7.82E-10 4.32E-10 16.822914 3.09E-10 0.89184924
-1.17E-06 -1.17E-06 -1.85E-13 -1.88E-13 5.10E-10 4.32E-10 16.822914 3.09E-10 0.89184932
-1.18E-06 -1.18E-06 -1.90E-13 -1.88E-13 5.35E-10 4.32E-10 16.822914 3.09E-10 0.89184931
-1.20E-06 -1.20E-06 -1.85E-13 -1.88E-13 5.23E-10 4.32E-10 16.822914 3.09E-10 0.89184941
-1.21E-06 -1.21E-06 -1.91E-13 -1.88E-13 6.16E-10 4.32E-10 16.822914 3.09E-10 0.89184949
3
-1.23E-06
-1.23E-06 -1.87E-13 -1.88E-13 3.45E-10 4.32E-10 16.822914 3.09E-10 0.89184953
-1.25E-06 -1.25E-06 -1.92E-13 -1.88E-13 6.93E-10 4.32E-10 16.822914 3.09E-10 0.89184967
-1.26E-06 -1.26E-06 -1.90E-13 -1.88E-13 5.12E-10 4.32E-10 16.822914 3.09E-10 0.8918497
-1.28E-06 -1.28E-06 -1.90E-13 -1.88E-13 4.31E-10 4.32E-10 16.822914 3.09E-10 0.89184968
-1.30E-06 -1.30E-06 -1.94E-13 -1.89E-13 7.88E-10 4.32E-10 16.822914 3.09E-10 0.89185004
-1.31E-06 -1.31E-06 -1.87E-13 -1.88E-13 4.55E-10 4.32E-10 16.822914 3.09E-10 0.89185004
-1.33E-06 -1.33E-06 -1.93E-13 -1.89E-13 6.81E-10 4.32E-10 16.822914 3.09E-10 0.89185027
-1.35E-06 -1.35E-06 -1.95E-13 -1.89E-13 8.34E-10 4.32E-10 16.822914 3.09E-10 0.89185068
-1.36E-06 -1.36E-06 -1.94E-13 -1.89E-13 7.67E-10 4.32E-10 16.822914 3.09E-10 0.89185109
-1.38E-06 -1.38E-06 -1.83E-13 -1.89E-13 8.56E-10 4.32E-10 16.822914 3.09E-10 0.89185165
-1.40E-06 -1.40E-06 -1.95E-13 -1.89E-13 8.13E-10 4.32E-10 16.822914 3.09E-10 0.89185217
-1.41E-06 -1.41E-06 -1.87E-13 -1.89E-13 5.08E-10 4.32E-10 16.822914 3.09E-10 0.89185221
-1.43E-06 -1.43E-06 -1.91E-13 -1.89E-13 4.53E-10 4.32E-10 16.822914 3.09E-10 0.89185226
-1.45E-06 -1.45E-06 -1.91E-13 -1.89E-13 4.99E-10 4.32E-10 16.822914 3.09E-10 0.89185226
-1.46E-06 -1.46E-06 -1.86E-13 -1.89E-13 6.36E-10 4.32E-10 16.822914 3.09E-10 0.89185236
-1.48E-06 -1.48E-06 -1.83E-13 -1.89E-13 8.78E-10 4.32E-10 16.822914 3.09E-10 0.89185301
-1.49E-06 -1.49E-06 -1.92E-13 -1.89E-13 5.46E-10 4.32E-10 16.822914 3.09E-10 0.891853
-1.51E-06 -1.51E-06 -1.89E-13 -1.89E-13 3.17E-10 4.32E-10 16.822914 3.09E-10 0.89185299
-1.53E-06 -1.53E-06 -1.89E-13 -1.89E-13 3.09E-10 4.32E-10 16.822914 3.09E-10 0.89185296
-1.54E-06 -1.54E-06 -1.85E-13 -1.89E-13 6.12E-10 4.32E-10 16.822914 3.09E-10 0.89185321
-1.56E-06 -1.56E-06 -1.78E-13 -1.88E-13 1.27E-09 4.32E-10 16.822914 3.09E-10 0.8918548
-1.57E-06 -1.57E-06 -1.92E-13 -1.88E-13 6.21E-10 4.32E-10 16.822914 3.09E-10 0.89185498
-1.59E-06 -1.59E-06 -1.85E-13 -1.88E-13 6.31E-10 4.32E-10 16.822914 3.09E-10 0.89185511
-1.61E-06 -1.61E-06 -1.87E-13 -1.88E-13 3.80E-10 4.32E-10 16.822914 3.09E-10 0.89185507
-1.62E-06 -1.62E-06 -1.84E-13 -1.88E-13 7.03E-10 4.32E-10 16.822914 3.09E-10 0.8918552
4
-1.64E-06
-1.64E-06 -1.91E-13 -1.88E-13 6.18E-10 4.32E-10 16.822914 3.09E-10 0.89185541
-1.66E-06 -1.66E-06 -2.00E-13 -1.89E-13 1.32E-09 4.32E-10 16.822914 3.09E-10 0.89185718
-1.67E-06 -1.67E-06 -1.95E-13 -1.89E-13 8.43E-10 4.32E-10 16.822914 3.09E-10 0.89185765
-1.69E-06 -1.69E-06 -1.91E-13 -1.89E-13 4.56E-10 4.32E-10 16.822914 3.09E-10 0.89185763
-1.71E-06 -1.71E-06 -1.92E-13 -1.89E-13 5.99E-10 4.32E-10 16.822914 3.09E-10 0.89185764
-1.72E-06 -1.72E-06 -1.94E-13 -1.90E-13 7.46E-10 4.32E-10 16.822914 3.09E-10 0.89185815
-1.74E-06 -1.74E-06 -1.85E-13 -1.89E-13 7.00E-10 4.32E-10 16.822914 3.09E-10 0.89185833
-1.76E-06 -1.75E-06 -1.83E-13 -1.89E-13 8.73E-10 4.32E-10 16.822914 3.09E-10 0.89185913
-1.77E-06 -1.77E-06 -1.89E-13 -1.89E-13 3.45E-10 4.32E-10 16.822914 3.09E-10 0.8918591
-1.79E-06 -1.79E-06 -1.98E-13 -1.89E-13 1.09E-09 4.32E-10 16.822914 3.09E-10 0.8918601
-1.80E-06 -1.80E-06 -1.88E-13 -1.89E-13 4.25E-10 4.32E-10 16.822914 3.09E-10 0.89186008
-1.82E-06 -1.82E-06 -1.84E-13 -1.89E-13 7.58E-10 4.32E-10 16.822914 3.09E-10 0.89186042
-1.84E-06 -1.84E-06 -1.86E-13 -1.89E-13 5.75E-10 4.32E-10 16.822914 3.09E-10 0.89186054
-1.85E-06 -1.85E-06 -1.91E-13 -1.89E-13 5.11E-10 4.32E-10 16.822914 3.09E-10 0.89186063
-1.87E-06 -1.87E-06 -1.87E-13 -1.89E-13 5.16E-10 4.32E-10 16.822914 3.09E-10 0.89186066
-1.89E-06 -1.89E-06 -1.91E-13 -1.89E-13 5.26E-10 4.32E-10 16.822914 3.09E-10 0.89186072
-1.90E-06 -1.90E-06 -1.90E-13 -1.89E-13 3.96E-10 4.32E-10 16.822914 3.09E-10 0.89186069
-1.92E-06 -1.92E-06 -1.96E-13 -1.90E-13 9.39E-10 4.32E-10 16.822914 3.09E-10 0.89186133
-1.94E-06 -1.94E-06 -1.97E-13 -1.90E-13 9.32E-10 4.32E-10 16.822914 3.09E-10 0.89186186
-1.95E-06 -1.95E-06 -1.93E-13 -1.90E-13 5.49E-10 4.32E-10 16.822914 3.09E-10 0.89186206
-1.97E-06 -1.97E-06 -1.88E-13 -1.90E-13 4.85E-10 4.32E-10 16.822914 3.09E-10 0.89186207
-1.99E-06 -1.98E-06 -1.86E-13 -1.90E-13 6.34E-10 4.32E-10 16.822914 3.09E-10 0.89186221
-2.00E-06 -2.00E-06 -1.92E-13 -1.90E-13 5.36E-10 4.32E-10 16.822914 3.09E-10 0.89186222
-2.02E-06 -2.02E-06 -1.92E-13 -1.90E-13 4.85E-10 4.32E-10 16.822914 3.09E-10 0.89186219
-2.03E-06 -2.03E-06 -1.91E-13 -1.90E-13 3.52E-10 4.32E-10 16.822914 3.09E-10 0.89186216
5
-2.05E-06
-2.05E-06 -1.92E-13 -1.90E-13 5.09E-10 4.32E-10 16.822914 3.09E-10 0.89186217
-2.07E-06 -2.07E-06 -1.93E-13 -1.90E-13 5.43E-10 4.32E-10 16.822914 3.09E-10 0.89186223
-2.08E-06 -2.08E-06 -1.94E-13 -1.91E-13 6.48E-10 4.32E-10 16.822914 3.09E-10 0.8918624
-2.10E-06 -2.10E-06 -1.86E-13 -1.90E-13 7.34E-10 4.32E-10 16.822914 3.09E-10 0.89186267
-2.12E-06 -2.12E-06 -1.81E-13 -1.90E-13 1.12E-09 4.32E-10 16.822914 3.09E-10 0.89186403
-2.13E-06 -2.13E-06 -1.93E-13 -1.90E-13 6.05E-10 4.32E-10 16.822914 3.09E-10 0.8918642
-2.15E-06 -2.15E-06 -1.92E-13 -1.90E-13 5.10E-10 4.32E-10 16.822914 3.09E-10 0.89186419
-2.17E-06 -2.17E-06 -1.93E-13 -1.90E-13 5.44E-10 4.32E-10 16.822914 3.09E-10 0.89186422
-2.18E-06 -2.18E-06 -1.86E-13 -1.90E-13 6.58E-10 4.32E-10 16.822914 3.09E-10 0.8918644
-2.20E-06 -2.20E-06 -1.96E-13 -1.90E-13 7.88E-10 4.32E-10 16.822914 3.09E-10 0.89186479
-2.22E-06 -2.22E-06 -1.93E-13 -1.90E-13 4.98E-10 4.32E-10 16.822914 3.09E-10 0.89186479
-2.23E-06 -2.23E-06 -1.97E-13 -1.91E-13 8.45E-10 4.32E-10 16.822914 3.09E-10 0.89186528
-2.25E-06 -2.25E-06 -1.89E-13 -1.91E-13 4.57E-10 4.32E-10 16.822914 3.09E-10 0.89186529
-2.27E-06 -2.27E-06 -1.94E-13 -1.91E-13 6.04E-10 4.32E-10 16.822914 3.09E-10 0.89186536
-2.28E-06 -2.28E-06 -1.93E-13 -1.91E-13 5.10E-10 4.32E-10 16.822914 3.09E-10 0.89186558
-2.30E-06 -2.30E-06 -1.87E-13 -1.91E-13 6.56E-10 4.32E-10 16.822914 3.09E-10 0.89186576
-2.32E-06 -2.31E-06 -1.88E-13 -1.91E-13 5.48E-10 4.32E-10 16.822914 3.09E-10 0.89186578
-2.33E-06 -2.33E-06 -1.92E-13 -1.91E-13 4.47E-10 4.32E-10 16.822914 3.09E-10 0.89186575
-2.35E-06 -2.35E-06 -1.92E-13 -1.91E-13 3.90E-10 4.32E-10 16.822914 3.09E-10 0.89186576
-2.36E-06 -2.36E-06 -1.88E-13 -1.91E-13 5.16E-10 4.32E-10 16.822914 3.09E-10 0.89186583
-2.38E-06 -2.38E-06 -1.90E-13 -1.91E-13 3.89E-10 4.32E-10 16.822914 3.09E-10 0.89186581
-2.40E-06 -2.40E-06 -1.91E-13 -1.91E-13 3.76E-10 4.32E-10 16.822914 3.09E-10 0.89186577
-2.41E-06 -2.41E-06 -1.91E-13 -1.91E-13 3.24E-10 4.32E-10 16.822914 3.09E-10 0.89186576
-2.43E-06 -2.43E-06 -1.94E-13 -1.91E-13 6.22E-10 4.32E-10 16.822914 3.09E-10 0.89186586
-2.45E-06 -2.45E-06 -1.89E-13 -1.91E-13 4.26E-10 4.32E-10 16.822914 3.09E-10 0.89186583
6
-2.46E-06
-2.46E-06 -1.83E-13 -1.90E-13 9.48E-10 4.32E-10 16.822914 3.09E-10 0.89186648
-2.48E-06 -2.48E-06 -1.91E-13 -1.90E-13 3.28E-10 4.32E-10 16.822914 3.09E-10 0.89186646
-2.50E-06 -2.50E-06 -1.92E-13 -1.90E-13 4.57E-10 4.32E-10 16.822914 3.09E-10 0.89186649
-2.51E-06 -2.51E-06 -1.91E-13 -1.90E-13 3.48E-10 4.32E-10 16.822914 3.09E-10 0.89186651
-2.53E-06 -2.53E-06 -1.86E-13 -1.90E-13 6.90E-10 4.32E-10 16.822914 3.09E-10 0.89186671
-2.54E-06 -2.54E-06 -1.91E-13 -1.90E-13 3.55E-10 4.32E-10 16.822914 3.09E-10 0.89186667
-2.56E-06 -2.56E-06 -1.84E-13 -1.90E-13 8.81E-10 4.32E-10 16.822914 3.09E-10 0.89186717
-2.58E-06 -2.58E-06 -1.90E-13 -1.90E-13 3.35E-10 4.32E-10 16.822914 3.09E-10 0.89186715
-2.59E-06 -2.59E-06 -1.87E-13 -1.90E-13 5.69E-10 4.32E-10 16.822914 3.09E-10 0.89186714
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-2.86E-06 -2.86E-06 -1.96E-13 -1.90E-13 9.02E-10 4.32E-10 16.822914 3.09E-10 0.89187186
7
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-2.90E-06 -2.91E-06 -1.98E-13 -1.90E-13 1.00E-09 4.32E-10 16.822914 3.09E-10 0.89187337
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-3.26E-06 -3.26E-06 -1.86E-13 -1.88E-13 5.74E-10 4.32E-10 16.822914 3.09E-10 0.89191989
8
-3.28E-06
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-3.29E-06 -3.29E-06 -1.89E-13 -1.88E-13 3.53E-10 4.32E-10 16.822914 3.09E-10 0.89192015
-3.31E-06 -3.31E-06 -1.82E-13 -1.88E-13 8.78E-10 4.32E-10 16.822914 3.09E-10 0.89192075
-1.69E-06 -1.69E-06 -1.91E-13 -1.89E-13 4.56E-10 4.32E-10 16.822914 3.09E-10 0.89185763
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-3.59E-06 -3.59E-06 -1.83E-13 -1.88E-13 7.98E-10 4.32E-10 16.822914 3.09E-10 0.89192361
-3.60E-06 -3.60E-06 -1.93E-13 -1.88E-13 7.68E-10 4.32E-10 16.822914 3.09E-10 0.89192388
-3.62E-06 -3.62E-06 -1.89E-13 -1.88E-13 3.83E-10 4.32E-10 16.822914 3.09E-10 0.89192388
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-3.65E-06 -3.65E-06 -1.96E-13 -1.89E-13 9.42E-10 4.32E-10 16.822914 3.09E-10 0.89192455
9
-3.67E-06
-3.67E-06 -1.98E-13 -1.89E-13 1.12E-09 4.32E-10 16.822914 3.09E-10 0.89192554
-3.69E-06 -3.69E-06 -1.89E-13 -1.89E-13 3.59E-10 4.32E-10 16.822914 3.09E-10 0.89192556
-3.70E-06 -3.70E-06 -1.99E-13 -1.90E-13 1.20E-09 4.32E-10 16.822914 3.09E-10 0.89192667
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-3.75E-06 -3.75E-06 -1.86E-13 -1.90E-13 6.24E-10 4.32E-10 16.822914 3.09E-10 0.89192676
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-4.06E-06 -4.06E-06 -1.92E-13 -1.90E-13 4.52E-10 4.32E-10 16.822914 3.09E-10 0.89193561
10
-4.08E-06
4.32E-10
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-4.47E-06 -4.47E-06 -1.78E-13 -1.89E-13 1.27E-09 4.32E-10 16.822914 3.09E-10 0.89194356
11
-4.49E-06
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12
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13
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14
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15
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16
